INVESTIGATION OF BOUNDARY LAYER PARAMETERS IN APG NOZZLE AND THE FLOW INTERFERENCE CAUSED BY SECONDARY INJECTION

APPENDIX A MULTIPORT INTERFERENCE EFFECTS WITH GASE O US INJECTION INTO A SUPERSONIC STREAM The following study presents a preliminary model of multi- port jet interference effects for the semi-empirical description of critical injection port spacing whereby the performance of secondary gaseous injectant in TVC can be improved.

The model employed envisages that the supersonic expansion of the injectants leads to impingement of the expanding jets result- ing in a step-like obstacle to the main flow. The critical injection port spacing c for the occurrence of impingement is determined cr in terms of fluid data pertaining to the primary and secondary flows.

An order-of-magnitude check is obtained with experimental data on rnultiport interference resulting in enhancement of TVC side force.

A. Model of Multiple-Jet-lnteraction in Supersonic Primary Stream If interaction occurs, the flow field obtained is that due to a two-shock system as described in Re[. 9. The injected jets expand into the effective pressure field, Peff' just downstream of the shock system. If the jet pressure is pj at the injection port of diameter dj, the supersonic expansion of an individual jet into the pressure Peff would result in a change of jet diameter from dj at pj to de[ f at Peff co m press- where (deff / dj)Z can be estimated fro m one-dime n sional ible flow formulas.

-35- In the model under consideration it is assumed that interfer- ence between jets occurs if the expanded jets of diameter def f inter- sect. Thus, if the injection ports are distributed along a line nor- mal to the flow direction, interference occurs if the injection port spacing, c, is less than a critical distance c = A(1) cr deff Under these conditions, the linear distribution of jets consti- tutes a"forward-facing step" at the wall boundary of the primary flow. The Pelf resulting from the two-shock system associated with the "step" is readily estimated in terms of the primary free stream data, Poo' Moo' ¥" _As noted above, the calculation of deff or Ccr in terms of Peff and the secondary injectant gas parameters d.j,pj, y j, is readily accomplished by one-dimensional compressible flow formulas.

For a finite number of interacting jets, the critical injection port spacing is anticipated to be somewhat smaller than c based cr on the model of the forward facing step. Thus, the c estimated cr in this analysis is an upper limit of the critical injection port spacing for the design of interacting injectant ports.

]3. Effective Pressure Relation The calculation of Pelf in a two-shock system is conveniently discussed with the aid of figure 74. It is well known that the jet issuing from the wall into the supersonic flow stream obstructs the flow in a manner resembling that due to a solid insert. In such a case the main stream is deflected through an angle 0- 2 by means of -36 - an oblique shock, across which the pressure ratio can be estimated by the empirical relation - 1 +_M 2 3.2 AC2)

Poo oo 8+ (M - 1) Z

oo based on the results of Ref. i0. This result is valid only for¥ = 1.4 (i.e. , for diatornic gases such as air), but more general semi- empirical results of this type can be obtained for arbitrary y on the basis of calculations in Ref. 3.

If under the deflection 0- 2 the flow reattaches itself to the body so that the flow direction is tangent to the radius of curvature of the body at reattachment, then the flow is not deflected a second time.

However, if the body projects sufficiently far into the mainstream, a second flow deflection occurs under a second oblique shock as shown in various experimental observations (e. g. Ref. 5, 9). We postulate that the injected jet in thrust vectoring application gener- ally results in such a two-shock system, as sketched in figure 74.

Thus, the P2 and M Z obtained after the first shock is assumed to undergo a second oblique shock leading to the effective pressure, Peff' given by appropriate application of equation A(2): P e l f _ 1 +_ (M2)2 [ 3 . 2 ] A ( 3 ) P2 8 + (M 2 - l ) 2 The pressure , P el f ' calculated by means of e q uations i_(2) and a_(3), is therefore the local pressure into which the secondary jet expands.

-37- The data pg / Pco , and M 2 vs. M required in the calculations OO for Pelf based on equations A(Z) , A(3) and oblique-shock charts in l_ef. iI are shown here in figure 75 for y = 1.4. The corresponding data for y = l.Z, based on P_ef. 3 and ll are shown here in figure 76.

C. Ex pansion of the Secondary Jet The expansion of the secondary jet is calculated from the well known formula (l%ef. 12) for isentropic flow relating the cross section A to the sonic cross section A T in one-dimensional flow: l l A(4)

(lJ

where P. is the total pressure of the secondary jet.

J

With sonic injection, therefore, equations A( ?- ), A(3)andA(4)

lead to l - 4 2 Z

Yj Yj

def f = Nj + 1 _--feff P oo A (5) dj _ _ 2 IPefflYJ (Poo)YJ

' oo l

where pj is the static pressure at the sonic injection port, i.e., from the compressible flow relations Ref. 12, pj is related to the total pres- -38- sure P. by O

Yj

Pj = P.j A(6) D. Critical Injection Port Spacing Ratio The results calculated for c = d by means of equation A (5) cr eff are obtained as follows. The required ratio

Pco Pz A(7)

is determined by calculation of the right hand term involving the fac- tors given by equations A(Z) and A(3) which can readily be obtained from figures 75 and 76 for y : 1.4 and ¥ = i. 2, respectively, over a range of free stream Mach number M : 2_ 3, 4. Next, we oo deff calculate -_. for a range of pj / pco, with M as a parameter implicit j oo in peff / Poo. Thus, in view of equation A (I) the results obtained for the critical injection port spacing are expressed over the range 5_< Pj / Poo-- < 100, Z_< Mco_< 4 withy = I. 2 and I. 4 as shown in table III. The blank spaces correspond to subcritical pressures P. relative to Peff" E. Comparison With Experimental Data The principal published data which provides evidence of multi- port interference effects is that reported by Rodriguez in Ref. 13.

A ir-to-air injection through a twenty-port sonic injection system (d. = . 094 in.), extending over a circumferential arc of 3. 54 in.

O -39 - yielded a side-force enhancement of about 50 percent (figures 20 and 21 of Ref. 13) corresponding to an 80 percent enhancement of the induced side force (figure Z6 of Ref. 13). These results are obtained in a 16:l bell nozzle at an expansion ratio of AR = 14.9.

From the port configuration data the injection port spacing ratio is C __3._4 .Z0_ / = 1.88 d. .094 J Inasmuch as no details are given as to the local Mach number of free stream pressure, we estimate these from data for conical nozzle at AR = 14.9: POO M : 4.4" 004 C It is further indicated in Ref. 13 that both primary and secondary injection are obtained from the same supply tank; therefore, we assume P = P.; and since pj / P = 5Z8 we estimate c j j " ' -. 528 Pj / Poo .--gg- 4 : 13Z It is clear that the extrapolation of the calculated data for N = 1.4 to Moo = 4.4 and pj / poo = 13Z leads to a slightly higher value of Ccr / dj than c / dj employed in the experiment which y ielded strong interference effects. The close agreement obtained here must be qualified by noting that a) the model employed is greatly simplified, and b) the use of conical nozzle flow data and assumption regarding P = P. are not strictly accurate. However, the order of magnitude c j -40 - agreement indicates that the model employed is plausible for predicting trends of the multiport interference effect with variation of fluid and injection parameter s.

-41 -

APPENDIX B MULTIPORT INTERFERENCE EFFECTS WITH GASEOUS INJECTION INTO A SUPERSONIC STREAM FOR ARBITRARY INJECTOR ANGLES In Appendix A a semiempirical formula is given for the critical injection port spacing required to achieve multiport interference effects with gaseous injection normal to the wall. The following analysis is a generalization of the critical injection port spacing formula applicable to pairs of impinging gaseous injectant jets.

A. Model For the previously considered parallel jets (Appendix A) it is postulated that the critical injection port spacing c which produces cr interference is determined by the following requirement: the jets which enter (with sonic speed at pressure pj) through the ports of diameter d. expand to dian_eter d by one-dimensional isentropic expansion J eff process across the pressure ratio Pj / Peff ' where Pelf is the ambient local pressure resulting from a two-step shock deflection of the main flow by the jets. The injection port spacing c = c = d which assures cr eff' contact between t he expanding jets is the critical value which causes in- terference. The penetration of the jets into the supersonic stream did not enter into consideration in calculation of c cr" In the present model for impinging jets the penetration depth is of primary importance in determining whether or not strong interference between adjacent injection ports occurs. To be sure, opposed jets , -43 - although more or less deflected by the main flow, will to some extent impinge sufficiently far downstream from the injection port sites. In order to assure strong interaction, it is necessary that the impinge- ment shall occur sufficiently close to the injection ports where the jets behave essentially as "rigid ''obstacles to the main flow. A criterion for characterizing the portion of the injected jet as "rigid ''can be formu- lated on the basis of the jet configuration analyzed in Ref. 14. In par- ticular, the latter reference describes the trajectory of the median element in the deflected jet; and the coordinates Xc, Yc of the median element which define the termination of the "rigid '_portion of the jet can be estimated on the basis of concepts relevant to the model of Ref. 14.

The coordinate Yc in effect defines the penetration distance of the jet injected into the main stream.

In order to utilize the developments of Ref. 14 in application to impinging jets we consider, with the aid of figure 77, the kinematics of > a jet injected with arbitrary velocity vector qj into the supersonic > stream of velocity qoo" The orthogonal coordinate system, 6, 4, > shown in figure 77 is oriented so that _ is along qoo' and the 6, _ plane > coincides with the wall. The components of qj are in general, qj,_ ,qj, , qj,% The trajectory of the deflected-jet median lies in a plane, the > > x-y plane containing the vectors qoo' qj" The x-y plane, therefore, forms a dihedral angle _ with the wall _ = tan -I qJ,__l__ B(1) qj , -44 - The contrastream direction of qj is specified by the angle = tan- 1 -qJ' % B(2) Y qj, _] which, together with [BE completely define the direction of qj.

The trajectory of the median in the x-y plane is described by orienting the y axis along the stream direction and taking the origin x = 0 to coincide with the injection port center, as sketched in figure 78.

The following features of the expanding jet are further illustrated in this figure. Immediately upon injection the jet expands from diameter d. to diameter d = Zb, corresponding to a pressure ratio of Pj / Peff' j elf according to Appendix A. Subsequently, the jet median, shown in figure 78 by the dotted curve, deflects under the aerodynamic forces as de- scribed in Ref. 14. However, the jet boundary remains coaxial with the median at the constant value of the jet diameter 2b. This assump- tion implies that the pressure in the neighborhood of the jet does not differ greatly from Peff in case of strong multiport interaction. (For the single-jet analysis of Ref. 14, the decreasing strength of the bow shock around the entry jet resulted in an elliptical rather than a circular cross section of the d e flected jet.) Another special assumption relates to the determination of the penetration depth or of the boundary which divides the jet into the upstream "rigid" portion and the downstream strongly deflected portion. The "rigid" jet is assumed to terminate at the median coordinates Xc, Yc shown in figure 78 which, as indicated in the figure, is obtained by the intersection of the median trajectory y = y (x, Mco, Poo' Pj .... [By) B(3) -45- and the dashed line C C y = (x = b) cot _y B(4) > The latter is parallel to velocity vector qj and is displaced an amount x _-b, downstream of the injection port center. The coordinate Yc ob- tained by simultaneous solution of equations B(3), B(4) is thus , by definition, an effective penetration depth.

Finally, we note the relation between _ in equation B(2) andpy in equations B(3) and B(4). The angle p . q refers to the _, -q, _ coordinate system introduced in this analysis. The angle _y refers to the x-y plane employed in the analysis of the median trajectory (Ref. 14). With the aid of figure 77 it is readily shown that = tan p . sin p_ B(5) tan p Y The injection port interference criterion for impinging jets can now be formulated with the aid of the sketch in figure 79 as follows. Figure 79 shows the aspect of the single jets seen by viewing along the primary stream direction. Impingement occurs at point P. The separation param- eter c is defined, in this case, as the chord between port centers. It is then postulated that if the intersection point P is in the "rigid" portion of the jet, injection port interference effects will be produced and, con- versely, figure 79 shows impinging jets at the threshold of interference with c = c . Thus, we infer with the aid of figure 79 cr Ccr = ZYc cos Pc + Zb sin Pc B(6) where Pc is the angle between the injection vector and the chord. Since, in practical cases, the local nozzle radius is far greater than the chord -46 - length c , the angle _3ciSpractically equal to the angle _3_contained be- tween the injection vector and the local nozzle-wall tangent plane.

B. Critical Port Spacing Ratio The coordinates of any point traced by the jet median in the x-y plane are given by the parametric equations of Ref. 14 as ¥-I c Zb , /+I 3_r Z _ / I + - I cos _3y-Sin c } O J 8 ff 1

\Poo

N-1 ( Pe ) _ in, cos _y

B(7)

Yc zb ¥+II 3_ _C_ PJ ¥i l+cos, l+sin_y

r, ¢ '1

B(81

In these expressions,

1 / 4

y+ i ¥+ i

Zb _ p- g iV

dj ¥ -1 ¥-1 m is the ratio of the expanded jet diameter def f = Zb to the port diameter d. and qb is the angle between a tangent line to the median and qoo" Solu- J tion of these eq_lations , in conjunction with the previously established relation Yc = (Xc - b) cot _y -47 - enable us to calculate the penetratration distance, Yc / dj, as a function of the variable parameters Moo, Pj / Pco and_y.

Figure 80 shows the dependence of penetration distance on free stream Mach number. It can be seen that the secondary jet penetrates further into the primary stream at the higher Mach numbers if the stagnation pressure ratio, Pj / poo, is maintained invariant. Figure 81 shows that the penetration distance at a constant Mach number increases with pressure ratio P' / Poo" Figure 82 shows that the penetration dis- J tance is maximized when injection is normal to the primary flow direc- tion.

The critical injection port spacing ratio is shown in figure 83 as a function of port inclination angle _ for various stagnation pressure ratios. Presumably, the widest spacing is desirable to provide the maximum blockage of the main stream flow. The widest spacing is given by the relation b - B(9) tan _ _ Yc which results from differentiation of the equation for the injection port spacing ratio previously given. This maximum is shown as a dashed line in figure 83.

A s seen in figure 83 the variation of the injection port spacing ratio with _ is relatively weak. Therefore, by use of equation B(9) in equation B(6) one obtains the following approximate formula in which _ does not appear explicitly: c -__ Zb 1 + B(10) -48 - In order to compare the latter with the criterion c = d eff reported earlier, we put equation B(8) in the form c = def f 1 + _deff ] B(ll) and note that since the penetration depth Yeff is generally of the order of def f , the impinging jet spacing for strong port interaction is typically twice as large as that for parallel injectant jets.

The results of tests of a configuration such as is cons i dered here are reported in Ref. 1. The two sonic ports had a spacing ratio of 3.9 and were inclined 30 ° toward each other and 45 ° upstream. This point is spotted on figure 83. According t o the present analysis , the critical spacing ratio would occur at a mass flow ratio, _s / *p , of •0425. In other words, at lower secondary flow rates, impingement of the jets would not occur with the given injection port spacing ratio.

The tests were conducted at mass flow ratios of .03, .06, and .09.

The results of the tests are reproduced in figure 84. Note that for meridional injection, the trend is for the side force to decrease con- tinuously as the mass flow ratio is increased. On the other hand, the side force produced by tangential opposed jets decreases at low mass flow rates when the secondary flow is increased , reaches a minimum , and subsequently increases. It can be postulated that the increase in side force begins when the secondary flow rate is great enough to cause impingement of the two jets. This critical mass flow ratio is seen to be • 06 from the test results , although intermediate data at points between -49 - • 03 and . 06 were not taken. Based upon these meager results, we can conclude that the present analysis may be used to calculate injection port spacings for test models and to estimate optimum injectant para- meters.

-50- A PPENDIX C AN A LYSIS OF SINGLE PORT FLOW INTERFERENCE WITH SECONDARY INJECTION The analysis of single port flow interference with secondary injection has received considerable attention in recent years. How- ever, many of the models formulated for the flow interference analysis do not appear to agree with the shock wave structures visualized from schlieren photographs and spark shadowgraphs.

The analysis in this study is confined to predicting the shock wave structure produced by the secondary injectant if the shape of the obstruction made by the injectant is known. For the present purpose, is is immaterial whether the obstruction is formed by gas injection or volatile liquid injection and it can be treated as a solid body obstruction. In the case of gas injection, it has not been possible to define a representative body shape for the obstruction from schlieren photographs. Therefore_ the injection of volatile liquid is used to forn_ulate the model since the obstruction can be seen on a schlieren photograph. The following model is based on schlieren and spark shadowgraph pictures obtained during freon injection tests conducted at Jet Propulsion Laboratory, California Institute of Technology. The details of these tests are given in Ref. Z.

-51 - A . Fo r mula tion of Single Port Flow In terference Model A study of the shock wave structure produced by the secondary injection revealed two types of pattern as shown in figures l and 2.

In both cases_ the interference pattern consisted of a bow-shock wave detached from the obstruction with an attendant shock wave formed by the boundary layer separation ahead of the obstruction.

The difference between the two types consisted of the magnitude of the separation-shock wave and its point of intersection with the bow-shock wave. The formulation of the interference model for predicting the shock wave structure consisted of predicting the separation-shock wave_ the bow-shock wave_ and the intersection point of the separation-shock wave with the bow-shock wave.

I. Separation-Shock Wave A method for predicting the shock angle formed by boundary layer separation has been presented by Mager in Ref. 3.

The analysis gave the shock angle as a function of the free stream Mach number and¥. The analysis predicts the shock angle of the separati o n-sh o ck wave of figures 1 and 2 very well.

2. Bow-Shock Wave The bow-shock wave formed by the obstruction is obtained by approximating the obstruction with a hemisphere capping a cylinder.

Since the o bstructi o n is a blunt-nosed shape_ the detached bow-shock wave can be located with good accuracy by replacing the o bstruction by a corresponding sphere of the same radius (see -5Z- figure 85). Let R b be the radius of this sphere. At y = 0 the standoff distance A is approximately the difference between the o shock wave curvature Rsh at the nose and the body radius Rb, i.e. , Rsh - R b = A ° at y --0 C(1) Rsh and A ° can be expressed in terms of R b and the density ratio by the above relation and the constant density approximation theory (Ref. 4). The constant density approximation theory is used to obtain /X since the value of A can be obtained analytically. _Also, o o the value of A agrees very well with the experimental data down o to a free stream Mach number of 2. 0. The relationships can be written as Rsh = R b C(2) and R b /,, = 1 + - _

o _ c(3)

where g

(, , , - _) M l + Z

= Z C(4)

(¥ + 1) M 1

¥ is the specific heat ratio, and M 1 is the free stream Mach number.

In the usual supersonic flow region, it is a good approximation to use the hyperbolic equation to represent the bow- shock wave. The asymptotes of the hyperbola are equal to the free -53- stream Mach wave. Therefore, by knowing the free stream condition and the radius of curvature of the shock wave at its nose, one can uniquely determine this hyperbola.

Let the hyperbolic equation be

2 2 cc5)

y = C I x - C 2 then its asymptotes are y = ± ClX.

Now, let the Mach wave angle be a , then 2 1 sin _ =

M_

and 2 1 1 = - -2- tan _ M Z - i _M J M I. The constant G l is, therefore, equal to where _M = 1 / _M" The radius of curvature of an arbitrary curve is given by

1 + (a-_)

R - c(6)

dZy 2 I Z Now, y = --_ x C2; differentiating twice_ one obtains

_ M

dy Z d z 1

(_) + y dx-_: -7--Z-

_M

-54- A further manipulation gives d Z -C 2 Y _

- T T - 3

_M y By equation C(6) and substituting negative Rsh for R due to the fact that they are in the other side of the curve, one obtains 1 -_- Z --_- Z

[

Rsh:_zz _M Y + _M

The value of R which is of interest is at y : 0, so that sh

1 p-J z

Rsh =-_2- M x Therefore, C Z can be determined. The final equation for the hyperbola is

z 1 z z Rz c(7)

Y : _---2 - x - _M sh

_M

Hence one can determine the origin of the coordinates and the shock wave position as shown in figure 86.

The shock wave caused by the boundary layer separation has been assu1_ed in our previous analysis to be a function of free stream Mach number only (Ref. 3 and 15). This shock wave is either a conical or a plane oblique shock wave_ depending on whether the injection port is a circular shape or a long slot. This shock wave will hit the bow-shock wave ahead of the blunt-nosed body. The bow-shock wave actually will change its shape and shift -55- its location by the boundary layer separation and the separation- shock wave. If the separation region is small, the change of the bow-shock wave is relatively small, because the local shape of the nose is not a critical factor in determining the shock shape and location. F urthermore, in the Mach number range of interest the shift of the bow-shock wave by using the free stream condition or the condition after an oblique shock wave is quite small.

Therefore, within the accuracy of our approximation this shift can be neglected.

3. Intersection of Two Shocks The intersection of the separation-shock wave with the bow-shock wave is treated locally as a plane oblique shock wave. A schematic of the intersection of the shock wave is shown in figure 3. Assuming the shock waves are free to adjust them- selves to satisfy the boundary conditions, namely, it does not create a reflection wave and yet satisfies both the pressure and flow direction, the following analysis can be made.

As shown in figure 3, the flow field can be divided into four regions. Locally, these shock waves can all be treated as plane oblique shock waves. Employing the conditions of Ref. 3 and 15, the first shock wave angle _Z is fixed along with the flow direction 0.Z" The boundary conditions are P4 = P3 C(8) °-4 = 0.2 + °-3 -56- Using the obliqL1e-shock wave relation Z Z PZ Zy M 1 sin _2 (y- i) Pl ¥ +l C(9) (y+ l) M 1 1 cot _2 = tan _g 21 Z 2 (M sin a2 - i) and equations C,(8) and C(9), one obtains 2 2.

Z¥ (¥ + i) M 1 sin _4 - (Y - I) (y + I) =

c(i o )

y M 1 sin o _ Z - (¥ l) 2y M Z 2 sin _3 (y - 1) and (¥ + 1) M 1 cot -1 2 = Z (M_ sin _4 i) (y + l) M Z Z + C(ll) cot -I tan _3 Z (M2z sin _3 - l) -I (¥ + l) M l _ cot Z (M 1 sin 2 oZ - I) where 2 (Y I)2 4 Z Z Z a M I sin _Z - 4 (M 1 sin _Z I) (¥ M 2 Z - 1 sin _2 + l) - 1 sm o _2 +2

: [2 = = )JL( ] MZ ¥ M I sin _2 (y - I y - I) M Z . Z

c ciz)

-57- Hence one can solve for _ and ' 3 4" Usually _4 is very close to _3 + _Z" For our purposes, to locate this intersection point on the bow-shock wave, an average value of _4 and _3 + _2 is used and is denoted as _3-4" The tan- gent point on the hyperbola can be obtained by differentiating equation C(7) ; it is dy _ i x - tan e3-4

_l-_ - -_M y

Now, eliminating x by the original equation, one obtains the y coordinate in terms of its tangent, i. e. , _5 M R sh Y - I / a C (13) Once the angle _3-4 is known its tangent is known and, therefore, the intersection point is located. Furthermore, since the separation- shock wave angle _Z is known the starting separation point can be located.

In solving for _3 and _4 explicitly, the following results are obtained. It is found from the analysis, that two solutions exist.

The first solution is obtained where wave B-C in figure 3 degenerated and became a Mach line and is called the limiting case. Then _4 = _Z C(14) = sin-I 1 (Mach wave) C(15) -58-

APPENDIX D TURBULENT BOUNDARY LAYER CALCULATION PROCEDURE A procedure for calculating turbulent boundary parameters in compressible flows with arbitrary pressure gradient is presented.

The method uses a modification of the techniques proposed in Refs. 6 and 7 to transform the compressible boundary layer equations to approximately an incompressible form. For the case of an insulated surface and Prandtl number of unity the transformation becomes exact.

A. Flow Geometry and Boundary Layer Eguations The flow under consideration may be either two-dimensional or axisymmetric with the following geometry.

n r(s)

X x - direction of main flow r(s) - distance from line of symmetry to solid surface s - distance measured along surface n - distance normal to and measured from wall -61 - The boundary layer equations are: Continuity:

)-u k -- k = 0 D(I)

( r ) +(pvr ) r_ k = 0 for two-dimensional flow , and k = 1 for axisymmetric flow.

Momentum: p u u + p v u :- + (I x u - (p v) u ) D(2) ,s ,n ,n ,n Energy: p u h + p v h = u + X (p v)' ) +TU

h'

, s , n ds , n , n , n D(3) In the above equations all bar values are understood to be tem- poral mean values. The bar (--) over two terms indicates the tem- poral mean of the product , and the primes indicate the instantaneous fluctuations from the mean. The commas before the subscripted vari- ables s and n indicate partial differentiation , for example , 8u ,s _s Transformation of Equations Define a new coordinate system by n s N = col(s) _ -P_ dn; S = _ _ O z(s ) ds 0 Po 0 8 a . 8 °a2 8 + N O D(4) O n - °al "P------ a'--N-- ' -- a s = --8S , s "aN Po -6Z - where Po is constant and arbitrary for the present.

Introducing the stream function defined by k -- -- k r p u = _ ; r p v : - _ D(5) _n ,s and using equation D(4) gives the continuity equation and velocities m u and p v as (U- rk) S + (_-rk) N: 0 J D(6) u : _ 0 1 U ; p v = Po (_Z V - N U) , S where k i k-- i

r _:-- qJN ; r V : 9 s

Po Po In order to transform the momentum equation, it is necessary to make an assumption regarding the transformation of the turbulent I I shear term - (p v) u F ollowing the suggestion of Ref. 7, it is assumed that the turbulent shear associated with an elemental mass of fluid is invariant, which requires that -- 1 I --Z I l p ( (p v) u ) ds dn : po (V U ) d S d N or --Z T ' ' PO ' '

( p v) u ::---- (v u ) a(s,N) :o_

p a(s, n) 1 _z Po (V u ) m(7)

Using equations D(4) and D(7) gives the momentum equation as

dU

__ T !

UU S +VU N : f(s, n) _ ____q_e i (- P --K-_o I U N o N , , e dS +-- -oa1 2 o o2 p V U ) Po _°l _g Po D(8) -63- where 1 1 d°_l --2 -- + u p ¢ o 1 dp

f(s , n) = d_I D(9)

I i --2 + U Pe _ i dp e The subscript (e) refers to external flow conditions outside the boundary layer. By choosing the product p_ to be evaluated at a refer- ence temperature (or enthalpy), that is, p M = Pref }_ref (s), equation D(8) gives the following relationship between _ 0 1 and _ 0 2.

_°I = °_2 (Po _o / Pref _ref ) D(10) The condition tha t p_ = Pref_ref transforms the laminar shear stress as u = _ ° 1 °_ 2 _o UN D(ll) ,n which is identical t o saying t hat the laminar shear associated with an elemental mass of fluid is invariant. The assumption made regarding the turbulent shea r transforma t ion is then in agreement wi t h the laminar shear transformation.

