The receptivity to freestream acoustic disturbances and the stability properties of hypersonic boundary layers are numerically investigated for boundary-layer flows over a 5 straight cone at a freestream Mach number of 6.0. To compute the shock and the interaction of the shock with the instability waves, the Navier-Stokes equations in axisymmetric coordinates were solved. In the governing equations, inviscid and viscous flux vectors are discretized using a fifth-order accurate...

Topics: NASA Technical Reports Server (NTRS), BOUNDARY LAYER STABILITY, FREQUENCY STABILITY, BOUNDARY LAYER...

The objective of this study is to examine the effect of flight, at off-design conditions, on the propagated sonic boom pressure signatures of a small "low-boom" supersonic aircraft. The amplification, or focusing, of the low magnitude "shaped" signatures produced by maneuvers such as the accelerations from transonic to supersonic speeds, climbs, turns, pull-up and pushovers is the concern. To analyze these effects, new and/or improved theoretical tools have been developed,...

Topics: NASA Technical Reports Server (NTRS), SONIC BOOMS, WAVEFORMS, SUPERSONIC AIRCRAFT, SUPERSONIC...

A document discusses a multi-Gigabit-per-second, Ka-band transceiver with a software-defined modem (SDM) capable of digitally encoding/decoding data and compensating for linear and nonlinear distortions in the end-to-end system, including the traveling-wave tube amplifier (TWTA). This innovation can increase data rates of space-to-ground communication links, and has potential application to NASA s future spacebased Earth observation system. The SDM incorporates an extended version of the...

Topics: NASA Technical Reports Server (NTRS), BIT ERROR RATE, COMMUNICATION NETWORKS, DECODERS, END-TO-END...

Three shapes of tensile specimens were tested--curved with a very low stress concentration factor and straight with either a circular hole or an elliptical hole. The nominal thickness was 125 micron with a net section 100 micron wide; the overall length of these microspecimens was 3.1 mm. They were fabricated by an improved version of deep reactive ion etching, which produced specimens with smooth sidewalls and cross-sections having a slightly trapezoidal shape that was exaggerated inside the...

Topics: NASA Technical Reports Server (NTRS), CERAMICS, SILICON CARBIDES, HOLES (MECHANICS), STRESS...

Studies have shown that significant vehicle mass and cost savings are possible with the use of ballutes for aero-capture. Through NASA's In-Space Propulsion program, a preliminary examination of ballute sensitivity to geometry and Reynolds number was conducted, and a single-pass coupling between an aero code and a finite element solver was used to assess the static aeroelastic effects. There remain, however, a variety of open questions regarding the dynamic aeroelastic stability of membrane...

Topics: NASA Technical Reports Server (NTRS), AEROELASTICITY, MEMBRANE STRUCTURES, FLEXIBILITY, BALLUTES,...

A methodology has been devised for accounting for uncertainties in the strengths of silicon carbide structural components of microelectromechanical systems (MEMS). The methodology enables prediction of the probabilistic strengths of complexly shaped MEMS parts using data from tests of simple specimens. This methodology is intended to serve as a part of a rational basis for designing SiC MEMS, supplementing methodologies that have been borrowed from the art of designing macroscopic brittle...

Topics: NASA Technical Reports Server (NTRS), MICROELECTROMECHANICAL SYSTEMS, SILICON CARBIDES,...

ANSYS/CARES/PDS is a software system that combines the ANSYS Probabilistic Design System (PDS) software with a modified version of the Ceramics Analysis and Reliability Evaluation of Structures Life (CARES/Life) Version 6.0 software. [A prior version of CARES/Life was reported in Program for Evaluation of Reliability of Ceramic Parts (LEW-16018), NASA Tech Briefs, Vol. 20, No. 3 (March 1996), page 28.] CARES/Life models effects of stochastic strength, slow crack growth, and stress distribution...

Topics: NASA Technical Reports Server (NTRS), CERAMICS, LIFE (DURABILITY), PROBABILITY THEORY, RELIABILITY,...

An analytical methodology is developed to predict the probability of survival (reliability) of ceramic components subjected to harsh thermomechanical loads that can vary with time (transient reliability analysis). This capability enables more accurate prediction of ceramic component integrity against fracture in situations such as turbine startup and shutdown, operational vibrations, atmospheric reentry, or other rapid heating or cooling situations (thermal shock). The transient reliability...

