Characteristics of a Confined Annular Jet Flow Field

Transcription

1 Characteristics f a Cnfined Annular Jet Flw Field Khaled J. Hammad, Ivana Milanvic, Nidal Al-Masud Abstract The flw field characteristics f a cnfined annular jet were studied by numerically slving the mass and mmentum cnservatin equatins gverning the steady laminar flw. Three primary flw regins were identified, a small inner recirculatin regin, a much larger uter recirculatin regin and a flw redevelpment regin. Wall shear stress and centerline velcity distributins are reprted and used t demnstrate the influence f the gverning parameters n the recirculatin and redevelpment features f the flw field. Fr a fixed Reynlds number, recirculatin lengths, recirculatin intensities, and redevelpment length were fund t increase with the annular nzzle diameter rati. Keywrds: Annular jets, cnfined jets, laminar jets, mdeling, CFD. d Inner nzzle diameter D Outer nzzle diameter D Outer wall diameter, D D NOMENCLATURE D h Hydraulic diameter f annular nzzle, Dh D d L Reattachment length, axial distance nrmalized with R r L x P r R Axial extent f the cmputatinal dmain Pressure Radial distance Outer nzzle radius R Hydraulic radius f annular nzzle, D h Re Reynlds number, ud b h u Streamwise velcity R u b Initial jet bulk velcity, urdr / R R x Streamwise distance Greek Letters Inner-t-uter annular nzzle diameter rati, d D h Central Cnnecticut State University (CCSU), 6 Stanley St., New Britain, CT 6, hammad@ccsu.edu University f Hartfrd, Blmfield Ave., West Hartfrd, CT 67, milanvic@hartfrd.edu Central Cnnecticut State University (CCSU), 6 Stanley St., New Britain, CT 6, almasudn@ccsu.edu ASEE Nrtheast Sectin Cnference Nrwich University Reviewed Paper March -6,

2 w i Viscsity Density Wall shear stress Intensity f inner recirculatin regin Intensity f uter recirculatin regin Superscripts/Subscripts b Bulk c Centerline f fully-develped h Hydraulic i Initial prperties, i.e. prperties at x Outer w Wall INTRODUCTION The flw behavir f annular jets can be influenced by many factrs such as inlet cnditins, swirl, c-flw, and cnfinement. An imprved fundamental understanding f this flw phenmenn is imprtant t the design f jet mixers, cmbustin chambers, chemical reactrs, and bilgical reactrs. A careful examinatin f the literature reveals that numerical, theretical, and experimental studies fcused n the flw behavir f cnfined laminar and turbulent rund jets [-6]. Previus wrk n uncnfined annular jets fcused n the characteristics f laminarturbulent transitin [7-8] and descriptin f the vrtex dynamics in the turbulent flw regime [9]. Hwever, available infrmatin n cnfined annular jet flws is scarce []. Cnfined flws f annular jets are typically characterized by a large uter and a small inner recirculatin regins as well as a flw redevelpment regin, illustrated in Figs. and. The fully-elliptic equatins f mtin are numerically slved in this study t investigate the impact f annular nzzle inner-t-uter diameter rati n the glbal and lcal flw field characteristics f a cnfined annular jet. Outer recirculatin regin Inner recirculatin regin Redevelpment regin FIG. FLOW REGIONS OF A CONFINED ANNULAR JET FIG. VECTOR FLOW FIELD OF A CONFINED ANNULAR JET ASEE Nrtheast Sectin Cnference Nrwich University Reviewed Paper March -6,

