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At least 649 records · Page 36

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NASA NTRS1990

Temporal-adaptive Euler/Navier-Stokes algorithm for unsteady aerodynamic analysis of airfoils using unstructured dynamic meshes

A temporal adaptive algorithm for the time-integration of the two-dimensional Euler or Navier-Stokes equations is presented. The flow solver involves an upwind flux-split spatial discretization for the convective terms and central differencing for the shear-stress and heat flux terms on an unstructured mesh of triangles. The temporal adaptive algorithm is a time-accurate integration procedure which allows flows with high spatial and temporal gradients to be computed efficiently by advancing each grid cell near its maximum allowable time step. Results indicate that an appreciable computational savings can be achieved for both inviscid and viscous unsteady airfoil problems using unstructured meshes without degrading spatial or temporal accuracy.

Kleb, William L.↗

NASA NTRS1992

Developing A Navier-Stokes Algorithm For Supercomputers

Report discusses development of algorithm for solution of Navier-Stokes equations of flow on parallel-processing supercomputers. Involves combination of prior techniques to form algorithm to compute flows in complicated three-dimensional configurations. Includes explicit finite-difference numerical-integration scheme applicable to flows represented by hierarchy of mathematical models ranging from Euler to full Navier-Stokes. Of interest to researchers looking for ways to structure problems for greater computational efficiency.

Swisshelm, Julie M.↗

NASA NTRS1991

Design optimization of transonic airfoils

Numerical optimization procedures were considered for the design of airfoils in transonic flow based on the transonic small disturbance (TSD) and Euler equations. A sequential approximation optimization technique was implemented with an accurate approximation of the wave drag based on the Nixon's coordinate straining approach. A modification of the Euler surface boundary conditions was implemented in order to efficiently compute design sensitivities without remeshing the grid. Two effective design procedures producing converged designs in approximately 10 global iterations were developed: interchanging the role of the objective function and constraint and the direct lift maximization with move limits which were fixed absolute values of the design variables.

Joh, C.-Y.↗

NASA NTRS1993

Finite element calculations of transonic flutter in cascades

Aeroelastic stability and response of turbomachinery cascades operating in the transonic regime are explored using a new computational approach. The two-dimensional unsteady Euler equations are used to model the transonic cascade flows, and the cascade blades are modeled as thin plates. To minimize the discretization incompatibility, both the fluid and the solid domains are discretized using finite element procedures. The fluid and the structural models are coupled at the element level by introducing a channel theory, which is analogous to a strip theory in the classical sense. The system of space-discretized equations is marched forward in time using an explicit four-stage Runge-Kutta scheme. Results of free vibration analyses of typical blades are presented and compared to published finite element and Rayleigh-Ritz results. Aeroelastic stability and response characteristics of several transonic cascades are investigated using the new quasi-3D model. These results demonstrate the present 3D finite element blade model is capable of capturing aeroelastic instabilities involving higher modes, including (plate-type) camber bending modes.

Hsiao, Chingteng↗

NASA NTRS1993

Software systems used for unstructured grid generation at NASA Langley

These viewgraphs provide an overview of grid generation system for 3D configurations (Euler Grids) and grid generators of viscous and inviscid flow, solution adaptive for steady and unsteady flow. The five systems presented are VGRID, FELISA, TETRA, NGP, and TGRID.

Michael J Bockelie↗

NASA NTRS1995

An outflow boundary condition for aeroacoustic computations

A formulation of boundary condition for flows with small disturbances is presented. The authors test their methodology in an axisymmetric jet flow calculation, using both the Navier-Stokes and Euler equations. Solutions in the far field are assumed to be oscillatory. If the oscillatory disturbances are small, the growth of the solution variables can be predicted by linear theory. Eigenfunctions of the linear theory are used explicitly in the formulation of the boundary conditions. This guarantees correct solutions at the boundary in the limit where the predictions of linear theory are valid.

Hayder, M. Ehtesham↗

NASA NTRS1997

Solution of Aeroacoustic Problems by a Nonlinear, Hybrid Method

Category 1, problem 3 (scattering of sound by a sphere) and category 2, problem 1 (spherical source in a cylindrical duct subject to uniform flow) are solved in generalized coordinates using the nonlinear Euler equations together with nonreflecting boundary conditions. A temporally and spatially fourth-order accurate finite-difference, Runge-Kutta time-marching technique is employed for the near-field calculations and a Kirchhoff method is employed for the prediction of far-field sound. Computations are all performed on parallel processors using the data-parallel paradigm.

