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Compressible fluid flow problems were solved using an adaptive finite element method. Supersonic flow past a wedge and Prandtl-Meyer expansion were considered. Computational grids are presented.
An optimization method was developed to design axisymmetric body shapes such as fuselages, nacelles, and external fuel tanks with increased transition Reynolds numbers in subsonic compressible flow. The method involves a constraint minimization procedure coupled with analysis of the inviscid and viscous flow regions, and linear stability analysis of the compressible boundary-layer. Boundary-layer transition is predicted by a 'hybrid' transition criterion based on Granville's transition criterion and a criterion using linear stability theory coupled with the e(sup n)-method. A tiptank of a business jet is used as an example to illustrate that the method can be utilized to design an axisymmetric body shape with extensive natural laminar flow. On the original tiptank boundary layer transition is predicted to occur at a transition Reynolds number of 6.04 x 10 6 on the original tiptank. On the designed body shape a transition Reynolds number of 7.22 x 10 6 is predicted using compressible linear stability theory coupled with e n -method.
An optimization method has been developed to design axisymmetric body shapes such as fuselages, nacelles, and external fuel tanks with increased transition Reynolds numbers in subsonic compressible flow. The new design method involves a constraint minimization procedure coupled with analysis of the inviscid and viscous flow regions, and linear stability analysis of the compressible boundary layer. Boundary-layer transition is predicted by a 'hybrid' transition criterion based on Granville's transition criterion and a criterion using linear stability theory coupled with the e(n)-method. A tiptank of a business-jet is used as an example to illustrate that the method can be utilized to design an axisymmetric body shape with extensive natural laminar flow. Boundary layer transition is predicted to occur at a transition Reynolds number of 6.04 x 10 to the 6th on the original tiptank. On the designed body shape, a transition Reynolds number of 7.22 x 10 to the 6th is predicted using compressible linear stability theory coupled with e(n)-method.
An optimization method has been developed to design axisymmetric body shapes such as fuselages, nacelles, and external fuel tanks with increased transition Reynolds numbers in subsonic compressible flow. The new design method involves a constraint minimization procedure coupled with analysis of the inviscid and viscous flow regions and linear stability analysis of the compressible boundary-layer. In order to reduce the computer time, Granville's transition criterion is used to predict boundary-layer transition and to calculate the gradients of the objective function, and linear stability theory coupled with the e(exp n)-method is used to calculate the objective function at the end of each design iteration. Use of a method to design an axisymmetric body with extensive natural laminar flow is illustrated through the design of a tiptank of a business jet. For the original tiptank, boundary layer transition is predicted to occur at a transition Reynolds number of 6.04 x 10(exp 6). For the designed body shape, a transition Reynolds number of 7.22 x 10(exp 6) is predicted using compressible linear stability theory coupled with the e(exp n)-method.
The Compressible Flow Toolbox is primarily a MATLAB-language implementation of a set of algorithms that solve approximately 280 linear and nonlinear classical equations for compressible flow. The toolbox is useful for analysis of one-dimensional steady flow with either constant entropy, friction, heat transfer, or Mach number greater than 1. The toolbox also contains algorithms for comparing and validating the equation-solving algorithms against solutions previously published in open literature. The classical equations solved by the Compressible Flow Toolbox are as follows: The isentropic-flow equations, The Fanno flow equations (pertaining to flow of an ideal gas in a pipe with friction), The Rayleigh flow equations (pertaining to frictionless flow of an ideal gas, with heat transfer, in a pipe of constant cross section), The normal-shock equations, The oblique-shock equations, and The expansion equations.
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An algorithm for laminar and turbulent viscous compressible two dimensional flows is presented. For the application of precise boundary conditions over an arbitrary body surface, a body-fitted coordinate system is used in the physical plane. A thin-layer approximation of tne Navier-Stokes equations is introduced to keep the viscous terms relatively simple. The flow field computation is performed in the transformed plane. A factorized, implicit scheme is used to facilitate the computation. Sample calculations, for Couette flow, developing pipe flow, an isolated airflow, two dimensional compressor cascade flow, and segmental compressor blade design are presented. To a certain extent, the effective use of the direct solver depends on the user's skill in setting up the gridwork, the time step size and the choice of the artificial viscosity. The design feature of the algorithm, an iterative scheme to correct geometry for a specified surface pressure distribution, works well for subsonic flows. A more elaborate correction scheme is required in treating transonic flows where local shock waves may be involved.
Prediction of compressible flow phenomena using the finite element method is of recent origin and considerable interest. Two shock capturing finite element formulations for high speed compressible flows are described. A Taylor-Galerkin formulation uses a Taylor series expansion in time coupled with a Galerkin weighted residual statement. The Taylor-Galerkin algorithms use explicit artificial dissipation, and the performance of three dissipation models are compared. A Petrov-Galerkin algorithm has as its basis the concepts of streamline upwinding. Vectorization strategies are developed to implement the finite element formulations on the NASA Langley VPS-32. The vectorization scheme results in finite element programs that use vectors of length of the order of the number of nodes or elements. The use of the vectorization procedure speeds up processing rates by over two orders of magnitude. The Taylor-Galerkin and Petrov-Galerkin algorithms are evaluated for 2D inviscid flows on criteria such as solution accuracy, shock resolution, computational speed and storage requirements. The convergence rates for both algorithms are enhanced by local time-stepping schemes. Extension of the vectorization procedure for predicting 2D viscous and 3D inviscid flows are demonstrated. Conclusions are drawn regarding the applicability of the finite element procedures for realistic problems that require hundreds of thousands of nodes.
