A Numerical Prediction of the Turbulence Parameters in Two-Dimensional Ventilated Rooms

Abstract

Turbulent flow in two-dimensional ventilated room has been numericallysimulated in the present research. A modified form of Wilcox's two-equation LRNk-w model is proposed for predicting internal turbulent ventilation flows. Themodifications include adding a turbulent cross-diffusion term in the w-equation,and re-establishing the closure constants and damping functions, with theapplication of the wall-function method. The turbulent cross-diffusion for specificrate, w, is modeled with two parts: a second-order diffusion term and a first-ordercross-diffusion term.The air was used as the working fluid, and the length of ventilation enclosure (9m), and height of ventilation enclosure (3 m). The study was made for Reynoldsnumber values of (Re=7.5´103).A finite volume method is used with a staggered grid arrangement. Thecontinuity, momentum and turbulence model equations are solved with hybridmethod by using SIMPLE algorithm. A computer program in FORTRAN (90) wasdeveloped to carry on the numerical solution. The Computational algorithm iscapable of calculating the hydrodynamic and turbulence properties such as thevelocity, and turbulent kinetic energy, specific dissipation rate (w), turbulentReynolds stress, and terms of convection, production, diffusion, destruction,turbulent cross-diffusion and square root mean of fluctuating velocity. The resultsshowed the peak value of velocity near the wall jet region and negative value ofvelocity near the bottom region (floor region) i.e. recirculating zone. Themaximum value of turbulent kinetic energy near wall jet region in the firsthorizontal section of ventilation enclosure, and the profile become flattened in thesecond section of ventilation enclosure room. The same behavior in the turbulentReynolds stress distribution because depending on velocity in his calculations. Thesame behavior between production term and destruction term but the values ofproduction term is positive and the value of destruction term is negative. Thedistribution approximately symmetry.The numerical results were compared with other previous theoretical results.The agreement was good, confirming the reliability of the proposed mathematicalmodel and computational algorithm in investigating the performance of turbulencemodel in numerical simulation of turbulent ventilation flows.