1、REPORT 1356INVESTIGATION OF SEPARATED FLOWS IN SUPERSONIC AND SUBSONIC STREAMS WITHEMPHASIS ON THE EFFECT OF TRANSITIONBy DEAN R. CHAPMAN, DONALD M. KUEHN, and HOWARD K. LARSONSUMMARYExperimental and theoretical research has been conducted onflow separation associated with steps, bases, compression
2、corners,curved surfaces, shock-wave boundary-layer reflections, and con-figurations producing leading-edge separation. Results wereobtained.from pressure-distribution measurements, shadow-graph observations, high-speed motion pictures, and oil-filmstudies. The maximum scope of measurement encompasse
3、dMach numbers between 0.4 and 3.6, and length Reynoldsnumbers between 4,000 and 5,000,000.The principal variable controlling pressure distribution inthe separated .flows was found to be the location of transitionrelative to the reattachment and separation positions. Classi-t_cation is made o-f each
4、8eparated flow into one of three regimes:“pure laminar“ with transition downstream of reattachment,“transitional“ with transition between separation and reattach-meat, and “turbulent“ with transition upstream o-f separation.By this means of classification it is possible to state rathergeneral result
5、s regarding the steadiness o-fflow and the influenceo Reynolds number within each regime.For certain pure laminar separations a theory-for calculatingdead-air pressure is advanced which agrees well with subsonicand supersonic experiments. This theory involves no empiricalinformation and provides an
6、explanation o why transition lo-cation relative to reattachment is important. A simple analysisof the equations .for interaction of boundary-layer and externalflow near either laminar or turbulent separation indicates thepressure rise to vary as the square root o-f the wall shear stressat the beginn
7、ing o-f interaction. Various experiments substan-tiate this variation .for most test conditions. An incidentalobservation is that the stability of a separated laminar mixinglayer increases markedly with an increase in Mach number.The possible significance of this observation is discussed.INTRODUCTIO
8、NFlow separation often is considered as a scourge to manytechnical devices which depend upon the dynamics of fluidsfor successful operation, inasmuch as separation often limitsthe usefulness of these devices. For example, the maximumlift of an airfoil and the maximum compression ratio of acompressor
9、 are limited by the occurrence of separation.Separuted regions can also occur near a deflected flap, arounda spoiler control, in an overexpanded rocket nozzle, behinda blunt base, on the leeward side of an object inclined atlarge angle of attack, and near the impingement of a shockwave from one body
10、 upon the boundary layer of another.Such occurrences make flow separation a very commonphenomenon warranting much research effort.Of the numerous experimental results on separated flows,a few have proved to be applicable throughout the subsonic,transonic, ond supersonic speed ranges. The first and m
11、ostimportant result involves the phenomenon of boundary-layertransition. In 1914 Prandtl (ref. 1) demonstrated that thepronounced effects of flow separation on the low-speed dragof a bluff body, such as were observed earlier by Eiffel (ref.2), are determined by the type of boundary-layer flow ap-pro
12、aching the separation point; that is, whether it is laminaror turbulent. In the initial post-war years, a number ofindependent investigations (refs. 3, 4, 5, and 6) were con-ducted in transonic and supersonic wind tunnels whichrevealed similar marked effects on compressible flow fieldswhen the bound
13、ary layer approaching separation waschanged from laminar to turbulent. These experimentsleave little doubt that separated flows with transition up-stream of separation are fundamentally different from thosewith transition downstream.From various experiments on separated flows, a secondgeneral result
14、 can be detected which may not have beenevident at the time the various experiments were conducted,but which is perceptible now through the medium of hind-sight coupled with the findings of more recent research.This second result concerns the importance of the locationof transition within a separate
15、d layer relative to the positionof laminar separation. Schiller and Linke (ref. 7) foundthat even under conditions where tim boundary-layer flowremains laminar at separation, the pressure distributionabout a circular cylinder depends significantly on how neartransition is to the separation position.
