Sensor Validation

Three different test cases for sensor calibration are considered in detail in the follow­ing sections showing the influence of the user defined critical values on the sensor value ф. The configuration of these simulations is given in Tab. 2.

In Fig. 1 the application of the sensor on a flow case, where a shock wave im­pinges on a compressible turbulent boundary layer (SWBLI) causing a local flow separation, is presented. The Spalart-Allmaras turbulence model [23] (referred to as ’S-A’) was applied for this simulation. Regardless the computational configur­ation, the sensor value ф exceeds 1 where the flow is separated. Downstream of the separation the boundary layer returns to an equilibrium state. Depending on the user defined critical Clauser parameter the suggested corresponding LES domain is smaller (for ва-и=8) or larger (for ва-и = 2). In section 3, this particular case is regarded thoroughly using RANS, LES and zonal RANS-LES computations.

Fig. 2 presents the resulting sensor values ф for the upper side of the DRA23032- profile for two different time steps. The Baldwin-Lomax turbulence model [1] (re­ferred to as ’B-L’) was applied for this case. The sensor value at time step t0 exceeds the allowed limit of 1 at 0.55 c where the shock is located. However, the flow does not separate before passing 0.65 c (not shown here). The high pressure gradient

and the rapid decline of Cf lead to an increase of ф. Downstream of the shock posi­tion the sensor value ф does not fall below 1 for more than several percent chord due to the reason that the boundary layer is locally separated and/or in a non-equilibrium state. The skin friction coefficient and Clauser parameter are the major contributors to the sensor value ф. At t0 the shock position is located further upstream which is in fact the most upstream location of the shock. This shows that the size of the inten­ded LES domain should be evaluated over a time span of several shock oscillations. This case is also thoroughly investigated with in section 3.

Figure 3 shows the results of the sensor application on the case of a subsonic profile at high angles of attack [4] (see Tab. 2 for two different values of Cf, crit). The turbulence model of Spalart and Allmaras was used for this case. Due to a laminar separation bubble at about 0.12 c the sensor value ф is higher than 1 up to 0.20 c. For a user defined critical Cf, crit of 1-10~4 the sensor predicts the end of the confidence domain at about 0.75 c which is located upstream of the experimentally determined separation point of 0.85 c. For cf, crt = 5-10~4 the sensor value ф exceeds the value 1 at about 0.60 c, thus the proposed LES domain is larger compared to the case using the lower cf, crit value. This is due to the more or less equal contribution of cf, в and Reynolds shear stress gradient V(u’v’) to the sensor value ф (see Eq. 1). This case was also extensively investigated by Celic and Hirschel [4] where the results agree with the present RANS simulation. The presented RANS simulation indicates that all the investigated turbulence models (algebraic, one, two-equation models and RSM) show an unsatisfying behavior from 0.7 c to the trailing edge due to the steep decline of cf and the beginning increase of (u’v’).

These three examples demonstrate that the sensor provides a comprehensible interpretation about the confidence domain of RANS solutions for different aero­dynamic flow configurations, i. e., various free stream Mach numbers and Reynolds numbers. Most shock boundary-layer interaction problems are transient problems with a time dependent behavior of i. a. cf, в, and (u’v’). As shown in the transonic flow case, the extreme positions of the critical sensor values ф at the upper side of the airfoil are used to span the flow field where the confidence in the RANS solution is low.