Wind Tunnel to Atmospheric Mapping for Static Aeroelastic Scaling

Wind Tunnel to Atmospheric Mapping for Static

Aeroelastic Scaling

d Ì † Jennifer Heeg , Charles V. Spain , J.A. Rivera NASA Langley Research Center, Hampton VA 23681.

Abstract Wind tunnel to Atmospheric Mapping (WAM) is a methodology for scaling and testing a static aeroelastic wind tunnel model. The WAM procedure employs scaling laws to define a wind tunnel model and wind tunnel test points such that the static aeroelastic flight test data and wind tunnel data will be correlated throughout the test envelopes. This methodology extends the notion that a single test condition- combination of Mach number and dynamic pressure- can be matched by wind tunnel data. The primary requirements for affecting this extension are matching flight Mach numbers, maintaining a constant dynamic pressure scale factor and setting the dynamic pressure scale factor in accordance with the stiffness scale factor. The scaling is enabled by capabilities of the NASA Langley Transonic Dynamics Tunnel (TDT) and by relaxation of scaling requirements present in the dynamic problem that are not critical to the static aeroelastic problem. The methodology is exercised in two example scaling problems: an arbitrarily scaled wing and a practical application to the scaling of the Active Aeroelastic Wing flight vehicle for testing in the TDT.

methodology extends the notion that a single test Introduction condition -combination of Mach number and dynamic pressure- can be matched by wind tunnel data. The Experimental research in aeroelasticity is often thought scaling is enabled by capabilities of the NASA Langley of as flutter testing. Because of safety, flutter clearance is Transonic Dynamics Tunnel (TDT) and by relaxation of considered critical in developing new aircraft systems and scaling requirements present in the dynamic problem that typically involves the development and testing of dynamic are not critical to the static aeroelastic problem.

aeroelastically-scaled wind tunnel models prior to full-scale Scaling a model such that it is statically- prototype development. Experimental static aeroelasticity aeroelastically similar to an airplane requires that its however, is often only considered after prototype characteristics under steady loads match those of the development, and typically involves flight testing of the airplane. A model that is statically-aeroelastically scaled full-scale aircraft. Modern aircraft however, may benefit to a flight vehicle deflects to the same shape and with from an increased emphasis on wind-tunnel static scaled magnitude under scaled static loads.

aeroelastic experimentation. For example, experiment- This paper explains the procedure used to develop based flexible stability and control derivatives would be scale factors for the statically-aeroelastically scaled wind more reliable than analysis-based, and would be available to tunnel model and the requirements for acquiring and designers prior to prototype development. This paper scaling the resultant data. Pertinent assumptions, describes how the classic aeroelastic scaling laws can be restrictions, limitations and implications of this adapted for static aeroelasticity, thereby making static methodology are also discussed. Two analytical aeroelastic wind-tunnel model development somewhat examples of applying the WAM methodology are easier and more practical. presented: a hypothetical arbitrarily scaled wing and the Wind tunnel to Atmospheric Mapping (WAM) is a Active Aeroelastic Wing.

methodology for scaling and testing a static aeroelastic wind Experimental implementation of this methodology is tunnel model. The WAM procedure employs scaling laws to expected to utilize unique features of the NASA Langley define a wind tunnel model and wind tunnel test points such Transonic Dynamics Tunnel (TDT). Thus, pertinent that the static aeroelastic flight test data and wind tunnel capabilities and systems of this facility are examined.

data correlate throughout the test envelopes. This Practical details and the effects of errors are examined.

Resolution limitations of wind tunnel instrumentation and uncertainties in calculated wind tunnel flow parameters d Senior Research Engineer, Aeroelasticity Branch, are mapped to flight test conditions, providing limits for Mail Stop 340, Senior Member AIAA the precision with which flight test conditions can be Ì Senior Research Engineer, Aeroelasticity Branch, matched.

Mail Stop 340 † Senior Aerospace Engineer, Aeroelasticity Branch, Mail Stop 340 American Institute of Aeronautics and Astronautics

sound for the test media at atmospheric sea level pressure are approximately 1115 ft/sec for air and Nomenclature 540 ft/sec for R134a. The higher density and lower speed of sound associated with the heavy gas enable a speed of sound more latitude in model construction. The variable b semi-span pressure allows for independent control over Mach E Young’s modulus number and dynamic pressure.

Fr Froude number g gravitational acceleration The TDT data system utilizes measurements of total h altitude pressure, static pressure, heavy gas purity and total I inertia temperature to compute additional flow parameters L length such as Mach number, dynamic pressure, density, M Mach number velocity and speed of sound. Calculations are M moment applied performed essentially in real time for isentropic flow p distributed load properties of a real gas, both thermally and P force applied calorically imperfect, valid for arbitrary mixtures of q dynamic pressure 1,2 R-134a and air.

