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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A Comparative Study of Compressible Turbulent Flows Between Thermally and Calorically Perfect Gases

Pp. 243-264 (22)

Xiaoping Chen


In this chapter, direct numerical simulations (DNSs) of compressible turbulent flows for thermally perfect gas (TPG) and calorically perfect gas (CPG), including two wall temperature of 298.15K (low temperature condition) and 596.30K (high temperature condition), are performed to investigate the influence of a gas model on the turbulent statistics and flow structures. The results show that the influence of TPG is negligible and remarkable for low and high-temperature conditions, respectively. Many of the statistical characteristics used to express low-temperature conditions for CPG still can be applied to high-temperature conditions for TPG. The smaller the influence of the gas model on the mean and fluctuating velocity, the stronger the Reynolds analogy. The static temperature for TPG is smaller than that for CPG, whereas an inverse trend is found for turbulent and root square mean Mach numbers. Omega could capture both strong and weak vortices simultaneously for compressible flow, even TPG, which is difficult from Q. Compared to the results of CPG, the vortex structure becomes smaller, sharper and more chaotic considering TPG.


Calorically perfect gas, Compressible flow, Direct numerical simulation, Thermally perfect gas, Vortex structure.


National-Provincial Joint Engineering Laboratory for Fluid Transmission System Technology, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018, China