Analysis Characteristics
- Steady-state
- 2D internal flow
- Laminar
- Incompressible
- Natural convection
Reference
Davis, G. De Vahl and Jones, I.P., “Natural convection in a square cavity: a comparison exercise”, Inter. Jour. for Num. Meth. in Fluids, 3, (1983).
Problem Description
Temperature and velocity distributions are calculated for laminar, buoyancy-driven flow in a square cavity. The top and bottom walls are insulated, and the left and right walls are at fixed temperatures differing by 1 K.
The Rayleigh number is computed from:
-
is the coefficient of volumetric expansion, defined as: 
- g is the acceleration of gravity
-
is the density -
is the specific heat - L is the length of the cavity
-
and 
are the temperatures of the left and right walls, respectively - k is the conductivity of the fluid
-
is the viscosity. - Here, the Rayleigh number is 10,000.
This problem is analyzed to verify the fluid flow and heat transfer modeling capabilities of Autodesk® CFD. Accuracy is assessed by comparing velocity components at specific locations in the cavity. Velocities and coordinates are normalized in accordance with Davies, et al. (1983) as follows:
Geometry and Boundary Conditions
Results
Using the expressions defined above for 
, 
, 
and 
, the following results are computed:
| Benchmark | 2015: Build 20131223 | % Error | 2016: Build 20150209 | % Error | |
|
16.178 | 15.862 | 1.952 | 15.907 | 1.673 |
|
0.823 | 0.826 | 0.404 | 0.826 | 0.404 |
|
19.617 | 19.458 | 0.809 | 19.538 | 0.402 |
|
0.119 | 0.113 | 4.373 | 0.115 | 3.132 |