Ryan Bomar Bond

A kinetic-theory approach for computing chemical-reaction rates in upper-atmosphere hypersonic flows

Recently proposed molecular-level chemistry models that predict equilibrium and nonequilibrium reaction rates using only kinetic theory and fundamental molecular properties (i.e., no macroscopic reaction-rate information) are investigated for chemical reactions occurring in upper-atmosphere hypersonic flows. The new models are in good agreement with the measured Arrhenius rates for near-equilibrium conditions and with both measured rates and other theoretical models for far-from-equilibrium conditions. Additionally, the new models are applied to representative combustion and ionization reactions and are in good agreement with available measurements and theoretical models. Thus, molecular-level chemistry modeling provides an accurate method for predicting equilibrium and nonequilibrium chemical-reaction rates in gases.

Manufactured Solution for Computational Fluid Dynamics Boundary Condition Verification

Order-of-accuracy verification is necessary to ensure that software correctly solves a given set of equations. One method for verifying the order of accuracy of a code is the method of manufactured solutions. This study documents the development of a manufactured solution that allows verification of not only the Euler, Navier-Stokes, and Reynolds-averaged Navier-Stokes equation sets, but also some of their associated boundary conditions: slip, no-slip (adiabatic and isothermal), and outflow (subsonic, supersonic, and mixed). To demonstrate the usefulness of this manufactured solution, it has been used for order-of-accuracy verification in a compressible computational fluid dynamics code. All of the results shown are on skewed, nonuniform, three-dimensional meshes. The manufactured solution and sequence of meshes are designed to allow asymptotic results to be obtained with reasonable computational cost. In addition to the order of accuracy of the full code for various equation sets and boundary conditions, the order of accuracy of code portions used to calculate solution gradients has been measured as well.

A Manufactured Solution for Verifying CFD Boundary Conditions, Part II

Order-of-accuracy veriflcation is necessary to ensure that software correctly solves a given set of equations. One method for verifying the order of accuracy of a code is the method of manufactured solutions. Part III of this study completes the development of a manufactured solution that allows veriflcation of not only the Euler, Navier-Stokes, and Reynolds-Averaged Navier-Stokes equation sets, but also some of their associated boundary conditions: slip, no-slip (adiabatic and isothermal), and out∞ow (subsonic, supersonic, and mixed). In order to demonstrate the usefulness of this manufactured solution, it has been used for order-of-accuracy veriflcation in a compressible computational ∞uid dynamics code. All of the results shown are on skewed, non-uniform, three-dimensional meshes. Modiflcations have been made to the manufactured solution and sequence of meshes from previous work to allow asymptotic results to be obtained with less computational cost. In addition to the order of accuracy of the full code for various equation sets and boundary conditions, the order of accuracy of code portions used to calculate solution gradients has been measured as well.

Assessment of Collisional-Energy-Based Models for Atmospheric Species Reactions in Hypersonic Flows

A recently proposed set of direct simulation Monte Carlo chemical reaction models, based solely on the collisional energy and the vibrational energy levels of the species involved, is applied to calculate equilibrium and nonequilibrium chemical reaction rates for atmospheric reactions in hypersonic flows. The direct simulation Monte Carlo model predictions are in good agreement with Parks model, several theoretical models, and experimental measurements. Physically plausible modifications to some of the direct simulation Monte Carlo models are presented that improve agreement. The observed agreement provides strong evidence that modeling of chemical reactions based on collisional energy and vibrational energy levels provides an accurate method for predicting equilibrium and nonequilibrium chemical reaction rates.

Computational Analysis of an Independent Ramjet Stream in a Combined Cycle Engine

A new concept for the low-speed propulsion mode in rocket-based combined cycle engines has been developed as part of the NASA GTX program. This concept, called the independent ramjet stream (IRS) cycle, is a variation of the traditional ejector ramjet (ER) design and involves the injection of hydrogen fuel directly into the airstream, where it is ignited by the rocket plume. The advantage of the IRS design is that it allows for a single large rocket instead of several smaller rockets, and its required combustor length is smaller than that of a traditional ER design. Both of these features make the IRS design lighter. Experiments and computational fluid dynamics are currently being used to evaluate the feasibility of the new design. In this work, a Navier‐Stokes code valid for general reactive flows is applied to the model engine under cold-flow, ER, and IRS cycle operation. Pressure distributions corresponding to cold-flow and ER operation are compared with experimental data. The engine response under IRS cycle operation is examined for different reaction models and grid sizes. The solutions exhibit a high sensitivity to both grid resolution and reaction mechanism but do indicate that thermal throat ramjet operation is possible through the injection and burning of additional fuel into the airstream.

