& CFD HT Introduction
Robert J. Ribando Mechanical & Aerospace Engineering University of Virginia
MAE/APMA 672 CFD & HT 1 January 16, 2008
1
Importance of CFD
Heat + Mass Transfer, Fluid Flow, Chemical Reaction Processes in engineering equipment, the environment and organisms Power Production - reactors, furnaces, heat exchangers, etc. Electrical/Electronic Equipment dissipation of heat
2
Importance of CFD (cont.)
Materials Processing - e.g., Casting Weather Prediction Design of Aircraft Automobile Aerodynamics external and internal Oil/Gas Reservoir Simulation
3
Understanding and Prediction
Allows Isolation of Effects. Complex interactions pre-test prediction post-test analysis Control of Properties. Control of Boundary Conditions. No Flow Disturbance.
4
The 3-Legged Stool
Theoretical FD & HT Experimental FD & HT
Computational FD & HT
5
Problems with CFD
Multidimensionality and Size. Turbulence Different Length and Time Scales Odd Geometry Validation
6
Governing Equations
Conservation Postulate Write Integral Statement for a Control Volume Deduce P.D.E. or Equation of Change
Mass, Energy, Momentum, Species, $ Finite-element Finite-volume Control-volume Finite-difference
7
Governing Equations (cont.)
Conservation of Mass
= i ( u ) t
Conservation of Momentum (Vector)
2 + u i u = u - p t
Temporal Convection Diffusion Pressure Gradient 8
Energy Equation (Thermal)
cp t
Storage
2 + u i T=k T
Advection Conduction
9
Equations of Generic Form:
2 + u i = + S t
( is the variable being conserved)
+ux +uy = 2 + 2 t x y x y
2 2
(in 2-D)
10
Heat Conduction
= t 2 + 2 x y
2 2
2 2
(Transient)
0= 2 + 2 x y
(Steady-State)
11
Heat Convection
+ux +uy =0 t x y
High Speed or
u x ,u y...