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We present a new multidomain spectral method for the solution of the compressible Navier-Stokes equations. In the subdomain interiors, Chebyshev spectral collocation is used. At interfaces, the advective terms are upwinded and the viscous terms are treated by a penalty method. The method is applied to the solution of a viscous hypersonic flow over a blunt body.
A series of Reynolds-averaged Navier-Stokes (RANS) simulations were performed using the FUN3D flow solver to explore the capabilities of the Langtry-Menter Shear-Stress Transport (LM-SST) transition model for predicting transition for aircraft inlet applications. Two geometries were simulated: a zero-pressure-gradient flat plate and an axisymmetric cone exposed to hypersonic flow. In addition to the transition-sensitized LM-SST model investigations, simulations were run with the one-equation Spalart-Allmaras (SA) and the two-equation Menter Shear-Stress Transport (SST-V) RANS models in fully turbulent mode to identify the natural RANS model transition behavior as a function of Mach number when executed in fully turbulent mode. The flat plate simulations showed that (1) the transition model was able to predict rapid transition at a freestream Mach number of 0.2, which is expected but (2) the predicted transition location moved downstream as the freestream Mach number was increased for the simulations that used the SST-V turbulence model. The latter is significant as it is usually assumed that one- and two-equation turbulence models will produce fully turbulent flow very near the boundary layer origin. The flat plate simulation freestream Mach number trend was confirmed with simulations using the Wind-US code, which also saw a similar trend when employing the SA turbulence model. For the axisymmetric cone simulations, the transition location was highly sensitive to the inflow turbulence levels. This is significant as the prediction of the transition location is crucial when trying to predict inlet performance, especially for hypersonic vehicle applications. It was also noted that the predicted transition location for the cone when using the SST-V turbulence model agreed well with the predicted transition location from the equivalent zero-pressure-gradient flat plate case.
The conditions that characterize aerospace flows are so varied, that a single diagnostic technique is not sufficient for its measurement. Fluid dynamists use knowledge of similarity to help categorize and focus on different flow conditions. For example, the Reynolds number represents the ratio of inertial to viscous forces in a flow. When the velocity scales, length scales, and gas density are large and the magnitude of the molecular viscosity is low, the Reynolds number becomes large. This corresponds to large scale vehicles (e.g Airbus A380), fast moving objects (e.g. artillery projectiles), vehicles in dense fluids (e.g. submarine in water), or flows with low dynamic viscosity (e.g. skydiver in air). In each of these cases, the inertial forces dominate viscous forces, and unsteady turbulent fluctuations in the flow variables are observed. In contrast, flows with small length scales (e.g. dispersion of micro-particles in a solid rocket nozzle), slow moving objects (e.g. micro aerial vehicles), flows with low density gases (e.g. atmospheric re-entry), or fluids with a large magnitude of viscosity (e.g. engine coolant flow), all have low Reynolds numbers. In these cases, viscous forces become very important and often the flows can be steady and laminar. The Mach number, which is the ratio of the velocity to the speed of sound in the medium, also helps to differentiate types of flows. At very low Mach numbers, acoustic waves travel much faster than the object, and the flow can be assumed to be incompressible (e.g. Cessna 172 aircraft). As the object speed approaches the speed of sound, the gas density can become variable (e.g. flow over wing of Learjet 85). When the object speed is higher than the speed of sound (Ma > 1), the presences of shock waves and other gas dynamic features can become important to the vehicle performance (e.g. SR-71 Blackbird). In the hypersonic flow regime (Ma > 5), large changes in temperature begin to affect flow properties, causing real-gas effects to occur (e.g. X-43 Scramjet). At even higher Mach numbers, chemistry and nonequilibrium effects come into play (e.g. Startdust re-entry capsule), further complicating the measurement. These limits can be predicted by calculating the ratio of chemical and thermal relaxation time to the flow time scales. Other non-dimensional numbers can be used to further differentiate types of aerospace flows.
