Discretization Error Estimation in Subsonic, Transonic and Supersonic Flows of an Inviscid Fluid Over a Bump

This paper presents a solution verification exercise for the simulation of subsonic, transonic and supersonic flows of an inviscid fluid over a circular arc (bump). Numerical simulations are performed with a pressure-based, single-phase compressible flow solver. Sets of geometrically similar grids covering a wide range of refinement ratios have been generated. The goal of these grids is twofold: obtain a reference solution from power series expansion fits applied to the finest grids; check the numerical uncertainties obtained from coarse grids that do not guarantee monotonic convergence of the quantities of interest. The results show that even with very fine grids it is not straightforward to define a reference solution from power series expansions. The level of discretization errors required to obtain reliable reference solutions implies iterative errors reduced to machine accuracy, which may be extremely time consuming even in two-dimensional inviscid flows. Quantitative assessment of the estimated uncertainties for coarse grids depends on the selected reference solution.

A Simple and Robust Shock-Capturing Approach for Discontinuous Galerkin Discretizations

The discontinuous Galerkin (DG) method has become popular in Computational Fluid Dynamics mainly due to its ability to achieve high-order solution accuracy on arbitrary grids, its high arithmetic intensity (measured as the ratio of the number of floating point operations to memory references), and the use of a local stencil that makes scalable parallel solutions possible. Despite its advantages, several difficulties hinder widespread use of the DG method, especially in industrial applications. One of the major challenges remaining is the capturing of discontinuities in a robust and accurate way. In our previous work, we have proposed a simple shock detector to identify discontinuities within a flow solution. The detector only utilizes local information to sense a shock/discontinuity ensuring that one of the key advantages of DG methods, their data locality, is not lost in transonic and supersonic flows. In this work, we reexamine the shock detector capabilities to distinguish between smooth and discontinuous solutions. Furthermore, we optimize the functional relationships between the shock detector and the filter strength, and present it in detail for others to use. By utilizing the shock detector and the corresponding filtering-strength relationships, one can robustly and accurately capture discontinuities ranging from very weak to strong shocks. Our method is demonstrated in a number of two-dimensional canonical examples.

Quantitative Visualisation of Compressible Flows

The paper demonstrates the feasibility of quantitative flow visualisation methods for investigation of transonic and supersonic flows. Two methods and their application for retrieving compressible flow field properties has been described: Background Oriented Schlieren (BOS) and Particle Image Velocimetry (PIV). Recently introduced BOS technique extends the capabilities of classical Schlieren technique by use of digital image processing and allow to measure density gradients field. In the presented paper a review of applications of BOS technique has been presented. The PIV is well established technique for whole field velocity measurements. This paper presents application of PIV for determination of the shock wave position above airfoil in transonic flow regime. The study showed that application of quantitative flow visualisation techniques allows to gain new insights on the complex phenomenon of supersonic and transonic flow over airfoils like shock-boundary layer interaction and shock induced flow separation.

Transonic and Supersonic Flows Past a Rectangular Cavity on Curved Wall

Investigations into cavity flows have been conducted for noise/vibration problem created in cavity system. The cavity system has been applied in engineering devices during rapid development of aerospace industry. Cavity on a curved wall has been seldom studied to the author’s best of knowledge. In the present study, the effects of channel shape on the cavity flow field on transonic and supersonic flow is investigated numerically. Time-dependent cavity flow characteristics with oscillating features were examined by using two-dimensional, mass-averaged Navier–Stokes computation based on a finite volume scheme. The results show that pressure loading on the cavity floor is observed to increase with increase in channel curvature for concave channels and decrease for convex channels. Drag in the flow channel increased as channel curvature increased. Unsteady flow characteristics are observed to be more dependent on channel curvature at supersonic free stream velocities.