1、(p!1fCOPYNATIONAL ADVISORY COMMITTEEFOR AERONAUTICSTECHNICAL NOTE 3488SOME MEASUREMENTS OF FLOW IN A RECTANGULAR CUTOUTBy Anatol RoshkoCalifornia Institute of TechnologyL II=.WashingtonAugust 1955YProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provi
2、ded by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-CNATIONAL ADVISORY COMMITYEE FOR AERONAUTICSTECm_CAL NOTE 5488SOME MEA_NTS OF FLOW IN A RECTANGULAR CUTOUTBy Anatol RoshkoSUMMARYThe flow in a rectangular cavity, or slot, in the floor of a windtunnel is des
3、cribed by the results of pressure and velocity measurements.Pressure distributions on the cavity walls as well as measurements offriction are presented. The effects of varying depth-breadth ratio areshown.INTRODUCTIONThis report is an account of some measurements of the pressure andvelocity fields s
4、et up by the flow over a rectangular cavity, or groove,in the floor of a wind tunnel. There exists at present little quantita-tive information about the flow in this or other cutouts in aerodynamicsurfaces. In the visualization techniques that have been employed, theprincipal result is to show the e
5、xistence of a vortex, or system ofvortices, within the cavity. The equilibrium of such vortex systemsmust evidently depend on the geometry of the cavity and the parametersof the outside flow, for example, boundary-layer thickness. However,it is not at all apparent which features are predominant in d
6、eterminingthis equilibrium, and there appear to be no published measurements whichmight help in setting up a model.Some quantitative results are given in two papers by Wieghardt(ref. I) and Tillmann (ref. 2), where a few other references will alsobe found. Their results for cavities are part of a la
7、rger study of thedrag of surface irregularities. In addition to some aluminum-powderpictures in reference l, their results for cutouts consist principallyof the drag coefficients, obtained by subtracting the drag values ofthe aerodynamic surface with and without cutout. It was also foundthat a syste
8、matic variation of the depth-breadth ratio of a given cavitygave a “periodic“ variation of the cavity drag coefficient, showingdefinite peaks. The net cavity drag must include the effects of pres-sure on the cavity walls, the friction on the floor, and the change offriction which is effected on the
9、aerodynamic surface by the presenceof the cavity. Without further study of these components itis diffi-cult to explain the drag variations and, more fundamentally, to getsome understanding of the flowmechanism.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from
10、IHS-,-,-2 NACATN 3488In addition to the interest in the effects on drag, there is anotherpractical problem arising from the fluctuating pressures and velocitieswhich may exist in and near a cavity. Fairly violent fluctuations areoften observed; they maybe due either to the turbulence of the flow ort
11、o intermittencies connected with instabilities of the vortex system.Such problems in aeronautics arise, for instance, in connection withbombbays, open cockpits, escape hatches_ and so forth. There alsoexist, of course, manynonaeronautical examples.Probably of even more interest from the fundamental
12、point of viewis the problem of the vortex mechanismitself. It appears that in mostof the flow problems involving separation, for instance, the base-pressureproblem, the flow past bluff bodies_ and even diffuser separation, theformation of reverse flows and vortices is an important part of themechani
13、sm. In most cases the vortices are nonsteady, making an experi-mental study rather difficult. In a cavity, on the other hand, thereis the possibility of obtaining a stationary, captive vortex and ofgaining from it someunderstanding of the mechanics of real vortices.Finally, there is the phenomenonof
14、 sound production in high-speedflow past such cavities, reported in reference 3. The production ofthese regular, periodic, high-intensity sound waves is not understood.Onepossibility is that they are associated with movementsof the vorticesin the cavity, the frequency being determined by the couplin
15、g between theacoustic field and the vortex field. The cavities used in the study ofreference 3 were too small to permit a detailed investigation of the flowinside them. It was intended that the present study, madeon a muchlarger cavity, should provide someinformation that might be useful inthe acous
16、tic problem.The work, which was conducted under the sponsorship and with thefinancial assistance of the National Advisory Committee for Aeronautics,is part of a program of turbulence and aerodynamic-noise studies at theGuggenheimAeronautical Laboratory, California Institute of Technology.The author
17、received valuable assistance from Mrs. Dietlind Wegenerandllr. Johannes de Bruyn, who helped with the measurementsand reductionof data.SYMBOLSbCDCFbreadth of cavitydrag coefficient of cavity, based on breadthfriction coefficientProvided by IHSNot for ResaleNo reproduction or networking permitted wit
