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NASA NTRS1983

Streamwise computation of three-dimensional parabolic flows

A new approach to calculate three-dimensional parabolic flows is presented. The flow field is computed by calculating velocity along a set of streamlines. The dependent variables commonly used in the computation of three-dimensional flows are the three velocity components. In contrast, the dependent variables in the present approach are the streamwise velocity and the two coordinates, in the cross-stream plane, of the chosen streamlines. The streamwise velocity is calculated from the finite difference equations obtained by applying Euler's momentum theorem to streamtubes constructed around the chosen streamlines; the streamline coordinates are calculated from the conservation of mass. Results of the calculations, based on the present approach, are compared with the experimental data for flow through rectangular ducts; the agreement is satisfactory.

Greywall, M. S.↗
DOE OSTI2026

A cell-centered AMR-ALE framework for 3D multi-material hydrodynamics. Part II: linesweep ALE rezoning for nonconformal block-structured AMR meshes

The simulation of flows presenting contact discontinuities, vorticity, and large variations in spatial scales can be performed in a framework coupling Arbitrary Lagrangian Eulerian (ALE) algorithms and Adaptive Mesh Refinement (AMR). This coupling requires adaptation of ALE rezoning techniques to meshes containing nonconformal nodes arising from both the AMR topology and the junction of mesh blocks. Here, in this paper, we present an ALE rezoning strategy that is compatible with such meshes, and that can also act as a disentangling algorithm. Emphasis is put on an algorithm that respects intrinsic Lagrangian mesh properties in order to preserve accuracy around discontinuities. To that end, we adapt the weighted linesweep algorithm to nonconformal block-structured AMR meshes. Then, we present control parameters introduced in the method for it to be applicable in practical situations. Notably, the method is coupled to a specific metric optimization in order to palliate some shortcomings of the linesweep method. Finally, numerical test cases are presented that feature the capabilities of the ALE-AMR algorithm for flows that present discontinuities, vorticity, and a variety of scales. Notably, we show that our ALE-AMR algorithm gives results at least similar to Euler-AMR, but provides better accuracy in cases where discontinuities are involved, thanks to a method that respects the Lagrangian features of the mesh. Additionally, it enables Euler-AMR-like computations on domains with temporally varying domain boundaries.

Adaptive mesh refinement↗
NASA NTRS1983

Spectral methods for inviscid, compressible flows

Report developments in the application of spectral methods to two dimensional compressible flows are reviewed. A brief introduction to spectral methods -- their history and especially their implementation -- is provided. The stress is on those techniques relevant to transonic flow computation. The spectral multigrid iterative methods are discussed with application to the transonic full potential equation. Discontinuous solutions of the Euler equations are considered. The key element is the shock fitting technique which is briefly explained.

Hussaini, M. Y.↗
NASA NTRS1985

Spectral methods for inviscid, compressible flows

Report developments in the application of spectral methods to two dimensional compressible flows are reviewed. A brief introduction to spectral methods - their history and especially their implementation - is provided. The stress is on those techniques relevant to transonic flow computation. The spectral multigrid iterative methods are discussed with application to the transonic full potential equation. Discontinuous solutions of the Euler equations are considered. The key element is the shock fitting technique which is briefly explained.

Hussaini, M. Y.↗
NASA NTRS1988

A point implicit unstructured grid solver for the Euler and Navier-Stokes equations

An upwind finite element technique that uses cell centered quantities and implicit and/or explicit time marching has been developed for computing hypersonic laminar viscous flows using adaptive unstructured triangular grids. A structured grid of quadrilaterals is laid out near the body surface. For inviscid flows the method is stable at Courant numbers of over 100,000. A first order basic scheme and a higher order flux corrected transport (FCT) scheme have been implemented. This technique has been applied to the problem of predicting type III and IV shock wave interactions on a cylinder, with a view of simulating the pressure and heating rate augmentation caused by an impinging shock on the leading edge of a cowl lip of an engine inlet. The predictions of wall pressure and heating rates compare very well with experimental data. The flow features are very distinctly captured with a sequence of adaptively generated grids. The adaptive mesh generator and the upwind Navier-Stokes solver are combined in a set of programs called LARCNESS, an acronym for Langley Adaptive Remeshing Code and Navier-Stokes Solver.