S wing area The tunnel operates most efficiently by testing V velocity along so-called wind-off total pressure lines, shown x spanwise coordinate in figure 1. These operational lines are the Mach y out-of-plane deflection number-dynamic pressure combinations generated by ρ density establishing a wind-off total pressure and increasing Mach and dynamic pressure by changing motor Scale Factors RPM. The operational lines differ from lines of λ (variable) ….. scale factor on (variable) constant total pressure because the tunnel has = (variable) /(variable) M A inefficiencies and is not a truly “closed system.” (example: λ =L /L =scale factor on length) L M A Subscripts & Superscripts Energy exchanges between the thermodynamic A …… pertaining to the aircraft system involved in the flow calculations and the M …… pertaining to wind tunnel model surroundings are primarily due to energy input by the ‘ …… non-dimensionalized quantity motor, and energy removal through cooling water o …… reference quantity and frictional heating. The energy losses experienced in operating a wind tunnel will vary from one facility Background to another, affecting a tunnel’s ability to obtain data required for implementing the current scaling The Active Aeroelastic Wing Program process. The energy losses in the TDT are The Active Aeroelastic Wing (AAW) program is a sufficiently small to allow efficient testing at cooperative effort among NASA, the Air Force conditions required to match constant altitude flight Research Lab and Boeing Aircraft Corporation. The data.

program objective is to develop technologies that will allow for the favorable use of aeroelastic properties of a Theory flexible wing aircraft. The program consists of flight testing, wind tunnel testing and analyses. The primary Aeroelastic similitude between a flight vehicle purpose of the wind tunnel activities is to provide a and a wind tunnel model can be achieved by testbed that is statically aeroelastically scaled to the matching non-dimensional parameters that govern the flight test vehicle. A three-way data correlation aerodynamics, the structure and their coupling. This involving flight test data, wind tunnel test data and problem was addressed in depth by W.G.Molyneux analytical predictions will be performed. Open loop 1 in 1964 . In this work, he presents the governing flight data has already been obtained; wind tunnel non-dimensional differential equations and discusses testing is scheduled to be conducted in the NASA simplifications appropriate to different flow regimes Langley Transonic Dynamics Tunnel (TDT) late this and for different aspects of wind tunnel testing.

year. This reversed schedule provides an opportunity to Much of the theory discussed here is credited to precisely match test conditions at which the flight test Molyneux- the reader is encouraged to consult data has been acquired by carefully selecting and reference 1 when extending these concepts to other setting the wind tunnel test conditions.

applications.

Aeroelastic similitude produces a long list of The Transonic Dynamics Tunnel required similarity parameters and constraints. For The TDT is a closed circuit reduced pressure tunnel similitude of the aerodynamics, the Mach number located at sea level. There are two choices of test and Reynolds number must match and the bodies medium: air and R134a heavy gas. The speeds of must be geometrically similar at the surface. This American Institute of Aeronautics and Astronautics implies that not only must the shapes of the different boundary layer using grit applied near the leading bodies be the same, but also there must be similarity in edge of the model.

their incidences to the flow and in their static elastic There are several types of static aeroelastic deformations. From the structural force-deflection model programs where the velocity ratio, or Froude equations, similitude requires that the ratio of stiffness number, can be important. The Froude number to aerodynamic forces be maintained as well as the determines the ratio of the deflections under steady distribution of the stiffness throughout the structure. gravitational load to deflections due to aerodynamic The vibration equations require mass ratio and stiffness and inertial loads. For a Froude-scaled model, the ratio (or reduced frequency) to be maintained. The aerodynamic and elastic forces are in proportion to mass ratio is a ratio of vehicle mass to mass of the the gravitational forces. In the case of a free-flying surrounding airspace; the reduced frequency represents model, Froude scaling is important because gravity is the ratio of speed associated with the oscillations to the providing one of the loads to achieve equilibrium.

forward speed of the vehicle. The equilibrium Neglecting Froude number would lead to the model equations require that mass ratio and Froude number be lift in the equilibrium condition being 1,4,5,6 maintained. disproportionate relative to that of the full-scale vehicle. In addition to the overall rigid body loads Simplifications being maintained, the load distribution for an Design, construction and testing of a static aeroelastic wing is important. In most cases, the aeroelastic wind tunnel model allows neglecting mass deflection due to gravitational loading for a cantilever ratio, Reynolds number and Froude number under model will be insignificant compared to the certain circumstances. aerodynamic loading. Froude scaling may be The mass ratio influences the aeroelastic problem if important, however, for low-speed aeroelastic the dynamics are considered. For studying static models . The gravitational contribution to the aeroelastic phenomena, the requirements pertinent to loading is important near zero velocity, but is quickly dynamic characteristics are not necessary and can be overwhelmed as the dynamic pressure increases.

neglected. This is a fundamental difference from the This is true in the case of either a free-flying or a required methodology for producing a scaled flutter supported model. For a free-to-roll model, Froude model. number might also be important because the The aerodynamic equations specify that the airfoil gravitational forces may be significant when shape must be preserved, along with the Reynolds considering out-of-plane motion. Finally, in some number and Mach number. The Reynolds number cases, the wing may twist enough to significantly dictates the flow behavior in the boundary layer. alter the center of gravity location and thus the Quoting Molyneux , “For model tests to represent full gravitational force distribution; this may be critical in scale conditions at reasonable air density (altitude) rolling power investigations .

conditions, a compressed air tunnel is required. The In the case of a cantilevered model, the difficulty arising from an excessive density scale supporting wall provides the forces and moments derives from the necessity to satisfy the Reynolds needed for equilibrium and restricts the model from number parameter. The Reynolds number is of rolling. Thus, Froude number matching is not paramount importance in relation to effects in the required.