Oezyoeruek, Yusuf↗

NASA NTRS1999

Investigation of Vortex Flaps and Other Flow Control Devices on Generic High-Speed Civil Transport Planforms

A parametric cranked delta planform study has been conducted in the Langley 14- by 22-Foot Subsonic Tunnel with the following objectives: (1) to evaluate the vortex flap design methodology for cranked delta wings, (2) to determine the influence of leading-edge sweep and the outboard wing on vortex flap effectiveness, (3) to evaluate novel flow control concepts, and (4) to validate unstructured grid Euler computer code predictions with modeled vortex and trailing-edge flaps. Two families of cranked delta planforms were investigated. One family had constant aspect ratio, while the other had a constant nondimensional semispan location of the leading-edge break. The inboard leading-edge sweep of the planforms was varied between 68 deg., 71 deg., and 74 deg., while outboard leading-edge sweep was varied between 48 deg. and 61 deg. Vortex flaps for the different planforms were designed by an analytical vortex flap design method. The results indicate that the effectiveness of the vortex flaps was only slightly influenced by the variations in the parametric planforms. The unstructured grid Euler computer code was successfully used to model the configurations with vortex flaps. The vortex trap concept was successfully demonstrated.

Kjerstad, Kevin J.↗

NASA NTRS2003

Computation of Large-Scale Structure Jet Noise Sources With Weak Nonlinear Effects Using Linear Euler

An approximate technique is presented for the prediction of the large-scale turbulent structure sound source in a supersonic jet. A linearized Euler equations code is used to solve for the flow disturbances within and near a jet with a given mean flow. Assuming a normal mode composition for the wave-like disturbances, the linear radial profiles are used in an integration of the Navier-Stokes equations. This results in a set of ordinary differential equations representing the weakly nonlinear self-interactions of the modes along with their interaction with the mean flow. Solutions are then used to correct the amplitude of the disturbances that represent the source of large-scale turbulent structure sound in the jet.

Dahl, Milo D.↗

NASA NTRS2003

Task III: Development of an Effective Computational Methodology for Body Force Representation of High-speed Rotor 37

A framework for an effective computational methodology for characterizing the stability and the impact of distortion in high-speed multi-stage compressor is being developed. The methodology consists of using a few isolated-blade row Navier-Stokes solutions for each blade row to construct a body force database. The purpose of the body force database is to replace each blade row in a multi-stage compressor by a body force distribution to produce same pressure rise and flow turning. To do this, each body force database is generated in such a way that it can respond to the changes in local flow conditions. Once the database is generated, no hrther Navier-Stokes computations are necessary. The process is repeated for every blade row in the multi-stage compressor. The body forces are then embedded as source terms in an Euler solver. The method is developed to have the capability to compute the performance in a flow that has radial as well as circumferential non-uniformity with a length scale larger than a blade pitch; thus it can potentially be used to characterize the stability of a compressor under design. It is these two latter features as well as the accompanying procedure to obtain the body force representation that distinguish the present methodology from the streamline curvature method. The overall computational procedures have been developed. A dimensional analysis was carried out to determine the local flow conditions for parameterizing the magnitudes of the local body force representation of blade rows. An Euler solver was modified to embed the body forces as source terms. The results from the dimensional analysis show that the body forces can be parameterized in terms of the two relative flow angles, the relative Mach number, and the Reynolds number. For flow in a high-speed transonic blade row, they can be parameterized in terms of the local relative Mach number alone.

Tan, Choon-Sooi↗

NASA NTRS1985

A numerical simulation of the NFAC (National Full-scale Aerodynamics Complex) open-return wind tunnel inlet flow

The flow into an open return wind tunnel inlet was simulated using Euler equations. An explicit predictor-corrector method was employed to solve the system. The calculation is time-accurate and was performed to achieve a steady-state solution. The predictions are in reasonable agreement with the experimental data. Wall pressures are accurately predicted except in a region of recirculating flow. Flow-field surveys agree qualitatively with laser velocimeter measurements. The method can be used in the design process for open return wind tunnels.

Kaul, U. K.↗

NASA NTRS1985

A numerical simulation of the NFAC (National Full-scale Aerodynamics Complex) open-return wind tunnel inlet flow

Kaul, U. K.↗

NASA NTRS1987

Simulation of transonic viscous flow over a fighter-like configuration including inlet

The simulation of transonic viscous flow over a modified F-16A including inlet is presented. A zonal approach is utilized which allows appropriate clustering suitable for viscous calculations on all solid surfaces. Computational efficiency is enhanced by solving the thin-layer Navier-Stokes equations in viscous zones adjacent to the aircraft and the Euler equations on those coarse zones away from the aircraft. The flow conditions for this transonic case are freestream Mach number of 0.9, angle of attack of 4.12 deg, and a Reynolds number (based on root chord) of 4.5 million. A total of 19 zones are utilized yielding a total of 350,000 grid points. This case required about 3000 iterations to reduce the residual by three orders, which takes about 10 hr of CPU time on the Cray X-MP/48 computer. Pressure distributions on the wing and on cross sections through the inlet region compare favorably with the experimental data for this transonic case.

