Under the assumption of a perfect gas with a constant specific heat ratio, the first approximation of the integral-relations method, which considers the entire shock layer as a single strip, is derived for axisymmetric bodies of arbitrary smooth contour. The resulting differential equations were then applied to a supersonic and hypersonic flow past a paraboloid of revolution. The shock shapes, shock wave detachment distances, locations of sonic lines; and velocity and pressure distributions for the body were calculated for γ = 1.4 and y = 5/3, and at Mach numbers of 3, 4, 6, 10 and 1000. These calculations were carried out on an IBM 1620 electronic computer. The results were compared with those obtained by Van Dyke's inverse method. The agreement between the two methods was found to be good, in view of the fact that only the first approximation of the integral relations method was used. / Master of Science

An investigation has been conducted to determine the effects of nose and corner radii on the pressure distribution and shock geometry for blunt bodies at angle of attack. Experimental pressure distributions were measured on a family of blunt, axisymmetric bodies which included a range of ratios of body radius to nose radius from 0 (flat face) to 0.707 and ratios of corner radius to body radius from 0 (sharp corner) to 0.4. The tests were made at a free stream Mach number and a unit Reynolds number (per foot) of approximately 8.0 and 4.10 x 10⁶, respectively. The range of angle of attack was 0º to 29º. Included in this investigation are pressure and velocity distributions, shock detachment distances measured from schlieren photographs, and a comparison of the experimental pressure and velocity distributions (at zero angle of attack) with theoretical predictions. / Master of Science

A complex chemical system of teflon/air mixture over an axisymmetric decoy at hypersonic reentry flight conditions has been analyzed by using the nonequilibrium viscous shock-layer method. The equilibrium catalytic wall boundary condition was used to obtain the species concentration at the wall. The species conservation equation for binary mixture (air/teflon) was solved to obtain the concentration of freestream air at the wall. Two test cases were chosen to demonstrate the capability of the current code. Due to lack of experimental or theoretical data, the surface measurable quantities from the current code(VSLTEF) were compared with the equivalent air injection and no-mass injection data obtained from VSL7S code. The current code predicts a higher total heat-transfer rate than that predicted by the seven species nonequilibrium air code (VSL7S) with the same injection rate due to the high diffusional heat-transfer rate. The wall pressure was not affected by blowing, while the skin-friction coefficient was decreased (i.e., 43 % reduction for teflon ablation case ; 53 % for nonequilibrium air injection case at 125 kft) when compared with that of no-mass injection case. A shock-layer peak temperature drop ( 1512° R for 125 kft altitude and 848°R for 175 kft altitude) was observed at both cases. The temperature drops were chiefly due to endothermic reactions (dissociation) of the teflon ablation species. Due to large blowing of teflon, the average molecular weight increased substantially and resulted in a reduction of the specific heat ratio γ and an increase in the Prandtl number at the wall. The impurity of sodium was the major source of free electrons near the wall at the end of the vehicle at 125 kft altitude; however, at 175 kft altitude NO⁺ was the major source of free electrons over the entire body. The peak concentration of Na⁺ increased along the body, but that of NO⁺ decreased at both altitudes; While the chemical reaction rate data used is believed to be the best currently available, uncertainties in this data as were cited by Cresswell et al.(1967) may lead to quantitative changes in the above teflon ablation results. / Ph. D.

This work uses computational fluid dynamics to study the flowfield around a hypersonic missile with two lateral jets to provide control in place of control surfaces. The jets exhaust an H2-O2 mixture at Mach number of 2.9 with a jet pressure ratio of roughly 10,500. The jets are staggered axially and circumferentially in such a way to produce pitch and yaw. The flowfield of such a jet configuration is characterized at several angles of attack and the corresponding force coefficients and amplification factors are provided. The freestream air and H2-O2 plume is treated as inert for the majority of the calculations. Special cases are treated with finite rate chemical kinetics and compared to the inert flowfield to ascertain the effects that chemical reactions have on the force coefficients. It was found that the flowfield was only slightly altered from the familiar one jet flowfield when the second jet is active. The flow topology and vortex structures tend to shift towards the second jet but the overall structure remains the same. The normal force amplification factors are close to unity over the range of angle of attack due to the thrust being so high with the two jet configuration having a lower amplification factor compared to firing a single jet. Treating the flowfield as chemically reacting did not affect the force values much: the difference being 0.3% for an angle of attack of 0°. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2017. / FAU Electronic Theses and Dissertations Collection

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERO. / Includes bibliographical references. / by Yoshiaki Kuwano. / M.S.

Aerothermodynamics is an integral component in the design and implementation of hypersonic transport systems. Accurate estimates of the aerodynamic forces and heat transfer rates are critical in trajectory analysis and for payload weight considerations. The present work seeks to investigate the ability of an unstructured Cartesian grid framework in modeling hypersonic viscous flows. The effectiveness of modeling viscous phenomena in hypersonic flows using the immersed boundary ghost cell methodology of this solver is analyzed. The capacity of this framework to predict the surface physics in a hypersonic non-reacting environment is investigated. High velocity argon gas flows past a 2-D cylinder are simulated for a set of freestream conditions (Reynolds numbers), and impact of the grid cell sizes on the quality of the solution is evaluated. Additionally, the formulation is verified over a series of hypersonic Mach numbers for the flow past a hemisphere, and compared to experimental results and empirical estimates. Next, a test case that involves flow separation and the interaction between a hypersonic shock wave and a boundary layer, and a separation bubble is investigated using various adaptive mesh refinement strategies. The immersed boundary ghost cell approach is tested with two temperature clipping strategies, and their impact on the overall solution accuracy and smoothness of the surface property predictions are compared. Finally, species diffusion terms in the conservation equations, and collision cross-section based transport coefficients are installed, and hypersonic flows in thermochemical nonequilibrium environments are studied, and comparisons of the off-surface flow properties and the surface physics predictions are evaluated. First, a 2-D cylinder in a hypersonic reacting air flow is tested with an adiabatic wall boundary condition. Next, the same geometry is tested to evaluate the viscous chemistry prediction capability of the solver with an isothermal wall boundary condition, and to identify the strengths and weaknesses of the immersed boundary ghost cell methodology in computing convective heating rates in such an environment.

