Experimental Study of the Constitutive Equation for an Axisymmetric Complex Turbulent Flow

Nonlinear constitutive equations have been proposed to overcome the limitations of linear eddy-viscosity models to describe complex turbulent flows. These new equations have been mainly indirectly compared to experimental data, through the outputs of numerical models. It is proposed in this paper to directly check the constitutive equation, using a projection of the stress tensor onto a tensor basis. The test case chosen is a complex axisymmetric flow generated by a double annular burner. Measurements have been taken on a fine grid, enabling the local estimate of the stress and strain tensors. A map of the Prandtl mixing-length is then given, together with the experimental evaluation of several invariants of the flow. The nonlinear constitutive equation is then tested using a 4 terms development. The angles of the stress tensor with the terms of the tensor basis are plotted, indicating which direction is predominant for each region of the flow. The different invariants are finally used to experimentally estimate the dissipation rate.