Search NASA⌕ Search

SEARCH · Search NASA

Results for “vortex-dominated flows”

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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Influence of numerical dissipation in computing supersonic vortex-dominated flows

Steady supersonic vortex-dominated flows are solved using the unsteady Euler equations for conical and three-dimensional flows around sharp- and round-edged delta wings. The computational method is a finite-volume scheme which uses a four-stage Runge-Kutta time stepping with explicit second- and fourth-order dissipation terms. The grid is generated by a modified Joukowski transformation. The steady flow solution is obtained through time-stepping with initial conditions corresponding to the freestream conditions, and the bow shock is captured as a part of the solution. The scheme is applied to flat-plate and elliptic-section wings with a leading edge sweep of 70 deg at an angle of attack of 10 deg and a freestream Mach number of 2.0. Three grid sizes of 29 x 39, 65 x 65 and 100 x 100 have been used. The results for sharp-edged wings show that they are consistent with all grid sizes and variation of the artificial viscosity coefficients. The results for round-edged wings show that separated and attached flow solutions can be obtained by varying the artificial viscosity coefficients. They also show that the solutions are independent of the way time stepping is done. Local time-stepping and global minimum time-steeping produce same solutions.

Kandil, O. A.↗
NASA NTRS1985

Vortex-dominated flow with viscous core structure

Recent theoretical studies of vortex-dominated flows are reviewed with special emphasis on those for which the viscous core structures play an important role. The problems to be described are: The interaction and merging of two-dimensional vortices and of curved vortex filaments, the roll-up and decay of trailing far wakes, and the initiation of vortex breakdown. The analysis utilizes finite-difference solutions of the Navier-Stokes equations complemented by asymptotic expansion techniques.

Liu, C. H.↗
NASA NTRS1986

Finite-volume and integral-equation techniques for transonic and supersonic vortex-dominated flows

Two computational techniques are developed to calculate the compressible vortex-dominated flows. The first technique is a finite-volume Euler Solver which uses four-Stage Runge-Kutta time stepping with second- and fourth-order dissipation terms. The technique is applied to supersonic conical and three-dimensional flows about sharp- and round-edged delta wings. Attached and separated-flow solutions have been obtained depending on the values of damping coefficients. The second technique is an integral-equation solver of the full potential equation which uses a volume-integral term in addition to the classical surface-integral terms. The technique is applied to transonic three-dimensional flows about sharp-edged delta wings. A hybrid technique which combines the finite-volume and the integral-equation solvers is also presented.

Kandil, O. A.↗
NASA NTRS1988

Unsteady vortex-dominated flows around maneuvering wings over a wide range of Mach numbers

The problem of unsteady flow around maneuvering wings is solved using the unsteady Euler equations. The unsteady conservative Euler equations are derived for the flow relative motion with respect to a moving (translating and rotating) frame of reference. The resulting equations can handle the most general case for unsteady three-dimensional flow around maneuvering wings or wing-body configurations undergoing six degrees of freedom motion; three translations and three rotations. The equations are solved using two computational schemes; an explicit multistage finite-volume scheme and an implicit approximately factored finite-volume scheme. The computational applications cover two cases. The first case is for a locally conical supersonic flow of rolling oscillation of a sharp-edged delta wing at zero angle of attack. The second case is for a pitching oscillation around a mean angle of attack of a NACA 0012 airfoil in transonic flow.

Kandil, Osama A.↗
NASA NTRS1988

Computation of steady and unsteady vortex-dominated flows with shock waves

The unsteady Euler equations have been derived in the conservation form for the flow relative motion with respect to a rotating frame of reference. The resulting equations are solved by using a central-difference finite-volume scheme with four-state Runge-Kutta time stepping. For steady flow applications local time stepping is used, and for unsteady applications the minimum global time stepping is used. A three-dimensional fully vectorized computer program has been developed and applied to steady and unsteady maneuvering delta wings. The capability of the three-dimensional program has been demonstrated for a rigid sharp-edged delta wing undergoing uniform rolling in a conical flow and rolling oscillations in a locally conical flow.

Kandil, Osama A.↗
NASA NTRS1990

Analysis and mitigation of numerical dissipation in inviscid and viscid computation of vortex-dominated flows

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 transformation in cross flow planes at the grid chord stations. The computational applications cover a steady flow around a delta wing whose results serve as the initial conditions for the unsteady flow around a pitching delta wing about a large angle of attack. The steady results are compared with the experimental data and the periodic solution is achieved within the third cycle of oscillation.

