# Two-Dimensional Prediction of Unsteady Turbulent Flow around a Square Cylinder Confined in a Channel

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## Abstract

This paper concerns with the application of the linear [1] and non-linear [2] low-Reynolds-number k − eddy-viscosity models in prediction of unsteady turbulent flow around a square cylinder confined in a channel, see figure 1. The Reynolds number based on the bulk velocity and obstacle side is Re = 2.2~104 . The present numerical results have been obtained using a finite-volume code which solves the governing equations in a vertical plane located at the lateral mid-point of the channel. The pressure field is obtained with the SIMPLE algorithm. A bounded version of the third-order QUICK scheme is used for the convective terms. As expected, comparisons of the numerical results with the experimental data of Lyn et al. [3], shown in Figure 2, indicate that the steady solution of the governing equations using the linear k − does not lead to correct flow field predictions in the wake region downstream of the square cylinder. Consequently, the time derivatives of dependent variables are included in the transport equations and are discretized using the second-order Crank-Nicolson scheme. The unsteady computations using the linear and nonlinear k − models significantly improve the velocity field predictions, see figures 2 and 3. As can be seen in figure 4, the linear k − model seriously underestimates the measured turbulence levels. Although the application of the non-linear k − model improves the turbulence field predictions, more refined turbulence models are needed for more accurate predictions. The predicted value for Strouhal number is 0.126 and 0.115 using the linear and non-linear turbulence k − models respectively which are in good agreement with the measured value of 0.132. The proposed paper would present the relevant equations and numerical methods involved and would also present a more comprehensive range of comparisons.

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