boundary layer. Experience has shown that it is generally of minor importance as far as aeroelastic Force-Deflection Relationship effects for main lifting surfaces are concerned. If the Understanding the requirements that arise from Reynolds number requirement is ignored, the density the force-deflection relationship is essential to scale becomes a free parameter, i.e., it is independent of understanding static aeroelastic scaling methodology.

the linear scale.” The general equations are given in reference 1; a The Reynolds number effects are neglected in the simple example of a force-deflection relationship will current design and testing procedure. With the TDT be given here. While these equations do not capabilities, it is usually impossible to match the flight represent realistic aerodynamic loading of an aircraft, test Reynolds number. If it could be matched, meeting the presented example evidences the scaling this criterion provides another constraint, limiting the relationship between the magnitude of the load and free parameter selection. In neglecting the Reynolds the structural response.

number, the inherent assumption is that the boundary Consider a uniform cantilevered beam under layer effects are not significant here. In the case of uniform distributed load of strength p , force per unit control surface aerodynamics, or flow separation length. The beam bending equation is shown, eqn 1.

1,4 phenomena, this may be a poor assumption . In order y d to circumvent concerns regarding boundary layer ) ( x M EI = Eqn 1 transition, aeroelastic testing often requires tripping the dx American Institute of Aeronautics and Astronautics Integrating twice and applying boundary conditions of The previous discussions lead to six free no deflection or slope at the cantilevered end, the parameters or independent variables in the deflection of the beam is given by eqn 2. cantilevered static aeroelastic model scaling problem: Mach number of the aircraft, altitude of the aircraft, p 3 4

( ) 6 1 24 1 bx x y + − = Eqn 2

Mach number of the model, dynamic pressure of the EI model, size and stiffness of the model. Additional The distribution of the force is buried in the integration.

variables are neglected, such as Reynolds’ number While this example utilizes a uniform force distribution, and mass ratio; others are fixed, such as size and a realistic aerodynamic or aeroelastic problem would stiffness of the flight vehicle.

utilize a Mach number-dependent pressure distribution.

Two constraints are applied, as dictated by the The following non-dimensional quantities are similitude requirements previously discussed: Mach introduced and denoted by ‘. Notice that the force, P, is number must be matched and the ratio of stiffness to non-dimensionalized in the same manner that an aerodynamic force must be matched. This reduces aerodynamic force is converted into a non-dimensional the number of free parameters to four. There are two coefficient.

important aspects implicit in the force-deflection y x b S E ′ ′ ′ ′ ′ y = ; ; ; ; x = b = S = E = relationship development: the distribution of the L L L E L 0 stiffness must be maintained and the distribution of ′ the aerodynamic forces must also be maintained .

I P PL P 1 ′ ′ ′ ; ; I = P = p p = = = Design of the wind tunnel model requires that ′ ′ I S q L S q Sb q b choices be made. A length scale factor and a Substituting the non-dimensional variables into the stiffness scale factor must be selected, thereby fixing governing force-deflection eqn, 2, yields model size and stiffness, and reducing the number of ′ ′ L S q p 4 3 4 4 free parameters to two.

′ ′ ′ ′

( ) 6 1 24 1 L x b L x L y + − =

Eqn 3 ′ ′ I I E E These two remaining independent variables are 0 0 chosen during the planning and conducting of the Rearranging, tests. During testing, there are four possible   ′ ′ S L q p 3 4   freedoms: Mach number of the airplane, altitude of

( ) 6 1 24 1 x b x y ′ ′ + ′ − = ′

Eqn 4   I E I E ′ ′ the airplane, Mach number of the wind tunnel and 0 0   dynamic pressure of the wind tunnel. Only two of The non-dimensional force-deflection equations for these are still independent variables. Choice of bodies of different sizes, materials and magnitude of airplane Mach number and altitude, exercised as loading are identical to each other provided that the choices of the two remaining free parameters, value of the bracketed quantity is preserved. Using the specifies a corresponding wind tunnel test Mach subscripts A to denote parameters pertinent to the number and dynamic pressure.

airplane and M to denote parameters pertinent to the It is important to note that the problem is not wind tunnel model, the requirement for force-deflection over constrained. For every choice of Mach number similitude is given by and altitude of the airplane, there will be a 4 4     L q L q corresponding Mach number and dynamic pressure in     = Eqn 5     the wind tunnel. Thus, all flight test conditions can I E I E 0 0 0 0     M A be mapped to wind tunnel test conditions.

which can be rewritten as   WAM Methodology

( )

L I E q 0 0   M M M Eqn 6 =  

( ) q I E

0 0 A L A   A Application of the WAM methodology involves several steps. The scale factors are developed based Defining scale factors, λ , as the ratios of wind tunnel on a single flight condition in the vehicle’s flight model parameters to airplane parameters, eqn 6 can be envelope and a single test condition in the wind written tunnel. These choices of test conditions must take λ λ λ = Eqn 7 into consideration the requirements for applying the L q EI scale factors throughout the test envelopes; these Equationss 4 through 7 each mathematically express considerations will be discussed shortly. The wind that deflection similitude requires equal values for the tunnel test points that correspond to the remaining ratio of applied force to structural stiffness. For the points in the flight test envelope are produced using static aeroelastic problem, the applied force is an the scale factors determined from that initial point.

aerodynamic load. Maintaining the relationship in eqn Corrections to the wind tunnel test conditions or to 7 is essential for static aeroelastic scaling.

the flight test conditions can be made after the first data set (either flight data or wind tunnel data) is Freedoms, Constraints & Choices American Institute of Aeronautics and Astronautics acquired. These corrections are discussed in a material doesn’t have to be as strong, but it also can’t subsequent section. be as stiff. This chasing of material properties relative to applied loads and model safety criteria is a Developing Scale Factors significant challenge in model design.

