1、NASA TECHNICAL NOTE .NASA TN D-2350 _ c ./ LOAN COPY: G 2 -0 -0 - AFWL (1 -I KIRTLAND A om 5 X - AFTERBODY PRESSURES ON BODIES HAVING TURBULENT BOUNDARY LAYERS AT MACH 5.98 TWO-DIMENSIONAL BOATTAILED Langley Research Center Langley Station, Hampton, va8 NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
2、0 WASHINGTON, D. C. JULY 1964 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TECH LIBRARY KAFB. NM AFTERBODY PRESSURES ON TWO-DIMENSIONAL BOATTAILED BODIES HAVING TURBULENT BOUNDARY LAYERS AT MACH 5.98 By W. Frank Staylor and Theodore J. Goldberg La
3、ngley Research Center Langley Station, Hampton, Va. NATIONAL AERONAUTICS AND SPACE ADMINISTRATION For sale by the Office of Technical Services, Department of Commerce, Washington, D.C. 20230 - Price $1.00 I Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS
4、-,-,-AFTERBODY PRESSLTRES ON TWO-DIMENSIONAL BOATTAILED BODIES HAVING TLJR3“T BOUNDARY LAYERS AT MACH 5.98 By W. Frank Staylor and Theodore J. Goldberg Langley Research Center An investigation has been conducted on a series of two-dimensional after- bodies to determine the effects of boattailing and
5、 angle of attack upon base and boattail pressures. angles of attack up to 14O were investigated at a free-stream Reynolds number sufficient to cause fully turbulent boundary layers to exist ahead of the after- bodies. resulted in surface Mach numbers from approximately 3 to 7. Afterbodies with boatt
6、ail angles from Oo to 18 at The models were tested at a free-stream Mach number of 5.98 which A simple semiempirical method is presented for estimating base pressures for boattailed bodies at angle of attack which is the result of a correlation of base-pressure data from previous studies and the pre
7、sent investigation. This method is a modification and extension of previous work and gives a good estimate for existing base-pressure data between the Mach numbers of 1.4 to 6.0. The empirical estimation of boattail pressures made possible predictions of afterbody drag. At zero angle of attack a nea
8、r minimum afterbody drag was obtained between the Mach numbers of 2 to 6 both experimentally and by calcu- lation with boattail angles ranging from 6O to 12O. INTRODUCTION Theoretical and experimental investigations have shown that afterbody drag constitutes a substantial portion of the total drag o
9、n two-dimensional airfoils at supersonic speeds (for example, see refs. 1to 11). Chapman (refs. 1, 2, and 7) reports that in certain cases afterbody drag can amount to as much as three-fourths of the total airfoil drag. At high-supersonic and hypersonic speeds, theoretical and limited experimental i
10、nvestigations have indicated that afterbody drag is still a major design parameter for optimum lift-drag profiles although its influence is somewhat lessened. Many of the existing two-dimensional afterbody investigations include the effects of angle of attack and boattailing upon base pressure; howe
11、ver, in most of these studies the pressures on the boattail surfaces were not measured. Therefore, experimental data for the determination of total afterbody-pressure drag are limited at supersonic Mach numbers and completely lacking in the hypersonic range. The verification of existing supersonic m
12、ethods for Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-predicting base pressure at hypersonic Mach numbers has not been possible because of the lack of such data. The purpose of the present investigation was to obtain hypersonic base- and boattai
13、l-pressure data at angles of attack for two-dimensional bodies having turbulent boundary layers. This investigation was limited to turbuler,t boundary layers because previous investigations have shown that Reynolds num- ber had a negligible effect on base pressure for bodies having fully turbulent b
14、oundary layers (refs. 1, 2, and 9) which would be representative of most full- scale hypersonic applications. This investigation was performed in the Langley 20-inch Mach 6 tunnel at a free-stream Reynolds number of 7.7 x 106 per foot. SYMBOLS component of axial-force coefficient due to afterbody dr
15、ag pressure coefficient based on free-stream conditions, P - Pa s, P - Pg so pressure coefficient based on conditions ahead of the base, boattail length Mach number static pressure dynamic pressure surface Reynolds number at junction of model and afterbody surface distance measured from center of ba
16、se model thi cknes s angle of attack boattail angle equivalent Prandtl-Meyer expansion angle from boattail to base, “1 - “0 critical turning angle (see eqs. (2) to (4) equivalent Prandtl-Meyer expansion angle from model to boattail, v - vm 2 Provided by IHSNot for ResaleNo reproduction or networking
17、 permitted without license from IHS-,-,-V Prandtl-Meyer expansion angle Subs cript s : 00 free-stream conditions 0 cond-itions ahead of base 1 conditions ahead of trailing shock b conditions at base m conditions on model surface ahead of boattail min minim Superscript : I average conditions on base