Topics: NASA Technical Reports Server (NTRS), RELIABILITY ANALYSIS, WEIBULL DENSITY FUNCTIONS, PROBABILITY...

Single crystal silicon carbide micro-sized tensile specimens were fabricated with deep reactive ion etching (DRIE) in order to investigate the effect of stress concentration on the room-temperature fracture strength. The fracture strength was defined as the level of stress at the highest stressed location in the structure at the instant of specimen rupture. Specimens with an elliptical hole, a circular hole, and without a hole (and hence with no stress concentration) were made. The average...

Topics: NASA Technical Reports Server (NTRS), FRACTURE MECHANICS, FRACTURE STRENGTH, SINGLE CRYSTALS,...

A methodology is shown for predicting the time-dependent reliability of ceramic components against catastrophic rupture when subjected to transient thermomechanical loads (including cyclic loads). The methodology takes into account the changes in material response that can occur with temperature or time (i.e., changing fatigue and Weibull parameters with temperature or time). This capability has been added to the NASA CARES/Life (Ceramic Analysis and Reliability Evaluation of Structures/Life)...

Topics: NASA Technical Reports Server (NTRS), MECHANICAL PROPERTIES, CERAMICS, TIME DEPENDENCE, TRANSIENT...

Present capabilities of the NASA CARES/Life (Ceramic Analysis and Reliability Evaluation of Structures/Life) code include probabilistic life prediction of ceramic components subjected to fast fracture, slow crack growth (stress corrosion), and cyclic fatigue failure modes. Currently, this code has the capability to compute the time-dependent reliability of ceramic structures subjected to simple time-dependent loading. For example, in slow crack growth (SCG) type failure conditions CARES/Life...

Topics: NASA Technical Reports Server (NTRS), CERAMICS, CRACK PROPAGATION, FATIGUE LIFE, LIFE (DURABILITY),...

An implicit method for the computation of unsteady flows on unstructured grids is presented. The resulting nonlinear system of equations is solved at each time step using an agglomeration multigrid procedure. The method allows for arbitrarily large time steps and is efficient in terms of computational effort and storage. Validation of the code using a one-equation turbulence model is performed for the well-known case of flow over a cylinder. A Detached Eddy Simulation model is also implemented...

Topics: NASA Technical Reports Server (NTRS), TURBULENCE MODELS, SEPARATED FLOW, UNSTEADY FLOW,...

High temperature and long duration applications of monolithic ceramics can place their failure mode in the creep rupture regime. A previous model advanced by the authors described a methodology by which the creep rupture life of a loaded component can be predicted. That model was based on the life fraction damage accumulation rule in association with the modified Monkman-Grant creep ripture criterion However, that model did not take into account the deteriorating state of the material due to...

Topics: NASA Technical Reports Server (NTRS), CREEP ANALYSIS, CREEP PROPERTIES, CERAMICS, CAVITATION FLOW,...

High temperature and long duration applications of monolithic ceramics can place their failure mode in the creep rupture regime. A previous model advanced by the authors described a methodology by which the creep rupture life of a loaded component can be predicted. That model was based on the life fraction damage accumulation rule in association with the modified Monkman-Grant creep rupture criterion. However, that model did not take into account the deteriorating state of the material due to...

Topics: NASA Technical Reports Server (NTRS), CREEP ANALYSIS, REGRESSION ANALYSIS, PREDICTION ANALYSIS...

Over the past few years, the development of the interface technology has provided an analysis framework for embedding detailed finite element models within finite element models which are less refined. This development has enabled the use of cascading substructure domains without the constraint of coincident nodes along substructure boundaries. The approach used for the interface element is based on an alternate variational principle often used in deriving hybrid finite elements. The resulting...

Topics: NASA Technical Reports Server (NTRS), FINITE ELEMENT METHOD, NONLINEARITY, THREE DIMENSIONAL...

The work presented in this paper include: 'Coupled and Uncoupled Bending-Torsion Responses of Twin-Tail Buffet'; 'Fluid/Structure Twin Tail Buffet Response Over a Wide Range of Angles of Attack'; 'Resent Advances in Multidisciplinary Aeronautical Problems of Fluids/Structures/Dynamics Interaction'; and'Development of a Coupled Fluid/Structure Aeroelastic Solver with Applications to Vortex Breakdown induced Twin Tail Buffeting.