The four principal scale factors for static It is desired to map the maximum Mach number aeroelastic scaling have been shown to be Mach at the minimum flight test altitude to a high dynamic number, length, structural stiffness, dynamic pressure pressure in the wind tunnel. The designer should and Mach number. The Mach number scale factor must consider leaving some margin in dynamic pressure be 1 for aerodynamic similitude and the other three between the maximum scaled wind tunnel test must be related as shown in eqn 7. The designer of a condition and the wind tunnel operating limits static aeroelastically scaled wind tunnel model has because 1) the conditions being flown will not always freedom to assign values to two of these three scale be precise; 2) the conditions being flown may be factors. The third becomes a dependent variable in the changed at some point in the test planning; 3) the design process. Historically and for practical reasons, atmosphere isn’t usually at standard-day conditions; the scale factor on stiffness has been relegated to be the 4) the speed of sound in the wind tunnel is a function dependent variable. of gas purity and temperature, neither one of which is The two choices to be made then are the scale within the experimenter’s control, i.e. these quantities factors for dynamic pressure and length. The dynamic are not known exactly ahead of time; and 5) placing a pressure scale factor can be determined by choosing an model in the tunnel changes the maximum operating altitude and Mach number of the airplane and a wind conditions of the tunnel. This latter point is tunnel dynamic pressure to correlate at that condition. particularly important if a splitter plate or a large The geometric length scale factor can either be selected model is being considered.

based on wind tunnel test section dimensions, to match the Froude numbers or to meet some other test criteria. Determining wind tunnel test points Once these decisions have been made, the constraints For the chosen scale factors, a single wind tunnel requiring Mach number matching and ratio of stiffness model is built, cementing the length and stiffness to aerodynamic force matching, eqn 7, fix the scale factors. The ratio of the dynamic pressures of remaining scale factors. the flight test conditions and the wind tunnel test conditions is thus also cemented due to the constraint Considerations for Multi-point Scaling given by eqn 7. Combining eqn 7 with the definition There are several practical issues of wind tunnel of the dynamic pressure scale factor and definitions model construction and testing to bear in mind when of Mach number and dynamic pressure yields the developing the scale factors. The choice of scale following requirement on wind tunnel dynamic factors must comply with wind tunnel test section size pressure.

and operational capabilities.

λ EI q q = A M Eqn 8 The goal of multi-point scaling is to have the entire λ L flight envelope map into the wind tunnel operating envelope. Factors that limit the capability of a wind 2 2 ) ( M a q ρ = Eqn 9 A A A tunnel include fan speed, blockage, contraction ratio and inefficiencies. As an example, at its maximum   λ EI 2 2   Mach number of 1.2 the TDT has a dynamic pressure

( ) ( ) M a q 2 1 ρ =

Eqn 10 A A M   limit of 340 psf when operating in heavy gas. For λ L   lower Mach numbers, the dynamic pressure capabilities The terms have been are higher. It is recommended that a high value of the grouped to emphasize the wind tunnel dynamic pressure at the maximum Mach connections with the number to be flown be used to determine the stiffness airplane parameters. Once scale factor.

created or built, the wind Using a lower dynamic pressure for scaling has tunnel model has a certain repercussions on the model design. Lowering the size and stiffness, which maximum scaling dynamic pressure lowers the are related to the full-scale aerodynamic force applied to the model. Recall that the quantities by the length ratio of stiffness to aerodynamic force is a parameter scale factor and the that must be scaled properly between the model and the stiffness scale factor, aircraft. Thus, as the dynamic pressure for testing the fixing the first term in model is reduced, the stiffness of the model must also parentheses. The second be reduced. Finding material that is sufficiently strong, parenthesized term is a but not overly stiff, is usually the crux of the design function of aircraft problem. The loads applied have been reduced, so the altitude; the third is a American Institute of Aeronautics and Astronautics function of aircraft Mach Hypothetical Wing number. The wind tunnel A simple testcase was generated to demonstrate must have the capability to the application of the WAM methodology. Two achieve a range of dynamic analytical models were generated: one representing pressure-Mach number the wing of a flight vehicle and one representing a combinations to satisfy eqn wind tunnel model that is static aeroelastically scaled 10 for all altitude-Mach to the flight vehicle. Static aeroelastic analysis was number combinations to be performed at Mach 0.85 over a range of dynamic flight tested. pressures, producing stability and control derivatives for both analytical models. As suggested by eqn 10, the test parameters- Mach number, aircraft altitude and wind tunnel dynamic The models consisted of pinned-root wings, pressure- form a three-dimensional space. Within this each with an aileron. An approximate planform of an three-dimensional test space, a surface exists that F-18 wing provided the geometry for this testcase. In corresponds to a single static aeroelastically scaled this simple example, length and dynamic pressure wind tunnel model -flight vehicle pair. The shape of scale factors were selected without regard to scaling the surface depends on the values of the length and to actual test points, testing within the limitations of a stiffness scale factors. The surfaces are referred to as given facility or using actual materials. The wind WAM surfaces. Figure 2 shows three possible WAM tunnel model was geometrically scaled to be ¼ the surfaces in the test space, corresponding to three size of the flight vehicle scale wing. The dynamic different values of the stiffness scale factor. The length pressure scale factor was specified as 1/5.

