SEARCH · Engineering Papers

Results for “Conservation equations”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9

All sources NASA NTRS DOE OSTI

DOE OSTI2020

Generalized Kompaneets formalism for inelastic neutrino-nucleon scattering in supernova simulations

Based on the Kompaneets approximation, we develop a robust methodology to calculate spectral redistribution via inelastic neutrino-nucleon scattering in the context of core-collapse supernova simulations. The resulting equations conserve lepton number to machine precision and scale linearly, not quadratically, with number of energy groups. The formalism also provides an elegant means to derive the rate of energy transfer to matter which, as it must, automatically goes to zero when the neutrino radiation field is in thermal equilibrium. Furthermore, we derive the next higher order in $ϵ/mc^2$ correction to the neutrino Kompaneets equation. Unlike other Kompaneets schema, ours also generalizes to the case of anisotropic angular distributions, while retaining the conservative form that is a hallmark of the classical Kompaneets equation. In this work, our formalism enables immediate incorporation into supernova codes that follow the spectral angular moments of the neutrino radiation fields.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1971

A numerical solution of the Navier-Stokes equations for supercritical fluid thermodynamic analysis

An explicit numerical solution of the compressible Navier-Stokes equations is applied to the thermodynamic analysis of supercritical oxygen in the Apollo cryogenic storage system. The wave character is retained in the conservation equations which are written in the basic fluid variables for a two-dimensional Cartesian coordinate system. Control-volume cells are employed to simplify imposition of boundary conditions and to ensure strict observance of local and global conservation principles. Non-linear real-gas thermodynamic properties responsible for the pressure collapse phenomonon in supercritical fluids are represented by tabular and empirical functions relating pressure and temperature to density and internal energy. Wall boundary conditions are adjusted at one cell face to emit a prescribed mass flowrate. Scaling principles are invoked to achieve acceptable computer execution times for very low Mach number convection problems. Detailed simulations of thermal stratification and fluid mixing occurring under low acceleration in the Apollo 12 supercritical oxygen tank are presented which model the pressure decay associated with de-stratification induced by an ordinary vehicle maneuver and heater cycle operation.

Heinmiller, P. J.↗

NASA NTRS1973

Prediction of free shear flows: A comparison of the performance of six turbulence models

The performance is evaluated of three distinct classes of turbulence model. These classes are: (1) Turbulent-viscosity models in which the length scale of turbulence is found by way of algebraic formulas, (2) turbulent-viscosity models in which the length scale of turbulence is found from a partial differential equation of transport, and (3) models in which the shear stress itself is the dependent variable of a partial differential conservation equation. Two models were examined in each class; thus, six different models were tested. A complete mathematical statement of these models is provided and a brief commentary on the models is included.

Launder, B. E.↗

NASA NTRS1992

Unsteady transonic Euler solutions using finite elements

A finite element solution of the unsteady Euler equations is presented and demonstrated for 2D airfoil configurations oscillating in transonic flows. Computations are performed by spatially discretizing the conservation equations using the Galerkin weighted residual method and then employing a multistage Runge-Kutta scheme to march forward in time. A mesh deformation scheme has been developed to efficiently move interior points in a smooth fashion as the airfoil undergoes rigid body pitch and plunge motion. Both steady and unsteady results are presented, and a comparison is made with solutions obtained using finite-volume techniques. The effects of using either a lumped or consistent mass matrix are presented; the finite element method provides an accurate solution for unsteady transonic flows about isolated airfoils.

Davis, Gary A.↗

NASA NTRS1972

Further analytical study of hybrid rocket combustion

Analytical studies of the transient and steady-state combustion processes in a hybrid rocket system are discussed. The particular system chosen consists of a gaseous oxidizer flowing within a tube of solid fuel, resulting in a heterogeneous combustion. Finite rate chemical kinetics with appropriate reaction mechanisms were incorporated in the model. A temperature dependent Arrhenius type fuel surface regression rate equation was chosen for the current study. The governing mathematical equations employed for the reacting gas phase and for the solid phase are the general, two-dimensional, time-dependent conservation equations in a cylindrical coordinate system. Keeping the simplifying assumptions to a minimum, these basic equations were programmed for numerical computation, using two implicit finite-difference schemes, the Lax-Wendroff scheme for the gas phase, and, the Crank-Nicolson scheme for the solid phase.