In order t o find the functional form of f(s , n) , it is necessary to know the density variation in the boundary layer. Since it is desired t o uncouple t he momen t um and energy equations , t he density varia t ion must be known in terms of the velocity distribution. It is well known that for flows with zero pressure gradient and both laminar and turbulent Prandtl numbers of unity (Ref. 16) that the enthalpy distribution is given by -64 -

-- hw + (ho- hw )(U / Ue) - (F_o -he)(U / Ue)z m(Iz)

where h w , h and h are the wall, stagnation and external static o e enthalpies respectively. For Prandtl numbers other than unity, it is acceptable to replace the stagnation enthalpy by the recovery enthalpy h . The density variation through the boundary layer may then be r approximated by -- h _p._ - e D(13) F ; e D ue to lack of knowledge regarding the enthalpy distribution with pressure gradients , it will be assumed here that the density variation is given by the quadratic form of equation D(I2), namely,

-_ _ _ _ - g -

_ (. _f_r w _ (_ ! .r e w+ _ _ ) (_ -- - -) - _ - 1 ) ( _ _-- -) Z D(14)

p _ h h u h u e e e e e e where the recovery enthalpy is defined by h -h r e = RF = ( Recovery Factor) o e Rearranging equation D(9) and using equation D(14) gives 1 +_ p ._.____ y M f(s , n)_ (_!u) = W(l_ u)+ r u (i_ u ) D(15)

i-d, -2] -

col dp u _ u h u u e e e e e e and choosing -- dco Z i +- 2 -- _--- z --YM 2 - o - I +' /-i M 2 2 e ' co I clp e he -65- the following relations for f (s,n) and _ 0 1 are obtained

u I - -

fCs,n) = _ (1 - _ + r _ u (1 - _ + (u___)2 D(16)

u _ u u

O e o e e e and

_1 = (_ / Po) z¥ D(17)

If the viscosity variation with enthalpy is given by _ --_o (_ / ho)w' the product p_ = Preferrer is then

Pref_ref Po _o (P / Po) (_ref / _o)w-1 D(18)

and _02 is given by , 3_-i, ¢ ° 2 = (_ref / _o)(W-I) (p / po_ 2¥ _ D(19) The reference enthalpy taken from Ref. 17 is given by _ref = _ + 1 e _ (L - _e ) + 0 . Z2 (hr - he ) D(20) The momentum equation D(8) becomes dU UU S + VU = f(s,n) U e U - V U ) D(21) , , N e dS + ( V o , N ,N The transformation becomes identical with Ref. 7 when RF = w = 1.0 and h = h . This is the particular case when the total enthalpy r w 1 Z distribution through the boundary layer is a constant , e.g. , h +_ u = constant.

-66 - Momentum Integral Ecluation Using equation D(6)and integrating equation D(ZI)across the boundary layer, the momentum integral equation is then

d 6M. r CRF-1)_M 2 -]

2 e _w6*i 6M i dU 6M. Gf.

-------!i + _g + +_ J e + k i dr _ I y-l M2 h ° 6Mi U dS r dS 2 dS l+ 2 e e D(ZZ) where 6M. and 6':-'.i are given by 6.

j 1 _ (1 _ )dN

6Mi o _

e e 6.

U 6':'-. = (1 .) dN

3o

e Using a power law for the velocity distribution through the boundary layer U / Ue = (N / 6i)i / m gives 6M. and 6;I".i as 6M. = 6.m / (m+l)l (re+Z); 6"-',i = 6i / (m+l) D(23) In Ref. 18 it is shown that the coefficient of fri c tion Gf. / 2 may be represented by m-1 2 m+l -- m+l G3 v ° ) D(24)

of. / z :: (--j-) (

1 U 6.

e 1 Using the definition of 6M. from equation D(23), equation D(24) i becomes -67- m-I 2 2 Gfi C3 m+l m+l -_ m+l m o ) D (25 ) "-2 --: ( -"m- - ' ) ( ' ( re + l) ( re + Z) ) ( Ue 6M.

In Ref. 18, C_ was found by choosing m = 7 and requiring that the m+l coefficient (C3 / m) became identical with the Blasius coefficient 0.0225. The value is C 3 = 0.0444. If the value of C 3 is taken as 0.04528, it is noteworthy to mention that equation D(25) for values of m of 7, 9 and Ii are extremely close to the experimental values of Prandtl, Young and Falkner.

C 3 m Calcula t ed 2 Experimental Source Per Cent Diff.

- i / V o 4 V o 4 - I / 7 0.01273 ( ) 0.0128 (- .) Prandtl 0.547 6M.U 6M.U e e 1 1 i i V i / 5 Vo 5 o 9 0.00879 ( ) 0. 00885 (- ) Young 1.81 6 M._ e 6M_ e 1 1

: i / 6 -: i / 6

11 0.00654 (. o } 0.00653 (. o ) Falkner -0.153 6M._ e 6M._T e 1 1 Although m varies with pressure gradient and Reynolds number, it is well known for incompressible flows that when m is assumed to be constant , the calculated values of momentum thickness 6M. are within the range of experimental error.

Using equation D(25) for Cf. / 2 and defining a new variable _ by _ = 6M.(_j e 6M. /V o ) 2 / (re+l) , assuming the recovery factor RF to be 1 1 -68 - constant, using the condition that U = a M (from equations D(6) and e o e D(17) and neglecting any heat conduction along the wall, i.e. dh / dS = 0 ' k'V the momentum integral equation may be integrated over S to give >'6 - @ >'3

L in e l +]_-2l _V_nJi r

>'Z s k k 3 >'4 ( l + _- IM2e) IV[ I ' -r (_ref / _ 9 {w-l)ds e D(Z6)

+ x _3 J s _I M2 x5

M l~r m ' (I + ) e 2 e where all dimensional lengths s , r and _ have been made nondimensional by a reference length R T, i.e., { 2 = _ / RT, r = r / R T and s = s / R T. The subscript(in) indicates initial conditions and _in' (href / ho) and the k's are given by _. = (160)(m + 3) / (m+l) D(27) in Mi n (a° RT / _o)

x :/

I + (0.5 + 0.2ZRF) 2 M 2 I ref _ e + -_ _ D(28)

Z 1 +_-i Mz

o 2 e X i = (_-%q-) 3 (m---_ + --m _Sw D(29) m+2 [.m+l m+3 ] kZ = (__I_RF) I_)'m+3 " D(30) .m+3 , D(31 ) >'3 = k (m-----Ti-) -69 - k4 = [m--%-i -) (m + l) (re + Z) , m+3,[ m 1 (22.1 m) D(32) 2 / (m+ / (m- l) / (m+l) + (i RF m + 3 D(33)

_5 = 2(¥-I) 2 ) m+1

xw D(34)

(m+3 m+2 1 k6 = m [_ "m+l where =__w -I

w

o From the calculated values of . _, the actual boundary layer parameters are f o und as follows: Momentum thickn e ss: (m+l) /(m+3) (i + y-i M z ) (y +l)/Z(y-1) 2 e " 6M = M 2 (m+3) RT / 2(m+3) D(35) e (ao Fo) Displacement thickne s s : "6':' = 6M _w + I) (_) (i + e) + RF 2 e D(36) I_ .m + 2 , X_21 M2 y-1 M2 ] Boundary layer thickness: ,m + 2, y-l_2i + RF + m + 2 D(37)

[ _:!Mz ]

"6 ='6M ( Z w + 1) (_ 1 (1 + 2 " "e' 2 e Friction coefficient:

- - (w-l)

Cf . m + l , 8__M (hre f/ ho)

T = ×4 <_-T y )

(I + 23_ M 2) (3¥-I) / 2(¥- I ) D(38) e -70 - Skin Friction Drag: The component of skin friction drag in the direction of main flow (x direction) is found as follows:

r<s)

!

i

_ I _ X The elemental component of drag force in the x direction is d D = T COS ¢ d A D(39) X W W where dA is the elemental surface area and is given by dA = (2_)k rk ds.

Since cos Cw ds = dx, the integrated drag force is then

D = k x k

x 3 TW r dx D(40) X.

Now divide by the stagnation pressure P and an 'area' defined by O --k 1+k A T= T (RT) and equation D(40) becomes X -- D 2k " Tw -k - P A P : 0 _ r dx D(41) o T x. o -71 -

_ -i 2 x / (x-11

e 2 M2 / (1 + _Z_ Me ) -- -- --2 and pe u / Po = _ / e Noting that Cf / 2 = Ww / PeUe the drag coefficient is then D - 2k S x Cf MZe rkdx D(42) CD = PoAT _ / -xi _ (1 + 2__iMe )¥ / (¥-i)-1 2 -77. -

APPENDIX E SEPARATION CRITERION FOR COMPRESSIBLE FLOW A method for predicting the separation point for a compressible turbulent boundary layer is presented based on an extension of the in- compressible separation criterion of Ref. 19. In the following analysis the following assumptions are made: (i) Th e surface is adiabatic.

(2) The recovery factor is unity.

Under these assumptions the momentum equation D(Zl) reduces to dU -- UU +-- VU = U e 8T E(1) Po ,S Po , N Po e dS + 8_ Following the approach of Ref. 19 , it is proposed that the boundary layer may be divided into two distinct regions, an outer region and an inner region. In the outer region it is assumed that the shear losses along a streamline are the same as for a flow without a pressure gradient. Chang- ing the variables on the left hand side of equation E(1) from S and N to S and jj gives dU aU Po U ( --8-S ) = Po U dS + ( a T e _ ) E(2)

s,_

For zero pressure gradient

OU* a T*

Po U* C 0---Z---) = ( 8 N ) E(3)

s,_

-73 - where the asterisk denotes the point where the pressure gradient is zero, immediately preceding the adverse pressure gradient region.

Under the assumption that (3T /0 N)s ' _b = (_T* / 0N*)s, _ the veloc- ity distribution along a streamline is then

UZ(s,_)= U,Z(s,_)+ U 2 _U,z;(_ >

e e Cjc ) E(4) Equation E(4) sta t e s the difference between the dynamic head _2 at any point in the boundary layer and the dynamic head of the external flow _2 is the same as for a flow without a pressure gradient. Differ- e entiating equation E(4) with respect to _ and noting that rku(0 / 0_)S equals (_) / 0N) S gives

0 U aU*

ON - ON* ; C_ _> _jc ) EC5) The stream function _ is N* %b = _,'. ' - = rk_ U':_dN* E(6) l m Choosing the velocity distribution U* = U* ) gives

_ _ (_

e U::: (l-m) / m) ON- m _ ( , ) ; (_ > c ) E(7) and m+l N* m %b = rk m+Im U*e 6. (--K_ , ) E(8) Neglecting the effects of inertia f o rces with respect t o pressure and shear forces in the inner layer gives a direct balance between the -74- pressure and shear forces as aT dU = -_o _ e .

e dS ' (q_ < _bjc) E(c ) ) Integrating equation E(9) for the case of zero shear stress at the sur- face, and introducing Prandtl's mixing length theory for the shear stress gives l -- I aN _ - Po

E 1 e d_ ; (%b< _bjc) E(10)

where K is the Karman constant. The velocity distribution and stream function are then

- g - Po Ue ----LedS N "(q_ , < _bjc) E(II)

I = r 3K -Po U N [

e dS ; (_ < _jc ) E(lZ)

I d 12 3e

The junction of the two regions is determined from the following conditions: (1) The velocity of the two regions must be equal m m U ( _ b < _bj c ) = U (+ > _bjc) ; (_b = _jc ) (Z) Continuity of mass flow must be satisfied, which require s that

+ (+ < +jc ) =_ (_ > q_jc) , (+ = O jc )

{3) The shear stress must be the same for the two regions.

This requires that the velocity gradients be matched.

-75-

_U _U

(_ < d_jc) = _ (_ > _jc) ; (_ = _jc)

_O 3

Equ a ting _ ( - 8 - -_) for the outer and inner reg i ons g i ves the refer- ence fl a t plate p os ition a s N:_' (2m-4) / m 3 K 4 -- E(13) OoUe dU e Z 4(re+l) (-m _ _ 6* ) e C o mparing UZ / (O_ O U / ON) f o r the fla t plate flow and actual flow gives (U I U*)Z = 3 1 (m+l) E(14) Substituting equati o n E(14) into E(4) gives Z

U z m

m - Z (--_-) E(15) (I e ,,)_ (__ 7 _i_)

U* z

e Eliminating (N* / 6*) between equations E(13) and E( 1 5) and defining

r - ¢I- z) gives

m-Z _ m- ? - = (--_--_ ) E(16) Lm2(m+l) The reference fla t plate boundary layer thickness is given by m-I C3 _ m+l Z m+l (m+Z)(rn+3) _ _ o m--'+- 5 6* - m m U_ S E(17) e Making all lengths nondimensional by dividing by the the reference length R T and using the transf o rmation relations U =aM e o e -76 - and S= _o ds 0 2 the separation criterion is then 2 2 m-2 m+3 m+3 M2 m M 2 A(m) (a°_) (Me) _2 (1 e d (1 e o E(18) 2- ) d"-_ M., . 'Z ) = m+l M* s e e c o d where 1 m-i m+l m-2 / X.(m) = __2(m+l ) (22. lm) (_----_-) E(19) [m[ 3K4 1_ m+3I m+2)m(m+31 m+3 m-2 2 and (_2 = _ref / ho ) + y-1 M 2 2(y-l) E(20) 2 e Equation E(18) is a provisional separation criterion for compressible turbulent flow, the accuracy of which must be dete r mined f r om expe rimental data.

-77-

APPENDIX F EXPERIMENTAL DATA AND RUN SCHEDULE Port Nominal Conical Nozzle APG-1 Nozzle Configuration V¢ / _¢ ,% Run No's. Run No's.

s p CTI3 3 I 15 6 Z 16 9 3 17 AT13 0 4 18 3 5 19 4 6 Z0 5 7 Z1 6 8 22 7 9 Z3 8 I0 24 9 Ii Z5 BTI3 3 IZ 26 6 13 27 9 14 Z8 ARZ Z Z9 47 3 30 48 4 31 49 5 32 50 CRIZ3 3 33 51 6 34 5Z 9 35 53 -79 - EXPERIMENTAL DATA AND RUN SCHEDULE (cont'd.)

Port Nominal Conical Nozzle APG-I Nozzle Configuration qv / _ , ,% Run No' s. Run No' s.

s p ARIZ3 0 36 54 3 37 55 4 38 56 5 39 57 6 4O 58 7 41 59 8 42 60 9 43 61 BR123 3 44 62 6 45 63 9 46 64 -80 - DATA SHEET TYPE Conical (CT i, 3) RUN NO. 1 PRESSURE RATIO, PRI M ARY, k p 526. 40 PRESSURE RATIO, SECONDARY, k s 228.37 PRESSUR E 99.81 p$ i o S E CO ND ARY PRESSURE 43.39 pslo FL O W RATIO, Ws / W p 0. 030 1 A MBI ENT PR E SSU RE 0. !90 pmla SIDE F O RCE 6. 14 LB AMPLIFI C ATI O N FAC T OR J. . 5 8I AX I AL F O RCE 125. 35 LB VA C UU M TH R UST COE F FI C I EN T 1. 647 PR E S SU R E D I ST RI B U T I O N T A P PRESSU R E R A TIO T A P PR E SSUR E RATI O LOC A TION P /P c LOC A TION P / Pc I .0032 1 8 .0039 2 .00.32 3 5 .. . 0 1 52 3 ,0032 .. . 19 , 0147 4 , 0032 3 6 .0125 5 . 0049 3 7 .0211 6 .0228 20 . 0278 7 . O 1 94 2 1 • 0059 31 .0297 22 .0054 B .0199 23 .0094 9 .0319 3 B .0090 I o .0270 3 9 .0164 ii .0140 24 .02 0 6 1 2 .0044 40 .0236 1 3 .0046 2 5 30 ,0036 ;,6 .0029 i 4 .Ol 57 27 .0 0 36 32 2B • 0184 .0093 3 3 29 • 0152 .0036 I 5 CAN • 0196 .0022 34 . 0315 9 0 .. .0 0 22 _ 6 .0246 91 . 0 0 22 1 7 .0 0 44 -81 - D ATA SHEET NOZZLE TYPE Conical (GT i , 3) RUN NO. 2 PRE SS UR E R A TI O , PRIMARY, k p 518.72 PR ES S UR E R A TI O, S EC O ND A R Y , k 1 CHAMBER PRESSUR E 99. 88 p s io S E COND A R Y PRESSURE 87, 20 p = la W E I GHT FL O W R AT IO, W $ / Wp 0. 0606 A M B IE N T P RE SS U R E 0 . 193 p = la TOTAL SIDE F O RCE 10. 60 LB AMPLIFICATION FAC TO R 1. 345 TOT A L AXIA L FOR C E 126. 30 L B VACUUM T HRUS T C OEFF ICI E N T 1. 658 P R ESSUR E D I S TRIBUTION TAP PRESSURE RATIO TAP PRE S SURE RATIO L OCATIO N P / Pc LOCATION P / P c .0030 I B .0039 2 .0030. 3 5 .0.189 ..

3 ,00 3 0 1 9 .0184 4 36 ,00 3 0 ,018.9 ....

5 ,0064 37 .0172 6 ,030q 20 .0266 7 .. . o ? . ? .,q .. 2 i .0059 3, ,Q226 2 2 .0074 I B .0320 23 o 0103 9 .0256 3 B .0088 IO 3 9 n_R .0177 ......

II 24 n ' _9 .0172 1 2 0 0 44 40 .0261 13 2 5 • 0049 ....

3 0 2 6 .0n39 .0027 14 27 o]_7 . 0 034 3 2 .0155 2 8 .0088 33 .0246 2 9 .0049 1 5 .0280 CAN . 0020 3 4 .026.1 90 ,_ 0 0020 16 91 .0334 .0020 .0044 -82- DATA SHEET NOZZLE TYPE Conical (CT i, 3) RUN NO $ PRESSURE RATIO, PRIMARY, ) ,p 523. 94 PRESSURE RATIO , SE C ONDARY, X i 677.43 CHAMBER PRESSURE 99.86 p,=ia SECO N DARY PRESSURE 1 27.39 pi l e W E IGHT FLOW RATIO , W s / W p 0. 0 907 AMBIENT PR E SSURE 0, 191 p = lo TOTAL SIDE FORCE 14.88 LB AMPLIFICATION FACTOR 1 . 258 TOTAL AXIAL FORCE 126. 65 LB VACUUM THRUST COEFFICIENT 1. 663 PR E SSURE DI ST RIBUTIO N T AP PRESSURE RATIO TAP PRESSURE RATIO LOCATION P / Pc LOCATI O N P / Pc i ,0027 Ie .0044 2 .002 . 7 35 ,0177 3 19 . 0027 , 017Z 4 3 6 • 0034 , 02 1 6 5 ,0084 37 .0206 6 , 0403 2 0 . 0 224 7 02.q q 2 1 . 0059 31 , Ol 23 2 2 .0069 8 .036q 23 . Ol 23 9 .0288 3B .0101 I0 39 . 0 366 .0216 it .0460 24 .0148 12 40 0044 . 023 1 13 2 5 • 0044 30 0034 2 6 .0030 14 27 • 014_ , 0037 3 2 28 • 01 2R .0093 33 29 • 0192 . 0054 1 5 .0334 CAN . 0025 3 4 .0270 9 0 . 0025 1 6 . 0364 9 1 . 0025 .0042 - 8 3 - DATA SHEET NO Z ZLE TYPE C onical {A__T 1, 3) R UN NO. 4 PRESSURE RATIO, PR I MARY, k p 502. 75 PRESSURE RATIO, SECONDARY, k I - - CH A M B ER PRES S U R E 99 . 77 p s io S E CO NDA R Y PRESS U RE -- p sJ o WEIGHT FLOW R A TIO, W$ / W p 0 AM B IENT PR E SSUR E 0. 198 psle TOT AL SIDE FOR C E 0. 28 x_ LB A M PL IFIC AT ION F A C TO R _ _ TOTAL A X IA L FORCE 124.] 0 . LB V A CUUM THRUST COEFFI C IENT 1 . 635 PRESSUR E DISTRIBUTIO N T A P PRESS U RE R A T IO T AP PRESS U RE RATIO L OC A TION P / Pc LOC A TION P / Pc .0040 IB .00 5 7 z .0042 35 .0062 3 o 0045 t9 .0064 4 , 0045 36 . 007 2 5 , 0055 3 7 . 00a4 6 .006 2 20 oo q 4 7 .0062 21 ,0055 31 .0069 2z .0050 8 ,0079 23 .0062 ......

9 ,0097 38 .0055 I 0 . Ol ]6 3 9 .0069 ......

i I .0141 24 .0082 12 . 00 5 7 40 .... 00 97 .....

1 3 .0062 2 5 30 , POSZ z6 .0030 1 4 . 0064 2 7 .0 0 37 3 2 , 0 0 67 2 8 . O0494______ 33 .0079 2 9 .0045 15 .0084 CAN .0025 34 .0099 9 0 1 6 .0!19 91 1 7 .0055 ;',_ Ports plugged but not fil l ed to form smooth contour.

- 84 - DATA SHEET NO Z Z L E TYPE Conical (AT I , 3 ) RUN NO 5 PR E SSURE R A T IO, P R I M A RY , ), p 508.85 PR ESSU R E R ATIO, SE C ONDA R Y, k! 23 8 .52 CHAMBER PRESSUR E 99. 94 psio SECONDARY PRESSURE 46. 75 psla WEIGHT FLOW RATIO, W$ / Wp O o 0208 AMBIE N T PRESSURE O. 196 p = la T O T A L SIDE F O RCE 5. 91 LB A MP L IFICA T IO N F AC T O R 1 . 540 T O T A L A XIAL F O RCE 1 24. 90 LB VA C UUM THRUST CO EFFI C IENT 1. 640 PR E SS U RE DI ST RIBUTIO N TAP PRESSURE RATIO TAP PRESSURE RATIO LOCATION P / Pc LOCATIO N P / Pc I .0037 I a .0059 2 ,00 3 7 a s 0086 3 19 • 00 3 7 . OoR Q 4 , 0038 3 6 . 0116 5 .00 3 7 37 . O19 7 6 0155 2 0 . 0261 7 , 01_6 2 1 ,0062 31 .0276 22 .0045 a .0182 23 .0087 9 .0 3 10 3B .0084 Io .0246 3 9 .01 33 II .0138 2 4 .0182 1 2 .0050 40 .0207 13 .0052 2 5 3o . 00 4 2 26 . 0025 14 .0165 27 .00 3 7 3 2 .0155 2 8 .0091 33 . 0177 2 9 . 0047 1 5 .0182 CAN . 0025 3 4 ,0300 9 0 .0028 16 91 • OZl 9 0028 1 7 .0062 - 8 5- DATA SHE E T NOZZLE TYPE Conical __AT i, 3) RUN NO 6 PRESSURE RATIO, PRIMARY, _kp 5 03. 5 6 PRESSURE RATIO, SECONDARY, )_s 314.65 CHAMBE R PRESSURE 99. 89 p si a SECONDARY P R E SSU R E 62.30 p,i o WEIGHT F L O W RATIO, Ws / W p 0 . 0400 A M B I EN T PRES SUR E 0. 198 pl i o TOT A L SIDE F ORCE 7. 47 LB A M P LI F I CA TION FA CTOR 1. 458 TOT A L A XI A L F ORC E 1 24. 31 LB V A CUUM T HRUST CO EFFI CIENT 1 . 634 PRESSURE D IS TRI B U TION TAP P R ESSU R E R ATIO T AP PRESSURE RATIO L OCAT I ON P / P c LOCAT I ON P / Pc ' .0035 ........... L8__ ..................... oo6 _ 9_ ...........

2 ................. 0.03 5 .............. 35 O_ . L04 3 19 0(' } 3 3 ........................... _ ......

4 .0043 36 .................. _Q.LO_7 _____ 5 .0040 3 7 .0173 s ..... 0185_ 20 ....... 0276 ....

7 Q12_ 9 2 _ OOJS_Q 3_ o 0259 22 .0043 S , Ot 98 _3 ...... g _O_8 _ Q_ ....

9 0303 38 ........ 0075 .........

t o .03 3 8 __ 39 ......... _ ...............

' ' 01 44 ......... 24 _ J _ 7 _8 .........

,2 .0050 ___ 40 0_239.........

1 3 2 5 .... 005 0 .................................

3o 0040 2 6 0028 ' 1 4 0179 2 7 0038 32 0141 28 0092 33 0227 2 9 0053 1 5 0158 CA N 0026 ' 34 t 0296 9 0 ................ O_OZ S _ ..............

I 6

/.......... o____ 5 _ 9 , ...... _o . 2.8_ ......... .J

I

]

1 7 l 0060 ] -86 - DATA SHEET NO ZZLE T Y P E Conical (AT I , 3 ) RUN NO 7 P RESSURE RAT I O , PRIM ARY, ). p 509. 12 P RESSURE R AT I O, SE C O N DARY, l I 403.38 C HAMBER PRESSURE 100. 03 p sia S E C ON D ARY PRESSURE 79. 06 ps l a WEIGHT F L OW RATI O , W$ / wp 0. 0505 AMBIEN T PR E SSURE O. 196 p,,la TOTAL SIDE FORC E 8. 97 LB AMPLIFICATIO N FACTOR 1 .372 TOTAL AXIAL FORCE 125. 57 LB VACUUM THRUST COEFFICI E NT 1 . 647 P R E SS U R E DIS TR IB U TI ON T AP PRESSURE R AT IO TA P PRESSUR E R A TIO L O C A TI O N P / Pc L O C A TION P / Pc i . 0038 I S .0058 z . 0036 35 _ 0 ] ] q 3 19 .003 ( , . Ol 22 4 3 6 .00 33 .0109 s .0046 3 7 .0159 6 .0225 2 0 ,0254 7 . 0144 2 1 . 0060 31 .0173 22 .0046 a ,0291 23 , 0075 9 .0252 3B ,0070 I O . 0377 3 9 .0105 I I 2 4 • 0314 .0161 12 40 , 0053 . 0242 13 25 • 005 3 3 0 : :'6 • 0043 .0024 14 27 . 0141 .0033 32 2 8 • O1 29 . noB7 33 29 • 0240 . 0053 I 5 CA N - . 0195 oo 1 9 3 4 • 0257 9 0 ,0021 16 91 ,03 7 2 . 0 024 1 7 .0060 -87 - DATA SHEET NOZZLE TYPE C_. g ni_cal..( A Tl , 3) RUN NO. 8 PRESSURE RATIO, PRIMARY, kp 506, 04 PRESSURE RATIO, SECONDARY, , k s . 480, 00 CH A M BER P RES S U R E _9 _ 9 . _92. psi(_ SE C O N DA R Y PRES S URE 94. 56 pslo W E I GHT F LO W RA TI O, Ws / W p 0. 0606 A M B I E N T PRES S URE O . ]Q7 ps l a T O T A L S IDE FOR C E 10, 30 LB AM P LI F ICATI ON FACTO R 1 . 309 T O T AL AXIA L F O RC E _ . ] . 2 _ 5 , _.7___ LB V A C UUM THRUST CO EF F I C I E NT 1,655 PRESSURE DISTRIB U TIO N TA P PR E SSURE RATIO TA P PRESSURE R AT I O LOCATION P / Pc LOCATION P / P c .0036 IB .0058 2 00.33_ .................... 3s. _ 01_3.9 3 19 ............. 9 _033 ..... 0___ 4 ............. ._ 0.33. 36 ............ 0 1 2 a _ 5 _ 37 6 2.0 1................. o26 7 ................... o 24o z _....................0164. _ ................ 2_ _oofi'_ 31 t | .0134 _2 0051 T 8 .0338 23 ............. O__O_Z_8_______ 9 ....... --_ 9 _z. z3_ ............ 30 ................. _o o7 ( I ...........

to o 0387 3 9 ................ I_ .............

)l o 0400 a4 _ O 1 54 !2 ) _ : 0_05_66 ........... 4_0 ............................ _0 2 4_ . __0 ...............

30 _F 26

......... ......... 0046_ ......... ................... o__o z6

3 2 28 ............... _01 _ 17 .............................................. O.O_9_D 33 2 9 • 023 5 ................ 00__6__.0 1 5 CA N 34 .... 0_2 X5 9 0 ............ 0_0_2 , 4 1 6 9 1 _............. -03- 85 ............................................. 00-2.6 1 7 . -0..0_0.

