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Effect of grid and constriction friction on flame propagation velocity, heat exchange and acoustic shock discontinuity formation in reactive media
Recent numerical investigations have focused attention once more on the role of intermediate shocks in MHD. Four types of intermediate shock are identified using a graphical representation of the MHD Rankine-Hugoniot conditions. This same representation can be used to exhibit the close relationship of intermediate shocks to switch-on shocks and rotational discontinuities. The conditions under which intermediate discontinuities can be found are elucidated. The variations in velocity, pressure, entropy and magnetic-field jumps with upstream parameters in intermediate shocks are exhibited graphically. The evolutionary arguments traditionally advanced against intermediate shocks may fail because the equations of classical MHD are not strictly hyperbolic.
Production of geomagnetic pulsations by solar wind shock discontinuities in interplanetary medium and interaction with magnetosphere
Shock tube discontinuities were used to test and extend a kinetic theory of turbulence. In shock wave and contact surface fluctuations, coherent phenomena were found which provide new support for the microscopic nonempirical approach to turbulent systems, especially those with boundary layer-like instabilities.
A pressure-ruptured shock tube and an arc driven shock tube, have been used to study the evolution of turbulent fluctuations at contact surfaces with N2O4-2NO2 mixtures and at ionizing shock fronts in argon. The study has focused on point density diagnostics derived from crossed light beam correlations and electric probes. Turbulent bursts are found for which dynamical and spectral analyses suggest a particle-like evolution of fluctuation segments with a unique and characteristic frequency, independent of flow history and overall flow conditions.
The discontinuous structure of the solar wind is described with emphasis on properties related to geomagnetic impulses. Some of the discontinuities are clearly hydromagnetic shocks and tangential discontinuities, and can produce a significant change in the momentum flux at the magnetosphere boundary. Such a change generates an impulse which propagates through the magnetosphere to the earth where it is observed world-wide as an impulse in magnetograms. The propagation process is not reviewed here, but the relation between the initial cause (discontinuity) and the final effect (geomagnetic impulse) is reviewed in detail. The various types of impulses are examined, and are related qualitatively to the various types of discontinuities. The magnitude of an impulse is related to the change in the momentum flux. The propagation time and the rise time depend on the propagation process rather than on the initial state.
A computational procedure has been developed to predict the inviscid super/hypersonic flow field of conical internal corners. The prediction of internal corner flow fields can be important in the design of supersonic 'box' type inlets. The computational procedure utilizes a second order finite difference marching technique to asymptote to the conical corner flow solution of Euler's equations. These flow fields are dominated by complex shock interactions. All discontinuities, shocks and slip surfaces are fitted with the appropriate jump conditions. The 'triple' points (the interaction of two shocks and a slip surface) are also computed exactly. Computed results are compared with experimental data and the computational results of other investigators. In addition, the sensitivity of these flow fields to a number of geometric parameters is studied, and the impact of these flows on inlet performance is assessed.
A collisionless quasi-parallel shock is simulated by Monte Carlo techniques. The scattering of all velocity particles from thermal to high energy is assumed to occur so that the mean free path is directly proportional to velocity times the mass-to-charge-ratio, and inversely proporational to the plasma density. The shock profile and velocity spectra are obtained, showing preferential acceleration of high A/Z particles relative to protons. The inclusion of the back pressure of the scattering particles on the inflowing plasma produces a smoothing of the shock profile, which implies that the spectra are steeper than for a discontinuous shock.
The far-field sound produced by a rigid body in arbitrary motion, with shock discontinuities close to the body, is studied. The analysis is based on the work of Ffowcs Williams and Hawkings (1969). An expression for the far-field sound pressure is obtained in the form of surface and line integrals carried out over a contracting sphere and its intersection with the body and shock surfaces. It is also found that in addition to the quadrupole distribution, the discontinuities in Lighthill stress at the shock, the fluid stresses at the body surface, and the curvatures (principal and mean) of the body and shock surfaces contribute to the sound field. Two examples are worked out.
