Simulation of Flow Pattern in Open Channels with Sudden Expansions

Transcription

1 Research Journal of Appled Scences, Engneerng and Technology 4(19): , 2012 ISSN: Maxwell Scentfc Organzaton, 2012 Submtted: May 11, 2012 Accepted: June 01, 2012 Publshed: October 01, 2012 Smulaton of Flow Pattern n Open Channels wth Sudden Expansons 1 J. Mamzadeh and 2 S.A. Ayyoubzadeh 1 Department of Water Engneerng, Ilam Unversty, Iran 2 Department of Water Structure, Tarbat Modares Unversty, Iran Abstract: Three-dmensonal flows n sudden expansons of rectangular channels have been nvestgated. In ths research, CFD smulaton model (FLUENT6.2) s used. The k-ε turbulence model s used to smulate turbulence. Desred canal wth coarse, medum and fne mesh sze s selected for smulaton. The results n canal wth sudden expanson showed that the vortex formed by coarse mesh sze and number of teraton more than 400 s asymmetrc and for small and medum mesh sze s symmetrc. In order to analyze expermentally and numercally more closely, the pattern of flow n a flume wth sudden expanson s nvestgated. Results showed that, asymmetrcal flow pattern can be vewed wth some mnor changes such as roughness coeffcent n any part of flume. Keywords: Flow pattern, sudden expanson, symmetrc flow INTRODUCTION Bfurcaton phenomena or crcular flow are frequently encountered n flud mechancs and hydraulcs. Some examples nclude transonc nvscd flows over arfols and cylnders, ncompressble and compressble vscous flows over arfols and ncompressble vscous flows through sudden expansons. The latter s the subect of the present study. A sudden expanson creates a separaton of the boundary layer from the wall, whch results n sgnfcant pressure loss. The magntude of the pressure loss depends upon the Reynolds number and the geometrc expanson rato. In most cases, t s desred to mnmze pressure loss n a ppng system, snce the pressure loss correlates to lost energy. Many expermenters have been observed that the flow n symmetrc expansons s asymmetrc. Some of these stuatons are documented n Graber (1982, 2006) who gave an explanaton of such phenomenon. He provded a predctve method that agreed well wth the expermental observatons and then extended t theoretcally to analyze proposed correctve measures. Asymmetrc flow patterns may occur n perfectly symmetrc abrupt expansons, n whch the man flow deflects and attaches arbtrarly to one wall of the expanson. The adverse effects nclude lengthenng of the dstance to full-wdth flow n expansons, neffcent operaton of screens n screen canals and ncreasng the potental for vortexng n pump ntakes. Cherdron et al. (1978) studed the detaled descrpton of the velocty characterstcs of the asymmetrc flows whch form n symmetrc, two-dmensonal, plane, sudden-expanson geometres by flow vsualzaton and laser-doppler anemometry. The flow and geometry boundary condtons whch gve rse to asymmetrc flow are ndcated and the reason for the phenomenon s shown to le n dsturbances generated at the edge of the expanson and amplfed n the shear layers. Zhou (1995), develop a depth average mathematcal model and test t n a canal wth sudden expanson. Result showed that the flow rate, flow lnes and vortex Formed on both sdes are asymmetrc. Alou and Souhar (2000), presents an expermental study of recrculatng flows downstream of a flat duct sudden expanson. Results of measurements of average and RMS quanttes of the pressure P and the axal velocty U exhbt the asymmetry of the flow behnd the sudden expanson as n the two-dmensonal case. Escuder et al. (2002), reported an expermental nvestgaton of turbulent flow through a plane sudden expanson. Not only was the mean flow found to be strongly asymmetrc, but ntegraton of the mean axal velocty profles revealed sgnfcant departures from two dmensonalty along the centerplane of the expanson duct. The numercal analyss of the turbulent flud flow through an axsymmetrc sudden expanson passage has been carred out by Roy et al. (2010). The recrculaton bubble generated due to the sudden expanson of the passage s observed to reduce n sze and strength wth the ncrease n the Reynolds number. But the sze and strength of the recrculaton bubble ncreases wth the ncrease n the expanson rato. Theoretcal studes have been made by Roul and Dash (2011) to determne the pressure drops caused by abrupt flow area expanson/contracton n small crcular ppes for twophase flow of ar and water mxtures at room Correspondng Author: J. Mamzadeh, 1 Department of Water Engneerng, Ilam Unversty, Iran 3852