No description available.

No description available.

New upwind kinetic-difference schemes have been developed for flows with nonequilibrium thermodynamics and chemistry. These schemes are derived from the Boltzmann equation with the resulting Euler schemes developed as moments of the discretized Boltzmann scheme with a locally Maxwellian velocity distribution. Application of a directionally-split Courant-Isaacson-Rees (CIR) scheme at the Boltzmann level results in a flux-vector splitting scheme at the Euler level and is called Kinetic Flux-Vector Splitting (KFVS). Extension to flows with finite-rate chemistry and vibrational relaxation is accomplished utilizing non-equilibrium kinetic theory. Computational examples are presented comparing KFVS with the schemes of Van-Leer and Roe for quasi-one-dimensional flow through a supersonic diffuser, inviscid flow through two-dimensional inlet, 'viscous flow over a cone at zero angle-of-attack, and shock-induced combustion/detonation in a premixed hydrogen-air mixture. Calculations are also shown for the transonic flow over a bump in a channel and the transonic flow over an NACA 0012 airfoil. The results show that even though the KFVS scheme is a Riemann solver at the kinetic level, its behavior at the Euler level is more similar to the the existing flux-vector splitting algorithms than to the flux-difference splitting scheme of Roe. A new approach toward the development of a genuinely multi-dimensional Riemann solver is also presented. The scheme is based on the same kinetic theory considerations used in the development of the KF VS scheme. The work has been motivated by the recent progress on multi-dimensional upwind schemes by the groups at the University of Michigan and the Von Karman Institute. These researchers have developed effective upwind schemes for the multi-dimensional linear advection equation using a cell-vertex fluctuation-splitting approach on unstructured grids of triangles or tetrahedra. They have made preliminary applications to the Euler equations using several wave decomposition models of the flux derivative. The issue of the appropriate wave model does not appear to be adequately resolved. The approach taken in the present work is to apply these new multi-dimensional upwind schemes for the scalar advection equation at the Boltzmann level. The resulting Euler schemes are obtained as moments of the fluctuations in the Maxwellian distribution function. The development is significantly more complicated than standard (dimensionally-split) kinetic schemes in that the Boltzmann discretization depends upon the direction of the molecular velocities which must be accounted for in the limits of integration in velocity space. The theoretical issues have been solved through analytic quadrature and Euler schemes have been developed. For this formulation it was not necessary to prescribe any explicit wave decomposition model. Encouraging preliminary results have been obtained for perfect gases on uniform Cartesian meshes with first-order spatial accuracy. Results are presented for a 29° shock reflection, a 45° shear discontinuity, and Mach 3 flow over a step. Finally, methods for obtaining accurate gas-dynamic simulations in the continuum transition regime are considered. In particular, large departures from translational equilibrium are modeled using algorithms based on the Burnett equations instead of the Navier-Stokes equations. Here, the same continuum formulation of the governing equations is retained, but new constitutive relations based on higher-order Chapman-Enskog theory are introduced. Both a rotational relaxation model and a bulk-viscosity model have been considered for simulating rotational non-equilibrium. Results are presented for hypersonic normal shock calculations in argon and diatomic nitrogen and comparisons are made with Direct Simulation Monte Carlo (DSMC) results. The present work closely follows that of the group at Stanford, however, the use of upwind schemes and the bulk-viscosity model represent new contributions. / Ph. D.

With the renewed interest in the supersonic and hypersonic flight vehicles, new inverse Euler methods are developed in these flow regimes where a space marching numerical technique is valid. In order to get a general understanding for the specification of target pressure distributions, a study of minimum drag body shapes was conducted over a Mach number range from 3 to 12. Numerical results show that the power law bodies result in low drag shapes, where the n=.69 (l/d = 3) or n=.70 (l/d = 5) shapes have lower drag than the previous theoretical results (n=.75 or n=.66 depending on the particular form of the theory). To validate the results, a numerical analysis was made including viscous effects and the effect of gas model. From a detailed numerical examination for the nose regions of the minimum drag bodies, aerodynamic bluntness and sharpness are newly defined. Numerous surface pressure-body geometry rules are examined to obtain an inverse procedure which is robust, yet demonstrates fast convergence. Each rule is analyzed and examined numerically within the inverse calculation routine for supersonic (M_∞= 3) and hypersonic (M_∞ = 6.28) speeds. Based on this analysis, an inverse method for fully three dimensional supersonic and hypersonic bodies is developed using the Euler equations. The method is designed to be easily incorporated into existing analysis codes, and provides the aerodynamic designer with a powerful tool for design of aerodynamic shapes of arbitrary cross section. These shapes can correspond to either "wing like" pressure distributions or to "body like" pressure distributions. Examples are presented illustrating the method for a non-axisymmetric fuselage type pressure distribution and a cambered wing type application. The method performs equally well for both nonlifting and lifting cases. For the three dimensional inverse procedure, the inverse solution existence and uniqueness problem are discussed. Sample calculations demonstrating this problem are also presented. / Ph. D.