Post on 31-Dec-2015
description
Lecture Objectives
• Review for exam – Course overview– Example questions from previous exams
• Discuss midterm project
Course Masterial Review
• Navier-Stokes equations and RANS
• Turbulence modeling
• Discretization and equation solver
• Boundary conditions
• Numerical properties
Conservation Equations Navier Stokes Equations
0z
v
y
v
x
v zyx
)(Sz
vμ
y
vμ
x
vμ
y
p)
z
vv
y
vv
x
vv
τ
vρ( yM2
y2
2
y2
2
y2
yz
yy
yx
y
TTgρ
xM2x
2
2x
2
2x
2x
zx
yx
xx S
z
vμ
y
vμ
x
vμ
x
p)
z
vv
y
vv
x
vv
τ
vρ(
zM2z
2
2z
2
2z
2z
zz
yz
xz S
z
vμ
y
vμ
x
vμ
z
p)
z
vv
y
vv
x
vv
τ
vρ(
qΦz
Tk
y
Tk
x
Tk)
z
TV
y
TV
x
TV
τ
T(ρc
2
2
2
2
2
2
zyxp
})y
v
z
v()
x
v
z
v()
x
v
y
v()
z
v()
y
v()
x
v{( 2zy2zx2yx2z2y2x
Reynolds Averaged Navier Stokes equations
xTy
ty
ty
tx
zx
yx
xx S]
z
V)μμ[(
z]
y
V)μμ[(
y]
x
V)μμ[(
xx
P)
z
VV
y
VV
x
VV
τ
Vρ(
yTy
ty
ty
ty
zy
yy
xy S]
z
V)μμ[(
z]
y
V)μμ[(
y]
x
V)μμ[(
xx
P)
z
VV
y
VV
x
VV
τ
Vρ(
zTy
ty
ty
tz
zz
yz
xz S]
z
V)μμ[(
z]
y
V)μμ[(
y]
x
V)μμ[(
xx
P)
z
VV
y
VV
x
VV
τ
Vρ(
]z
v)μμ(
y
v)μμ(
x
v)μμ[(
zSS z
ty
tx
tztzzTz
sSSimilar is for STy and STx
0z
V
y
V
x
V zyx
Momentum:
Continuity:
4 equations 5 unknowns → We need to model
1)
2)
3)
4)
tμ
Modeling of Turbulent Viscosity
μtμ
Fluid property – often called laminar viscosity
Flow property – turbulent viscosity
......
-k
-k
-k
Re
3
2
1Re
-k
Eq.
Two
Eq.-One
TKEM
constantMVM
μon based Models
t
t
fk
kl
l
Curvature
Buoyancy
Low
Layer
Layer
Layer
bounded
wall
Free
High
lengthmixing
MVM: Mean velocity modelsTKEM: Turbulent kinetic energy equation models
LES: Large Eddy simulation modelsRSM: Reynolds stress models
Additional models:
Discretization and equation solver
Step1: solve V* from momentum equations
Step2: introduce correction P’ and express V = V* + f(P’)
Step3: substitute V into continuity equation solve P’ and then V
Step4: Solve T , k , e equations
Guess p*
end
Converged (residual check)
yes
no
p=p*
Discretization of RANS SIMPLE algorithm
Boundary Conditions
– Surfaces (wall functions)• Velocity • Temperature• Concentration
– Inlets and outlets• Supply diffusers and • Outlets
Laminar sub-layer
Velocity profile
Surface cell
momentum sources
Numerical properties that affect the solutions
• Grid distribution- Grid dependent/independent solution
• Differencing scheme- Numerical diffusion
• Convergence - Residual and Number of iterations
• Stability - Relaxation
• Tests the solution - Check the conservation of mass, concentration, and energy
Exam
• Open book, open notes • 120 minutes • 25% of your final grade• Comprehensive • Several short problems and • Several questions
Examples are posted on the course website !
Example of short questions
(yes no or very short answer) 1) Reynolds stresses describe the property of fluid or
flow?
2) What is the difference between the shear stresses and Reynolds stresses?
3) Is the relaxation is necessary for the system of linear equations?
4) Is the SIMPLE algorithm explicit method for solving of system of equations?
5) Why do we use QUICK discretization scheme?
6) How many Reynolds stresses we have in two dimensional flow?
Explanation questions
• Describe the difference between explicit and implicit method. Which are the advantages and disadvantages of both?
• Explain how the dispersion of contaminant in the boundary layer depends on velocity field.
• Describe how the temperature field affects the airflow. Identify the term in conservation equation that link energy and velocity equation, and describe which assumption we used to get this term.
Project 1
T1=30C
T2=20C
outletinlet
outlet
outletinlet
inlet
T1
T2
Pat a) Numerical diffusion The purpose of this project part is to analyze how mesh size and orientation affects the accuracy of result.
Pat b) Learn how to: 1) Model: geometry, heat sources, concentration sources, diffusers, 2) Select important simulation parameters 3) Generate appropriate mesh4) Check the results 5) Present the results