Unsteady transonic flow calculations for realistic aircraft configurations
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Batina, John T.↗
Engineering topics
Batina, John T.
Publications and source records attributed to Batina, John T..
Unsteady Euler airfoil solutions using unstructured dynamic meshes
Two algorithms for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis of oscillating airfoils. Both algorithms were developed for use on an unstructured grid made up of triangles. The first flow solver involves a Runge-Kutta time-stepping scheme with a finite-volume spatial discretization that reduces to central differencing on a rectangular mesh. The second flow solver involves a modified Euler time-integration scheme with an upwind-biased spatial discretization based on the flux-vector splitting of Van Leer. The paper presents descriptions of the Euler solvers and dynamic mesh algorithm along with results which assess the capability.
Batina, John T.↗
Unsteady Euler algorithm with unstructured dynamic mesh for complex-aircraft aeroelastic analysis
A finite-volume unstructured-grid FEM scheme with multistage Runge-Kutta time stepping is applied to the three-dimensional time-dependent Euler equations for inviscid flows on complex aircraft configurations undergoing structural deformation. The derivation of the model, the solution procedure, and the computer implementation are described, and results are presented graphically for a NASA Langley supersonic fighter aircraft model in steady and unsteady (harmonic oscillation in complete-vehicle bending mode) flow regimes. Good agreement between FEM predictions and experimental data is demonstrated.
Batina, John T.↗
Supersonic far-field boundary conditions for transonic small-disturbance theory
Characteristic far-field boundary conditions for supersonic freestream flow have been developed and implemented within a transonic small-disturbance code. The boundary conditions have been implemented within the CAP-TSD code which has been developed recently for aeroelastic analysis of complete aircraft configurations. These boundary conditions improve the accuracy of the solutions for supersonic freestream applications. They also allow the extent of the grid to be much smaller, thus providing savings in the computational time required to obtain solutions. Comparisons are shown between surface pressures computed using large and small grid extents for the NACA 0012 airfoil and the F-5 wing at various Mach numbers and angles of attack. Both steady and unsteady results are presented and comparisons are made with Euler results and with experimental data to assess the accuracy of the new far-field boundary conditions. Comparisons of these results show that the supersonic boundary conditions allow a much smaller grid to be used without losing accuracy.
Gibbons, Michael D.↗
Euler flutter analysis of airfoils using unstructured dynamic meshes
Modifications to a two-dimensional unsteady Euler code for the aeroelastic analysis of airfoils are described. The modifications involve including the structural equations of motion and their simultaneous time-integration with the governing flow equations. A novel aspect of the capability is that the solutions are obtained using unstructured grids made up of triangles. Comparisons are made with parallel calculations performed using linear theory and a structured grid Euler code to assess the accuracy of the unstructured grid Euler results. Results are presented for a flat plate airfoil and the NACA 0012 airfoil to demonstrate applications of the Euler code for generalized force computations and aeroelastic analysis. In these comparisons, two different finite-volume discretizations of the Euler equations on unstructured meshes were employed. Sensitivity of the Euler results to changes in numerical parameters were also investigated.
Rausch, Russ D.↗
Unsteady aerodynamics methods for transonic aeroelastic analysis
The paper describes the current status of methods development for transonic aeroelastic analysis within the Unsteady Aerodynamics Branch at NASA Langley. The paper first highlights the development of an approximate factorization (AF) algorithm for solution of the unsteady transonic small-distribution (TSD) equation. The AF algorithm has been used as the basis for a three-dimensional TSD code for complete aircraft applications. The paper also describes the development of solution algorithms for the unsteady Euler equations based on the use of unstructured meshes. These Euler methods contain a dynamic mesh algorithm, which is a general procedure to move or deform the mesh so that it continuously conforms to the instantaneous shape of the aeroelastically deformed vehicle.
