Sensor Development

To identify adequate sensor parameters for aerodynamic problems, simple internal flows at variable pressure gradient were investigated. Especially the experimental data of Driver and Johnston [5] was used. In the experiment, an axial incompress­ible flow over a cylinder is subjected to a variable pressure gradient. It is known that there is a consistent correlation between pressure gradient and local maximum of main Reynolds stress tensor component. The quality of the prediction of the skin friction coefficient and (u’v’)max highly depends on the RANS-turbulence model that is used for that kind of flow. Upstream of the boundary layer separation point the local quantities Cf = Tw/ (0.5pu^) , cp = pw/ (0.5pu^) and (u’v’)max deviate from the experimental findings, because the wall bounded boundary layer is in a non-equilibrium state [5]. Turbulence models such as algebraic, one – and two equa­tion models do not account for such type of boundary layer flow since for instance turbulent production and dissipation are no longer in the same order of magnitude. The thorough investigation of the flow field yielded the main influence parameters of the sensor; the Clauser-parameter /3 = 5i/rw the wall shear stress coefficient Cf, and the local maximum of the main component of the Reynolds shear stress (u’v’)max. Other parameters such as turbulent production and dissipation could not be used separately because they were not applicable for all kinds of turbulence mod­els. The value ф of the sensor is computed by applying the following summation:

with

 

Sensor Development

{u’v’)

 

7і = Пд—J8, Pcrit

 

T3 — Y3V

 

(2)

 

u

 

where T1, T2 and T3 depend on Cf, в and (u’v1) and their user defined critical values (Cf, crit and ecrit). The values of the prefactor yi, that contains reference values being extracted at a zero pressure gradient location in the flow domain, determine the priority of each term in Eq. 1. The calibration of the sensor is done via critical values where the RANS solution is no longer expected to yield reliable solutions. The sensor in this form should not be applied to flows with highly three-dimensional boundary layers or strong vortex interactions. An example configuration for three different flow cases is given in Tab. 1.

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