Application of the PITM Method Using Inlet Synthetic Turbulence Generation for the Simulation of the Turbulent Flow in a Small Axisymmetric Contraction

We investigate the turbulence modeling of second moment closure used both in RANS and PITM methodologies from a fundamental point of view and its capacity to predict the flow in a low turbulence wind tunnel of small axisymmetric contraction designed by Uberoi and Wallis. This flow presents a complex phenomenon in physics of fluid turbulence. The anisotropy ratio of the turbulent stresses τ ₁₁/τ ₂₂ initially close to 1.4 returns to unity through the contraction, but surprisingly, this ratio gradually increases to its pre-contraction value in the uniform section downstream the contraction. This point constitutes the interesting paradox of the Uberoi and Wallis experiment. We perform numerical simulations of the turbulent flow in this wind tunnel using both a Reynolds stress model developed in RANS modeling and a subfilter scale stress model derived from the partially integrated transport modeling method. With the aim of reproducing the experimental grid turbulence resulting from the effects of the square-mesh biplane grid on the uniform wind tunnel stream, we develop a new analytical spectral method of generation of pseudo-random velocity fields in a cubic box. These velocity fields are then introduced in the channel using a matching numerical technique. Both RANS and PITM simulations are performed on several meshes to study the effects of the contraction on the mean velocity and turbulence. As a result, it is found that the RANS computation using the Reynolds stress model fails to reproduce the increase of anisotropy in the centerline of the channel after passing the contraction. In the contrary, the PITM simulation predicts fairly well this turbulent flow according to the experimental data, and especially, the “return to anisotropy” in the straight section of the channel downstream the contraction. This work shows that the PITM method used in conjunction with an analytical synthetic turbulence generation as inflow is well suited for simulating this flow, while allowing a drastic reduction of the computational resources.