Impingement of Water Droplets on NACA 65A004 Airfoil at 8 deg Angle of Attack

NATIONAL ADVISORY COMMITTEE

FOR AERONAUTICS

TECHNICAL NOTE 3155 IMPINGEMENT OF WATER DROPLETS ON NACA 65A004 AIRFOIL AT 8 0 ANGLE OF ATTACK By Rinaldo J . Brun, Helen M. Gallagher, and Dorothea E. Vogt Lewis Flight Propulsion Laboratory Cleveland, Ohio Washington July 1954

NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS TECHNICAL NOTE 3155 IMPINGEMENT OF WATER DROPLETS ON NACA 65A004 AIRFOIL AT 8° ANGLE OF ATTACK By Rinaldo J. Brim, Helen M. Gallagher, and Dorothea E. Vogt SUMMARY The trajectories of droplets in the air flowing past an NACA 65AO04 80 were determined.. The amount of airfoil at an angle of attack of water in droplet form impinging on the airfoil, the area of droplet im- pingement, and the rate of droplet impingement per unit area on the air- foil surface were calculated from the trajectories and presented to cover a large range of flight and atmospheric conditions. These impingement characteristics are compared briefly with those previously reported for the same airfoil at an angle of attack of 40.

INTRODUCTION The data presented herein are a continuation of the study reported in reference 1 on the impingement of cloud droplets on a low-drag, thin airfoil. The airfoil studied in both the reference cited and in this report is a 4-percent-thick symmetrical NACA 65A004 airfoil. In refer- ence 1 the impingement characteristics of the airfoil were reported with the airfoil set at an angle of attack of 4 ; whereas, the data herein apply for an angle of attack of 8 0 . The data calculated for 8 0 angle of attack, along with those data for presented in reference 1, permit the evaluation of the impingement characteristics for circling, landing, and some types of flight plans for pursuit or fighter aircraft.

The trajectories of atmospheric water droplets about an NACA 65A004 airfoil at 80 angle of attack at subsonic velocities were calculated with the aid of a differential analyzer at the NACA Lewis laboratory.

From the computed trajectories, the rate, distribution, and surface ex- tent of impinging water were obtained and summarized in this report.

SYMBOLS The following symbols are used in this report: droplet diameter, microns (micron = 3.28X10 d 6 ft)

NACA TN 3155 , dimensionless (the density of inertia parameter, 1.704xl0 K water, 1.94 slugs/cu ft, is included in the constant) airfoil chord length, ft L free-stream Remolds number with respect to droplet, 4.813X106 Re 0 dPaU dimensionless distance on surface of airfoil measured from leading-edge chord S point, ratio to chord length U flight speed, mph U local air velocity, ratio to free-stream velocity rate of water impingement per unit span of airfoil, lb/(hr)(ft span) W rate of total water impingement per unit span of airfoil, lb/(hr) WM (ft span) local rate of water impingement, lb/(hr)'(sq ft) liquid-water content in cloud, g/cu m w x,y rectangular coordinates, ratio to chord length dy0 local impingement efficiency, -, dimensionless viscosity of air, slugs/(ft)(sec) density of air, slugs/cu ft P a Subscripts: lower airfoil surface 7.

airfoil surface s upper airfoil surface u free stream

NACA TN 3155 RESULTS AND DISCUSSION In order to obtain the extent of impingement and the rate of droplet impingement per unit area on the airfoil, the cloud droplet trajectories with respect to the airfoil were determined. The method for calculating the droplet trajectories is described in reference 2. A solution of the differential equations that describe the droplet motion was obtained with the use of the mechanical analog (described in ref. 3) based on the prin- ciple of a differential analyzer. The air-flow field around the airfoil was obtained by the vortex substitution method described in reference 2, except that, for the NACA 65AO04 airfoil, the velocities at the surface of the airfoil were calculated by the method described in reference 4, whereas the surface velocities on the 65 1_ 212 and 651_208 airfoils dis- cussed in reference 2 were obtained from wind-tunnel measurements of the pressure coefficients. The values of the surface velocities for the 65AO04 airfoil were calculated by the Douglas Aircraft Corporation for the Lewis laboratory (see fig. 1). Although the droplet trajectories were calculated for an incompressible flow field, the results of the calculations can be applied up to the flight critical Mach number (ref. 5).

