计算流体力学(CFD)概论
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difference. Iteration Start iteration Failed Plot velocity or other variable to assist identifying the reason(s) Potential changes in: relaxation factors, mesh, initial guess, numerical schemes, etc. Converged solution Eventually, solution converged.
Development of the mathematical model
Governing equations
Equations: momentum, thermal (x), multiphase (x), … Phase 1: 2D, steady; Phase 2: unsteady, …, The flow is turbulent!
------------------------- -------------- -------------- -------------- -------------- -------------- --------------
net
8.098238 0.12247093 8.2207089 13.221613 0.199 13.421566
1. INTRODUCTION
What is CFD?
Computational fluid dynamics (CFD):
CFD is the analysis, by means of computer-based simulations, of systems involving fluid flow, heat transfer and associated phenomena such as chemical reactions.
An example (cont.)
Discretization of the equations
Start with 1st order upwind, for easy convergence Consider to use QUICK for velocities, later. There is no reason for not using the default SIMPLER for pressure.
we would like to consider using a RNG or a low-Re model
Mesh generation
Finer mesh near the wall but not too close to wall Finer mesh behind the pipe
Boundary conditions
Decide the computational domain Specify boundary conditions
Inlet: Flat inlet profiles V=25m/s Turbulence=5%
10D
Symmetry Flow
10D Outlet: fully developed zero gradient
CFD involves ...
What does CFD involve?
Specification of the problem Development of the physical model Development of the mathematical model
Governing equations Boundary conditions Initial conditions
=
−
∂P ∂z
+
ρgz
+
⎛
μ⎜
⎝
∂ 2w ∂x 2
+
∂ 2w ∂y 2
+
∂
Baidu Nhomakorabea
2
w
⎞ ⎟
∂z2 ⎠
Why CFD? (cont.)
Flow in a pipe
• For laminar flow:
U
=
U
0
⎡ ⎢1 ⎢⎣
−
⎜⎛ ⎝
r R
⎟⎞2
⎤ ⎥
⎠ ⎥⎦
• For turbulent flow:
? U
Smooth wall
20D
An example (cont.)
Development of the mathematical model (cont.)
Turbulence model
Initially, a standard 2-eq k-ε turbulence model is chosen for use. Later, to improve simulation of the transition, separation & stagnation region,
Mesh generation Discretization of the governing equations Solution of discretized equations Post processing Interpretation of the results
An example
Numerical methods Finite difference discretization Finite volume discretization Solution of linear equation systems Solution of the N-S equations
Why CFD?
Continuity and Navier-Stokes equations for
incompressible fluids:
∂u + ∂v + ∂w = 0 ∂x ∂y ∂z
ρ⎛⎜
⎝
∂u ∂t
+
u
∂u ∂x
+
v
∂u ∂y
+
w
∂u ∂z
⎞ ⎟ ⎠
=
−
∂P ∂x
+
ρgx
+
⎛
μ⎜
=
U
0
⎜⎛ ⎝
y R
⎟⎞1 / n ⎠
Or u + = 2.5 ln y + + 5.5
Important conclusion: There is no analytical solution even for a very simple application, such as, a turbulent flow in a pipe.
Analytical solutions are available for only very few problems.
Experiment combined with empirical correlations have traditionally been the main tool - an expensive one.
• Tidal current: 10 to 20m/s • Waves (unsteady): -5m/s to +5m/s
Depth of sea: 500m ~ 1000m
• Diameters: 150~200mm • Gap above sea bed: 10mm
An example (cont.)
COMPUTATIONAL FLUID DYNAMICS
Han Chen （陈 瀚） Department of Mechanics School of Civil Engineering & Mechanics Huazhong University of Science and Technology
Governing equations Simplified mathematical models Classification of flows
3. Introduction to numerical methods
Components of a numerical solution method (mathematical model, discretization method, coordinate/vector system, grid, finite approximation, solution method, etc)
An example (cont.)