Flores, Jolen↗

NASA NTRS1991

A multiple-block multigrid method for the solution of the three-dimensional Euler and Navier-Stokes equations

A multiple block multigrid method for the solution of the three dimensional Euler and Navier-Stokes equations is presented. The basic flow solver is a cell vertex method which employs central difference spatial approximations and Runge-Kutta time stepping. The use of local time stepping, implicit residual smoothing, multigrid techniques and variable coefficient numerical dissipation results in an efficient and robust scheme is discussed. The multiblock strategy places the block loop within the Runge-Kutta Loop such that accuracy and convergence are not affected by block boundaries. This has been verified by comparing the results of one and two block calculations in which the two block grid is generated by splitting the one block grid. Results are presented for both Euler and Navier-Stokes computations of wing/fuselage combinations.

Atkins, Harold↗

NASA NTRS1988

The use of direct solvers for compressible flow computations

The feasibility of using a vectorized direct solver for the compressible Euler and Navier-Stokes equations is examined for both single-grid and multi-grid strategies. A procedure is developed for comparing the computational effort required for the direct method with that of the vertical line Gauss-Seidel iteration scheme in order to provide a criteria for choosing between the two techniques. The direct method is shown to have a relatively wide range of application on a vector processor with large memory. Results for both inviscid and viscous test problems in two-dimensions are examined.

Riggins, David↗

NASA NTRS1989

Euler solvers for transonic applications

The 1980s may well be called the Euler era of applied aerodynamics. Computer codes based on discrete approximations of the Euler equations are now routinely used to obtain solutions of transonic flow problems in which the effects of entropy and vorticity production are significant. Such codes can even predict separation from a sharp edge, owing to the inclusion of artificial dissipation, intended to lend numerical stability to the calculation but at the same time enforcing the Kutta condition. One effect not correctly predictable by Euler codes is the separation from a smooth surface, and neither is viscous drag; for these some form of the Navier-Stokes equation is needed. It, therefore, comes as no surprise to observe that the Navier-Stokes has already begun before Euler solutions were fully exploited. Moreover, most numerical developments for the Euler equations are now constrained by the requirement that the techniques introduced, notably artificial dissipation, must not interfere with the new physics added when going from an Euler to a full Navier-Stokes approximation. In order to appreciate the contributions of Euler solvers to the understanding of transonic aerodynamics, it is useful to review the components of these computational tools. Space discretization, time- or pseudo-time marching and boundary procedures, the essential constituents are discussed. The subject of grid generation and grid adaptation to the solution are touched upon only where relevant. A list of unanswered questions and an outlook for the future are covered.

Vanleer, Bram↗

NASA NTRS1996

High Resolution Euler Solvers Based on the Space-Time Conservation Element and Solution Element Method

The I-D, quasi I-D and 2-D Euler solvers based on the method of space-time conservation element and solution element are used to simulate various flow phenomena including shock waves, Mach stem, contact surface, expansion waves, and their intersections and reflections. Seven test problems are solved to demonstrate the capability of this method for handling unsteady compressible flows in various configurations. Numerical results so obtained are compared with exact solutions and/or numerical solutions obtained by schemes based on other established computational techniques. Comparisons show that the present Euler solvers can generate highly accurate numerical solutions to complex flow problems in a straightforward manner without using any ad hoc techniques in the scheme.

Wang, Xiao-Yen↗

NASA NTRS1985

A Numerical Method of Calculating Propeller Noise Including Acoustic Nonlinear Effects

Using the transonic flow fields(s) generated by the NASPROP-E computer code for an eight blade SR3-series propeller, a theoretical method is investigated to calculate the total noise values and frequency content in the acoustic near and far field without using the Ffowcs Williams - Hawkings equation. The flow field is numerically generated using an implicit three dimensional Euler equation solver in weak conservation law form. Numerical damping is required by the differencing method for stability in three dimensions, and the influence of the damping on the calculated acoustic values is investigated. The acoustic near field is solved by integrating with respect to time the pressure oscillations induced at a stationary observer location. The acoustic far field is calculated from the near field primitive variables as generated by NASPROP-E computer code using a method involving a perturbation velocity potential as suggested by Hawkings in the calculation of the acoustic pressure time-history at a specified far field observed location. the methodologies described are valid for calculating total noise levels and are applicable to any propeller geometry for which a flow field solution is available.

Korkan, K. D.↗