CHARTS FOR EQUILIBRIUM FLOW PROPERTIES OF AIR IN HYPERVELOCITY NOZZLES
Charts for equilibrium flow properties of air in hypervelocity nozzles
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Charts for equilibrium flow properties of air in hypervelocity nozzles
Charts for equilibrium flow properties of carbon dioxide in hypervelocity nozzles
The Hollweg et al. (1990) analysis of MHD surface waves in a stationary equilibrium is extended. The conservation laws and jump conditions at Alfven and slow resonance points obtained by Sakurai et al. (1990) are generalized to include an equilibrium flow, and the assumption that the Eulerian perturbation of total pressure is constant is recovered as the special case of the conservation law for an equilibrium with straight magnetic field lines and flow along the magnetic field lines. It is shown that the conclusions formulated by Hollweg et al. are still valid for the straight cylindrical case. The effect of curvature is examined.
Symmetrical equilibrium flow past blunt body at superorbital reentry conditions calculated by integrating motion equations across shock layer
Convective stagnation-point heat transfer in partial equilibrium flow of highly ionized nitrogen
The goal of this paper is to generalize the well-balanced approach for non-equilibrium flow studied by Wang et al. [26] to a class of low dissipative high order shock-capturing filter schemes and to explore more advantages of well-balanced schemes in reacting flows. The class of filter schemes developed by Yee et al. [30], Sjoegreen & Yee [24] and Yee & Sjoegreen [35] consist of two steps, a full time step of spatially high order non-dissipative base scheme and an adaptive nonlinear filter containing shock-capturing dissipation. A good property of the filter scheme is that the base scheme and the filter are stand alone modules in designing. Therefore, the idea of designing a well-balanced filter scheme is straightforward, i.e., choosing a well-balanced base scheme with a well-balanced filter (both with high order). A typical class of these schemes shown in this paper is the high order central difference schemes/predictor-corrector (PC) schemes with a high order well-balanced WENO filter. The new filter scheme with the well-balanced property will gather the features of both filter methods and well-balanced properties: it can preserve certain steady state solutions exactly; it is able to capture small perturbations, e.g., turbulence fluctuations; it adaptively controls numerical dissipation. Thus it shows high accuracy, efficiency and stability in shock/turbulence interactions. Numerical examples containing 1D and 2D smooth problems, 1D stationary contact discontinuity problem and 1D turbulence/shock interactions are included to verify the improved accuracy, in addition to the well-balanced behavior.
A WKB theory is formulated for large-n ballooning modes in axisymmetric, toroidal plasmas with sheared equilibrium flows. The validity of the standard ballooning respresentation is severely restricted in the presence of sheared toroidal flow, despite the fact that to leading order in (1/n), where n is the azimuthal number, the eigenmode equation contains only derivatives along a field line. Necessary and sufficient conditions for stability are obtained in a high-beta ordering for rigid toroidal rotation as well as field-aligned flows.
Spatially-resolved nitric oxide (NO) planar laser-induced fluorescence (PLIF) rotational thermometry was performed on a Mach 5 non-equilibrium flow around a blunt-body specimen in the Hypersonic Materials Environmental Test System (HyMETS) arc-heat wind tunnel at the NASA Langley Research Center. Transitions within the (0,0) band in the A(exp 2)∑(sup +) - X(exp 2)Π system of NO were excited with a 10 Hz pulsed ultra-violet laser. A multi-line fitting algorithm was applied to the PLIF spectra and transitions were filtered based on an iterative method that maximizes thermometry accuracy. NO PLIF thermometry results are compared to non-equilibrium computational fluid dynamics (CFD) simulations reported in the literature. Differences between the experiment and CFD are quantified for the free-stream, post-shock, shear-layer, and expansion-fan regions of the flow. Potential sources of error, applicable to both the CFD and experiment, are discussed.