Post processing
Interpretation of results
Force vector: (1 0 0)
pressure viscous
total pressure viscous
total
zone name
force
force
force coefficient coefficient coefficient
n
n
n
------------------------- -------------- -------------- -------------- -------------- -------------- --------------
pipe 8.098238 0.12247093 8.2207089 13.221613 0.1999 13.421566
Objectives
The course aims to convey the following information/ message to the students:
What is CFD
The main issues involved in CFD, including those of
Outline of the course
1. Introduction
What is CFD What can & cannot CFD do What does CFD involve … CFD applications
2. Governing equations and classification of fluid flows
Initiation of the problem
DP Offshore Ltd is keen to know what (forces ) caused the damage they recently experienced with their offshore pipelines.
Properties of numerical solution methods (consistency, stability, convergence, etc)
4. Finite difference methods 5. Finite volume methods 6. Solution of linear equation systems 7. Methods for unsteady problems 8. Solution of the N-S equations
⎝
∂ 2u ∂x2
+
∂ 2u ∂y2
+
∂
2u
⎞ ⎟
∂z2 ⎠
⎛
ρ⎝⎜
∂v ∂t
+u
∂v ∂x
+v
∂v ∂y
+
w
∂v ∂z
⎞ ⎟ ⎠
=
−
∂P ∂y
+
ρg y
+
μ
⎛ ⎝⎜⎜
∂ 2v ∂x 2
+
∂ 2v ∂y 2
+
∂ 2v ∂z 2
⎞ ⎠⎟⎟
ρ⎛⎜
⎝
∂w ∂t
+
u
∂w ∂x
+
v
∂w ∂y
+
w
∂w ⎞
∂z
⎟ ⎠
Development of the physical model
After a few meetings with the company, we have finally agreed on a specification of the problem (It defines the physical model of the problem to be solved):
Solver
Use Uncoupled rather than coupled method Use default setup on under-relaxation, but very likely, this will need to be changed later Convergence criterion: choose 10-5 initially: check if this is ok by checking if 10-6 makes any
Development of the mathematical model
Governing equations
Equations: momentum, thermal (x), multiphase (x), … Phase 1: 2D, steady; Phase 2: unsteady, …, The flow is turbulent!
------------------------- -------------- -------------- -------------- -------------- -------------- --------------
net
8.098238 0.12247093 8.2207089 13.221613 0.199 13.421566
1. INTRODUCTION
What is CFD?
Computational fluid dynamics (CFD):
CFD is the analysis, by means of computer-based simulations, of systems involving fluid flow, heat transfer and associated phenomena such as chemical reactions.
An example (cont.)
Discretization of the equations
Start with 1st order upwind, for easy convergence Consider to use QUICK for velocities, later. There is no reason for not using the default SIMPLER for pressure.
we would like to consider using a RNG or a low-Re model
Mesh generation
Finer mesh near the wall but not too close to wall Finer mesh behind the pipe
Boundary conditions
Decide the computational domain Specify boundary conditions
Inlet: Flat inlet profiles V=25m/s Turbulence=5%
10D
Symmetry Flow
10D Outlet: fully developed zero gradient
CFD involves ...
What does CFD involve?
Specification of the problem Development of the physical model Development of the mathematical model
Governing equations Boundary conditions Initial conditions
=
−
∂P ∂z
+
ρgz
+
⎛
μ⎜
⎝
∂ 2w ∂x 2
+
∂ 2w ∂y 2
+
∂
Baidu Nhomakorabea
2
w
⎞ ⎟
∂z2 ⎠
Why CFD? (cont.)
Flow in a pipe
• For laminar flow:
U
=
U
0
⎡ ⎢1 ⎢⎣
−
⎜⎛ ⎝
r R
⎟⎞2
⎤ ⎥
⎠ ⎥⎦
• For turbulent flow:
? U
Smooth wall
20D
An example (cont.)