-88 - DATA SHEET NOZZLE TYPE Conical (AT i, 3 ) RUN NO 9 PRESSURE RATIO, PRIMARY, L p 513. 7 PRESSURE RATIO, SECONDARY, X $ 565.69 CHAMBER PRESSURE 99. 92 psia SECONDARY PRESSURE 110. 3 1 p =l a WEIGHT FLOW RATIO, W l / _ / p 0. 0706 AMBIENT PRESSURE 0. 195 p i le TOTAL SI D E FORCE 11.77 LB A M PL IFtCA T I ON F A CT O R 1. 2 8 0 TOT A L A XIAL FORCE 126. 40 LB VACUUM THRUST COEFFICIENT 1 . 65 9 PRESSURE DISTRIBUTION TA P P RE SS UR E R AT I O TA P PR E SSUR E R A TI O LO C A TI O N P / Pc LO C A TI O N P / Pc .0088 I S ,0 0 58 2 . 0086 35 _ ( 3 ] _ 4 3 0086 19 . 01 59 4 O O R 6 36 , 0 ] R ? , 5 .0061 57 01 5 7 s .031 2 2 0 . 0228 7 . 0184 2 1 .0063 31 .0 113 22 .0056 e .0351 23 ,0086 9 .0231 3B ,0073 IO . 0373 39 . OI 03 )i .0420 24 . 0147 ) 2 ,0056 4 o .0233 13 2 5 .0O58 3 0 .0046 26 .0 027 14 27 . 0117 .0036 32 .01 05 28 ,0090 33 . 0213 29 .006 1 15 .0290 C A N . 0024 34 .0223 90 , 0027 16 . 03 7 3 9 1 _ 0027 ) 7 .006 1 - 89 - DATA SHEET NOZZLE TYPE _ ; onical A_A_.T_I , 3) RUN NO. I0 PRESSURE RA T I O, PRIMA RY , Xp 503.44 PRESSU RE R A TI O, SECONDA R Y, _. s 631.87 C H A M BER PRESSURE 99.9 1 ps i a S ECONDA R Y P R ESSURE 1 25. 11 p|io W EIGHT FLO W RATIO, w s / w p 0. 080 7 AMBIE N T PRESSURE 0 , 198 pila T O TAL SI D E FORCE 13. 26 L B A M P L IFICATION F ACTO R 1. 261 TOTAL AX I AL FO R CE 1 26. 40 LB VACUU M TH RUS T COEFF I CIE N T 1. 660 PRESSURE DIST RIB U TI ON TA p PR E SSURE RAT I O TAP PRES S U R E R A TI O I ...................

L LOCATIO N P / Pc LOCATION P / Pc f 0034 Ie .0051 .......... J 2 .................. 00 3 -4 3 5 . O1 5 2, .

3 19 . A _03 4 n] 0 4 4 ............. , Q -0_4 3 6 .01"7 4 5 : ..... ., , _o._. 1 37 c)] 74_ ............

s L .0351 2 0 n2] G 7 . 0204 2 t . 0059 __.

................................................

,_l .0090 2 2 .0054 8 .0326 2 3 .0090 9 .0 282 3B .007.3_ .........

IO .0346 39 . 0098 .................

i l 0464 24 .0140 ,2 .0051 40 . 01_2_5 .......

i 3 .0054 30 _ 0041 26 ° 0027 14 . O11 0 27 . 0036 3 2 _0095 2 B ....... --00_090 33 .0186 2 9 .0063 t 5 .0301 CAN .............. . 0_02_77 , 3 4 ...... 0238 90 ................. 0 027 9 1 i 7 , 0056 -90- DA T A SHEET TYPE Conical _AT i, 3) RUN NO Ii RA T IO, PRI M A R Y, kp 520.92 PRE S SURE RA T I O , SE C ONDARY, X s 656.09 PRESSURE 99 . 74 p $ i o SECONDARY PRESSURE 125.97 p,la FLOW RATIO, Ws / w p 0. 081 9 AMBIENT PRESSURE 0. 192 p=ta SIDE FORCE 13. 28 LB AMPLIFICATIO N FACT O R 1 . 193 AXIAL FORCE 1 26.70 LB VACUUM THRUST COEFFICIENT 1 . 666 PR E SS U R E DISTRIBUTI ON TAP PRESSURE R A T I O TA P P R E S SURE RAT I O LO C A TI ON P / Pc LO C A TI O N P / Pc I .0030 I B ,004 7 2 0028 3 5 0148 3 .0028 1 9 n] 63 4 l I ,0 0 3 2 3 6 0 1 85 5 .0060 3 7 nl qn B n34_ 20 .0212 7 2 1 ....... nTn? . no57 3 l " 0089 _ 2 " 0055 lll o .0 3 32 23 .0096 9 , 0284 38 .0 077 i o ,0 343 3 9 , O l Ol i I .0466 24 .0 1 38 12 ., 0047 40 .0222 1 3 25 • 005 0 3 0 . 0 0 40 26 . 00 30 _ 4 . 0 1 0 6 27 .0 0 35 3 2 .0 089 2 B .0092 33 29 •0175 .0064 I 5 C AN .0309 .0025 34 90 • 0242 . 0 0 25 16 9 1 ..... n _ _ h 0 0 2 _ 17 . 0 052 -91 - DATA SHEET TYPE _Con_ic_al__ _ Z - I, 3) RUN NO . 12 PRESSURE RAT I O, PRIMARY, )p 512.78 PRESSURE RAT I O, SECONDARY, )k s 225.49 PRESSURE 99. 74 p sio SECONDARY PRESSURE 43. 9 7 p s lo FLOW RATIO, W s / W p 0. 0 300 AMB I ENT PRESSURE 0. 105 pmlo SIDE FORCE 5. 93 LB A M PLIFICATION FACTOR 1. 5 33 AX IAL FORCE 125. ] 9 LB VA C UUM THR U ST C OE FFICI EN T 1,647 PR E S SURE D I STRIBUTION T AP PRESSURE RAT I O TA P PRESSURE R AT I O LOCAT I O N P / Pc LOCAT I O N P / Pc .0032 Ia .0053 2 .0032 3 5 .0107 3 o 0032 19 .0102 4 .0028 3 6 .0131 5 ,0035 37 .0205 6 ,0191 2o .0220 7 ....... 0151 21 .0063 3_ ...... .0299 22 .0053 a . 0191 23 _J_Ol 0_7_ .....

9 .0299 38 . 00__7 I0 39 • o] 66 _ , o1_6 3 .................

II 24 • O1 41 017_6 1 2 .0048 40 . Ol 27 13 .00 48 25 30 .0038 26 .0028 14 .0191 z 7 .0038 3 2 _ 021 0 2 8 .00_ .......

33 _ .019_5 2 9 .0043 I 5 CAN 0__200 .............. QQ2 , _I ............

3 4 9 0 02,7_9 ....... 002,3 .....

1 6 91 =_0053 -92.- DATA SHEET NOZZ L E T Y P E Conical B(__B_.T_I , 3 ) RUN N O. 13 PR ES S U R E R A TI O, P R IMAR Y, ),p 516. 04 P RE SS URE R A TI O, SECO ND A RY , ) 's 457° 63 CH A MBER PRESSURE 99. 87 p$io SEC ON DARY PRESSURE B8.78 p s lo W E IGHT FLOW RATIO, W,, / Wp 0. 0604 AMBIENT PR E SSUR E 0 o ]94 p = lo TOTAL SIDE FORCE 10.47 LB AMPLIFICATIO N FACTOR 1 o 33 1 TOTAL AXIAL FORCE J.26. 43 LB VACUUM THRUST COEFFICIENT 1 . 66 0 P RES SUR E DIS TR I B UTION TAP PRESSURE RATIO TAP PRESSURE RATIO LOCATION P / Pc LOCATION P / Pc I , 0029 I e .0053 2 35 nn ? 9 . O l 56 3 19 .00Z9 .0151 4 3 6 = 0 0 29 . 0117 5 37 n(_4.R (3 ] 6 , 1 6 2 0 • 0294 .0252.

7 .0201 2 1 ,0065 3 1 .0208 22 .0070 a .03 29 23 , 0095 9 .0245 a e , 0075 Io .0368 3 9 .0166 _ .0292 2 4 .0174 1 2 .0043 4 0 .0228 13 .0046 2 5 3 0 .0038 2 6 .0033 14 .0181 27 .0041 3 2 .0169 2B .0095 33 .0270 29 .0053 1 5 .0223 CAN . 0029 54 . 0257 9 0 . 0029 16 91 • 0343 . 0029 .0053 -93 - DATA SHEET NOZZ L E TYPE C __o_n_c_a _ l (_B__T l , 3) RUN N O 14 PRESSURE RAT I O, PR I MARY, X p 513 . 26 PRESSURE RA TI O , SE CO NDARY, ; k s 6 72.97 CHAMBER PRESSURE 99.84 psi a SE C ONDARY PRESSURE 131. 23 psJa W E IGHT FLOW RATIO, Ws / W p O. 0902 AMBIENT PRESSURE O. 195 p m lo T OTAL S I D E FORCE 14.44 L B A M P LIF I CATIO N F A C T O R io 2 25 TOTAL AX I AL FORCE 126, 86 LB VACUU M THRUST COEFF I C I ENT 1 ° 667 PR ESS U RE D ISTR IBU T I O N T A P PRE SS UR E RA T IO TA P PRE SS UR E RA T IO L O CAT I O N P / Pc LOCA TION P / P c i .0029 18 .0053 2 0029 3 5 . Ol 96 I 3 . 0029 1 9 .0206 4 o 0033 36 . 0201 5 .0070 3 7 ° 0164 6 ,0171 20 . OZZ5 7 ,0265 z l .0065 31 .0107 22 .0078 8 .0397 23 .Ol 07 9 . .02 4 5 3 0 ..... .0078 I0 0358 3 9 0186 I I . 0437 2 4 .... C)!56 12 ,0048 40 , 0 0__.3_.5 _ ......

13 2 5 •0051 ....

30 . 00_i _ 26 . 0 0 24 14 0161 27 .0 0 33 32 .01 29 28 .0088 33 .0196 2 9 .0048 15 .0331 CAN .0021 34 . 0 225 9 0 __ .0024 I S ,0358_ 9 1 .0 024 17 .005..3 -94- DATA SHEET NOZZLE T YPE APG-I (CT i, 3 ) RUN NO. 15 PRESSURE R AT I O , P RI MARY , _ .p 51 7. 23 P R E S SUR E R A TI O, SEC O N D ARY , h e 239. 12 CH A MBE R P RE SS U R E 100. 10 p s io SEC O NDAR Y PRESS U RE 46.39 p s lo WEIGHT FL O W RA T IO, _ V e / W p 0,0299 AMBI ENT PRESSURE 0.1 94 p$ I o T OT A L S ID E F O R C E 6. 76 Le A MP L IF I CAT I ON FA C T O R 1 , 759 TO T AL AXIAL FO R CE 1 24 . 6 0 L B VACUUM T H R UST COEFFICIENT 1, 633 PR E SSU RE D IST R I B U T I ON TAP PRESSU R E R A TIO T A P PR E SSURE R A TIO LOC A TION P / Pc L OC A TION P / Pc I 0445 36 • ,0080 2 . Ol 1 0 37 .0068 3 I 7 • 0125 31 . OlT q 3e .007 1 4 0150 39 • , 0083 5 .0105 le ,011_ 6 . Ol 50 19 . Ol 57 7 .0194 2o .0083 e .0145 zl .0063 9 .0088 40 .0063 Io .0103 z2 .0098.

32 .0 12 2 z3 .0132 i i . Ol I 2 24 .00 7 8 I 2 . Ol 07 26 .0044 33 .Ol 27 2 7 . 0044 34 ,0 14 7 ZS .0078 I 3 ,009 , .?, 2 9 .0044 30 .0093 2 5 .0044 35 .0120 C AN . 0019 I4 . Ol 56 90 .0024 I 5 .0132 91 , 0019 1 6 .0098 -95- DA T A SHEE T NOZZLE TYPE AP G -I (_C_T_ i , 3) RUN NO. 16 __ PRESSURE RATIO, PRI M ARY, Xp 5__13_.86_ PRESSURE RAT I O, SECONDARY, _ ! ___,_LT__._._O L 0___ CH AM BE R PR E SSURE 99. 95 p _ i a SECO ND ARY PRESSURE ____3.___I_]___.__ p sla W E I GHT FLO W RAT I O, W, / W p ..... 0. Q 6 DQ _ A M B I ENT PRESSURE 0, 195 p$ i o TOTAL S I DE FORCE 11.8 8 LB A M PL I F I CAT I ON FACTOR I.,_.,,= L ,___ TOTAL AXIAL FOR C E 1 24. 62 LB VACUU M THRUST CO E FF I C I ENT i,636 P R E S S U R E D I STR I B U T IO N TAP PRESSURE R ATIO TAP PRESSURE RATIO LOC ATI ON P / P c LOC AT I O N P /P c i .0884 36 .0088 2 .01 __1 37 0 0 88 3 .0073 38 .Ol 22 31 .0058 ..........................

39 . O1 27 4 _._0122 5 0216 1 8 ,0103 6 0167 19 .0147 z 0137 20 .0226 B 0211 21 .0068 9 0265 4 0 .0054 i o 0132 2 2 .0063 23 . 0113 3 2 , 0087 24 .0196 it ° 0113 26 .0044 i 2 .0058 ................

33 , 006_8__ 27 . 0044 28 .0078 3 4 . O1 03 29 . 0046 i3 .__O15Z 30 .0142 25 .0049 35 .0191 CAN .0019 9o .0024 I 4 .0132 16 .0117 -96- D A T A SHEET NOZZLE TYPE APG-I (CT i, 3) RUN NO, 17 P R ESSURE RA TI O, P R IMA R Y, X p _ 506.44 PRE S SURE RAT I O, S E CON DARY, Aj 679 . 39 CHAM B ER PR E SSU R E 100.00 p_i o SE C O N DA R Y PRES S URE 133.84 p.,=a W E IGHT FLOW RATIO, _V s / Wp 0. 0872 AMBI E NT P R E SSURE 0. 1 97 p, , io TOT A L SIDE FORCE 16 . 1 7 LB AMPLIFICATION F ACTOR 1.425 T O TAL AXIAL F O R CE 126. 20 L B V ACUUM THRUST COEFFICIE N T ] . 6 , . 56 P R ESSU R E DIS TRI B U T I O N TAP P R ESSU R E R ATIO T AP PRESSURE RATIO LOC A TI O N P / Pc LOCATI O N P / Pc l .1 279 3 6 .0061 2 .0265 3 7 .0061 3 1 7 • 00 97 31 . 0044 3B . 0105 4 39 0085 . 01 89 5 .0162 IS , 0164 6 1 9 .0255 .0132 7 .0191 20 .0284 8 21 , O181 ,009 3 9 , 0309 40 , 0088 I 0 . 0314 22 , 00 9 3 3 2 ,0068 23 .0093 II 24 • 0206 .0181 1 2 2 6 .0049 .0044 3 5 27 • no4 q .0044 3 4 006a 28 .0078 1 3 29 • 0117 .0044 3o . O117 2 5 .0044 35 ,0_II CAN . 0019 1 4 , 0216 90 .0024 15 91 • O184 .0 0 14 1 6 . 0302 -97- D A T A SHEET NOZZLE TYPE . APG-1 (AT 1, 3 ) RUN NO . ] 8 PRESSURE RATIO, P R IMA R Y, A. p 5_ . __62. ] . . 0 _ _- PRESSURE R ATIO, SECONDARY, , ks -- CHAMBER P RESSURE 99. 95 p _ i o SECONDAR Y P R ESSURE -- p sl a W E IGHT F LO W R A TIO , W s / Wp 0 AMB IE NT P R ESSURE 0. 178 ps to TO TAL S I DE FO R CE 0°3 2.# L B AMPL IFI CA T I O N FACT O R -- T OT AL AXIAL FORCE lZ5 . 43 L B V ACU U M T H R U ST COE FF ICIEN T 1° 64 2 _ .

PRESSURE DISTRIBUTIO N TAP PRESSURE RATI O TAP PRESSU R E RATIO L O CATION P / Pc LOCATIO N P / Pc I . 0058 3 6 ,00_8 2 ,0 0_ , 8 3z nn4.r 3 17 , 0048 31 .0046 3 8 .0048 4 _ O( l_ . q 39 , 0048 5 00 4 S 18 . 0048 6 f9 . 0 048 _ 0063 7 .0053 2 0 .0078 8 oO O q_ 2 1 . 0058 9 .0087 40 .0048 Io . OlOZ a 2 .004,8 32 ,0073 2 3 .005 1 I I . 01 1 7 24 .0058 1 2 .0 0 63 26 .00 4 3 3_ ,0058 __ 2 7 .00 4 3 34 .0058 2 a .0 0 8Z I 3 .0063 2 9 .00 4 3 30 ,0068 25 .00 4 3 ] , 5 CA N .0048 . 0019 14 .0051 90 ,0019 15 .0063 91 .0014 oo q 2 Ports plugged bu t no t filled to form s m ooth contour.

- 98 - DATA SHEET NOZZLE TYPE A]PG-I (AT I , 3) RUN NO, 19 P R ESSU R E RA TIO , PRIMARY, k p __ P R ESSURE RAT IO , SECON DARY, _ '1 241, _B CHAMBE R PRESSU R E 100. 07 p $ io SEC O NDAR Y PRE S SURE 47. 07 p s l a W E IGHT FL O W R ATIO, W s / Wp _. _0 _. ,_____ AMBI E NT PR E SSU R E 0, 200 p s lo T O TAL S I DE FO R C E _ 6. 86 __ L 8 AMPLI F I CA TI O N FA CTOR 1. 7 8 3 TOTA L AXIAL FORCE 124. 7 3 LB VAC U U M T H R US T C OEFFI C IE NT 1.6 37 PR E SSURE DISTRIBU T IO N TAP PRE S SURE RAT I O TAP PR ESS UR E RA T I O LO C ATION P / P c LOCATION P / P c I .1240 3 6 0077 2 .0042 3 7 n n ( _7 3 .0062 17 31 .0185 38 .0067 4 .0140 3 9 .0077 5 . Ol 06 IS . Ol Ol 6 19 • 0150 . 0121 7 .0194 20 .0077 8 .0165 2 1 .0047 9 . 008, 0 4 0 .... .005 ?- Io .0099 22 .0086.

32 .006 q 23 .0077 if .0113 2 4 . 0071 I 2 .0079 2 6 . 0042 3 3 27 _ 0 ] 23 .0 0 42 34 28 _ n ] 4R . 0077 I3 , , 0099 2 9 .0042 30 .0089 25 ,0042 3 5 ,0113 CAN . 0017 4 ,0145 9 0 .0015 i 5 . 0165 91 . 0013 1 6 •0091 -99- DATA SHEE T NOZZLE TYPE AP G -I LA___T I, 3) RUN NO, Z0 PRE SSU R E R A T IO, PR IM A R Y, Xp 500.42 P RE SS URE RAT I O, SEC O NDA R Y , ' _l 323, 25 C HA M B E R PR E SS U R E 100o 04 p si o SECO N DA R Y P R ES SUR E 63 . 68 p sl o W E I GH T F L O W R A T I O , Ws /w p O. 040 5 AMB IE N T P R E SS U R E O. 200 pst o T O TAL S I DE F O R CE 8. 7 0 L B A MP L IF ICAT ION F AC TOR 1. 664 TOTAL AX I A L F ORC E 1 25. ] 8 LB V ACUUM T HRUS T CO E F FICI EN T 1 . 643 PRESSUR E DISTRI B U TI ON T A P PRESSURE R A TIO TAP PR ES SURE R A TI O L O C A T I ON P / Pc L O CA T I ON P / Pc I ,1771 3 6 .0o9 2 2 .OOZe; 3 7 __ .00 9 7 3 17 . 0057 31 ._ 0 _i_(_ 3B .0097 4 , 0224 39 _ , 0097 5 ,-01 / 6 _8 . , .0087 19 0175 6 .0! Z! . - 7 . 0170 20 .OOBZ 9 .0097 4 0 .0048 Io .0102 22 0072 32 .0062 2 3 . 0131 I I .O116 24 . 0190 I2 .0062 2 6 .0043 33 .0087 2 7 00 4 3 34 . Ol 41 Z 8 ..0077 I 3 .0161 29 _ 00 4 3 3 5 ,0116 CAN . 0018 I 4 . O 1 21 90 .0013 I ,5 o OZI5 91 . 0 013 16 . 0 092 -i00- DATA SHEET NO Z ZLE TYPE APG-I (AT I , 3 ) RUN NO 21 PRE S SURE RAT I O, P R IM ARY, _ p 504.65 PRES S U R E RAT I O, S E C ONDA R Y, A s 402.9 3 C HAM B E R P R ESSU R E 100. 15 a s ia SECO N DARY P R E S S URE 79. 78 psta

W EI GHT FL O W R AT I O, _ s / _ / p 0= 5 1 2 A M B I ENT PRE SSUR E 0 . 198 psla

TOTA L SIDE FORCE 10. 58 LB AMPL I FICATION FACTOR 1. 602 TO TAL AX I AL F ORC E 125. 1 2 L B VA C UU M T H R US T CO EF F ICIEN T 1. 640 P R ES S U R E DISTRI B UTION TAP PRESS U RE RAT I O TAP PRESSURE RA T I O LO C AT I ON P / Pc L O C AT I ON P / P c I ,.2204 3 6 .0090 2 .0 0 65 3 7 . 0 0 92 3 .0055 17 31 .0085 3B _ .013 1 4 .0207 39 .Oll q 5 .0188 IS .00 9 5 6 .0114 19 .0171 7 .0161 20 .0136 a .0230 21 .0065 9 . 0|85 4 0 . 0055 io .0102 22 .0075 32 .0053 23 .0124 Ii .0114 24 .0212 12 .0053 2 6 .0041 33 .0070 27 , 0041 34 .0112 28 , 0077 1 3 .0171 2 9 ,0041 3o .0166 25 .0046 35 .0176 CAN .0016 14 .0114 9 0 .0011 15 91 ,0230 .0009

.oo95

-I01- DA TA SH E E T NO Z Z LE TY PE APG-I (AT I , 3) R U N NO. 22 PRESSURE RATI O , PRIMARY, ) ,p - 504.08 P R ESSURE RATIO , SECONDARY , _' l 4 7 4.09 CH A MBER PR ESSU R E 100. 03 pt i o SE C O NDA R Y PR E S SU R E 93 . 87 psl a W E IGHT F L O W R AT I O , V q s / W p 0. 0600 A MBI E NT PR E SSURE 0. 198 pslo T O T AL S I D E F O R CE 12. 30 L 8 AM P LI F ICATION F A C TO R 1. 587 T O TAL AXIA L F O RCE 125. 29 L B VACUUM THRUST C O EF F ICIENT 1. 644 PRESSURE DISTRIBU T IO N TAP PRESS URE RAT IO TA P PRESSURE R A TIO LOCATION P / P c LOCATION P / Pc l .2644 36 .0072 z 0072 37 • .. 0076 3 f 7 . 0042 3_ . 0027 3e .0 1 36 4 .0155 39 ,0148. ..

5 .0224 1 8 .01.13 6 19 _ nl 2] . 0162 7 .0150 zo .0221 9 . 0256 4o . 0072 io . 0108 22 .0072 J . .

3 z ,0 052 23 .0 1 18.

t I . O 1 18 z 4 .0216 I 2 . 0050 a s .0042 33 .0059 z 7 00 . 42 3 4 .0 0 94 2 8 , 00 79 13 .0175 2 9 0052 30 . 0170 2 5 .0072 35 . 0 21 6 C AN ,0020 14 . O113 90 ,001:) t 5 .0226 9 1 , 0 008 1 6 .0099 , , -I0 2 - D A T A SHEET TYPE APG-I (AT 1 , 3) RUN NO. 23 PRESSURE R A T I O , P R IMA R Y , , k p 507. 09 PRESSURE R A TI O , S E CONDA R Y , A s 554.67 PR E SS U RE 1 00. l 3 pti o SEC O NDARY P R ESSURE 109. 2 7 ps_ a F L OW R A T I O , _V s / Wp 0. 0699 A M BI E NT P RES S U R E 0. 19 7 psl o S I DE F O R CE 13 .80 L B A MPLI FI CA T ION FACT O R 1. 516 AX I AL F O R CE 1 2 6. 31 L B VACUUM T HRUST COE F F ICIENT 1. 655 PRESSURE DI ST RIBUTION T A P PRESSURE R A T IO TAP PR E SSUR E R AT I O LOCATION P / Pc LO C ATION P / Pc I .31 04 36 .0064 2 .0084 37 ,0069 3 17 • 0042 31 .0076 3B . Ol 23 4 . 0108 39 .0155 5 ,0853 IB ,0138 6 .0170 19 .0157 7 .0140 20 .0258 8 .0211 2 1 ,00 9 9 9 . 0270 4 0 ,0096 io .0172 22 . 0084 3 z .0054 23 • 0116 t l .0113 24 • 021 1 I 2 .0052 2 6 .0042 33 . 0050 2 7 .0042 34 .0081 Z B .0079 I 3 0150 29 0072 3O • 0143 25 .0081 35 CAN ,0251 .0020 I 4 .0140 90 . 0018 15 9l • 0216 ,001 2 • O157 -103- D A T A SHEET NO ZZ L E TY P E AP G -1 (AT 1 , 3) RUN NO 24 PRESSURE R AT I O, P R IM A R Y, k p 509. 05 PRESSUR E R AT I O , SECON D A R Y, k s 6 30. 46 CHA M B ER PRESSURE I00. 02 ps io S E COND A R Y PR E SSUR E 1 23. 57 ps lo WEIGHT FLOW R A TI O, _ V s / W p 0. 0798 A MBIENT PRESSURE 0. 196 ps lo T O TA L SIDE F O RCE 15. 02 L B AMPLIFICATI O N FACTOR 1 . 442 T O TAL AXIAL F O RCE 1 2 6 . 60 L B V ACUUM T HRUST COEFFICIENT 1 . 661 PRE S SU R E DIS TR IBU T ION TAP PRESSURE RATI O TAP PRESSURE RATIO LOCATION P / Pc LOCATION P / Pc I , 3499 36 .0052 2 . 0 0 99 3 7 .... .0055 3 17 . 0045 .....

31 .0067 3o . 0 113 4 ,0 0 94 3 9 .0158 5 .0251 18 .0165 6 19 .02 0 2 , 0155 7 .0138 2 o . 0 28 0 s .0204 21 0101 9 .0278 . 4o , O1 08 Is .0266 2 2 .01 0 8 32 .00 5 0 23 . O113 i i 0116 24 0209 L_. • ........ • , .

I 2 .0050 2 6 .0042 ......

33 . 0 047 2 7 . 0042 34 ,0079 aS . .0079 1:3 29 ,01 3 8 ..... .00 8 2 30 . Ol 28 2 5 . 0 0 8 9 35 .027 1 CAN . 0018 _4 ..... 0167 90 .0 0 23 1 5 9 1 • OZl 2 ,002_, .02 5 1 ..