Hung, W. S. Y.↗

NASA NTRS1984

High altitude chemically reacting gas particle mixtures. Volume 1: A theoretical analysis and development of the numerical solution

The overall contractual effort and the theory and numerical solution for the Reacting and Multi-Phase (RAMP2) computer code are described. The code can be used to model the dominant phenomena which affect the prediction of liquid and solid rocket nozzle and orbital plume flow fields. Fundamental equations for steady flow of reacting gas-particle mixtures, method of characteristics, mesh point construction, and numerical integration of the conservation equations are considered herein.

Smith, S. D.↗

NASA NTRS1988

Preshock region acceleration of implanted cometary H(+) and O(+)

A self-consistent, three-fluid model of plasma transport and implanted ion acceleration in the unshocked solar wind is presented. The solar wind plasma is depleted by charge exchange with the expanding cometary exosphere, while implanted protons and heavy ions are produced by photoionization and charge transfer and lost by charge exchange. A generalized transport equation describing convection, adiabatic and diffusive velocity change, and the appropriate production terms is used to describe the evolution of the two cometary ion components, while the moments of the Boltzmann equation are used to calculate the solar wind density and pressure. The flow velocity is obtained self-consistently by combining the conservation equations of the three ion species. The results imply that second-order Fermi acceleration can explain the implanted spectra observed in the unshocked solar wind. Comparison of measured and calculated distribution indicates that spatial diffusion of implanted ions probably plays an important role in forming the energetic particle environment in the shock vicinity.

Gombosi, Tamas I.↗

NASA NTRS1990

Gust response analysis for cascades operating in nonuniform mean flows

The linearized unsteady aerodynamic response of a cascade of airfoils subjected to entropic, vortical, and acoustic gusts is analyzed. Field equations for the first-order unsteady perturbation flow are obtained by linearizing the full time-dependent mass, momentum, and energy conservation equations about a nonlinear, isentropic, and irrotational mean or steady flow. A splitting technique is then used to decompose the unsteady velocity field into irrotational and rotational parts leading to field equations for the unsteady entropy, rotational velocity, and irrotational velocity fluctuations that are coupled only sequentially. The entropic and rotational velocity fluctuations can be described in terms of the mean-flow drift and stream functions which can be computed numerically. The irrotational unsteady velocity is described by an inhomogeneous linearized potential equation which contains a source term that depends on the rotational velocity field. This equation is solved via a finite difference technique. Results are presented to indicate the status of the numerical solution procedure and to demonstrate the impact of blade geometry and mean blade loading on the aerodynamic response of cascades to vortical gust excitations. The analysis described leads to very efficient predictions of cascade unsteady aerodynamic phenomena making it useful for turbomachinery aeroelastic and aeroacoustic design applications.

Hall, Kenneth C.↗

NASA NTRS1991

Gust response analysis for cascades operating in nonuniform mean flows

The linearized unsteady aerodynamic response of a cascade of airfoils subjected to entropic, vortical, and acoustic gusts is analyzed. Field equations for the first-order unsteady perturbation flow are obtained by linearizing the full time-dependent mass, momentum, and energy conservation equations about a nonlinear, isentropic, and irrotational mean or steady flow. A splitting technique is then used to decompose the unsteady velocity field into irrotational and rotational parts leading to field equations for the unsteady entropy, rotational velocity, and irrotational velocity fluctuations that are coupled only sequentially. The entropic and rotational velocity fluctuations can be described in terms of the mean-flow drift and stream functions which can be computed numerically. The irrotational unsteady velocity is described by an inhomogeneous linearized potential equation which contains a source term that depends on the rotational velocity field. This equation is solved via a finite difference technique. Results are presented to indicate the status of the numerical solution procedure and to demonstrate the impact of blade geometry and mean blade loading on the aerodynamic response of cascades to vortical gust excitations. The analysis described leads to very efficient predictions of cascade unsteady aerodynamics phenomena making it useful for turbomachinery aeroelastic and aeroacoustic design applications.

