Engineering Papers⌕ Search

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.

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

At least 757 records · Page 42
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Diffraction of a shock wave by a compression corner. I - Regular reflection

The unsteady, two-dimensional flowfield resulting from the interaction of a moving planar shock wave with a compression corner is determined using a second-order, discontinuity-fitting, finite-difference approach. The time-dependent Euler equations are transformed to normalize the distance between the body and peripheral shock and to include the existing self-similar property of the flow. The resulting set of partial differential equations in conservation-law form is then solved in a time-dependent fashion using MacCormack's scheme. The vortical singularity, which lies on the body surface, and the single reflected shock are both treated as discontinuities in the numerical procedure. The results of the numerical simulation compare quite favorably with existing experimental interferograms and yield better flowfield resolution than previous first-order, shock-capturing, numerical solutions.

Kutler, P.↗
NASA NTRS1977

An implicit factored scheme for the compressible Navier-Stokes equations

An implicit finite difference scheme is developed for the numerical solution of the compressible Navier-Stokes equations in conservation-law form. The algorithm is second-order-time accurate, noniterative, and spatially factored. In order to obtain an efficient factored algorithm, the spatial cross-derivatives are evaluated explicitly. However, the algorithm is unconditionally stable and, although a three-time-level scheme, requires only two-time-levels of data storage. The algorithm is constructed in a 'delta' form (i.e., increments of the conserved variables and fluxes) that provides a direct derivation of the scheme and leads to an efficient computational algorithm. In addition, the delta form has the advantageous property of a steady-state (if one exists) independent of the size of the time step. Numerical results are presented for a two-dimensional shock boundary-layer interaction problem.

Beam, R. M.↗
NASA NTRS1978

Prediction of plasma properties in mercury ion thrusters

A simplified theoretical model was developed which obtains to first order the plasma properties in the discharge chamber of a mercury ion thruster from basic thruster design and controllable operating parameters. The basic operation and design of ion thrusters is discussed, and the important processes which influence the plasma properties are described in terms of the design and control parameters. The conservation for mass, charge and energy were applied to the ion production region, which was defined as the region of the discharge chamber having as its outer boundary the surface of revolution of the innermost field line to intersect the anode. Mass conservation and the equations describing the various processes involved with mass addition and removal from the ion production region are satisfied by a Maxwellian electron density spatial distribution in that region.

Longhurst, G. R.↗
NASA NTRS1979

Numerical simulation of steady supersonic viscous flow

A noniterative, implicit, space-marching, finite-difference algorithm is developed for the steady thin-layer Navier-Stokes equations in conservation-law-form. The numerical algorithm is applicable to steady supersonic viscous flow over bodies of arbitrary shape. In addition, the same code can be used to compute supersonic inviscid flow or three-dimensional boundary layers. Computed results from two-dimensional and three-dimensional versions of the numerical algorithm are in good agreement with those obtained from more costly time-marching techniques.

Schiff, L. B.↗
NASA NTRS1980

Acoustic behavior of fibrous bulk materials

A semiempirical model of the acoustic behavior of fibrously constructed bulk materials of Hersh and Walker (1979) is generalized to take into account the filtration or removal of particles by fibrous mats and heat conduction between the material fibers and the surrounding fluid. Equations governing the propagation and attenuation of sound waves in a fibrous material are derived on the basis of a solution of the Navier Stokes equation for momentum conservation and a one-dimensional model of heat transfer between the sound field and the fibers. A comparison of the two propagation constants and material impedance specified by the model and experimental measurements for Kevlar 29 indicates the accuracy of the model over a wide range of sound frequencies, material porosities and specimen thickness. It is also found that heat transfer effects are relatively unimportant, while the attenuation constants and material characteristic impedance are a function of fiber orientation relative to sound field propagation direction.

Hersh, A. S.↗
NASA NTRS1981

Numerical simulation of steady supersonic flow

A noniterative, implicit, space-marching, finite-difference algorithm was developed for the steady thin-layer Navier-Stokes equations in conservation-law form. The numerical algorithm is applicable to steady supersonic viscous flow over bodies of arbitrary shape. In addition, the same code can be used to compute supersonic inviscid flow or three-dimensional boundary layers. Computed results from two-dimensional and three-dimensional versions of the numerical algorithm are in good agreement with those obtained from more costly time-marching techniques.

