1、NASA TN D-52: TECHNICAL NOTE 0-523 INVESTIGATION OF THE FLOW IN A RECTANGULAR CAVITY IN A FLAT PLATE AT A NlACH NUMBER OF 3.55 By Russell W. McDearmon Langley Research Center Langley Field, Va. NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON September i960 HASA-TN-D- 523) IN VESTIGATTON OF
2、THE PLOW 889-709 M IN A BECTANGULAR CAVITY IN A PLAT PLATE 8ACH NUMBEB OF 3.55 (NASA. I Langley Research Center) 43 p Unclas AT A 00/34 01990 38 c Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 8 TECHNIC
3、AL NOTE D-523 . INVESTIGATION OF IXE FLOW IN A RECTANGULAR CAVITY IN A FLAT PLATE AT A MACH NUMBER OF 3.53 By Russell W. McDearmon SUMMARY An investigation has been made in the Mach 3.5 blowdown jet of the Langley High-Temperature Fluid Mechanics Section of the flow in a rectangular cavity in a flat
4、 plate. The results indicate that a criti- cal value of the ratio of depth to chord length existed between 0.093 and 0.146 such that the pressure distribution in the cavity was very sensitive to depth changes for ratios of depth to chord length less than the critical value and was insensitive to dep
5、th changes for ratios of depth to chord length greater than the critical value. tions had large effects on the pressure distribution only in the narrow cavities (cavities having ratios of span to chord length less than 0.25) at the moderately shallow depth (ratio of depth to chord length equal to 0.
6、093). Varying the upstream and downstream lip radii caused large changes in the pressure distribution only in the moderately wide (ratio of span to chord length equal to 0.75), moderately shallow cavity. Span varia- The critical depth of the cavity and the pressure distribution in the, very shallow
7、cavity (ratio of depth to chord length equal to 0.042) were predicted analytically over the supersonic Mach number range, and the predictions agreed with experiment at a Mach number of 3.55. The boundary layer of the flow approaching tne cavity v distances upstream of cavity lip are considered negat
8、ive, and distances downstream-of cavity lip are considered positive Y perpendicular distance above top of plate 6 thickness of boundary layer V Prandtl-Meyer angle (angle through which a supersonic stream is turned to expand from i.1 = 1 to ?I 1) cp Subscripts : two-dimensional flow-deflection angle
9、 through shock 0 1 conditions immediately upstream of cavity (fig. 11) conditions in upstream corner of very shallow cavity (fig. 11) 2 conditions in midportion of very shallow cavity (fig. 11) 3 corditions in downstream corner of very shallow cavity (fig. 11) Provided by IHSNot for ResaleNo reprodu
10、ction or networking permitted without license from IHS-,-,-4 4 W conditions immediately downstream of cavity (fig . 11) free-stream conditions * APPARATUS Wind Tunnel The tests were conducted in the Mach 3.5 blowdown jet of the Langley High-Temperature Fluid Mechanics Section. For this facility, dry
11、 air from high-pressure storage tanks is exhausted through a stagnation cham- ber to a nozzle with a rectangular test section about 5 inches square. The air then passes through a fixed diffuser to the atmosphere. pressure in the stagnation chamber can be controlled and held constant. The Models A dr
12、awing of the model is presented in figure 1. The pressure distributions in the cavity were obtained by means of 0.020-inch- diameter orifices in the model and a multiple-tube mercury manometer. The locations of the orifices are given in figure 2. The various depths of the cavity and the provisions f
13、or varying the upstream and downstream lip radii are also shown in figure 2. 0 The cavity was located in the plate so that the Mach lines from the corners of the leading edge fell outside of the cavity side faces. The model was made of steel and the top of the plate and the interior surfaces of the
14、cavity were highly polished. The leading edge of the plate was made as sharp as possible. the cavities were varied by means of metal inserts, and the span and lip-radii variations were obtained by using mahogany inserts. in the exposed surfaces resulting from the insertions were carefully filled in
15、with plaster. The depth and chord length of Any gaps All model configurations were tested with and without an aluminum- oxide transition strip on the plate (abbreviated “t.s.“ on the figures). The strip was approximately 0.007 inch thick; other dimensions and the locations of the strip are given in
