Entropy and vorticity corrections for transonic flows

Abstract

SUMMARYDifferent models for inviscid transonic flows are examined. The common assumptions that the flow is isentropic and irrotational are critically evaluated. Entropy and vorticity correction procedures for potential and stream function formulations are presented, together with the details of the treatment of shocks and wakes, and drag and lift calculations. The non-uniqueness problem of the potential formulation is studied using different artificial viscosity forms. Numerical results are compared with Euler solutions.

Time-linearised transonic computations including entropy, vorticity and shock wave motion effects

“…The shock-generated entropy and vorticity effects, similiar to those reported by Hafez and Lovell (3) , Whitlow et al (4) , Batina (5) and Dang and Chen (6) , are incorporated into the steady analysis, so that flowfields with embedded strong shock waves can be simulated accurately. Rotational effects become influential when strong shock waves exist in the flowfield, since vorticity is generated due to the entropy changes along the shock.…”

“…The wake boundary condition requires that the pressure be continuous across the wake surface, and since the pressure formula is now no longer containing just the isentropic term, the isentropic wake boundary condition must be modified to accommodate such changes. Hafez and Lovell (3) show that the changes due to vorticity approximately cancel the changes due to entropy, and consequently the isentropic pressure formula is still valid in the modified theory. As a result, the wake boundary condition of Fig.…”

“…In addition, a Mathematica package was developed to assist the grid-generation process and graphical postprocessing of the computed results. First modification is the inclusion of the shock-generated entropy and vorticity effects (Hafez and Lovell (3) , Whitlow et al (4) , Batina (5) and Dang and Chen (6) ) to enhance the capability of TranFlow2D in simulating flowfields with embedded strong shock waves. The second modification involves a procedure, which we have referred to as the shock jump correction procedure (Ly and Gear (2) ), that allows one to include the shock wave motion effects by correcting the solution values behind the shock wave, such that the time-linearised form of the shock jump condition will be satisfied.…”

Comparison of Euler and Modified Tsp Solutions for Unsteady Transonic Flow Calculations

“…Considerable progress has been made over the past few decades in developing methods for aeroelastic analysis in the flutter critical transonic speed range [1][2][3][4][5][6][7][8][9][10]. Much of this progress has been achieved by developing finite-difference computer codes for solving transonic small perturbation (TSP) potential equation, although significant efforts are currently underway at the higher equation levels as well.…”

Numerical simulations of transonic aerodynamic flows based on a hierarchical formulation

“…It includes potential ow as a special case, if entropy terms and the rotational component of the velocity are dropped. We can also include only the entropy corrections and ignore the vorticity, if the shock curvature is negligible [15,16]. The isentropic Euler equations can be also obtained if the pressure is calculated from the normal momentum equations and the rotational component of the velocity from the tangential momentum equation while the energy equation is replaced by the isentropic relation, which in turn, provides the density.…”