analysis of influence of the thermal dependence of air thermophysical properties on the accuracy of simulation of heat transfer in a turbulent flow in case of applying different methods of averaging navier-stokes equations

There is theoretically investigated the influence of thermal dependence of air thermophysical properties on accuracy of heat transfer problems solution in a turbulent flow when using different methods of averaging the Navier-Stokes equations.

There is analyzed the practicability of using particular method of averaging the NavierStokes equations when it’s necessary to clarify the solution of heat transfer problem taking into account the variability of air thermophysical properties.

It’s shown that Reynolds and Favre averaging (the most common methods of averaging the Navier-Stokes equations) are not effective in this case because these methods inaccurately describe behavior of large scale turbulent structures which strongly depends on geometry of particular flow. Thus it’s necessary to use more universal methods of turbulent flow simulation which are not based on averaging of all turbulent scales.

In the article it’s shown that instead of Reynold and Favre averaging it’s possible to use large eddy simulation whereby turbulent structures are divided into small-scale and large-scale ones with subsequent modelling of small-scale ones only. But this approach leads to the necessarity of increasing the computational power by 2-3 orders.

For different methods of averaging the form of additional terms of averaged Navier-Stokes equations in case of accounting pulsation of thermophysical properties of the air is obtained.

On the example of a submerged heated air jet the errors (which occur when neglecting the thermal dependence of air thermophysical properties on averaged flow temperature) in determination of convectional and conductive components of heat flux and viscous stresses are evaluated. It’s shown that the greatest increase of solution accuracy can be obtained in case of the flows with high temperature gradients.

Finally using infinite Teylor series it’s found that underestimation of convective and conductive components of heat flux and viscous stresses can reach 3,7%, 31,3% and 32%, respectively.