Numerical Modeling of Inclined Negatively Buoyant Jets · Numerical Modeling of Inclined Negatively...

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

Outline

• Introduction • Objectives • Definitions • Numerical Details • Results • Conclusions • Future Work • References


Hollywood sewage outfall

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

From: http://www.cbc.ca Al Ghubrah desalination plant (biggest in Oman). (photo by

Hamdi Al-Barwani)

St. Lawrence River. From: EC


Introduction (Cont’d)

Effluent Discharges into the water body: 1. Surface Discharges 2. Submerged Discharges

From: www.sciencephoto.com

From: www.sciencephoto.com


Introduction (Cont’d)

Submerged Discharges a. Negatively Buoyant Jets b. Positively Buoyant Jets


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


Definitions

• Dilution a

a

CCCCS

−−

= 0 C0: Concentration at Source Ca: Ambient Concentration C: Concentration at Mesh Grid


Definitions (Cont’d)

Outer-half

inner-half


Numerical Details Governing Equations

Cont.

Mom.

Temp.

0=∂

∂

j

j

xu

)(kk

effj

j

xT

xk

xTu

tT

∂∂

∂∂

=∂

∂+

∂∂

Heat transfer coefficient Effective kinematic viscosity teff υυυ += 0

0

0

PrPrυυ

+=t

teffk

Con. )(kkj

j

xC

xD

xCu

tC

∂∂

∂∂

=∂

∂+

∂∂

ρρυ

ρ∆

−∂∂

∂∂

+∂∂

−=∂∂

+∂∂

ij

ieff

jiij

j

i gxu

xxPuu

xtu )(1)(

Millero and Poisson (1981)


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


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)


Numerical Details (Cont’d)

Simulation process priority in OF


Seven RANS Turbulence Models:

Numerical Details (Cont’d) Turbulence Modeling

Four LEVMs

Standard k-ε

RNG k-ε realizable k-ε SST k-ω

Two RSMs Launder-Gibson

LRR

One NLEVM: nonlinear k-ε Buoyant wall jet study

Inclined dense jet study


Results

45° inclined dense jet, LRR turbulence model


Numerical test cases

Case Inclined Angle

ϴ

Initial Inlet

Height y0

(mm)

D (mm)

U0 (m/s)

Δρ/ρ0 (%)

Fd Lm (mm)

y0/Lm

1 30.00 11.17 6.50 1.00 1.98 28.10 172.00 998.20

2 45.00 12.92 6.00 1.17 1.98 34.30 193.00 999.97

Results (Cont’d)


Results (Cont’d)

Normalized terminal rise height as a function of initial discharge angle


Results (Cont’d)

Minimum dilution at the return point as a function of initial discharge angle


Results (Cont’d)

Comparison of numerical and experimental coefficients for 45° inclined jets

Avg=1.62

Avg=3.08

Avg=1.48

Avg=1.48

Avg=1.80

Avg=0.44


Results (Cont’d) Inclined dense jet

Normalized concentration profiles at various downstream cross-sections for a 30° jet



Comparison of concentration spread width along the trajectory. Lower bc Comparison of concentration spread width along the trajectory. Upper bc


• 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 outer-half of the jet as well as closer area to source than the inner-half.

Conclusions


• Improved mesh grid system: unstructured, non-conformal, etc.

• Improved turbulence models

• More advanced numerical schemes

• Ambient water characteristics: cross-flow, stratification, wave, etc.

Future Work


References Bleninger, T., and Jirka, G. H. (2008). “Modeling and environmentally sound

management of brine discharges from desalination plants.” Desalination, 221:585–597.

Huai, W., Li, Z. Qian, Z., Zeng, Y., & Han, J. (2010). ”Numerical Simulation of

Horizontal Buoyant Wall Jet.” J. of Hydrodynamics, 22(1):58-65. 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):161-174. OpenCFD Limited. (2011). OpenFOAM - Programmer’s Guide, Version 2.1.1. Shao, D., nad Law, A. W. (2010). “Mixing and boundary interaction of 30 and 45

inclined dense jets.” J. Environ. Fluid Mech., Springer 10:521-553. 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, 59:527-534, London, UK.


Thank you!


Thank you!

Numerical Modeling of Turbulent Wall Jets in Stationary Ambient Water

Definitions General

• Densimetric Froude #

• Momentum Length Scale

• Source Length Scale

Dimensional Analysis

Numerical Modeling of Thermal/Saline Discharges in Coastal Waters

Numerical Details


Numerical Modeling Procedure

Mathematical Model (PDEs, BC)

Descritization Method (FDM, FVM, FEM)

Finite Approximation (Numerical Schemes)

Solution Method

Convergence Criteria (Stopping Condition)

Numerical Details (Cont’d) FVM


Numerical Details (Cont’d) Other Properties


Numerical Schemes: 1st and 2nd order schemes div(phi,S) Gauss upwind;

Gaussian Integration Interpolation Scheme

Numerical Solution Preconditioned bi-conjugate gradient

Diagonal incomplete-LU

Numerical Details (Cont’d) Turbulence Modeling

NS RANS Take Average

jiuuρ


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 Velocity Boussinesq assumption

RSM: A transport Eqn. for Reynolds stress tensor

Centerline trajectory. Fr # about 12

Results (Cont’d) Buoyant wall jet


Centerline trajectory. Fr # about 20

Comparison of the maximum velocity decay



Spanwise w-velocity profiles at y=ym for case # 3



Streamwise temperature profiles for case # 3



Spanwise temperature profiles for case # 3



Comparison of the maximum temperature decay





Normalized centerline trajectory for 30° inclined dense jet Normalized centerline trajectory for 45° inclined dense jet



Normalized vertical location of centerline peak as a function of initial discharge angle



Normalized horizontal location of return point as a function of initial discharge angle



Normalized variation of dilution along the inlet height level for a 30° jet Normalized variation of dilution along the inlet height level for a 45° jet



Comparison of normalized centerline max velocity decay for a 30° jet Comparison of normalized centerline max velocity decay for a 45° jet



Cross-sectional C distribution at various downstream locations



Normalized velocity profiles at various downstream cross-sections for a 30° jet

Numerical Modeling of Inclined Negatively Buoyant Jets · Numerical Modeling of Inclined Negatively...

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