Experimental study of the constitutive equation for an axisymmetric complex turbulent flow

Nonlinear constitutive equations have been proposed to overcome the limitat ions of linear eddy-viscosity models to describe complex turbulent flows. T hese new equations have been mainly indirectly compared to experimental dat a, through the outputs of numerical models. A is proposed in this paper do directly check the constitutive equation using a projection of the stress t ensor onto a tensor basis. The test case chosen is a complex axisymmetric f low 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 experime ntal evaluation of several invariants of the flow. The nonlinear constituti ve equation is then tested using a 4 terms development. The angles of the s tress tensor with the terms of the tensor basis are plotted, indicating whi ch direction is predominant for each region of the flow. The different inva riants are finally used to experimentally estimate the dissipation rate.