Schiff, L. B.↗
NASA NTRS1982

Finite difference methods for the solution of unsteady potential flows

Various problems which are confronted in the development of an unsteady finite difference potential code are reviewed mainly in the context of what is done for a typical small disturbance and full potential method. The issues discussed include choice of equations, linearization and conservation, differencing schemes, and algorithm development. A number of applications, including unsteady three dimensional rotor calculations, are demonstrated.

Caradonna, F. X.↗
NASA NTRS1982

Computations of transonic flow over an oscillating airfoil with shock-induced separation

A numerical study is presented on unsteady transonic flow over an airfoil in pitching oscillation at a moderately high incidence. The study was focused on the effects of unsteady shock-wave/boundary-layer interactions and subsequent flow separations. An implicit finite-difference scheme was used to solve the full time-dependent compressible Navier-Stokes equations in conservation-law form. The algorithm adopted for this study is the Beam-Warming spatially factored scheme. It is, however, constructed in a body-fitted curvilinear coordinate system for efficient unsteady flow computations. The computational results are compared with experimental data measured in the Ames 11- by 11-Foot Transonic Wind Tunnel.

Chyu, W. J.↗
NASA NTRS1983

A viscous shock-layer flowfield analysis by an explicit-implicit method

An implicit analogue of a widely used explicit method to external axisymmetric laminar flows with strong entropy gradients is extended. The details of the "numerics" of the implicit part are provided in a body oriented coordinate system with a moving outer (shock) boundary during the transient part of the solutions. The limiting values of the Courant number are obtained when the shock boundary is treated explicitly. The solution algorithm outlined includes the treatment of the source term associated with the equations in weak conservation form. From the results obtained for two sample problems, it becomes clear that accuracy of predictions is, indeed, very good at higher values of the Courant number. There is a significant saving in overall computing time, depending on the Courant number used and the flow Reynolds number. These properties combined with the simplicity of programming the implicit analog may appeal to researchers for using it in the analysis of 3-D flow problems.

Gupta, R. M.↗
NASA NTRS1983

Numerical analysis of a scramjet inlet flow field using the three-dimensional Navier-Stokes equations

A computer program has been developed to analyze supersonic combustion ramjet (scramjet) inlet flow fields. The program solves the three-dimensional Euler or Navier-Stokes equations in full conservation form by a well-known explicit, predictor-corrector technique. Turbulence is modeled by an algebraic eddy-viscosity model. Detailed laminar and turbulent flow results are presented for a symmetric wedge corner and a comparison is made with the available experimental results to allow assessment of the program. Results are then presented for an actual scramjet inlet configuration.

Kumar, A.↗
NASA NTRS1983

A theory of nondilute spray evaporation based upon multiple drop interactions

Drop interactions, changes in drop temperature, and the evolution of the ambient conditions due to heating and evaporation were taken into account in a theory of drop evaporation. A sphere of influence is defined for each drop, with all droplets having equal separation distances. Global conservation and state equations for a droplet spray are formulated, together with equations for single drop evaporation in finite surroundings. A criterion is defined for complete evaporation and the dynamics of spray evaporation are discussed. The theory is noted to be applicable for both dilute and nondilute spray evaporation effects.

Bellan, J.↗
NASA NTRS1983

Viscous shock-layer flowfield analysis by an explicit-implicit method

The present work extends the recently reported implicit analogue of MacCormack's earlier widely-used explicit method to external axisymmetric laminar flows with strong entropy gradients. The details of the 'numerics' of the implicit part are provided in a body-oriented coordinate system with a moving outer (shock) boundary during the transient part of the solutions. The limiting values of the Courant number are obtained when the shock boundary is treated explicitly. The solution algorithm outlined includes the treatment of the source term associated with the equations in weak conservation form. From the results obtained for two sample problems, it becomes clear that accuracy of predictions is, indeed, very good at higher values of the Courant number. There is a significant saving in overall computing time, depending on the Courant number used and the flow Reynolds number. These properties combined with the simplicity of programming the implicit analogue may appeal to researchers for using it in the analysis of three-dimensional flow problems.