Cosmic-ray transport near discontinuities in the background fluid velocity is considered. Matching conditions for the cosmic-ray distribution are derived for both shear and compressive (shock) discontinuities, keeping terms to second order in the ratio of fluid speed to energetic-particle speed. Acceleration is found at shear discontinuities, which is not present in the first-order theory, and a modification of the matching condition at shocks. If there is no particle source concentrated at a shock, the new condition reduces to that obtained from first-order theory. Monte Carlo simulations show good agreement with the theory.
A scramjet/airframe integration program and a technique for simulating thermally perfect scramjet exhaust flows (freon/argon gas blends) is studied to extend the technique to more complicated flows approaching the actual exhaust flow in complexity. The state of the flow and the accuracy of the substitute gas simulation are analyzed in the case of a shock discontinuity present. Findings are: scramjet exhaust flow is essentially frozen throughout the expansion at Mach 6 and Mach 8; flow behind moderate shocks remains frozen; the technique can accurately track static distributions in scramjet exhaust flows (shocked or unshocked).
This paper presents a new computational method for the calculation of discontinuous solutions of hyperbolic systems of conservation laws, which deal effectively with both shock and contact discontinuities. The method consists of two stages: in the first stage a standard finite-difference scheme is hybridized with a nonoscillatory first order accurate method to provide for the monotonic variation of the solution near discontinuities, and in the second stage artificial compression is applied to sharpen transitions at discontinuities. This modification of a standard finite-difference method results in a scheme which preserves the order of truncation error of the original method and yet yields a sharp and oscillation free transition for both shocks and contact discontinuities. The modification can be easily implemented in existing computer codes.
The temporal evolution of the solar wind from one steady state to another is explored when momentum deposition produces multiple critical points in the flow. It is shown that the wind always evolves in time to a new steady state compatible with the solution of the steady state equation of motion. However, for the same initial state and identical asymptotic momentum deposition rate, the temporal evolution pattern of the wind depends on the detailed time history of momentum addition and is therefore not unique. This feature plays an important role in the particular case when multiple (three in this study) steady states exist for identical boundary conditions; each one of these solutions is thus shown to be physically accessible. The details of the temporal evolution pattern of the wind reveal the formation of a shock discontinuity whenever the flow becomes supersonic at a critical point upstream from the initial critical point. If the flow remains supersonic at that inner critical point, the shock can become a standing one, depending on the strength and the temporal history of momentum addition. The results of this study indicate that the time scale required for the solar wind to evolve between steady states is of the order of 30-60 hours. Furthermore, the results also reveal the interesting and novel phenomenon that a standing shock is likely to develop in the inner solar wind flow within this time frame, in particular, in coronal hole regions with rapidly diverging geometries.
Experiments in weak-shock dynamics were conducted using a 17-in. diameter shock tube. Weak shocks were generated in air by a compressed nitrogen driver gas; the incident shock waves were brought to a focus by reflecting them from concave cylindrical reflectors at the endwall of the tube. It was found that the behavior of a shock discontinuity at a focus is determined by nonlinear gasdynamic processes. Consideration is also given to nonlinear resonance phenomena, i.e., phenomena associated with oscillatory motion in ducts, with amplitude so large that weak shocks occur. Attention is given to nonlinear resonance in open and closed tubes and to thermal and relaxation effects.
Maximizing both accuracy and efficiency has been the primary objective in designing a numerical algorithm for computational fluid dynamics (CFD). This is especially important for solutions of complex three dimensional systems of Navier-Stokes equations which often include turbulence modeling and chemistry effects. Recently, upwind schemes have been well received for their capability in resolving discontinuities. With this in mind, presented are two new flux splitting techniques for upwind differencing. The first method is based on High-Order Polynomial Expansions (HOPE) of the mass flux vector. The second new flux splitting is based on the Advection Upwind Splitting Method (AUSM). The calculation of the hypersonic conical flow demonstrates the accuracy of the splitting in resolving the flow in the presence of strong gradients. A second series of tests involving the two dimensional inviscid flow over a NACA 0012 airfoil demonstrates the ability of the AUSM to resolve the shock discontinuity at transonic speed. A third case calculates a series of supersonic flows over a circular cylinder. Finally, the fourth case deals with tests of a two dimensional shock wave/boundary layer interaction.