-104- DATA SHEET NOZZLE TYPE _ APQ:!_(A_T i , 3) RUN NO 25 PRESSURE RATIO, PRI M ARY, X p 506.7_7 .... PRESSURE RATIO, SECONDARY, ) ' m 680° 05 CHAMBER PRESSURE 100. 07 p,_o SECONDARY PRESSURE 133. 97 psla WEI GHT FL OW RA TIO, W s / Wp 0. 0866 A M B I E N T P RE SS UR E 0. 197 p ,lo T OTAL SID E F OR C E 15. 97 _ LB A M P LI F IC A TION FA C T OR 1. 424 TO T A L AX I A L F ORCE 125. 7 0 L B V A CUUM T HRUS T COE FF ICI E NT 1.649 PR ES SURE DISTRI B U TI ON T AP PRESS UR E R A T IO T AP P RE S SURE RA TIO LOC A T I ON P / Pc LOC A TION P / Pc I .3498 36 .0052 2 , 0098 3z . 0054 3 17 .0044 31 .0066 38 o O113 4 0093 39 0157 5 .0250 I B .0167 6 ,02 .01 19 , O155 r .0137 20 .0280 B . OZOl 21 ,0101 9 .0300 40 , 0108 Io .0268 2 2 .0108 32 .0052 23 . O113 I I .0118 24 .0209 I 2 , 0052 26 . 0042 3 5 27 . 0049 .0042 34 2 8 0081 .0078 1 3 29 • 0140 .0081 30 25 ..0130 .0088 3 5 , 0270 CAN . 0020 ...

14 .0167 90 .0012 I 5 ,0211 91 ,0010 1 6 .0250 -i05- DATA SHEET NO ZZLE TYPE APG-I (BT I , 3) R U N NO . 2 6 PRE S SURE RA TI O, PR IM ARY, ),p _._8_ 9_ _ PRES S U R E RAT I O, SECONDARY, A s CHA M BER P RESSURE 99. 99 p si o SECONDARY PRESSURE 47.3 8 p slo WEI GHT F L OW RA T I O, Ws / Wp _ .... A MBI EN T P RESSURE 0. 198 p.= o T O TA L S I DE FO R C E 6 . 52 LB A MPLIFICAT IO N F A CT O R 1. 7 1 0 TOT A L AXIA L FORCE 124 _ 3_9 .... LB VACUUM TH R UST COEFFICI E NT 1 . 633 PRESSU R E DISTRIBUTIO N T A P PRESSURE RAT IO TAP P R ESSU R E R A TIO L O C ATIO N P / Pc L OC A TIO N P / Pc I • .0966 36 .0067 z . o065 37 ._ . 0057 3 .0082 17 3 1 .0183 38 .0067 4 ,Ol48 3 9 . 0053 5 .0134 18 .0121 6 1 9 .016.3 . 0121 7 .Ol83 2 0 .0077 B , 0116 2 1 .0057

9 . 008 2. 4 0 .0 0 65

Io . 0 094 zz . 0 097 3 z .0097 z 3 .0109 II .011 2 2 4 .0057 I2 .0116 26 0043 3 5 . O158 2 7 . 0043 3 4 .0141 28 .0080 1 3 . 0082 29 . 0043 30 .0077 2 5 ,0043 35 ,,, 0119 CAN . 0018 14 , O156 90 . 0 023 1 5 9 l . 0082 . 0013 1 6 .0092 -106- DATA SHEET NOZZLE TYPE APG-1 ( BT 1 , 3) RUN NO, 27 PR E SSURE R AT I O, PRIMAR Y, Xp 516.93 PR ES SURE R AT I O, SECONDARY, ; k| 499.90 CH AMB E R PR E S SU R E i 0 0 . 04 ps i o SECONDARY PRESSURE 96.9 8 p s l o W E IGHT FL O W R A T I O, Ws / W p 0. 0601 A MB IE NT P RE SSURE 0. 194 pml o T O T AL S# D E F O R CE 11.9 7 LB AM P L IFICATION FACT O R 1 . 53 2 , T O T A L AXIAL F O R CE I 26. 12 L B VACUUM T H R UST C OE FFICI E N T 1 . 654 PRESSU R E DIS T R IBUTION TA P PR E S S U RE R AT I O T AP PR E SSUR E R AT I O L O C AT I ON P / Pc L OC A TI ON P / Pc I , , 2017 36 .0094 2 ,0 109 37 .0102 3 17 • 0053 , .

31 0062 3 B 0151 4 3 9 • 0l 1 9 , , 0148 6 1 9 .0158 OI_ R 7 20 ,0143 .0205 s . 0224 21 .0067 9 . 0254 40 .0055 io .0111 ,. 2 2 .0067 32 .0072 2z .O116 I _ .0136 2 4 . 0200 i 2 .0053 26 .0043 33 .. , 0055 2 7 . 0043 3# . 0082 2B .0080 13 29 •0165 .0077 30 25 , O141 .0048 35 .0219 CAN . 0021 1 4 .0175 90 . 0023 I 5 .0271 9 _ .0016 1 6 .0104 -I07- DATA SHEET NOZZLE TYPE APG-I (B_TI , 3) RUN NO. 28 P RE SS U RE R A TI O , P R IM A R Y , Xp 514. 57 PRESSUR E RAT I O, SECONDARY , _ e 681.64 C H AM B ER PRES S URE 1 0 0. 0 9 p _ i o SE C O ND A R Y PR E S SU R E 132. 98 p s i (} W EIG H T F LO W R A T IO , W$ / W p 0 . 0_ R3 q ..... AM B IE N T P RESSU R E 0. 195 p $io T O TA L S I DE FO R CE 15.64 .... LB AMPLI F I C A TION F AC T O R 1 . 434 T OTA L AXI AL F ORC E _, _ 8 . 5 ...... L 8 V A CUUM T H R U ST COE FF ICI E NT 1o662 PR ES SURE D IS T RIBUTI ON T A P P R ESS U RE R AT I O T AP P R ES SUR E R AT I O LO C A TION P / P c LOCA TI ON p / P c ° 2771 3 6 ,0060 2 0148 3 7 • ,0060 3 1 7 • 0070 31 0043 38 4 0077 39 0170 5 O1R7 1 8 . 0187 6 , O__P59 L 19 . 0136 7 ,0160 z o .0281 S .0185 21 .0097 9 .03 08 4o . oo99 Io , Q3_Q S _ 22 ...... 00 9 2, 32 _____ 23 • 0099 f I LO_O16 0 2 4 _.Q1 9_.2_ f 2 ___ ,0048 z 6 004_3_ 3,3 27 0048 ....

3 4 2 8 • 0072 .0080 30 2 5 , 0 097 0082 35 _ CAN .... .00Z3 I 4 .0222 9 0 ............ _0__ i 5 ...... 0197 9i 0016 ____ 16 . 0293 -108- DATA SHEET N O ZZLE TYPE Conical (AR 2) R UN N O. 29 P R ESSU R E RATIO, PRIMARY, ) . p .512, 2.7 PRESSU R E RA T IO, SECONDARY, X ! 314, 6_ .

C HAMBER PR E SSUR E 9 9- 64 ,, p sio SECONDARY PRESSURE 61.35 p s la WEIGHT FLOW RATIO, W s / W p O o0192. AMBIENT P RESSURE O. 1Q5 p s lo TOTAL SIDE F ORCE 4, 5_ LB AM P LIFICATION F ACTOR 1 . 865 TOTAL A X IA L FOR C E _ LB VACUUM THRUST C OE FFI C IENT 1 . 635 PRESS UR E DI S TR I BUTI O N TA P PRESSURE R A T I O TAP P R E S S UR E R A TIO L O CATI ON P / Pc LOCA TIO N P / Pc I .0040 18 .0095 2 3 5 .0040 , O1 24 3 19 • 0043 . O129 4 3 6 • 0040 . O193 5 • 0040 3 7 . 0174 6 ,, 017_ 20 . 00 9 5 7 21 . O] 93 nn_,_ 3 1 .0178 2 2 . 0060 S . 0235 2 3 ,, .0109 9 . 01 00 3B . O1 0 9 Io .0124 3 9 .0181 I I .... 0149 2 4 . 0095 _2 .0058 40 .0095 1 3 .0058 25 30 .0050 2 6 . 0030 14 27 , 0178 . 0035 3 2 .0354 2B .0095 33 . 0183 29 .0040 1 5 .0223 CAN . 0026 3 _ . l . 0100 9 0 . 0030 I S . 0124 91 _ 0030 • 0058 -I09- D A T A SHEET NO Z ZLE T Y P E Conical (AI__ 2) RU N NO. 3 0 PRE S SUR E RATIO, PRIMAR Y, kp 512.78 PRE SSURE RATI O , SEC O ND A RY, )' s 487 .44 CHAM BE R PR E SSURE 9 9. 74 psio SEC ON D A R Y PRESSURE 95. 05 p = ia WEIGHT F LO W RATI O, Ws / W p 0. 0300 A MBIE N T PR E SSURE 0. 195 pile TOTAL S I DE FORCE 6 o89 L B A MPLIFICATION FACTOR 1 o 797 . .

T O T A L AX I A L FORCE 123.96 L B VACUUM TH R UST COE FFICI E NT i=631 PRESSURE D I ST RIB U TION T AP P R ES S U RE R A TIO T AP P R E SSUR E R A TIO L O CATI O N P / P c LO C AT I O N P / Pc I . 0032 I S . 00 7 0 2 .0032 .... 3 5 1 0 2 7 2 l 3 , Q032 19 (_ 7 ( _& 4 .0026 3 6 ( ] I AR 5 .0026 37 .0230 6 .0 1 76 2 0 .01,34 7 ....... 0141 21 . 0060 31 .0301 22 .0065 a .0242 2 3 , .0099 9 .0228 3 e .0104 IO ,Q119 3 9 .0210 II . 0139 2 4 0193 12 40 ,00 , 50 .0094 13 ,0060 25 30 .0040 26 . 0028 14 ,0117 27 .0038 3 2 .0274 28 o 0070 33 .018 8 . 29 , 0043 15 C AN 34 90 .. .0203 _ . 0026 16 ,01!7 91 . 0028 _7 .0050 -110- D A T A SH EET NOZZLE TYPE Conical A_ 2) RUN NO. 31 PRESSURE RATIO, PRIMARY, ) .p 526.00 PRESSURE RATIO, SECONDARY, _.s 667.63 CH A MBER PR E SSURE 99. 75 p$ia SEC O NDARY PRESSURE 126.85 p =ta W E IGHT FL O W R A TI O , Ws / w p O . 0403 A M B IE N T PR E SSURE O. lqO p m ia T O TAL SIDE F O RCE 8. 74 LB A MPLIFICATION F A C T OR 1. 695 TOTAL AXIAL FORCE 124. 16 LB VACUUM THRUST C OE FFICI E NT 1 . 63 2 PRESSURE DI S TR I B U T IO N TAP PRE S SURE RATIO TAP PRESSURE RATIO L O C A TI O N P / Pc LOCATION P / Pc i .0035 Ie .0048 2 .0035 35 n284 ] 19 .0033 . O365 4 3 6 .0030 .0208 5 3 7 nolo .0242 6 .0163 zo .0259 7 .0144 zl .0058 31 . 0420 22 .0082 e , 0227 23 .0134 9 .0296 3 8 .0094 io 39 .0139 , 0820 II 24 .0139 ,02_7 12 .0050 4o ,015...1 13 . 0060 25 3 0 26 • 0040 . 0028 14 27 .0114 . 0038 3 2 2 8 • 0i36 . oo92 3 3 29 • O3 28 . 0058 15 CAN .0235 .0023 3 4. . 0272 9 0 . 0023 1 6 9 1 . O1 29 . 0026 1 7 ,0045 -IIi - DATA S H EET NOZ Z LE TYPE Conical (AR. Z ) RUN NO . 32 P RE S S U R E R A TI O , PR IM A R Y , Xp 512.73 P RES S URE R ATIO, S E C O N DA RY , k I 704,82 C H A M BER PRE SS U R E 99. 73 psl o S ECONDA R Y PRESSURE 137.44 p =la WEIGHT FLOW RATI O , W$ / Wp 0. 043 6 AMBIENT PRESSURE Q, 19._ p = la T O TAL SIDE F O RCE 9. 06 LB A MPLIFI C ATI O N F ACT O R 1. 622 TOTAL AX I AL FO R C E 124 .33 LB V A CUUM T HRUST C O E F FICI E N T 1. 636 PRES S UR E DISTRIBU T IO N TA P P R ESSU R E R A TI O TAP PR ESS URE R AT IO LO C AT I ON P / P c LO C AT I O N P / Pc i .0035 le , 0050 2 , 0035 35 o_4 3 .0032 19 0%7_ 4 .0028 3 6 .016 " _ 5 . 0030 3 7 , 0237 6 .0173 20 , 0262 7 ...... : 0153 21 .005 7 31 .0427 2 2 .0082 B 0222 2 3 0151_ Q .

9 . 0129 6 3 B , 010]- Io .0168 3 9 . , 0224 Ii .0138 2 4 .02",0 1 2 40 .0050. . 0212 13 .0064 25 30 .0040 2 6 • 00Z8 14 , 0 1 31 2 7 .0037 32 . 0136 28 ...0092 33 . 0355 2 9 .0057 1 5 0_30 CAN , ,002 3 3 4 . 0294 9 0 .0023 16 9 1 01 4 R ° 002_ 17 0045 L.

-l l Z- DATA SHEET NOZZ L E TY P E Conica l (C1:_ i , 2 , 3 ) R U N NO 33 P RESSURE RAT I O, P RIMARY, kp 512. 6_ P RESSURE R ATIO , SECONDARY, k s 165. 54 CHAMB ER PRESSUR E 99 . 72 psia SECOND AR Y PRESSURE 32. 28 p$1o W E IGHT FLOW RATI O , Ws / Wp O . 0303 AMBIENT PR E SSURE O. ]9_ p s le TOTAL SIDE FORCE 7.40 LB A MPLIFICATION F A CTOR 1 . 8 9 8 TOTAL AXIAL FORCE 124. 78 LB V A CUUM THRUST COEFFI C I E NT 1 . 642 PRESSURE D ISTR I B U T I ON TAP PRESSURE RATIO TAP PRESSURE R AT I O LOCATION P / P c LOCATION P / P c i .0036 I B .0048 2 , 0041 35 . 0277 3 .0053 . 19 0 7 .70 4 • 0073 36 . 0221 5 . 0068 3 7 . 0144 6 . 03 ] 7 2 0 . 0093 7 .0309 2 1 .0056 31 . 0231 22 .0051 8 ..... 0147 23 .0263 9 .0096 3B ,0149 i o ,0117 39 - o194 tl .0142 2 4 .0093 1 2 4 0 , 0061 . 0095 1 3 25 ,0063 30 . 0053 26 . 0029 14 27

,0354 . . 003.6

33 . 023 1 29 . 00.3.8 I 5 CAN ,0174 .0024 3 4 9 0 . 0098 ,002,4 ' ' 1 16 91 _ o ] ]7 .0026 1 7 .0053 -I13- DATA SHEET NO ZZL E TYPE Conical C_R 1 , 2 , 3 ) RUN NO. 34 PRE SS U RE R A TIO , PR I M A R Y, k p 51 3. 18 PRESSURE R A TIO , S EC ONDAR Y, k I 32 7.08 C HAM B E R PRESSURE 99. 82 psi a SE C ONDARY PRESSURE 63. 78 p = la W E IGHT FLOW RA T IO, W s / Wp 0. 0604 AMBIE N T PR E SSURE 0. 195 p , te TOTAL S I D E FOR C E 13. 07 LB AMPLIFICA T I O N F AC T OR 1. 669 .

TOTAL AXIAL FORCE 1 25.77 L B V A CUUM THRUST C O EFFICIE N T . 1 , 65 5 PRESSURE DISTRIBUTION TAP PRES SURE RATIO TAP PRESSURE RATIO L O CATION P / Pc LO C ATION P / P c I .0033 JB .0038 2 0041 35 ......... .. 0348 = Q358 3 , 0046 1 9 4 .00_ ; ! 36 • Q250 5 0041 37 • , ozBo 6 .0375 20 .0250 7 , 0375 2 1 = 0056 31 .0277 22 ,0041 8 . 0297 23 .0193 9 .0272 3 8 .0265 I 0 .0117 3 9 _02_ If ,01 3 9 . 2 ,, .. n?_ 12 40 , 00 5.3 . _n_.2_ ......

i 3 ,0051 z 5 30 ,0043 26 , 0.029 t 4 .0467 2 7 .0036 3 2 ,04 ;30 20 .. . . 0090 33 .0 2 75 29 .0061 15 .02 9 7 C AN , 0024 F 34 . 0272 9 0 .0024 16 91 ; O] 15 .0026 i 7 ,0043 -114- DA T A S HE E T NOZZLE TYPE Conical _ i , 2 , 3) RUN NO.. 35 PR ESS URE R A TIO, P R I M A RY, X p 51 2. 88 PR E SSURE R A TIO, SECOND A R Y, ),= 48 1 .38 C H AMBER PR ES SURE 99.76 p $ io S ECO NDA R Y PRESSURE 93. 87 p = lo W E IGHT FLOW RATIO , W a / Wp 0. 0897 AMBIENT PRESSURE O. 1 95 pslo TOTAL SIDE FORCE 17. 57 LB AMPLIFICATION FAC T OR l . 493 TOTAL AXIAL FORCE 1 27 .39 LB VACUUM THRUST COEFF I CIENT 1 . 675 PRE S S U RE D I S T R I B U TION T AP PRESSURE RATIO TAP PRESSURE RATIO LOCATION P / Pc LOCATION P / Pc I .0036 I e .0038 2 .... .0036 3 5 .035_ 3 .0036 19 .0356 4 . 0031 36 .0356 5 .0033 37 . 0280 s .0383 2 0 .0331 7 .0356 2 i on_ 3 1 .0437 2 2 , 0038 B .0326 2 3 .0203 9 . 0358 3 B .0255 Io ,0368 39 .0299 I I . 0233 24 .0265 i2 ,0051 4 0 .031_4 ...

1 3 2 5 •005 1 30 .0041 .. 26 .0034 1 4 27 • 0Z97 , 0 036 32 28 .0386 .009 0 3:5 29 • 0457 .0065 i5 .0304 C A N . 0Q26 3 4 .0304 90 , 00 26 16 91 . 0368 .0029 J , 0043 -115- DATA SHEET NOZZLE TYPE Conical.(AR I, 2, 3) RUN NO. 36 PRESSURE RATIO, PRIMARY, kp 516. 09 PRESSURE RATIO, SECONDARY, X l -- CH A M BE R PRESS UR E 99.88 p sio S E C ON D A RY PRESSU R E -- p l ta W E IGHT FL O W RAT I O , W$ / W p 0 AMBI EN T P RE S SUR E 0. 194 p $1 o TO TAL SlO E F O R CE - . 09 X ." LB A M P LIF ICAT I O N F A C T O R -- T O T AL A X IAL F ORCE 124. 77 L 8 V A C UUM THRU S T COE FFICI ENT 1. 639 PR ESSU R E O ISTRIBUT I ON TAP PR E SSUR E RATIO TA P PR E S S UR E R AT I O LOCA TION P / P c LO CA TION P / Pc .0037 .. = IB _ .0052 2 _ O0 3q 35 . 0059 3 19 _00_9 . 0061 4 36 . n039 . 0069 5 37 nn_Lt .0084 6 20

, 005,9 .... 009 ; }

7 ..... 005q 2l .... , 004 7 _ 3 1 22 .... ,. 0069 ..................... . 0042 B ,0079 23 .0054 9 38 0047 . ,0096 ................. • to .0116 .... , 39 ,0066

t J .0140 24 .0076

, . , -- ........ . .........

1 2 .0054 4 0 .0093. ....

3 .0056 25 30 .0047 z6 .............. O.Q_LQ _ 14 .0061 2 7 0 034 ........ m 32 . 0064 28 .0091 33 .0074 29 ................. 0_03_.7.

5 .0084 CAN ......... OOZZ _ _ 34 ...... 0098 90 .... . 0 Q.24 1 6 .0116 91 ,00_4 i 7 .0047 - ' :, Ports plugged but not filled to form smooth contour.

-I16- DATA SHEET NOZZ L E TYPE Conical (AIR.I , 2, 3) RUN NO. 3 7 P R ESSU R E RAT I O, PR I M A R Y, kp 513. 03 PRESSU R E RA TI O , SE C O N D ARY, X I 164. 87 C H A M BE R PR ES S URE 99. 79 p$io SE CON DARY P R E SSU R E 32. 15 p lt e WEIGHT FL O W R AT I O, WI / W p 0. 0301 A M B I EN T PR E SSURE 0f 195 p il e T O TAL SIDE F O RCE 7. 15 LB AMPLIFICATION FACT O R 1 . 8 60 T OTA L AX I A L F O R C E 123. 96 LB V ACUUM THRUST COE FFICI E NT 1. 632 PR ESS URE D IS TR I BUTI O N T AP P R ESS UR E RATIO T AP PR ESSU R E RATIO L OCATIO N P / Pc LOC A T I ON P / Pc I .0030 I B .0035 2 35 .0030 o O205 3 ) 9 • 003.5 .0242 4 3 6 .0030 .0200 5 3 7 . 0030 . 0242 6 . 02 9 6 2 0 .0151 7 .0362 2 1 ,0050 31 .0224 2 2 .0055 8 , O_z_ 2 3 .0148 9 . 0269 3 B .0119 )o . 0114 3 9 ,0197 I) . 0138 24 . 0 ?- 05 ) 2 . 0045 40 , 0099 13 .0047 2 5 30 . 0040 2 6 . 0030 14 . 0261 27 .0035 3 2 .0335 28 .0092 33 .021 2 2 9 , 0040 1 5 .0261 CAN . 0023 3 , ) .0222 9 0 . 0023 16 91 • 0114 , 0025

• oo._o

-i17 - DATA SHEET NOZZLE TYPE C onical (AI%. I, 2, 3) RUN NO . 38 PR ESS UR E RA TIO, P RI M ARY, k p 507. 80 P R ESS UR E R A T IO, SE C ONDARY, _ , = 218, 77 C H A MB E R PR ES SUR E 99. 77 p s io SE CON D A R Y PRESSURE 42. 88 p st e W E IGHT FLOW RAT IO , Ws / W p 0.0404 AMBIE N T PRESSURE 0. 1 96 p m la T O T AL SIDE F O RC E 9. 2 9 LB A MP L IFICATI O N F A C TO R 1. 8 00 T O T A L AXIA L F O RCE 124. 00 LB VACUUM T H RUST CO E F F ICI ENT 1 ° 63 2 PR ESS UR E D I S TRIBU T I O N T A P PRESSU R E R A TIO T A P PR E SSURE R AT IO LOCATIO N P / Pc LOC A TIO N P / Pc .00z} l _e ° 0043 2 .0041 35 .0193 3 .0041 1 9 . 0260 4 .0036 3 6 .0181 5 .0038 3 7 .0250 S .0238 2 0 .0260 7 .0282 21 . 005 3 31 .0287 2 2 .0053 a .0275 23 ,0159 9 .0302 38 ,0129 IO .0142 39 .0196 II , _ • 0139 2 4 .0225 12 .0053 4 0 . 0203 _ 3 . .0058 2 _ 30 .0043 2 6 .0031 1 4 .0238 27 . 0038 3 2 .0304 28 .0090 3 3 .0260 2 9 . 0051 15 .0260 CAN .0026 3 4 , 0297 9 0 .0026 16 91 _ 0132 . oozq 17 .0046 -118- DATA SHEET N O ZZL E TY P E Conical ( ARt, 2 , 3 ) RUN N O. 39 PRESSURE RAT IO, P R IM AR Y , Xp 531.34 PRES SURE RA TI O, SE C ONDAR Y , k t 282_ 07 CH A M BER PRESS URE 99.70 p sio SEC ON DAR Y PR E SSURE 53.03 p tto W E IGH T F LO W RATI O, Ws / W p 0 . 0500 A M B IENT PR ES SURE 0. 188 pm io T OTA L SI D E F ORC E 10. 87 LB A M PL IFI CAT I ON F ACTO R 1. 702 T O TAL A X IA L FORC E 124. 07 LB V A CU U M T HRUST C O EFFICI E NT 1, 63_ P R ESSURE DIST R IBUTION TAP PRESSURE RAT I O TAP P RESSU R E RAT I O L OCAT I ON P / Pc LOCATION P / P c I .0031 1 8 . 0033 2 .003 1 3 5 019t., 3 .0031 1 9 4 .0026 36 FII QA 5 ,0023 3 7 .0250 6 .0242 2 0 .0284 r .0267 2e 0048 31 .0338 2 2 .0045 B . 0272 23 ,0213 9 .0314 3 8 .0161 I0 39 • 02.4 O O] q £ II 2 4 . O139 02.'_ o 1 2 4. 0 . 0040 .0245 1 3 25 .0043 30 26 : 00"_"_ .0026 1 4 2 7 • 0245 .0031 32 . 0284 2 8 .008,,7 .

33 .0304 2 9 .0053...

15 .0257 CAN .0070 3 4 ,0309 9 0 .0067 1 6 91 .0210 .0070 1 7 . 0033 - 11 9 - DATA SHEET NOZZ L E T YPE C ortical (AR 1, Z , 3) RUN N O 40 PR ESS UR E R A TIO , PRIMA R Y , ). p 505. 05 PR ES SURE RATIO, SECONDARY , )'s 3 1 9. 59 C H A MB E R PR ES SUR E 99.7 3 p $ io S E C O N D A R Y PRES S URE 62 0 96 p = lo W E IGHT F L O W R AT I O , W $ / Wp 0. 0600 A MBI EN T P RES S U R E 0. 197 p = lo T O TAL S I DE F O R CE 12. 45 LB A M P L I FICATION F A C T O R ]. . 620 TOTA L A XI AL F O R C E ]24. 18 L B V AC UUM T HRUS T COEFFI C IE N T 1. 635 PRESSURE DISTRIBUTION TA P PRESS UR E R A T I O TA P P RE S SURE R A T IO LOC AT ION P / P c L OCAT I ON P / P c I .0036 IB 0036 2 ..0 0 36 ...... 3 5 .0.208.

3 0036 19 0285 • . , - • . , L 4 00 ; _9 3 6 0228 .... !

5 .0 0 33 3 7 .023.5 6 ,0235 20 02 9 q 7 .0253 2 _ ... On4_ 3 1 .03 83 2 2 , 0043 a . 0287 2 3 .02ll 9 . 0327 3 e 0166 , q a _o , 0 2 95 39 .0! 9 1 If .0139 2 4 .0226 1 2 .0046 4 0 .0270 1 3 25 . 0 0 5 1 30 . oo_ 26 _ , 0_ g 02__ 1 4 2 7 . 023 8 .0036 3 2 2 8 025R _ , o09_ 33 _ 2 9 .0058 15 . 0265 CAN . 0026 3 4 .0327 9 0 , 0026 1 6 91 _.. .0287 .0029 1 7 .0038 ,, -120- DATA SHEET NOZZ LE TYPE Cnni_1 (AP. i, 2 , 3 ) RUN N O 41 PR ESS U R E RA TI O , PR IM ARY, ). p 507. 88 P R E S SU RE RAT I O, S E C ONDARY, ) 'I 375.35 CHA M BER PRESSURE 99 . 79 p s i o SECONDA R Y PRESSURE 73. 57 psl a WEIGHT FLOW R ATIO , Ws / w p 0.696 AM B IE N T P RESSUR E 0 .196 pslo TOTAL SID E FOR C E 14.42 LB AMPLIFIC AT ION FAC T OR 1 . 603 TOTAL AXIAL F O R CE 125. 38 LB VACUUM THRUST CO E FFICIENT 1o 649 PR E SSURE DISTRIBUTIO N TA P PRESSU RE R A TI O TA P PRES S URE RATI O L O CATION P / Pc LOC A TIO N P / Pc l .0032 . I S .003Z 2 . 003 Z 3 5 , 0209 3 .0030 1 9 . 0278 4 .0027 36 . 0293

5 , o030 37 . o229

6 , O_6 2 0 . 030 R 7 21 .0229 0047 31 .0 9 21 22 . 0047 8 . 031_ 2 3 .02,19 9 ,0347 3 3 . o185 .