Gupta, R. N.↗
NASA NTRS1983

A model to determine open or closed cellular convection

The horizontal asymmetry of cellular convection is demonstrated to be detectable by consideration of the vertical asymmetry of the driving force. A two-dimensional numerical model for convection in an internally heated and cooled fluid is presented, based on equations for the conservation of temperature and vorticity. Attention is focused on the steady-state finite-amplitude solutions for fixed Rayleigh number, Prandtl number, and aspect ratio. Temperature in the model corresponds to potential temperature under dry conditions and the equivalent potential temperature under saturated conditions. Slowly varying convection driven by asymmetric boundary fluxes is expressed in terms of steady-state convection driven by an asymmetric internal heat source. It is shown that heating near the ground produces open convection patterns where most of the fluid is descending, while cooling near the top of the flow leads to closed cellular patterns with a preponderance of ascending fluid. Extension of the model to three dimensions is indicated.

Helfand, H. M.↗
NASA NTRS1983

Application of a full potential method for predicting supersonic flow fields and aerodynamic characteristics

A nonlinear aerodynamic prediction technique which solves the conservative full potential equation has been applied to the analysis of three waverider configurations. This technique was selected based on its capability to analyze the off-design characteristics of the waveriders. Very good correlations were achieved with surface pressure data for both the Mach 4 elliptic cone waverider and the Mach 6 caret-wing derivative. Off-design Mach number and angle-of-attack pressure correlations were very good for the elliptic cone waverider. The range of correlation with data exceeded that expected based on the theory limitations. A surface pressure integration routine was demonstrated and agreement between predicted aerodynamic forces and experimental force data for the Mach 4 waverider was excellent. Analysis of a nonconical waverider configuration was initiated where a discrete input option is used to achieve the computational gridding. Preliminary analysis of this configuration indicates the correct shock location will be predicted.

Jones, K. M.↗
NASA NTRS1984

Transonic flow calculations using a flux vector splitting method for the Euler equations

A study of the flux vector splitting method of Steger and Warming for the solution of the time dependent Euler equations in strong conservation law form for arbitrary two-dimensional geometries is presented. The procedure employed here differs from that of Buning and Steger in that it uses a different algorithm and employs implicit boundary conditions. Moreover, the method, as implemented here, does not contain any explicit smoothing or any adjustable parameters. Calculations were carried out for an NACA 0012 airfoil at various Mach numbers and angles of attack, and cylinders. Steady symmetric solutions were obtained for the full cylinder at a freestream Mach number of .5 without imposing a symmetry condition. In general, good agreement with other methods was obtained.

Seaford, C. M.↗
NASA NTRS1985

A space-marching method for incompressible Navier-Stokes equations

This paper deals with the development of a space-marching method for incompressible flows. The method solves the continuity and momentum equations as a coupled system at each streamwise station. The character of the system of equations has been changed from elliptic to hyperbolic/parabolic in order to enable the equations to be marched in space. The present method has many advantages compared to the existing parabolic or space-marching methods for incompressible flow: (1) it avoids the solution of Poisson equations, (2) it conserves the mass flow with no additional computation, (3) it does not require the specification of an assumed pressure field when used in the prediction of duct flows. The present method can capture strong secondary velocities and strong transverse pressure gradients. Predictions of the flow through straight and curved ducts are in good agreement with analytical and experimental results.

Pouagare, M.↗
NASA NTRS1985

Results of the SPAS-01 RCS plume impingement test

The Orbiter RCS flowfield is modeled in the free molecular region and an impingement analysis is performed to characterize on-orbit plume interactions with nearby bodies, such as the SPAS-01 satellite. The flow in the far field is treated with a source flow model at any point 40 ft from the nozzle. Impingement is calculated according to Newtonian impact theory. The flow density in the far field is expressed in terms of a conservation of energy equation, with account taken of the expansion of the gas, cooling, and the angular distribution. The SPAS-01 platform gathered data at eight different positions around the Orbiter to test the model predictions. Excellent agreement was obtained in predictions of the torque and rotation rate induced on the SPAS by firing the thrusters.

Lazaron, M. P.↗
NASA NTRS1985

Numerical simulation of flow through scramjet inlets using a three-dimensional Navier-Stokes code

A three-dimensional Reynolds-averaged Navier-Stokes code has been used to numerically analyze flow through a two-strut, supersonic combustion ramjet (scramjet) inlet configuration. It solves the governing equations in full conservation form using either the fully explicit or explicit-implicit method due to MacCormack. An algebraic two-layer eddy viscosity model is used for turbulent flow calculations. The analysis allows inclusion of end effects which are caused by the aft placement of the cowl on the underside of the inlet. A special grid has been developed to accommodate the struts embedded in the inlet flow field. Detailed numerical results are presented here for the two-strut configuration, and a comparison is made with the available experimental results.

Kumar, A.↗