The Influence of Stabilization Parameters in the SUPG Finite Element Method for Hypersonic Flows

This paper examines the influence of particular forms of the stabilization parameters which appear in the streamline-upwind Petrov-Galerkin (SUPG) finite element discretization of the calorically perfect Euler and Navier-Stokes equations at hypersonic conditions. The particular emphasis of the investigation is (i) the construction of the upwind-bias weighting function and (ii) a comparison of discontinuity capturing operators. Various representations of these terms have appeared in the literature over the years, and a number of comparison studies have been performed, primarily in the inviscid 2D setting. The length scale used in the SUPG weighting function is shown to have a critical effect on the stagnation-point heat transfer predicted to blunt bodies in three dimensions. The structure of the discontinuity capturing operator (required to achieve stable solutions in the presence of strong shock waves) is also considered in detail. Two classical approaches are compared, which differ primarily in the coordinate system in which they operate. Of the two approaches, it is found that the operator formed in reference element computational space (the so-called formulation) has superior convergence properties and produced a crisper shock than a physical space formulation (the scheme), however both schemes produce essentially the same jump conditions. To achieve the proper jump conditions we show that it is critical that the interplay of the SUPG and shock capturing operators be adequately addressed to avoid “over-stabilizing” the problem.

A Streamline-Upwind Petrov-Galerkin Finite Element Scheme for Non-Ionized Hypersonic Flows in Thermochemical Nonequilibrium

This paper considers the streamline-upwind Petrov-Galerkin (SUPG) method applied to the thermochem- ical nonequilibrium Navier-Stokes equations in conservation-variable form. The governing equations for a non-ionized reacting mixture of perfect gases in thermal nonequilibrium - including the the thermochemistry, chemical kinetics, and transport properties - are reviewed. The implementation within the FIN-S code, in- cluding spatial discretization, time discretization, and solution scheme, is briefly discussed. The performance of the formulation is then investigated by considering a two separate problems, inviscid flow in thermochemical nonequilibrium and viscous flow in chemical nonequilibrium. The influence of freestream density on thermal nonequilibrium is investigated for the inviscid case, while both mesh and iterative convergence results are presented for the viscous case. When the time scale associated with chemical reactions in the flow is much less than the fluid dynamic time scales, tchemtflow, the gas can be assumed to be in equilibrium. In this situation the equilibrium principle holds and the state of the gas is uniquely determined by any two independent thermodynamic properties. Conversely, when the time scale associated with chemical reactions is much greater than the fluid dynamic time scales, tchemtflow, the gas is said to be frozen. In this case the chemical composition of the gas is fixed throughout the domain, and the fluid may be adequately modeled as a nonreacting mixture of thermally perfect gases. Between these two extremes is the regime of chemical nonequilibrium. In this case chemical and fluid dynamic time scales are comparable. The chemical composition at any point in the domain is then not only a function of local conditions, but also of the streamline history. Conceptually, the gas will begin to adjust to reach its equilibrium state, but before this process has completed it will have convected downstream. It will then seek a new equilibrium state dictated by the local conditions. In this situation tchem ≈ tflow, and the chemical composition of the gas itself must be determined. In this regime the flow is said to be in chemical nonequilibrium. For applications of interest in aerospace engineering, these flows can be modeled to good approximation by a chemically reacting mixture of perfect gases. Note this approach assumes that intermolecular forces are negligible and hence each chemical species in the flow obeys the perfect gas law, an assumption which is generally valid, except for very high pressures at low temperature 1 . Considering a diatomic molecule, shown schematically in Figure 1. It is clear that there are four possible modes in

Stabilized Finite Element Scheme for High Speed Flows with Chemical Non-Equilibrium.

A streamline upwind Petrov-Galerkin finite element method is presented for the case of a reacting mixture of thermally-perfect gases, using chemical non-equilibrium. Details of the stabilization scheme and nonlinear solution are presented. The authors have independently implemented the proposed algorithm in two separate codes, for both single temperature and and two temperature models. Example problems invoving a cylinder in Mach 20 crossflow, as well as a three-dimensional blunt nosetip are shown and compared to established codes.

Measuring progress in order-verification within software development projects

This document proposes one answer to the question: how does one measure and communicate progress in code verification? The question is addressed within the scope of verifying the order-of-accuracy of codes that solve partial differential equations. A process is described whereby order-verification exercises may be conducted within software development projects. The process entails domain-definition, test-suite construction, and test-suite demonstration phases. Progress measures are proposed to monitor the latter two phases particularly with regard to how close they are to completion. A fitness measure is introduced which measures the verification-fitness of a code relative to a given application.

Assessment of reaction-rate predictions of a collision-energy approach for chemical reactions in atmospheric flows.

A recently proposed approach for the Direct Simulation Monte Carlo (DSMC) method to calculate chemical-reaction rates is assessed for high-temperature atmospheric species. The new DSMC model reproduces measured equilibrium reaction rates without using any macroscopic reaction-rate information. Since it uses only molecular properties, the new model is inherently able to predict reaction rates for arbitrary non-equilibrium conditions. DSMC non-equilibrium reaction rates are compared to Park’s phenomenological nonequilibrium reaction-rate model, the predominant model for hypersonic-flow-field calculations. For near-equilibrium conditions, Park’s model is in good agreement with the DSMC-calculated reaction rates. For far-from-equilibrium conditions, corresponding to a typical shock layer, significant differences can be found. The DSMC predictions are also found to be in very good agreement with measured and calculated non-equilibrium reaction rates, offering strong evidence that this is a viable and reliable technique to predict chemical reaction rates.