3 GOVERNING EQUATIONS The cnservatin f mass and mmentum equatins gverning the laminar and steady flw f an incmpressible Newtnian fluid in a cylindrical gemetry are: ( rv) u r r x () u u p u u u v r x r x x r r r () v v p v v v u v r x r r r r r x r () Fr a fixed cnfinement rati, i.e. D D, the axisymmetric velcity and pressure fields btained via numerically slving the gverning equatins, i.e. Eqs. ()-(), are a functin f the Reynlds number, Re Du h b, and d D. METHOD OF SOLUTION Equatins ()-() are slved numerically utilizing a staggered, variable grid-size, finite-difference scheme. Fully secnd-rder accurate finite-difference apprximatins are used fr the derivatives appearing in the gverning equatins. Centered differences are used in all cases with the exceptin f the cnvective streamwise derivatives, which are upwinded, using first rder apprximatins. Mre details n the finite-difference frm f the gverning partial differential equatins and detailed slutin methdlgy can be fund in []. The resulting system f algebraic equatins is slved via an iterative marching technique. The linearized equatins are slved simultaneusly alng lines in the radial directin using a blck-tridiagnal matrix inversin technique. The cnvergence parameter emplyed is the magnitude f the maximum residual in the difference equatins. The discretizatin is made in such a way that the cntinuity equatin is always satisfied at any stage f the slutin prcedure. Therefre, cnvergence is checked fr the tw mmentum equatins and the iterative prcedure is terminated when the residual becmes less than -7. The finite-difference scheme presented abve has been tested and validated using particle image velcimetry measurements []. GEOMETRY AND BOUNDARY CONDITIONS The present flw prblem requires the impsitin f bundary cnditins at the cnfining planes. The flw gemetry and the bundary cnditins are illustrated in Fig.. At the upstream bundary, i.e. at x =, the fllwing bundary cnditins are enfrced: At r R: u, v (a) At Rr R: u ub, v (b) At R r R: u, v (c) Alng the centerline (axis f symmetry), i.e. at r, the fllwing bundary cnditins are enfrced: u p v r r () ASEE Nrtheast Sectin Cnference Nrwich University Reviewed Paper March -6,

4 Fr the uter radial bundary, i.e. r R : u, v (6) Fully-develped utlet bundary cnditins were impsed, i.e. at u At r R: v x x L : x (7) D d Annular jet C L v=( )/r = x D v=u= v=( )/x = v=u= FIG. COMPUTATIONAL DOMAIN AND BOUNDARY CONDITIONS The utlet bundary cnditins were applied sufficiently far dwnstream the jet exit plane t ensure that the cmputed results were independent f the lcatin f applicatin f these bundary cnditins. All cmputatins emplyed a grid. A grid led t centerline velcity and wall shear stress distributins that were identical t thse btained using the grid. Vertical grid spacing was varied t achieve grid clustering near the centerline and uter wall cnfining wall. The hrizntal grid spacing was als varied t prduce grid clustering in the vicinity f the jet surce, i.e. at x =. RESULTS AND DISCUSSION The flw field characteristics f a cnfined annular jet, as depicted in Fig., are influenced by the Reynlds number, Re, the inner-t-uter annular nzzle diameter rati,, and the uter wall diameter, D. The results t be presented here were btained frm a parametric study where Re,, and D were assigned the fllwing values: Re={}; = {,.,.8}; D ={D}. The selected parameters ensured steady and laminar jet flw cnditins thrughut the whle flw field. Flws f highly viscus fluids r gases inside small scale devices are typically laminar. Varying allws fr the investigatin f cnfined rund and annular jets. All fluid prperties are assumed cnstant. Velcity Fields The dmain f influence f the cnfined annular jet is best illustrated by inspecting cnturs f the velcity magnitude shwn in Fig. (a)-(c) fr =,., and.8, respectively. The red regins, representing the highest velcity magnitudes, are cncentrated at the entrance and within the jet ptential cre. The extent f the jet ptential cre decreases with indicating a mre rapid grwth f the jet shear-layer. At a certain dwnstream distance, the velcity magnitudes are t lw indicating the disappearance f a distinct cnfined jet. Further, the jet shear-layer ASEE Nrtheast Sectin Cnference Nrwich University Reviewed Paper March -6,

5 regin, primarily green clred, displays velcity magnitudes that are distinctly higher than thse f the surrunding pints, thus effectively marking the radial extent f the cnfined jet. (a) (b) (c) FIG. CONTOURS OF VELOCITY VECTOR MAGNITUDE FOR,.,.8 Streamlines The primary features f the cnfined annular jet flw field are clearly displayed in the streamlines shwn in Fig. (a)-(c) fr =,., and.8, respectively. Only an uter recirculatin regin exists fr =. Hwever, bth a small inner and a much larger uter recirculatin regins can be seen fr =. and.8. The length and recirculatin intensity, f bth regins, increase with. In general, the length and intensity f the uter recirculatin regin are always much larger than thse f the inner ne. ASEE Nrtheast Sectin Cnference Reviewed Paper Nrwich University March -6,