16、 They observed thatan increase in either Reynolds number or turbulence levelmoved transition upstream in the separated layer to a posi-tion closer to separation, and that such movement consid-erably affected the drag and pressure distribution. Closelyrelated to these findings are some isolated obser
17、vations thattransition location often correlates with an abrupt pressuret Supersedes NACA TN 38_ by Dean R. Chapman, Donald M. Kuehn, and Howard K. Larson, 1957.421Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-422 REPORT 1356-NATIONAL ADVISORY COMM
18、ITTEE FOR AERONAUTICSrise when the separated layer is laminar. This correlationis found within “separation bubbles“ on airfoils (ref. 8),and in many other cases, both at low speed and supersonicspced, as is discussed in detail later. Thus with a separatedlayer remaining laminar, a variation ill Reyn
19、olds numberchanges the location of transition relative to the separationpoint and this varies the pressure rise associated with tran-sition; the consequence is an effect of Reynolds number onpressure distribution which is especially pronounced in theseparated flow behind a base. (See refs. 5 and 6.)
20、 Aninitial approach to the computation of such effects has beenmade by Crocco and Lees (ref. 9) who consider explicitlythe movement of transition along a separated layer. Thesynoptic result of these various investigations is that thelocation of transition relative to separation is a variablegenerall
21、y important to separated flows wherein the boundarylayer is laminar at separation.In most previous experiments attention generally hasbeen directed to the type of boundary-layer flow existingat: separation and to the relative distance between transi-tion and separation; less attention has been given
22、 to thetype of boundarydayer flow existing at reattachment andto the relative distance between transition and reattach-ment. (“Reattachment“ is taken herein to mean the local-ized zone wherein a separated layer either meets a surfaceor another separated layer.) At sufficiently low Reynoldsnumbers, a
23、 type of separation can exist where transitionis downstream of the reattachment zone, or perhaps evennowhere in the flow field. In order to achieve this purelaminar _ type of separation in a low-speed flow, however,the Reynolds number must be very low (e. g., the orderof several thousand for a circu
24、lar cylinder). In view ofthe unusually low Reynolds number required, and the factthat the reattachment position is not steady in a subsonicwake, it is understandable that conditions at reattachmentpreviously have received relatively little emphasis in inves-tigations of separated flow. An isolated e
25、xample of purelaminar separation was observed by Liepmann and Fila(ref. 10) behind a small, half-cylinder, roughness elementplaced within a subsonic laminar boundary layer.The present investigation, which is concerned in consider-able part with flow conditions near reattachment, was con-ducted in th
26、ree phases differing greatly in purpose andscope. Such division was not planned but was dictated bysome rather surprising and encouraging results obtainedduring the initial phase of experimentation, coupled withsome major revisions in the wind-tunnel facility made dur-ing the interval over which the
27、 research was conducted.The initial experiments (conducted in 1953) were concernedwith the manner in which Reynolds number variation atsupersonic speed affects the separated-flow region upstreamof two-dimensional steps of various might. Comparisonof the results of the initial experiments with those
28、of other* For reasons explained later, many flows commonly designated as “laminar“ separationsin previous investigations really are affected significantly by the presence of transition locallyin the reattachment zone; such flows are referred to herein as *transitional“ separations.Consequently, it i
29、s desirable for purposes or emphasis and contradistinction to use an unam-bignous terminology, such as “pure laminar,“ for those flows which truly are mmffectedby transition,experiments revealed several intriguing similarities amongvarious separatc(t flows on presumably unrelated configura-tions. Th
30、ese similarities (discussed in detail later) sug-gested that the location of transition relative to reattach-ment might be just as fundamental to any separated flowas is the location of transition relative to separation. Inorder to explore this possibility, a second phase of experi-ments was conduct
31、ed with a variety of model shapes ratherthan just a step. A third phase of experiments was con-ducted after modifications were made to the wind tunnelwhich enabled operation over an extended Mach numberand Reynolds number range. Inasmuch as an ultimatehope was to improve the understanding of separat
32、ed flows,it was thought mandatory to include measurements at sub-sonic as well as supersonic speeds as an integral part of theresearch. All measurements were made on two-dimensionalmodels.This report covers three subjects: (1) a general survey ofthe experimental results grouped according to whether