I 0 . 034 2 , 39 .... Ol 94 II 24 _ OI 40 . 0214 t2 40 . 0042 .0283 13 25 • 0047 3 0 l' . 00 5 2 : )6 . 0030 14 27 . 020 7 .0034 3 2 28

n2_ , . o 9 89

35 .0349 29 . 0059 _5 .0298 CAN . 0025 ___ 3 4 ,0 3 37 9 0 .0025 l " 1 6 91 0335 .0025 • 0034 . , .

-IZI - DATA SHEET NOZZLE TYPE _d, 9 . , _l, 2, 3) RUN NO. 42 PR ES SUR E R A T IO, PR I M A R Y, ) , p 507.58 PR E SSURE R A T IO , SE C ONDA RY , k t 431.43 C HAM B E R P R ESSU RE 99= 73 p si o S EC ONDA R Y PRESSURE 84. 56 p= la WEI GHT FL O W R A TI O, W s / W p 0. 0803 AMB I ENT PRESSURE 0. 1.96 p=lo TOTAL SI D E FOR C E 15. 80 LB AMPLIF ICA TI O N FACTOR 1. 518 TOT AL A XI A L F O RCE 1 25. 73 LB VAC UUM THRUST COEFFICI E NT 1 =654 PR E SS UR E D ISTRI BUT ION T A P PR ESSU R E RA T IO TAP P R ESS U R E R AT IO L OCATION P/P c L OC A TION P/P c .0036 IB .0041 2 .... 003.,6 .. 3 5 .0199 3 .0036 1 9 . 0 273 4 .003,4 3 6 .037q 5 ,0056 3 7 . 0 248 6 02_3 2 0 0_02 , . , _ ...... .

T .0241 Z I NO44 3 1 o 0,.45.3 22 .0044 B 0332 23 0221 9 .0357 3B .0Z14 ,0 .0366 39 ,0219 L II .0162 24 .0211 1 2 .0054 40 02_5 ......... 9, 13 .0061 25 30 .0044 2 6 .0029 1 4 .0209 2 7 ._0036 3 2 .0229 2B .0091 3 3 .03 47 29 ____O_O_6__!

I 5 . 03 29 CAN _ o02q 3 4 ,0354 9 o .0027 ._ _ 6 o 0359 , 91 .0029 7 .0041 -IZZ- DATA SHEET NOZZLE TYPE Conical (AR 1 , 2, 3) RUN NO 43 P RESSURE R A T IO , PRI M ARY, k p 507. 52 PRE SS URE RAT IO, SE CO ND A R Y, _ .I 476. 53 CHAMBER PRESSUR E 99.72 ps i o SEC O NDARY PRESSURE 93. 40 p = ta WEIGHT FL O W RATI O , W$ / Wp 0. 0893 AMBI E N T PRESS U RE O. 196 p= lo TO T AL SI D E F O RC E 16 . 98 L 8 A M P L IFIC AT IO N FA C T O R 1. 455 TOT A L AX IAL F O R C E 126 . 10 LB VACUUM TH RUST COE FF IC IE N T 1. 65(_ P RESSURE DI S TRIB U TION TAP PRESSURE RATIO T A P PRESSURE RA T IO L O CATI O N P / Pc LOC A TION P / Pc i .0035 PB , 0040 z , 0035 3 5 ..... n] R8.

3 19 • 0035 _ 0265 4 , 0033 3 B _ 032& . = 5 0035 37 _ 0277 6 2 0 .025R ..0306 7 21 n ?( -,_ .. ,0050 3 1 22 ,0476 . 00;,.t5 8 .0348 23 .0ZI 8 9 .0348 3 B .0242 to .0373 3 9 .0252 I I .0228 .. 2 4 .922.3 _ z .0053 40 .0289 . , 13 .0060 25 30 .0058 zs .0 . 028 I 4 . OZ18 27 .9038 32 . 0237 28 .0.092 33 .0351 2 9 . 0063 1 5 .0351 C AN . 0028 w 3 4 , 0333 90 . 0028 16 91 ...... tq_ 70. . O02R • 0043 -123- DATA SHEET NO Z Z L E T Y P E Conical (BR. I , 2, 3 ) RUN NO . 44 PRESSURE RAT I O, PR IM ARY, kp 50 7. 90 PRE S SURE RA TI O, SECONDARY, k s 162 .81 C HAM BE R PRESSU R E 99. 75 p$io SECON DA R Y PRESSURE 31. 91 p=l a WEIGH T F LO W R A TIO , W s / w p 0 . 0305 A MBI EN T PR ES SURE 0. 196 pi le T O T A L SI DE F O RC E 7. 3 6 LB AM PL I F I C A T I ON F A C T O R 1 . 8 4 8 TOTAL A XI AL FORCE 125. 05 LB VAC UUM THRUST COEFFI C IE N T 1.645 PRE SS UR E DI STRI BUT IO N TA P P R ESS UR E R AT I O TA P PR E S S URE RATI O LOCATION P / Pc L OCAT I ON P / Pc i .0033 I e .0043 2 , 0033 35 .... .0228 3 19 • 0038 . .. 0.25.8 4 . O OA = i , 3 6 ...... .0218 5 .003_ 37 . 0221 6 .0_2_ .. 20 .oo90 7 .0314 2 1 .0053 31 0250 2 2 • ,0046 8 .0248 23 .0166 9 .OlO0 3B .Ol 22 IO .0117 3 9 _Olql II , .,0142 24 .0149 12 .0053 40 • 0093 13 .0051 25 30 .0043 s 6 .003!

14 .0339 27 . .. 0041 32 .0294 2a . ,.0090 33 .0240 2 9 .0041 15 .o0250 CA N . 0026 34 .01 O0 9 0 .0026 1 6 .0117 9 1 .0029 iz .0051 -124- DATA SHEET NOZZLE TYPE Conical B_ 1 , 2 , 3) RUN NO 45 PRESSURE RATIO, PRI M ARY, ) ,p 523. 63 PRESSURE RATIO, SECONDARY, X$ 318. 02 C HA M BE R P RESSURE 99. 69 psia SE CO NDA R Y PRESSURE 62. 65 pst a W E IGHT F LO W R A TI O, Ws / W p 0. 0604 A M B I EN T P R ES SUR E 0. 19 7 p ile TOT AL SID E F O RCE 12. 7 7 LB A M PL IFI CAT I ON F A C T OR 1. 639 TOT AL AX I A L F O R C E 125. 13 L B V A CUUM T HRUS T C OEFFI C I EN T 1 ° 648 P RESSUR E DIS T RIBUTI ON TAP PRESSURE RA TI O TAP P RESSURE RATIO L OCA TI ON P / Pc L OCAT I ON P / Pc i .0034 l a .0038 z .00_4 3 5 ,02 , 16 3 19 . 00 31 . 0287 4 3 6 . o02 q .0231 5 3 7 h031 . O255 6 2O o_o2 .02q0 7 21 n_nv , 0046 3) .0393 2 2 .0036 B .0275 Z 3 .0221 9 .0332 3 8 .0211 Io .0319 3 9 .0211 It .0142 24 .0238 1 2 .0051 40 .0Z38 ,, 13 .0051 2 5 30 .0041 26 .0026 i 4 .0282 27 .0034 3a .0329 2 e . 007.0 33 .0337 29 .0061 1 5 .0255 C AN . 0024 34 .0319 90 .0024 IS .0300 9 1 , 0026 ,0041 -125- DATA SHEET NOZZLE TYPE Conical _B___.__R i , 2 , 3) RUN NO. 46 PR ESS UR E R A TIO , PRIMAR Y, k p 512.65 PRE SSURE RATI O, SE CONDARY , ) ' s 475.90 CH A M BE R P RES S URE 99 °72 psiQ S E CO NDARY PRESSURE 92. 80 p =la WEIGHT FL O W RATIO , W l / w p 0. 0 900 AMBIENT PR E SSURE 0. 195 p=l o TOTAL SIDE FORC E 17. 4 0 LB AMPLIFICATIO N FAC T OR 1.494 T O TAL AXIAL F OR C E 125. 55 LB VA C UUM TH R UST C OE FF ICIEN T 1. 6 52 PR ESSURE DI ST RIBU T I ON TA P PRESSU R E RA TI O T A P P R E S S UR E R A TI O LOCA TI O N P / Pc L OCA TI ON P / P c I .0031 I S .0036 2 .0029 3 5 0216 3 .. 0029 1 9 .0307 4 . 0 0 2.6 3 6 L 0307 S ,, ,.0029 37 . 0248 6 ,0295 20 . 0 2 0 7 z .0255 21 _ noa.R 31 .0474 22 ,0038 B o 031 2 2 3 _ 6)2 ] 3 9 0 3 46 3 B 0238 .. . , • I0 .0376 3 9 .0258 I, .0263 24 .0238 12 .0048 4 0 0295 . . f 13 .0051 25 30 .0038 2 6 .0026 14 .0287 27 .0026 3 2 .029,2 2a , . . 0088 33 .0381 29 .00.63 15 .0297 CAN =..0021 34 .03 3 2 9 0 ..0021 1 6 .0368 91 , 0026 17 .0041 -126- DATA SHEET N OZZL E TY P E APG-I .( AIR . 2 ) RUN NO . 47 PRESSURE RA TI O , PRIMARY, Xp 519 . 18 P RESSURE R ATIO , SECONDA RY , A t, 364.53 CHAMBER PRESSURE 99 ° 71 p _ io SE C ONDARY PRES S URE 69 o 99 p,= o W E IGHT F L OW RATIO , Ws / w p 0. 0200 AMBIENT PR E SSURE 0 . 19 2 psl o T OT AL S I DE FO R CE 5.74 LB AMP L IFICATION F AC T O R 2. 245 TOTAL AXIAL FO R CE 124 . 1 6 LB VACUUM TH R U S T COEFFICIENT 1 .634 P RE SS U R E DIS TR IBUTIO N T AP P R ESSU R E R A TI O T AP P RE SS U R E RATIO LO C A TIO N P / Pc LOC AT ION P / Pc I , , 1..237 3 6 . O1 29 2 . ooaz 3z .0085 3 17 . o2o8 ....

31 38 n il 2 _ . 01o7 4 ,0139 3 9 ,01 3 6 ....

5 . .0159 le .0124 6 . Ol 09 19 0058 ..... a 7 . 0058 2o .0077 a 0063 21 006 7 9 .0085 4 0 . 009 7 I 0 , 010 0 2 2 . 0114 32 .0058 23 .0050 II .Ol 12 24 . 0058 i 2 , O1 98 2 6 .0 04 3 33 . 0141 27 .0 0 43 34 . O109 28 .0080 I 3 .0141 29 0043 30 . 0139 25 . 0043 35 . , 0151 CAN ,0018 I 4 ,0087 90 , 0 0 1.3 15 91 . O06Z , , . 001 3 1 6 • O09Z -1 2 7- DATA SHEET NOZ ZLE T Y P E / _-PG-1 ( A .R 2) RUN NO, 48 P R ESSU R E RA TI O , P R IM ARY, ) , p 523. 87 P R ESSURE RAT I O, SE C ONDARY, A s 490.1 6 CH A MBE R P R E SSU R E 99.84 psi o S EC ON D ARY P R E S SU R E 93.6 2 o , Ja WEIGHT F LO W R A TI O, _ / $ / Wp _ __0 ._ = 03 01 _ AM BIE NT P RE S S U R E 0. 1 _ psl o T OT AL S I DE F O R CE 8. 38 LB AM P L I F I C ATION FACT O R 2. 169 TOTAL A X I A L FO R C E 1 24. 56 LB V AC U U M T H R U S T COE FFICIENT 1° 636 P R ES S U R E DI ST RI BU T ION TAP PRESSURE R AT I O TAP P RE SSURE RA T I O LOCAT I ON P / P c LOCA TI ON P / P c l . 1858 3 6 .0126 z 0079 3 7 0180 3 Iz ,0089 31 _ 0190 38 ,0,094 4 .Ol 26 39 ,.0121 5 .0146 IB .0148 6 .0170 1 9 : 1")084 7 .0148 z o , 0 0 77 8 ,.0064 21 .0074 9 .0 08 9 4 0 .0082 io , Q 1 04 zz .0126 32 ...... 0057 23 ...... Ol 21 II .... _ .... 24 . 0057 _ 2 ,0084 2s , 0 045 33 .0214 2 7 .......

3 4 28 .0136 , 0,0 7 9 1 3 29 . O l 23 .0 0 4 7 3 0 25 .Ol 21 .0047 35 . Ol 65 CAN , 0021 i 4 ,0168 90 ....... _0_ 9/ _5 _ 1 5 0062 91 0013 ,-- , t , " 6 .0094 -128- DATA SHEET NOZZLE TYPE APG-I (AR 2) RUN NO. 49 PR E SSURE R A T IO, P R I M A R Y, Xp 523.35 P R E S S U RE RATIO, SE C ONDARY, _'s 652 ,.41 C H A M BER P R E S S U R E 99 , 74 p _i o SE C OND A RY P R ESSU RE 12 -4 . 61 ps l o WEI GHT F L OW R A T IO, W s / W p __0_ . _0_ 0 402 AMBIEN T P R E SSU R E 0 . 191 psl o TOTAL SIDE FORCE 9, 8 7 __ LB A MP LIFIC AT IO N FACTOR 1, 9 2 5 TOTAL AXIAL FORCE 12.3,78 LB V A CUU M TH R US T COEF FI CIE N T 1 , 628 PRE S SUR E D ISTRI BUT I ON TAP PRESSURE RATIO TAP PRESSURE RAT I O LOCATION p / Pc LOCAT IO N P / Pc I .2465 36 .0074 z , 0076 37 . Ol 85 3 17 • 0071 31 .0236 3B . O1 1 8 4 .0145 39 .0118 5 .0140 IB .0145 6 ..0177 19 , 0155., 7 .0185 z o .0076 S .0106 2 1 ._ ,0130 9 . 0089 40 ,0079 Io .0103 2 2 .0116 32 .0054 23 0150 ii .0116 2 4 .0066 I2 .0069 26 .0042 33 . O1 53 2 7 .0044 34 .0209 Z B .0079 I 3 . O1 23 29 . 0047 30 .0118 25 .0047 35 .0170 CAN .0020 14 .0177 90 .0012 I 5 .0096 91 . 001 2 1 6 .0091 -129- DATA S H EET NOZZ L E TY P E APG-1 (AR 2 ) RUN NO 50 P R E S SU R E RAT I O, P R IMAR Y, , _ p 5 1 0. 40 PRESSURE RATI O, SEC O ND A RY , )'8 703. 90 CH A M BE R PRES SU RE 99.78 p t io SECONDARY PR E SSU RE 1 3 7. 26 psl o W E I GHT FLO W RAT I O , _ / s / W p 0. 0444 A M BIENT PRESSURE 0 . 195 p s_o TOTAL SI D E FORCE 10. 44 LB A M PL I F I C ATI ON FAC T O R 1. 8 3 8 TOTA L AX I AL F O R CE 1 24, 08 LB VAC UUM T HRUST C OEF F ICI E N T 1. 632 PRESSUR E DISTRIBUTIO N TAP PRESSURE RATI O T AP PR E S S UR E R A TI O L O C ATI O N P / P c LO CA T I ON P / Pc I .2707 36 .0064 2 ,0071 3 7 _ ,0162 3 0071 3B .0145 3) .0233 a .0164 39 . O113 5 .0140 IS .0145 6 .0180 1 9 .0174 7 .0194 ao .0078 B .0135 21 .0150 9 . 0091 4 0 . 0086 io .0103 a2 .0113 3 2 ,0056 23 , O157 Ii .0175 a n .0088 12 .0076 26 .0041 3 , ; . 0231 2s . Q_O_7.B 1 3 . 0130 29 ........ __0_0___ 3 0 ,01 Z5 25 .., 0046 35 .0174 CAN .0021 1 4 .0177 90 . 0017 i 5 . 0130 9 1 0012 16 . 0093 -130- DATA SHEE T NO ZZ LE T YPE APG-I (CR l, 2, 3) RUN NO. 51 PRE SS URE RA T IO, PRI M ARY, X p 500.54 PRE SS U R E RATIO, S E C ONDARY, A s 167.39 CHAMBE R PRESSU R E 99. 82 ps i o SECOND A RY PR ES S UR E 33.31 p s m W EI GHT FLO W RATIO, W s / Wp 0 . 0302 A MBI EN T P R ESS U R E 0. 199 psl o T O TAL SIDE F O R CE 8, 64 LB AMPLI F I CAT IO N FACTO R 2• 235 T O TA L AXIAL F O R CE 124. 1 3 LB VAC UUM T H R US T COE FF I CI ENT 1 . 6 3 3 PRESS UR E DI ST R IB UT I ON TAP PR E SSURE R AT I O TAP PRESSURE R A T I O LOCATIO N P / P c LOC A TIO N P / Pc I .0617 36 .0036 t , • - , 2 0209 3z 0177 3 17 • OIZ5 31 .. , 0159 38 . 0145 4 .0164 3 9 ,0150 5 o 0132 IB , Q120 6 .0061 19 .0061 7 . 0056 2o .0081 8 .0066 21 . OiZO 9 .0086 40 . O115 Io • 00(_8_..... 2 2 .0130 32 ,0233 23 .0051 II .Ol 10 z 4 .0056 I 2 ..0243 2 6 .0046 33 . 01.64 2 7 . 0046 34 ,0164 z8 .0083 I 3 . Ol 64 . 2 9 , 0046 30 25 • 0164 .0046 35 .0086 CAN 0 0 17 I4 .0056 90 ,0031 I 5 .,0061 91 .0017 l6 . 0090 -131 - DATA SHEET NOZZL E T Y P E _ A/ _G-1 ( G R I , Z , 3) R UN NO. 52 P RESSURE RATI O, PRIM A RY , , _ p 510.05 PRESS U RE RAT I O , S E CON D A RY , X$ 336.77 CH A MBER PR E SSURE 99.71 p s_a SECO N D A R Y PRESSURE 65 . 67 p, la WE I GH T FLO W R AT I O, ws / W p 0. 0601 A M B I ENT P R E S S URE 0, 195 p,_ o TO T AL S I DE F O RC E 14.81 LB AM P LIFIC A TI O N FACTOR I. 910 T O T A L AX I A L FORCE 1 2 5. 21 LB VAC UUM T HRUST CO E F FICI E NT i . 648 PRESSURE DISTRIBUTION T A P PRES S U R E R A T I O TAP PRES S URE R A TIO LOCATION P / P c LOCAT I ON P / Pc I 36 2 .0116 3 7 n N ql " 3 .0185 iz ....

31 0229 3B .0204 I' t ,, , , 4 . 0195 39 .0167 S •01.90 1 8 .0165 6 19 .0204 .0204 7 .0214 a o .0076 O . 0209 21 ..... . 0 052 .......

9 . 0 0 84 40 . O155 _o 00 qq 22 .0130 3 2 23 ; 0n84 ,0180 t I . O1 13 2 4 0200 I 2 .Ol 03 z 6 .... 0042 ....

3 s ,0172 27 . 00 42 3 4 .0234 2 8 .0076 13 l . 0192 29 , , 008 9 30 2 5 ,0192 . 0 089 35 . ,, 0185 CA N .0017 14 . 02 0 0 9 0 ° 0 022 1 5 .0204 91 . 00 17 16 .0091 -13Z- DATA SHEET N O ZZ LE TY P E AI : ) -Czzj_ C(__, 2, 3) RUN NO. 53 P RE S SURE RATI O , P R IMAR Y, ,_ p 504 = 65 PRE S SURE R A T IO , S ECO N DARY, As 488 .88 C HAMBER PR ES S U RE 99. 65 ps io SECONDARY PRESSU R E 9 6. 31 . ps lo WE I GHT FLOW R A T IO , W $ / Wp 0, 08c_____ AMBIENT PRESSURE 0. 1 97 p s to TOTAL SIDE F O R CE 19.14 LB AMPLI F ICATI O N F A CT O R 1o645 T O TAL AXIAL FORCE 12 5 . _ _ __ L B V A CUUM TH R UST COEFFICIENT 1 . 6 5 9 ..

PRESSU R E DIST R IBUTION TAP P RESSURE R AT IO TAP PRESS U RE RAT I O LO C AT I ON P / Pc LOCATI O N P / Pc l I , .1790 , 36 .. .0027 2 .0136 37 ,009_ 3 17 • . O150 ......

3 1 027q 38 0200 , . . ° ,. , = • 4 0239 39 022q 5 ( B .... 021 0 .01 95 6 .0219 19 .0219 7 .0229 t o .Ol 1 1 e .0234 2 1 .0047 9 . Ol ZI 40 . Ol Zl Io .0096 22 .0170 32 .0081 2 3 .0180 If .0111 2 4 .0229 i 2 . Ol 11 2 6 .004Z 3 _ . Ol 26 27 .0042 3 4 .0237 28 .0076 13 .0239 29 .0116 30 .0234 25 .Ol ZI 3 5 . 0219 C A N 0027 ., = 1 4 .0210 90 , ,0027 15 91 ,0234 .0017 16 ,0091 -133- D A TA SHEET NOZZLE TYPE APG-I (.AR . I , 2 , 3) RUN NO. 54 P RE SSU R E R ATIO, P R IMARY , . _ p 5 13 . 84 P R E SSU RE R ATIO, SECOND A R Y , ; k s -- C HAMBE R PRESSU R E 99. 59 psio SECONDARY P R E S S URE -- pslo W E IGH T FL O W R AT I O , _ V s / W p 0 _ _ A M B IENT P R ESSURE 0. 195 psio TOTAL S I D E FOR CE 0. 36 _ LB A M PL I F I CAT I O N F ACTOR -- TOT A L AX I AL F ORC E 1 2. 4° 85 LB VAC UUM THRUST CO EF F ICIENT 1 , 6 3 9 PRES S U R E DIS TR IBU T I O N T AP P RESS U R E R A TIO T AP P R E S SU RE RA T I O L O C A TI ON P / P c LOCATION P / P c | , , , i 0064 36 .0057 .... • • , , .

2 .0054 3 7 . . 0050 3 1 7 .0 05 0 3 1 _ a n 4? 3 0 .0047 4 nn_ 39 .0047 v ---- 5 . .0052 . . 1 8 .. .0050 6 19 nn_ . 0059 7 N O q q 20 .0076 a . 006 4 21 . 0052 9 . 0 088 4 0 ..0045 Io .0100 2 2 . OO 4 7 32 . 0071 23 .0050 II .0111 z 4 .0057 I 2 . 0 062 z 6 . 004 0 33 0057 2 7 . , 00 40 3 4 .0057 Z B .0076 13 . 00,59 2 9 . , 00 4 3.

30 .0062 2 5 . 00 45 35 . 0 047 C AN .0 0 17 r 1 4 9 0 , 0052 . 0017 I 5 .0062 91 . 0 0 12 , 6 . 00 9 0 ....

* Ports plugged but not filled to _form smooth contour.

-134- DATA SHEET NOZZLE TYPE APG-I_ i , 2 , 3) RUN NO. 55 PRESSURE RA T IO, PR I MARY, )_p 523:1"_ __ PRESSURE RAT I O, SECONDARY, _ ,g 173.46 CHA M BER PRE S SURE 99. 71 p_io SECONDARY PRESSURE 33. 13 ps l a W E IG HT F LOW RATIO, _ / s / Wp 0.03 0 2 - ......... A M BI E NT PR E SS UR E 0. 191 p slo TO T AL S I D E FORC E 8o 2 9 ..... LB A M P L IF I CAT I O N FACTOR 2 . 139 TOTAL AXIAL FO R CE 1 24° 64 LB VAC U U M T H RUST COE FFI CIE NT i. 639 . , _ PRE S S U RE DISTRIBUTION T AP PR E SSURE R AT I O TAP P R E SSUR E R A TI O LOCAT I ON P / Pc L OCAT I ON P / P c .0615 36 __ . 0083 2 _ ,0152 3 7 ,0164 3 o0221 iz 31 .... 0 ! 6_6__ 38 ° 01 05 4 _.0 _ 166 39 _0132 6 01 66 19 _ ___.__ _0_0_7_3__ z .0102 20 .0078 s _ 2, ......... _.__0_0_85.

9 _0 _ _ 4 0 ._ _0_ _ IO D.D.o _ 22 . Ol Z5 32 _ 0068 2.3 . _0_i _ .[_5.

II ........ 0 _ _i_07 .......... ..... 24 . 0056 2 . Ol 22 2 6 . 0043 33 . ,0196 27 .0046 3 4 _ , _0 / _ ; 5__?_ 2B .0078 )3 __ __ ]_ L 2 9 .0043 30 25 __,_0014_9_ .0046 3 5 __01_6._ CA N __ .0019 1 4 _ 90 . _._0_0_19_ 15 91 o 0066 _____._ 0 _009 1 6 ,00_9_5_ -135- DAT A SHEET NOZZL E T YP E A P G-I (AR I, 2 , 3) R UN NO 56 PR E SSURE RAT I O, PRIMARY , Xp 507.58 P RE S S U R E RATI O, S E C O ND A R Y, ; kI 224.90 CH A M BE R PRESSUR E 99. 7 3 p, i a SECONDARY PRESSURE 44. 08 ps_a W EIGHT FLO W RATIO, Ws / W p 0. 0405 __ AMBIENT PRESSURE 0. 196 p , _ o T O T AL S I DE FO R C E 10, 42 L B AM P L W iC A T (ON F A C TOR 2 . . 01 2 T O T AL AX I AL FORC E 124 . 00 LB VACUUM TH R U ST C OEFFIC I ENT ] . 632 PRESSUR E DIST R IBUTI ON T A P PRES SU RE R A TI O T AP P R ESS U RE RATIO L O C AT I ON P / Pc LOCAT I ON P / Pc I .0824 3 6 .0046 2 . O10Z 3 7 . O125 3 .0262 17 31 ,0166 3B . 0159 4 ,, 0 166 39 , O1 25 5 , , 0181 IS .0144 B .0186 19 __, 017 1 }" .0174 z o .0078 8 .0083 2 1 ........ 01!7 __ 9 . 0083 4 0 _ 0082 io .0098 zz __._O XL 2__.____ 3 2 .0038 23 .015 2 I I . 01 07 z 4 ......_Q83__!_ I 2 . 0078 2 6 . 004_3_ 33 ,0147 z z 0043 34 2 8 . , 0186 __ . 007]_ 13 :;' 9 ,0154 0043 30 .0159 2, 5 , Q043 3_ ,0!74 CAN .0019 1 4 , 01 8 4 __ 90 _ 0 __I_.4,_________ 1 5 9J • 0085 . 0009 • 009 Z .

-136- DATA SHEE T NOZZLE TYPE APG-1 (AR I, Z, 3) RUN NO. 57 PRESSURE RAT I O, PR IM ARY, X p 502.60 P R E SSU R E RAT I O, S ECO ND ARY, _' s 275 . 35 CH A M BER P R E S SURE 99.74 p ,i o SECON D A R Y PR ESSURE 54. 5Z ps I o W E IGHT FLO W RAT I O, W s / W p 0o 0504 A M B I ENT P RE SSUR E 0. 198 p._ o TOTAL SIDE FORCE IZ. 37 LB A M PLIFICATION FACTOR 1.909 TOTAL AXIAL FORCE 124 . 74 LB VACUU M THRUST COEFFICIENT 1.642 P RE SS U R E D ISTR IB UTION TA P P RESSURE R AT IO T AP PRESSU R E RATIO LO C A T IO N P / Pc LOCA TI O N P / Pc I .1001 36 .0040 2 . O1 07 3z .0094 3 1 7 •028Z 31 ,0191 3B .0168 4 .0176 3 9 , Ol z_z_ 5 . O186 1 8 , 0_41 6 .0200 19 . Ol 93 7 .0196 zo . 0077 8 .0131 21 .0122 9 . 0085 40 O117 Io .0099 2 2 .0109 .