6 (a) (b). (c).8 FIG. FLOW FIELD STREAMLINES FOR,.,.8 Centerline Velcity Decay Influence f the inner-t-uter annular nzzle diameter rati n the centerline velcity decay is demnstrated in Fig. 6 fr =,., and.8. The centerline velcity, U c, is nrmalized with the fully-develped value achieved at the end f the flw redevelpment regin, U c,fd.. The curves clearly illustrate the impact f n the jet evlutin behavir, length and intensity f the inner recirculatin regin, and flw redevelpment length. Negative Uc U c, fd values are btained within the inner recirculatin regin fr =. and.8. The dwnstream axial lcatin crrespnding t Uc Uc, fd marks the length f the inner recirculatin regin, apprximately.r and R fr =., and.8, respectively. The lengths f the inner regin are much smaller than thse f the uter regin. The uter recirculatin regin lengths, r reattachment lengths, fr =,., and.8 are represented by the three arrws in Fig. 6. The larger negative U c /U c,fd values btained fr =.8 indicate a mre intense recirculatin within the inner regin. The asympttically apprached axial lcatin crrespnding t Uc Uc, fd, marks the flw redevelpment length, which increases with. ASEE Nrtheast Sectin Cnference Nrwich University Reviewed Paper March -6,

7 u c u c,fd FIG. 6 DECAY OF THE JET CENTERLINE VELOCITY FOR,.,.8 Wall Shear Stress Influence f the inner-t-uter annular nzzle diameter rati n the wall shear stress distributin is demnstrated in Fig. 7 fr =,., and.8. The wall shear stress, w, is nrmalized with the fully-develped value achieved at the end f the flw redevelpment regin, w, fd. The curves clearly illustrate the impact f n the length and intensity f the uter recirculatin regin, and flw redevelpment length. Outer recirculatin regin is characterized by w w, fd. The axial lcatins crrespnding t w w, fd, highlighted by the three arrws in Fig. 7, mark the reattachment lengths, i.e. uter recirculatin regin length. The reattachment lengths fr =,., and.8, are 6.6R, 6.R, and.6r, respectively. In general, larger negative w w, fd values indicate a mre intense recirculatin within the uter regin. The asympttically apprached axial lcatin crrespnding t w w, fd, marks the flw redevelpment length, which increases with as shwn in Fig. 7. w w,fd FIG. 7 WALL SHEAR STRESS DISTRIBUTION FOR,.,.8 Reattachment lengths and recirculatin intensities f the inner and uter regins are listed in Table fr =,., and.8. The table clearly indicates that increasing the annular nzzle diameter rati results in larger and mre intense recirculatin regins. TABLE. REATTACHMENT LENGTH, INTENSITIES OF OUTER AND INNER RECIRCULATION REGIONS FOR,.,.8 L r /R Ψ Ψ i ASEE Nrtheast Sectin Cnference Nrwich University Reviewed Paper March -6,