Thareja, Rajiv R.↗
NASA NTRS1990

Euler and Navier-Stokes computations for two-dimensional geometries using unstructured meshes

A general purpose unstructured mesh solver for steady-state two-dimensional inviscid and viscous flows is described. The efficiency and accuracy of the method are enhanced by the simultaneous use of adaptive meshing and an unstructured multigrid technique. A method for generating highly stretched triangulations in regions of viscous flow is outlined, and a procedure for implementing an algebraic turbulence model on unstructured meshes is described. Results are shown for external and internal inviscid flows and for turbulent viscous flow over a multi-element airfoil configuration.

Mavriplis, D. J.↗
NASA NTRS1990

Hypersonic waverider design from given shock waves

An attempt is made to generate waverider flows from given shock wave geometries using two approaches. In the first approach, axisymmetric flows are used to construct more general flows based on the concept of osculating cones. Conical waverider design can thus be extended to yield results also for shocks forming a slope surface. The second approach involves solving the ill-posed problem of prescribing a shock wave and finding the flow field behind it. A new numerical marching technique with some features of characteristic cross marching is used to solve the Euler equation. The code selection and some test cases are discussed.

Sobieczky, H.↗
NASA NTRS1991

A two-dimensional Euler solution for an unbladed jet engine configuration

A two dimensional nonaxisymmetric Euler solution in a geometric representation of a jet engine configuration without blades is presented. The domain, including internal and external flow, is covered with a multiblock grid. To construct the grid, a domain decomposition technique is used to subdivide the domain and smooth grids are dimensioned and placed in each block. The grid contains 44 blocks which cover the external field, the inlet, bypass duct, core duct and nozzle of the nonaxisymmetric engine configuration. The geometry is symmetric about the meanline of the hub, but the grid is not since there is no symmetry condition applied to the grid between the two halves. With a symmetric grid at zero angle of attack, the measures of the solution would cancel exactly. With an asymmetric grid, the solution will not necessarily be symmetric and the lift coefficient will not necessarily be zero. Thus, grid asymmetry can be exploited to verify the resolution of the solution. The solution may be verified on the basis of five theoretical quantities: conservation of mass and energy, deviation of the lift coefficient from zero, deviation of the drag coefficient from zero, deviations from constant entropy, and deviations in the pressure distributions over the symmetric surfaces of the components. This technique is suitable for obtaining numerical solutions in complex geometries and provides a foundation for complete engine throughflow calculations.

Stewart, Mark E. M.↗
NASA NTRS1992

Convergence acceleration of the Proteus computer code with multigrid methods

Presented here is the first part of a study to implement convergence acceleration techniques based on the multigrid concept in the Proteus computer code. A review is given of previous studies on the implementation of multigrid methods in computer codes for compressible flow analysis. Also presented is a detailed stability analysis of upwind and central-difference based numerical schemes for solving the Euler and Navier-Stokes equations. Results are given of a convergence study of the Proteus code on computational grids of different sizes. The results presented here form the foundation for the implementation of multigrid methods in the Proteus code.

Demuren, A. O.↗
NASA NTRS1993

Energy considerations in computational aeroacoustics

A finite-volume multistage time-stepping Euler code is used to investigate the use of CFD algorithms for the direct calculation of acoustics. The 2D compressible inviscid flow about an accelerating or decelerating circular cylinder is used as a model problem. The time evolution of the energy transfer from the cylinder to the fluid, as the cylinder is moved from rest to some nonnegligible velocity, is clearly seen. By examining the temporal and spatial characteristics of the numerical solution, a distinction can be made between the propagating acoustic energy, the convecting energy associated with the entropy change in the fluid, and the energy contained in the local aerodynamic field. Systematic variation of the cylinder acceleration shows that the radiated acoustic energy depends strongly upon the rate of acceleration or deceleration. The computational grid has a large effect on the ratio of acoustic energy to nonphysical entropy associated energy, while the role of the explicit artificial viscosity seems to be of second order. The entropy term was nearly negligible in all cases the cylinder was started slowly.

