Calculation of the Pressure Field for Turbulent Flow around a Surface-Mounted Cube Using the SIMPLE Algorithm and PIV Data

Abstract

The calculation of the pressure field on and around solid bodies exposed to external flow is of paramount importance to a number of engineering applications. However, conventional pressure measurement techniques are inherently linked to problems principally caused by their point-wise and/or intrusive nature. In the present paper, we attempt to calculate a time-averaged two-dimensional pressure field by integrating PIV (particle image velocimetry) velocity measurements into a CFD code and modifying them by the respective correction step of the SIMPLE algorithm. Boundary conditions are applied from the PIV data as a three-layer area of constant velocities adjacent to the boundaries. A novel characteristic of the approach is the straightforward inclusion of the Reynolds stresses into the source terms of the momentum equations, calculated directly from the PIV statistics. The methodology is applied to three regions of the symmetry plane parallel to the main boundary layer flow past a surface-mounted cube. In spite of findings of deviations from the planar 2D flow assumption, the derived pressure fields and the adjusted velocity fields are found to be reliable, while the intrinsic turbulent nature of the flow is considered without modelling the Reynolds stresses.

Numerical calculation of the turbulent flow past a surface mounted cube with assimilation of PIV data

“…Here, the algorithm will be applied for calculating the pressure field and correcting the velocity field. The OpenFOAM toolbox [40][41][42] formulation is used, which is slightly different than the one used in [39] and consists of a momentum predictor, shown in (3), that determines a velocity field u * which satisfies the momentum equation for a given pressure field p k , at the k + 1−th iteration:…”

“…Alternatively, to the SIMPLE based method [39], a Poisson equation may be solved to calculate the pressure from uncorrected PIV data [24]. The pressure Poisson equation is devised by taking the divergence of the momentum equation for the PIV velocity field and assuming that the PIV data conform to the continuity equation:…”

“…This approach ensures that only interpolations are performed, avoiding extrapolating the experimental data. Also, contrary to [39] it ensures that the PIV planes and CFD grids have precisely the same dimensions and boundaries. In figure 1, the cell nodes where the PIV data are known are colored in red, while the cell centers where the values are stored in OpenFOAM are colored in blue.…”

“…Similarly, in [38], two-dimensional PIV data were utilized to compute pressure fields for laminar, incompressible, steady, and unsteady flows. The use of two-dimensional PIV data to calculate pressure fields for turbulent, incompressible time-averaged flows was recently achieved using the Reynolds stresses from the PIV statistics and including them in the source terms of the RANS equations [39].…”

“…The method is similar to the previously mentioned applications of the SIMPLE method [37,38], but here it is applied to a turbulent flow with direct insertion of the Reynolds stresses in the equations, as they were measured by the PIV method rather than applying a turbulence model. The application is similar to that in [39], but here, a different code, SIMPLE algorithm variant and boundary conditions are applied. After the solver is verified based on experimental data [43,44], both nudging and Kalman filtering methods are applied.…”