scale factor has been held constant. Figure 3 shows Substituting these values into eqn 7 gives the three different possible surfaces in the test space, stiffness scale factor, eqn 11.

corresponding to three values of length scale factor.

4 4 00078125 . 0 25 . 0 2 . 0 = × = = λ λ λ Eqn 11 L q EI The stiffness scaling has been kept constant in producing these surfaces.

In this example, the material thickness was scaled A single WAM surface, as illustrated in Figure 4, is using the length scale factor, establishing the scale produced by choice of length and stiffness scale factors; factor on area moment of inertia, eqn 12. The the various points on the surface define flight test material stiffness (Young’s modulus) was scaled such point/wind tunnel test point pairs. An example test that eqn 7 was obeyed, eqn 13.

point pair is denoted by the black circle lying on the surface at Mach 1.2, flight altitude 5000 ft and wind Eqn 12 λ λ λ λ λ = = L E I E EI tunnel dynamic pressure 369 psf. The projection of this 4 4 pair onto the flight test surface and the wind tunnel test 2 . 0 = = →  = = λ λ λ λ λ λ λ Eqn 13 E q L E L q EI surface are shown in the figure by the blue circles.

Figure 5 shows the projection of the entire WAM Note that the same effect could be produced by surface from figure 4 onto the flight test plane. All maintaining the same material for the flight vehicle combinations of Mach number from 0.85 to 1.2 and and wind tunnel model, but scaling the material altitude from 5000 to 30000 ft are considered as thickness separately from the in-plane geometry. A possible flight test points. Figure 6 shows the combination of these two approaches is more like the projection of the WAM surface from figure 4 onto the procedure required in designing an actual wind tunnel wind tunnel test plane. The corresponding wind tunnel model.

test points occupy the colored region from Mach 0.85 to The structure of the main wing was a flat plate 1.2 and dynamic pressure from 66 to 369 psf.

with a thickened aft-sweeping region. The aileron was a single-thickness plate, structurally connected to In comparing the flight test envelope and the wind tunnel test envelope, it is important to recognize that the the wing by two tabs. The structural finite element model with element thickness is shown in the figure highest altitude point at a given Mach number is mapping into the lowest dynamic pressure point. It is 7. The thicknesses in the figure are for the wind tunnel model scale; due to the length scale factor interesting to note that a line of constant flight vehicle altitude maps very nearly to a line of constant wind chosen, thickensses for the flight vehicle are 4 times as large. tunnel density.

Requiring a match of the Froude number Static aeroelastic trim analyses were run for throughout the test space would lead to a single line of these models. The resulting rigid pressure scaled points instead of a surface. This line would distributions, aeroelastic pressure distributions and correspond to a line of constant flight vehicle altitude deflections were compared. The results were and a line of roughly constant wind tunnel density.

identical in pattern and correctly scaled relative to each other.

The lift curve slope, C , and the lift coefficient Analytical Examples L α due to aileron deflection, C , are shown in figures 8 L δ American Institute of Aeronautics and Astronautics and 9. In comparing the results, the dynamic pressures The Mach number must be the same as the flight associated with the wind tunnel model were multiplied vehicle. Specifying Mach number, dynamic pressure, by the dynamic pressure scale factor that was generated purity and temperature establishes the other variables in association with the model scaling. The results are of the wind tunnel, such as velocity, speed of sound, identical, demonstrating that for a simple construction density, and pressure. Thus, scale factors for speeds flight vehicle wing, using hypothetical materials of sound, velocity, and density have also been without any strength consideration, without any rigid established.

body motion influences, without any wind tunnel Chosen wind tunnel test values: effects, or other complicating real-world effects, the M =1.2 = 250. psf q M M WAM scaling and comparison methodology work Resulting wind tunnel parameters: perfectly.

a = 540. ft/sec M V =M*a =648 ft/sec M M Active Aeroelastic Wing 2 3 ρ =2*q / V = 0.0011907 slugs/ft M M M The following shows an example of applying the As a result of choosing the above test point pair, WAM methodology to the scaling of the Active the dynamic pressure scale factor is fixed, eqn 14.