2 Res. J. Appl. Sc. Eng. Technol., 4(19): , 2012 temperature and near atmospherc pressure. The pressure drop s determned by extrapolatng the computed pressure profles upstream and downstream of the expanson/contracton. Based on the numercal results as well as expermental data, correlatons are developed for two-phase flow pressure drops caused by the flow area contracton as well as expanson. The above revew research ndcates that few studes done on flow pattern n sudden and gradual expansons and therefore evaluated n ths study. In ths research, flow pattern n sudden expansons studed wth laboratory work and CFD smulaton model. MATERIALS AND METHODS FLUENT s a Computatonal Flud Dynamcs (CFD) software package to smulate flud flow problems. It uses the fnte-volume method to solve the governng equatons for a flud. It provdes the capablty to use dfferent physcal models such as ncompressble or compressble, nvscd or vscous, lamnar or turbulent, etc. Geometry and grd generaton s done usng GAMBIT whch s the preprocessor bundled wth FLUENT. Ths software uses a control-volume-based technque to convert a general scalar transport equaton to an algebrac equaton that can be solved numercally. Pressure-velocty couplng s acheved by usng fve algorthms: SIMPLE, SIMPLEC, PISO, Coupled and Fractonal Step. In the case of ncompressble turbulent flow and averaged n tme, conservaton of mass (1) And momentum conservaton (2) Expressed as follows: u u u t 0 u 1 p g u ( u u ) (1) (2) where, u = velocty component n x drecton, υ = knematc vscosty, ρ = densty, g = gravty acceleraton component n x drecton, p = pressure and = Reynolds stress. Ths equaton contans four man components of the unknown velocty n three drectons and pressure. Also ncludes sx components of unknown Reynolds stress equaton. Thus, system of equatons s not closed and turbulence model must be used. k ε turbulence model s used n ths study. In the other part of research, flow pattern n sudden expansons studed wth laboratory flume n tarbat modares unversty-ran (Mamzadeh, 2009). RESULTS AND DISCUSSION Smulated flow pattern n sudden expanson: Ths part of research, compare the result of flow pattern n a sudden expanson (90 degree angle from centerlne of canal) canal wth FLUENT model and developed mathematcal model by Zhou (1995). The entrance canal s 1.4 m wde and 14 m long and the expanded canal s 2.8 m wde and 14 m long. There s no bed slope n the canal. The upstream entrance veloctes are u = 0.63 m/s, v = 0 and the flow depth y = 0.2 m as the downstream boundary condton s consdered (Fg. 1). In accordance to Fg. 2, the velocty nlet along wth nlet turbulence ntensty and hydraulc depth are the upstream boundary condton and outflow s the downstream boundary condton. Boundary condton for bottom and sde wall of canal s wall. Symmetry boundary condton s used for top of the canal. Hydraulc flow feld detals table s shown n Table 1. Turbulent and under crtcal flow s establshed n canal. Due to the turbulent flow, turbulence models have been used. SIMPLE algorthm for couplng the velocty feld and pressure s used. Fg. 1: Canal for smulaton (Zhou, 1995) 3853

3 Res. J. Appl. Sc. Eng. Technol., 4(19): , 2012 Fg. 2: (a) Coarse mesh: 9726 node, (b) medum mesh: node, (c) fne mesh: node Fg. 3: Flow pattern n canal coarse mesh sze: (a) after 400 teraton, (b) after 2000 teraton Table 1: Hydraulc propertes of canal Turbulence ntensty Hydraulc depth (m) Re Fr V (m/s) Q (m3/s) Desred canal wth coarse, medum and fne mesh sze s selected for smulaton. Coarse and medum mesh sze are Δx = Δy = 0.28 m and Δx = Δy = 0.14 m. Fne mesh sze was carred out n complance wth frst node spacng crtera from the wall. The frst node spacng s calculated for k ε and RSM equal to m. Fgure 2 shows the three types of coarse, medum and fne mesh sze for problem solvng. Fgure 3 showed the results of the coarse grd model after 400 and 2000 teraton. Flow pattern formed after 400 teraton n the Fg. 4a conssts of two symmetrcal vortex on both sdes expanson and a hgh flow velocty n the central lne wll be gradually slowed down n x drecton. Fgure 4b showed that after 2000 Iteraton, the flow dverted to one sde and an asymmetrc flow pattern occurred. Asymmetrc flow pattern n ths case are due to coarse mesh and also added errors for hgher teratons. It should be noted that these results s smlar to Zhou (1995) results. Fgure 4 showed the results of model for the medum and fne mesh. Flow pattern conssts of two symmetrcal vortex on both sdes expanson and a hgh flow velocty n the central lne wll be gradually slowed down n x drecton. Fgure 5 showed comparng the results of model for coarse, medum and fne mesh. Longtudnal and transverse axs represents the canal wdth and velocty magntude respectvely. Durng the 9 m of canal (Fg. 5a) Results do not dffer much, but n sudden expanson place for example 15 m (Fg. 5b), coarse and medum mesh sze do dffer much because of wall functon crtera and the accuracy of ther answers s slghtly low. Also coarse mesh sze showed the hgher velocty magntude n the centerlne of canal rather than medum and fne mesh sze. Flow pattern smulaton n laboratory flume wth sudden expanson: In order to examne more closely the flow pattern n the sudden expanson, a laboratory flume s constructed and a seres of experments were performed on t. Then flume s studed wth fluent numercal model. The flume conssts of two sectons. Secton 1 (Rver secton) have 5 m Length, 16 cm wdth, 30 cm depth and no bed slope. Secton