Brentner, Kenneth S.↗
NASA NTRS1997

Computational Considerations for the Simulation of Discontinuous Flows

The numerical study of aeroacoustic problems places stringent demands on the choice of a computational algorithm, because it requires the ability to propagate disturbances of small amplitude and short wavelength. The demands are particularly high when shock waves are involved, because the chosen algorithm must also resolve discontinuities in the solution. In a previous work the capabilities and deficiencies of shock-capturing methods for aeroacoustic problems were demonstrated using a high-order essentially nonoscillatory (ENO) numerical method. It was shown that first-order results are obtained when simulating time-dependent flows with discontinuities. The present study reaffirms this conclusion by comparing the ENO results with those obtained using a conventional linear scheme. A sixth-order-accurate compact implicit finite difference scheme is used to investigate various discontinuous flows. The design order of accuracy is achieved in the smooth regions of a steady-state, quasi-one-dimensional Euler test case, as well as in the time-dependent Burgers' equation. However, in the unsteady Euler sound-shock interaction, first-order results are obtained downstream of the shock. A comparison is made between the linear and nonlinear results, noting the advantages of each method. A discontinuous linear model problem is then used to identify the cause of the first-order results. Here, the nature of the solution error is quantified as being predominantly a numerical phase shift, and a post-processing procedure is demonstrated which increases the solution accuracy downstream of the discontinuity to second-order.

Carpenter Mark H.↗
NASA NTRS2008

Output-Adaptive Tetrahedral Cut-Cell Validation for Sonic Boom Prediction

A cut-cell approach to Computational Fluid Dynamics (CFD) that utilizes the median dual of a tetrahedral background grid is described. The discrete adjoint is also calculated, which permits adaptation based on improving the calculation of a specified output (off-body pressure signature) in supersonic inviscid flow. These predicted signatures are compared to wind tunnel measurements on and off the configuration centerline 10 body lengths below the model to validate the method for sonic boom prediction. Accurate mid-field sonic boom pressure signatures are calculated with the Euler equations without the use of hybrid grid or signature propagation methods. Highly-refined, shock-aligned anisotropic grids were produced by this method from coarse isotropic grids created without prior knowledge of shock locations. A heuristic reconstruction limiter provided stable flow and adjoint solution schemes while producing similar signatures to Barth-Jespersen and Venkatakrishnan limiters. The use of cut-cells with an output-based adaptive scheme completely automated this accurate prediction capability after a triangular mesh is generated for the cut surface. This automation drastically reduces the manual intervention required by existing methods.

Park, Michael A.↗
NASA NTRS2010

Modeling the Launch Abort Vehicle's Subsonic Aerodynamics from Free Flight Testing

An investigation into the aerodynamics of the Launch Abort Vehicle for NASA's Constellation Crew Launch Vehicle in the subsonic, incompressible flow regime was conducted in the NASA Langley 20-ft Vertical Spin Tunnel. Time histories of center of mass position and Euler Angles are captured using photogrammetry. Time histories of the wind tunnel's airspeed and dynamic pressure are recorded as well. The primary objective of the investigation is to determine models for the aerodynamic yaw and pitch moments that provide insight into the static and dynamic stability of the vehicle. System IDentification Programs for AirCraft (SIDPAC) is used to determine the aerodynamic model structure and estimate model parameters. Aerodynamic models for the aerodynamic body Y and Z force coefficients, and the pitching and yawing moment coefficients were identified.

Hartman, Christopher L.↗
NASA NTRS2019

Predicting Transonic Flutter Using Nonlinear Computational Simulations

This paper builds on the computational aeroelastic results published previously and generated in support of the second Aeroelastic Prediction Workshop for the NASA Benchmark Supercritical Wing configuration. The computational results are obtained using FUN3D, an unstructured flow solver developed at the NASA Langley Research Center. Flutter analyses are performed using various aerodynamic models including linear doublet lattice, Euler solutions, Reynolds averaged Navier-Stokes and Delayed Detached Eddy Simulations. The analyses are performed across the transonic Mach range for a range in angle of attack from 0° to 5°, with focus on identifying the transonic dips in the flutter onset boundaries.