16、figure 1. PRECIS ION . The estimated probable errors in the test parameters and variables are as follows: L 5 1 8 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-5 M. kO.05 For lCpl = 0.010 kO.0004 For ICpl = 0.200 kO.008 For lCpl = 1.300 kO.030 d/c
17、kO.001 b/c kO.O1 ru/c . kO.01 cp : x/c kO.002 rd/c . koa01 The angle of attack of the top of the flat plate was maintained at Oo, within +O.lO and -O.Oo. Throughout the tests the moisture content in the tunnel was ascer- tained (by dewpoint measurements) to be so low that the effects of condensation
18、 were negligible. RESULTS AND DISCUSSION Boundary Layer In order to identify the boundary layxr of the flow approaching (The exact location of the survey was 97 percent of the the cavity, pitot surveys were made immediately ahead of the upstream cavity lip. distance from the plate leading edge to th
19、e upstream cavity lip on the longitudinal center line of the plate.) without a transition strip affixed near the plate leading edge. Surveys were made with and The boundary-layer Mach number distributions obtained in tne surveys are presented in figure 3(a). strip had little effect on the shape of t
20、he curve, although it increased the boundary-layer thickness from approximately 0.043 inch to 0.054 inch. The presence of the transition Nondimensional velocity profiles were computed and are compared with theoretical laminar profiles from reference 8 and theoretical tur- bulent profiles in figure 3
21、(b). The experimental profiles with the transition strip off and on agree well with the 1/9-power turbulent profile; this indicates that natural transition from laminar to turbu- lent flow occurred on the plate upstream of the cavity. Pressure-distribution measurements ir, the cavity with the transi
22、- tion strip off and on were made over the range of depth, span, and Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6 . (. lip-radii variations of the tests. effects on the pressure distributions; therefore the data with the tran- sition strip on wi
23、ll not be presented. The transition strip had negligible Effects of Depth on Flow in Cavity Pressure distributions.- The effects of depth on the pressure dis- tribution in the cavity are shown in figure 4. The data presented were obtained for the widest cavity tested for each chord length (b/c = 2.0
24、0 for c = 0.500 inch and c = 1.000 inch; b/c = 1.25 for L c = 1.500 inches) 5 data was minimized. 1 8 so that the influence of the cavity side faces on the Figure 4 shows that markedly different pressure distributions were obtained for d/c = 0.042 and d/c = 0.093. Increasing d/c from 0.093 to 0.146
25、further changed the pressure distribution, whereas nearly the same distributions were obtained on the upstream face and bottom for d/c = 0.202, 0.329, and 0.457 as for d/c = 0.146. This indicated that a critical value of after referred to as tion was very sensitive to depth changes for d/c existed b
26、etween 0.093 and 0.146 (herein- (d/c)critica such that the pressure distribu- d/c (d/c)critical. Figure 4 also shows that for the wide cavities d/c was a suffi- cient parameter for defining the pressure distribution; that is, the pressure distribution was independent of c at all depths except for sm
27、all effects of c in the downstream corner. Schlieren photographs and shadowgraphs.- Figure 5 presents schlieren photographs and shadowgraphs of the shock structure immediately above the wide cavities over the range of depths for which pressure distribu- tions were measured. Study of the schlieren ph
28、otographs and shadow- graphs and the corresponding pressure distributions of figure 4 indi- cates that the flow phenomena in the cavities were as shown in the following sketches: Shock waves, / Expansion fan b/c = 1.23 and 2.00. Provided by IHSNot for ResaleNo reproduction or networking permitted wi
29、thout license from IHS-,-,-7 L 5 1 8 Sketch (b) d/c = 0.093; b/c = 1.25 and 2.00. Shock wave I Sketch (c) d/c = 0.146; b/c = 1.25 and 2.00. Figure 4(a) shows that for d/c = 0.042 the flow became attached to the cavity bottom, as depicted in sketch (a); that is, a large pres- sure decrease XES this v
30、alue will be designated Figures 4(c) to 4(f) show that for the flow was also detached from the bottom, as depicted for in sketch (c), although the flow phenomena were different from those for d/c = 0.093. (See sketch (b).) existed between 0.042 and 0.093 at which the flow just became (d/c)detached.
