EFFECTS OF INLET BOUNDARY CONDITIONS ON SPIRAL CASING SIMULATION

Transcription

1 Scienific Bullein of he Poliehnica Universiy of Timisoara Transacions on Mechanics Tom 5(66), Fascicola 6, 007 nd IAHR Inernaional Meeing of he Worgroup on Caviaion and Dynamic Problems in Hydraulic Machinery and Sysems Timisoara, Romania Ocober 4-6, 007 EFFECTS OF INLET BOUNDARY CONDITIONS ON SPIRAL CASING SIMULATION Berhanu MULU GEBERKIDEN * Michel CERVANTES Deparmen of Applied Physics and Mechanical Deparmen of Applied Physics and Mechanical Engineering Engineering Division of Fluid Mechanics Division of Fluid Mechanics Luleå Universiy of Technology Luleå Universiy of Technology *Corresponding auhor: SE-9787 Luleå, Sweden Tel.: , , Berhanu.Mulu@lu.se ABSTRACT The resuls of numerical simulaions of hreedimensional urbulen viscous flow hrough he spiral casing and disribuor of he Hölleforsen hydraulic urbine (Turbine-99 es case) are presened. Two CAD geomeries, wih and wihou he pensoc, are analyzed in deails o deermine he effecs of he upsream geomery, i.e. he inle boundary condiions o he spiral casing. Conservaion of mass and momenum equaions of he flow are analysed using finie volume mehods wih he commercial sofware ANSYS CFX0.0. Sandard -ε wih scalable wall funcion and SST -ω based urbulence models are applied o sudy he flow characerisics. Comparisons are made beween he numerical simulaions wih and wihou he pensoc and available experimenal resuls. The numerical resuls are found o more closely mach wih he experimenal resuls when he pensoc is included in he simulaion. Therefore, deailed inle boundary condiions are necessary o simulae accuraely he spiral casing flows if he pensoc is no included in he simulaion. The numerical simulaions also seem o show lile sensiiviy o he urbulence model. KEYWORDS Iniial boundary condiion, spiral casing, urbulence model, pensoc.. INTRODUCTION The flow in hydropower urbines is very complex wih several flow phenomena appearing simulaneously such as: hree dimensionaliy, unseadiness, separaion, swirling flow and urbulence. Due o hese circumsances i is highly challenging for compuaional fluid dynamics (CFD). CFD involves he soluion of he governing equaions for fluid flow a housands of discree poins on a compuaional grid in he flow domain. When appropriaely validaed, a CFD analysis allows engineers o deermine he magniude, direcion and speed of flow a any poin in he flow domain. Unlie a physical model, he geomery of he CFD model can be changed on he compuer and re-analyzed o explore differen opions in he projec design and in he operaional condiions o solve problems involving fluid flow. To predic urbulen flow in complex geomeries wih compuer simulaion insead of model experimens can significanly reduce he cos of he projec and enhance a profound nowledge of he flow problem. Much aenion has been direced o runner and draf ube simulaions, while he spiral casing has received minor aenion since he losses are minor compared o he runner losses. The flow in he waer inae and he pensoc delivers he flow enering he spiral casing, see Fig.a of he Hölleforsen model. Spiral casing is a major componen of reacion urbines. The funcion of he Spiral casing is o disribue he waer as evenly as possible o he say and guide vanes and hen o he urbine runner. The undersanding of he waer passage hrough he spiral casing o say vanes is very imporan in diminishing he losses of he flow and insures a symmerical flow o he runner. Also he design of he casing mus mee he requiremen of he urbine performance in order o aain beer overall economic benefi of hydroelecric power plans and o wihsand he bursing pressure of maximum headwaer plus waer hammer. The waer inae and pensoc being upsream of he spiral casing, hey are responsible for he flow

