Numerical Modeling of Inclined Negatively Buoyant Jets

Transcription

1 Numerical Modeling of Inclined Negatively Buoyant Jets Presentation by: Hossein Kheirkhah Graduate Student in Civil Engineering Dep. of Civil Engineering University of Ottawa CANADA ICDEMOS April2014

2 Outline Introduction Objectives Definitions Numerical Details Results Conclusions Future Work References Hollywood sewage outfall

3 Introduction Effluent (USEPA Definition): Wastewater, treated or untreated, that flows out of a treatment plant, sewer, or industrial outfall. Generally refers to wastes discharged into surface waters. Effluent Sources Desalination Plants (arid and semi-arid countries) Nuclear Power Plants Municipal Effluents Al Ghubrah desalination plant (biggest in Oman). (photo by Hamdi Al-Barwani) From: St. Lawrence River. From: EC

4 Introduction (Cont d) Effluent Discharges into the water body: 1. Surface Discharges 2. Submerged Discharges From: From:

5 Introduction (Cont d) Submerged Discharges a. Negatively Buoyant Jets b. Positively Buoyant Jets

6 Objectives Evaluating the performance of numerical model Finding the appropriate numerical model/solver Implementations in the base-code Evaluation of various turbulence models Finding the stable numerical schemes

7 Definitions Dilution S C C a = 0 C 0 : Concentration at Source C a : Ambient Concentration C C C: Concentration at Mesh Grid a

8 Definitions (Cont d) Outer-half inner-half

9 Numerical Details Governing Equations Cont. Mom. Temp. = 0 j j x u ) ( k k eff j j x T x k x Tu t T = + Heat transfer coefficient Effective kinematic viscosity t eff υ υ υ + = Pr Pr υ υ + = t t k eff Con. ) ( k k j j x C x D x Cu t C = + ρ ρ υ ρ + = + i j i eff j i i j j i g x u x x P u u x t u ) ( 1 ) ( Millero and Poisson (1981)

10 Numerical Details (Cont d) OF toolbox The OpenFOAM (OPEN Field Operation And Manipulation) CFD Toolbox is a free, open source CFD software package produced by OpenCFD Ltd (2011). Advantages: Open Source Finite Volume Method Working on LINUX OS Variety of Utilities and Applications

11 Numerical Details (Cont d) Solver Solver: mypisofoam A transient solver for incompressible flow Transport Eqns. for U, S and T are solved implicitly P is solved explicitly in PISO algorithm Density varies with S and T (Millero and Poisson, 1981)

12 Numerical Details (Cont d) Simulation process priority in OF

13 Numerical Details (Cont d) Turbulence Modeling Seven RANS Turbulence Models: Four LEVMs Standard k-ε RNG k-ε realizable k-ε SST k-ω Two RSMs Launder-Gibson LRR Buoyant wall jet study One NLEVM: nonlinear k-ε Inclined dense jet study

14 Results 45 inclined dense jet, LRR turbulence model

15 Results (Cont d) Numerical test cases Case Incline d Angle ϴ Initial Inlet Height y 0 (mm) D (mm) U 0 (m/s) Δρ/ρ0 (%) F d L m (mm) y 0 /L m

16 Results (Cont d) Normalized terminal rise height as a function of initial discharge angle

17 Results (Cont d) Minimum dilution at the return point as a function of initial discharge angle

18 Results (Cont d) Avg=1.62 Avg=3.08 Avg=1.48 Avg=1.48 Avg=1.80 Avg=0.44 Comparison of numerical and experimental coefficients for 45 inclined jets

19 Results (Cont d) Inclined dense jet Normalized concentration profiles at various downstream cross-sections for a 30 jet

20 Results (Cont d) Inclined dense jet Comparison of concentration spread width along the trajectory. Lower Upper b c

21 Conclusions Numerical results of selected turbulence models show good agreement for the velocity and concentration fields between both experimental and numerical studies. Realizable k-ε and LRR turbulence models performed best amongst the seven models investigated. Geometrical characteristics of inclined dense jets have been predicted fairly well. Cross-sectional U & C profiles follow the Gaussian pattern better in outerhalf of the jet as well as closer area to source than the inner-half.

22 Future Work Improved mesh grid system: unstructured, non-conformal, etc. Improved turbulence models More advanced numerical schemes Ambient water characteristics: cross-flow, stratification, wave, etc.