Hall, Kenneth C.↗

NASA NTRS1997

Combined Numerical/Analytical Perturbation Solutions of the Navier-Stokes Equations for Aerodynamic (Ejector Nozzle) Flows

In spite of the rapid advances in both scalar and parallel computational tools, the large number and breadth of variables involved in aerodynamic systems make the use of parabolized or even boundary layer fluid flow models impractical for both preliminary design and inverse design problems. Given this restriction, we have concluded that reduced or approximate models are an important family of tools for design purposes. This study of a combined perturbation/numerical modeling methodology with an application to ejector-mixer nozzles (shown schematically in the following figure) is nearing completion. The work is being funded by a grant from the NASA Lewis Research Center to Texas A&M University. These ejector-mixer nozzle models are designed to be of use to the High Speed Civil Transport Program and may be adopted by both NASA and industry. A computer code incorporating the ejector-mixer models is under development. This code, the Differential Reduced Ejector/Mixer Analysis (DREA), can be run fast enough to be used as a subroutine or to be called by a design optimization routine. Simplified conservation equations--x-momentum, energy, and mass conservation--are used to define the model. Unlike other preliminary design models, DREA requires minimal empirical input and includes vortical mixing and a fully compressible formulation among other features. DREA is being validated by comparing it with results obtained from open literature and proprietary industry data. Preliminary results for a subsonic ejector and a supersonic ejector are shown. In addition, dedicated experiments have been performed at Texas A&M. These experiments use a hydraulic/gas flow analog to provide information about the inviscid mixing interface structure. Final validation and documentation of this work is expected by May of 1997. However, preliminary versions of DREA can be expected in early 1997. In summary, DREA provides a sufficiently detailed and realistic ejector-mixer nozzle model at a computational cost compatible with preliminary design applications.

DeChant, Lawrence J.↗

NASA NTRS1990

Flowfield computation of entry vehicles

The equations governing the multidimensional flow of a reacting mixture of thermally perfect gasses were derived. The modeling procedures for the various terms of the conservation laws are discussed. A numerical algorithm, based on the finite-volume approach, to solve these conservation equations was developed. The advantages and disadvantages of the present numerical scheme are discussed from the point of view of accuracy, computer time, and memory requirements. A simple one-dimensional model problem was solved to prove the feasibility and accuracy of the algorithm. A computer code implementing the above algorithm was developed and is presently being applied to simple geometries and conditions. Once the code is completely debugged and validated, it will be used to compute the complete unsteady flow field around the Aeroassist Flight Experiment (AFE) body.

Prabhu, Dinesh K.↗

NASA NTRS1994

Can a variable alpha induce limit cycle behavior and exponential luminosity decay in transient soft x ray sources?

There has been, recently, a revival of the stability problem of accretion disks. Much of this renewed interest is due to recent observational data on transient soft X-ray novae, which are low-mass X-ray binaries. It is widely believed that nonsteady mass transfer from the secondary onto the compact primary, through an accretion disk, is the reason for the observed spectacular events in the form of often repetitive outbursts, with recurrence times ranging from 1 to 60 yr and duration time on the scale of months. Though not having reached yet a consensus about the nature of the mechanism that regulates the mass transfer, the disk thermal instability model seems to be favored by the fact that the rise in the hard X-ray luminosity is prior to the rise in the soft X-ray luminosity, while the mass transfer instability model seems to be hindered by the fact that the luminosity during quiescence is unable to trigger the thermal instability. However, it should be stressed that, remarkably, the X-ray light curves of these X-ray novae all show overall exponential decays, a feature quite difficult to reproduce in the framework of the viscous disk model, which yields powerlike luminosity decay. Taking into account this observational constraint, we have studied the temporal evolution of perturbations in the accretion rate, under the assumption that alpha is radial and parameter dependent. The chosen dependence is such that the model can reproduce limit cycle behavior (the system is locally unstable but globally stable). However, the kind of dependence we are looking for in alpha does not allow us to use the usual Shakura and Sunyaev procedure in the sense that we no longer can obtain a linearized continuity equation without explicit dependence on the accretion rate. This is so because now we cannot eliminate the accretion rate by using the angular momentum conservation equation.

Meirellesfilho, C.↗

NASA NTRS1985

Flow structure capturing on overset patched meshes

The present paper describes the application of a simple, robust stable implicit approach to solutions of the conservative equations of gasdynamics on either composite or overset meshes to capture flow structures such as shocks with high resolution in complex geometric domains. Without requiring special flux conservative operators, but rather, interpolating conservative variable data at mesh boundaries, the well posed upwind method provides accurate and oscillation free solutions, even when shocks cross the interior patch boundaries. In three problems with flow complexities that require grid refinement, the paper demonstrates the capability to conveniently carry out for gasdynamics the adaptive refined meshing strategy in overset patches proposed by Berger and Oliger (1984), and it extends this technique to rapidly convergent implicit methods for the Euler and Navier-Stokes equations. The numerical experiments show concretely, in a realistic aerodynamic problem, the savings in mesh points (about an order of magnitude here in two dimensions) for similar accuracy that flow structure aligned adaptive patched meshing affords compared to uniform grid refinement.