32 .0050 23 .0166 If .0114 2 4 .0161 I 2 . 0055 26 . 0043 3_ 0 1 09 a7 • , OO43 34 ,0215 2 8 .0077 I3 . 0173 29 .0053 30 2 5 •0173 .0058 35 C AN • 0181 .0018 I n .0198 90 0016 I 5 .01 49 91 . 0008 16 .0094 -137- DATA SHEET NOZ Z LE TYPE APG-I (A R i, 2, 3) RUN NO 58 PRESSURE RAT I O, PR I MARY, kp 5___08_; 25 _ PRESSURE RAT I O, SECONDARY, ) . it 331.9_.__ .

CHAMBER PRESSURE 99. 86 p_ i o SECONDARY PRESSURE 65° 07 p slo W E I GH T F L OW RA T I O , W s / Wp 0 _. 060Q .......... A M B I E NT PRE SSURE 0_196 p s i a T OTAL SIDE F O RC E 13. 99 LB AM P L I F I CA TI ON F ACTO R i. 805 T OTAL AX I AL FORCE 125.32 LB VACUUM THRUST COEFFIC I ENT i. 647 P RESS U R E DI STR I BUT I ON T A P P RE S SU R E RAT I O TAP P R ESSURE R AT I O L O C AT I O N P / Pc LOCA T IO P / P c I 36 • , 1233 , , .0072 2 . O1 07 3 7' 0099 3 .0274 iz 4 . 0183 39 0200 5 . 0180 t 8 0178 s ___ 1 9 023 2 z .0203 20 O1 09 S .0185 21 0139 9 . 00,90 40 O180 i o .009_ z2 0151 32 . 0055 23 Ol 93 If . 0116 24 0232 I z .0060 2s 0072 33 .00.90 22 0072 3 a ,0205 28 .0107 13 ,0190 Z9 .0102 30 25 . O188 . O1 21 35 CAN . 0048 i a ,0225 9 0 ,0045 15 9l .0225 ...... __03dB 1 6 . O124 -138- DATA SHEET NOZZLE TYPE APG-I (AR i , 2 , 3) RUN NO. 59 P RE S S U R E RAT I O , PR IM A R Y , }kp 513.36 PRESSU R E RAT I O, SECONDA RY , As 384. 21 C H AMB E R PRESSURE 99.86 p , i o SECONDARY PRESSURE 74. 92 p s la WEI GHT F LOW RATIO, W s / W p 0. 0696 A M BIENT PRE SSURE 0. 195 ps)o T OTAL SIDE FO R CE 1 5 . 63 LB A MP LIFIC A TION FACTOR 1. 737 TOTAL AX I AL FORCE 125. 50 L B VAC UUM T H R UST COEF FICIENT 1. 649 P RES S U R E DISTRI B UTION TAP P R ESS U R E R AT I O TAP P RE SSU RE RA TI O LOCATION P / Pc LOCATION P / P c i . .1375 36 , 0060 -- . = 2 0099 3 7 0084 3 1 7 . o150 31 .0155 aS .0173 a 0197 39 , ,O1 7 3 5 ,0192 Is ,01_6 • O1 92 19 _ __ 7 .0197 2o .0101 O .0210 21 .0114 9 . 0116 40 .0150 I o .0094 a 2 _ _._OiZ3 32 .0067 23 ,., I I . O1 09 z4 _ _ l a .0082 2 6 .0040 33 . 0089 27 . 0045 34 ,0170 z 8 .0074 1 3 2 9 ,0205 ,0077 30 25 • 0207 .0084 35 CAN ,019 ; _ ,0015 1 4 9 0 ,0178 .0013 )5 91 • 021 0 . 0013 1 6 • 0o9 ' i- -139- DATA SHEET NOZZLE TYPE _AP G T _ L _(_AR_I, 2 , 3) RUN NO _____._Q____ PRE S S UR E R A T I O, P R IM AR Y , Ap 5 11_ Q3 PR ESSURE R A T I O , S E C O N D A R Y, k s 438 . 5 6 CHAMBER PR ESSU R E 99. 91 p,io SECON D ARY P R ESSU R E 85° 52 p si(} W EIGHT FLOW RATIO, w s / Wp ___0;.080_ AMBIENT PRESSURE __ 0. I O L S_ p s i o TOTAL SIDE FORCE 17.33 __ LB AMPLIFICATION FACTOR 1 676 TOTAL AXIAL FORCE __ / 125_ , !4 L B VACUU M THRUST COEFFICIENT. io644 _ PRE SS U R E D IST RI B UTION TAP PRE S S U R E R AT IO TAP P R E SS U R E R A T }O LOCA TI ON P / P c LOCAT I O N P / Pc i 1540 36 .... _ ,0089 3 .0141 17 3_ .0172 3B 0172 4 . 0200 39 ............ O 1 _ 5 .020 9 _ t8 O] 33 6 ....... 2 1_ 9 _ 5 _ ................ _9__ ...... O! 75 r .0131 2o °01 _6_ S __ . 0209 2_ n]4] 9 _0 I_Q.I___7__ 40 , 0131 o .___._OZO_6_ 22 ............ 0! 2 _6______ 32 ........... ._0105_ ....... ................ 23 ......... 01.4 / I 2 ........ __.____,,3._ (X _ 2 6 ..... O_O!_r,._ .....

33 2 7 03._3 6 _...................................... O_OA2.__ 3 4 28 0 / _7_0. 0077 I 3 .0202 2 9 . 0067 .......................

30 .0209 25 .0067 35 .0212 CAN . 0023 1 4 . O 168 90 . 00 18 1 6 ,0099 -140- D A T A SHEET NOZZLE T YPE APG-1 A_A__R_I , 2 , 3) RUN NO. 61 PRESSURE RATIO, PR IM ARY, X p __5503.91 PRE S SURE RATIO, SECONDARY, X! 479 .3 4 CHAMBE R PR E S S U R E 100. 00 p t i o SECONDARY P RE SSU R E 94, 91 ps l o WEIG HT F L OW RATIO , Ws / W p 0 . 0895 A M BIEN T PRESS UR E 0. 198 ps l o T O TA L S I DE FOR C E 18o 60 L B A MPL I F ICA T IO N F A CTO R 1. 616 T OTA L AXIAL F O R CE 124 . 78 LB VAC UUM T HR UST C OE FF ICI ENT 1 o 638 PRESSURE DIS T RIBUTION T AP PRESSU R E R ATIO T AP PRESSURE R A T IO LO CAT IO N P / Pc L O CA T IO N P / Pc I .1729 36 .0096 2 0088 3 7 . _ , O155 3 1 7 , 0133 ..........

31 38 • 0165 _ , 0169 4 3 9 olR7 .0162 5 .0206 18 . 0 142 6 1 9 • 0211 _ 0l q7 7 .0184 2 o .0167 S .0206 21 . Ol 52 9 , 0_1 , _ n o .0133 Io 2 2 .0128 n] 1 o 3 2 . 0115 2 3 . 01 3 8 II .0110 za .01 9 _2 2 .0140 z 6 .0044 33 .0138 z 7 .0044 34 .0160 28 ,0076 I 3 .0192 z 9 .0066 30 .0199 25 .0071 35 . 0221 CAN , 0020 14 . 0184 90 .0015 I 5 . 0206 91 .0007 ,0125 -141 - DATA SHEET NOZZLE TYPE ._._'-..P___{__ . -__]_..LB___ _ _], 2, 3) RUN NO __62.___ PRESSURE RATIO, PRI M ARY, )W.p .__5__0__, 22 PRESSURE RATIO, SECONDARY, _' s _L7_0___3..0___.

CH AM BER PR ES S U R E c ) C ) o86 p_io SECONDARY P R ESSURE_7_2,._pslo WEIGHT FLOW RATIO, Ws / Wp . _0 _ __Q3.02..... A M BIENT PRESSURE 0__1_9_ ..... psia TO TAL S I OE FORCE _.8_,OL 0 - ...... LB A M PL i F iC AT iO N FAC TO R .... 2_ _ 29_ TOTAL AXIAL FORCE _124, 27 I_B VACUUM THRUST CO E FFICIENT 1. 6 34 __ PRESSURE OIS TRtBUTION TAP PRESSURE RATIO TAP PRESSURE RATIO LOCATION P / Pc LOCATION P / Pc . 1392 36 o0042 2 ,0146 32 .0126 3 J7 ..... 0227.

31 ___0__L ......... 3B .01 23 4 .0160 39 01_-I 5 .0168 _B .0153 6 ......... _ 1_.3........... 19 .01 01 z .0143 2 0 .0077 O .0064 21 . OiZl 9 .0079 40 .0091 IO _ 0 Q_9_ ...... 22 0131 32 .158_ 23 .0136 II .0104 2 a ° 0057 I2 .0126 26 ° 00 45 3._ . O192 ............. a z ............... _000_.4.5____ 3 a .0141 28 ................. 007_7_9.

30 .0140 25 o 0045 35 . 01 68 CAN , 0018 I 4 . O1 68 90 ,002.8__ ......

i 5 . . 0059 91 0_018 L_ r6 . 0091 : -14Z- D A TA SHEET NOZZ L E T YPE AP G -I B_IB_R i , 2 , 3) RUN NO, 63 PR E SSURE R A TI O, P R IMAR Y, X p 495. 84 P RESSU RE RA TI O, SEC O NDARY , A= 330° 20 C H A M B ER PR E S S UR E 99o 62 p _ io SECONDARY P RESS U RE 66. 37 psia W E IGH T F LO W R AT I O , Ws / Wp 0. 0603 A M B I E NT PRES S U R E 0. Z01 pst o T OTA L SIDE F O R CE 14 . 30 L B A M PL I F ICATI O N FACTO R 1o 847 TOTA L AXIAL FORCE 124.47 LB VAC U U M T HRUST COE FFI CIENT 1 . 641 PRE S SURE DISTRIBUTION TAP PRESS U RE R AT I O TAP PRESSURE RATI O LOCATION p / Pc LOCATION P / Pc I ° 1440 36 .0036 2 .0107, ,__. 3 7 . 0072 3 1 7 .0272 31 ., 0215 38 .0196 4 = 0193 39 o 0171 5 18 .0191 .0164 6 ° 0203 19 .0203 z .0206 20 .0080 s .0193 2 1 ° 0082 9 .0077 40 .0171 I0 ._ 0 0 _ 2 22 32 _ , 1793 23 ,0181 I_ .0105 24 0186 I2 .0065 26 , 3 3 1.L_ L L___ 2 7 0043 34 2 8 .0211 .0077 13 2 9 .0186 .0085 30 2 5 ,0196 .0087 3.5 .0191 CAN . 0018 I a .OZOl 90 .0023 I5 .0186 91 , 0016 1 6 .0.095 -143- DA T A SHEE T NOZ Z L E TYPE . _.A_I:___G_.-I_I:_. I , 2 , 3) RUN NO 64 P R E S SURE R A TI O , P R IM A RY, X p _ _ _ 5 _ 505o 50 __ PRE SSU R E RAT I O, S E C ON D ARY, _ . g 4 9 Zo 13

C HA M BE R P R E SSUR E 99° 8 2 p,_ i o SECONDARY PRESSURE 96 ° 95 psio

W E I G HT F L O W R ATIO, W$ / W p _ 0. 0 8 9 __ A M BIE N T P R E SS U R E 0° 107 psi o TOT AL SI DE FORC E 18. 7 ] L 8 AM P L IF I C AT I O N F A CT OR 1 . 6 0 9 TOT AL AX I A L F ORCE 1 26. 55 L B V AC UUM T HRUST COE FF I C I E N T ]. _ 664 P R ES SU R E D (STRIBU T (ON TAP PRES S URE RAT I O TAP PRESS UR E R AT I O LOCAT I ON P / Pc LOCAT I ON P / Pc I o 1544 5_ 0036 z .Ol 27 3z .................. 005_ 3 .0201 i ;' 31 .0287 3 8 .0186 4 0235 3 9 0222 5 .01 9 _8_ IB .................. OZOI 6 19

__ 021_6 ............................................ _ 0 _2 2 .2

7 o 0230 20 . OO?O 3 2 . 1259_ z 3 018 1 II o 0100 24 = 0223 t 2 o 0056 z 6 0 0 41 33 0053 a7 0043 ................................ = , .

3 4 _0Z0i__ ............. 28 .................. 00_18_

t 3 ,O Z 2_ / _3 ......... z 9 ....... 0_1_0 /

3 0 25 .0218 0107 3 5 ___________,_Q_ 1 6 C A N .............. 0 00______ 4 ___0213 9 0 ,00 2 1 1 5 9 1 .02 3 3 0 / 116 ' I 6 , ___D.9 3 ____ ....

-144- REFERENCES i. Hozaki, S., et al, "Thrust Vector Control System Utilizing an Adverse Pressure Gradient in the Nozzle, " National Engineering Science Co. , Pasadena, Calif., Final Report Contract No.

NASw_-Z49, NASA N62-i1727, April (196Z).

g. Dowdy, M. W. , and Newton, J. F. , "Wind Tunnel Experiments on Freon-IZ Secondary Injection, " JPL Report SPS 37-17, Vol. 4, (196Z).

3. Mager, A. , "On the Model of Free, Shock-Separated, Turbulent Boundary Layer, '_J. Aero. Sci., Feb. (1956).

4. Hays, W.D. and Probstein, R.F., "Hypersonic Flow Theory," Academic Press, N.Y., (1959).

5. Cubbison, R.W., Anderson, B.H., and Ward, J.J., '_Surface Pressure Distributions with a Sonic Jet Normal to Adjacent Flat Surfaces at Mach 2. 92 to 6. 4, '_(NASA TND-580), Lewis Research Center, Cleveland, Ohio, February (1961).

6. Stewartson, K. , "Correlated Incompressible and Compressible Boundary Layers, " Proc. Roy. Soc. (London), Set. A., Vol. ZOO, No. AI060, Pec. ZZ, pp. 84-100, (1949).

7. Mager, A. , "Transformation of the Compressible Turbulent Boundary Layer, '_Jour. Aero. Sci., Vol. Z5, No. 5, pp. 305-311, May (1958).

8. McLafferty, G.H. , and Barber, R.E., "The Effect of Adverse Pressure Gradients on the Characteristics of Turbulent Boundary Layers in Supersonic Streams, " Journal Aero. Sci. , Vol. 29, No. i, pp. i-I0, January (196Z).

9. Romeo, D.J. and Sterrett, J.R. , "Aerodynamic Interaction Effects Ahead of a Sonic Jet Exhausting Perpendicularly from a Fiat Plate into a Mach Number 6 Free Stream," NASA TN D-743 April (1961).

I0. Sterrett, J.R. and Emery, J.C., "Extension of Boundary-Layer- Separation Criteria to a Mach Number of 6. 5 by Utilizing Flat Plates with Forward-Facing Steps," NASA TN D-618, Dec. (1960).

11. "Equations, Tables, and Charts for Compressible Flow, " Ames Research Staff, NACA Report I135 (1953).

12. Shapiro, A.H. , "The Dynamics and Thermodynamics of Compressible Fluid Flow," The Ronald Press Company, New York, (1953).

-145- 13. Rodriguez, C.J. , '_An Experimental Investigation of Jet-Induced Thrust Vector Control Methods , " presented at the Seventeenth Annual JANAF-ARPA-NASA Solid Propellant Meeting , Denver , Colorado , May Z3-g5 (1961).

14. Gagnon , R. , "Thrust Vector Control of Plug Nozzles , " Final Report Contract No. 61-1Z5 , January (196Z). (Confidential Rept.)

15. Wu , J.M. , Chapkis , R.L. , and Mager , A. , "Approximate Analysis of Thrust Vector Control by Fluid Injection , " J. of ARS , Dec. (1961).

16. Van Driest , J. Aeronaut. Sci., 18 , p. 145 (1951).

17. Jakob , M. , "Heat Transfer , " Vol. II , John Wiley and Sons , Inc. , New Y o rk (1957).

18. Donaldson , C. duP. , "On the Form of the Turbulent Skin-Friction Law and its Extension to Compressible Flows , " NACA TN Z69Z , {195Z).

19. Stratford , B.S. , "The Prediction of Separation of the Turbulent Boundary Layer , " J. Fluid Mech. , Vol. 5 , Part 1 (1959).

-146- TABLE I Test parameters for opposed-tangential port configuration.

Nozzle Port Port Dia. Port Spacing Spacing Weight Flow Total Type Config. d. P_atio Be twee n Ratio C a se s J c / d. Port C_L V_ / _V J c s p Conical Opp. -Tan. . 188 2 . 1 . 395 0, 3, 4, 5, 6, 7, 8, 9% 8 2. 6 .489 3, 6, 9 % 3 f 3. Z .602 3, 6, 9% 3 I_ i APG - 1 2. I .395 3, 6, 9_ / 0 3 ' 2.6 ,489 0, 3,4, 5, 6, 7, 8, 9_ / 0 8 i I I 3. Z .602. 3 , 6, 9 % 3 Total Cases for Phase I = Z8 Sketch of Port Spacing Notation C -147- TABLE II Test parameters for multiradial port configuration.

Nozzle Port Port Dia. Port Spacing Spacing Weigh t Flow Total Type Config. d. Ratio Between Ratio Case s J c / d. Port % w / tic j s p C Conical 1-Rad. . 188 - - 2, 3, 4, 5 % 4 3-Rad. 1. 8 . 3 3 6 0, 3, 4, 5, 6 , 7, 8, 9 °/ 0 8 i 2. 5 .470 3, 6, 9% 3 1 ') 3. 5 .658 3, 6 , 9% 3 APG - I l-Rad. - 2, 3, 4, 5% 4 I 3-Rad 1.8 .336 3 , 6, 9% 3

I

z._ .4vo o, 3,4, _,6,v, 8,9 o zo 8

i ,' i 3 . 5 . 658 3 , 6 , 9% 3

Total Cases for Phase II = 36 Sketch of Port Spacing Notation -148- TABLE III VALUES OF CRITICAL INJECTION PORT SPACING RATIOS, Ccr / d j

Pj / P o

M 5 i0 2.5 50 I00 oo 2 i. 04 i. 23 1.65 2. lO 2. 84 ¥= I. 2 3 I. 03 i. 29 1.60 2. 03 4 1.04 i. lO I. 32 1.66 2 1.04 I. 20 1.63 1.92 2.44 y= 1.4 3 i. 06 1,41 1. 61 2.00 4 I. O0 I. 31 1.46 i. 79 -149 -

I

BOUNDARY JET F) o

=

INJECTANT, WAVE AS SHOCK TEMPERATURE FREON-12 BOW- WITH (INJECTION .

WAVE REF SHOCK PHOTOGRAPH, FROM SEPARATION - FIGURE SCHLIEREN ENLARGED >-' U1 o BOUNDARY JET _75°F)

=

INJECTANT, WAVE AS TEMPERATURE FREON-12 BOW - SHOCK ITH JECTION W N (I .

WAVE REF PHOTOGRAPH, FROM SEPARATION-SHOCK ENLARGED FIGURE SCHLIEREN f-' \J1 f-' D M I v

%

C) _, (i)

SHOCK WAVE TO SEPARATION MI SLIP FIGURE 3 NOTATION FOR INTERSECTION O F SHOCK WAVE AND ITS F LOW F IELD -15Z- THEORY (LIMITING CASE) JPL TEST (REF 2) Moo = 2.01 Rb -- !.0 / / i

r i.4 /

/

I I M_ _ BOW-SHOCK W AVE

I------- __7

// i JET BOUNDARY I SEPARATION-SHOCK :::::::::::::::::::::::::::::::::::::

, k

Rb ........... .

/ .°." *o" " ". • .........

/ I ....... :: .......... :_

/ ........ :: ...........

I 2 3 4 5 6 7 FIGURE 4 SHOCI< WAVE STRUCTURE CONSTRUCTED FROM THEORY (LIMITING CASE) COMPARED TO VISUAL OBSERVATION FROM SCHLIEREN PHOTOGRAPH (REF. 2) ' " " • " ' ' / , .°" "°, / .°. ,°.°,, ' ' ' ' ' / '°.°,°. / ... • .°.°, • °, ' ' " ' / • •, .,, ....°,°...°.°°°°, ' / '°" '°'°'°, ...°..°...°,°, ,°,.., I ................... 'Z'X'Z'Z'X'Z'Z.Z.:.Z ,-4 i"r" ,..,,°°,.., Z // °,.,, o ,", v.v.v. : ._Ov.v.v.." _ "-" r--4 z ".v.v.'.v.'. _v.v.v."" N £rl ' / .L'.' . '.'.".'. I'Y'.','.".'.'.'° ° o I v.v.v.'.v,_v,..v.v.. < N \ _ v.',v.v...., _-v.v.v.v 0 ' _ t v,v.v.v,',_,v.v.v." ,--1 < N

½

Z'X'Z'Z'_°'X'X'XC i _

'::::::::: S:::"'::: o

.................. _ r.-4 O \ _.X.Z.X.Z.:_,X.Z.X.Z ;z; _, / ,v.'.v.'.v.'.a-v.v.v.v. r-4 0 \ .X-:.X.Z.Z.__}Z.Z.ZC. O __ ' " / "" / "°'"°'° J "°'"' / "'°'°' \. \ '.'X':'Z'Z'X':':'Z.'-"Z: _ © r.4 r-4 3::; ,--, • -b.... / ° ° .,°. ., , . // ,°, ZC'"}Z- ? "Z'X'Z" _ ,-1 "' -', "':'Z".'.':'X':'X':'Z N O

....... :i:i:i:i:i: o

o _ 0 -r •_ o ;D 0 a3 >- uJ N o _" rr • ,_ [-4 _ _ _ _ _ 0 0 . . u _ W 0 D

' I Qm

I m 0

{

Jo _ m ', ,.)

_r) oJ -- 0 -_54-

4 1

f" _ TRACE OF BOW-SHOCK WAVES o _ /" PLATE ) / ff ''" I (IN PLANE NORMAL TO /f t .5 / (I) I-- ° C Z / / , / i -LOCUS OF MAXIMUM '

r_ / / /4/ I . .- ff__ . . _" L PRESSURE OOEFF , C , ENT

o / . , I" / /',_' / I , - -

',' / ,//" - _ / _" i

<° , / / i / ./ _ ', !

, F- / / L_ (..) I / ' / " ' 0 / / o / . ._ S , _ I PRESSURE RATIO - Pj / P 0 ' 677

/ , ,,/ ,247

o I I[

-I 0 2 5 4 5 6 DISTANCE DOWNSTREAM OF JET - IN.

JET LOCATION F IGURE 6 DEPENDENCE O F SHOCK WAVE C ON F IGURATION ON GASEOUS INJECTANT F LOW KATE THROUGH A CIRCULAR PORT IN F LAT PLATE (REF, 5) FIGURE 7 DISPLACEMENT THICKNESS FOR APG-t NOZZLE (TEST NOZZLE SIZE)

-156-

.016 w , .012 rn o " r _ o . 008 n. - o w ,004 d n"

o N

0 6 7 8 9 I0 I 12 x RATIO OF AXIAL DISTANCE FROM THROAT TO THROAT RADIUS RT .08

f

rr e LEFT SIDE W w .06 / OF EQ.

< E (_8) ----'_ a . . 04 J _o

/

F- 0 RIGHT rr .02 _ SIDE <[ r OF EQ.

Q_ W POINT OF , E(18) e3 SEPARATIO N.I__ __.._ 0 h 6 7 8 9 I0 I 12 x RATIO OF AXIAL DISTANCE FROM THROAT TO THROAT RADIUS RT FIGURE 8 SEPARATION POINT AND PRESSURE DISTRIBUTION IN APG-I NOZZLE WITH NO SECONDARY INJECTION -157- O . O6 I I Q .

... / -- X p= 20 ,-, o.o5 g ..

-- I I - I: E 0.04 t 1 LLI rr 03 I 03 I- - - n. - w n 0.03 E rr" oo "r 0.0 2 _ < _ _.p= 47 0 Z , ( J i. . 4_ 0 , I 0 I- I-- J < (

/

I

_ J° . , . - X D=3 9 0 TO I10 oo o , "-_-__ 1 /.

T H EORE T ICAL_ _ --__ _ I // I ......... I _--: _ _'_' -" "" o ' _ , 4 5 6 7 8 9 I0 II 1 2 15 R A T I O O F A XI A L D I ST A NCE F ROM T HRO A T T O T HROA T RA D I US - X / R T FIGURE 9 EFFECT OF TEST PRESSURE RATIO ON THE WALL PRESSURE DISTRIBUTION WITH NO SECONDARY INJECTION IN THE APG-1 NOZZLE

EXIST I NG _ECT_0N ---X 0PPOSED-'ANGENT , AL PORT

_EW R,NG-_ \ C0NF , GURAT,0N

EXrST I N G SECTION _ \ _ , f --] !

M U L TI RA DI A L P O R T C ON FIGURATION F IGURE l 0 SKETCH OF CONICAL NOZZLE WITH MODI F ICATION AND TYPICAL INJECTION PORT CON F IGURATIONS I O PP OS ED - T AN GI _NT I AL P ORT CONFIq URATIO N FIGURE 1 1 SKETCH OF APG-I NOZZLE WITH MODI F ICATION AND TYPICAL INJECTION PORT CONFIGURATIONS FIGURE 12 APG -l AND CONICAL NOZZLES -1 61-

N OR MAL TO W ALL SECTION I-I FIGURE 1 3 SKETCH SHOWING INJECTION PORT ORIENTATION -16Z- _. 188 20g__ , _F"-- 1,316 --- 4 _, TYPICAL SECTION PORT C 8 ° = 60 I_IGUR]_ 14 I:_ORT O R IENTATION AN D SPACING OF MULTIRA D IAL I:_O R T CO N FIGURATIO N FOR CONICAL N OZZLE -163- _ 67 6 PORT A 8 °= 180 i ' t #1 #2 PORT B 8 °= 300

=.,8.- / '_

-_ _' / .. _- ,,,,-- _.

, _ PORT C 8 ° = 60 TYPICAL S E CTION FIGURE 1 5 PORT ORIENTATION AND SPACING OF MULTIRADIAL PORT CONFIGURATION FOR APG-1 N O ZZLE -164- . 595 6 6 -0 3 PORT A 8 " = 180 .489 PORT B 8 ° = 3 00 _-. 26 ° '_7 ",--. 74 - --- _.195 \

69_

PO R T C TYPIC AL SECTION 0 ° = 60 FIGURE 16 PORT ORIENTATION AND SPA C ING O F OPPOSED-TANGENTIAL PORT CONFIGUR A TION F OR CONICAL NOZZLE -165- ""TL • • TVC COR TY . MINNESOTA n , ETC CIL/ '"' :IE I<:/iTIO SIZE, r/J .

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C- ASSEMB

...... 0' -0 FIGURE Z l P R F __SURE TA P LOCATION FOR CONICAL NOZZLE -171 - 3 .

900" FIGURE MEASURED MULTIRADIAL PRESSURE 2 .

PORT " CONFIGURATION TAP LOCATIONS I .

1.000"

I

FROM INSPECTION 9 .

3 .

- 382"

J R

944" !

IN CONICAL NOZZLE,

I

• f----t--- .

898"

x

1145" I.

839" -t--- .

605" -l 5 .

002" 5.1 4 1" 5.

999" TAP NO 4 C 10 13 14 15 16 17 1 18 B 1 19 20 21 4A 4B 5A 5B 5C I I 12 1 1 8A 8C 6 7 8 9 3A 3B 2 3 C .

2 . 2 . 3 . 2 1 5 1. 1. 1. 2 10 2 . 2 . 3 . 1. 1. 1. 2. 2 .

1. 1. 2 14 1. 1.4 1 1. 4 4 4 2 . 2 . 3 .