High enthalpy arc-jets are unique facilities particularly suited for producing complex flows in the aerospace field, such as the aerothermodynamics of a re-entry vehicle. Arc-jets are often used to evaluate important design factors that include heat shield materials and vehicle design. Characterization of these facilities is important, as studies often aim to match specific in-flight environments during experiments. Due to the complex environment produced by an arc-jet, with effects such as thermodynamic and chemical non-equilibrium occurring in the flow, characterization experiments are significantly more difficult than in conventional blow-down wind tunnels. The current work aims to characterize an arc-jet facility through spatially-resolved measurements of flow unsteadiness, temperature, and velocity. To achieve this goal, a non-intrusive imaging technique called “planar laser-induced fluorescence” was performed in the NASA Langley Hypersonic Materials Environmental Test System arc-jet facility. The experimental data was analysed to produce the quantitative measurements in multiple regions of the flow around a blunt body specimen. A three-temperature low fidelity numerical solver was created to simulate the flow in order to investigate thermal non-equilibrium effects occurring outside the imaging region in the arc-jet nozzle. Unsteadiness in the test section of the arc-jet was minimized by analyzing a subset of data assessing the gas injection configuration. Radial velocity, rotational temperature and translational temperature measurements are provided that can be used to validate future computational studies. The temperature measurements revealed rotational non-equilibrium occurring behind the bow-shock near the specimen surface. Computational results show the facility is capable of producing thermal non-equilibrium flow in the arc-jet nozzle. This work provides the first experimental and computational evidence of thermal trans-rotational non-equilibrium occurring in multiple regions of this arc-jet facility. Significant improvements to the methodology are also identified as recommendations for future arc-jet characterization studies.
High enthalpy arc-jets are unique facilities particularly suited for simulating complex flows in the aerospace field, such as the aerothermodynamics of a re-entry vehicle. Arc-jets are often used to evaluate important design factors such as heat shield materials and vehicle design. Characterization of these facilities is important, as studies often match specific in-flight environments during experiments. Due to the complex environment produced by an arc-jet, with effects such as thermodynamic and chemical non-equilibrium occurring in the flow, characterization experiments are significantly more difficult than in traditional blow-down wind tunnels. The current work aims to characterize an arc-jet facility in terms of flow temperature, velocity and unsteadiness, in a spatially-resolved analysis. To achieve this goal, a non-intrusive imaging technique called “planar laser-induced fluorescence” was performed in the NASA Langley Hypersonic Materials Environ-mental Test System arc-jet facility. The experimental data was analyzed to produce the quantitative measurements in multiple regions of the flow around a blunt body sample. A quasi-1D low fidelity solver was created to numerically simulate the flow to investigate non-equilibrium effects occur-ring outside the imaging region in the arc-jet nozzle. Unsteadiness in the test section was minimized by analyzing a subset of data assessing the gas injection location. Radial velocity, rotational temperature and translational temperature measurements are provided that can be used to validate future high-fidelity computational studies. The temperature measurements revealed rotational non-equilibrium potentially occurring in the flow. This work provides a methodology for characterizing arc-jet facilities, identifying and correcting sources of systematic error, and estimating the uncertainty associated with the quantitative measurements.
This paper presents a finite element method for the solution of Navier-Stokes equations with the assumption of thermodynamic and chemical equilibrium. The method employs an upwind finite element technique with an implicit time-marching scheme for the solution, and uses an adaptively generated unstructured triangular mesh with several layers of quadrilateral elements near solid walls. The complexity associated with the assumption that the flow is in equilibrium is treated consistently, and the inviscid flux Jacobian matrices are derived. Several problems involving inviscid and viscous hypersonic flow past blunt are solved. Results are compared with other numerical results and experimental data, and generally good agreement is observed.
A new time accurate coupled solution procedure for solving the chemical non-equilibrium Navier-Stokes equations over a wide range of Mach numbers is described. The scheme is shown to be very efficient and robust for flows with velocities ranging from M less than or equal to 10(exp -10) to supersonic speeds.