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Simulations of simple compressible flows have been performed to enable the direct estimation of the pressure-dilatation correlation. The generally accepted belief that this correlation may be important in high-speed flows has been verified by the simulations. The pressure-dilatation correlation is theoretically investigated by considering the equation for fluctuating pressure in an arbitrary compressible flow. This leads to the isolation of a component of the pressure-dilatation that exhibits temporal oscillations on a fast time scale. Direct numerical simulations of homogeneous shear turbulence and isotropic turbulence show that this fast component has a negligible contribution to the evolution of turbulent kinetic energy. Then, an analysis for the case of homogeneous turbulence is performed to obtain a formal solution for the nonoscillatory pressure-dilatation. Simplifications lead to a model that algebraically relates the pressure-dilatation to quantities traditionally obtained in incompressible turbulence closures. The model is validated by direct comparison with the simulations.
The present paper describes the verification and validation of a quasi one-dimensional pressure based finite volume algorithm, implemented in Generalized Fluid System Simulation Program (GFSSP), for predicting compressible flow with friction, heat transfer and area change. The numerical predictions were compared with two classical solutions of compressible flow, i.e. Fanno and Rayleigh flow. Fanno flow provides an analytical solution of compressible flow in a long slender pipe where incoming subsonic flow can be choked due to friction. On the other hand, Raleigh flow provides analytical solution of frictionless compressible flow with heat transfer where incoming subsonic flow can be choked at the outlet boundary with heat addition to the control volume. Nonuniform grid distribution improves the accuracy of numerical prediction. A benchmark numerical solution of compressible flow in a converging-diverging nozzle with friction and heat transfer has been developed to verify GFSSP's numerical predictions. The numerical predictions compare favorably in all cases.
A set of compressible flow relations for a thermally perfect, calorically imperfect gas are derived for a value of c(sub p) (specific heat at constant pressure) expressed as a polynomial function of temperature and developed into a computer program, referred to as the Thermally Perfect Gas (TPG) code. The code is available free from the NASA Langley Software Server at URL http://www.larc.nasa.gov/LSS. The code produces tables of compressible flow properties similar to those found in NACA Report 1135. Unlike the NACA Report 1135 tables which are valid only in the calorically perfect temperature regime the TPG code results are also valid in the thermally perfect, calorically imperfect temperature regime, giving the TPG code a considerably larger range of temperature application. Accuracy of the TPG code in the calorically perfect and in the thermally perfect, calorically imperfect temperature regimes are verified by comparisons with the methods of NACA Report 1135. The advantages of the TPG code compared to the thermally perfect, calorically imperfect method of NACA Report 1135 are its applicability to any type of gas (monatomic, diatomic, triatomic, or polyatomic) or any specified mixture of gases, ease-of-use, and tabulated results.
Compressible viscous flow around two-dimensional cavities, that model the midplane flow in and around an airborne telescope cavity, are obtained through numerical simulation. Numerical solutions using the patched grid CSCM scheme for compressible, unsteady flow are presented for the cavities, with and without blowing. The time evolving solutions show interesting flow features. Relevant results for a limited number of problems presented here show the unsteady nature of the flow and its dependence on various parameters such as Reynolds number, the wall conditions, etc. The voluminous data of time evolving flow field solutions are analyzed through movies of the velocity vectors, and contours of other flow variables.
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The present study was motivated to analyze the complex flow field involving gaseous oxygen (GOX) flow in a relief valve (RV). The 9391 RV, pictured in Figure 1, was combined with the pilot valve to regulate the actuation pressure of the main valve system. During a high-pressure flow test at Marshall Space Flight Center (MSFC) the valve system developed a resonance chatter, which destroyed most of the valve body. Figures 2-4 show the valve body before and after accident. It was understood that the subject RV has never been operated at 5500 psia. In order to fully understand the flow behavior in the RV, a computational fluid dynamics (CFD) analysis is carried out to investigate the side load across the piston sleeve and the erosion patterns resulting from flow distribution around piston/nozzle interface.
To make computer codes for two-dimensional compressible flows more robust and economical, wall functions for these flows, under adiabatic conditions, have been developed and tested. These wall functions have been applied to three two-equation models of turbulence. The tests consist of comparisons of calculated and experimental results for transonic and supersonic flow over a flat plate and for two-dimensional and axisymmetrical transonic shock-wave/boundary-layer interaction flows with and without separation. The calculations are performed with an implicit algorithm that solves the Reynolds-averaged Navier-Stokes equations. It is shown that results obtained agree very well with the data for the complex compressible flows tested, provided criteria for use of the wall functions are followed. The expected savings in cost of the computations and improved robustness of the code were achieved.