Aeroelatic Wing (AAW) wind tunnel model. In this 250   psf q M actual design case, the flight test points had been   2076 . 0 = = = λ Eqn 14 q   1204 psf q established and the capabilities of the TDT were   A employed in determining the various scale factors and The second major step in applying the WAM wind tunnel test points. Because this model is actually procedure for this application is choosing the length being built, it is required that it be constructed of scale factor. The length scale factor was chosen materials which actually exist, rather than just as through the Froude number, eqn 15. The choice was mathematical constructs.

made to match the Froude number, eqns 16 and 17, at This application of the WAM methodology the test point pair designated previously. The model proceeds in two steps: 1) selection of the test point will not be Froude scaled for other points in the test pair, which fixes the dynamic pressure scale factor and envelopes. As discussed previously, Froude scaling 2) selection of the length scale, which in combination is not required. It produced a convenient size scale with step 1 and eqn 7 fixes the stiffness scale factor.

factor in this instance, eqn 18.

These two steps can also be described as choosing a V Fr = point in the 3-dimensional test space and then choosing Eqn 15 gb from the infinite number of WAM surfaces that pass through that point. The details of these choices follow.

Fr Fr = Eqn 16 M A A Mach number and altitude combination was chosen from the flight test envelope. Choosing an   V b altitude fixed the speed of sound and the density to be M M Eqn 17   =   used in the scaling process. For developing the scale V b   A A factors, a standard atmosphere was assumed; implications of this assumption are discussed later. sec) / ( 648   ft Eqn 18   2609 . 0 = = = λ λ V L Through these choices, the flight vehicle’s dynamic   sec) / ( 1269 ft   pressure and velocity were specified.

The stiffness scale factor is determined, eqn 19, by Chosen flight test values: enforcing eqn 7. Figures 4 through 6 show the WAM M =1.2 h =15,000 ft A A surfaces corresponding to this example.

Resulting flight condition parameters: 4 4 000962 . 0 2609 . 0 2076 . 0 = × = = λ λ λ Eqn 19 a = 1057 ft/sec L q EI A ρ = 0.001496 slugs/ft3 A Using these scale factors, finite element models 2 2 = ½ * ρ *M *a =1204 psf q of the flight vehicle and the wind tunnel model A A A A design have been developed and analyzed. The V = M * a = 1269 ft/sec A A A aerodynamic models utilized in this study are linear A dynamic pressure was chosen for the wind models; the wind tunnel model’s aerodynamic box tunnel test condition to correspond to the above flight layout is a geometrically scaled version of the flight test condition. This choice established the dynamic vehicle’s aerodynamic box layout. Subsonic analyses pressure scale factor. In the scaling process, estimated utilize doublet lattice aerodynamic theory; the gas purity and operating total temperature have to be supersonic analyses use ZONA51 aerodynamics. assumed. Based on historical TDT data, the values The AAW wind tunnel model is structurally chosen for use were 95% purity and 100 ° F. These are composed of a contoured center plate that will have a estimates of the conditions that will occur in the tunnel, balsa wood aerodynamic shell applied to it. The not parameters over which control can be exercised.

contouring of the center plate was the result of an The consequences of errors in these estimates will be iterative design process, matching first the structural discussed subsequently.

American Institute of Aeronautics and Astronautics stiffness properties and then the aeroelastic properties For both the flight vehicle and the wind tunnel model of the flight vehicle. The resultant conceptual design design, the coefficient changes substantially with the for the center plate is shown in figure10. incorporation of flexibility. In the case of the aileron Static aeroelastic analyses were performed; effectiveness, both the trend and the magnitude agree stability and control derivatives were calculated for the well in comparing the wind tunnel model and the configurations assuming first that the flight vehicle and flight vehicle. Because the hinge moments being wind tunnel model are rigid and second with flexibility applied to and by the trailing edge control surface are incorporated. Sample analytical results are shown in much lower than those encountered by the leading figures 11 through 13. As with the simple test case, the edge control surface, the strength requirements are rigid aerodynamic results were identical for the flight not nearly as restrictive. The wind tunnel model vehicle and the wind tunnel model. Figure 11 shows designer had sufficient freedom to tailor the material the test conditions for the flight vehicle at 5000 ft and thickness distribution near the aileron and in its load the wind tunnel model at corresponding wind tunnel conduction path. Thus, the control derivative test conditions. These test conditions correspond to test associated with the aileron matches that of the flight points shown on the WAM surface in figures 4 through vehicle more closely than that associated with the 6 by the dashed green trajectory lines. leading edge control surface derivative.

Figures 12 and 13 show the change in control Because this is an example of an actual design surface effectiveness for the leading edge outboard process, with the required design compromises for control surface and the aileron. Both are presented as construction and testing, the comparisons of static functions of Mach number. Four sets of data are aeroelastic properties are not as good as demonstrated plotted in each figure: the flight vehicle assuming no in the previous simple scaling example.

flexibility (rigid); the flight vehicle with aeroelastic effects at 5000 ft altitude; the wind tunnel model Influence of changes, errors, and assuming no flexibility (rigid); and the wind tunnel uncertainties model with aeroelastic effects at the wind tunnel dynamic pressures corresponding to 5000 ft. The Many issues that can arise as data is acquired trends shown in the figures correspond to expected influence the WAM process and data interpretation.

trends for an aft-swept wing. The trailing edge control Additionally, known issues exist which will limit surface is less effective with flexibility incorporated.

precision of test point correlation. These issues and The leading edge control surface becomes more their anticipated influences are presented.

effective with flexibility effects incorporated.

