Numerical and experimental evaluation of turbulent models for natural convection simulation in a thermally driven square cavity.

 Natural convection in a thermally driven square cavity filled with air is studied numerically. Since the thermal Rayleigh number of the configuration ranges between 108 and 1012, the flow is turbulent and k-& models are used to predict the behavior of the flow. For this natural convection problem, the viscous sublayer must be discretized and the behavior of the turbulent quantities is damped within this sublayer through low-Reynolds number modelling. Two models are evaluated in detail (the model proposed by Henkes and Hoogendoorn for the EUROTHERM/ERCOFTAC workshop organised in 1992 and the low-Reynolds number model developed by Abrous) and one model is compared for one point (the low-Reynolds number model proposed by Chien). An evaluation of these models is first perfonned. The average heat transfer rate, the maximum vertical velocity, the vertical thermal stratification at cavity center computed with the Henkes and Hoogendoorn model and the Abrous model highlight different behavior of these models, especially in the range of the transition Rayleigh number. A computation performed with all models tested for a Rayleigh number of 1010 stresses these differences. Numerical results obtained with the Henkes and Hoogendoorn model and the Abrous model for a Rayleigh number of l.7xI09 are next compared with experimental results obtained in an air filled cavity ( 1mx 1m vertical section). Three different simulations have been carried out considering adiabatic or perfectly conductive horizontal walls. Even if the heat losses through the cavity walls are extremely small, the comparison of velocity and temperature measurements with numerical simulation shows the influence of the vertical gradient of temperature existing in the experimental cavity. A good agreement between experimental and numerical results is shown for the Abrous model but the Henkes model overestimates the diffusion process as predicted in the former part of this study.