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.
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,
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):
• 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.)
Mesh generation Discretization of the governing equations Solution of discretized equations Post processing Interpretation of the results
An example
Development of the mathematical model
Governing equations
Equations: momentum, thermal (x), multiphase (x), … Phase 1: 2D, steady; Phase 2: unsteady, …, The flow is turbulent!
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
Numerical methods Finite difference discretization Finite volume discretization Solution of linear equation systems Solution of the N-S equations
Initiation of the problem
DP Offshore Ltd is keen to know what (forces ) caused the damage they recently experienced with their offshore pipelines.
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⎜
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
=
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.
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.
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
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
Boundary conditions
Decide the computational domain Specify bounБайду номын сангаасary conditions
Inlet: Flat inlet profiles V=25m/s Turbulence=5%
10D
Symmetry Flow
10D Outlet: fully developed zero gradient
=
−
∂P ∂z
+
ρgz
+
⎛
μ⎜
⎝
∂ 2w ∂x 2
+
∂ 2w ∂y 2
+
∂
2
w
⎞ ⎟
∂z2 ⎠
Why CFD? (cont.)
Flow in a pipe
• For laminar flow:
U
=
U
0
⎡ ⎢1 ⎢⎣
−
⎜⎛ ⎝
r R
⎟⎞2
⎤ ⎥
⎠ ⎥⎦
• For turbulent flow:
? U
⎝
∂ 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
⎟ ⎠
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.
COMPUTATIONAL FLUID DYNAMICS
Han Chen （陈 瀚） Department of Mechanics School of Civil Engineering & Mechanics Huazhong University of Science and Technology