Journal of Hydraulics

Journal of Hydraulics

The Effect of Nonlinear Form in Direct Numerical Simulation of Channel Flow Analysis

Document Type : Technical Note

Authors
E. Rajabi
M.R. Kavianpoor
10.30482/jhyd.2011.85507
Abstract
Analysis of turbulent plane channel flow is performed by direct numerical simulation. In this paper common forms of the nonlinear term are applied to solve Navier-Stokes equations by using pseudo spectral method. The Navier-Stokes equations are expanded with Chebychev and Fourier series in PS method and commonly used forms of the nonlinear terms υtot. ∇υtot are explained and applied, referred to as divergence, convection, skew-symmetric, rotational, alternating and linearized form. The results of channel flow analysis are presented due to those six forms of the nonlinear terms .The computational grids of 128×65×128 in computational domain of Ω=[0,4π]×[-1,1]×[0,2π] are used in the x, y and z directions, respectively. The friction Reynolds number for channel flow is set to be Reτ=175.
The comparison is made between turbulent quantities such as the turbulent statistics uu, vv,ww The results show that that the rotational and linearized forms are more appropriate than other schemes, especially than skew-symmetric form. But it must be noted that linearized form is not energy-conserving so it is not stable and applicable in all situations. Hence the choice of nonlinear term reduces to the rotational form in analysis of pseudo spectral method which satisfies robustness and accuracy and reduces the computational cost at about 62% (compared to other schemes). From practical point of view, different types of nonlinear term do affect in reduction of total running time at higher Reynolds number and greater domain in fluid flow, which provides decreased cost and time in direct numerical simulation of channel flow if final decision rests on economics.

  • Receive Date 23 March 2011