Heeg, Jennifer↗
NASA NTRS2022

Validation of a High-Fidelity Supersonic Parachute Inflation Dynamics Model and Best Practice

The parachute inflation dynamics (PID) of a Disk-Gap-Band (DGB) parachute system travelling at supersonic velocities in the high-altitude Earth atmosphere is simulated using a high-fidelity, multiphysics, massively-parallel computational framework. The sensitivity of the simulation results with respect to critical modelling and simulation parameters, including the fluid mechanical governing equations (Euler vs Navier-Stokes with RANS turbulence closure vs Navier-Stokes with LES turbulence closer), the interaction between the flow and the suspension lines (accounted for vs not accounted for), the dynamics of the payload (restrained vs free), and the material model of the heterogeneous fabric canopy (Saint-Venant Kirchoff vs mechanics-informed multiscale neural network), is extensively investigated. The parameter investigation is enabled by advancements to the state-of-the-art in the modelling and simulation of the supersonic parachute inflation process, which are presented as part of the computational framework. The predictive quality of the computational framework in the context of supersonic PID is validated by comparison of the simulation results with the experimental results from NASA’s Advanced Supersonic Parachute Research (ASPIRE) project. Through the validation, best practices for the modelling and simulation of supersonic PID are developed and proposed.

Rabinovitch, Jason↗
NASA NTRS1999

Development and Validation of a Fast, Accurate and Cost-Effective Aeroservoelastic Method on Advanced Parallel Computing Systems

Progress to date towards the development and validation of a fast, accurate and cost-effective aeroelastic method for advanced parallel computing platforms such as the IBM SP2 and the SGI Origin 2000 is presented in this paper. The ENSAERO code, developed at the NASA-Ames Research Center has been selected for this effort. The code allows for the computation of aeroelastic responses by simultaneously integrating the Euler or Navier-Stokes equations and the modal structural equations of motion. To assess the computational performance and accuracy of the ENSAERO code, this paper reports the results of the Navier-Stokes simulations of the transonic flow over a flexible aeroelastic wing body configuration. In addition, a forced harmonic oscillation analysis in the frequency domain and an analysis in the time domain are done on a wing undergoing a rigid pitch and plunge motion. Finally, to demonstrate the ENSAERO flutter-analysis capability, aeroelastic Euler and Navier-Stokes computations on an L-1011 wind tunnel model including pylon, nacelle and empennage are underway. All computational solutions are compared with experimental data to assess the level of accuracy of ENSAERO. As the computations described above are performed, a meticulous log of computational performance in terms of wall clock time, execution speed, memory and disk storage is kept. Code scalability is also demonstrated by studying the impact of varying the number of processors on computational performance on the IBM SP2 and the Origin 2000 systems.

Goodwin, Sabine A.↗
NASA NTRS2015

The Prediction of Scattered Broadband Shock-Associated Noise

A mathematical model is developed for the prediction of scattered broadband shock-associated noise. Model arguments are dependent on the vector Green's function of the linearized Euler equations, steady Reynolds-averaged Navier-Stokes solutions, and the two-point cross-correlation of the equivalent source. The equivalent source is dependent on steady Reynolds-averaged Navier-Stokes solutions of the jet flow, that capture the nozzle geometry and airframe surface. Contours of the time-averaged streamwise velocity component and turbulent kinetic energy are examined with varying airframe position relative to the nozzle exit. Propagation effects are incorporated by approximating the vector Green's function of the linearized Euler equations. This approximation involves the use of ray theory and an assumption that broadband shock-associated noise is relatively unaffected by the refraction of the jet shear layer. A non-dimensional parameter is proposed that quantifies the changes of the broadband shock-associated noise source with varying jet operating condition and airframe position. Scattered broadband shock-associated noise possesses a second set of broadband lobes that are due to the effect of scattering. Presented predictions demonstrate relatively good agreement compared to a wide variety of measurements.

Miller, Steven A. E.↗
NASA NTRS1991

Potential flow applications to complex configurations

Recent advances in CFD methods have enabled the analytic calculation of the carriage loads for stores mounted on complex aircraft. The latest results have demonstrated excellent agreement with test data for the F-15 at M = 0.98. However, in a preliminary design environment, the necessity of generating and validating a Euler grid to fit the aircraft and store arrangement may not be feasible, particularly when effects of configuration changes are considered. For that reason alternative approaches which require less time to arrive at an answer deserve consideration. The paper presents the results of a study to determine if potential flow solutions can give acceptable estimates of store carriage loads at transonic speeds in a timely manner.

Cenko, A.↗