Figure 12 shows that the values of C for the L δ LEO Accounting for pilot being off-condition or rigid flight vehicle and the rigid wind tunnel model are non-standard atmospheric conditions identical, showing that the scaling of the aerodynamic Small variations in the aircraft altitude or Mach loads and the geometry are correct. Comparing the number can be accounted for by altering the wind aeroelastic coefficients to the rigid coefficients shows tunnel test conditions, in effect moving to a different that in both the flight vehicle and the wind tunnel model point on the WAM surface. In altering the wind design, there is a substantial change in the coefficient.

tunnel test point that is to correspond to the new Both the flight vehicle and wind tunnel model exhibit flight test condition, the Mach number must match the same trends with Mach number and with the actual flight test Mach number. The dynamic incorporation of the aeroelastic effects. However, the pressure for wind tunnel test point should be change in the leading edge outboard control surface calculated using the actual dynamic pressure obtained effectiveness is larger for the flight vehicle than for the during the flight test.

wind tunnel model in the transonic regime, indicating To account for a non-standard day, the that some areas of the wind tunnel model are stiffer corresponding mapped surface can be generated by than those areas of the flight vehicle. The root cause of adjusting the table of densities and speeds of sound this difference is associated with fabrication and testing corresponding to a given altitude. A different altitude constraints. Testing requirements in NASA Langley or velocity means that the wind tunnel’s matching wind tunnels force the model design to be very strong, condition is a different point on the original mapped requiring that certain parts of the wing cannot be made surface.

as thin as would be required for matching the properties of the flight vehicle more precisely. This mis-match in Effect of wind tunnel speed of sound properties is particularly true for regions near the variations leading edge control surfaces, where substantial The speed of sound in the TDT is primarily a material thickness had to be added to meet strength function of the purity and temperature of the gas.

requirements.

When R134a was first introduced at the TDT, a speed In figure 13 the values of C for the rigid flight L δ ail of sound of 525 ft/sec was predicted. When vehicle and the rigid wind tunnel model are identical.

American Institute of Aeronautics and Astronautics experimental data was obtained, a value of 540 ft/sec atmosphere tables, and the TDT tunnel was measured. The difference is primarily attributed to parameters program.

the purity of the gas being less than 100%, i.e. the test Instruments that measure total pressure, static medium is a mixture of air and R-134a. Since the speed pressure, gas purity and total temperature specify the of sound in air (1116 ft/sec) is substantially higher than test conditions in the TDT. These measurements are the speed of sound in heavy gas, even a 1% impurity made and values input to a tunnel parameters raises the test medium speed of sound noticeably.

computer program that computes additional flow The Froude number of the airplane and the model parameters, including Mach number and dynamic match when the ratio of their speed of sound squared pressure.

equals the length scale factor.

For this study, the resolutions of the pressure 2 2 λ = a /a L M A readings were assumed to be 0.1 psf, the purity of the If the speed of sound in the wind tunnel differs gas 0.1% and the total temperature 0.1 ° F.

from that used to originally compute the length scale Additionally, the uncertainties have been established factor, the model is now Froude scaled for a different as follows. For the pressures, the manufacturer of the airplane speed of sound and therefore different altitude.

transducer quotes the accuracy as 0.016% of reading The changed speed of sound affects intermediate +/- 0.008% of full scale (full scale reading 2100 psf).

scale factors for velocity and density, but in such a way A temperature fluctuation of 10 ° R was used in this that their individual effects cancel each other when study. The gas purity measurement is assumed computing the stiffness scale factor. The same is true accurate to +/- 3%.

for the dynamic pressure point. The dynamic pressure The influence of measurement errors was at which a wind tunnel test point is acquired is not examined at the maximum and minimum changed because of an inaccuracy in the tunnel speed of sound employed in the design procedure. Preserving test conditions flown in the AAW flight test the dynamic pressure, however, means that the density program. The results for the Mach 0.85, and speed of sound differ from those used in the design 5000 ft flight test point are presented in process. The density and speed of sound of the tunnel figure 14, which represents a very small test medium will be different for different purities. This region of the projection of the WAM is an issue of practical concern, as the tunnel has leaks, which result in a decrease in the gas purity. The surface, figure 4, onto the flight test plane.

observable effect is a reduction in tunnel operating The conclusions, summarized below, limit.

indicate the impact of measurement errors on test condition specifications and also Measurement uncertainties and instrument resolution indicate which measurement errors most limitations Uncertainties in wind tunnel measurements and significantly impact the ability to precisely resolution limitations of instruments, herein referred to match flight test conditions.

as measurement errors, were the subjects of a parameter Instrument resolution used in measuring TDT tunnel sensitivity study. The results provide limits for how parameters translates into flight test altitude precisely a specified flight test condition can be resolution of 31 feet. This is the additive resolution matched using the wind tunnel instrumentation.

associated with the instruments used in measuring Conversely, the results provide bounds for the precision total pressure, static pressure, temperature and heavy with which the flight test condition should be specified gas purity. Instrument resolution also impacts Mach for purposes of correlating with the wind tunnel results.

number resolution. Mach number can be resolved to To perform this study, flight test points were 0.0015.

