Swirling Strength Based Subgrid Scale Model And Its Application In Large Eddy Simulation Of Incompressible Flows

While the performance of Large Eddy Simulation(LES) is better than Reynolds aver-aged modeling(RANS) in unsteady flow for high fidelity and more details, more calculation time is needed. With the increase of powerful computer, LES shows much potential in en-gineering applications. The main idea of LES is filtering the Navier-Stokes(NS) equations with a low-pass filter, so that the large scales are calculated directly, with the smaller sub-grid scale modeled. Many subgrid models have been proposed with different characteristics, but none provide a good transition to Direct Numerical Simulation(DNS). To overcome this discrepancy, a model based on swirling strength with eddy viscosity hypothesis is presented, with vanishing local subgrid viscosity when the local swirl strength becomes zero. This new model is tested numerically for incompressible turbulent flow past a square cylinder at differ-ent Reynolds number and incompressible natural convection in a differential heated square cavity, with an improved4th order algorithm.The LES results of turbulent flow past square cylinder at low and high Reynolds number with the subgrid model based on swirling strength show that,(1) At low Reynolds number(Re∈[2.5×103,10×103]) and high Reynolds number(Re∈[1.25×105,3.5×105]), Strouhal number have no influence on Reynolds number, and the averaged drag coefficient CD have little difference in all cases, the averaged lift coefficient CL is about zero, both independent of Reynolds number. However, the averaged drag coefficient CD increase with the Reynolds number when Re∈[1.0×103,2.5×103]. The results also indicate that no critical drag loose exist in the square cylinder cases as that in the cycle cylinder.(2) The profiles of averaged and RMS value of normalized velocity are consistent with the experiment, and have little influence with the Reynolds number.(3) Both averaged and RMS value of νsr increase with Reynolds number and the maxi-mum values always appear in two regions of the cylinder downstream, where vortex interaction is more intense.(4) Contours of Komogorov microscale show that dissipation of turbulent kinetic energy is more intense near the cylinder walls. The instantaneous factor of swirling strength intermittency(FSI) exhibits some laminated structure associated with vortex shedding in addition to relatively small vortex structure in the cylinder wake.(5) The difference of face averaged Nusselt number between top and bottom of the square cylinder indicates that the t-z averaged flow field is asymmetrical to the y=0.5line. Large eddy simulation of natural convection in a differential heated square cavity indi-cates that,(1) Flow loops near the wall, and induced more vortex with reverse direction between the loop and the core of cavity, and some smaller and more complex eddy are generated at corner of left top and right bottom, as can been seen in the profiles of temperature, velocity and vorticity at different locations.(2) When Ra=1.58×109, the profiles of velocity near the left hot wall on the horizontal centerline in the mid plane(z=0) agree well with experiment data at the inner region of the wall and the core, while the maximum velocity slightly higher than that in the experiment, and the profiles agree well also on the vertical centerline. Meanwhile, the temperature on the horizontal centerline is underestimate and shows little difference on the vertical centerline, but both the profiles of velocity and temperature have influence with the Rayleigh number.(3) The RMS value, v’and θ’, agree well with the experiment at Ra=1.58×109, but u’ is obviously underpredicted, which may evidently cause the under-prediction of turbulent shear stress near the heating wall. The fluctuation of main velocity in the wall loops is enhanced with the increasement of Rayleigh number, while the velocity perpendicular to the wall shows little diffence, and the fluctuation of temperature is also suppressed.(4) Face averaged Nusselt numbers have a relative discrepancy of about8%with the Fusegi theory, when Ra=1.58×109. The Nusselt number at the top wall increases along x direction but decreases at the bottom wall, and increases along y direction at left hot wall, decreases along y direction at right cold wall.In conclusion, the comparison of LES results with the existing experimental data in the cases of turbulent flow past square cylinder at low and high Reynolds numbers and natural convection in the cavity shows that the subgrid model based on swirling strength and the improved algorithm are effective.