Batina, John T.↗
Application of the CAP-TSD unsteady transonic small disturbance program to wing flutter
The application and assessment of a computer program called CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) for flutter predictions are described. Flutter calculations are presented for two thin swept-and-tapered wing planforms with well-defined modal properties. One planform is a series of 45-degree swept wings and the other planform is a clipped delta wing. Comparisons are made between the results of CAP-TSD using the linear equation and no airfoil thickness and the results obtained from a subsonic kernel function analysis. The calculations cover a Mach number range from low subsonic to low supersonic values, including the transonic range, and are compared with subsonic linear theory and experimental data. It is noted that since both wings have very thin airfoil sections, the effects of thickness are minimal.
Bennett, Robert M.↗
Accurate solutions, parameter studies and comparisons for the Euler and potential flow equations
Parameter studies are conducted using the Euler and potential flow equation models for steady and unsteady flows in both two and three dimensions. The Euler code is an implicit, upwind, finite volume code which uses the Van Leer method of flux vector splitting which has been recently extended for use on dynamic meshes and maintain all the properties of the original splitting. The potential flow code is an implicit, finite difference method for solving the transonic small disturbance equations and incorporates both entropy and vorticity corrections into the solution procedures thereby extending its applicability into regimes where shock strength normally precludes its use. Parameter studies resulting in benchmark type calculations include the effects of spatial and temporal refinement, spatial order of accuracy, far field boundary conditions for steady flow, frequency of oscillation, and the use of subiterations at each time step to reduce linearization and factorization errors. Comparisons between Euler and potential flow results are made, as well as with experimental data where available.
Anderson, W. Kyle↗
Modern wing flutter analysis by computational fluid dynamics methods
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Cunningham, Herbert J.↗
Accurate solutions, parameter studies and comparisons for the Euler and potential flow equations
Parameter studies are conducted using the Euler and potential flow equation models for unsteady and steady flows in both two and three dimensions. The Euler code is an implicit, upwind, finite volume code which uses the Van Leer method of flux-vector-splitting which has been recently extended for use on dynamic meshes and maintain all the properties of the original splitting. The potential flow code is an implicit, finite difference method for solving the transonic small disturbance equations and incorporates both entropy and vorticity corrections into the solution procedures thereby extending its applicability into regimes where shock strength normally precludes its use. Parameter studies resulting in benchmark type calculations include the effects of spatial and temporal refinement, spatial order of accuracy, far field boundary conditions for steady flow, frequency of oscillation, and the use of subiterations at each time step to reduce linearization and factorization errors. Comparisons between Euler and potential flows results are made as well as with experimental data where available.
Anderson, W. Kyle↗
Recent advances in transonic computational aeroelasticity
A transonic unsteady aerodynamic and aeroelasticity code called CAP-TSD was developed for application to realistic aircraft configurations. The code permits the calculation of steady and unsteady flows about complete aircraft configurations for aeroelastic analysis in the flutter critical transonic speed range. The CAP-TSD code uses a time accurate approximate factorization algorithm for solution of the unsteady transonic small disturbance potential equation. An overview is given of the CAP-TSD code development effort and results are presented which demonstrate various capabilities of the code. Calculations are presented for several configurations including the General Dynamics 1/9 scale F-16 aircraft model and the ONERA M6 wing. Calculations are also presented from a flutter analysis of a 45 deg sweptback wing which agrees well with the experimental data. Descriptions are presented of the CAP-TSD code and algorithm details along with results and comparisons which demonstrate these recent developments in transonic computational aeroelasticity.
Batina, John T.↗
Efficient algorithm for solution of the unsteady transonic small-disturbance equation
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Batina, John T.↗
Wing flutter calculations with the CAP-TSD unsteady transonic small disturbance program
The application and assessment is described of CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code for flutter prediction. The CAP-TSD program was developed for aeroelastic analysis of complete aircraft configurations and was previously applied to the calculation of steady and unsteady pressures. Flutter calculations are presented for two thin, swept-and-tapered wing planforms with well defined modal properties. The calculations are for Mach numbers from low subsonic to low supersonic values, including the transonic range, and are compared with subsonic linear theory and experimental flutter data. The CAP-TSD flutter results are generally in good agreement with the experimental values and are in good agreement with subsonic linear theory when wing thickness is neglected.