Expanded uncertainties of measurements were also mapped into the TDT test space using the examined. Uncertainty in the total pressure WAM methodology and expressed in terms of primarily impacts the Mach number. Uncertainty in primary tunnel parameters. These calculated static pressure significantly affects both Mach parameters serve as simulated measurements, number and altitude (110 ft). The temperature to which measurement errors were applied.

uncertainty produces Mach number uncertainty (0.001) and altitude uncertainty (65 ft). The purity Tunnel parameters reflecting these uncertainty produces Mach number uncertainty of measurement errors were computed and 0.002 and altitude uncertainty of 132 ft.

mapped back to the flight test Mach number Variability in TDT temperature and purity can and altitude. Applying this procedure required cause misinterpretation of mis-scaling of altitude. To the dynamic pressure scale factor, standard avoid the mis-scaling, scale each flight condition using the dynamic pressure scale factor and use real- time measurements of tunnel temperature and purity.

American Institute of Aeronautics and Astronautics 2 Kvaternik, R.G., “Computer programs for calculating the isentropic flow properties for Concluding Remarks mixtures of R-134a and air,” NASA TM-2000- 210622, November 2000.

Static aeroelastic wind-tunnel research being 3 Keller, D.F., Farmer, M., Kvaternik, R.G., and performed at NASA Langley Research Center is an Cole, S.R., Personal communications, scaling essential part of the Active Aeroelastic Wing (AAW) computer program and unpublished documents program. Wind Tunnel to Atmospheric Mapping including (Kvaternik, R.G. “Computer Programs (WAM) is the process through which the wind-tunnel for Calculating the Isentropic Flow Properties for model is scaled to correlate with the AAW Flight Mixtures of R-134a and air: Source code Vehicle. WAM involves adapting the classic listings,” November 2000) aeroelastic scaling laws for developing statically scaled 4 Kuntz, W.H., Wasserman, L.S. and Alexander, wind tunnel models, circumventing some of the H.R., “Dynamically similar model tests of rotary difficult issues associated with typical aeroelastically wing and prop types of VTOL aircraft” scaled models. For this type of testing, a practical wind tunnel model can be designed and built such that 5 Bisplinghoff, Ashley and Halfman, multiple flight vehicle test conditions map to the wind “Aeroelasticity,” Addison-Wesley Publishing, tunnel envelope. For the AAW and similar static Reading, Massachusetts, 1955.

aeroelasticity programs, matching multiple test 6 Guyett, P.R., “The use of flexible models in conditions would not be possible if the traditional aerospace engineering,” RAE Technical Report No. 66335, November 1966.

scaling requirements used on flutter models were imposed, specifically mass ratio, reduced frequency and Froude number matching. Characteristics of the NASA Langley Transonic Dynamics Tunnel, particularly the variable pressure capability and the heavy-gas test medium, enable the multi-point scaling.

Reproducing the static aeroelastic characteristics of a full-scale vehicle in a wind tunnel model requires that several non-dimensional parameters be identical for both vehicle and model. Similitude requires that testing be conducted at matching Mach numbers and that the ratio of stiffness to aerodynamic forces must be the same. The aerodynamic pressure distribution and the stiffness distribution within the structure must also be maintained. In the static aeroelastic design and test space, two free parameters remain after the model is constructed. These freedoms consist of the Mach number and either the altitude of the flight vehicle or the Mach number and dynamic pressure of the wind tunnel model. Variation of the free parameters and calculation of the third creates a 3-dimensional surface on which the wind tunnel model and the flight vehicle operate. Thus, all flight test conditions map to wind tunnel test conditions.

Detailed design of a model to duplicate the static aeroelastic response of a flight test vehicle requires much diligence and balancing of strength criteria with stiffness matching requirements, as discussed in the Figure 1. Test envelope of the Transonic Dynamics AAW design problem. Model safety criteria dictating Tunnel, operating with heavy gas test strength requirements cut into the ability to produce a medium model that is a precise representation of the flight vehicle.

References 1 Molyneux, W. G. , “Aeroelastic modeling”, RAE Technical note number Structures 353, March 1964.

American Institute of Aeronautics and Astronautics Figure 5. WAM surface showing flight vehicle test envelope Figure 2. WAM surfaces for several stiffness scale factors; length scale factor = 0.26 Figure 6. WAM surface showing wind tunnel test envelope Figure 3. WAM surfaces for several length scale factors; stiffness scale factor = 0.00962 Figure 7. Structural model of hypothetical wing test case Figure 4. WAM surface for stiffness scale factor = 0.00962, length scale factor = 0.26 Figure 8. Comparison of hypothetical wing flight vehicle and wind tunnel model: lift curve slope American Institute of Aeronautics and Astronautics Figure 12. Comparison of AAW analytical results Figure 9. Comparison of hypothetical wing flight for flight vehicle and wind tunnel model; lift vehicle and wind tunnel model: lift coefficient due to coefficient due to leading edge outboard control control surface deflection surface deflection Figure 10. Conceptual design of wing core for AAW wind tunnel model; planform view showing material thickness Figure 13. Comparison of AAW analytical results for flight vehicle and wind tunnel model; lift coefficient due to trailing edge outboard control surface (aileron) deflection Figure 11. Test points corresponding to 5000 ft altitude Figure 14. Effect of wind tunnel measurement uncertainties and resolution limitations for the flight test point at Mach 0.85, 5000 ft altitude American Institute of Aeronautics and Astronautics