Development of the mathematical model (cont.)
Turbulence model
Initially, a standard 2-eq k-ε turbulence model is chosen for use. Later, to improve simulation of the transition, separation & stagnation region,
Mesh generation Discretization of the governing equations Solution of discretized equations Post processing Interpretation of the results
An example
Numerical methods Finite difference discretization Finite volume discretization Solution of linear equation systems Solution of the N-S equations
Why CFD?
Continuity and Navier-Stokes equations for
incompressible fluids:
∂u + ∂v + ∂w = 0 ∂x ∂y ∂z
ρ⎛⎜
⎝
∂u ∂t
+
u
∂u ∂x
+
v
∂u ∂y
+
w
∂u ∂z
⎞ ⎟ ⎠
=
−
∂P ∂x
+
ρgx
+
⎛
μ⎜
=
U
0
⎜⎛ ⎝
y R
⎟⎞1 / n ⎠
Or u + = 2.5 ln y + + 5.5
Important conclusion: There is no analytical solution even for a very simple application, such as, a turbulent flow in a pipe.
Analytical solutions are available for only very few problems.
Experiment combined with empirical correlations have traditionally been the main tool - an expensive one.
• Tidal current: 10 to 20m/s • Waves (unsteady): -5m/s to +5m/s
Depth of sea: 500m ~ 1000m
• Diameters: 150~200mm • Gap above sea bed: 10mm
An example (cont.)
COMPUTATIONAL FLUID DYNAMICS
Han Chen （陈 瀚） Department of Mechanics School of Civil Engineering & Mechanics Huazhong University of Science and Technology
Governing equations Simplified mathematical models Classification of flows
3. Introduction to numerical methods
Components of a numerical solution method (mathematical model, discretization method, coordinate/vector system, grid, finite approximation, solution method, etc)
An example (cont.)
Post processing
Interpretation of results
Force vector: (1 0 0)
pressure viscous
total pressure viscous
total
zone name
force
force
force coefficient coefficient coefficient
n
n
n
------------------------- -------------- -------------- -------------- -------------- -------------- --------------
pipe 8.098238 0.12247093 8.2207089 13.221613 0.1999 13.421566
Objectives
The course aims to convey the following information/ message to the students:
What is CFD
The main issues involved in CFD, including those of
Outline of the course
1. Introduction
What is CFD What can & cannot CFD do What does CFD involve … CFD applications
2. Governing equations and classification of fluid flows
Initiation of the problem
DP Offshore Ltd is keen to know what (forces ) caused the damage they recently experienced with their offshore pipelines.
Properties of numerical solution methods (consistency, stability, convergence, etc)
4. Finite difference methods 5. Finite volume methods 6. Solution of linear equation systems 7. Methods for unsteady problems 8. Solution of the N-S equations
⎝
∂ 2u ∂x2
+
∂ 2u ∂y2
+
∂
2u
⎞ ⎟
∂z2 ⎠
⎛
ρ⎝⎜
∂v ∂t
+u
∂v ∂x
+v
∂v ∂y
+
w
∂v ∂z
⎞ ⎟ ⎠
=
−
∂P ∂y
+
ρg y
+
μ
⎛ ⎝⎜⎜
∂ 2v ∂x 2
+
∂ 2v ∂y 2
+
∂ 2v ∂z 2
⎞ ⎠⎟⎟
ρ⎛⎜
⎝
∂w ∂t
+
u
∂w ∂x
+
v
∂w ∂y
+
w
∂w ⎞
∂z
⎟ ⎠
Development of the physical model
After a few meetings with the company, we have finally agreed on a specification of the problem (It defines the physical model of the problem to be solved):
Solver
Use Uncoupled rather than coupled method Use default setup on under-relaxation, but very likely, this will need to be changed later Convergence criterion: choose 10-5 initially: check if this is ok by checking if 10-6 makes any