Comparison of a Singularity- and an Inverse Design Method for Axial Flow Fans Based on Numerical Simulations

In this contribution two different design methods for axial flow profiles are presented. A direct method based on a singularity method (SDM) is compared with an inverse design method (IDM). For the application of the SDM a profile is used with a circular arc camber line and a thickness distribution of bisuper-ellipses. The stagger angle is adjusted in such a way that the turning of the flow on the cross section is realized. For the adjustment of the stagger angle of the cross section the fast working SDM is applied. The stagger angle is varied until the corresponding deflection angle calculated by the SDM is reached. The IDM consists of an inverse boundary layer- and an inverse potential theory method. Along the suction side the shape factor of the boundary layer is prescribed conveniently for the laminar and turbulent part. The velocity distribution at the outer edge of the boundary is calculated by an inverse boundary layer method. On the pressure side the velocity distribution is chosen in such a way that a corresponding circulation is realized for turning the flow. Finally, the whole geometry of the cascade is calculated by the inverse potential theory method. The examination of one cross section is done numerically using the commercial RANS Solver ANSYS CFX. Low Reynolds number of approximately 4.25 × 105 and the transition from laminar to turbulent are taken into account by the transition SST model.

Indentation of a Transversely Isotropic Thermoporoelastic Half-Space by a Rigid Circular Cylindrical Punch

Exact solutions to the three-dimensional (3D) contact problem of a rigid flat-ended circular cylindrical indenter punching onto a transversely isotropic thermoporoelastic half-space are presented. The couplings among the elastic, hydrostatic, and thermal fields are considered, and two different sets of boundary conditions are formulated for two different cases. We use a concise general solution to represent all the field variables in terms of potential functions and transform the original problem to the one that is mathematically expressed by integral (or integro-differential) equations. The potential theory method is extended and applied to exactly solve these integral equations. As a consequence, all the physical quantities of the coupling fields are derived analytically. To validate the analytical solutions, we also simulate the contact behavior by using the finite element method (FEM). An excellent agreement between the analytical predictions and the numerical simulations is obtained. Further attention is also paid to the discussion on the obtained results. The present solutions can be used as a theoretical reference when practically applying microscale image formation techniques such as thermal scanning probe microscopy (SPM) and electrochemical strain microscopy (ESM).

Spectral relationships of the integral equation with logarithmic kernel in some different domains

In this work, the Fredholm integral equation (FIE) with logarithmic kernel is investigated from the contact problem in the plane theory of elasticity. Then, using potential theory method (PTM), the spectral relationships (SRs) of this integral equation are obtained in some different domains of the contact. Many special cases and new SRs are established and discussed from this work.

The Elasto-Electric Field for a Rigid Conical Punch on a Transversely Isotropic Piezoelectric Half-Space

This paper exactly analyzes the problem of a rigid conical punch indenting a transversely isotropic piezoelectric half-space. The potential theory method is employed and generalized to include the piezoelectric effect. By using the previous results of pure elasticity, exact solution is derived. It is found that all the elastoelectric variables are expressed in terms of elementary functions. Numerical results are finally performed.