Current Developments in Mathematical Sciences

Current Developments in Mathematical Sciences

Volume: 2

Liutex-based and Other Mathematical, Computational and Experimental Methods for Turbulence Structure

The knowledge of quantitative turbulence mechanics relies heavily upon the definition of the concept of a vortex in mathematical terms. This reference work introduces the reader to Liutex, which is ...
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Direct Numerical Simulation of Incompressible Flow in a Channel with Rib Structures

Pp. 210-231 (22)

Ting Yu, Duo Wang, Heng Li and Hongyi Xu


This chapter applied the state-of-the-art flow simulation method, i.e. the Direct Numerical Simulation (DNS), and strongly coupled the DNS with the heat-transfer governing equation to solve the thermal turbulence in both 2-dimensional (2D) and 3- dimensional (3D) channels with the rib tabulator structures. An innovative approach was applied to the simulations. The surface roughness effects of the cooling vane were directly tackled by including the roughness geometry in the DNS and applying the immersedboundary method to handle the geometry complexities due to the roughness. Two inlet conditions, namely the uniform flow and full-developed turbulence, were applied at the inflow surface of the channel. Half height of the channel was used as the scale length. The Prandtl (Pr) number was set at Pr = 0.7. Five Reynolds (Re) number of 1000, 2500, 5000, 7500 and 10000 were calculated in the 2D cases and the Reynolds numbers of 2500 and 5000 were applied in 3D cases where a periodical condition was applied in the spanwise direction. Additionally, Reynolds number of 10000 was set in the case with roughened surface. The stream-wise velocity, turbulence intensity, and the Nusselt (Nu) number were analyzed. Results in the 2D and 3D cases presented a significant difference on flow structure. At the same time, with increasing Reynolds number, the length of recirculation zone and the enhancement of heat transfer showed a decreasing trend.


Direct Numerical Simulation, Heat Transfer, Rib Tabulator, Roughness, Rortex.


Aeronautics and Astronautics Department, Fudan University, Shanghai, PR China