This report provides a user guide for the Compressible Flow Toolbox, a collection of algorithms that solve almost 300 linear and nonlinear classical compressible flow relations. The algorithms, implemented in the popular MATLAB programming language, are useful for analysis of one-dimensional steady flow with constant entropy, friction, heat transfer, or shock discontinuities. The solutions do not include any gas dissociative effects. The toolbox also contains functions for comparing and validating the equation-solving algorithms against solutions previously published in the open literature. The classical equations solved by the Compressible Flow Toolbox are: isentropic-flow equations, Fanno flow equations (pertaining to flow of an ideal gas in a pipe with friction), Rayleigh flow equations (pertaining to frictionless flow of an ideal gas, with heat transfer, in a pipe of constant cross section.), normal-shock equations, oblique-shock equations, and Prandtl-Meyer expansion equations. At the time this report was published, the Compressible Flow Toolbox was available without cost from the NASA Software Repository.
Time-accurate computational fluid dynamics (CFD) algorithms are among the basic requirements as an engineering or research tool for realistic simulations of transient combustion phenomena, such as combustion instability, transient start-up, etc., inside the rocket engine combustion chamber. A time-accurate pressure based method is employed in the FDNS code for combustion model development. This is in connection with other program development activities such as spray combustion model development and efficient finite-rate chemistry solution method implementation. In the present study, a second-order time-accurate time-marching scheme is employed. For better spatial resolutions near discontinuities (e.g., shocks, contact discontinuities), a 3rd-order accurate TVD scheme for modeling the convection terms is implemented in the FDNS code. Necessary modification to the predictor/multi-corrector solution algorithm in order to maintain time-accurate wave propagation is also investigated. Benchmark 1-D and multidimensional test cases, which include the classical shock tube wave propagation problems, resonant pipe test case, unsteady flow development of a blast tube test case, and H2/O2 rocket engine chamber combustion start-up transient simulation, etc., are investigated to validate and demonstrate the accuracy and robustness of the present numerical scheme and solution algorithm.
Considerable progress over the past thirty years has been made in the development of large-scale computational fluid dynamics (CFD) solvers for the Euler and Navier-Stokes equations. Computations are used routinely to design the cruise shapes of transport aircraft through complex-geometry simulations involving the solution of 25-100 million equations; in this arena the number of wind-tunnel tests for a new design has been substantially reduced. However, simulations of the entire flight envelope of the vehicle, including maximum lift, buffet onset, flutter, and control effectiveness have not been as successful in eliminating the reliance on wind-tunnel testing. These simulations involve unsteady flows with more separation and stronger shock waves than at cruise. The main reasons limiting further inroads of CFD into the design process are: (1) the reliability of turbulence models; and (2) the time and expense of the numerical simulation. Because of the prohibitive resolution requirements of direct simulations at high Reynolds numbers, transition and turbulence modeling is expected to remain an issue for the near term. The focus of this paper addresses the latter problem by attempting to attain optimal efficiencies in solving the governing equations. Typically current CFD codes based on the use of multigrid acceleration techniques and multistage Runge-Kutta time-stepping schemes are able to converge lift and drag values for cruise configurations within approximately 1000 residual evaluations. An optimally convergent method is defined as having textbook multigrid efficiency (TME), meaning the solutions to the governing system of equations are attained in a computational work which is a small (less than 10) multiple of the operation count in the discretized system of equations (residual equations). In this paper, a distributed relaxation approach to achieving TME for Reynolds-averaged Navier-Stokes (RNAS) equations are discussed along with the foundations that form the basis of this approach. Because the governing equations are a set of coupled nonlinear conservation equations with discontinuities (shocks, slip lines, etc.) and singularities (flow- or grid-induced), the difficulties are many. This paper summarizes recent progress towards the attainment of TME in basic CFD simulations.