18、or boattail surfaces APPARATUS AND TEST MECHODS Wind Tunnel The present investigation was conducted in the Langley 20-inch Mach 6 tun- nel. This tunnel is an intermittent tunnel that exhausts through a movable second minimum to atmosphere with the aid of an annular ejector. pressure and temperature
19、were approximately 400 psia and 400 F corresponding to a Reynolds number per foot of 7.7 X 106 for all tests. description of the tunnel is given in reference 12. Stagnation A more complete Model and Support Presented in figure 1 are sketches and photographs of the model, support, and afterbodies. Th
20、e model was 13 inches long, 9 inches wide, and 1 inch thick with a l5O half-angle wedge nose with a maximum leading-edge diameter of 0.005 inch. Afterbody configurations having boattail angles from 0 to 18O, in 3O increments, plus one circular-arc configuration were attached to the rear of the model
21、 each with 13 pressure orifices located at the midspan. tional orifices were located on the model at the midspan, one on the upper and lower surface. Transition strips were bonded to the upper and lower sur- faces for all but one of the test runs. These strips consisted of 0.050-inch- diameter grit
22、and were 0.3 and 0.6 inch wide on the wedge and plate surfaces, respectively, as shown in figure l(b). Two addi- The model was supported from its sides in the center of the test section by four vertical struts and was pivoted about the rear struts for angle-of- attack variation (see fig. l(c). The m
23、odel was tested at nominal angles of 3 4 - -. . . . . Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-attack of Oo, ?3 , d, kgo, and Ll.2, but the actual measured angles varied as much as 2O from these values as a result of wind loads on the model an
24、d support. At both positive and negative angles of attack the pressures were equal on the windward surfaces; however, small pressure differences were noted on the lee- ward surfaces at high angles of attack. Therefore, only positive angle-of- attack data (leeward surface opposite to the support syst
25、em) are presented. A flat-plate model with similar dimensions was previously tested in the Langley 20-inch Mach 6 tunnel at angles of attack from -8O to 5 (ref. 12). This model had several orifices located along the span 2.5 inches from each edge, and it was found that the pressures were constant in
26、 the spanwise direction. Test Methods and Techniques Static pressures on the model and afterbodies were recorded by photo- graphing two multiple-tube manometers - one with butyl phthalate as the fluid for measuring pressures less than 1.0 psia, the other with mercury for higher pressures. Tunnel sta
27、gnation pressure was measured with a Bourdon gage which was photographed simultaneously with the manometers. based on a nominal free-stream Mach number of 5.98. inaccuracies of the pressure coefficients are: All calculations were The estimated maximum due to Mach number variation . . . . . . . . . .
28、 . . . . . . . . f0.0020 due to pressure measurement errors . . . . . . . . +0.0015 for Cp,m 0.12 EP,W KP, a, AcP, ,O0 The angles of attack were set at nominal angles of Oo, 3O, 6O, 9O, and 12O, but the actual angles as determined from photographs are believed accurate to m.1. RESULTS AND DISCUSSION
29、 Data Presentation Variation of Mach number and Reynolds number.- Presented in figure 2 is a plot of Mach number on the windward and leeward surfaces of the model as a function of angle of attack. and 12) based on the ratio of measured static pressure to theoretical total pressure behind the oblique
30、 shock are shown. A comparison of the experimental Mach numbers obtained with the Oo and 12O boattails indicates that the after- bodies do not influence flow conditions on the model. These values agree with the trend of the shock-expansion method at all angles of attack on the windward surface and t
31、o about 5O angle of attack on the leeward surface beyond which angle flow separation is believed to occur. expansion method are used for dl subsequent calculations. Shock-expansion and experimental values (p = Oo Mach numbers obtained by the shock- 4 Provided by IHSNot for ResaleNo reproduction or n
32、etworking permitted without license from IHS-,-,-The surface Reynolds number at the junction of the model and afterbody is plotted against Mach number on the model surface in figure 3. numbers were calculated with the assumption that shock-expansion flow existed on the model surfaces. investigation
33、conducted in the same tunnel are included in figure 3 in order to establish regions of boundary-layer transition (ref. 13). that these data from reference 13 were for natural transition (no roughness) on flat plates and therefore had a turbulence level less than that of the present investigation. Th
