Andreas Haselbacher

Accurate and efficient discretization of Navier-Stokes equations on mixed grids

The discretization of Navier-Stokes equations on mixed unstructured grids is discussed. Because mixed grids consist of different cell types, the question arises as to how the discretization should treat these cell types in order to result in a stable and accurate solution method. This issue is addressed in relation to the discretization of inviscid and viscous fluxes. The discretization of the inviscid fluxes is carried out with both a centered and an upwind scheme. For the centered scheme, problems exist on mixed grids with the damping properties of the fourth-difference operator. The problems with the fourth-difference operator are investigated for two stencils by both truncation error and Fourier analysis. It is shown that one form exhibits superior damping for high frequencies, which is corroborated using numerical experiments. For the upwind scheme, a commonly used gradient-reconstruction method based on the Green-Gauss theorem does not show satisfactory behavior on mixed grids. Another gradient reconstruction method based on a Taylor series expansion previously derived in two dimensions is extended to three dimensions. This method is more accurate on mixed grids but requires more storage

An efficient and robust particle-localization algorithm for unstructured grids

An efficient and robust particle-localization algorithm for unstructured grids is presented. Given a particle position and the cell containing that position, the algorithm determines the cell which contains a nearby position. The algorithm is based on tracking a particle along its trajectory by computing the intersections of the trajectory and the cell faces. Compared to previously published particle-localization algorithms, the new algorithm has several advantages. First, it can be applied to grids consisting of arbitrary polyhedral cells. Second, the algorithm is not limited to small particle displacements. Third, the interaction of particles with boundaries is dealt with correctly and naturally. Fourth, the algorithm is more efficient than other published algorithms. A modified version of the present algorithm is also presented which can detect inconsistencies and take appropriate corrective action. With these modifications, the computational cost becomes comparable to other published algorithms which cannot detect inconsistencies without resorting to fall-back algorithms such as exhaustive or Octree search.

On the unsteady inviscid force on cylinders and spheres in subcritical compressible flow

The unsteady inviscid force on cylinders and spheres in subcritical compressible flow is investigated. In the limit of incompressible flow, the unsteady inviscid force on a cylinder or sphere is the so-called added-mass force that is proportional to the product of the mass displaced by the body and the instantaneous acceleration. In compressible flow, the finite acoustic propagation speed means that the unsteady inviscid force arising from an instantaneously applied constant acceleration develops gradually and reaches steady values only for non-dimensional times c∞t/R≳10, where c∞ is the freestream speed of sound and R is the radius of the cylinder or sphere. In this limit, an effective added-mass coefficient may be defined. The main conclusion of our study is that the freestream Mach number has a pronounced effect on both the peak value of the unsteady force and the effective added-mass coefficient. At a freestream Mach number of 0.5, the effective added-mass coefficient is about twice as large as the incompressible value for the sphere. Coupled with an impulsive acceleration, the unsteady inviscid force in compressible flow can be more than four times larger than that predicted from incompressible theory. Furthermore, the effect of the ratio of specific heats on the unsteady force becomes more pronounced as the Mach number increases.

A massively parallel multi-block hybrid compact-WENO scheme for compressible flows

A new multi-block hybrid compact-WENO finite-difference method for the massively parallel computation of compressible flows is presented. In contrast to earlier methods, our approach breaks the global dependence of compact methods by using explicit finite-difference methods at block interfaces and is fully conservative. The resulting method is fifth- and sixth-order accurate for the convective and diffusive fluxes, respectively. The impact of the explicit interface treatment on the stability and accuracy of the multi-block method is quantified for the advection and diffusion equations. Numerical errors increase slightly as the number of blocks is increased. It is also found that the maximum allowable time steps increase with the number of blocks. The method demonstrates excellent scalability on up to 1264 processors.

Shock interaction with a deformable particle: Direct numerical simulation and point-particle modeling

The interaction of shock waves with deformable particles is an important fundamental problem. In some applications, e.g., the detonation of explosives loaded with metal particles, the pressure behind the shock wave can be significantly larger than the yield strength of the particle material. This means that particles can deform severely during their interaction with the shock wave. The experimental and theoretical studies of shock interaction with deformable particles (SIDP) are extremely challenging because of its highly transient nature. As a result, no accurate model exists yet that can be used in simulations. The objective of this paper is to develop a simple point-particle model that accurately captures the unsteady force and heat-transfer in SIDP. In the development of this model, we build on earlier models by Ling et al. (Int. J. Multiphase Flow 37, 1026–1044 (2011)) for the unsteady force and heat-transfer contributions for rigid particles. Insights gained from direct numerical simulations (DNS) guide the extension of these models to deforming particles. Results obtained with the extended model for the interaction of a deforming particle with a shock wave and a Chapman-Jouguet detonation wave compare well with DNS results and therefore offer significant improvements over standard models.