This study presents a new class of turbulence model designed for wall bounded, high Reynolds number flows with separation. The model addresses deficiencies seen in the modeling of nonequilibrium turbulent flows. These flows generally have variable adverse pressure gradients which cause the turbulent quantities to react at a finite rate to changes in the mean flow quantities. This "lag" in the response of the turbulent quantities can t be modeled by most standard turbulence models, which are designed to model equilibrium turbulent boundary layers. The model presented uses a standard 2-equation model as the baseline for turbulent equilibrium calculations, but adds transport equations to account directly for non-equilibrium effects in the Reynolds Stress Tensor (RST) that are seen in large pressure gradients involving shock waves and separation. Comparisons are made to several standard turbulence modeling validation cases, including an incompressible boundary layer (both neutral and adverse pressure gradients), an incompressible mixing layer and a transonic bump flow. In addition, a hypersonic Shock Wave Turbulent Boundary Layer Interaction with separation is assessed along with a transonic capsule flow. Results show a substantial improvement over the baseline models for transonic separated flows. The results are mixed for the SWTBLI flows assessed. Separation predictions are not as good as the baseline models, but the over prediction of the peak heat flux downstream of the reattachment shock that plagues many models is reduced.
Six months of funding was received for the proposed three year research program (funding for the period from March 1, 1997 to August 31, 1997). Although the official starting date for the project was March 1, 1997, no funding for the project was received until July 1997. In the funded research period, considerable progress was made on Phase I of the proposed research program. The initial research efforts concentrated on applying the 10-, 20-, and 35-moment Gaussian-based closures to a series of standard two-dimensional non-reacting single species test flow problems, such as the flat plate, couette, channel, and rearward facing step flows, and to some other two-dimensional flows having geometries similar to those encountered in chemical-vapor deposition (CVD) reactors. Eigensystem analyses for these systems for the case of two spatial dimensions was carried out and efficient formulations of approximate Riemann solvers have been formulated using these eigenstructures. Formulations to include rotational non-equilibrium effects into the moment closure models for the treatment of polyatomic gases were explored, as the original formulations of the closure models were developed strictly for gases composed of monatomic molecules. The development of a software library and computer code for solving relaxing hyperbolic systems in two spatial dimensions of the type arising from the closure models was also initiated. The software makes use of high-resolution upwind finite-volumes schemes, multi-stage point implicit time stepping, and automatic adaptive mesh refinement (AMR) to solve the governing conservation equations for the moment closures. The initial phase of the code development was completed and a numerical investigation of the solutions of the 10-moment closure model for the simple two-dimensional test cases mentioned above was initiated. Predictions of the 10-moment model were compared to available theoretical solutions and the results of direct-simulation Monte Carlo (DSMC) calculations. The first results of this study were presented at a meeting last year.
A heating analysis for a 15.2 m diameter Lunar Transfer Vehicle (LTV) at 0 and 10.6 deg angle of attack for a nominal trajectory through the earth's atmosphere is described. The analysis utilizes the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) with thin-layer, Navier-Stokes, thermochemical nonequilibrium options. Radiative heating levels are calculated using the Langley Optimized RAdiative Nonequilibrium (LORAN) and the Non-EQuilibrium AIr Radiation (NEQAIR) codes. At peak heating, the shock layer is substantially in equilibrium. Comprehensive spatial and spectral grid convergence studies have been implemented to quantify grid effects on the convective and radiative heating levels. Axisymmetric tests including the coupled effects of radiative energy transfer show negligible change to the convective heating and a 20 percent reduction in the radiative heating.
The work performed during this year has involved further assessment and extension of the k-epsilon-v(exp 2) model, and initiation of work on scalar transport. The latter is introduced by the contribution of Y. Shabany to this volume. Flexible, computationally tractable models are needed for engineering CFD. As computational technology has progressed, the ability and need to use elaborate turbulence closure models has increased. The objective of our work is to explore and develop new analytical frameworks that might extend the applicability of the modeling techniques. In past years the development of a method for near-wall modeling was described. The method has been implemented into a CFD code and its viability has been demonstrated by various test cases. Further tests are reported herein. Non-equilibrium near-wall models are needed for some heat transfer applications. Scalar transport seems generally to be more sensitive to non-equilibrium effects than is momentum transport. For some applications turbulence anisotropy plays a role and an estimate of the full Reynolds stress tensor is needed. We have begun work on scalar transport per se, but in this brief I will only report on an extension of the k-epsilon-v(exp 2) model to predict the Reynolds stress tensor.
Hypersonic nonequilibrium flow and its underlying thermodynamic relations, including real gas effects
Determining exit conditions that result when heat is withdrawn from rocket thrust chamber and added to gas flow in nozzle