34、erefore, the boundary layer at the junction is believed to be fully turbulent on the windward surface and also on the leeward surface to the point of flow separation (a Oo, respectively. In the present study it is proposed that the critical turning angle may further be used to estimate base pressure
35、s on boattailed bodies at small angles of attack (see sketch 3) w5th the use of the e quati on It is assumed that the base pressure is primarily a function of the flow con- ditions on the windward surfaces and that both 6 and E are determined from Sketch 3 7 Provided by IHSNot for ResaleNo reproduct
36、ion or networking permitted without license from IHS-,-,-these conditions. Critical turning angles were calculated with equation (4) from pressure data at angles of attacks up to 14O and then were converted to vdues. These data are denoted as solid symbols in figure 10, and the validity of the prese
37、nt proposal may be seen. cP, 0 Equation (4) reduces to equations (2) and (3b) when the appropriate terms are dropped to satisfy the requirements originally proposed by Love (a = p = Oo) and C0rtrigh.t and Schroeder (a = Oo) . Therefore, equations (1) and (4) together with figure 9 can be used to est
38、imate the base pressures on boattailed bodies at angles of attack from Mach numbers of 1.4 to 6.0. An example calculation is presented in the appendix to clarify details that are not discussed here. In figure ll(a) experimental base values are presented and com- pared with the calculated values for
39、boattail angles of Oo, 6O, 12O, and 18O. The agreement is very good for afterbodies with small boattail angles through- out the angle-of-attack range of the investigation. The present method over- predicts base pressures on the p = l5O and p = 180 afterbodies which can be attributed to total separat
40、ion of the flow from the boattail surfaces. The pressures were essentially equal on all surfaces of these afterbodies at small angles of attack (figs. 4(f) and 4(g) which indicates that the flow had sep- arated at the junctions of the model and afterbodies. not sense the existence of these afterbodi
41、es and their base pressures, in general, can be better predicted by the p = Oo base-pressure estimate (see sketch 4). In effect, the flow does Sketch 4 Leeward boattail.- Experimental leeward boattail C; values are pre- ,O0 sented in figure ll(b) along with estimated values which are complicated by
42、flow separation occurring forward of the afterbody at may be used to estimate the pressures on the leeward boattail surfaces in a manner similar to that employed for the windward surfaces when the flow is believed to be attached. sure is approximately equal to the base pressure at high angles of att
43、ack; a 5O. Equation (1) Experimental data show that the leeward boattail pres- 8 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-these pressures are approximated by the base-pressure values when the flow is believed to be separated forward of the aft
44、erbody. Aft erbody Drag Experimental and estimated components of axial-force coefficient due to afterbody drag obtained from integration of the experimental and estimated pressures over the afterbody surfaces are presented in figure 12. At zero angle of attack, afterbody drag was reduced from 0.0256
45、 for 0.0195 (25-percent reduction) for afterbodies decreased with increasing angle of attack with minimum drag occurring on the 12O afterbody. At a = 130 afterbody drag was reduced as much as 70 percent as the result of boattailing the model. drag coefficients are well predicted by the present estim
46、ates for are underpredicted for larger angles because of flow separation. mentioned, a better estimate may be obtained for the larger boattail angles by assuming that the ward boattail surfaces. p = Oo to about j3 = 6O, go, or 12O. Drag on the boattailed The experimental j3 5 12 but As previously p
47、= Oo base-pressure estimates exist on the base and lee- Experimental and calculated minimum afterbody-drag coefficients and their associated boattail angles at zero angle of attack are presented in figure 13. These coefficients are based on afterbody length-to-height ratio of 1.15 which approximates
48、 the models used for the present investigation and for those of reference 5. relatively insensitive to boattail angle within k3; minimum drag occurred both experimentally and theoretically at approximately Mach numbers of 2 to 6. + Experimentally, the minimum drag coefficients were found to be p = g
49、o between the CONCIUDING RENARKS Afterbody pressures have been investigated at a free-stream Mach number of 5.98 along a series of two-dimensional boattailed bodies at various angles of attack. A simple semiempirical method for estimating base pressures for boattailed bodies at angle of attack with turbulent boundary layers is pre- sented which
