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MODELLING OF FLOW IN RECTANGULAR SEDIMENTATION TANKS BY AN EXPLICIT THIRD‐ORDER UPWINDING TECHNIQUE
Author(s) -
Gerges Hany,
McCorquodale John A.
Publication year - 1997
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/(sici)1097-0363(19970330)24:6<537::aid-fld506>3.0.co;2-7
Subject(s) - upwind scheme , numerical diffusion , mathematics , discretization , turbulence , flow (mathematics) , vector field , mechanics , mathematical analysis , geometry , physics
A new numerical model has been developed to simulate the transport of dye in primary sedimentation tanks operating under neutral density conditions. A multidimensional algorithm based on a new skew third‐order upwinding scheme (STOUS) is used to eliminate numerical diffusion. This algorithm introduces cross‐difference terms to overcome the instability problems of the componentwise one‐dimensional formulae for simulating multi‐dimensional flows. Small physically unrealistic overshooting and undershooting have been avoided by using a well‐established technique known as the universal limiter. A well‐known rotating velocity field test was used to show the capability of STOUS in eliminating numerical diffusion. The STOUS results are compared with another third‐order upwinding technique known as UTOPIA. The velocity field is obtained by solving the equations of motion in the vorticity–streamfunction formulation. A k – ϵ model is used to simulate the turbulence phenomena. The velocity field compares favourably with previous measurements and with UTOPIA results. An additional differential equation governing the unsteady transport of dye in a steady flow field is solved to calculate the dye concentration and to produce flow‐through curves (FTCs) which are used in evaluating the hydraulic efficiency of settling tanks. The resulting FTC was compared with both measurements and numerical results predicted by various discretization schemes. © 1997 by John Wiley & Sons, Ltd.