Numerical Modelling and Experimental Validation of a Turbulent Separated Reattached Flow

Transcription

1 Numercal Modellng and Expermental Valdaton of a Turbulent Separated Reattached Flow Florn Popescu, Tănase Panat Abstract An expermental study was conducted to analyse the feld velocty of a fully developed turbulent ncompressble flow behnd a backward-facng step wth a curved nose shape. The laser Doppler anemometry was used as measurement technque. The Reynolds number, Re, based on the step heght, h, and the maxmum velocty U0max of the velocty dstrbuton at the nlet, was A Fluent smulaton of the flow for the same geometrcal and flow condtons as the expermental ones was performed. The resulted velocty felds of the numercal smulaton and of the expermental study were compared and analysed. Both the numercal and expermental results shows the exstence of four nteractng zones: separated free shear layer, the recrculatng regon under the shear layer, the reattachment regon and the attached/recovery regon. Keywords backward-facng step, turbulent separatng reattachng flows, laser Doppler anemometry, numercal smulaton. I. INTRODUCTION The separaton and reattachment of turbulent flows occur n many practcal engneerng applcatons, both n nternal flow systems such as dffusers, combustors and channels wth sudden expansons, and n external flows lke flows around arfols and buldngs. In these stuatons, the flows experences an adverse pressure gradent,.e., the pressure ncreases n the drecton of the flow, whch causes the boundary layer to separate from the sold surface. The flow subsequently reattaches downstream formng a recrculaton bubble. In some applcatons such as combustors, the presence of the recrculaton and turbulence due to separaton can help enhance the mxng of fuel and ar. On the other hand, Manuscrpt receved Feburary 15, 007, revsed August 1, 007. Florn Popescu s PhD, professor at the Unversty Dunărea de Jos of Galaţ, Faculty of Mechancs, Department of Thermotechncs, 47, Domneasca, str., , Galaţ, Romana (correspondng author to provde phone: , fax: ; e-mal: florn.popescu@ugal.ro). Tănase Panat s PhD, professor at the Unversty Dunărea de Jos of Galaţ, Faculty of Mechancs, Department of Thermotechncs, 47, Domneasca, str., , Galaţ, Romana (correspondng author to provde phone: , fax: ; e-mal: tanase.panat@ugal.ro). separaton n ppe and duct flows causes loss of avalable energy. Thus, understandng the flow separaton and reattachment phenomena s mportant n engneerng desgn. The research has been conducted for dfferent geometrc confguratons, some of whch are shown n fgure 1. Among the flow geometres used for the studes of separated flows, the most frequently used s the backwardfacng step, the normal flat plate wth a spltter plate and the blunt flat plate; n all these cases the separaton lne s straght and fxed by the geometry. Consderable work has been carred out on the flow over a backward-facng step due to ts geometrcal smplcty. The separaton pont s fxed at the step; thus one can avod the dffculty resultng from the oscllaton of the separaton pont. Furthermore, unlke flow over an obstacle, the backward-facng step produces only one separaton bubble; and the streamlnes approachng the step are nearly parallel to the wall. Fnally, from the computatonal vew pont, the rectangular doman of the backward-facng step allows for smple grd structure. In spte of the large amount of expermental work on the backward-facng step flows, the physcs of the reattachment s stll not fully understood. The reason, as ponted out by Eaton and Johnson (1981), les partally on the nadequacy of cross-wre hot-wre probes n hghly turbulent flows used n early studes. Even wth the advent of the laser anemometer and the pulsed-wre anemometer, velocty measurements, partcularly n the separated flow regon where nstantaneous flow reversal occur, may stll be the subect to errors caused by velocty bas (Adams & Eaton, 1988). The obectve of ths report s to present a set of detaled measurements of the flow over a backward step (Fg.1.(a)), the results obtaned wth a Fluent smulaton and to perform an analyss of the data. The experment and the Fluent smulaton have been both conducted for the same geometry and for Re = 84000, calculated on the bass of the step heght. Issue 1, Volume 1, 007 7