8 CONCLUDING REMARKS The present study investigated the flw characteristics f a cnfined annular jet within the laminar steady flw regime via numerically slving the cnservatin f mass and mmentum gverning equatins using a finitedifference scheme. Three primary flw features were identified, a large uter and a small inner recirculatin regins, and a flw redevelpment regin. The centerline velcity decay and wall shear stress curves were presented fr three annular nzzle inner-uter diameter ratis, =,., and.8. The centerline velcity decay curves clearly illustrated that increasing the annular nzzle diameter rati results in larger and mre intense inner recirculatin regin, and in lnger flw redevelpment length. On the ther hand, the characteristics f the wall shear stress curves demnstrated that increasing the annular nzzle diameter rati increases bth the length and intensity f the uter recirculatin regin as well as the flw redevelpment length. REFERENCES [] Landfried, D.T., Jana, A., Kimber, M.L.,, Characterizatin f the Behaviur f Cnfined Laminar Rund Jets, Prceedings f the ASME Fluids Engineering Summer Meeting, Paper n. FEDSM- 77. [] Revuelta, A., Sanchez, A. L., and Linan, A.,, Cnfined axisymmetric laminar jets with large expansin ratis, J. Fluid Mechanics, 6, pp. 9. [] Sarma, A., Sundararajan, T., and Ramjee, V.,, Numerical simulatin f cnfined laminar jet flws, Int. J. Numer. Meth. Fluids,, pp [] Milanvic, I.M., and Hammad, K.J.,, PIV Study f the Near-Field Regin f a Turbulent Rund Jet, Prceedings f the ASME rd Jint US-Eurpean Fluids Engineering Summer Meeting: Vlume, Sympsia Parts A, B, and C, Paper n. FEDSM-ICNMM-9. [] Hammad, K.J. and Shekarriz, A., 998, Turbulence in cnfined axisymmetric jets f newtnian and nn- Newtnian fluids, Prceedings f the ASME 998 Fluids Engineering Summer Meeting, Paper n. FEDSM98-7. [6] Revuelta, A., Sanchez, A. L., and Linan, A.,, The virtual rigin as a first-rder crrectin fr the farfield descriptin f laminar jets, Physics f Fluids, (6), pp [7] Del Taglia, C., Mser, A., Blum, L., 9, Spntaneus Break f Symmetry in Uncnfined Laminar Annular Jets, Trans. ASME, J. Fluids Eng.,, 8(-8). [8] Del Taglia, C., Blum, L., Gass, J., Ventiks, Y., Pulikaks, D.,, Numerical and Experimental Investigatin f an Annular Jet Flw With Large Blckage, Trans. ASME, J. Fluids Eng., 6, pp [9] Patte-Ruland, B., Lalizel, G., Mreau, J., Ruland, E.,, Flw Analysis f an Annular Jet by Particle Image Velcimetry and Prper Orthgnal Decmpsitin, Meas. Sci. Technl.,, pp.. [] Sheen, H.J., Chen, W.J., Wu, J.S., 997, Flw patterns fr an annular flw ver an axisymmetric sudden expansin, J. Fluid Mechanics,, pp [] Hammad, K.J.,, Depth f Penetratin f a Submerged Viscplastic Nn-Newtnian Jet, Prceedings f the ASME Fluids Engineering Summer Meeting, Paper n. FEDSM-76. [] Hammad, K. J., Otugen, M. V., and Arik, E. B., 999, A PIV study f the laminar axisymmetric sudden expansin flw, Exp. Fluids, 6, 66. ASEE Nrtheast Sectin Cnference Nrwich University Reviewed Paper March -6,

9 Khaled J. Hammad Prf. Khaled J. Hammad received his Ph.D. in Mechanical Engineering frm The Plytechnic Institute f New Yrk University and did his pstdctral wrk at the Pacific Nrthwest Natinal Labratry. He jined the Department f Engineering at Central Cnnecticut State University in August after wrking mre than years fr Dantec Dynamics. He is a member f ASME, AIAA and AIChE. His technical expertise and research interests include Laser Diagnstics, Fluid Flw, Heat/Mass Transfer, Nn-Newtnian Fluids, and Energy Cnversin. Prf. Hammad rganized many Sympsia/Fra & chaired numerus technical sessins in internatinal ASME cnferences. Prf. Hammad is a cntributing authr fr 6 peer reviewed publicatins. He chaired the ASME Fluid Mechanics Technical Cmmittee and is the current "ASME Fluids Engineering Hnrs and Awards Cmmittee" chair. Ivana Milanvic Prf. Milanvic is a full-time faculty member in the Mechanical Engineering Department at the University f Hartfrd. Her area f expertise is therm-fluids with research interests in vrtical flws, cmputatinal fluid dynamics, multiphysics mdeling, and cllabrative learning strategies. Prf. Milanvic is a cntributing authr fr mre than 7 jurnal articles, NASA reprts, cnference papers and sftware releases. Prf. Milanvic s hnrs include five NASA Faculty Fellwship Awards, Award fr Innvatins in Teaching and Learning, and Outstanding Teacher Award f the University f Hartfrd. Nidal Al-Masud Dr. Al-Masud, Assciate Prfessr, earned his Ph.D. in Mechanical Engineering frm University at Buffal, The State University f New Yrk in. Dr. Al-Masud has taught at bth graduate and undergraduate level curses at University at Buffal, he jined Central Cnnecticut State University as an Assistant Prfessr in. At CCSU, he teaches curses at all levels in the three majr areas in mechanical engineering, namely: mechanics, Thermfluid, and Cntrl Systems and Dynamics. Dr. Al-Masud research interests are in the fields f Cntrl Systems and Dynamics, HVAC systems, and Engineering Educatin. He has numerus jurnal and cnference prceeding publicatins in the afrementined area, and was the winner f the ASEE Mechanics Divisin Best paper Award in 6. He has an extensive experience in Heating Ventilatin and Air Cnditining Systems (HVAC) design. ASEE Nrtheast Sectin Cnference Nrwich University Reviewed Paper March -6,