2 8 Proceedings of he nd IAHR Inernaional Meeing of he Worgroup on Caviaion and Dynamic Problems in Hydraulic Machinery and Sysems profile enering he spiral casing. Quesions are raised abou he inle boundary condiions a he enrance of he spiral casing due o he presence someimes of an elbow jus upsream; see Fig.a. However, mos simulaions of he spiral casing are generally performed wihou he waer inae and he pensoc. For example Carlos Eduardo [] performed simulaion of he Hölleforsen model casing wihou he waer inae and he pensoc. The correlaion beween he simulaion and he experimenal resul available were no opimum. The presen wor focuses on simulaions of he flow hrough spiral casing and he disribuor (guide vanes and say vanes) and inends o sudy he effec of upsream boundary condiions on spiral simulaion. The effecs of upsream geomery and urbulence model are invesigaed in deails. The Hölleforsen es case used for Turbine-99 ( is used, since an exensive se of experimenal daa are available in he spiral casing o validae he simulaions. The objecive is o ge boundary condiions for subsequen simulaions including he runner and ulimaely he enire sysem. The curren paper is srucured as follows. Secion presens he es case, he geomery, grid, he boundary condiions, he urbulen models used and he experimenal resuls available. In Secion 3 he numerical resuls are presened wih deail comparison and analysis of he deviaions wih he experimens. Secion 4 presens he conclusions of his sudy.. TEST CASE The full scale uni of he hydropower plan Hölleforsen is siuaed on he river Indalsälven in Sweden. I consiss of hree Kaplan urbines unis wih a oal insalled capaciy of 50 MW a he operaional head of 7 m, wih a runner diameer of 5.5 m each and a discharge capaciy of 30 m 3 /s per urbine. The Hölleforsen hydropower plan Kaplan urbine model is nown as he Turbine-99 es case. An exensive se of experimenal daa in he spiral casing and he draf ube are available. Numerical Simulaions are herefore performed on he model. I is a : scale of he prooype urbine wih a runner diameer of 500 mm and a runner speed of 595 rpm. The operaional condiion close o he bes efficiency for he scheme a he operaional head of 4.5 m, a 60% load is chosen. For his operaional condiion he volume flow rae is 0.5 m 3 /s... Geomery and grid The geomery of he model is presened in Fig.. Two geomeries are available: one wih and one wihou he waer inae and he pensoc. The saor has 4 guide vanes and 0 say vanes. All he guide vanes are idenical and have a symmerical ouline. In conras, he say vanes have unlie profile, see Fig.. Mars # and # show say vanes wih idenical profile beween each oher and he res of say vanes have idenical profile. Figure : CAD model of he pensoc, spiral casing and disribuor of he Hölleforsen urbine (a, c, d) wih he pensoc wihou he pensoc (N.B. all he dimensions are in meers).

3 Proceedings of he nd IAHR Inernaional Meeing of he Worgroup on Caviaion and Dynamic Problems in Hydraulic Machinery and Sysems 9 Figure : Say vanes and guide vanes of he spiral casing. For he say vanes, # mars hose wih devian shapes and # mars hose posiioned in devian angles. The compuaional grid consiss of unsrucured hexahedral elemens creaed in ICEM CFD. The grid generaion ool is based on a global bloc opology and generaes 3D muli-bloc srucured or unsrucured hexahedral volume grids. The bloc opology model is generaed direcly on he fundamenal CAD geomery. Two high densiy hexahedral grids wih approximae firs node wall disances of y + = 50 and y + = were generaed for each numerical simulaions of he compuaional domain wih and wihou he pensoc, see Table. Gride A and B were used for he -ε model, where grids C and D are used wih he SST model. The grid from he inle spiral casing o he oule is idenical on boh cases. The grids have a good qualiy. Some high y + values are obained on he mos op par of he spiral casing. This is due o he presence of pinched elemens in his region, which produce inadequae values. Pinch elemens are hexahedral blocs wih one collapse surface or wo collapse edges. They do no have any influence on he resuls. Maximum and average y + values as well as minimum face angle and number of nodes for he differen grids are presened in Table. Table. Characerisics of he grids used. No. of Node Max. y + Ave. y + Min. angle A 7,800, º B 7,499, º C 3,80, º D 3,356, º Noe A: Wih he pensoc: y + = 50 B: Wihou he pensoc: y + = 50 C: Wih he pensoc: y + = D: Wihou he pensoc: y + =.. Boundary condiion The number and ype of boundary condiions mus accord wih he governing equaions of he flow. Differen boundary condiions may cause quie differen simulaion resuls. Improper ses of boundary condiions may inroduce non-realisic resuls or convergence problems. So orchesraing he boundary condiions for differen problems is very essenial. Mean ime, differen variables in he environmen may have differen boundary condiions according o cerain physical problems. Therefore, i is imporan o se boundary condiions ha accuraely reflec he real siuaion o allow you o obain accurae resuls. Inle boundary condiion can be se in a number of ways depending on how we wan o specify he condiions and wha paricular physical models we are using for he simulaion. In he curren research wor he boundary mass flow rae is specified along wih he flow direcion. The mass flow rae which moves from he supply reservoir owards he inae of he pensoc is equivalen o he iniial boundary condiion, which is specified currenly as inle flow rae 0.5 m 3 /s. The wall is he mos common boundary, encounered in confined fluid flow problems. The velociy of he fluid a he wall boundary is se o zero, no slip boundary condiion. The oule boundary condiion can be used where i is nown ha flow is direced ou of he domain. In our case he relaive saic pressure over he oule boundary is specified. For all oher ranspor equaions he oule value of he variables is par of he soluion..3. Turbulence modeling Two differen ypes of RANS models, sandard -ε wih scalable wall funcion and SST -ω Based urbulence model are applied o sudy he flow characerisics. Turbulence models are based on hypoheses abou urbulen processes and require empirical inpu in he form of consans or funcions. The mos successful compuaional models for pracical engineering purposes are hose relaing wo or more ranspor equaions, because hey acquire wo quaniies o characerize he lengh and ime scales of urbulen processes. The sandard -ε model wih scalable near wall funcion is he firs model uilized for he differen calculaions. As a wo equaion model, i uses an eddy viscosiy hypohesis for he Reynolds sresses, which assumes ha he urbulen sresses are proporional o he mean velociy gradien and relae hem linearly.