Venkatapathy, E.↗

NASA NTRS1991

Nonequilibrium thermo-chemical calculations using a diagonal implicit scheme

A recently developed computer program for hypersonic vehicle flow analysis is described. The program uses a diagonal implicit algorithm to solve the equations of viscous flow for a gas in thermochemical nonequilibrium. The diagonal scheme eliminates the expense of inverting large block matrices that arise when species conservation equations are introduced. The program uses multiple zones of grids patched together and includes radiation wall and rarefied gas boundary conditions. Solutions are presented for hypersonic flows of air and hydrogen air mixtures.

Imlay, Scott T.↗

NASA NTRS1991

HANA - A three-dimensional Navier-Stokes code for chemically reacting flows

A recently developed computer program for analyzing chemically reacting flows is described. The program uses a diagonal implicit algorithm to solve the equations of viscous flow for a gas in thermochemical nonequilibrium. The diagonal scheme eliminates the expense of inverting large block matrices that arise when species conservation equations are introduced. The program uses multiple zones of grids patched together and includes a k-epsilon turbulence model. Solutions are presented for hypersonic flows of air, hypersonic flows of Martian atmospheric gases, combusting flows of hydrogen/air mixtures, and combusting flows of methane/air mixtures.

Imlay, Scott T.↗

NASA NTRS1979

Acoustic power balance in lined ducts

It is shown that the two common definitions of acoustic energy density and intensity in uniform unlined ducts carrying uniform flow are compatible to the extent that both energy densities can be used in an appropriate variational principle to derive the convected wave equation. When the duct walls are lined both energy densities must be modified to account for the wall energy density. This results in a new energy conservation equation which utilizes a modified definition of axial power and accounts for wall dissipation. Computations in specific cases demonstrate the validity of the modified acoustic energy relation.

Eversman, W.↗

DOE OSTI2020

Coupling solidification kinetics with phase-behavior computations in hydrodynamic simulations of high-pressure, dynamic-compression processes

In this study, we report a numerical scheme to integrate models for the kinetics of solidification processes together with phase-behavior computations in the context of continuum-scale hydrodynamic simulations. The objective of the phase-behavior computations is to determine the pressure and temperature, given the following three sets of inputs: (1) an appropriate equation of state to describe our system, (2) the phase fraction(s) produced by the kinetic models, (3) and the volume and internal energy obtained by solving the conservation equations that govern the hydrodynamic behavior. The kinetics are assumed to be governed by the Kolmogorov–Johnson–Mehl–Avrami equation, and the nucleation and growth rates that enter into that equation are functions of the pressure and temperature produced by the phase-behavior computations. Our formulation allows for the fluid and solid phases to be at different temperatures (thermal nonequilibrium) and pressures (arising from surface-tension-induced Laplace contributions). The formulation is presented in a fairly general setting that is independent of any particular material, although we demonstrate it in some examples related to high-energy-density science applications where materials are rapidly compressed to pressures exceeding several gigapascals in less than a microsecond. We conclude with a critical evaluation of our approach and provide suggestions for future work to improve the predictive capabilities and generality of the models.

42 ENGINEERING↗

NASA NTRS1991

Progress in the development of PDF turbulence models for combustion

A combined Monte Carlo-computational fluid dynamic (CFD) algorithm was developed recently at Lewis Research Center (LeRC) for turbulent reacting flows. In this algorithm, conventional CFD schemes are employed to obtain the velocity field and other velocity related turbulent quantities, and a Monte Carlo scheme is used to solve the evolution equation for the probability density function (pdf) of species mass fraction and temperature. In combustion computations, the predictions of chemical reaction rates (the source terms in the species conservation equation) are poor if conventional turbulence modles are used. The main difficulty lies in the fact that the reaction rate is highly nonlinear, and the use of averaged temperature produces excessively large errors. Moment closure models for the source terms have attained only limited success. The probability density function (pdf) method seems to be the only alternative at the present time that uses local instantaneous values of the temperature, density, etc., in predicting chemical reaction rates, and thus may be the only viable approach for more accurate turbulent combustion calculations. Assumed pdf's are useful in simple problems; however, for more general combustion problems, the solution of an evolution equation for the pdf is necessary.

Hsu, Andrew T.↗