4 Res. J. Appl. Sc. Eng. Technol., 4(19): , 2012 Fg. 4: Flow pattern n canal: (a) medum mesh sze, (b) fne mesh sze Fg. 5: Result for smulaton (a) coarse mesh, (b) medum mesh, (c) fne mesh Table 2: Hydraulc propertes of flume Turbulence ntensty Hydraulc depth (m) Re Fr V (m/s) Q (L/s) (reservor secton) have 10 m length, 96 cm wdth and longtudnal slope 2%. At the end of flume a wer located wth 45 cm elevaton. Hydraulc flow feld detals gve n Table 2. Turbulent and under crtcal flow n a canal s establshed. Due to the turbulent flow, k-ε and RSM turbulence model s used. SIMPLE algorthm for couplng the velocty feld and pressure s used. In ths case, nput velocty perpendcular to the boundary s used for upstream boundary condton and outflow for downstream boundary condton. In order to calculate the flow feld, turbulence ntensty and hydraulc dameter n upstream 0.3 and 5% s appled, respectvely. Wall boundary condton for the walls and the symmetry boundary condton for top of the canal are appled. Accordng to the frst node Calculaton (4 mm from bottom of canal), mesh near the wall are small and growth 20% n two adacent cells farther from wall. Fgure 6 shows the result of turbulence model n whch flow feld are symmetrcal at dfferent levels of depth, longtudnal and transverse drecton. Smulated flow pattern smulaton wth non-unform roughness and geometry: Flow pattern formed n the laboratory flume wth sudden expanson, usng the numercal model was symmetrcal and was asymmetrc wth the expermental observatons. In the other hand, numercal model and expermental results dd not match together. So n ths part non-unformty of roughness and geometry on the flow pattern s studed. In order to evaluate the effect of non-unform wall roughness on the flow feld, the roughness coeffcent of flume n the left part s selected 50% hgher than rght part of the flume. For evaluaton of non unform 3855

5 Res. J. Appl. Sc. Eng. Technol., 4(19): , 2012 Fg. 6: X velocty n flume Fg. 7: Stream lne for surface layer of flume (a) unform roughness, (b) non unform roughness Fg. 8: Stream lne for surface layer of flume (a) unform geometry, (b) non unform geometry geometry, the wdth of canal measured from the centerlne n the left part s consdered 5% less than rght part of the flume. Fgure 7 and 8 show the streamlne n the surface layer of flow for these two condtons. In the case of same roughness and geometry, rver flows nto the reservor completely symmetrc, whle for the change of the roughness and geometry s deflected to the rght. Increased roughness of the canal and reservor, cause more resstance aganst the flow and the resultng flow s deflected to the rght part. CONCLUSION In ths Research, flow pattern n the sudden expanson are nvestgated. In ths condton for medum and fne mesh sze, the flow pattern was symmetrcal. In the case of coarse mesh sze, ncreasng the number of teratons cause the nstablty of flow and symmetrc flow pattern. Also, the flow pattern n a laboratory flume wth sudden expanson s studed. Symmetrc flow pattern s obtaned n these condtons. Fnally, for study the effect of roughness and geometry 3856

6 Res. J. Appl. Sc. Eng. Technol., 4(19): , 2012 on the flow pattern, the wall of flume s changed and the asymmetry flow observed n ths case. ths result showed that asymmetrc flow pattern could be observed due to mnor changes n flume. REFERENCES Alou, F. and M. Souhar, Expermental study of turbulent asymmetrc flow n a flat duct symmetrc sudden expanson. J. Fluds Eng., 122(1): Cherdron, W., F. Durst and H. Whtelaw, Asymmetrc flows and nstabltes n symmetrc ducts wth sudden expansons. J. Flud Mech., 84: Escuder, M., P. Olvera and R. Poole, Turbulent flow through a plane sudden expanson of modest aspect rato. J. Phys. Fluds, 14(10), DOI: org/ / Graber, D., Asymmetrc flow n symmetrc expansons. J. Hydr. Dv., 108: Graber, D., Asymmetrc flow n symmetrc supercrtcal expansons. J. Hydr. Eng., 132: Mamzadeh, J., The effect of entrance dvergng angle and hydraulc-sedment propertes on pattern of delta progress n dam reservors. Ph.D. thess, Faculty of Agrculture Tarbat Modares Unversty, Iran. Roul, M.K. and S.K. Dash, Two-phase pressure drop caused by sudden flow area contracton/expanson n small crcular ppes. Int. J. Numer. Meth. Fl., 66(11): Roy, V., S. Maumder and D. Sanyal, Analyss of the turbulent flud flow n an ax-symmetrc sudden expanson. Int. J. Eng. Sc. Technol., 2(6): Zhou, G., Velocty depth couplng n shallow water flows. J. Hydr. Eng., 121: