Ioannis Nompelis

A parallel unstructured implicit solver for hypersonic reacting flow simulation

Publisher Summary The chapter focuses on two aspects of the solver, as well as the parallel performance of the hybrid implicit method. A new parallel implicit solver for the solution of the compressible Navier–Stokes equations with finite rate chemistry on unstructured finite volume meshes is presented in the chapter. The solver employs the data-parallel line relaxation (DPLR) method for implicit time integration along the lines of cells that are normal to the wall. A point-implicit method is used in the regions where surface-normal lines are not constructed. The new method combines the robustness and efficiency of the implicit DPLR method with the flexibility of using unstructured discretizations. The solver employs a low-dissipation pure-upwind numerical scheme based on the Steger-Warming split flux method, as well as a MUSCL-type scheme designed for unstructured discretizations. The DPLR method is superior to other parallel methods, such as matrix-based point-implicit methods designed for chemically reacting hypersonic flow simulations.

Effect of numerics on Navier-Stokes computations of hypersonic double-cone flows

A systematic study of the effects of the numerics on the simulation of a steady hypersonic flow past a sharp double cone is presented. Previous studies have shown that the double-cone flow is challenging to compute, making it useful for testing both numerical schemes and physical models. We focus on the numerical aspects only and show that the results are very sensitive to the numerical flux evaluation method and slope limiter used

Effect of Vibrational Nonequilibrium on Hypersonic Double-Cone Experiments

Recent numerical simulations of hypersonic double-cone experiments overpredict the heat-transfer rate to the model by about 20%. We present a systematic analysis of the experimental facility and the physical modeling to explainthisdiscrepancy.Nozzlee owe eldsimulationsareusedtoinvestigatetheeffectofvibrationalnonequilibrium in the test section. These simulations show that the vibrational modes of the nitrogen gas freeze near the nozzle throatconditions, resulting inanelevated vibrationaltemperatureinthetestsection. Thislowersthekineticenergy e ux, reducing the heat transfer to the model. The effect of slip boundary conditions is also studied, and it is shown that weak accommodation of vibrational energy at the surface further reduces the heat-transfer rate to the model. The combination of these two effects brings the predicted heat-transfer rate into agreement with the experiments. In addition, weak e ow nonuniformity in the test section is shown to slightly modify the predicted separation zone, further improving the agreement.

An improved potential energy surface and multi-temperature quasiclassical trajectory calculations of N2 + N2 dissociation reactions

Accurate modeling of high-temperature hypersonic flows in the atmosphere requires consideration of collision-induced dissociation of molecular species and energy transfer between the translational and internal modes of the gas molecules. Here, we describe a study of the N2 + N2⟶N2 + 2N and N2 + N2⟶4N nitrogen dissociation reactions using the quasiclassical trajectory (QCT) method. The simulations used a new potential energy surface for the N4 system; the surface is an improved version of one that was presented previously. In the QCT calculations, initial conditions were determined based on a two-temperature model that approximately separates the translational-rotational temperature from the vibrational temperature of the N2 diatoms. Five values from 8000 K to 30,000 K were considered for each of the two temperatures. Over 2.4 × 10(9) trajectories were calculated. We present results for ensemble-averaged dissociation rate constants as functions of the translational-rotational temperature T and the vibrational temperature T(v). The rate constant depends more strongly on T when T(v) is low, and it depends more strongly on T(v) when T is low. Quasibound reactant states contribute significantly to the rate constants, as do exchange processes at higher temperatures. We discuss two sets of runs in detail: an equilibrium test set in which T = T(v) and a nonequilibrium test set in which T(v) < T. In the equilibrium test set, high-v and moderately-low-j molecules contribute most significantly to the overall dissociation rate, and this state specificity becomes stronger as the temperature decreases. Dissociating trajectories tend to result in a major loss of vibrational energy and a minor loss of rotational energy. In the nonequilibrium test set, as T(v) decreases while T is fixed, higher-j molecules contribute more significantly to the dissociation rate, dissociating trajectories tend to result in a greater rotational energy loss, and the dissociation probabilitys dependence on v weakens. In this way, as T(v) decreases, rotational energy appears to compensate for the decline in average vibrational energy in promoting dissociation. In both the equilibrium and nonequilibrium test sets, in every case, the average total internal energy loss in the dissociating trajectories is between 10.2 and 11.0 eV, slightly larger than the equilibrium potential energy change of N2 dissociation.

Unstructured grid approaches for accurate aeroheating simulations

The use of tetrahedral, prismatic, and hybrid hexahedral-prismatic-tetrahedral grids for the accurate prediction of aerodynamic heating at hypersonic conditions is investigated. We find that tetrahedral grids introduce significant error in the vicinity of strong shock waves, which results in unacceptable aeroheating predictions. The source of this error is studied with an idealized model, and it is found that a large spurious component of post-shock velocity is generated by triangular and tetrahedral elements. This type error is much smaller and easier to control on quadrilateral or hexahedral grids. Thus, we are very skeptical about the utility of tetrahedral grids for accurate hypersonic aeroheating predictions. Several comparisons of heating predictions for a three-dimensional sphere are made, and it is found that the stagnation region results are very sensitive to the grid design. Based on this work and our experience, we advocate the use of unstructured hexahedral grids which increase the grid design space, reduce the element count for many geometries, and result in accurate aeroheating predictions.

CFD Validation for Hypersonic Flight: Hypersonic Double-Cone Flow Simulations

Abstract : At the 2001 AIAA Aerospace Sciences Meeting there was a blind comparison between computational simulations and experimental data for hypersonic double-cone and hollow cylinder-flare flows. This code validation exercise showed that in general there was good agreement between the continuum CFD simulations and experiments. Also, in general, there was good agreement between direct simulation Monte Carlo (DSMC) calculations and the experiments in regions of attached flow. However, in almost all of the computations, the heat transfer rate on the forebody of the cone was over-predicted by about 20%. The purpose of this paper is to report on our analysis of this difference. We perform CFD simulations of the hypersonic nozzle flow to assess the importance of vibrational nonequilibrium on the test conditions. We then recompute the flows using a new set of vibrational nonequilibrium conditions and consider the effects of a slip boundary condition at the model surface. Additionally, we analyze new heat transfer rate data on sharp and blunt 25-degree cones over a wider range of test conditions. This analysis appears to explain the discrepancy between the previous calculations and the experiments.

Navier-stokes predictions of hypersonic double-cone and cylinder-flare flow fields

The interaction between a shock wave and a separated region in a hypersonic flow is a very challenging problem for computational fluid dynamics. Recent calculations on double-cone and hollow-cylinderflare geometries have shown significant differences between computations and experiments. Therefore, experiments have been performed in the Large Energy National Shock (LENS) facility at the Calspan University at Buffalo Research Center (CUBRC) to provide a benchmark dataset at well calibrated hypersonic test conditions with fully laminar flow. These flows are test cases for the NATO Research and Technology Organization (RTO) Working Group 10 CFD code validation activities. In this paper, we discuss several parametric studies of these flows. We show that the experiments are not sensitive to small nosetip bluntness and slight model misalignment. We do not expect non-continuum effects or vibrational excitation to be significant in these flows. The calculations require grids of about a half million points, but more importantly, the results are very sensitive to the numerical flux evaluation method used. Finally, we present our results for two double-cone and hollow-cylinder with extended flare geometries for comparison with the experimental data.

Direct molecular simulation of nitrogen dissociation based on an ab initio potential energy surface

The direct molecular simulation (DMS) approach is used to predict the internal energy relaxation and dissociation dynamics of high-temperature nitrogen. An ab initio potential energy surface (PES) is used to calculate the dynamics of two interacting nitrogen molecules by providing forces between the four atoms. In the near-equilibrium limit, it is shown that DMS reproduces the results obtained from well-established quasiclassical trajectory (QCT) analysis, verifying the validity of the approach. DMS is used to predict the vibrational relaxation time constant for N2–N2 collisions and its temperature dependence, which are in close agreement with existing experiments and theory. Using both QCT and DMS with the same PES, we find that dissociation significantly depletes the upper vibrational energy levels. As a result, across a wide temperature range, the dissociation rate is found to be approximately 4–5 times lower compared to the rates computed using QCT with Boltzmann energy distributions. DMS calculations predict a quasi-steady-state distribution of rotational and vibrational energies in which the rate of depletion of high-energy states due to dissociation is balanced by their rate of repopulation due to collisional processes. The DMS approach simulates the evolution of internal energy distributions and their coupling to dissociation without the need to precompute rates or cross sections for all possible energy transitions. These benchmark results could be used to develop new computational fluid dynamics models for high-enthalpy flow applications.

Development of the US3D Code for Advanced Compressible and Reacting Flow Simulations

Aerothermodynamics and hypersonic flows involve complex multi-disciplinary physics, including finite-rate gas-phase kinetics, finite-rate internal energy relaxation, gas-surface interactions with finite-rate oxidation and sublimation, transition to turbulence, large-scale unsteadiness, shock-boundary layer interactions, fluid-structure interactions, and thermal protection system ablation and thermal response. Many of the flows have a large range of length and time scales, requiring large computational grids, implicit time integration, and large solution run times. The University of Minnesota / NASA US3D code was designed for the simulation of these complex, highly-coupled flows. It has many of the features of the well-established DPLR code, but uses unstructured grids and has many advanced numerical capabilities and physical models for multi-physics problems. The main capabilities of the code are described, the physical modeling approaches are discussed, the different types of numerical flux functions and time integration approaches are outlined, and the parallelization strategy is overviewed. Comparisons between US3D and the NASA DPLR code are presented, and several advanced simulations are presented to illustrate some of novel features of the code.

Particle and continuum method comparison of a high-altitude, extreme-mach-number reentry flow

Stardust reentry flows have been simulated at an altitude of 80 km for a freestream velocity of 12.8 km/s using direct simulation Monte Carlo (DSMC) and computational fluid dynamics (CFD). Five ions and electrons were considered in the flowfield, and ionization processes were modeled in DSMC. The ion-averaged velocity method in DSMC was validated to maintain charge neutrality in the shock. Collision and energy-exchange models for DSMC were reviewed to ensure adequacy for the high-energy flow regime. Accurate electron-heavy particle collision cross sections and an electron-vibration relaxation model using Lees relaxation time were implemented in DSMC. Although the DSMC results agreed well with CFD for the collision-only case, discrepancies between DSMC and CFD were observed in the shock with the relaxation model activated. Furthermore, with full chemical reactions and ionization processes, DSMC results were compared with CFD. It was found that the assumption of electron temperature is crucial for the prediction of degree of ionization. At 80 km, the degree of ionization predicted by DSMC was found to be approximately 5 %, but in CFD, the degree of ionization is greater than 25 % for the case of T e = T tr and 9% for the case of T e = T vib· In DSMC, the electron-vibration relaxation model was found to be important to predict electron and vibrational temperatures at this altitude, and the electron temperature is the same order as the vibrational temperature. Therefore, compared to the DSMC solution, the assumption of T e = T vib is preferable in CFD. In addition, using the Mott-Smith model, good agreement was obtained between the analytical bimodal distribution functions and DSMC velocity distributions. An effective temperature correction in the relaxation and chemical reaction models using the Mott-Smith model may reduce the continuum breakdown discrepancy between DSMC and CFD inside the shock in terms of degree of ionization and temperatures, but a general implementation is not clear.