Topics: NASA Technical Reports Server (NTRS), AEROELASTICITY, ANGLE OF ATTACK, VORTEX BREAKDOWN, AEROSPACE...

The desirable properties of ceramics at high temperatures have generated interest in their use for structural applications such as in advanced turbine systems. Design lives for such systems can exceed 10,000 hours. Such long life requirements necessitate subjecting the components to relatively low stresses. The combination of high temperatures and low stresses typically places failure for monolithic ceramics in the creep regime. The objective of this work is to present a design methodology for...

Topics: NASA Technical Reports Server (NTRS), CREEP PROPERTIES, CERAMICS, FINITE ELEMENT METHOD, LIFE...

Accomplishments achieved during the reporting period are listed. These accomplishments included 6 papers published in various journals or presented at various conferences; 1 abstract submitted to a technical conference; production of 2 animated movies; and a proposal for use of the National Aerodynamic Simulation Facility at NASA Ames Research Center for further research. The published and presented papers and animated movies addressed the following topics: aeroelasticity, computational fluid...

Topics: NASA Technical Reports Server (NTRS), COMPUTATIONAL FLUID DYNAMICS, DELTA WINGS, AEROELASTICITY,...

The unsteady compressible, full Navier-Stokes (NS) equations and the Euler equations of rigid-body dynamics are sequentially solved to simulate the delta wing rock phenomenon. The NS equations are solved time accurately, using the implicit, upwind, Roe flux-difference splitting, finite-volume scheme. The rigid-body dynamics equations are solved using a four-stage Runge-Kutta scheme. Once the wing reaches the limit-cycle response, an active control model using a mass injection system is applied...

Topics: NASA Technical Reports Server (NTRS), NAVIER-STOKES EQUATION, DELTA WINGS, RIGID STRUCTURES,...

The buffet response of the flexible twin-tail/delta wing configuration, a multidisciplinary problem, is solved using three sets of equations on a multi-block grid structure. The first set is the unsteady, compressible, full Navier-Stokes equations which are used for obtaining the flow-field vector and the aerodynamic loads on the twin tails. The second set is the coupled aeroelastic equations which are used for obtaining the bending and torsional deflections of the twin tails. The third set is...

Topics: NASA Technical Reports Server (NTRS), BUFFETING, MULTIBLOCK GRIDS, NAVIER-STOKES EQUATION,...

The buffet response of the twin-tail configuration of the F/A-18 aircraft; a multidisciplinary problem, is investigated using three sets of equations on a multi-block grid structure. The first set is the unsteady, compressible, full Navier-Stokes equations. The second set is the coupled aeroelastic equations for bending and torsional twin-tail responses. The third set is the grid-displacement equations which are used to update the grid coordinates due to the tail deflections. The computational...

Topics: NASA Technical Reports Server (NTRS), AERODYNAMIC CONFIGURATIONS, DELTA WINGS, BUFFETING, UNSTEADY...

Computational study of the far-field turbulent vortex-wake/exhaust plume interaction for subsonic and high speed civil transport (HSCT) airplanes is carried out. The Reynolds-averaged Navier-Stokes (NS) equations are solved using the implicit, upwind, Roe-flux-differencing, finite-volume scheme. The two-equation shear stress transport model of Menter is implemented with the NS solver for turbulent-flow calculation. For the far-field study, the computations of vortex-wake interaction with the...

Topics: NASA Technical Reports Server (NTRS), TURBULENT FLOW, VORTICES, NAVIER-STOKES EQUATION, SUPERSONIC...

The unsteady, three-dimensional, full Navier-Stokes (NS) equations and the Euler equations of rigid-body dynamics are sequentially solved to simulate the natural rolling response of slender delta wings of zero thickness at moderate to high angles of attack, to transonic and subsonic flows. The governing equations of fluid flow and dynamics of the present multi-disciplinary problem are solved using the time-accurate solution of the NS equations with the implicit, upwind, Roe flux-difference...

Topics: NASA Technical Reports Server (NTRS), NAVIER-STOKES EQUATION, SWEPT WINGS, DELTA WINGS, RIGID...

The buffet response of the flexible twin-tail configuration of the F/A-18 and a generic F-111 aircraft are computationally simulated and experimentally validated. The problem is a multidisciplinary one which requires the sequential solution of three sets of equations on a multi-block grid structure. The first set is the unsteady, compressible, full Navier-Stokes equations. The second set is the aeroelastic equations for bending and torsional twin-tail responses. The third set is the...