High-speed aerospace engineering applications rely heavily on computational fluid dynamics (CFD) models for design and analysis. This reliance on CFD models necessitates performing accurate and reliable uncertainty quantification (UQ) of the CFD models, which can be very expensive for hypersonic flows. Additionally, UQ approaches are many-query problems requiring many runs with a wide range of input parameters. One way to enable computationally expensive models to be used in such many-query problems is to employ projection-based reduced-order models (ROMs) in lieu of the (high-fidelity) full-order model (FOM). In particular, the least-squares Petrov–Galerkin (LSPG) ROM (equipped with hyper-reduction) has demonstrated the ability to significantly reduce simulation costs while retaining high levels of accuracy on a range of problems, including subsonic CFD applications. This allows LSPG ROM simulations to replace the FOM simulations in UQ studies, making UQ tractable even for large-scale CFD models. This work presents the first application of LSPG to a hypersonic CFD application, the Hypersonic International Flight Research Experimentation 1 (HIFiRE-1) in a three-dimensional, turbulent Mach 7.1 flow. This paper shows the ability of the ROM to significantly reduce computational costs while maintaining high levels of accuracy in computed quantities of interest.
Recent NASA initiatives for space exploration have reinvigorated research on Apollo-like capsule vehicles. Aerothermodynamic characteristics of these capsule configurations during reentry play a crucial role in the performance and safety of the planetary entry probes and the crew exploration vehicles. At issue are the forebody thermal shield protection and afterbody aeroheating predictions. Due to the lack of flight or wind tunnel measurements at hypersonic speed, design decisions on such vehicles would rely heavily on computational results. Validation of current computational tools against experimental measurement thus becomes one of the most important tasks for general hypersonic research. This paper is focused on time-accurate numerical computations of hypersonic flows over a set of capsule configurations, which employ a counterflow jet to offset the detached bow shock. The accompanying increased shock stand-off distance and modified heat transfer characteristics associated with the counterflow jet may provide guidance for future design of hypersonic reentry capsules. The newly emerged space-time conservation element solution element (CESE) method is used to perform time-accurate, unstructured mesh Navier-Stokes computations for all cases investigated. The results show good agreement between experimental and numerical Schlieren pictures. Surface heat flux and aerodynamic force predictions of the capsule configurations are discussed in detail.
This final report summarizes the research accomplished. The research performed during the grant period can be divided into the following major areas: (1) Computation of chemically reacting Supersonic combustion ramjet (scramjet) flowfields. (2) Application of a two-equation turbulence model to supersonic combustion flowfields. (3) Computation of the integrated aerodynamic and propulsive flowfields of a generic hypersonic space plane. (4) Computation of hypersonic flows with finite-catalytic walls. (5) Development of an upwind Parabolized Navier-Stokes (PNS) code for thermo-chemical nonequilibrium flows.
An analytical and experimental investigation has been made to provide a space shuttle orbiter wing design that met the guideline requirements of landing performance, stability, and hypersonic trim for a specified center-of-gravity envelope. The analytical study was facilitated by the use of the Optimal Design Integration system (ODIN) and the experimental part of the investigation was conducted in the Langley low-turbulence pressure tunnel and the Langley continuous-flow hypersonic tunnel.