Open-Ended Shock Tube Flows: Influence of Pressure Ratio and Diaphragm Position

The influence of the pressure ratio and the diaphragm location on the flow from open-ended shock tubes is investigated. In contrast to previous studies, in which attention was focused on the discharge of the shock wave from the shock tube, we consider also the influence of the contact discontinuity and the expansion fan. It is found that if the pressure ratio is large enough to lead to supersonic flow behind the contact discontinuity, the flow at the open end relaxes from the conditions behind the contact discontinuity to sonic conditions once the tail of the expansion fan arrives at the open end. Theory indicates that the time scale over which the flow relaxes to sonic conditions is nearly independent of the initial Mach number. Also, the time scale is much longer than that required by the acceleration of subsonic conditions behind the contact discontinuity to sonic conditions. The relaxation process is shown to influence the evolution of the Mach-disk shock, the barrel shock, and the reflected shock wave in an underexpanded jet.

Theoretically based optimal large-eddy simulation

Large eddy simulation (LES), in which the large scales of turbulence are simulated while the effects of the small scales are modeled, is an attractive approach for predicting the behavior of turbulent flows. However, there are a number of modeling and formulation challenges that need to be addressed for LES to become a robust and reliable engineering analysis tool. Optimal LES is a LES modeling approach developed to address these challenges. It requires multipoint correlation data as input to the modeling, and to date these data have been obtained from direct numerical simulations (DNSs). If optimal LES is to be generally useful, this need for DNS statistical data must be overcome. In this paper, it is shown that the Kolmogorov inertial range theory, along with an assumption of small-scale isotropy, the application of the quasinormal approximation and a mild modeling assumption regarding the three-point third-order correlation are sufficient to determine all the correlation data required for optimal LES m...

Equation of motion for a drop or bubble in viscous compressible flows

The problem of unsteady motion of a spherical bubble or drop is analyzed in the limit of vanishing Mach and Reynolds numbers. Linearized viscous compressible Navier-Stokes equations are solved inside and outside of the spherical bubble/drop and an expression of the transient force is first obtained in the Laplace domain and then transformed to the time domain. The total force is separated into the quasi-steady, the inviscid unsteady, and the viscous unsteady contributions. The new force expression reduces to known results in the limits of a drop in an incompressible flow or a rigid particle in a compressible flow. We observe that in all compressible flow cases, the viscous unsteady kernel shows a 1/t decay at sufficiently short times. This is in contrast to the behavior in an incompressible flow where the viscous unsteady kernel on the bubble reaches a constant value at short times.

A numerical source of small-scale number-density fluctuations in Eulerian-Lagrangian simulations of multiphase flows

Eulerian-Lagrangian simulations of multiphase flow are known to suffer from two errors that can introduce small-scale fluctuations in the number-density of the dispersed phase. These errors can be reduced by increasing the number of particles in the simulation. Here, we present results to demonstrate that a third error exists that can also generate small-scale number-density fluctuations. In contrast to the two known errors, this error cannot be lowered by increasing the number of particles. Analysis shows that this error is caused by spatial variation at the subgrid scale in the interpolation error of the fluid velocity to the particle location. If the particle velocity divergence is zero, the particle concentration error remains at the subgrid scale. However, if particles preferentially accumulate either due to their inertia or due to divergence of the underlying fluid-velocity field, this error manifests as number-density fluctuations on the grid scale. The only mechanism of reducing these errors is through higher-order accurate interpolation. By studying two model problems, estimates for the errors are derived. These estimates are shown to be quite accurate for simulations of shock and expansion waves interacting with particles.

Super-Resonances in AEDC Altitude Test Cells

We report on simulation and analysis efforts to understand and predict the high amplitude aeroacoustic resonances (& 160dB) that have been observed in Arnold Engineering Development Center (AEDC) jet engine test cells. The basic configuration of these cells is a jet exhausting through a cylindrical duct. We summarize progress in developing analytical tools to diagnose the energetics of the resonating acoustic modes, direct numerical simulations to investigate the phenomenology of the resonance in model geometries, and full-scale simulation tools to anticipate resonances.