.450 .72 . .472 . .720 .97 975 460 455 445 976 471 204 068 207 72 96 470 208 Z1 2 068 720 217 212 X 198 2 7 2 2. 2.002 1.738 2.

2 . 2 . 2 . 1 2 . 2 . 1. 1. 1. 1. 4 1. 1. Z. 2 . 2 . 2 . 1. 1. 1 . 39 1 1. 1 . 1.

2. 2. 2 . 1 .998 003 252 084 083 084 788 563 165 997 999 474 338 339 253 086 082 088 00 788 740 562 392 304 R 66 77 1 1 2 . 1 10 . 1 5 . 1 13.640 13 1 0 . 14 . 1 1 2 . lZ 1 7 .

17. 15.933 14.725 1 1 13 3. 2. 2.578 9.497 7. 6 . 6 . 5 . 3. 7 . 721 6 . 2.578 9.497 6 .

3.

. .

.

-173-

032 72 875 250 400 933 640 640 032 250 725 578 578 875 173 A 1 640 640 640 578 578 190 200 ZOO 200 200 200 200 Z10 180 180 180 180 180 1 180 180 1 1 180 1 1 180 1 1 190 1 1 1 1 90 90

e 80 80 80 80 80 80 90 90 90

TA NO.

22A 22B 2 23 24 25A 25B 25C 26 27A 27B 27C 28 29A 29B 29C 30A 30B 30C 31 32 33 34 35 36 37 38 39 2C P 1.215 1. 1. 2 13 2 . 2 . 7 1 6 1. 2 1. 2 1 1 1. 1. 1. 2 10 1. 2 1 2 2 . 1. 2 1 3 1. 2 1 5 1. 2 1 0 1. 2 18 1. 2 16 1.200 2 . 2. 2 . 2 . 2 . 2 . 2 . 7 1 7 2 . 2.467 Z.

.

069 975 469 220 470 97 47 967 X 210 210 722 210 075 218 2.083 2 . 2 . 2.084 2.252 2 . 2. 2 . 2 . 2 . 2 . 2.081 2 . 2.084 1. 1 2.084 1. 2 . 1. 1.735 1.649 1. 1. 1 1 1. 1 . 1.

.564 .649 .564 082 787 083 083 084 083 475 083 082 084 081 087 649 476 650 477 R 785 736 1 3 . 13.640 13.640 10 13.640 1 1 15 13 13 1 3 . 1 3. 1 3 . 13 . 13 . 13 . 1 3 . 10 6 . 8 . 9.497 8 .

7 . 3.6 3.640 6.875 8.543 7 . 9.497 8 . 6.875 . . . . .

A 640 032 933 640 875 640 640 640 640 640 640 72 640 640 543 543 032 721 543 4 0 210 210 2 10 210 210 2 70 270 270 1 1 1 1 190 190 1 200 200 ZOO 21 0 2 10 2 10

e

90 90 90 80 90 70 70 70 0 0 0 0 0 3 .9 0 0 " I· 1-- FIGURE MEASURED OPPOSED - - --- TANGENTIAL PRESSURE 2.

" TAP PORT LOCATIONS CONF IGURATION

I~

I

O"

FROM INSPECTION 9 .

---L-----

3 .

" " R

I

IN CONICAL

t-

NOZZLE .

8 " x -t , ---- 1.145" - -+ .

5 " 5 .

002" 5 .1 " 5 .9 9 9 " TAP N O .

4A 4B 4C 5A 5B 5C 10 11 12 13 A 13B 13C 14 1 5 16 17 1 18 B 18 C 19 20 2 1 8 9 8A 1 2. 3 6 7 1. 1. 1. 1. 1. 1. 2.068 2 . 2. 2 . 3 . 3 . 1. 1. 1. 2.068 2.720 3.217 1. 1. 1.455 2 . 2 1 2 2 .

.471 .72 . . . .975 .

X 971 462 462 458 969 470 462 460 976 472 209 212 206 207 722 215 72 2 10 2 13 2 0 2 2 . 2 . 2 . 2 . 2. 2 .

2 . 2.253 2. 2 . 2.083 2.085 1. 1. 1.998 1. 1. 1 1. 1. 1 . 1 . 1. 1. 1. 1. 1. 1 . 1.

.562 084 997 997 477 304 08 083 085 997 997 999 R 339 166 788 740 392 252 788 563 391 165 738 474 338 17. 15. 1 13. 13. 13. 12.529 12 12. 10 15 13 13 13 10 . 14.725 12. 12 12 . 17.

4. 9 . 7.72 6. 9.497 6 . 5 . 7 . 721 6 . 6 .

. . . . . . .

A 933 725 644 644 644 529 032 497 875 250 400 933 644 644 644 032 250 529 529 529 875 173 17 529

-175-

3 1 180 18 0 180 180 180 180 180 1 180 180 180 190 190 190 190 190 190 200 200 200 200 200 20 0 210 180 180 L80 J80 190

e

T N O .

22 2.2B 22C 23 24 25A 25B 25C 26 27A 27B 2 7C 28 29 29B 29C 30A 30B 30C 3 1 32 3 3 34 35 36 37 38 39 40 AP A A 1. 2 10 1. 1.209 2 . 2 . 7 16 1. 1. 1. 1.209 1 . 1. 2 . 1 . 1. I. 1. 2 13 1. 1. 2.469 2 . 2.47 2 . 2 . 2.47 2.7 2.

2 . 2 .

.

X 2 08 069 975 210 205 203 722 205 2 10 209 210 208 208 206 220 970 075 2 18 467 967 0 1 Z. 2 . 2.084 1 . 1. 2.083 2 . 2.086 2. 2 . 2 . 2 . 1. 2 . 2 . 2 2 . 2.084 2 .

1. 1. 1. 1. 1. 1. 1 . 1. 7 1. 1.

.

.0 R 083 084 787 564 085 252 084 085 083 475 084 083 085 083 649 735 649 476 785 649 564 650 477 13 13 . 13 . 10 . 13.644 13 . 13 . 1 1 3 . 13.644 13 . 1 3 .

13 . 13 . 13 . 13.644 13 . 10 .

7 . 5.933 6 . 8 . 9 . 8 . 6 . 8. 9 . 8.

7.72 6 .

.

A 644 644 644 032 72 644 644 644 64 875 644 644 644 644 644 543 497 543 875 032 543 497 875 1 4 2 10 210 210 2 10 2 10 2 7 0 270 27 0 17 170 17 0 1 1 190 1 200 200 200 210 2 10 2 10

e

90 90 90 80 90 90 0 0 0 0 0 0

l

__

3 .

" FIGURE MEASURED MULTIRADIAL PRESSURE 2 .

PORT 2" ---- CONFIGURATION TAP LOCATIONS -f- - --+ 1.

002" FROM -- -.

- INSPECTION -- 9.4 -- " 5.486"

~ IN

APG-I R NOZZLE,

.-

x 1.5 0 / 1"

I •

1 .

4 .

627" " 5 .1 0" 5 .

-

654" --- TA NO.

lA I B lC 11 1 2 1 3 14 15 16 17 18 19 20 21A 2 1B 21C 2 3 5 6 7 8 9 P l. l. 2.21 2 . 2 . 3 . 3 . 1. 2.47 3 . 1 2 . 2.97 l. 1. 4 74 .405 .406 .405 .728 .965 .72 .979 .722 .411 . .

X 471 969 408 411 7 17 971 458 979 222 477 229 224 8 1 0 1 2.454 2 . 2 . 2. 3 2. 2. 201 2. 2 . l. l. 2 . 2 . 2 . 1. 2. 2 . 1 l. 1. 2.453 2.454 2 .

1 1. 1. l.

.958 R 454 454 869 624 956 453 337 126 043 67 678 626 529 395 200 044 333 682 93 24 1 18.9 18.919 18 17. 15.2 1 4 . 17 3 1 3 . 12.032 1 0 . 18.005 1 13. 1 1 7 . 1 4 . 1 12 1 18 18 8.9 8.9 8.867 8. 7.345 0. 8. 8 .

5.2

-

. 0 0 5 . 0 3 2 . .

A 867 919 919 14 3 113 986 296 113 986 296 143

177-

19 19 19 19 19 1 1 180 180 1 180 180 1 1 1 1 180 18 1 190 190 190 190 200 200 200 200 2 10 210 2 10

e

80 80 80 80 80 80 80 90 TAP NO.

40 90 91 22 23 24 25 26 27 28 29 30 3 1 32A 3 32C 33 34 35 36A 36 36C 37 38 39 2B B 1. 1. 2 . l. 2 . l. 1 1 . 1.481 l. l. l. l. -.

.728 · 4 1 1 . . . .727 · 41 1 . .4 · .

X 470 972 469 474 47 976 471 467 400 405 973 408 224 949 0 239 243 732 312 1 1 2.20 2.043 2.453 2 . 2 . 2 . 2.271 2. 2.339 Base Base 1. 2.200 2 . 3 2 . 1. 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 .

R 869 455 454 453 454 453 20 68 20 202 267 333 265 12 393 199 1 1 1 3 15 13 . 10.986 1 5. 2 1 9 18 . 1 5. 15 1 5. 16 . 1 1 1 18 . 1 1 6 . 14. 18.919 18 . 18 18.005 16 1 5. 2 19 17 8.867 8.9 8.9 1.143 A . 2 19 . . 9 19 . . 1 113 005 219 219 219 919 919 160 173 160 60 19 43 210 210 210 270 1 7 0 1 1 190 1 190 1 190 200 200 200 200 200 200 210

e

80 90 90 90 90 0 0 0 .

3 .

899" FIGURE MEASURED OPPOSED- TANGENTIAL PRESSURE 2 .

852" -- TAP PORT ----t----+- LOCATIONS CONFIGURATION 1.00 FROM 2 " ------ INSPECTION 9.468 "

_ L. 5.489"

IN APG --------- -I R NOZZLE,

x

~1.499"1 , •

I

4 . . 6 2 996" 8" 5 .

100" 5 .

652" TAP NO.

lA IB lC 16 17 18 19 20 21A 21 21C 10 11 12 13 14 15 2 3 5 6 8 9 .B 1. 2.458 2.979 2.470 3.229 1. 2. 2.971 1. 1. 971 2.218 3. 3.477 1. 1.

.415 . 4 19 .414 .728 . .721 .979 .414 .417 .

471 717 222 474 969 722 224 414 X 2. 2.451 2 2. 2.337 2. 201 2. 126 2. 395 2. 200 1. 624 2. 333 2.124 1. 2.452 2.451 2.452 2. 043 1. 958 1. 673 1. 678 1. 626 1. 2. 044 1. 1.

.4 R 452 "869 393 956 682 18 18.886 18.005 17. 1 14. 173 12.0 18 . 886 18.886 14. 173 13.113 12.032 10 . 986 18 . 15 13.113 10. 17. 143 18.886 18.886 5.219 8.867 8 . 296 8 . 296 8 . 867 7.345

.886 -179-

A . 2 143 005 986 19 32 180 18 0 180 180 180 180 180 190 200 200 200 200 210 210 210 180 180 180 1 180 1 19 1 190 19 0

e

80 80 90 TAP NO 40 90 22 23 24 25 26 27 28 29 30 31 32A 32B 32C 33 34 35 36A 36B 36C 37 38 39 91 .

1. 2.469 1. 1. 2.976 1.467 1. 239 1. 243 1. 727 1. 1.481 - . 320 1. 1.

.723 . . . . . .413 . 4 15 . 732 .949 470 972 474 470 471 414 416 413 973 416 X 224 0 2.043 2.394 2 . 2 . 2.452 2.393 2.271 2 . 199 2.339 Base Base 2 . 201 1. 869 2 . 200 2.201 1. 2.201 2. 2 . 2 . 2.452 2 . 2. 333 2 . 2 . 451 R 452 452 452 680 202 267 265 123 15.2 13 . 10 . 15.219 18.005 15.219 15.219 16 18 . 18 18 11. 16 14. 18.886 18. 18 . 1 16 . 15 . 17. 143 15 . 2 19 8 . 8.005 .1 . . .1 A 986 867 886 886 886 886 886 219 113 143 173 160 60 60 210 270 190 200 200 200 200 200 200 210 210 210 170 180 19 190 190 1 19

e

90 90 0 0 0 0 0 I I 2.2 I I (x / L )in j = 0 . 6 9

._ 2o _ dj = o.la8 _NcH

(Z_----C) dj = 0.256 (REF. I) I 1.8 n_ o F- u_

° \

1.6 _ Z < (Z)..

u_ 1.4 "_ "_ ._..

Q..

1.2

3_

< 0 0.02 0.04 0.06 008 0.10 0.12 WEIGHT FLOW RATIO -- VVs / Wp F IGURE 27 EFFECT OF INJECTION PORT DIAMETER ON THE AMPLI F ICATION F ACTOR USING SINGLE PORT IN- JECTION IN THE CONICAL NOZZLE -181 - a. ° 0.05 I i i I 1 " -- (x / L ) i n j - 0. 69 I

" I - - I

o w s / wp - 0. 0 3 i

m _- 0.0 4 I _ d j = 0,1 88 I N C H

I

W CZ)- --- -C_ dj . = 0 . 2 5 6 I N CH (R E El) I .......... UNDISTURBED W A LL P R ESSURE I

0,03 ,} , i l I f )

n _ I u a _ I

n_ / "' 1

w 0 . 02 m / I / ,,, < / _jI I "r" I NI ¢J N m ol , o 0.01 "', i - - ... I I ._j " , ... I • " " I"

o ............. ,,,_ . _. _ , 0 I N JECTIO N PO R T y

° I , J 0 _ / i I I 4 5 6 7 8 9 I0 II 1 2 R A TIO OF AX I A L DIST A N C E FROM THRO A T TO THROAT R A DI U S - x / R T F IGURE 28 E F FECT O F INJECTION PORT DIAMETER ON THE WALL PRESSURE DISTRI- BUTION IN MERIDIONAL PLANE IN THE CONICAL .NOZZLE USING SINGLE PORT INJEC TION (x / L)inj = 0.69

Ws / wp = o.o3

dj = 0.188 INCH C_)---_ dj = 0.256 INCH (REF I) ......... UNDISTURBED WALL PRESSURE I 0.04 o X I-- x - 7.5 x = 70 -- = 6.5 R T _ RT n- , w D _ _ r r .j Oo o. 0.02

,,, o.o

i n.- W m T u O.OI 0 ...............................

I,--- ...........................

.. A o 0 o 0 I0 20 30 0 I0 20 30 0 I0 20 30 , _1 CIRCUMFERENTIAL ANGLE - 6' - DEGREES FIGURE 29 EFFECT OF INJECTION PORT DIAMETER ON THE WALL PRESSURE DISTRIBUTION IN CIRCUMFERENTIAL PLANE IN THE CONICAL NOZZLE USING SINGLE PORT INJEC TION 2.6 I w ] (x / L) inj = 0.95 di = 0 . 188 INCH 2.4 --C:)---O dj : 0.256 INCH (REE I)- • _ 2.2 _ 2.0 n.- U

o

1.8 \

z \

£ \

U -- 1.6 J Q.

1.4

I

1,2 < 0 0.02 0.04 0.06 0.08 0.10 0,12 WEIGHT FLOW RATIO -- Ws / _ / p FIGURE 30 EFFECT OF INJECTION PORT DIAMETER ON THE AMPLIFICATION FACTOR USING SINGLE PORT INJECTION IN THE APG-I NOZZLE -184- U -- I I l n 0.0 5 j O .

, (x / L) i n j = 0.95 I

P. Wszwp : o.o3 I '

0.04 <_ _1 dj = 0.188 INCH W rr C_-'--"'C) d j = 0. 2 5 6 INCH (R E E I) O3 co ........... UNDISTURBED WALL PRESSURE

w 003 t

13:: O_ W X m wJ :_ 0.02 --r w i (. ) _ IJ J _ -- It N _n O O ' _ 0.01 z_ "-..o.

_I • • ,, - .... , . , , ° . .oo,,. o • • .. - _: I. . . Jl o T 0 " 4 5 6 7 8 9 I0 II 12 RATIO OF AXIAL DISTANCE FROM THROAT TO THROAT R ADIUS- x / R T FIGURE 3 1 EFFECT OF INJECTION PORT DIAMETER ON THE WALL PRESSURE DISTRI- BUTION IN MERIDIONAL PLANE IN THE APG-I NOZZLE USING SINGLE PORT INJEC TION (x / L) inj = 0 . 95

ws / wp : 0 . 03

_ dj = 0.188 INCH 0 d j = 0. 2 56 I N CH (REF. I) ........... UNDISTURBED WALL PRESSURE ,., 0.05 r , I o 0.04 = I0 . 0 _L = 9.0 I - 8.0 n -" RT RT RT w n."

_ n 0.03 U ') W 13-

, _. _: cD

_ . w 0 0 2 / " "_ o00, . .

--J .................................................................

o -J O 0 I0 20 30 0 I0 20 :50 0 0 20 50 CIRCUMFERENTIAL ANGLE - 0 - DEGREES

FIGURE 3 2

EFFECT OF INJECTION DIAMETER ON THE WALL PRESSURE DISTRIBUTION

IN CIRCUMFERENTIAL PLANE IN THE APG-I NOZZLE USING SINGLE PORT

INJEC TION

2.6 I I I I

APG -I NOZZLE, (x / L)in j = 0.95 _7----_ CONICAL NOZZLE , (x / L)in j - 0.69 2.4 (_ CONICAL NOZZLE, (x / L)in j =0.95 , (REF I)-

, ,, ]

2.2 _ 2.0 I x . _ '_,.

1 .8 "_ I \ n_ < 1.6 t L Z

_o c:_

_- 1.4 ( J tl_ _ 1.2

]

0 0.02 0.04 0.06 0.08 0.10 0.12 WEIGHT FLOW RATIO -- W s / Wp F IGURE 33 COMPARISON O F THE AMPLI F ICATION F A C TOR BETWEEN THE APG-I AND CONICAL NOZZLES USING SINGLE PORT INJECTION -187- o Q , .

__ 0.04 I I I I I I

, t

,-, (x / L) inj = 0.95 I

i _ / s I Wp = 0.03 I

o_ 0.03

<] 'Q dj = 0.188 INCH, APG -I NOZZLE I "¢ I a::: C)----C) dj = 0.256 INCH , CONICAL NOZZLE (REF. I) I

o.o 2 ,I

u_ I a_ \ xl ,,, '" O.OI I'_J' E ' L _ \ I ,,, ' rrl / -J Oo _ / N Oo .:_ / N , T C_ 0

\ w l

o 0 < . _ _._---C)---_ _ z L__ ) o

_ k

o INJECTION POR uJ i rn

n - 0.Ol ____A /

4 5 6 7 8 9 I0 I 12 p- O r ) RATIO OF AXIAL DISTANCE FROM THROAT TO THROAT RADIUS -- x / R T FIGURE 34 COMPARISON OF WALL PRESSURE DISTRIBUTION IN MERIDIONAL PLANE IN THE APG-I AND CONICAL NOZZLES USING SINGLE PORT INJECTION (× / L)inj = 0.95 W / W = 0 . 03 dj : 0.188 INCH, APG - I NOZZLE C) dj = 0.256 INCH, CONICAL NOZZLE (REF I) o. 0.04 i Q.

I 0 X X X -- = I0.0 -- = 9 . 0 -- = 8 . 0 _- R T RT R T <:[ a: 0 . 03 W n-- u 3 ¢,3 w 0.02 n - o.

I W CO -..o, o_T 0.01 C_,__ _ _ "" _-.._ o F-.- ,'-, 0 w nn rr" E3 I- Go _' 0.01 L 0 I0 20 30 0 I0 20 30 0 I0 20 30 CIRCUMFERENTIAL ANGLE -- 8 -- DEGREES F IGURE 35 COMPARISON OF WALL PRESSURE DISTRIBUTION IN CIRCUM F ERENTIAL PLANE IN THE APG-I AND CONICAL NOZZLES USING SINGLE PORT INJECTION 2 . 6 2.4 MULTIRADIAL PORT 0 c / dj = 1.8 [] c / dj = 2.5 /k c / d : = :5.5 2.2 ----- J -- SINGLE PORT

°1 •5 "--_ V dj = 0.188 INCH

C) dj = 0.256 INCH (REF. t)

2.0

I i- 1.8 (..)

I.i_ Z o 1.6 u __ ... / n 1. 4 ............... "_--"_ i I 1.2 ....

r

o 1 t

0 0.02 004 0.06 0.08 0.10 0.12 WEIGHT FLOW RATIO-- Ws / Wp FIGURE 36 INFLUENCE OF WEIGHT FLOW RATIO ON THE AMPLI- FICATION FACTOR USING SINGLE AND MULTIRADIAL PORT INJECTION AT (x / L)inj = 0.69 IN THE CONICAL NOZZLE -190- 2 .4 2. 2 V

2 .o

I 1.8 W s / W p= 0 . 0 3 _r o z 1, 6 0 . 0 6 L -3 1.4 0.09 o_ 1 . 2

>

o ]--^

V 0 1.6 2.0 2 .4 2.8 3.2 3.6 4.0 INJECTION PORT SPACING-- C / dj F IGURE 37 E FF ECT OF INJECTION PORT SPACING ON THE AMPLI F ICATION F ACTOR USING MULTIRADIAL PORT INJECTION IN THE CONICAL NOZZLE -191 - 0.06 I ' ' I I (x / L) in j = 0.69 o 0 0 c / dj -" 1 . 8 Q..

"" / 0 .... -1 3 c / d i = 2.5 J " 0. 0 5

P

I z3-----.-._ c / di = 3.5 o ........... UNDISTURBED WA L L PRESSURE 0- 004 W if) w _. o.os I, , / u .....

t--

0. / / -

w ,,.o _ 0.02 0 0 F- Z 0.01 "_ 0 " " ........... "" d INJECTION POR,T I )_

o %

4 5 6 7 8 9 I0 II 1 2 RATIO OF AXIAL DISTANCE FRO M THROAT TO THROAT RADIUS -- x / RT FIGURE 3 8 WALL PRESSURE DISTRIBUTION IN MERIDIONAL PLANE OF INJECTION IN THE CONICAL NOZZL E USING MULTIRADIAL PORT INJECTION (_ / ,_ = 0. 03) s p (x / L) inj = 0.69 c / dj = 1.8 El-----El C / dj = 2 . 5 _---.-- - -.-A c / dj = 3.5

.......... ,,,,,o,sto,,,,_ o,, ,, ,.L P,_ssu,,_

._°°_ .. l I

I = 7.5 _ : ZO x - 6.5 I--0 RT RT RT ,,_ 0.04 a: _..

0.03 rr "\ / _'----,, .._ w O, 02 \\ "_ "-.._ i _ I ._ / "_" "_ \ o 0.01 ........ i. ....... i ........

(..)

o J 0 j 0 I0 20 30 0 I0 20 30 0 I0 20 30 CIRCUMFE R ENTIAL ANGLE - 8 - DEGREES F IGURE 39 WALL PRESSURE DISTRIBUTION IN CIRCUMFERENTIAL PLANE IN THE CONICAL NOZZLE USING MULTIRADIAL PORT INJECTION (@ / ,_ = 0.03) s p | 0.0 5 I i I n °... _ MU L TI R ADIA L PO R T, c / dj = 1.8 , _ / s / Wp = 0.03 I rt ?- - -_ 7 SI N G L E POR T , d i , = 0 .188 I NCH , _ / s / W p = 0 . 0. 3 I I I o 0 . 04 _ ..... UN D ISTURBE D W A LL P R ESSU RE I ¢Y ILl n."

_0 0.0 3 ( J _ l I n x W nn Q0 2

,,, _ !/, T \

:= I/ ',. 7 ' "

t-_ I . N ' 0 Z ""'l.

t-- 0.01 ....

. J "--... . .

| 0 i ........ "J I NJ EC T IO N POINT ^ = , V 0 4 5 6 7 8 9 I0 I I 12 RATIO OF A XI AL DIS TA NCE F R O M THROAT TO T HROAT R ADIUS x / R T FIGURE 40 COMPARISON OF THE WALL PRESSURE DISTRIBUTION IN MERIDIONAL PLANE IN CONICAL NOZZLE USING SINGLE AND MULTIRADIAL PORT INJECTION MULTIRADIAL PORT, c / dj = 1.8 , Ws / W p = 005 _----_ SINGLE PORT , dj = 0.188 INCH, Ws / W p = 0.0 3 ............. UNDISTURBED WALL PRESSURE 0.05 I t o I ,._ 0.04 x x ' l x -- = 75 -- = ZO ' -- = 6 . 5 n r R T RT i Ilg m 003 "- I f ) _, .

l.,u \ t Y \ " - m 0 . 02 I _ ,' - ,.0 _ i _, .- Ln , c_ , , . .."

, 3- / _- _- J_" c.) I | o

i I- 001 I " " -,,_

_J I _ ......... 4 ........ d ........

o _i

0 I

0 I0 20 30 0 I0 20 30 0 I0 20 30 CIRCUMFERENTIAL ANGLE - 8 - DE G REES FIGURE 4l COMPARISON OF THE WALL PRESSURE DISTRIBUTION IN CIRCUMFERENTIAL PLANE IN CONICAL NOZZLE USING SINGLE AND MULTIRADIAL PORT INJECTION 0.06 , r I (x / L) inj = 0 . 69 u 13..

"-. 0--------0 c / dj = I. B 0.

I [3- .... -El c / dj = 2. 5 o 0.05 _--.--.--Z& c / dj = 3. 5 -- 4 I-- ,.......... UNDISTURBED WALL PRESSURE r' t- n. 0.04 I I m // n-- n n- 0.03 T , 0.02

o ,,I

' t NI _. A "'... . _ N _ , ° I c _ 0 . 01 , O • " .

° ° . . • . . , . .... ° . . _ 4 5 6 7 8 9 10 II 12 RATIO OF AXIAL DISTANCE FROM THROAT TO THROAT RADIUS - x / R T FIGURE 42 WALL PRESSURE DISTRIBUTION IN MERIDIONAL PLANE OF INJECTION IN THE CONICAL NOZZLE USING MULTIRADIAL PORT INJECTION (_ s / _ = 0. 06) P (x / L) i n j = 0.69 0---------.0 c / dj : I. 8 [3------.[3 c / dj = 2 , 5 Z&.- .... -A c / dj : 3.5 .......... UNDISTURBED WALL PRESSURE 0.06 a. x : 7. _..L =7.0 x'--&-- : 6 . 5 u. 5 _" "_T RT RT o / _"'- 0 0 4 / " k,. ' _ _ J.

W •

, _ o.o2

0 001 I-- ......... . ................ I .......................

