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Mass injection effect on compressible three- dimensional laminar boundary layers analyzed for nonreacting gas, using conservation equations for flow velocity profiles
Ion and electron conservation equations used in analysis of instability of linear Hall current accelerator
The concept and theory of potential vorticity in drift wave turbulence are extended to the case of an inhomogeneous magnetic field. A one-field magnetic potential vorticity conserving equation is derived via the use of conservative gyrokinetics. The similarity between the corresponding systems for drift wave turbulence and shallow water theory is discussed in detail. Zonal flow physics in an inhomogeneous magnetic field is discussed. In particular, a Charney–Drazin type nonacceleration theorem is derived from the novel system, which conserves magnetic potential vorticity. Extensions of the turbulent equipartition theory to the transport of magnetic potential vorticity are proposed.
Changes to Program Laura (Langley Aerothermodynamic Upwind Relaxation Algorithm) are presented which enhance both stability and accuracy of the algorithm. A discussion of iteration/sweeping strategies and their relation to computer architectures is included to best exploit the capabilities of serial, vector, and parallel processor machines. Test cases for Mach 10 perfect gas flow and Mach 32 real gas flow in chemical nonequilibrium over a blunt, raked elliptic cone using the thin-layer Navier-Stokes equations are presented in order to demonstrate the current improved capabilities. Algorithm changes include the use of volume averaging, application of a symmetric total variation diminishing (TVD) scheme, and stronger interaction between the grid/shock alignment routine and the relaxation algorithm. Good comparisons with heat transfer and pitching moment data at three different angles of attack for the Mach 10 tests serve to further validate the present algorithm. Parameters are defined which control the coupling of the specie continuity equations with the solution of the mixture conservation equations. A discussion of the consequences involved in the choice of strong versus weak coupling is presented, and a sample nonequilibrium calculation on a fine grid over a full scale model of the Aeroassist Flight Experiment (AFE) demonstrates current capabilities.
This report outlines the development of a general purpose aerodynamic solver for compressible turbulent flows. Turbulent closure is achieved using either two equation or Reynolds stress transportation equations. The applicable equation set consists of Favre-averaged conservation equations for the mass, momentum and total energy, and transport equations for the turbulent stresses and turbulent dissipation rate. In order to develop a scheme with good shock capturing capabilities, good accuracy and general geometric capabilities, a multi-block cell centered finite volume approach is used. Viscous fluxes are discretized using a finite volume representation of a central difference operator and the source terms are treated as an integral over the control volume. The methodology is validated by testing the algorithm on both two and three dimensional flows. Both the two equation and Reynolds stress models are used on a two dimensional 10 degree compression ramp at Mach 3, and the two equation model is used on the three dimensional flow over a cone at angle of attack at Mach 3.5. With the development of this algorithm, it is now possible to compute complex, compressible high speed flow fields using both two equation and Reynolds stress turbulent closure models, with the capability of eventually evaluating their predictive performance.
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.
A combined experimental and detailed numerical study was conducted on the interaction between chemically inert solid particles and strained, atmospheric methane/air and propane/air laminar flames, both premixed and non-premixed. Experimentally, the opposed jet configuration was used with the addition of a particle seeder capable of operating in conditions of varying gravity. The particle seeding system was calibrated under both normal and micro gravity and a noticeable gravitational effect was observed. Flame extinction experiments were conducted at normal gravity by seeding inert particles at various number densities and sizes into the reacting gas phase. Experimental data were taken for 20 and 37 (mu) nickel alloy and 25 and 60 (mu) aluminum oxide particles. The experiments were simulated by solving along the stagnation streamline the conservation equations of mass, momentum, energy, and species conservation for both phases, with detailed descriptions of chemical kinetics, molecular transport, and thermal radiation. The experimental data were compared with numerical simulations, and insight was provided into the effects on extinction of the fuel type, equivalence ratio, flame configuration, strain rate. particle type. particle size. particle mass, delivery rate. the orientation of particle injection with respect to the flame and gravity. It was found that for the same injected solid mass, larger particles can result in more effective flame cooling compared to smaller particles, despite the fact that equivalent masses of the larger particles have smaller total surface area to volume ratio. This counter-intuitive finding resulted from the fact that the heat exchange between the two phases is controlled by the synergistic effect of the total contact area and the temperature difference between the two phases. Results also demonstrate that meaningful scaling of interactions between the two phases may not be possible due to the complexity of the couplings between the dynamic and thermal parameters of the problem.
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An integral method which has previously been applied to the hypersonic blunt body thermal problem is improved and extended to obtain downstream flux predictions and to improve stagnation predictions. To account for the effect of downstream conditions propagated upstream through the subsonic shock layer region, the normal momentum equation is solved simultaneously with the other governing conservation equations. The effects of viscosity, conduction, dissociation and ionization, nongray radiation, surface emissivity, and ablation are included. Illustrative results are presented for body models of hemispheres and a continuous curvature body which closely approximates a hemispherically blunted wide angle (60 half angle) cone. The atmospheric models are air and a 50% Co2-50% N mixture at low densities, which should be representative of the Martian or Venusian atmospheres.
