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
Numerical Modeling of Inclined Negatively Buoyant Jets
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: http://www.cbc.ca
St. Lawrence River. From: EC
Numerical Modeling of Inclined Negatively Buoyant Jets
Introduction (Cont’d)
Effluent Discharges into the water body:
1. Surface Discharges
From: www.sciencephoto.com
2. Submerged Discharges
From: www.sciencephoto.com
Numerical Modeling of Inclined Negatively Buoyant Jets
Introduction (Cont’d)
Submerged Discharges
a. Negatively Buoyant Jets
b. Positively Buoyant Jets
Numerical Modeling of Inclined Negatively 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
Numerical Modeling of Inclined Negatively Buoyant Jets
Definitions
• Dilution
C0 − C a
S=
C − Ca
C0: Concentration at Source
Ca: Ambient Concentration
C: Concentration at Mesh Grid
Numerical Modeling of Inclined Negatively Buoyant Jets
Definitions (Cont’d)
Outer-half
inner-half
Numerical Modeling of Inclined Negatively Buoyant Jets
Numerical Details
Governing Equations
Cont.
∂u j
∂x j
=0
Mom.
∂ui
∂ui
∂
∂
∆ρ
1 ∂P
+
+
(u j ui ) = −
(υ eff
) − gi
∂x j
∂t ∂x j
ρ ∂xi ∂x j
ρ
Temp.
∂ ∂T
∂T ∂Tu j
(
)
+
= keff
∂t
∂x j
∂xk ∂xk
Con.
∂C ∂Cu j
∂ ∂C
(
)
+
=D
∂t
∂x j
∂xk ∂xk
Millero and Poisson (1981)
υt
υ0
Heat transfer coefficient
k eff =
Effective kinematic
viscosity
υ eff = υ 0 + υ t
Prt
+
Pr0
Numerical Modeling of Inclined Negatively Buoyant Jets
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 Modeling of Inclined Negatively Buoyant Jets
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 Modeling of Inclined Negatively Buoyant Jets
Numerical Details (Cont’d)
Simulation process priority in OF
Numerical Modeling of Inclined Negatively Buoyant Jets
Numerical Details (Cont’d)
Turbulence Modeling
Seven RANS Turbulence Models:
Standard k-ε
RNG k-ε
Four LEVMs
realizable k-ε
SST k-ω
Two RSMs
Launder-Gibson
LRR
Buoyant wall jet study
One NLEVM: nonlinear k-ε
Inclined dense jet study
Numerical Modeling of Inclined Negatively Buoyant Jets
Results
45° inclined dense jet, LRR turbulence model
Numerical Modeling of Inclined Negatively Buoyant Jets
Results (Cont’d)
Numerical test cases
D
(mm)
U0
Δρ/ρ0
(m/s) (%)
30.00
Initial
Inlet
Height
y0
(mm)
11.17
6.50
1.00
1.98
28.10 172.00
998.20
45.00
12.92
6.00
1.17
1.98
34.30 193.00
999.97
Case
Incline
d Angle
ϴ
1
2
Fd
Lm
(mm)
y0/Lm
Numerical Modeling of Inclined Negatively Buoyant Jets
Results (Cont’d)
Normalized terminal rise height as a function of initial discharge angle
Numerical Modeling of Inclined Negatively Buoyant Jets
Results (Cont’d)
Minimum dilution at the return point as a function of initial discharge angle
Numerical Modeling of Inclined Negatively Buoyant Jets
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
Numerical Modeling of Inclined Negatively Buoyant Jets
Results (Cont’d)
Inclined dense jet
Normalized concentration profiles at various downstream cross-sections for a 30° jet
Numerical Modeling of Inclined Negatively Buoyant Jets
Results (Cont’d)
Inclined dense jet
Comparison of concentration spread width along the trajectory. Upper
Lower bc
Numerical Modeling of Inclined Negatively Buoyant Jets
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.
Numerical Modeling of Inclined Negatively Buoyant Jets
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.
Numerical Modeling of Inclined Negatively Buoyant Jets
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.
Numerical Modeling of Inclined Negatively Buoyant Jets
Thank you!
Numerical Modeling of Inclined Negatively Buoyant Jets
Thank you!
Numerical Modeling of Turbulent Wall Jets in Stationary Ambient Water
Definitions
General
Dimensional Analysis
• Densimetric Froude #
• Momentum Length Scale
• Source Length Scale
Numerical Modeling of Thermal/Saline Discharges in Coastal Waters
Numerical Details
Mathematical Model
(PDEs, BC)
Descritization Method
(FDM, FVM, FEM)
Numerical Modeling
Procedure
Finite Approximation
(Numerical Schemes)
Solution Method
Convergence Criteria
(Stopping Condition)
Numerical Modeling of Thermal/Saline Discharges in Coastal Waters
Numerical Details (Cont’d)
FVM
Numerical Modeling of Thermal/Saline Discharges in Coastal Waters
Numerical Details (Cont’d)
Other Properties
Numerical Schemes: 1st and 2nd order schemes
div(phi,S)
Gauss
upwind;
Gaussian Integration
Interpolation Scheme
Preconditioned bi-conjugate gradient
Numerical Solution
Diagonal incomplete-LU
Numerical Modeling of Thermal/Saline Discharges in Coastal Waters
Numerical Details (Cont’d)
Turbulence Modeling
NS
Take Average
RANS
ρ ui 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
Results (Cont’d)
Buoyant wall jet
Centerline trajectory. Fr # about 20
12
Numerical Modeling of Thermal/Saline Discharges in Coastal Waters
Results (Cont’d)
Buoyant wall jet
Comparison of the maximum velocity decay
Numerical Modeling of Thermal/Saline Discharges in Coastal Waters
Results (Cont’d)
Buoyant wall jet
Spanwise w-velocity profiles at y=ym for case # 3
Numerical Modeling of Thermal/Saline Discharges in Coastal Waters
Results (Cont’d)
Buoyant wall jet
Streamwise temperature profiles for case # 3
Numerical Modeling of Thermal/Saline Discharges in Coastal Waters
Results (Cont’d)
Buoyant wall jet
Spanwise temperature profiles for case # 3
Numerical Modeling of Thermal/Saline Discharges in Coastal Waters
Results (Cont’d)
Buoyant wall jet
Comparison of the maximum temperature decay
Numerical Modeling of Thermal/Saline Discharges in Coastal Waters
Results (Cont’d)
Inclined dense jet
Normalized centerline trajectory for 45°
30° inclined dense jet
Numerical Modeling of Thermal/Saline Discharges in Coastal Waters
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
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
Results (Cont’d)
Inclined dense jet
Normalized variation of dilution along the inlet height level for a 45°
30° jet
Numerical Modeling of Thermal/Saline Discharges in Coastal Waters
Results (Cont’d)
Inclined dense jet
Comparison of normalized centerline max velocity decay for a 45°
30° jet
Numerical Modeling of Thermal/Saline Discharges in Coastal Waters
Results (Cont’d)
Inclined dense jet
Cross-sectional C distribution at various downstream locations
Numerical Modeling of Thermal/Saline Discharges in Coastal Waters
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