Kandil, Osama A.↗
NASA NTRS1990

Computation of vortex-dominated flow for a delta wing undergoing pitching oscillation

The conservative, unsteady Euler equations for the flow relative to a moving frame of reference are used to solve for the three-dimensional steady and unsteady flows around a sharp-edged delta wing. 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 transformation in crossflow planes at the grid-chord stations. The computational applications cover a steady flow around a delta wing, whose results serve as the initial conditions for the unsteady flow around a pitching delta wing at a large mean angle of attack. The steady results are compared with the experimental data, and the unsteady results are compared with results of a flux-difference splitting scheme.

Kandil, Osama A.↗
NASA NTRS1989

Vortex-dominated conical-flow computations using unstructured adaptively-refined meshes

A conical Euler/Navier-Stokes algorithm is presented for the computation of vortex-dominated flows. The flow solver involves a multistage Runge-Kutta time stepping scheme which uses a finite-volume spatial discretization on an unstructured grid made up of triangles. The algorithm also employs an adaptive mesh refinement procedure which enriches the mesh locally to more accurately resolve the vortical flow features. Results are presented for several highly-swept delta wing and circular cone cases at high angles of attack and at supersonic freestream flow conditions. Accurate solutions were obtained more efficiently when adaptive mesh refinement was used in contrast with refining the grid globally. The paper presents descriptions of the conical Euler/Navier-Stokes flow solver and adaptive mesh refinement procedures along with results which demonstrate the capability.

Batina, John T.↗
NASA NTRS1990

The semidiscrete Galerkin finite element modeling of compressible viscous flow past an airfoil

The primary project was the numerical simulation, by a finite element/finite difference method, of the viscous flow about an airfoil. The secondary project involved the numerical simulation of the three-dimensional separated and vortex-dominated flow about a hemispherically capped cylinder in the transonic regime. Preliminary calculations were started for the hemisphere-cylinder at 0 and 5 degree angle of attack. The solution of the flow field about airfoils and wings is required to determine the important parameters of lift, moment, and drag. Viscous effects must be accounted for if the drag is to be accurately calculated. At present there are basically two approaches to the numerical simulation of the flow field, the use of fully viscous models and the inviscid/viscous models. The fully viscous models require the solution of an approximation of the Navier-Stokes equations and therefore should simulate most of the physical mechanisms. A fast, accurate, and computationally efficient inviscid flow solver was recently developed by Hartwich. It is thought that Hartwich's program coupled to a fast, accurate, and computationally efficient boundary layer code, will make an excellent tool for airfoil design. The purpose of the primary project was to develop a compressible boundary layer code using the semidiscrete Galerkin finite element method. The numerical scheme employed used the combination of a Dorodnitsyn formulation of the boundary layer equations, with a finite difference/finite element procedure (semidiscrete Galerkin method), in the solution of the compressible two-dimensional boundary layer equations. A laminar compressible boundary layer code was developed and tested for a NACA 0012 airfoil at a Mach number of 0.5, a Reynolds number of 5000, and zero angle of attack. At present the boundary layer program solves up to, but not beyond, separation.

Meade, Andrew J.↗
NASA NTRS1982

Approximate boundary condition procedure for the two-dimensional numerical solution of vortex wakes

Research on efficient computational methods for general vorticity fields has been conducted in connection with a need for basic research on vortex-dominated flows. The present investigation is concerned with the evolution of vortex wakes behind aircraft wings. An efficient procedure is presented for the calculation of the boundary values used in the numerical solution of the unsteady, incompressible, two-dimensional Navier-Stokes equations for an unbounded flow field. The extent of the computational grid can be reduced compared to methods utilizing standard boundary conditions, without loss of accuracy. The efficiencies realized make it feasible to calculate the vortex wake development for realistic wing configurations, including the merging of multiple vortices, for Reynolds numbers of about 10,000 based on wing chord.