4 0 Proceedings of he nd IAHR Inernaional Meeing of he Worgroup on Caviaion and Dynamic Problems in Hydraulic Machinery and Sysems ρ u u i j U i U j = µ + ρδ ij x j x i 3 = µ Eij ρδ ij 3 () ρ is he fluid densiy, u i velociy flucuaions, U i mean velociy componens, E ij is he mean srain rae ensor, µ is he eddy viscosiy and is he urbulen ineic energy of he flow. The urbulen eddy viscosiy is relaed o he ineic energy of he urbulen flow by: µ =ρc µ ε () where ε is he urbulen dissipaion per uni mass and C µ is a consan. The ranspor equaions for he urbulen quaniies are: _ ρ µ + div ρu = div µ + µ E E ρε + ij ij _ ρε µ + div ρε U = div µ + ε ε ε ε + C ε µ Eij Eij Cε ρ (3) (4) The model closure coefficiens for he calculaion in he presen wor are: C µ = 0.09, =.00, ε =.30, C ε =.44 and C ε =.9. Shear sress ranspor model (SST) is he second urbulen model uilized. I is an eddy-viscosiy model, which combines he -ω model in he inner boundary layer and -ε model in he ouer region. I limis he shear sress in adverse pressure gradien regions. The ranspor equaions for he urbulen quaniies afer some mahemaical manipulaions ae he form: _ ν + div U = div ν + ' + ν E. E β ω ij _ ω + div ω U = ν div ν + ω + ω ωω ω + α ν Eij. Eij β ω ij ( F ) ω (5) (6) where ω is he dissipaion per uni urbulence ineic energy (ω ~ ε/) and he eddy viscosiy defined as: a ν = (7) max( aω, SF ) where F and F are a blending funcion and S is an invarian measure of he srain rae such as: 500ν 4ρ F = anh min max, ', β ωy y ω CDw ω y F 500ν = anh max, ' β ωy y ω 4 (8) (9) where y is he disance o he neares wall and ν is he inemaic viscosiy and: 0 CD w = max ρ ω,.0 *0 (0) ω ω The model consans used for he calculaion are: ' β = 0.09, α = 0.556, α = 0.44, β = 0.075, =.76, =, = and = Experimenal resul The experimenal daa used for evaluaion of he compuaion in his wor are provided by Håan Nilsson, Chalmers Universiy of Technology Sweden. The measuremens are included in his PhD hesis [5], in which all deails of he experimenal se up, he LDA echnique and how he measuremens were performed can be found. However for he expediency of comparison we ried o include a summary of he basic poins and resuls. Exising experimenal daa were measured using he laser Doppler anemomeer (LDA) echnique along a measuremen plane a he spiral casing secion. The LDA echnique uses he Doppler shif effec of refleced ligh from paricles o deermine he insananeous velociy in a single poin. The resuling Doppler frequency is proporional o he measured velociy. The locaion of he measuremens from a op view of he spiral casing and he verical view of he direcion of he measuremen grid is shown in Fig. 3. Differen regions in he plane were invesigaed, see Fig. 4. A measuremen he velociy normal o he measuremen plane and he verical velociy componen (which are angenial and axial velociy componens), a measuremen he angenial velociy componens and he velociy componen along he measuremen plane (which is he radial velociy componens) and a measuremen 3 he angenial and axial velociy componens were measured. ω ω

