Search NASA⌕ Search

SEARCH · Search NASA

Results for “Shock-capturing”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

Internal and external axial corner flows

The inviscid, internal, and external axial corner flows generated by two intersecting wedges traveling supersonically are obtained by use of a second-order shock-capturing, finite-difference approach. The governing equations are solved iteratively in conical coordinates to yield the complicated wave structure of the internal corner and the simple peripheral shock of the external corner. The numerical results for the internal flows compare favorably with existing experimental data.

Kutler, P.↗
NASA NTRS1975

Implicit approximate-factorization schemes for the low-frequency transonic equation

Two- and three-level implicit finite-difference algorithms for the low-frequency transonic small disturbance-equation are constructed using approximate factorization techniques. The schemes are unconditionally stable for the model linear problem. For nonlinear mixed flows, the schemes maintain stability by the use of conservatively switched difference operators for which stability is maintained only if shock propagation is restricted to be less than one spatial grid point per time step. The shock-capturing properties of the schemes were studied for various shock motions that might be encountered in problems of engineering interest. Computed results for a model airfoil problem that produces a flow field similar to that about a helicopter rotor in forward flight show the development of a shock wave and its subsequent propagation upstream off the front of the airfoil.

Ballhaus, W. F.↗
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 NTRS1976

Numerical solution of periodic transonic flow through a fan stage

A numerical method of solution of the inviscid, compressible, two-dimensional unsteady flow on a blade-to-blade stream surface through a stage (rotor and stator), or a single blade row, of an axial flow compressor or fan is described. A cyclic procedure has been developed for representation of adjacent blade-to-blade passages, which asymptotically achieves the correct phase between all passages of a stage. A shock-capturing finite-difference method is employed in the interior of the passage, and a method-of-characteristics technique is used at the boundaries. The blade slipstreams form two of the passage boundaries, and are treated as moving contact surfaces capable of supporting jumps in entropy and tangential velocity. The Kutta condition is imposed by requiring the slipstreams to originate at the trailing edges, which are assumed to be sharp. Results are presented for several transonic fan rotors, and compared with available experimental data consisting of holographic observations of shock structure and pressure contour maps. A subcritical stator solution is also compared with results from a relaxation method. Finally, a periodic solution for a stage consisting of 44 rotor blades and 46 stator blades is discussed.

Erdos, J. I.↗
NASA NTRS1976

Diffraction of a shock wave by a compression corner; regular and single Mach reflection

The two dimensional, time dependent Euler equations which govern the flow field resulting from the injection of a planar shock with a compression corner are solved with initial conditions that result in either regular reflection or single Mach reflection of the incident planar shock. The Euler equations which are hyperbolic are transformed to include the self similarity of the problem. A normalization procedure is employed to align the reflected shock and the Mach stem as computational boundaries to implement the shock fitting procedure. A special floating fitting scheme is developed in conjunction with the method of characteristics to fit the slip surface. The reflected shock, the Mach stem, and the slip surface are all treated as harp discontinuities, thus, resulting in a more accurate description of the inviscid flow field. The resulting numerical solutions are compared with available experimental data and existing first-order, shock-capturing numerical solutions.

Vijayashankar, V. S.↗
NASA NTRS1977

Diffraction of a shock wave by a compression corner. II - Single Mach reflection

The two-dimensional time-dependent Euler equations which govern the flow field resulting from the interaction of a planar shock with a compression corner are solved for initial conditions which result in single Mach reflection of the incident planar shock. The Euler equations are first transformed to include the self-similarity of the flow field. A second transformation is employed to normalize the distances between the ramp and the reflected shock and between the wall and the Mach stem. The resulting equations in strong conservation-law form are solved using a second-order discontinuity-fitting finite-difference approach. The results are compared with experimental interferograms and existing first-order shock-capturing numerical solutions.