A second-order model which predicts the modulation of turbulence in jets laden with uniform size solid particles or liquid droplets is discussed. The approach followed is to start from the separate momentum and continuity equations of each phase and derive two new conservation equations. The first is for the carrier fluid's kinetic energy of turbulence and the second for the dissipation rate of that energy. Closure of the set of transport equations is achieved by modeling the turbulence correlations up to a third order. The coefficients (or constants) appearing in the modeled equations are then evaluated by comparing the predictions with LDA-measurements obtained recently in a turbulent jet laden with 200 microns solid particles. This set of constants is then used to predict the same jet flow but laden with 50 microns solid particles. The agreement with the measurement in this case is very good.
A diagnostic study of the forcing of the Ferrel cell by eddy fluxes in the Northern Hemisphere is carried out. The quasi-geostrophic omega equation, and Oort and Rasmusson's (1971) data set, are used. The effects of condensation associated with the large scale motions are introduced to the omega equation by using the quasi-geostrophic moisture conservation equation. Thus, the dry static stability is replaced by a moist static stability, and the forcing of the Ferrel cell by eddy latent heat fluxes as well as sensible heat and momentum fluxes is included. Both effects tend to enhance the forcing of the Ferrel cell. The numerical analysis indicates that the effects are small in January, but in July the maximum vertical velocities are enhanced by about 30 percent.
Flow analyses have been performed to determine the nature of the three-dimensional flow field in the vicinity of the aft-most field joint of the Space Shuttle Redesigned Solid Rocket Motor (RSRM). Specific objectives included the quantification of the circumferential pressure and velocity gradients at the joint location which might be caused by the non-uniform erosion of the rubber inhibitor which protrudes from the wall into the flow field. Three-dimensional Navier-Stokes equations have been solved in conjunction with the conservation equation for the turbulence energy and the dissipation rate. The numerical predictions have been compared with the measurements from a 7.5 percent scale cold flow model of the redesigned solid rocket motor.
This study deals with the computational analysis of buoyancy-induced instability in the nearfield of an isothermal helium jet injected into quiescent ambient air environment. Laminar, axisymmetric, unsteady flow conditions were considered for the analysis. The transport equations of helium mass fraction coupled with the conservation equations of mixture mass and momentum were solved using a staggered grid finite volume method. The jet Richardson numbers of 1.5 and 0.018 were considered to encompass both buoyant and inertial jet flow regimes. Buoyancy effects were isolated by initiating computations in Earth gravity and subsequently, reducing gravity to simulate the microgravity conditions. Computed results concur with experimental observations that the periodic flow oscillations observed in Earth gravity subside in microgravity.
A computational model to study the stability characteristics of an evolving buoyant helium gas jet in ambient air environment is presented. Numerical formulation incorporates a segregated approach to solve for the transport equations of helium mass fraction coupled with the conservation equations of mixture mass and momentum using a staggered grid method. The operating parameters correspond to the Reynolds number varying from 30 to 300 to demarcate the flow dynamics in oscillating and non-oscillating regimes. Computed velocity and concentration fields were used to analyze the flow structure in the evolving jet. For Re=300 case, results showed that an instability mode that sets in during the evolution process in Earth gravity is absent in zero gravity, signifying the importance of buoyancy. Though buoyancy initiates the instability, below a certain jet exit velocity, diffusion dominates the entrainment process to make the jet non-oscillatory as observed for the Re=30 case. Initiation of the instability was found to be dependent on the interaction of buoyancy and momentum forces along the jet shear layer.
This paper deals with the computational analysis of buoyancy effects in the near field of an isothermal helium jet injected into quiescent ambient air environment. The transport equations of helium mass fraction coupled with the conservation equations of mixture mass and momentum were solved using a staggered grid finite volume method. Laminar, axisymmetric, unsteady flow conditions were considered for the analysis. An orthogonal system with non-uniform grids was used to capture the instability phenomena. Computations were performed for Earth gravity and during transition from Earth to different gravitational levels. The flow physics was described by simultaneous visualizations of velocity and concentration fields at Earth and microgravity conditions. Computed results were validated by comparing with experimental data substantiating that buoyancy induced global flow oscillations present in Earth gravity are absent in microgravity. The dependence of oscillation frequency and amplitude on gravitational forcing was presented to further quantify the buoyancy effects.
The present paper revisits the derivation of the WKB approximation for small-amplitude magnetohydrodynamic waves, allowing for possible spatial variation of the background entropy. The equation of variation of wave amplitude is rederived; it is a bilinear equation which, it turns out, can be recast in the action conservation form. It is shown that this action conservation equation is in fact equivalent to the action conservation law obtained from Lagrangian treatments.
Coulomb collision is a fundamental diffusion process in plasmas that can be described by the Landau-Fokker-Planck (LFP) equation or the stochastic differential equation (SDE). While energy and momentum are conserved exactly in the LFP equation, they are conserved only on average by the conventional corresponding SDEs, suggesting that the underlying stochastic process may not be well defined by such SDEs. Here, in this study, we derive new SDEs with exact energy-momentum conservation for the Coulomb collision by factorizing the collective effect of field particles into individual particles and enforcing Newton's third law. These SDEs, when interpreted in the Stratonovich sense, have a particularly simple form that represents pure diffusion between particles without drag. To demonstrate that the new SDEs correspond to the LFP equation, we develop numerical algorithms that converge to the SDEs and preserve discrete conservation laws. Simulation results are presented in a benchmark of various relaxation processes.
Computer program solves time-dependent energy and state equations for gas reservoirs, using the solutions of conductor conservation equations as mass and energy rate changes to reservoirs.