_J (.3 " 0 0 I0 20 30 0 I0 20 30 0 I0 20 30 CIRCUMFER E NTIA L ANGLE - e -- DE G REES FIGURE 43 WALL PRESSURE DISTRIBUTION IN CIRCUMFERENTIAL PLANE IN THE CONICAL NOZZLE USING MULTIRADIAL PORT INJECTION (_ /qv : 0. 06) s p 0 . 06 l , I 1 I (x / L ) inj = 0. 69 O O c / dj = 1 . 8 o 12} O c / d, = 2.5 n J \ 0.05 ,,% .... /k c / d- = 3 , 5 J I ............... UNDISTURBED WALL PRESSURE

o I

rr 0.04 ....

iii u 'J _9 Q::

"' / /li

n ,- a" 0. 0 3 i _ / I --r- o 0.02 • _ O ILl 0 0 O / I-- N N • .J I O m < I, ". Z o 0,01 • "" • -

, o ! "

d - ..... [ • . . , ° . , , • . . ° 0 -_,, -. ,, 0 _ 4 5 6 7 8 9 I0 I 12 RATIO OF AXIAL DISTANCE FROM THROAT TO THROAT RADIUS--x / R T FIGURE 44 WALL PRESSURE DISTRIBUTION IN MERIDIONAL PLANE OF INJECTION IN THE CONICAL NOZZLE USING MULTIRADIAL PORT INJECTION ( 4 Vs / _ V p = 0.09) (x / L)in j = 0 . 69 0 0 c / dj = 1.8 []- [] c / d j : 2 . 5 A, -_ c / d j = 35 ............ UNDISTURBED WALL PRESSURE a _ \ _ x ,-, _ = 7 . 5 = 6.5

ooo I

,_[ _, - _" ""_ , _,, _rg 0.0:5 "-- ""t I , "\ I ]--'_:---"'_,..- 03 n -" , a_ "" ].,.._ -. D ILl , m 0.02 - 1- o I- 0.01 .J ......... , ......... • ............

t ) ......... _ ......... ,.........

o .._1 0 I0 20 5 0 0 I0 20 30 0 I0 20 30 CIRCUMFERENTIAL ANGLE - 8 - DEGREES FIGURE 45 WALL PRESSURE DISTRIBUTION IN CIRCUM F ERENTIAL PLANE IN THE CONICAL NOZZLE USING MULTIRADI A L PORT INJECTION (@ / @ = 0. 09) s p O.05 1 _ .u MULTIRADIAL PORT Q .

i (3--- - -- -- 0 c / dj = 1 . 8 _ / s / Wp =.0 6 O } .

nr Z 3------ _ c / dj = 3 . 5, _ / s / _, ' p = . 0 6 <_ 0.0 4 / _i . _.._ E] ---' E ] c / dj : 2.5, Ws / W p = . O6 4 n- _ " S INGLE PORT ( / ) (_ 0.03 _- ..... "_ Ws / w p = .02 L d t_ I - - 1 3_ X n ," W w 0.02 t',o "3- N

. -," " 2/ ..," " "'

o o ( . .) lUL l..._ / O N O INJECTION PORT ' o < _ - ° 'J 0.01 "_ 7 i_ _ _ z J O _ %, ' ' J 0 4 5 6 7 8 9 I 0 II 12 RATIO OF AXIAL DISTANCE F R O M TH R OAT TO THROAT R ADIUS--x / R T FI G URE 46 WALL PRESSURE DISTRIBUTION IN MERIDIONAL PLANE OF INJECTION IN THE CONICAL NOZZLE USING SINGLE AND MULTIRADIAL PORT INJECTION 0 . 06 SINGLE PORT DATA--Ws / VVp=.02 MU L TI R ADIAL PO R T DA T A--

. 0.05 v_s / Wp =.06

im I PRESSURE FROM SUPER - O POSITION OF SINGLE PORT DATA I,.- < .......... UNDISTURBED WALL P R ESSURE 00 3 / i _ _ - \ .... I " \ ' , ffl I "1- r_ u 0 0 2 : __ _ < O ._1 ............ _.. . _._. . _ .......

INJECTION PORT LOCATIONS I _ I o i I , FIGURE 47 COMPARISOi_ OF THE WALL PRESSURE IN CIRCUMFERENTIAL PLANE (x / R T = 7. 0) OBTAINED FROM SUPERPOSITION OF SINGLE PORT DATA WITH MULTIRADIAL PORT DATA IN THE CONICAL NOZZLE

006 I I

S I NGLE PORT DATA--VTVs / W p =.O2 M ULTIRADIAL PORT DATA-- a?... 0 . 05 _ / s / _ / p=0 6 I I / "_ PRESSURE F R OM SUPE R - o / _ POSITION OF SIN G LE PO R T DATA \ .......... UNDISTURBED WALL PRESSURE "" / 0 0 4 ' \ • I I "' / \ I m t L / \ u _ I J / \ a: _ \ a. 0.03 / i \ r,o .-r 002 ..... " o -\ , o _ F- -

- ,/

< 0.01 . -.. r

0 1 L t J

-50 -4( -3 0 -2 0 -_0 0 _0 20 3 0 40 50 6 0

CIRCUMFERENTIAL ANGLE - 8 -- DEGREES FIGURE 48 COMPARISON OF THE WALL PRESSURE IN CIRCUMFERENTIAL PLANE (x / R T = 6. 5) OBTAIN ED F ROM SUPERPO S I T ION O F S INGLE PORT D AT A WITH MULTIRADIAL PORT DATA IN THE CONICAL NOZZLE 2.4 2 . 0 _ \, I ,, o \ "<oz<_ _ 1.8 .\\\_ 1.6 -- MULTIRADIAL PORT "' I.,I..

d 0 c / d i = 1 . 8 n ,I < [] c / dj = 2 . 5 1.4 A c / di = 5.5 SINGLE PORT dl = 0.188 INCH 1 . 2 0 dj = 0 . 256 INCH (REEl)

0 [ L

0 0.02 0.04 0.0 6 0.08 QIO 0.12 WEI G H T FLO W RA TIO--W s / W p FIGURE 49 IN F LUENCE O F WEIGHT FLOW RATIO ON THE AMPLIFICATION F ACTOR USING MULTIRADIAL PORT INJECTION AT ..(x / L)in j = 0.95 IN THE APG-I NOZZLE -203 = 2.4 Ws l Wp = 0.03 2.2 j

_ 2.o

___-- 0 . 06 I 1.8 1.6 _ _ _ 0.09 Z

-, L4

0_ 1.2

>

o %

0 1.6 2 . 0 2. 4 2.8 3.2 3 . 6 4 . 0 INJECTION PORT SPACING-- c / dj FIGURE 50 EFFECT OF INJECTION PORT SPACING ON THE AMPLIFI- CATION FACTOR USING MULTIRADIAL PORT INJECTION AT " - j(x l L)in- = 0.95 IN THE APG-I NOZZLE -204- ¢. ) a_ 0.05

"- I I I '

" I

I (x / L) inj : 0.95 I o 0 0 c / dj : 1.8 I

I

n .- < 0 . 04 [] -0 c / dj : 2.6 1

.... 7',, c / dj : 3 . 5 I W rr .............. UNDISTURBED WALL PRESSURE I

I

0.03 O0

w hi

I_ X a_ / w w 0.02 m m J] t' o I 0 0 _ Z k ) n

, __-._

o 0.01 0 , _ . INJECT ION PORT "-J 0 _ / " ' J 0 4 5 6 7 8 9 I0 II 12 RATIO OF AXIAL DISTANCE FROM THROAT TO THROAT RADIUS-- x / R T FIGURE 5 l WALL PRESSURE DISTRIBUTION IN MERIDIONAL PLANE OF INJECTION IN THE APG-I NOZZLE USING MULTIRADIAL PORT INJECTION (_ /v % = 0. 03) s p (x / L) . . : 0 .9 5 In } 0 0 c / d i = I . 8 o c_ [] ..... - C ] c / dj : 2 • 5 -% Q .

Z_. "_ c / dj = 3. 5 I ......... UNDISTURBED WALL PRESSURE o t - .'- '_ 0.04 £K L U X : I0. X_E_= 9 . 0 _E_ x = 8.0 R n- " -- R T R T T co 0 0 3 ( . 0 b J rr (3_ I 0 n"

, o

0.01

o __ _._ . _

u 0 o 0 0 20 30 0 I0 20 30 0 I0 2 0 5 0 _ J CI R CUMFERENTIA L ANG LE -- O -- DEGR E ES FIGURE 52 WALL PRESSURE DISTRIBUTION IN CIRCUM F ERENTIAL PLANE IN THE APG-I NOZZLE USING MULTIRADIAL PORT INJECTION (¢v / ,_, , = 0. 03) s p u

o.o5 ] T T T T I

R (x / L) inj " 0.95 o_ 0 0 c / dj = 1 . 8 I I - r,- <[ 0 . 04 -- E]'----- ' -_ c / d j = 2.5 1 z_ - _ c / dj = 3.5 n--

" ' !

::3 ............. UNDISTURBED WALL PRESSURE m 0.03 bJ (3- A _" X l LI.I OC m 0.02 w ,,_ .j o "1- N 0.0t i 0 Z 1 L) INJEC ION PORT

I

0 4 5 6 7 8 9 I0 II 12 RATIO OF AXIAL DISTANCE FROM THROAT TO THROAT R ADIUS - × / R T FIGURE 53 WALL PRESSURE DISTRIBUTION IN MERIDIONAL PLANE OF INJECTION IN THE APG-I NOZZLE USING MULTIRADIAL PORT INJECTION (_Vs / fV = 0. 06) P (x / L) i n j = 0 . 95 0 0 c / dj = i. 8 [] c / d j = 2 .5 _- --- - L _ c / d j .=3 . 5 .............. UNDISTURBED WALL PRESSURE "-,. ,. , 0.05 1 I x x x o 0.04 _-- = 10.0 -- = 90 . -- = 8 . 0-- RT -- R T -- RT n'- n,- 00 3 U ) UJ L U g o _ 1---_ / ,_ 0.01 _ o o Io 20 50 o I0 20 3o 0 I0 20 50 CIRCUMFERENTIAL ANGLE - 8 - DEGREES FIGURE 54 WALL PRESSURE DISTRIBUTION IN CIR C UMFERENTIAL PLANE IN THE APG-I NOZZLE USING MULTIRADIAL PORT INJECTION (¢v / ¢v = 0. 06) s p

O05 1 T [ I T !

n -.. (x / L)in_ = 0.95 O.

I 0 0 c / dj = 1.8 2 0.04 D _ c / dj = 2.5 1 _- _.- .... #k c / d, = 3 . 5 I J a C ................. UNDISTURBED WALL PRESSURE I I Ld 2 D _ ( _ O D 3 w .. // \ n '_ X =_ 0.02 \" m L < \

_- /I II

o o \ " 1 _ 0 N _- / N - J 001 I 0 i . . | _j • . ° • ° o . . ....... _ ........ • . .

INJI'CTION PORT

o k

0 __ _ .... I 11 0 4 5 6 7 8 9 I0 II 12 RATIO OF AXIAL DISTANCE FROM THROAT TO THROAT RADIUS--x / R T F IGURE 55 WALL PRESSURE DISTRIBUTION IN MERIDIONAL PLANE OF INJECTION IN THE APG-I NOZZLE USING MULTIRADIAL PORT INJECTION (w / ¢v = 0. 09) s p (x / L )in j = 0. 9 5 (_ 0 c / dj = 1 . 8 El--- ---- - E l c / dj = 2 .5 _---.--,_ c / dj = 3.5 ........... UNDISTURBED WALL PRESSURE rl 0.05 I I ,.1 x = I0 . 0 x = 9.0 x .... 8.0 I RT RT R T - 0.04 l-- cr hi n - O 0 . 03 ( , 9 hi I D o cr I n- _-_-_ .., __-,...,.

w 0.0 2 I .. • _ :.

_ , . . .,._. _._........_. _._.,_ o 0.01 ; / ' I . / "' j ........ hi P.__ .< ................ I................................................................

o J O 0 I0 20 30 0 I0 20 30 0 I0 2 0 30 CIRCUMF E R E NTIAL ANG L E -- 8 --D E GRE E S FI G URE 56 WALL PRESSURE DISTRIBUTION IN CIRCUMFERENTIAL PLANE IN THE AP G- 1 NOZZLE USING MULTIRADIAL PORT INJECTION (Ws / ,_ , = 0.09) P

o .os I I

I -_ri ° O-------Q M U L TIRADIA L PO R T, C / dj = 1.8 I Q.

I 0-----_] M ULTIRADIAL P O RT, c / dj = 2 . 5 I _o 0 . 0 4 < ]_ ..... - < _ SINGLE PORT 1 ........... UNDISTURBED WALL PRESSURE rr I n.-

"' I I i

0. 0 3 I ( / 9 W e: I n _ ,-n 0 . 02 ' ' 1 I

! -

W _ I W " T - J N b a ,_ I.- 0.01 z I .d I _ _ I _ ... _._ N ........ _ .......... " Ou INJECTION PORT I 0 _A__ i 0 4 5 6 7 8 9 I0 II 12 R ATIO OF AXIAL DISTANCE FRO M T H ROAT TO T H ROAT RADIUS--x /R T FIGURE 57 COMPARISON OF WALL PRESSURE DISTRIBUTION IN MERIDIONAL PLANE OF INJECTION IN THE APG-I NOZZLE WITH SINGLE AND MULTIRADIAL PORT INJECTION (,_ / @ : 0.03) s p (_ MULTIRADIAL PORT, C / dl = 1.8 [_----{_ MULTI R ADIAL PORT, ¢ / dj = 2.5 <_- ..... _ SINGLE PORT ........... UNDISTURBED WALL PRESSURE 0 . 05 13 . . o I o 0.0 4 -- X X 1( k.- -- = I 0.0 -- = 9.0 -- = 8.0 R T RT RT 1.1.1 D 0 . 03 O9 O3 W rr" 13- ' _ _ _--- .

m 0.0 2

, _ L_-=--= L_._- _ _._

/

O .... " ........................... ' ' "" " .... ' ........

_J ¢_ ., , ...... ° , i ................

0 I0 20 30 0 I0 20 30 0 I0 20 30 CIRCUMFERENTIAL ANGLE - 8 - DEGREES FIGURE 58 COMPARISON OF WALL PRESSURE DISTRIBUTION IN CIRCUMFERENTIAL PLANE IN THE APG-I NOZZLE WITH SINGLE AND MULTIRADIAL PORT INJECTION

( , i , / ¢ , = o . o31

s p 2 2 0 c l dj -- 2 . I FI c / d_ = 2.6 2 0 J -' A c / d j = 3.2 u-lu 2 I o I 6 A (-3

%

z I 4

£

,_ __ °__ _ ________

_J I 2 0 " ' 0 0.02 0.04 0.06 0.08 0.10 WEIGHT FLOW RATIO - Ws / Wp F IGURE 59 IN F LUENCE OF WEIGHT FLOW RATIO ON THE AMPLIFICATION FACTOR USING OPPOSED- TANGENTIAL PORT INJEC TION AT (x / L)inj = 0. 69 IN THE CONICAL NOZZLE -213-

>

1%

1,6 2 , 0 2,4 2,8 3,2 :5.6 4,0 INJ E CTION PORT SPACING -- c / dj FIGURE 6O EFFECT OF INJECTION PORT SPACING ON THE AMPLIFICATION FACTOR USING OPPOSED- TANGENTIAL PORT INJECTION AT (x / L)inj = 0. 69 IN THE CONICAL NOZZLE -214- ' (x / L)inj = 0.(_9 i 0 0 c / dl = 2. I J _.a- 0" [] c / dj = 2.6 " 0,05 Z_-- - -- ' -_ c / dj = 3.2 -

I

o 0 c / dj = 3,7 (REF. I) i-- ............. UNDISTURBED WALl PRESSURE rr 0,04 i m or " Z3 w 0.03 / ", .,_ n ,- / x, _ . j , W 1:13 J •

"' C

_ < _

_ 212 ILl, ! J U' O F- " N: " " - , . O _j 0.01 z

" i ...... __

INJE

o ,. • • • ' ! IoN - • O!T "

o %

4 5 6 7 8 9 I0 II 12 RATIO OF AXIAL DISTANCE FROM THROAT TO THROAT RADIUS -- x /R T FIGURE 61 WALL PRESSURE DISTRIBUTION IN MERIDIONAL PLANE OF INJECTION IN THE CONICAL NOZZLE USING OPPOSED-TANGENTIAL PORT INJECTION ( v t , s / _ = 0.03) P ( x / L)inj = 069 0 0 c / dj = 2.1 E]' [] c / dj = 2.6 _'- -A c / dj = :5. 2 0 c / dj : 3.7 (REE I ) .............. UNDISTURBED WALL PRESSURE 005 ,-' I _ , I × X 0 0.04 - 7.5 -- = 7.0 = 6.5-- _ R T R T R T r Y hi

,-,- 1

m m 003 I i rr .\

' "

o [ _ I..- • .j 0.01 ,{..) ........................

0 .......................

J 0 I0 20 50 0 I0 20 :50 0 I0 20 :50 CIRCUMFERENTIAL ANGLE -- 8 - DEGREES FIGURE 62 WALL PRESSURE DISTRIBUTION IN CIRCUMFERENTIAL PLANE IN THE CONICAL NOZZLE USING OPPOSED-TANGENTIAL PORT INJECTION (<Vs / _ = 0. 03) P u 0.05

a_ I I i I I

_ " - - J(x / L )in" = 0.6 9 I 0 0 c / dj = 2. I _ - E ] _ c / dj = 2 . 6 A-- -.A c / oj : 3 . 2 LL I ........... UNDISTURBE D WA LL PRESSURE m 0.03 / 1 "

(. , o [ : [ 7] I- < _

n ,-

L\ x

13._ • w uJ 0 . 0 2 a 3 : _ uJ < _ -J T N I _ ". N b , J ". 0 " • . Z I F - " ....

i J " *" -- i io ° _ . _ 0 INJECTI ON PORT

oo.ol I

J 0 _ / I J 4 5 6 7 8 9 I0 II 12 R A TI O O F A XI A L DI S T A NCE FR O M THR OA T TO THR OA T R A DIU S -- x / R T FI G URE 63 WALL PRESSURE DISTRIBUTION IN MERIDIONAL PLANE OF INJECTION IN THE CONICAL NOZZLE USIN G OPPOS E D-TANG E NTIAL PORT INJECTION

( q+ / , D = o . o6)

s p (x / L) inj : 0.6 9 c / dj = 2 . I [] .... -C] c / dj = 2 . 6 A .... --_ c / dj = 3.2 u n ............. UNDISTURBED WALL PRESSURE I ',:::[ X X X = 7 . 5 -- = 7 . 0 -- =6.5 o r" RT RT R T c 2 -_- 0.04 _. ILl Dn" 0.03 \ -_ W -.,. ",,, I 13_ 0.02 ,,, I'--.-:_ • i m 0 ................................

............ i ........... i ...........

z O0 1 0 ........... ' ........... " .........

l-- _J , _ 0 U o 0 IO 2_0 30 0 I0 20 30 0 I0 20 30 _1 CIRCUMFERENTIAL B NGLE -- 0 -- DEGREES FIGURE 64 WALL PRESSURE DISTRIBUTION IN CIRCUMFERENTIAL PLANE IN THE CONICAL NOZZLE USING OPPOSED-TANGENTIAL PORT INJECTION (¢Vs / CV = 0. 06) P 2.2 E ) c / d j = 2.1 [] c / dj = 2.6 /k c / d i = :3 . 2 ._:, , ' , 1. _ 2.0 (Z) c / dj= 3 . 7 (REE t)

I 1.8

n - o 1.6

_o

-5 1.4 0 _ 1.2 0 i 0 0 . 02 O.04 0 . 06 0 . 08 O . I0 O . 1 2 WEIGHT F L O W R ATIO -- W s / Wp FIGURE 65 INFLUENCE OF WEIGHT FLOW RATIO ON THE AMPLI- FICATION FAC TOR USING OPPOSED- TANGENTIAL PORT INJECTION AT (x / L)inj = 0.95 IN THE APG-I NOZZLE

-Z19-

2 2 ._-

2 o

W-_- S = 0 0 3 . , ...-I_ W p n_ 0.09 ._ 1 6 /

/

Z _o < I 4 - 0.06 U- _ J

>

<

%

1.6 2 . 0 2 . 4 2.8 3.2 3 . 6 INJECTION PORT SPACING - c / d: J FIGURE 66 EFFECT OF INJECTION PORT SPACING ON THE AMPLIFI- CATION FACTOR USING OPPOSED-TANGENTIAL PORT INJECTION AT . . {x / L)in j = 0.95 IN THE APG-I NOZZLE -220- o 0.05 " ( x / L) inj = 0,95 1

I

OI C_ 0 C / dj = 2. I I 0.04 ([Z)--------(ZZ) c /d j = 3.7 (REE I) --1 ............ UNDISTURBED WALL PRESSURE I

,,, ! I

I

w

_ /// __lx

uJ 0.0 ? _ w _ j < / N r-J c._ 0

, _ o ool " -- i " lJ 1

-J ......... I "'" _

-

U O INJECTION P O RT

T

-J 0 A V i L 4 5 6 7 8 9 I0 II 1 2 RATIO OF AXIA L DISTANCE FROM THROAT TO THROAT RADIUS -- x / R T FIC_JRE 67 WALL PRESSURE DISTRIBUTION IN MERIDIONAL PLANE OF INJECTION IN THE APG-I NOZZLE USING OPPOSED-TANGENTIAL PORT INJECTION

(4 v s l ,& = o. 09)

P (x / L)in j = 0.95 O- Q c / d = 2. I Q c / d -- 3 7 (REE I) _ L _ " .......... : U N I ISTU RB E D W A LL P R ESSU RE i i 0.05 I o x _ = 9 0 ix-- L - = 8. 0

_- - _ T = Ioo R T I R T

_r 0.04 . .

IJ.I E : (I) u ') 0 . 03 n, - n W

" c_

' m 0.02 r ---._ _) t ,, a I "r F- i "_ ......

o o . oi £ _ / ._fl ) 0 (') _ _1 " " " ............ ' ............... J..................

J 0 O IO 20 30 O IO 20 30 O I0 2 0 30 CIRCUMFERENTIAL AN G LE-- 8 -DE G REES FIGURE 68 WALL PRESSURE DISTRIBUTION IN CIRCUMFERENTIAL PLANE IN THE APG-1 NOZZLE USIN G OPPOSED-TAN G ENTIAL PORT INJECTION (_Vs / _ V = O.09) P - ZZ3 - (x / L) i n j = 0.95 0 0 c / dj = 2. i E:}- .... _ c / dj = 2.6 _-"-- - -- - -------_ c / d i = 3 . 2 # ............ UNDISTU R BED WALL PRE S SURE r Q 0 . 05 r'l I _ = I0 . 0 x = 9.0 _ =8.0 O R T R T RT I-.

< 0.04 tY ol _ n 0.03 L d i b.J b_ n ,- _ 0.02 i 2 .. _ "" {

_ o o.o, _ _ . ___ ._

-J ............................ "T . ._ _. ' 1 " .._ . .................................

o J 0 0 I0 20 30 0 I0 20 30 0 I 0 20 30 CIRCUMFERENTIAL ANGLE-- e --DEGREES FIGURE 7 0 WALL PRESSURE DISTRIBUTION IN CIRCUMFERENTIAL PLANE IN THE APG-I NOZZLE USING OPPOSED-TANGENTIAL PORT INJECTION_(CVs / _ = 0.03) P

o . o_ 1 i 1 1 i

,,. (x / L)in j = 0.95 I 0 0 c / dj = 2 . 1 I

I

o 0.04 [3 -El c / dj = 2 . 6 I _- _ c / dj : 5.2 I rr .............. UNDISTURBED WALL PRESSURE I

"' r I

D I

_ 0.03 t I

w W i & X m 0.02 _ t . .

_ 7 ._ , _ _..,-I

i , _r

/ \\ _ t\.k , I

[._ £ . ) , N N

" % 4/ 't2 ! i1 ! ""

, I-- 0 , 01 --" - " " I-- ....

_ .

0 .

0 J ....... I 0 l ,,_ RT I 0 4 5 6 7 8 9 I0 II 12 RATIO OF AXIAL DISTANCE FROM THROAT TO THROAT RADIUS--x / R T FIGURE 7 i WALL PRESSURE DISTRIBUTION IN MERIDIONAL PLANE OF INJECTION IN THE APG-I NOZZLE USING OPPOSED-TANGENTIAL PORT INJECTION

(_Vs / ¢ = o. o6)

P (x / L) inj : 0.95 0 0 c / dj = 2 I [_ ..... [] c/ dj = 2.6 _----_.---_ ¢ / dj = 5.2 ............ UNDISTURBED WALL PRESSURE 0.05 ....

0.

I X X X

o__ _ =,o.o , 7=,9 . 0 --=R, B.o

0.04 t......

n_ L_J n_ c o 0.03 W n I O_ w 0.02 W rn "i- "_. _'_ " -_.--_. _ _._ o 0 . 01 - . - :. -: :-...... .-_-._ . . . -_..._-_ ................................. . ..............................

o o -_ 0 0 I0 2 0 30 0 I0 20 30 0 I0 20 30 CIRCUMFERENTIAL ANGLE-- 8 -DEGREES F IGURE 72 WALL PRESSURE DISTRIBUTION IN CIRCUMFERENTIAL PLANE IN THE APG-1 NOZZLE USING OPPOSED-TANGENTIAL PORT INJECTION (_ / ¢v = 0.06) s p -ZZ7 - SECOND SHOCK JET SURFACE FIRST SHOCK 'Poo P2 Moo o -2

Pj

FIGURE 74 M ODEL OF TWO-SHOCK SYSTE M -228 - 5.0 4.0 .0 1.5 2.0 2.5 5.0 :3.5 4.0 Moo FIGURE 75 PRESSURE RATIO OF TURBULENT BOUNDARY LAYER SEPARATED BY CONICAL SHOCK, y = 1.4 .0 , -- 1.0 1 . 5 2.0 2.5 3 . 0 3.5 4.0 M= FIGURE 7 6 PRESSURE RATIO OF TURBULENT BOUNDARY LAYER SEPARATED BY CONICAL SHOCK, _ : 1.2 FIGURE 77 KINEMATIC RELATIONS F OR INJECTANT VELOCITY VECTOR - Z31 - \

' _ / _c

C cr = 2Yc Cos / 3 c + Z b S i n /3 c FIGURE 79 IMPINGING JET CONFIGURATION AT MULTIPORT INTERAC TION - Z 3 3 - I ..........

Pj / Pa:, = 1.0 -'ci

" -" B y =0

,_ , _ Y =I.4 / W Z t--

m 3

Z I--

- S

b - W Z a..

2 3 /

FREE STREAM MACH NUMBER FIGURE 8O EFFECT OF FREE STREAM MA C H NUMBER ON PENETRATION DISTANCE -234- o.-._ "[D

o 3

CD CO

z Moo = 4

0 e

_y : 40

rr 7 " = 1. 4

E L I Z L L I Q-

0 .2 .4 .6 .8 1.0

Pj / Poo

FIGURE 81 EFFECT OF JET-TO-PRIMARY STREAM STAGNATION PRESSURE RATIO ON P ENETRATION DISTANCE -Z35-

Mo , \

\ ( D W O Z <

2 Pj / P,,,, = I.O

a

M_, = 4

z 7 , : 14

n_ W Z W n

0 0 ° 20 ° 30 ° 40 o 50 0

INJECTION ANGLE, / 3 y

FIGURE 8P .

EFFECT OF INJECTION ANGLE ON PENETRATION DISTANCE

- 236 -

I I • !::i!iii::iiiiiii!i : i :.ii %, J

/ \

8 (Ws /Wp) j / Poo_)

FIGURE 83

EFFECT OF PORT INCLINATION ANGLE ON PORT SPACING

-Z37-

2.4

_ Z 2 ....

--MERIDIONAL INJECTION

1.1_ LI-

o 2.0

Z

o

U.

z OPPOSE D -- TANGE N

(.9 _ 1.8 ...... _ j ....

<

INJECTION

1 . 6 .

1.2

0 .02 .04 .06 .08 1.0

WEIGHT FLOW RATIO, Ws / Wp

FI GU RE 84 T E ST RESULTS (FROM REFEREN C E I) SHOWING MAGNIFICATION FACTOR FOR MERIDIONAL AND OPPOSE D - TANG E NTIAL INJEC TION -238 - FIGUR E 85 SCHEMATIC O F THE BOW S H OCK WAVE CREATED BY A SPHER_ R b -239 - FIGURE 86 sCHE M ATIC SHO W ING THE POSITION AND COORDINATES O F THE BOW SHO C K W A VE -Z40 - A PPE NDIX G DISTRIBUTION LIST COPIES RECIPIENT NASA Western Operations Office 150 Pico Blvd.

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