5 Proceedings of he nd IAHR Inernaional Meeing of he Worgroup on Caviaion and Dynamic Problems in Hydraulic Machinery and Sysems Figure 3. Locaion of measuremens from he op view of he spiral casing and he corresponding measuremen plane. Figure 4. Schemaic locaion of he Measuremens [5] grid spacing and conrol volume size is reduced o zero and all he RMS residuals of he momenum, mass and he urbulen equaions are drop down below he argeed level. In order o validae our mehodology and o assess he accuracy of he numerical resuls comparisons wih he available experimenal daa are performed, which is imporan o see ha he numerical resuls are qualiaively and quaniaively correc before hey are furher used. The firs comparison is conduced a measuremen, in he disribuor and pars of he spiral casing, see Fig. 4. There, he angenial velociy componen increases oward he runner vanes, see Fig. 5, and he axial velociy componen increases a he bend before he leading edge of he say vanes and decreases oward he railing edge of he guide vanes, see Fig. 6. In boh figures, he velociy componens are compared wih he experimenal daa and he resuls obained from he CFD simulaions achieved using boh urbulen models wih and wihou he pensoc. From Figure 5, he angenial velociy from he numerical simulaions of boh urbulen models wihou he pensoc is similar. However, hey deviae considerably from he experimenal values. The simulaions resuls wih pensoc of boh urbulen models have a iny variaion beween each oher. They agree quie well wih he experimen, he velociy is overesimaed before passing he say vane and underesimaed afer he passage. The imporance of he pensoc in he simulaion is poined ou. 3. RESULTS ANSYS CFX0.0, sae of he ar commercial sofware is used o perform he RANS simulaions in his sudy. I is based on he finie volume mehod and has a coupled unsrucured solver. To solve he numerical equaions, he advecion scheme high resoluion is used. High resoluion advecion scheme mean Blend facor values vary hroughou he domain based on he local soluion field in order o implemen a boundedness crierion. For accuracy Blend facor will be close o.0 in flow regions wih low variable gradiens and 0 in areas where he gradiens change sharply o preven over and under esimaion and mainain robusness. Seing Blend facor of 0 and.0 for he advecion scheme is equivalen o using he firs order advecion scheme and second order differencing for he advecion erms, correspondingly []. The simulaion process sared wih seady sae calculaion of he flow. Convergence is achieved for boh urbulen models wih and wihou he pensoc, by his we mean ha he soluion of he discreized equaions ends o he exac soluion as he Figure 5. Tangenial velociy conour plo a measuremen in m/s experimens and are from he SST urbulen model wih and wihou he pensoc and are from he -ε urbulen model wih and wihou he pensoc, respecively.

6 Proceedings of he nd IAHR Inernaional Meeing of he Worgroup on Caviaion and Dynamic Problems in Hydraulic Machinery and Sysems The axial velociy resuls from he numerical simulaion have all a similar shape independenly of he case, see Fig. 6. The SST urbulen model wih pensoc has a good ballpar figure wih he experimen, while he hree oher cases have a similar shape wih an underesimaion of he maximum velociy region. Figure 8. The axial velociy has lower values near he upper wall of he casing and has a highes value a he ouer verical wall owards he lower par of he scroll casing, see Fig. 9. Figure 6. Axial velociy conour plo a measuremen in m/s experimens and are from he SST urbulen model wih and wihou he pensoc and are from he -ε urbulen model wih and wihou he pensoc, respecively The second comparison is carried ou a measuremen, a he enrance of he disribuor, see Fig. 4. In his secion he angenial velociy componens is examined, see Fig. 7. There, he angenial velociy componen increases owards he enrance of he say vanes and decreases owards he ouer verical wall of he scroll casing. The resul obained from he -ε urbulen model wih pensoc has he bes similariy wih he experimen a he boom par of he measuring secion. However, he SST urbulen model wih pensoc shows a beer agreemen wih he experimen weighing agains o he oher. The oupus from he numerical simulaion of boh urbulen models wihou pensoc are similar and indicae inverse correlaion, see Fig. 7. The hird comparison is performed for measuremen 3, an exension of measuremen near he ouer wall of he spiral casing, see Fig. 4. In his secion, he angenial velociy componen increases owards he cenre of he runner and decreases around he ouer mos verical wall of he spiral casing, see Figure 7: Tangenial velociy conour plo a measuremen in m/s experimens and are from he SST urbulen model wih and wihou he pensoc and are from he -ε urbulen model wih and wihou he pensoc, respecively. The angenial velociy has a similar shape for all cases. Similarly o he oher measuremen secions, he numerical simulaions wih pensoc presen he bes agreemen wih he experimens, see Fig. 8. A slighly beer agreemen is obained wih SST. In Figure 9, he correc shape is no capured by any cases. However, dissimilariy a he righ boom corner wih he experimens is found wihou pensoc no obained wih pensoc. I should no be forge ha we are looing a small velociy variaion. The accuracy of CFD simulaions depends srongly on he deails of he urbulence model formulaion and he corresponding boundary condiions. One would expec ha he selecion of suiable urbulence model for he simulaions migh no be ha difficul, bu here he auhors would lie o address ha i is challenging. Generally he selecion of urbulen model for a cerain applicaion depends on he underlying flow regimes and he level of accuracy required. According o he presen resuls, he