Shankar, V.↗
NASA NTRS1977

Computation of unsteady transonic flows through rotating and stationary cascades. 1: Method of analysis

A numerical method of solution of the inviscid, compressible, two-dimensional unsteady flow on a blade-to-blade stream surface through a stage (rotor and stator) or a single blade row of an axial flow compressor or fan is described. A cyclic procedure has been developed for representation of adjacent blade-to-blade passages which asymptotically achieves the correct phase between all passages of a stage. A shock-capturing finite difference method is employed in the interior of the passage, and a method of characteristics technique is used at the boundaries. The blade slipstreams form two of the passage boundaries and are treated as moving contact surfaces capable of supporting jumps in entropy and tangential velocity. The Kutta condition is imposed by requiring the slipstreams to originate at the trailing edges, which are assumed to be sharp. Results are presented for several transonic fan rotors and compared with available experimental data, consisting of holographic observations of shock structure and pressure contour maps. A subcritical stator solution is also compared with results from a relaxation method. Finally, a periodic solution for a stage consisting of 44 rotor blades and 46 stator blades is discussed.

Erdos, J. I.↗
NASA NTRS1977

Comparison of numerical and experimental 'conical' flow fields in supersonic corners with compression and/or expansion

The flow field produced by the intersection of two plane solid surfaces in a supersonic stream is a complex interference flow. These flows can be fully compressive, fully expansive, or of mixed compression-expansion nature. This paper presents a comparison of the experimentally obtained flow-field structure in an axial corner with that predicted numerically by using a shock-capturing finite-difference method. The effect of sweep and surface deflection are evaluated, and the general influence of each is presented for the three classes of corner flow. The results show that the numerical method is a valuable aid in understanding the flow structure for simple configurations. In addition, confidence in the numerical method is gained for use in solving more general three-dimensional configurations where the flow is nonconical and several wave interaction may be presented.

Anderson, D. A.↗
NASA NTRS1978

Transonic flow over the NACA 64A006 with an oscillating flap-calculations based on the Euler equations

Exploratory calculations of transonic flows over the airfoil with a quarter-chord oscillating flap were made using a program which obtains approximate solutions to the Euler equations with an explicit, shock-capturing, finite-difference scheme. The calculations, essentially inviscid and for the airfoil at zero angle-of-attack in a free-stream, are at Mach numbers and reduced frequencies which were tested in experiments by Tijdeman. The oscillatory lifts from analogus calculations by various investigators generally agree with one another better than they agree with Tijdeman's data. Inclusion in the calculations of an approximate modelling of boundary conditions expected at slotted wind tunnel walls tends to shift some of the results closer to the experimental values.

Magnus, R. J.↗
NASA NTRS1980

Calculation of two-dimensional inlet flow fields in a supersonic free stream by an implicit marching code with nonorthogonal mesh generation: User's manual

An implicit, shock-capturing finite-difference code which is used to calculate two-dimensional inlet flow fields in a supersonic free stream is explained. The Euler equations are subjected to general nonorthogonal transformation and a body-fitted coordinate system is employed. The mathematical formulation of the problem is given along with the numerical algorithm. Initial and boundary conditions, numerical stability, program limitations, and accuracy is discussed. An overall program logic as well as instructions for program use and operation are also furnished.

Biringen, S. H.↗
NASA NTRS1980

A supersonic, three-dimensional code for flow over blunt bodies: User's manual

A computer code is described which may be used to calculate the steady, supersonic, three-dimensional, inviscid flow over blunt bodies. The theoretical and numerical formulation of the problem is given (shock-capturing, downstream marching), including exposition of the boundary and initial conditions. The overall flow logic of the program, its usage, accuracy, and limitations are discussed.

Chaussee, D. S.↗
NASA NTRS1980

Calculation of inlet flow fields by an implicit technique

Two-dimensional inlet flow fields in a supersonic free stream are calculated by an implicit, shock-capturing, finite-difference method. The Euler equations are subjected to a general curvilinear transformation and a body-fitted coordinate system is employed. The method is used to solve supercritical, critical, and subcritical flow fields which are simulated by prescribing appropriate conditions at the inlet outflow boundary. Results are presented for a drooped-cowl inlet.