Topics: NASA Technical Reports Server (NTRS), AEROELASTICITY, ANGLE OF ATTACK, VORTEX BREAKDOWN,...

This report describes the activities and accomplishments under this research grant, including a list of publications and dissertations, produced in the field of prediction and control of vortex dominated and vortex wake flows.

Topics: NASA Technical Reports Server (NTRS), VORTICES, ACTIVE CONTROL, PREDICTIONS, TURBULENT FLOW,...

Pneumatic active control of asymmetric vortical flows around a slender pointed forebody is investigated using the three dimensional solution for the compressible thin-layer Navier-Stokes equation. The computational applications cover the normal and tangential injection control of asymmetric flows around a 5 degree semi-apex angle cone at a 40 degree angle of attack, 1.4 freestream Mach number and 6 x 10(exp 6) freestream Reynolds number (based on the cone length). The effective tangential angle...

Topics: NASA Technical Reports Server (NTRS), ANGLE OF ATTACK, FINITE VOLUME METHOD, FLUX DIFFERENCE...

This progress report documents the accomplishments achieved in the period from December 1, 1992 until November 30, 1993. These accomplishments include publications, national and international presentations, NASA presentations, and the research group supported under this grant. Topics covered by documents incorporated into this progress report include: active control of asymmetric conical flow using spinning and rotary oscillation; supersonic vortex breakdown over a delta wing in transonic flow;...

Topics: NASA Technical Reports Server (NTRS), ACTIVE CONTROL, COMPUTATIONAL FLUID DYNAMICS, NAVIER-STOKES...

Research on Navier-Stokes, dynamics, and aeroelastic computations for vortical flows, buffet, and flutter applications was performed. Progress during the period from 1 Oct. 1992 to 30 Sep. 1993 is included. Papers on the following topics are included: vertical tail buffet in vortex breakdown flows; simulation of tail buffet using delta wing-vertical tail configuration; shock-vortex interaction over a 65-degree delta wing in transonic flow; supersonic vortex breakdown over a delta wing in...

Topics: NASA Technical Reports Server (NTRS), BODY-WING AND TAIL CONFIGURATIONS, BUFFETING, COMPUTATIONAL...

The main objectives of our research are to present a self-contained overview of fuzzy sets and fuzzy logic, develop a methodology for control system design using fuzzy logic controllers, and to design and implement a fuzzy logic controller for a real system. We first present the fundamental concepts of fuzzy sets and fuzzy logic. Fuzzy sets and basic fuzzy operations are defined. In addition, for control systems, it is important to understand the concepts of linguistic values, term sets, fuzzy...

Topics: NASA Technical Reports Server (NTRS), AIRCRAFT CONTROL, CONTROL SYSTEMS DESIGN, CONTROLLERS, FREE...

The accomplishments which have been achieved in the present year covering the period from Dec. 1, 1991 until Nov. 30, 1992 are given. These accomplishments include publications, national and international presentations, NASA Research Highlights and presentations, and the research group supported under this grant.

Topics: NASA Technical Reports Server (NTRS), SUPERSONIC FLOW, VORTEX BREAKDOWN, VORTICES, ASYMMETRY, FLOW...

The unsteady, compressible, thin-layer, Navier-Stokes (NS) equations are solved to simulate steady and unsteady, asymmetric, vortical laminar flow around cones at high incidences and supersonic Mach numbers. The equations are solved by using an implicit, upwind, flux-difference splitting (FDS), finite-volume scheme. The locally conical flow assumption is used and the solutions are obtained by forcing the conserved components of the flowfield vector to be equal at two axial stations located at...

Topics: NASA Technical Reports Server (NTRS), ASYMMETRY, COMPUTATIONAL FLUID DYNAMICS, NAVIER-STOKES...

The unsteady, compressible, thin-layer Navier-Stokes equations are used to obtain three-dimensional, asymmetric, vortex-flow solutions around cones and cone-cylinder configurations. The equations are solved using an implicit, upwind, flux-difference splitting, finite-volume scheme. The computational applications cover asymmetric flows around a 5 semi-apex angle cone of unit length at various Reynolds number. Next, a cylindrical afterbody of various length is added to the conical forebody to...

Topics: NASA Technical Reports Server (NTRS), COMPRESSIBLE FLOW, COMPUTATIONAL FLUID DYNAMICS,...