18、hout license from IHS-,-,-NACA TN 3488 3CpdPpPlU_UxYPpressure coefficientdepth of cavitystatic pressurepitot pressurestatic pressure at reference pointfree-stream velocitymagnitude of velocity anywhere in flowdistance measured along flow directiondistance measured normal to any surfacecoefficient of
19、 viscositydensityEXPERIMENTAL ARRANGEMENTThe measurements were made in the Merrill Wind Tunnel at theCalifornia Institute of Technology. This has a vented test section42 inches wide and 36 inches high and may be operated at speeds up to160 mph.The cavity consisted of an open, Duralumin box set into
20、the tunnelfloor as shown in figure I. The box opening was of fixed dimensions,4 inches by 52 inches, with the long side normal to the flow.The depth of the cavity could be varied from 0 to i0 inches bychanging the position of the bottom. This could be set at any depth bymeans of the screw jack to wh
21、ich it was attached. The corners betweenthe bottom and the sides were not sealed during the measurements. Acomparison of pressure distributions with and without sealing indicatednegligible difference; thus considerable inconvenience was avoided bynot having to seal after each change of depth.It will
22、 be noted that the box flanges, resting on the tunnel floor,were not set flush. Since it was necessary, in any case, to use what-ever boundary layer already existed on the tunnel floor, the 3/16-inchflange made no essential difference to the goal of the experiments.Provided by IHSNot for ResaleNo re
23、production or networking permitted without license from IHS-,-,-4 NACA TN 3488The sides_ bottom, and flanges of the box wer_ equipped with staticholes for static-pressure measurements. In addition, there were accessholes for admitting pitot probes. Of standard type with flattenedopenings, each pitot
24、 tube could be traversed normal to the surface bymeans of a micrometer head mounted outside the box. The locations ofthe static holes and pitot tubes are indicated by sketches in the fig-ures in which the results are presented.RESULTSIn the results of the measurements, which appear in figures 2 to 9
25、,distances have been normalized by the streamwise breadth of the cavity b,which had the fixed value of 4 inches. Most of the runs were made at anominal tunnel speed of 75 feet per second; some additional measurementswere made, for comparison, at 210 feet per second.The free-stream velocity U_ was ac
26、tually measured at a staticorifice i_ inches upstream of the cavity, the pitot pressure being meas-2ured outside the tunnel boundary layer. This velocity was used to nor-malize the measured pressures_ which were always measured relative tothe pressure Pl at an orifice 1/2 inch ahead of the cavity:P
27、- PlCp =1PU_ 2Skin-friction coefficients were obtained from velocity profiles usingthe relationStatic Pressures on Cavity BottomFigure 2 shows the pressure distributions on the bottom for severaldifferen% depths. The results here are mainly for shallow cavities ofdepth-breadth ratios d/b = 0.016, 0.
28、031, 0.047, 0.063, and 0.094. Inaddition, the results for deeper cavities with d/b = 0.25 and d/b = iare shown for comparison.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATN 3488 5In all cases but the shallowest there is initially a drop in pr
29、es-sure downstreamof the front edge, followed by a rather rapid rise.(Even in the shallowest case there maybe a similar behavior; the ori-fice spacing was not close enough to resolve this.) This initial behavioris typical of the base-pressure problem, that is, flow over a step. Overmost of the remai
30、nder of the bottom, the pressure increases at first withincreasing depth, but eventually it begins to decrease. There is a kindof upper envelope to the set of curves at pressure coefficients of theorder of 0.2. It will be observed that the pressures in the shallowcavities are considerably higher tha
31、n those in the deeper ones oTd_ = 0.25 and i.The outer portions of the curves are showndotted, for it was notpossible to obtain measurementsout to the bottom corners. Instead,the curves are faired into the points measuredat the top back cornerand at orifice i, 1/2 inch ahead of the cavity.The variat
32、ion of pressure with depth is shownmore explicitly infigure 3- For this, the pressure at a single point, orifice 14, at thecenter of the bottom was chosen for study. Figure 5 shows how the pres-sure coefficient there first rises and then falls as the bottom islowered, attaining a maximum value of ab
33、out 0.18 at d/b = 0.06. Essen-tially the same result is obtained for both speeds, 75 and 210 feet persecond. Included in the same figure are measurements of the pitot pres-sure p obtained with a flattened pitot tube set close to the bottomsurface at station 14 and facing upstream. These measurements