33、tran-sition is downstream of reattachment, between separationand reattachment, or upstream of separation; (2) a descrip-tion and experimental test of a theory of the fundamentalmechanism near reattachment which governs the dead-airpressure in a separated region (this theory is used to pro-_dde an ex
34、planation of why transition location relative toreattachment is of importance to separated flows); (3) asimple analysis and pertinent experiments on “free inter-action“ type flows wherein the boundary layer interactsfreely with an external supersonic flow in the manner orig-inally pictured by Oswati
35、tsch and Wieghardt (ref. 11). Apreliminary report presenting briefly some of the salientresults of this investigation has been published as reference 12.In the three-year interim over which the present experi-ments and theoretical research were conducted, variousresults of other studies appeared whi
36、ch benefited and influ-enced the course of this research. A thorough investiga-tion of turbulent separation induced by steps and by inter-action of oblique shock waves with the turbulent boundarylayer on a wind-tunnel wall was published by Bogdonoff(ref. 13) and by Bogdonoff and Kepler (ref. 14). As
37、 aresult it was deemed unnecessary to investigate turbulentseparations for these two cases, except to provide incidentalcomparisons and checks with their data. Similarly, exten-sive results of Gadd, Holder, and Regan (ref. 15) becameavailable for the case of shock-wave-induced separation.In these la
38、tter experiments, separated flows with transitiondownstream of reattachment were observed as were fullyturbulent flows and flows with transition between separationand reattachment. The importance of transition locationrelative to reattachment is clearly recognized by Gadd, etal. More recently, the r
39、esearch of Korst, Page, and Childs(ref. 16) became available, in which nearly the same funda-mental theoretical meclmnism was employed in their calcu-lations of base pressure for thin turbulent boundary layersas that mechanism described and experimentally testedherein for thin laminar boundary layer
40、s. Comparison ofresults from these various recent and independent researchesis made later in the report.|!V!|lProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-|INVESTIGATION OF SEPARATED FLOWS WITH EMPHASIS ON THE EFFECT OF TRANSITION 423NOTATIONlocal
41、 skin-friction coefficient,C,cl ratio of Cio at a given R_ o to corresponding valueR=o= 10 6h height of step or basel, characteristic streamwise length over which inter-action takes placeL body length (see fig. 2)m mass-flow rate per unit span31 _Iach numberp pressurePr Prandtl numberpu 2q dynamic p
42、ressure, _-R reattachment pointRL,Rxo Reynolds number, _ and uox0, respectivelyPO POS separation pointT absolute temperatureu velocityz distance along model measured from leading edgea angle of attack relative to surface having length L? ratio of specific heats, 1.40 for airmixing-layer or boundary-
43、layer thickness* displacement ttlickness of boundary layerviscosity coefficientkinematic viscosity, -_pp densityT shear stressSUBSCRIPTSo conditions at beginning of interaction in supersonicflow, or at location of minimum pressure insubsonic flowtest-section stream conditionsd dead aire outer edge o
44、f mixing layer, or edge of boundarylayerp plateau conditions (for laminar separation), orpeak conditions (for turbulent separation)r reattachment points separation pointT, _- 1- 2t total conditions (e. g., 7-1+:_:M )* ratio of quantity to corresponding value at edge( T -_-ete)of mixing layer e. g.,
45、T.-_, _. _,w wallSUPERSCRIPTS conditions downstream of reattachment region- conditions along dividing streamline of mixinglayer.APPARATUS AND TEST METHODSWIND TUNNELExperiments were conducted in the Ames 1- by 3-footsupersonic wind tunnel No. 1. This tunnel operates con-tinuously with dry air over a
46、 range of reservoir pressures.For the initial portion of experiments, the range of tunnelpressures available was limited to between 2.5 and 30pounds per square inch absolute, and the Mach numberwas limited t,o about 24. Revisions to the tunnel structure,flexible-plate nozzle, and drive motors were m
47、ade in 1955so that subsequent experiments could be made over therange of pressures between about 2 and 60 psia and at Machnumbers up to about 3.6. Subsonic speed control(0.40 resulted from excessive flow deflection over the lowersurface, and this caused transition to occur prematurely onthe upper su
48、rface. Under such conditions, the pressuredistribution in transitional-type separations differed fromthat obtained at the same Mo, but with an expansion waveat tile leading edge. In some cases of laminar separation,small differences in the shape of pressure distribution-butnot in the pressure rise t
49、o separation-were observed atthe same Mo for the two types of settings. These smalldifferences are attributed to known differences in tunnel-empty pressure distribution at the different nozzle settings.Optical techniques.-One or more shadowgraphs weretaken for each pressure distribution in order to determinethe location of transition. Relatively long exposure timeswere used (_6 to _00 sec) since the mean position of transitionwas desired rather than an instantaneous position. Inthe first two phases of experimentation, fi
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