Computational simulation and study of shock/vortex interaction and vortex-breakdown modes are considered for bound (internal) and unbound (external) flow domains. The problem is formulated using the unsteady, compressible, full Navier-Stokes (NS) equations which are solved using an implicit, flux-difference splitting, finite-volume scheme. For the bound flow domain, a supersonic swirling flow is considered in a configured circular duct and the problem is solved for quasi-axisymmetric and...

Topics: NASA Technical Reports Server (NTRS), COMPUTATIONAL FLUID DYNAMICS, S WAVES, SHOCK WAVES,...

The accomplishments achieved during the period include conference and proceedings publications, journal papers, and abstracts which are either published, accepted for publication or under review. Conference presentations and NASA highlight publications are also included. Two of the conference proceedings publications are attached along with a Ph.D. dissertation abstract and table of contents. In the first publication, computational simulation of three-dimensional flows around a delta wing...

Topics: NASA Technical Reports Server (NTRS), AEROELASTICITY, BUFFETING, COMPUTATIONAL FLUID DYNAMICS,...

The unsteady, compressible, thin-layer Navier-Stokes equations are used to numerically study the passive control of steady and unsteady supersonic asymmetric flows around circular and noncircular cones. The main computational scheme of the present study is an implicit upwind, flux-difference splitting, finite-volume scheme. Passive control of flow asymmetry is studied by using a vertical fin in the leeward plane of geometric symmetry and side strakes with and without thickness at different...

Topics: NASA Technical Reports Server (NTRS), ASYMMETRY, CIRCULAR CONES, COMPUTATIONAL FLUID DYNAMICS,...

The problems of asymmetric flow around slender bodies and its control are formulated using the unsteady, compressible, thin-layer or full Navier-Stokes equations which are solved using an implicit, flux-difference splitting, finite-volume scheme. The problem is numerically simulated for both locally-conical and three-dimensional flows. The numerical applications include studies of the effects of relative incidence, Mach number and Reynolds number on the flow asymmetry. For the control of flow...

Topics: NASA Technical Reports Server (NTRS), ASYMMETRY, COMPUTATIONAL FLUID DYNAMICS, NAVIER-STOKES...

An extensive computational study of supersonic quasi-axisymmetric vortex breakdown in a configured circular duct is presented. The unsteady, compressible, full Navier-Stokes (NS) equations are used. The NS equations are solved for the quasi-axisymmetric flows using an implicit, upwind, flux difference splitting, finite volume scheme. The quasi-axisymmetric solutions are time accurate and are obtained by forcing the components of the flowfield vector to be equal on two axial planes, which are in...

Topics: NASA Technical Reports Server (NTRS), AXISYMMETRIC FLOW, COMPUTATIONAL FLUID DYNAMICS, DUCTED FLOW,...

Topics relative to the analysis and control of asymmetric vortex flow and supersonic vortex breakdown are discussed. Specific topics include the computation of compressible, quasi-axisymmetric slender vortex flow and breakdown; supersonic quasi-axisymmetric vortex breakdown; and three-dimensional Navier-Stokes asymmetric solutions for cones and cone-cylinder configurations.

Topics: NASA Technical Reports Server (NTRS), AXISYMMETRIC FLOW, COMPUTATIONAL FLUID DYNAMICS, SUPERSONIC...

The unsteady, compressible Navier-Stokes equations are used to compute and analyze compressible quasi-axisymmetric isolated vortices. The Navier-Stokes equations are solved using an implicit, upwind, flux difference splitting finite volume scheme. The developed three dimensional solver was verified by comparing its solution profiles with those of a slender, quasi-axisymmetric vortex solver for a subsonic, quasi-axisymmetric vortex in an unbounded domain. The Navier-Stokes solver is then used to...

Topics: NASA Technical Reports Server (NTRS), COMPRESSIBLE FLOW, COMPUTATIONAL FLUID DYNAMICS, STEADY FLOW,...

Analysis and computation of steady, compressible, quasi-axisymmetric flow of an isolated, slender vortex are considered. The compressible, Navier-Stokes equations are reduced to a simpler set by using the slenderness and quasi-axisymmetry assumptions. The resulting set along with a compatibility equation are transformed from the diverging physical domain to a rectangular computational domain. Solving for a compatible set of initial profiles and specifying a compatible set of boundary...