34、 indicatethat separation occurs at station 14 soon after the maximum pressureis reached.The relation of the shallow-cavity regime to deeper cavities isshown in figure 4 where the static pressure at station 14 was measuredfor depths up to lO inches. The Cp values of figure 3 are includedon a rather m
35、ore compressed scale. The shallow-cavity regime standsout clearly in relation to the whole range. The extended points shownby bars indicate pressures which varied intermittently. The intermittentregions occur at values of d/b from about 0.5 to 0.87 and above 2. Thechange from intermittent to steady
36、pressures at d/b = 0.87 occurs quitesharply. Some tuft studies indicated that a steady, single vortex in thecavity is first formed at this value of the depth.Pressure at Downstream Top CornerThe pressure distributions for the shallow cavities show a steeppressure rise at the downstream end. Apparent
37、ly the boundary layer,which separates at the front edge, diffuses into the cavity, so thatthe velocity on the streamline approaching the downstream edge has somevalue greater than zero. This value increases, at first, as the depthProvided by IHSNot for ResaleNo reproduction or networking permitted w
38、ithout license from IHS-,-,-6 NACATN 3488is increased, and consequently the stagnation pressures near the backedge increase at first. Whenthe cavity depth exceeds a certain value(d_ _ 0.i), the separated boundary layer no longer reattaches to thebottom. It is probably at about this value that a gene
39、ral vortex systemis first set up, in contrast with shear-layer diffusion at shallowerdepths.With the expectation that the pressure near the back edge should besensitive to changes of flow regime, measurementswere madethere by meansof a small pitot tube set on the top surface, as shownin the sketch o
40、ffigure 5, at the position marked 30. The center of the pitot orificewas actually about 0.01 inch above the edge, but it maybe expected togive a fair measure of the pressure on the cavity wall immediately belowthe edge, except for the shallowest cavities. The variation of the pres-sure at station 30
41、 with varying depth is shownin figure 5- Becauseofthe finite height of the orifice above the edge, the values at veryshallow depths are in error; at d = 0 the value of Cp should actuallybe zero. As d decreases, the expected pressure peak is obtained, fol-lowed by a minimum, at about d/b = 0.2. The r
42、ange of intermittent changesobserved previously again appears, while at larger depths there is ahysteresis loop. In the vicinity of d_ = i the absence of hysteresisand intermittency indicates the stability of the single vortex in acavity of square section.The pressure at station 30 remains at a rela
43、tively high level forall depths.Pressure Distributions on Cavity WallsFor the larger depths_ pressure distributions were obtained on thecavity walls as well as on the bottom. These are given in figures 6(a)to 6(f).Figure 6(b), against which the others may be conveniently compared,shows the distribut
44、ion in a cavity of square section d_ = i. Thepressures at all points were steady. (To understand the plotting ofthe figure, it is to be noted that the values for the walls are plottedon the same abscissa as those for the bottom; that is, the curves showthe continuous variation of pressure along the
45、perimeter.) The lowerpressures near the center of the walls and bottom and the high pressuresat the corners are typical of the single, stable vortex. The contribu-tion to the cavity drag of the pressure on the walls gives CD = 0.033.The value at station 30 is off scale, but it will be noted that the
46、reis a rather abrupt transition to much low_r pressures on the top surfacedownstream of the edge.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATN 3488 7The figure includes measurementstaken with and without sealing ofthe bottom corners. (Tape w
47、as used for sealing.) It showsthe negligi-ble effect of leaving the corners unsealed.Also shownis the distribution for U_ = 210 feet per second, forcomparison with the case of U_ = 75 feet per second. There is no essen-tial difference, but the higher value of U_ gives somewhatlargeramplitudes of pre
48、ssure coefficient, which maybe taken as indication ofa “stronger“ vortex.Figure 6(a) shows the results of similar measurementsfor a gap ofd/b = 0.75, that is, a value slightly below that at which a single,stable vortex first forms. The intermittent nature of the flow is indi-cated by the variations
49、of pressure, which are represented by the bars.These correspond to the excursions of pressure observed on the alcoholmanometer. They are not periodic vibrations but rather erratic, inter-mittent variations. No account was taken Of the damping and inertia ofthe alcohol manometer, so that the recorded changes are not necessarilythe exact pressure variations in the