The geometric chord line of the airfoil is oriented at an angle of with the x-axis of the rectangular coordinate system, and the leading edge is placed at the origin of the coordinates, as shown in figure 2.

The airfoil orientation presented in references 1 and 2 is retained here- in, except for the magnitude of the angle of attack. At an infinite distance ahead of the airfoil, the uniform air flow carrying the cicud droplets is assumed to be approaching the airfoil from the negative x-- direction and parallel to the x-axis. All distances are dimensionless, because they are ratios of the respective actual distance to the airfoil chord length L.

Rate of Water Interception The rate of total water interception, in pounds per hour per foot of wing span, is determined by the tangent droplet trajectories (fig. 2), by the speed of the aircraft, and by the liquid-water content in the cloud. The flight speed and size of the airfoil, as well as the droplet size in the cloud, are the principal variables that affect the spacing between the two tangent trajectories. The amount of water that strikes the airfoil is proportional to the spacing y0 0 ,, and the rate of ,u - y , total water interception per unit span of the airfoil on that portion of the airfoil surface bounded by the upper and lower tangent trajectories can be calculated from the relation (1) Wm = O.33UwL ( yo, - Yo , j)

NACA TN 3155 The values of y0,u - y 0,2 are given in figure 3 in terms of the recip- rocal of the inertia parameter 1/K and the free-stream Reynolds number Re0 . The inertia parameter K is a measure of the droplet size, the flight speed and size of the airfoil, and the viscosity of the air through the relation U (2) K = 1.704Xl0-12 d The density of water and the acceleration of gravity, which are expressed as part of the conversion factor, are 62.4 pounds per cubic foot and 32.17 feet per second per second, respectively. The free-stream Reynolds number is defined with respect to the droplet as Re0 = 4.813X10 6 dpaU (3) A graphical procedure for determining values of the dimensionless param- eters K and Re 0 in terms of airplane speed, chord length, altitude, and droplet size is presented in appendix B of reference 2.

The variation of rate of water interception with airfoil speed is summarized for an altitude of 20,000 feet in figure 4, in which the ordi- is the total rate of water impingement per foot span of air- nate Wm/W foil per unit liquid-water content (g/cu m) in the cloud. Several chord lengths ranging in value from 2 feet to 20 feet are considered. The val- ues in figure 4 are for flight through clouds composed of uniform drop- lets 15, 20, 30, and 40 microns in diameter. The values of Wm/w. given in figure 4 are based on the most probable icing temperature as a func- tion of altitude presented in figure 15 of reference 2. (The most prob- able icing temperature was obtained from approximately 300 icing obser- vations in flights.) As shown in reference 2, a change in altitude of 10,000 feet will change the rate of water impingement by approximately 7 percent. The droplet size and the liquid-water content of clouds are seldom known with sufficient accuracy (ref. 3) to permit the rate of water impingement to be calculated within 10 percent; therefore, within practical limits of application, the results of figure 4 can be used over a wide range of altitudes (approx. ±10,000 ft, see ref. 2).

The effect of wing taper can also be obtained from figure 4, provid- ed that for each section of span considered the taper is small enough that two-dimensional flow over the section is approximated, as is men- tioned in reference 2.

NACA TN 3155 Extent of Impingement The limit of impingement is determined by the point of tangency on the airfoil surface of the two tangent trajectories. The rearward limits of impingement on the upper surface are shown in figure 5(a), and on the lower surface in figure 5(b). The distances S and S are measured on the airfoil surface from the point of intersection of the geometric chord line with the leading edge (fig. 2) in terms of the chord length.

The limits of impingement are given in figure 5 in terms of the recipro- cal of the inertia parameter and free-stream Reynolds number.

At an angle of attack of 80 the extent of impingement on the upper surface is always less than 2 percent of chord = 0.02), which is the largest value possible for the extreme conditions where 1/K = 0. The value of S for 11K = 0 was obtained from simple geometric relations.

The remaining values of presented in figure 5(a) were obtained from Su calculated trajectories. These calculated values may be quite inaccu- rate, because of the sharp-edged shape of the airfoil at the leading edge.

The accuracy of determination of is unimportant in an application Su to airfoil icing calculations, because all values of must be less Su than 0.02. The estimated accuracy for the values given in figure 5(a) is ±20 percent.

