Engineering topics

Shankar, V.

Publications and source records attributed to Shankar, V..

28 records · Page 2

NASA NTRS1982

An efficient full potential implicit method based on characteristics for analysis of supersonic flows

A nonlinear aerodynamic prediction technique based on the full potential equation in conservation form has been developed for the treatment of supersonic flows. The method uses the theory of characteristic signal propagation to accurately simulate the flow structure, which includes shock waves and mixed elliptic-hyperbolic crossflow. An implicit approximate factorization scheme is employed to solve the finite-differenced equation. The necessary body-fitted grid system in every marching plane is generated numerically, using an elliptic grid solver. Results are shown for conical and nonconical wing-body combinations and compared with experimental data and Euler calculations. The method demonstrates an enormous savings in execution time and memory requirements over Euler methods.

Shankar, V.↗

NASA NTRS1981

Numerical boundary condition procedure for the transonic axisymmetric inverse problem

Two types of boundary condition procedures for the axisymmetric inverse problem are described. One is a Neumann type boundary condition (analogous to the analysis problem) and the other is a Dirichlet type boundary conditon, both requiring special treatments to make the inverse scheme numerically stable. The dummy point concept is utilized in implementing both. Results indicate the Dirichlet type inverse boundary condition is more robust and conceptually simpler to implement than the Neumann type procedure. A few results demonstrating the powerful capability of the newly developed inverse method that can handle both shocked as well as shockless body design are included.

Shankar, V.↗

NASA NTRS1981

An implicit marching procedure for the treatment of supersonic flow fields using the conservative full potential equation

A new aerodynamic prediction technique based on the conservative full potential equation is developed for the treatment of supersonic flow fields. This new technique bridges the gap between simplistic linear theory methods and complex Euler solvers. A novel local density linearization concept and a second order accurate retarded density scheme, both producing the correct artificial viscosity, are introduced in developing an implicit marching scheme for solving the scalar phi. The method produces results that compare well with Euler solvers and requires an order of magnitude less computer time and significantly less computer memory over existing nonlinear codes. The scalar phi formulation can be extended to handle subsonic pockets in the marching direction and also is suitable for developing inverse procedures where the shape corresponding to a prescribed loading is sought.

Shankar, V.↗

NASA NTRS1981

Treatment of conical and nonconical supersonic flows by an implicit marching scheme applied to the full potential equation

An aerodynamic prediction technique based on the full potential equation in conservation form is developed for the treatment of supersonic flows. This technique bridges the gap between simplistic linear theory methods and complex Euler solvers. A novel local density linearization concept and a second order accurate retarded density scheme, both producing the correct artificial viscosity, are introduced in developing an implicit marching scheme for solving the scalar potential. Results for conical flows over delta wings and a wing-body combination and for non-conical flows over bodies of revolution at angles of attack are compared with Euler and nonconservative full potential calculations and experimental data. The present formulation requires an order of magnitude less computer time and significantly less computer memory over Euler codes and exhibits a considerable improvement in computational efficiency and generality over an existing nonconservative full potential code.

Shankar, V.↗

NASA NTRS1979

A computational model for three-dimensional incompressible wall jets with large cross flow

A computational model for the flow field of three dimensional incompressible wall jets prototypic of thrust augmenting ejectors with large cross flow is presented. The formulation employs boundary layer equations in an orthogonal curvilinear coordinate system. Simulation of laminar as well as turbulen wall jets is reported. Quantification of jet spreading, jet growth, nominal separation, and jet shrink effects due to corss flow are discussed.

Murphy, W. D.↗

NASA NTRS1979

A consistent design procedure for supercritical airfoils in free air and a wind tunnel

A computational inverse procedure for transonic airfoils in which shapes are determined supporting prescribed pressure distributions is presented. The method uses the small disturbance equation and a consistent analysis-design differencing procedure at the airfoil surface. This avoids the intermediate analysis-design-analysis iterations. The effect of any openness at the trailing edge is taken onto account by adding an effective source term in the far field. The final results from a systematic expansion procedure which models the far field for solid, ideal slotted, and free jet tunnel walls are presented along with some design results for the associated boundary conditions and those for a free flight.

Shankar, V.↗

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 NTRS1976

Computation of the inviscid supersonic flow over an external axial corner

A second-order finite-difference procedure is used to evaluate the inviscid supersonic flowfield surrounding an external axial corner composed of swept planar compression surfaces and representing the inlets on existing high-speed aircraft. The governing partial differential equations in conservation-law form are hyperbolic with respect to the axial coordinate and are solved iteratively by means of MacCormack's algorithm. The procedure treats both the peripheral shock wave and vortical singularities as discontinuities. Numerical results are presented for two parametric studies regarding the effects on the flowfield of varying the free-stream Mach number and the leading edge sweep of the horizontal wedge. Results of parametric Mach number study agree with the Mach number independence principle in that as the Mach number increases, such characteristics as shock shape, cross-flow sonic line location, and vortical singularity position approach an asymptote.

Kutler, P.↗

NASA NTRS1975

Numerical solutions for supersonic corner flow

Analytical solutions for inviscid supersonic corner flows are virtually nonexistent due to the complexity of the interference geometry. In view of this, numerical solutions for swept-compressive and swept-expansive corner flows are obtained. The governing equations are written in strong conservation-law form and are solved iteratively in nonorthogonal conical coordinates by use of a second-order, shock-capturing, finite-difference technique. The computed wave structure and surface pressure distributions are compared with high Reynolds number experimental data and show very good agreement. The results clearly show that supersonic corner flow at reasonably high Reynolds numbers including the effect of sweep is dominated by the inviscid field.

Shankar, V.↗

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.↗