Weston, R. P.↗
NASA NTRS1987

The numerical simulation of subsonic flutter

The present paper describes a numerical simulation of unsteady, subsonic aeroelastic responses. The technique accounts for aerodynamic nonlinearities associated with angles of attack, vortex-dominated flow, static deformations, and unsteady behavior. The fluid and the wing together are treated as a single dynamic system, and the equations of motion for the structure and flowfield are integrated simultaneously and interactively in the time domain. The method employs an iterative scheme based on a predictor-corrector technique. The aerodynamic loads are computed by the general unsteady vortex-lattice method and are determined simultaneously with the motion of the wing. Two models are used to demonstrate the technique: a rigid wing on an elastic support experiencing plunge and pitch about the elastic axis, and a continuous wing rigidly supported at the root chord experiencing spanwise bending and twisting. The time domain solution coupled with the unsteady vortex-lattice method provides the capability of graphically depicting wing and wake motion. Several graphs that illustrate the time domain behavior of the wing and wake are presented.

Strganac, Thomas W.↗
NASA NTRS1987

A Numerical Model of Unsteady, Subsonic Aeroelastic Behavior

A method for predicting unsteady, subsonic aeroelastic responses was developed. The technique accounts for aerodynamic nonlinearities associated with angles of attack, vortex-dominated flow, static deformations, and unsteady behavior. The fluid and the wing together are treated as a single dynamical system, and the equations of motion for the structure and flow field are integrated simultaneously and interactively in the time domain. The method employs an iterative scheme based on a predictor-corrector technique. The aerodynamic loads are computed by the general unsteady vortex-lattice method and are determined simultaneously with the motion of the wing. Because the unsteady vortex-lattice method predicts the wake as part of the solution, the history of the motion is taken into account; hysteresis is predicted. Two models are used to demonstrate the technique: a rigid wing on an elastic support experiencing plunge and pitch about the elastic axis, and an elastic wing rigidly supported at the root chord experiencing spanwise bending and twisting. The method can be readily extended to account for structural nonlinearities and/or substitute aerodynamic load models. The time domain solution coupled with the unsteady vortex-lattice method provides the capability of graphically depicting wing and wake motion.

Strganac, Thomas W.↗
NASA NTRS1987

Numerical solution of the Navier-Stokes equations with emphasis on rotorcraft applications

Recent advances in CFD are surveyed, with a focus on the applicability of codes based on the Navier-Stokes (NS) equations to helicopter aerodynamics. The developmental history of two- and three-dimensional NS codes is recalled; the formulations employed by codes of increasing complexity are outlined; and previous reviews are noted. Particular attention is given to Reynolds-averaged NS methods and their use in analyzing subsonic, transonic, and vortex-dominated flows. Typical numerical results are compared with experimental data in diagrams and graphs, and a number of outstanding problems are considered.

Holst, Terry L.↗
NASA NTRS1988

Prediction of unsteady loads on maneuvering delta wings using time-accurate Euler schemes

Three-dimensional steady and unsteady vortex-dominated flows around sharp-edged delta wings are considered in this paper. The problem is formulated by using the unsteady conservative Euler equations for the flow relative motion with respect to a moving frame of reference. An implicit approximately-factored finite volume scheme is used to solve the resulting equations on a three-dimensional computational grid which is generated by using a modified Joukowski transformation in cross-flow planes at the grid chord stations. The scheme is applied to a delta wing undergoing pitching oscillation around a large angle of attack. The initial conditions correspond to a steady flow around a delta wing of aspect ratio of one, freestream Mach number of 0.3 and mean angle of attack of 20.5. The steady flow results are compared with those of an explicit computational scheme and the experimental data, and they are in good agreement.