Current efforts to develop new reusable launch vehicles and to pursue low-cost robotic planetary missions have led to a renewed interest in understanding arc-jet flows. Part of this renewed interest is concerned with improving the understanding of arc-jet test results and the potential use of available computational-fluid- dynamic (CFD) codes to aid in this effort. These CFD codes have been extensively developed and tested for application to nonequilibrium, hypersonic flow modeling. It is envisioned, perhaps naively, that the application of these CFD codes to the simulation of arc-jet flows would serve two purposes: first. the codes would help to characterize the nonequilibrium nature of the arc-jet flows; and second. arc-jet experiments could potentially be used to validate the flow models. These two objectives are, to some extent, mutually exclusive. However, the purpose of the present discussion is to address what role CFD codes can play in the current arc-jet flow characterization effort, and whether or not the simulation of arc-jet facility tests can be used to eva1uate some of the modeling that is used to formu1ate these codes. This presentation is organized into several sections. In the introductory section, the development of large-scale, constricted-arc test facilities within NASA is reviewed, and the current state of flow diagnostics using conventional instrumentation is summarized. The motivation for using CFD to simulate arc-jet flows is addressed in the next section, and the basic requirements for CFD models that would be used for these simulations are briefly discussed. This section is followed by a more detailed description of experimental measurements that are needed to initiate credible simulations and to evaluate their fidelity in the different flow regions of an arc-jet facility. Observations from a recent combined computational and experiment.al investigation of shock-layer flows in a large-scale arc-jet facility are then used to illustrate the current state of development of diagnostic instrumentation, CFD simulations, and general knowledge in the field of arc-jet characterization. Finally, the main points are summarized and recommendations for future efforts are given.
The use of molecular Rayleigh scattering for measurements of gas velocity and temperature is evaluated. Molecular scattering avoids problems associated with the seeding required by conventional laser anemometry and particle image velocimetry. The technique considered herein is based on the measurement of the spectrum of the scattered light. Planar imaging of Rayleigh scattering using a laser light sheet is evaluated for conditions at 30 km altitude (typical hypersonic flow conditions). The Cramer-Rao lower bounds for velocity and temperature measurement uncertainties are calculated for an ideal optical spectrum analyzer and for a planar mirror Fabry-Perot interferometer used in a static, imaging mode. With this technique, a single image of the Rayleigh scattered light from clean flows can be analyzed to obtain temperature and one component of velocity. Experimental results are presented for planar velocity measurements in a Mach 1.3 air jet.
Methods of grid adaptation are reviewed and a method is developed with the capability of adaptation to several flow variables. This method is based on a variational approach and is an algebraic method which does not require the solution of partial differential equations. Also the method was formulated in such a way that there is no need for any matrix inversion. The method is used in conjunction with the calculation of hypersonic flow over a blunt nose. The equations of motion are the compressible Navier-Stokes equations where all viscous terms are retained. They are solved by the MacCormack time-splitting method and a movie was produced which shows simulataneously the transient behavior of the solution and the grid adaptation. The results are compared with the experimental and other numerical results.
Experimental observations and a theoretical model for the onset and disappearance of condensation are given for hypersonic flows of pure nitrogen at M = 10, 14 and 18. Measurements include Pitot pressures, static pressures and laser light scattering experiments. These measurements coupled with a theoretical model indicate a substantial non-equilibrium supercooling of the vapor phase beyond the saturation line. Typical results are presented with implications for the design of hypersonic wind tunnel nozzles.
This study involves numerical modeling of a normal sonic jet injection into a hypersonic cross-flow. The numerical code used for simulation is GASP (General Aerodynamic Simulation Program.) First the numerical predictions are compared with well established solutions for compressible laminar flow. Then comparisons are made with non-injection test case measurements of surface pressure distributions. Good agreement with the measurements is observed. Currently comparisons are underway with the injection case. All the experimental data were generated at the Southampton University Light Piston Isentropic Compression Tube.
Methods of grid adaption are reviewed and a method is developed with the capability of adaption to several flow variables. This method is based on a variational approach and is an algebraic method which does not require the solution of partial differential equations. The method has also been formulated in such a way that there is no need for any matrix inversion. The method is used in conjunction with the calculation of hypersonic flow over a blunt nose. The equations of motion are the compressible Navier-Stokes equations where all viscous terms are retained. They are solved by the MacCormack time-splitting method and a movie has been produced which shows simultaneously the transient behavior of the solution and the grid adaption. The results are compared with the experimental and other numerical results.