Bennett, Robert M.↗
Unsteady transonic small-disturbance theory including entropy and vorticity effects
Modifications to unsteady transonic small disturbance theory to include entropy and vorticity effects are presented. The modifications were implemented in the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code. The code permits the aeroelastic analysis of complete aircraft configurations in the flutter critical transonic speed range. Entropy and vorticity effects were incorporated within the solution procedure to more accurately analyze flows with strong shock waves. The modified code includes these effects while retaining the relative simplicity and cost efficiency of the TSD formulation. Detailed descriptions are presented of the entropy and vorticity modifications along with calculated results and comparisons which assess the modified theory. These results are in good agreement with parallel Euler calculations and with experimental data. Therefore, the present method now provides the aeroelastician with an affordable capability to analyze relatively difficult transonic flows without having to solve the computationally more expensive Euler equations.
Batina, John T.↗
Steady and unsteady transonic small disturbance analysis of realistic aircraft configurations
A transonic unsteady aerodynamic and aeroelasticity code CAP-TSD (Computational Aeroelasticity Program-Transonic Small Disturbance) has been developed for application to realistic aircraft configurations. The code uses a time-accurate approximate factorization (AF) algorithm for solution of the unsteady transonic small-disturbance potential equation. The paper gives an overview of the CAP-TSD code development effort and reports on recent algorithm modifications. The algorithm modifications include: an Engquist-Osher (E-O) type-dependent switch to treat regions of supersonic flow, extension of the E-O switch for second-order spatial accuracy, nonisentropic effects to treat strong-shock cases, nonreflecting far field boundary conditions for unsteady applications, and several modifications to accelerate convergence to steady state. The modifications have significantly improved the stability of the AF algorithm and hence the reliability of the CAP-TSD code in general. Calculations are also presented from a flutter analysis of a 45-deg sweptback wing which agree well with experimental data. The paper present descriptions of the CAP-TSD code and algorithm details along with results.
Batina, John T.↗
Computational transonic flutter boundary tracking procedure
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Gallman, John W.↗
Mach number effects on transonic aeroelastic forces and flutter characteristics
Transonic aeroelastic stability analysis and flutter calculations are presented for a generic transport-type wing based on the use of the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) finite-difference code. The CAP-TSD code was recently developed for transonic unsteady aerodynamic and aeroelastic analysis of complete aircraft configurations. A binary aeroelastic system consisting of simple bending and torsion modes was used to study aeroelastic behavior at transonic speeds. Generalized aerodynamic forces are presented for a wide range of Mach number and reduced frequency. Aeroelastic characteristics are presented for variations in freestream Mach number, mass ratio, and bending-torsion frequency ratio. Flutter boundaries are presented which have two transonic dips in flutter speed. The first dip is the usual transonic dip involving a bending-dominated flutter mode. The second dip is characterized by a single degree-of-freedom torsion oscillation. These aeroelastic results are physically interpreted and shown to be related to the steady state shock location and changes in generalized aerodynamic forces due to freestream Mach number.
Mohr, Ross W.↗
Modern wing flutter analysis by computational fluid dynamics methods
The application and assessment of the recently developed CAP-TSD transonic small-disturbance code for flutter prediction is described. The CAP-TSD code has been developed for aeroelastic analysis of complete aircraft configurations and was previously applied to the calculation of steady and unsteady pressures with favorable results. Generalized aerodynamic forces and flutter characteristics are calculated and compared with linear theory results and with experimental data for a 45 deg sweptback wing. These results are in good agreement with the experimental flutter data which is the first step toward validating CAP-TSD for general transonic aeroelastic applications. The paper presents these results and comparisons along with general remarks regarding modern wing flutter analysis by computational fluid dynamics methods.
Cunningham, Herbert J.↗