7 Proceedings of he nd IAHR Inernaional Meeing of he Worgroup on Caviaion and Dynamic Problems in Hydraulic Machinery and Sysems 3 Figure 8: Tangenial velociy conour plo a measuremen 3 in m/s experimens and are from he SST urbulen model wih and wihou he pensoc and are from he -ε urbulen model wih and wihou he pensoc, respecively. Figure 9: Axial velociy conour plo a measuremen 3 in m/s experimenal and are from he SST urbulen model wih and wihou he pensoc and are from he -ε urbulen model wih and wihou he pensoc, respecively. numerical simulaions of he spiral casing are nearly insensiive o he urbulence model chosen, indicaing a nearly in viscous flow. However, he SST model presens more accurae resuls. The correcness of he inle boundary condiions has a more sriing influence on he resuls. An analysis of he oule boundary condiion should also be conduced. 4. CONCLUSION Numerical simulaions of hree-dimensional flow of he Hölleforsen spiral casing and disribuor wih and wihou pensoc have been performed wih finie volume mehod and wo urbulence models: -ε and SST. Comparisons wih available experimenal resuls indicae clearly he imporance of he pensoc o perform accurae simulaion. Therefore, deailed inle boundary condiions are necessary o simulae accuraely he spiral casing flows if he pensoc is no included in he simulaion. The resuls found from he numerical simulaion show ha he urbulen models SST and he -ε give similar resul. However, he SST model performed slighly beer. ACKNOWLEDGEMENTS The research presened was carried ou as a par of Swedish Hydropower Cenre SVC. SVC has been esablished by he Swedish Energy Agency, Elfors and Svensa Krafnä ogeher wih Luleå Universiy of Technology, The Royal Insiue of Technology, Chalmers Universiy of Technology and Uppsala Universiy. REFERENCE [] H.K. Verseeg and W. M. Alalaseera An inroducion o compuaional Fluid Dynamics, he finie volume mehod Firs published 995, ISBN [] J.H. Ferziger, M. Peric Compuaional Mehods for Fluid Dynamics, Springer-Verlag, Berlin, Heidelberg, 3 rd ediion, 00, ISBN [3] D.C. Wilcox Turbulence Modelling for CFD ISBN , November, 994, California. [4] M.J. Cervanes, T.F. Engsröm and L.H. Gusavsson Proceeding of he hird IAHR / ERCOFTAC Worshop on draf ube flow, Turbine -99 III Luleå Universiy of Technology, Sweden, 005. [5] H. Nilsson Numerical Invesigaions of Turbulen Flow in Waer Turbines, Chalmers Universiy of Technology, Docoral hesis, Göeborg, Sweden, 00. [6] T.F. Engsröm Simulaions and Experimens of Turbulen Diffuser Flow wih Hydropower Applicaions Luleå Universiy of Technology, Docoral hesis 003:0, Luleå, Sweden, 003.

8 4 Proceedings of he nd IAHR Inernaional Meeing of he Worgroup on Caviaion and Dynamic Problems in Hydraulic Machinery and Sysems [7] R. Löhney Applied CFD echniques An inroducion based on Finie elemen Mehods school of compuaional sciences, George Mason Universiy, Fairfax, Virginia, USA ISBN [8] H.C. Radha Krishna Hydraulic Design of Hydraulic Machinery Inernaional Ediorial Commiee Chairman, Duan C G, secreary, A P Boldy, ISBN [9] M.J. Cervanes., Effecs of Boundary Condiions and Unseadiness on Draf Tube Flow, Luleå Universiy of Technology, Docoral hesis 003:, Luleå, Sweden, 003 [0] W. Rodi and F. Marelli, Engineering Turbulence Modelling and Experimens, Florence, 993, ISBN: [] ANSYS CFX and ANSYS ICEM Help manual. [] L.C.E.O. Souza Hydraulic Turbines Spiral Casing Numerical Simulaion Universiy of Brazil, deparmen of Mechanical Engineering, 4 January 005, Brazil.