High-speed aerospace engineering applications rely heavily on computational fluid dynamics (CFD) models for design and analysis due to the expense and difficulty of flight tests and experiments. This reliance on CFD models necessitates performing accurate and reliable uncertainty quantification (UQ) of the CFD models. However, it is very computationally expensive to run CFD for hypersonic flows due to the fine grid resolution required to capture the strong shocks and large gradients that are typically present. Furthermore, UQ approaches are “many-query” problems requiring many runs with a wide range of input parameters. One way to enable computationally expensive models to be used in such many-query problems is to employ projection-based reduced-order models (ROMs) in lieu of the (high-fidelity) full-order model. In particular, the least-squares Petrov–Galerkin (LSPG) ROM (equipped with hyper-reduction) has demonstrated the ability to significantly reduce simulation costs while retaining high levels of accuracy on a range of problems including subsonic CFD applications. This allows computationally inexpensive LSPG ROM simulations to replace the full-order model simulations in UQ studies, which makes this many-query task tractable, even for large-scale CFD models. This work presents the first application of LSPG to a hypersonic CFD application. In particular, we present results for LSPG ROMs of the HIFiRE-1 in a three-dimensional, turbulent Mach 7.1 flow, showcasing the ability of the ROM to significantly reduce computational costs while maintaining high levels of accuracy in computed quantities of interest.
A series of experiments are reported using inclined circular wall jets in rectangular scramjet combustion chambers configured as constant area ducts. A free piston shock tunnel was used to create inlet flow Mach numbers between 4.2 and 5.5, at enthalpies corresponding to flight speeds of between 3.5 and 5.3 km/s. Measurements of duct static pressure levels indicated that significant mixing and combustion was achieved. Using hydrogen as a fuel, it was found that multipoint injection from two sides of the duct gave a larger, and more rapid, pressure rise. In hypersonic flow, it was found that combustion only occurred for the same duct dimensions and operating conditions that supported combustion with central injection from a two-dimensional strut. Wall injection from discrete orifice circular jets was found to be more effective than two-dimensional wall injection across the whole width of the duct.
Computational fluid dynamics (CFD) has made great strides in the detailed simulation of complex fluid flows, including the fluid physics of flows heretofore not understood. It is now being routinely applied to some rather complicated problems, and starting to impact the design cycle of aerospace vehicles and their components. In addition, it is being used to complement and is being complemented by experimental studies. In this paper some major elements of contemporary CFD research, such as code validation, turbulence physics, and hypersonic flows are discussed, along with a review of the principal pacing items that currently govern CFD. Several examples are presented to illustrate the current state of the art. Finally, prospects for the future of the development and application of CFD are suggested.
An implicit, time-dependent approach is taken to solve the inviscid conservative equations in a vertex-based finite-volume formulation. The convective fluxes are estimated by a modified Riemann solver, and higher-order accuracy is obtained by means of the MUSCL. Implicit techniques are adopted to deal with the equation stiffness as a result of the clustered grid and chemical source term. The real-gas Roe matrix and the ADI and LU schemes have been tested on the sample problems: hypersonic flow over blunt configurations, such as the forebody of a double ellipse, and the near wake of a conic aerobrake. Temperature distribution and standoff distance are validated against the shock-fitting, central-differencing results. Equilibrium temperature may be recovered by artificially increasing the chemical rates at the wall. The present method satisfactorily resolves the flow structure, including the strong expansion behind the flat base. The relative merits and performance of the real-gas TVD and implicit schemes are discussed briefly.
Computational fluid dynamics (CFD) has made great strides in the detailed simulation of complex fluid flows, including the fluid physics of flows heretofore not understood. It is now being routinely applied to some rather complicated problems, and starting to impact the design cycle of aerospace flight vehicles and their components. In addition, it is being used to complement, and is being complemented by, experimental studies. In the present paper, some major elements of contemporary CFD research, such as code validation, turbulence physics, and hypersonic flows are discussed, along with a review of the principal pacing items that currently govern CFD. Several examples of pioneering CFD research are presented to illustrate the current state of the art. Finally, prospects for the future development and application of CFD are suggested.