Nearly all the water impinging on the airfoil impinges on the lower surface between the leading-edge chord point and the lower limit given in figure 5(b). As was discussed in reference 1 for the NACA 65A004 air- foil at 40 angle of attack, the tangent trajectories approach the lower surface of this airfoil very gradually. This very gradual approach of the lower-surface tangent trajectories leads to uncertainties as to the location of the tangent point, and the values of S are therefore sub- ject to individual interpretation. The uncertainties in the location of the tangent point can range from ±4-percent chord at 1/K 1 to ±7 percent at 1/K 3 and back to at 1/K 100. For the ex- ±4 percent treme case of 1/K = 0, the impingement extends to the trailing edge of the airfoil section. The lower-surface limits are summarized in figure 6 for the same speeds, chord lengths, droplet sizes, and altitude given in figure 4.

Impingement Distribution on Surface Trajectory starting ordinate as function of point of impact. - The manner in which water is distributed on the surface of an airfoil can be obtained if the starting point of a droplet trajectory is known with respect to the point of impingement on the surface. The starting

NACA TN 3155 ordinate y0 at infinity of any impinging trajectory, including trajec- tories bounded by the upper and lower tangent trajectories (fig. i), can be found in figure 7 with respect to the point of impingement on the sur- face. The values for the starting and ending positions of the trajec- tories are shown in figure 7 for four values of free-stream Reynolds nuin- ber. For each value of Re 0 , curves for several values of 1/K are given.

The amount of water impinging between any two given points on the airfoil surface may be found by applying the results of figure 7 in the relation (4) W = 0.33UwL(y0 1 - y02 ) obtained from the end points of each The values of y0 - y0 'U curve in figure 7 are the same as the values given in figure 3. The for 1/K = 0 (not shown in fig. 7) is -0.139 at value ofy0 S = 1.00229 (airfoil trailing edge) for all values of Re0.

Local rate of droplet impingement. - The local rate of droplet im- pingement per unit area of airfoil surface can be determined from the expression d.y0 = 0.33Uw— = 0.33Uw13 (5) which is related to equation (4), with proper consideration for the fact that y0 and S are based on the wing chord L. The values of the as a function of the airfoil distance local impingement efficiency 1 S are given in figure S. These values were obtained from the slopes of the curves in figure 7.

(fig. 8) are very As is discussed in reference 1, the values of 1 3 sensitive to the shape of the y0 against S curves (fig. 7). Because of the geometry of the sharp-nosed NACA 65A004 airfoil and the manner in which the trajectories approach the airfoil surface, small errors in the calculated trajectories result in considerable error in the slopes of due to the curves of figure 7. The possible error in the values of 13, the computational procedure, for surface positions other than near the stagnation point, is estimated in reference 1 to be somewhat less than ±10 percent for the values reported therein. Because of improved tech- given in figure niques in the computational procedure, the values of 8 herein are in error by somewhat less than ±2 percent for surface posi- tions other than within 1 percent of the surface distance where the peak

NACA TN 3155 occur. Since the total water impinging is directly relat- values of 1 3 ed. to (ThS I U dS (6)

= I

yo,u - YO )I J-s1 in figure 8 a check on the computational accuracy of the values of was also obtained by comparing the area under each 13 curve with the given in figure 3. The area values checked with- values of y - y , lu in ±1.5 percent of the corresponding values for total water interception.

P is also improved in this The accuracy in the maximum value of report as compared with that reported in reference 1. The possible error was estimated to be ±25 percent for the maximum values of 13 reported in the reference cited; whereas, the possible error in the maximum val- given in figure 8 is estimated to be less than ±12 percent.

ues of 1 3 As was discussed in reference 2, this possible error is not considered very serious, because only a small portion of the total water impinging on the airfoil is involved in the error.

Comparison of Impingement at 8 0 with Impingement at 40 Angle of Attack Rate of total water interception. - For all values of the reciprocal of inertia parameter and free-stream Reynolds number, the rate of total water interception is greater at an angle of attack of 80 than at an angle of attack of 40 This comparison can be made between figure 3 of this report and figure 3 of reference 1. The comparison is summarized in the following table for conditions established at 300 miles per hour, a chord length of 9.4 feet, and an altitude of 10,000 feet: Ratio of rate of Free-stream Droplet Reciprocal Y0,u - Yo,2 total water at diameter, Reynolds of inertia Angle of attack 80 to rate at 40 d, number, parameter, microns Re0 11K 0.099 0.053 1.87 80 594 .021 2.05 25 190 .043 .005 3.40 59 .017 100 8 The value of free-stream Reynolds number tabulated is the value obtained from equation (3) for the physical conditions established for this comparison.