2 Fgure 1 Flow confguratons wth separaton and reattachment I. THE FLOW TOPOLOGY AND THE IDENTIFICATION OF COHERENT STRUCTURES A separatng/reattachng flow can be dvded nto four nteractng zones (see fgure ). The zones are: the separated free shear layer, the recrculatng regon under the shear layer, the reattachng regon and the attached/recovery regon. Each flow regon bears some smlartes to well-studed flow cases such as mxng layers and boundary layers, whle the reattachng and recrculatng regons are unque to separated flows. There more crtera used to dentfy the coherent structures n turbulent flows: crtera based on the vortcty or on the pressure. It seems that for the flow over a backward-facng step, the most effcent crteron s the Hunt crteron of dentfcaton of the coherent structures (1988) or the Q crteron. We consder that ths crteron mght be an element that could be developed n the future by the Fluent development team. Hunt et all. defned a coherent structure on the bass of the second nvarant of the term u, quantty whch must be postve to have a coherent structure: 1 Q = F ( ΩΩ S where Ω and S represent the antsmetrc and smetrc parts of of the deformaton tensor u / u. Otherwse, we have: 1 u u 1 u u Ω = ( ), S = S ( ), + Physcally, the regons where the Q s postve are regons where the vortcty s superor to the shear stress. ) Fgure Flow confguraton I. EXPERIMENTAL STUDY AND FLUENT SIMULATION OF THE FLOW OVER A BACKWARD FACING STEP The experment was conducted on the hydrodynamc tunnel from the Laboratory of Geophyscal and Industral Flows Ecole Natonale Polytechnque de Hydraulque et Mecanque from Grenoble. The measurements doman and the velocty dstrbuton at the nlet are llustrated n fgures 3 and 4.. We used the laser Doppler anemometry method to measure the velocty feld. Issue 1, Volume 1, 007 8

3 z u (z) 0 1 mm H H Measurement regon 0 H 6 H x 1 mm Fgure 3. The measurements doman (H=10mm) The Fluent smulaton was performed for the same geometry and flow propertes as the expermental ones. The flow model was k-ε. Fgures 5a, 5b, 5c llustrates both the expermental and the numercal results for the mean veloctes Ux at dfferent dstances from the step. The profles are represented for all Fgure 4. The velocty dstrbuton at the nlet (H=10mm) the three regons of the flow. Fgures 6a and 6b llustrate the contours of the mean veloctes Ux for the expermental data and the Fluent smulaton whle fgure 7 llustrates the contours of Urms veloctes but only for the expermental data. Fgure 5a Mean velocty profle x = H Fgure 5b Mean velocty profle x = 5H Issue 1, Volume 1, 007 9

4 We observe an nflecton pont on the profle of the velocty at the outlet. It results that even at ths dstance from the step we can not fnd a classcal profle of a boundary layer. A well known characterstc of the flow over a backward-facng step s the slow velocty of reft of the flow after the reattachng regon. An analyss of Urms veloctes data reveals the exstence of a maxmum mmedately after the step and the tendency of ths quantty to a constant value as we advance. Ths structure s practcally the proof of the redevelopment of a classcal boundary layer after the step. Fgure 5c Mean velocty profle x = 10H Fgure 6a The profles of the axal mean velocty Ux (Fluent smulaton) Fgure 6b The profles of the axal mean velocty Ux (expermental data) Issue 1, Volume 1,

5 Fgure 7. The profles of the velocty fluctuatons Urms (expermental data) I. CONCLUSIONS The results shows that an nternal shear layer, mbedded n the nner part of the orgnal boundary layer, emanates mmedately from the step edge. Ths shear layer has many smlartes wth a plane mxng layer, but does not resemble exactly. The no-slp condtons mposed on the flow n the reattachng regon lmt further growth of the mxng-layerlke flow, promotng a new nternal boundary layer developng on the wall down-stream of reattachng. The data show that the structure of the nternal layer attans quasequlbrum, wth producton and dsspaton of turbulent knetc energy approxmately equal, by 0H from the step. REFERENCES [1] E.W. Adams, & J.K. Eaton, An LDA study of the backward-facng step flow, ncludng the effects of the velocty bas, J. of Fluds Eng., 110, pp.75-8, 1988 [] F. Delcayre, Etude par smulaton des grandes échelles d un écoulement décollé : la marche descendante. Thése - l Insttut Polytechnque de Grenoble, 1999, [3] J.K. Eaton & J.P. Johnston, A Revew of research on subsonc turbulent flow reattachment, AIAA J, 19, pp , [4] Hung Le & Parvz Mon Drect Numercal Smulaton of Turbulent Flow Over a Backward-Facng Step, Report No. TF-58, Stanford Unversty, [5] S. Jovc An Expermental Study of a Separated/Reattached Flow Behnd a Backward-Facng Step. Reh= NASA Techncal Memorandum , [6] M. Kya & K. Sasak, Structure of a turbulent separaton bubble. Journal of Flud Mechancs, 137, , [7] F. Popescu, Contrbut la studul mscar fludelor în urul corpurlor proflate, PhD Thess, 000. [8] F., Popescu, T. Panat Expermental Study of the Separatng- Reattachng Flow over a Backward-Facng Step, 5th WSEAS Int Conf on Flud Mechancs (FLUID 08), Acapulco, Mexco, January 5-7, 008. Issue 1, Volume 1,