Biringen, S.↗
NASA NTRS1981

On various treatments of potential equations at shocks

The potential equation that governs transonic inviscid flowfields is elliptic in subsonic regions and hyperbolic in supersonic regions. The transition from supersonic to subsonic flow may occur either continuously or across a surface of discontinuity known as a shock. Because of the changing type of governing equation and the presence of the surfaces of discontinuity, special treatments of the governing equations are needed at shocks to preserve mass conservation and to ensure satisfaction of the governing equation. In the so-called shock-capturing techniques, shocks are captured by smearing the discontinuity over several mesh cells in the computational domain. Most existing conservative schemes conserve mass flux throughout the flowfield, including shock boundaries; however, they also introduce zero-order errors in the approximation to the governing equation. It is shown that the zero-order errors, which do not diminish as the mesh spacing approaches zero, can cause discrepancies in the prediction of shock strength and location. These parameters are extremely sensitive features of transonic inviscid flowfield calculations. It is also shown that the zero-order errors can be avoided by developing higher-order schemes that properly model the governing equation at shocks.

Chen, L. T.↗
NASA NTRS1982

Computation of blast wave-obstacle interactions

Numerical simulations of the interaction of a planar blast wave with various obstacles are presented. These obstacles are either ground structures or vehicles flying in the atmosphere. For a structure on the ground, the blast wave encounter is side-on, while for the flying vehicles the encounter is either head-on or oblique. Second-order accurate, finite-difference, and shock-capturing procedures are employed to solve the two-dimensional, axisymmetric, and three-dimensional unsteady Euler equations. Results are presented for the flow field consisting of blast wave striking obstacles that are at rest, moving subsonically and moving supersonically. Comparison of the numerical results with experimental data for a configuration at rest substantiates the validity of this approach and its potential as a flow analysis tool.

Champney, J. M.↗
NASA NTRS1982

Nonlinear Green's function method for unsteady transonic flows

Advantages to employing Green's function in describing unsteady three-dimensional transonic flows are explored. The development of the function for application to linear subsonic and supersonic unsteady aerodynamics is reviewed. It is shown that unique solutions are possible for external flows, with all functional expressions being defined in Prandtl-Glauert space. The development of methods of using the Green's function for transonic flows is traced, noting the necessity of including the effects of significant nonlinear terms. The steady-state problem is considered to demonstrate the shock-capturing ability of the method and the usefulness of the function in the incompressible, subsonic, transonic, and supersonic areas of potential unsteady three-dimensional flows around complex configurations. Computational time is asserted to be an order of magnitude less than with finite difference methods.

Tseng, K.↗
NASA NTRS1982

Iterative spectral methods and spectral solutions to compressible flows

A spectral multigrid scheme is described which can solve pseudospectral discretizations of self-adjoint elliptic problems in O(N log N) operations. An iterative technique for efficiently implementing semi-implicit time-stepping for pseudospectral discretizations of Navier-Stokes equations is discussed. This approach can handle variable coefficient terms in an effective manner. Pseudospectral solutions of compressible flow problems are presented. These include one dimensional problems and two dimensional Euler solutions. Results are given both for shock-capturing approaches and for shock-fitting ones.

Hussaini, M. Y.↗
NASA NTRS1983

Spectral methods for the Euler equations

Spectral methods for compressible flows are introduced in relation to finite difference and finite element techniques within the framework of the method of weighted residuals. Current spectral collocation methods are put in historical context. The basic concepts of both Fourier and Chebyshev spectral collocation methods are provided. Filtering strategies for both shock-fitting and shock-capturing approaches are also presented. Fourier shock capturing techniques are evaluated using a one-dimensional, periodic astrophysical 'nozzle' problem. Examples of shock-fitting approaches include a shock/acoustic wave interaction, shock/vortex interaction, and the classical blunt body problem. While the shock capturing spectral method does not yet show a clear advantage over second-order finite differences, equivalent accuracy can be obtained using shock fitting with far fewer grid points.

Hussaini, M. Y.↗
NASA NTRS1984

One-dimensional unsteady modeling of supersonic inlet unstart/restart

A quasi-one-dimensional unsteady inviscid analysis of mixed-compression supersonic inlet flow is presented with emphasis on modeling of inlet unstart/restart phenomena. Numerical solution of the governing equations of motion is performed using a computationally efficient shock-capturing split-characteristics algorithm. Inlet unstart is modeled using a mass balance method which relates the expelled normal shock position ahead of the inlet cowl to the amount of spilled mass flow over the inlet housing. Comparison of computed results with experimental data for an axisymmetric inlet at a free-stream Mach number of 2.50 shows quite reasonable agreement over an entire unstart/restart transient which includes centerbody translation and retraction as well as bypass mass flow variations.

Adams, J. C., Jr.↗