23 References Bleninger, T., and Jirka, G. H. (2008). Modeling and environmentally sound management of brine discharges from desalination plants. Desalination, 221: Huai, W., Li, Z. Qian, Z., Zeng, Y., & Han, J. (2010). Numerical Simulation of Horizontal Buoyant Wall Jet. J. of Hydrodynamics, 22(1): Kheirkhah Gildeh, H., Mohammadian, M., Nistor, I., and Qiblawey, H. (2012). Numerical modeling of turbulent buoyant wall jets in stationary ambient water., Submitted to J. Hydraul. Eng., ASCE. Kheirkhah Gildeh, H., Mohammadian, M., Nistor, I., and Qiblawey, H. (2013). Numerical modeling of 30 and 45 inclined dense turbulent jets in stationary ambient., Submitted to J. Environ. Fluid Mech., Springer. Law, A. W., and Herlina. (2002). An experimental study on turbulent circular wall jets. J. Hydraul. Eng., 128(2): OpenCFD Limited. (2011). OpenFOAM - Programmer s Guide, Version Shao, D., nad Law, A. W. (2010). Mixing and boundary interaction of 30 and 45 inclined dense jets. J. Environ. Fluid Mech., Springer 10: Sharp, J. J. (1975). The use of a buoyant wall jet to improve the dilution of a submerged outfall. Proc. Instn. Civ. Engrs, Part 2, 59: , London, UK.

24 Thank you!

25 Thank you! Numerical Modeling of Turbulent Wall Jets in Stationary Ambient Water

26 Definitions General Dimensional Analysis Densimetric Froude # Momentum Length Scale Source Length Scale Numerical Modeling of Thermal/Saline Discharges in Coastal Waters

27 Numerical Details Mathematical Model (PDEs, BC) Numerical Modeling Procedure Descritization Method (FDM, FVM, FEM) Finite Approximation (Numerical Schemes) Solution Method Convergence Criteria (Stopping Condition) Numerical Modeling of Thermal/Saline Discharges in Coastal Waters

28 Numerical Details (Cont d) FVM Numerical Modeling of Thermal/Saline Discharges in Coastal Waters

29 Numerical Details (Cont d) Other Properties Numerical Schemes: 1 st and 2 nd order schemes div(phi,s) Gauss upwind; Gaussian Integration Interpolation Scheme Numerical Solution Preconditioned bi-conjugate gradient Diagonal incomplete-lu Numerical Modeling of Thermal/Saline Discharges in Coastal Waters

30 Numerical Details (Cont d) Turbulence Modeling NS Take Average RANS ρu i u j? Algebraic Models: An algebraic Eqn. for turbulent viscosity 1 Eqn. Models: A transport Eqn. is solved (for turbulent kinetic energy) 2 Eqn. Models: Two transport Eqn. is solved (e.g. for k & ε) Reynolds Stress Boussinesq assumption Velocity RSM: A transport Eqn. for Reynolds stress tensor Numerical Modeling of Thermal/Saline Discharges in Coastal Waters

31 Results (Cont d) Buoyant wall jet Centerline trajectory. Fr # about Numerical Modeling of Thermal/Saline Discharges in Coastal Waters

32 Results (Cont d) Buoyant wall jet Comparison of the maximum velocity decay Numerical Modeling of Thermal/Saline Discharges in Coastal Waters

33 Results (Cont d) Buoyant wall jet Spanwise w-velocity profiles at y=y m for case # 3 Numerical Modeling of Thermal/Saline Discharges in Coastal Waters

34 Results (Cont d) Buoyant wall jet Streamwise temperature profiles for case # 3 Numerical Modeling of Thermal/Saline Discharges in Coastal Waters

35 Results (Cont d) Buoyant wall jet Spanwise temperature profiles for case # 3 Numerical Modeling of Thermal/Saline Discharges in Coastal Waters

36 Results (Cont d) Buoyant wall jet Comparison of the maximum temperature decay Numerical Modeling of Thermal/Saline Discharges in Coastal Waters

37 Results (Cont d) Inclined dense jet Normalized centerline trajectory for inclined dense jet Numerical Modeling of Thermal/Saline Discharges in Coastal Waters

38 Results (Cont d) Inclined dense jet Normalized vertical location of centerline peak as a function of initial discharge angle Numerical Modeling of Thermal/Saline Discharges in Coastal Waters

39 Results (Cont d) Inclined dense jet Normalized horizontal location of return point as a function of initial discharge angle Numerical Modeling of Thermal/Saline Discharges in Coastal Waters

40 Results (Cont d) Inclined dense jet Normalized variation of dilution along the inlet height level for a jet Numerical Modeling of Thermal/Saline Discharges in Coastal Waters

41 Results (Cont d) Inclined dense jet Comparison of normalized centerline max velocity decay for a jet Numerical Modeling of Thermal/Saline Discharges in Coastal Waters

42 Results (Cont d) Inclined dense jet Cross-sectional C distribution at various downstream locations Numerical Modeling of Thermal/Saline Discharges in Coastal Waters

43 Results (Cont d) Inclined dense jet Normalized velocity profiles at various downstream cross-sections for a 30 jet Numerical Modeling of Thermal/Saline Discharges in Coastal Waters