# Turbulent Natural Convection Inside a Tall Cavity

In this application, AcuSolve is used to simulate the natural convection of a turbulent flow field within a tall rectangular cavity. AcuSolve results are compared with experimental results as described in Betts and Bokhari (2000). The close agreement of AcuSolve results with experimental results validates the ability of AcuSolve to model cases with natural convection of turbulent flow within a tall cavity.

## Problem Description

The problem consists of air within a tall cavity with a hot wall and a cold wall, as shown in the following image, which is not drawn to scale. The cavity is 2.18 m tall, 0.0762 m wide, and 0.52 m deep. The cavity's vertical walls differ in temperature, causing the fluid to transfer the heat, leading to natural convection. The temperature of the hot wall is 307.85 K, while the temperature of the cold wall is 288.25 K. The horizontal walls of the cavity are adiabatic. The length-to-width ratio of 28.6 and temperature difference of 19.6 K produce a turbulent flow field within the cavity with a Rayleigh number of 8.6X105 (Betts and Bokhari 2000). The flow medium is air, with a Boussinesq approximation for density, a specific heat of 1005 J/kg-K, and a viscosity of 1.781 X 10-5 kg/m-s. Gravity is applied to the flow as a body force.
The simulation was performed as a two dimensional problem by constructing a volume mesh that contains a single layer of elements in the extruded direction, normal to the flow plane and by imposing symmetry boundary conditions on the extruded planes.

## AcuSolve Results

The AcuSolve solution converged to a steady state and the results reflect the mean flow conditions. The natural convection of the flow is generated by heat transfer from the vertical walls to the fluid in the cavity. The temperature gradients created by this heat transfer cause differing densities within the flow region. The warmer air rises to the top of the cavity due to its lower density while the colder air sinks to the bottom of the cavity due to its higher density. This produces flow near the hot vertical wall in the positive vertical direction and flow near the cold wall in the negative vertical direction.
The AcuSolve results of the temperature and vertical velocity within the cavity are compared to the corresponding experimental values in the plots shown below. The temperature of the air is lowest near the cold vertical wall, remains relatively steady in the middle of the cavity, and then peaks near the hot vertical wall. Following a similar trend, the AcuSolve results show that the velocity is lowest near the cold vertical wall, due to the air sinking, and then steadily increases as the air begins to rise near the hot vertical wall. The velocity at the walls is zero due to the no-slip boundary condition. Additional comparisons are made to evaluate the performance of four turbulence models, Spalart-Allmaras (SA), shear stress transport (SST), K-Omega and K-ε.

## Summary

In this application, turbulent flow developed by natural convection, at a Rayleigh number of 8.6X105, is studied within a tall cavity. The AcuSolve results compare well with the experimental data for temperature and vertical velocity along a horizontal line at a location of y/H=0.05 in the tall cavity, with the two-equation models capturing the velocity gradient with greater accuracy. A temperature difference occurs within the flow region due to the heat transfer from the vertical walls of the cavity. The hotter, less-dense air rises to the top of the cavity while the colder, denser air sinks to the bottom, giving rise to recirculation. AcuSolve demonstrates the ability to accurately predict the natural convection of turbulent flow within a tall cavity.

## Simulation Settings for Turbulent Natural Convection Inside a Tall Cavity

AcuConsole database file: <your working directory\cavity_turbulent_heat\cavity_turbulent_heat.acs

Global

• Problem Description
• Analysis type - Steady State
• Turbulence equation - Spalart Allmaras
• Auto Solution Strategy
• Relaxation factor - 0.2
• Material Model
• Air
• Type - Boussinesq
• Density - 1.225 kg/m3
• Specific Heat - 1005 J/kg-K
• Viscosity - 1.781e-5 kg/m-sec

Model

• Volumes
• Volume
• Element Set
• Material model - Air
• Surfaces
• Back
• Simple Boundary Condition
• Type - Symmetry
• Bottom
• Simple Boundary Condition
• Type - Wall
• Temperature BC type - Flux
• Heat Flux - 0.0 W/m2
• Cold
• Simple Boundary Condition
• Type - Wall
• Temperature BC type - Value
• Temperature - 288.25 K
• Front
• Simple Boundary Condition
• Type - Symmetry
• Hot
• Simple Boundary Condition
• Type - Wall
• Temperature BC type - Value
• Temperature - 307.85 K
• Top
• Simple Boundary Condition
• Type - Wall
• Temperature BC type - Flux
• Heat Flux - 0.0 W/m2

## References

P.L. Betts and I.H. Bokhari. "Experiments on Turbulent Natural Convection in an Enclosed Tall Cavity". International Journal of Heat and Fluid Flow 21:675-683. 2000.