NACA TN 3155 Extent of impingement. - Although the limit of impingement on the than for upper surface is farther rearward for an angle of attack of 0 , the total extent is very small in both cases. At 4 0 angle of attack Su is always less than 0.02 for values of 1/K> 1. At 8 0 angle of attack Su is always less than 0.01 for values of 1/K> 1.

The impingement on the lower surface extends back to the trailing edge at both angles of attack for 1/K = 0. The lower-surface limit is summarized in the following table for the same flight and atmospheric conditions given in the preceding section on rate of total water inter- ception: Limit of impingement Reciprocal Droplet Free-stream on lower surface, Sj of inertia diameter, Reynolds d, number, parameter, Angle of attack microns Re0 1/K 8° 0.74 0.53 80 594 .17 190 .34 10 25 59 .21 .03 100 8 1 Local rate of droplet impingement. - At a given point on the lower is greater at an angle surface, the local rate of droplet impingement 13 of attack of 8 0 than at 40 . For both 8 0 and 4°, the maximum rate of local impingement occurs between 0 and S = 0.01 on the lower surface.

than at 4. At 8 0 angle of The peak values of 13 are higher at 8 0 attack the peak values are between 0.8 and 1.0; whereas, at 4 the peak values are reported as low as 0.3 and none higher than 0.56. These large differences cannot all be accounted for by the possible estimated error in determining the peak values.

CONCLUDING REMARKS The data presented herein apply directly to flights in clouds com- posed of droplets that are all uniform in size and to nonswept wings of high aspect ratio. A detailed procedure for weighting the impingement of droplets for flights in nonuniform clouds is presented in reference 3.

A method for extending the impingement calculations for nonswept wings to swept wings is presented in reference 6. As is discussed in refer- ence 5, the impingement results should be applicable for most engineering uses throughout the subsonic region, because the subsonic compressibility of air does not affect the droplet trajectories appreciably.

Lewis Flight Propulsion Laboratory National Advisory Committee for Aeronautics Cleveland, Ohio, May 20, 1954

NACA TN 3155 REFERENCES 1. Brun, Rinaldo J., Gallagher, Helen M., and Vogt, Dorothea E.: Im - pingement of Water Droplets on NACA 65A004 Airfoil and. Effect of Change in Airfoil Thickness from 12 to 4 Percent at 4 Angle of Attack. NACA TN 3047, 1953.

2. Brim, Rinaldo J., Gallagher, Helen M., and Vogt, Dorothea E.: Im- 212 Airfoils at pingement of Water Droplets on NACA 651-208 and 65 40 Angle of Attack. NACA TN 2952, 1953.

3. Brun, Rinaldo J., and Mergler, Harry W.: Impingement of Water Droplets on a Cylinder in an Incompressible Flow Field and Evaluation of Rotating Multicylinder Method for Measurement of Droplet-Size Dis- tribution, Volume-Median Droplet Size, and Liquid-Water Content in Clouds. NACA TN 2904, 1953.

4. Theodorsen, T., and Garrick, I. E.: General Potential Theory of Arbi- trary Wing Sections. NACA Rep. 452, 1943.

5. Brim, Rinaldo J., Serafini, John S., and Gallagher, Helen M.: Im- pingement of Cloud. Droplets on Aerodynamic Bodies as Affected by Compressibility of Air Flow Around the Body. NACA TN 2903, 1953.

6. Dorsch, Robert G., and Brim, Rinaldo J.: A Method for Determining Cloud-Droplet Impingement on Swept Wings. NACA TN 2931, 1953.

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Figure 4. - Continued. Total rate or water impinge- ment on 85A004 airfoil. Angle of attack, 8; alti- tude, 20,000 feet most probable icing temperature, -11° F.

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Figure 4. - Concluded. Total rate of water impingement on 65A004 airfoil. Angle of attack, 8 0 ; altitude, 20,000 feet; most probable icing temperature, _110 F.

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