31、d/c = 0.146, 0.X2, 2.529, axd 0.437 d/c = 0.146 In conclusion, d/c not only influenced the pressure distribution for depths sufficiently small for the flow to be attached to the cavity Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-a b bottom (d/c (
32、d/c)detached), but continued to affect the pressure dis- s tribution beyond the depth (d/c = 0.093) for which the flow was com- pletely separated from the bottom. (d/c)nri+ina, a value of d/c assume a “constant“ character which was unaltered by further depth increases. Only when the depth reached be
33、tween 0.093 sn8 Q-146, 552 the fky .-* .L “ b/c = 0.13 or 0.19. The flow turned downward into the cavity at approximately the same angle as shown for the very wide (b/c = 2.00), very shallow cavity (d/c = 0.042) in sketch (a) of a preceding section, but the flow appar- ently did not become attached
34、to the bottom, as occurred for Increasing b/c shown in sketch (b) of a preceding section. d/c = 0.042. to 0.25 caused the flow phenomena to revert to that Effects of Spanwise Iocation on Pressure Distribution in Cavity Figure 8 presents the effects of spanwise location on the longitu- dinal pressure
35、 distribution in a moderately wide cavity (b/c = 0.75). Nearly identical pressure distributions were obtained in the center and near the side for the shallow and deep versions of this cavity, indi- cating that the spanwise location of the pressure measurements had no effect on the pressure distribut
36、ion in a moderately wide cavity. Effects of Upstream and Downstream Lip Radii on Flow in Cavity Pressure distributions.- The effects of qstreaa and downstream lip radii on the pressure distribution in the cavity are presented in figure 9. (b/c = 0.75) of the moderately shallow cavity (d/c = 0.093),
37、changing both r c and ra/c from 0 to 0.08 markedly changed the pressure rdc from 0 to 0.08 distribution, whereas either changing ru/“ or while the other remained 0, or changing both ru/c and rd/c from 0 to 0.03, did not affect the pressure distribution. shows that the pressure distributions in the d
38、eep versions of the moderately wide cavity were unaffected by the variations in lip radii. For the very narrow (b/c = 0.13), moderately shallow cavity (d/c = 0.093), figure g(b) shows a general trend toward slightly Figure 9(a) shows that for the moderately wide version u/ FIgce g(a) also Provided b
39、y IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-10 reduced pressures in the downstream corner when the downstream lip was rounded. For the very wide (b/c = cc?eratz1;- s.Zalluw cavity (d/c = 0.093), figure 9(c) shows that the pressure distribution was unaffect
40、ed by variations in lip radii. Schlieren photographs and shadowgraphs.- Figure 10 presents schlieren photographs showing the effects of upstream and downstream lip radii on the shock structure immediately above the moderately wide (b/c = 0.73), moderately shallow cavity (d/c = 0.093). Study of the p
41、hotographs and the corresponding pressure distributions of figure 9( a) indicates that changing both ru/c and rd/c from 0 to 0.08 caused changes in the flow phenomena which were quite similar to those obtained reduced from “Effects of Span on Flow in Cavity.“) erately shallow cavity were very sensit
42、ive to configuration changes, since either of the above changes caused the flow to change from dipping slightly into the cavity to dipping deeply into the cavity and probably striking the bottom. “hus the value of d/c for which the flow just became detached from the bottom of the very wide cavity (b
43、/c = 2.00) may have been close to 0.093. L 1 8 in the square-lipped cavities having d/c = 0.093 when the span was 5 b/c = 0.25 to 0.19. (See the preceding section entitled The flow phenomena in the mod- Prediction of Critical Depth of Cavity An attempt has been made to predict the critical depth of
44、the cavity over the supersonic Mach number range. This attempt consisted of determining (d/c)detached for the cavity by analyzing a simplified version of supersonic flow in a very shallow two-dimensional cavity and then studying the changes in the flow pattern which occurred as the depth was increas
45、ed to Figure 11 presents a sketch of the simplified version of the flow. The boundary layer was neglected and the flow was assumed to turn abruptly upon attaching to and sepa- rating from the cavity bottom, whereas more gradual turning of the flow occurred in actuality, such as was depicted in sketc
46、h (a). predicted (d/C)detached would be expected to exceed the actual (d/c)detachea. Experimentally, (d/c)critical was larger than (d/c)detached in Cavity“), and therefore the predicted (d/c)detached a fair estimate of (d/c),itical. The details of the method of pre- dicting (d/c)detached are present
47、ed in a subsequent section of this report. (d/C)detached. Thus the (see preceding section entitled “Effects of Depth on Flow should provide The predicted variation of (d/C)detached with 0 and comparison Q = 3.55 are presented in figure 12. with the experimental results at Provided by IHSNot for Resa
48、leNo reproduction or networking permitted without license from IHS-,-,-ll L 5 1 8 Comparison of Experimental Pressure Distribution in Very Shallow Cavity With Predicted Pressure Distribution (d/c) = 0.042) is compared with a predicted pressure distribution in figure 13. The method of predicting the
49、pressure distribution is explained in a subsequent section of this report; the simplified ver- sion of the flow which was used in predicting (d/c)detached is also used in predicting the pressure distribution. Figure 13 shows that the predicted pressure distribution agreed well with experiment on the upstream and downstream faces, but that pressure gradient
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