计算流体力学教程

To observe the temperature distribution in laminar and turbulent flow
Re = 1000
Figure 3.9.1 Temperature plot in a laminar flow
Re = 5 x 104
Figure 3.9.2 Temperature plot in a turbulent flow
MIET-2012 Computational Fluid Dynamics
What information we need?

Spatial Variation (x,y,z) & Time (t) of: Velocity (u,v,w in Cartesian coordinate) Pressure (P) Density Temperature (T) Concentration of Chemical Species (C) Turbulence quantities [turbulent kinetic energy (k), dissipation rate (ε) or frequency (ω)]
k
MIET-2012 Computational Fluid Dynamics
Example 3.2 (Continuity equ Nhomakorabeation)

L = 0.05 m H = 0.01 m U = 0.01 m/s = 1.2 kg/m3 air = 2 x 10-5 kg/m.s
MIET-2012 Computational Fluid Dynamics
Example 3.7 (Energy equation)
Case 1

Re = 6



L = 0.05 m H = 0.01 m U = 0.01 m/s = 1.2 kg/m3(air) = 2 x 10–5 kg/ms k = 0.026 W/mc (Thermal conductivity) Tw = 50 c Tin = 20 c
Figure 3.7.1 Temperature contour plot with k = 0.026 W/m.c (thermal conductivity)
Re = 6 Case 2

k = 0.00026 W/mc (Thermal conductivity
Figure 3.7.2 Temperature contour plot k = 0.00026 W/m.c (thermal conductivity)
MIET-2012 Computational Fluid Dynamics
Questions in CFD - II





What is the meaning of monitoring curves? How is the numerical procedure terminated? What are solution errors? How is a computational solution assessed to be correct, numerically accurate and physically meaningful? When dealing with more complex flow problems, are there any other available methods/techniques or practical experiences or general guidelines that can assist in overcoming convergence difficulties? Are there any additional illustrative examples using CFD and how the solution can be better analyzed? What are the future advancements in CFD?
Internal (Pipe, Channel)
External (Airfoil, Ship)
MIET-2012 Computational Fluid Dynamics
Questions in CFD - I


What are the physical flow processes of the CFD problem? How is the flow physics described in mathematical equations? What are the equations governing the fluid flow and heat transfer? Why are boundary conditions important and how are they applied? What are the physical meanings of the boundary conditions? How are the mathematical equations solved? Why does a flow domain require to be sub-divided into many smaller non-overlapping sub-domains or a computational mesh/grid? How are computational methods/techniques employed?
MIET-2012 Computational Fluid Dynamics
How do we obtain?

From governing equation based on Mass Conservation Momentum Conversation Energy Conversation
Figure 3.10.1 Velocity vector plot
Figure 3.10.2 Turbulent kinetic energy plot
MIET-2012 Computational Fluid Dynamics
Figure 3.8.1 Laminar flow velocity profile plot Re = 5 x 105
Figure 3.8.2 Turbulent flow velocity profile plot
MIET-2012 Computational Fluid Dynamics
Example 3.9 (Laminar and turbulent flow with heat transfer)2
Computational Fluid Dynamics
MIET-2012 Computational Fluid Dynamics
Overview of CFD
Computational Fluid Dynamics & Heat Transfer Transient/Unsteady Steady


Re = 6
L = 0.05 m H = 0.01 m U = 0.01 m/s = 1.2 kg/m3 (air) = 2 x 10–5 kg/ms
Figure 3.5.1 Laminar flow velocity profile plot with = 2 x 10 –5 kg/m.s Re = 600
u v w Γ Γ Γ S t x y z x x y y z z u v w If 1 mass: x y z 0
u u 1 p If T Su S' u u momentum: T u y z z x
If T Energy: ST q specific heat generation
Case 2

= 2 x 10–7 kg/ms Figure 3.5.2 Laminar flow velocity profile plot with = 2 x 10 –7 kg/m.s
Figure 3.5.3 Laminar flow velocity profile plot with = 2 x 10 –7 kg/m.s by increasing channel length to L = 0.1 m
Inviscid Fluid
Viscous Fluid
Heat Transfer
Compressible (Panel Method)
Laminar
Turbulent
Conduction
Convection Fluid
Radiation
Compressible (Air, Acoustic)
Incompressible (Water, Low speed air)

on local basis

in a finite volume shrink volume to zero x 0 partial differential (governing) equations
MIET-2012 Computational Fluid Dynamics
A Generic Form of Basic Equations
MIET-2012 Computational Fluid Dynamics
Example 3.8 (Laminar and turbulent flow)

To observe the flow velocity profiles in laminar and turbulent flow