Kandil, Osama A.↗
NASA NTRS1990

Conical Euler simulation and active suppression of delta wing rocking motion

A conical Euler code was developed to study unsteady vortex-dominated flows about rolling highly-swept delta wings, undergoing either forced or free-to-roll motions including active roll suppression. The flow solver of the code involves a multistage Runge-Kutta time-stepping scheme which uses a finite volume spatial discretization of the Euler equations on an unstructured grid of triangles. The code allows for the additional analysis of the free-to-roll case, by including the rigid-body equation of motion for its simultaneous time integration with the governing flow equations. Results are presented for a 75 deg swept sharp leading edge delta wing at a freestream Mach number of 1.2 and at alpha equal to 10 and 30 deg angle of attack. A forced harmonic analysis indicates that the rolling moment coefficient provides: (1) a positive damping at the lower angle of attack equal to 10 deg, which is verified in a free-to-roll calculation; (2) a negative damping at the higher angle of attack equal to 30 deg at the small roll amplitudes. A free-to-roll calculation for the latter case produces an initially divergent response, but as the amplitude of motion grows with time, the response transitions to a wing-rock type of limit cycle oscillation. The wing rocking motion may be actively suppressed, however, through the use of a rate-feedback control law and antisymmetrically deflected leading edge flaps. The descriptions of the conical Euler flow solver and the free-to-roll analysis are presented. Results are also presented which give insight into the flow physics associated with unsteady vortical flows about forced and free-to-roll delta wings, including the active roll suppression of this wing-rock phenomenon.

Lee, Elizabeth M.↗
NASA NTRS1981

An empirical method for computing leeside centerline heating on the Space Shuttle Orbiter

An empirical method is presented for computing top centerline heating on the Space Shuttle Orbiter at simulated reentry conditions. It is shown that the Shuttle's top centerline can be thought of as being under the influence of a swept cylinder flow field. The effective geometry of the flow field, as well as top centerline heating, are directly related to oil-flow patterns on the upper surface of the fuselage. An empirical turbulent swept cylinder heating method was developed based on these considerations. The method takes into account the effects of the vortex-dominated leeside flow field without actually having to compute the detailed properties of such a complex flow. The heating method closely predicts experimental heat-transfer values on the top centerline of a Shuttle model at Mach numbers of 6 and 10 over a wide range in Reynolds number and angle of attack.

Helms, V. T., III↗
NASA NTRS1989

High resolution flow field prediction for tail rotor aeroacoustics

The prediction of tail rotor noise due to the impingement of the main rotor wake poses a significant challenge to current analysis methods in rotorcraft aeroacoustics. This paper describes the development of a new treatment of the tail rotor aerodynamic environment that permits highly accurate resolution of the incident flow field with modest computational effort relative to alternative models. The new approach incorporates an advanced full-span free wake model of the main rotor in a scheme which reconstructs high-resolution flow solutions from preliminary, computationally inexpensive simulations with coarse resolution. The heart of the approach is a novel method for using local velocity correction terms to capture the steep velocity gradients characteristic of the vortex-dominated incident flow. Sample calculations have been undertaken to examine the principal types of interactions between the tail rotor and the main rotor wake and to examine the performance of the new method. The results of these sample problems confirm the success of this approach in capturing the high-resolution flows necessary for analysis of rotor-wake/rotor interactions with dramatically reduced computational cost. Computations of radiated sound are also carried out that explore the role of various portions of the main rotor wake in generating tail rotor noise.

Quackenbush, Todd R.↗
NASA NTRS1989

Application of unstructured grid methods to steady and unsteady aerodynamic problems

The purpose is to describe the development of unstructured grid methods which have several advantages when compared to methods which make use of structured grids. Unstructured grids, for example, easily allow the treatment of complex geometries, allow for general mesh movement for realistic motions and structural deformations of complete aircraft configurations which is important for aeroelastic analysis, and enable adaptive mesh refinement to more accurately resolve the physics of the flow. Steady Euler calculations for a supersonic fighter configuration to demonstrate the complex geometry capability; unsteady Euler calculations for the supersonic fighter undergoing harmonic oscillations in a complete-vehicle bending mode to demonstrate the general mesh movement capability; and vortex-dominated conical-flow calculations for highly-swept delta wings to demonstrate the adaptive mesh refinement capability are discussed. The basic solution algorithm is a multi-stage Runge-Kutta time-stepping scheme with a finite-volume spatial discretization based on an unstructured grid of triangles in 2D or tetrahedra in 3D. The moving mesh capability is a general procedure which models each edge of each triangle (2D) or tetrahedra (3D) with a spring. The resulting static equilibrium equations which result from a summation of forces are then used to move the mesh to allow it to continuously conform to the instantaneous position or shape of the aircraft. The adaptive mesh refinement procedure enriches the unstructured mesh locally to more accurately resolve the vortical flow features. These capabilities are described in detail along with representative results which demonstrate several advantages of unstructured grid methods. The applicability of the unstructured grid methodology to steady and unsteady aerodynamic problems and directions for future work are discussed.

Batina, John T.↗