Topics: NASA Technical Reports Server (NTRS), COMPRESSIBLE FLOW, FLUID DYNAMICS, MACH NUMBER, STEADY FLOW,...

The conservative unsteady Euler equations for the flow relative motion in the moving frame of reference are used to solve for the steady and unsteady flows around sharp-edged delta wings. The resulting equations are solved by using an implicit approximately-factored finite volume scheme. Implicit second-order and explicit second- and fourth-order dissipations are added to the scheme. The boundary conditions are explicitly satisfied. The grid is generated by locally using a modified Joukowski...

Topics: NASA Technical Reports Server (NTRS), DISSIPATION, EULER EQUATIONS OF MOTION, INVISCID FLOW, STEADY...

Two methods are presented for inviscid transonic flows: unsteady Euler equations in a rotating frame of reference for transonic-vortex flows and integral solution of full-potential equation with and without embedded Euler domains for transonic airfoil flows. The computational results covered: steady and unsteady conical vortex flows; 3-D steady transonic vortex flow; and transonic airfoil flows. The results are in good agreement with other computational results and experimental data. The...

Topics: NASA Technical Reports Server (NTRS), AIRFOIL PROFILES, EULER EQUATIONS OF MOTION, FLOW...

The development of a subharmonic secondary instability in a boundary layer with pressure gradients controlled by suction was investigated. The effect of suction control on this early stage leading to transition is evaluated. The secondary three-dimensional instability problem for compressible boundary layers was formulated to investigate theoretically the effect of finite amplitude two-dimensional wave on the growth of three-dimensional perturbations in compressible boundary layers. Only a...

Topics: NASA Technical Reports Server (NTRS), BOUNDARY LAYER CONTROL, BOUNDARY LAYER TRANSITION, FLOW...

The steady full-potential equation is written in the form of Poisson's equation, and the solution for the velocity field is expressed in terms of an integral equation. The integral solution consists of two surface integrals and one volume integral. The solution is obtained through successive iteration cycles. Each cycle of iteration consists of two sub-cycles, an inner cycle for wake relaxation and an out cycle for the strength of the source distribution integrals representing the flow...

Topics: NASA Technical Reports Server (NTRS), COMPRESSIBLE FLOW, COMPUTATIONAL FLUID DYNAMICS, DELTA WINGS,...

Classical and zero-total pressure-loss sets of Euler equations were applied to sharp- and round-edge delta wings. The origin of the total pressure was explained in the classical set. For sharp-edged delta wings, all sets of Euler equations produce the same separated flow solutions. For round-edged delta wings and for coarse grids, the solution depends on the level of dissipation, the accuracy of the surface boundary condition, and the type of Euler equations set. For round-edged delta wings and...

Topics: NASA Technical Reports Server (NTRS), COMPUTATIONAL FLUID DYNAMICS, DELTA WINGS, EULER EQUATIONS OF...

Two transonic computational schemes which are based on the Integral Equation Formulation of the full potential equation were presented. The first scheme is a Shock Capturing-Shock Fitting (SCSF) scheme which uses the full potential equation throughout with the exception of the shock wave where the Rankine-Hugoniot relations are used to cross and fit the shock. The second scheme is an Integral Equation with Embedded Euler (IEEE) scheme which uses the full potential equation with an embedded...

Topics: NASA Technical Reports Server (NTRS), AIRFOILS, COMPUTATIONAL FLUID DYNAMICS, EULER EQUATIONS OF...

Papers resulting from work performed from January 1, 1987 to July 31, 1987 are listed. Transonic computational schemes based on Integral Equation Formulation of the full potential equation were presented. Classical and zero-total pressure-loss sets of Euler equations applied to delta wings were examined.

Topics: NASA Technical Reports Server (NTRS), AIRFOILS, BOUNDARY VALUE PROBLEMS, COMPUTATIONAL FLUID...

The well developed surface panel method is extended by adding a volume integral term allowing calculation of the full effect of compressibility. The full effect of compressibility is calculated by using mixed type finite difference scheme consistent with the mixed nature of transonic flow. The solution is obtained through successive iteration cycles for subcritical flows and for critical flows the solution is obtained through satisfying the Rankine-Hugoniot relations across the captured shock...

Topics: NASA Technical Reports Server (NTRS), AIRFOILS, COMPRESSIBILITY, COMPUTATIONAL FLUID DYNAMICS,...