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NASA NTRS2019

Adjoint-Based Anisotropic Mesh Adaptation for a Stabilized Finite-Element Flow Solver

An adjoint solver is implemented in the FUN3D stabilized finite-element flow solver. The adjoint solution is used to generate anisotropic, adapted meshes to control error in scalar out- put functionals, such as lift or drag coefficient. The inviscid and turbulent adjoints are verified with a finite-difference derivative approximation and can be used in design optimization in addition to mesh adaptation. The adjoint capability represents an extension of previous research using the FUN3D stabilized finite-element capability with metric-based mesh adaptation and interpolation-based error estimates to generate highly anisotropic adapted meshes for turbulent flows. In the present work, a metric-based approach is again utilized, where the adjoint and the primal solutions both contribute to the generation of a metric tensor field that is subsequently used to produce the required anisotropic mesh for each adaptation cycle. Adaptive results are then shown for an inviscid supersonic flow over a diamond airfoil, inviscid transonic flow over the ONERA M6 wing, and viscous laminar flow over the NACA 0012 airfoil, all using drag force as the output functional. Adjoint-based adaptation is compared with a multiscale solution-based approach that controls the L norm of Mach number interpolation error to demonstrate the effectiveness and effciency of the adjoint-based adaptive mesh technology.

Balan, Aravind↗

NASA NTRS1978

Theoretical and experimental study of the drag of multielement airfoils

The viscous/potential flow past single-element and multielement airfoils is studied theoretically and experimentally. A computerized analysis, based on iteratively coupled potential-flow and boundary-layer analysis, is used to predict the flow field of the airfoil. The method yields detailed characteristics of conventional laminar and turbulent boundary layers, turbulent wakes, and confluent boundary layers. The viscous flows are analyzed with a method that uses finite-difference solutions of the boundary-layer equations. Reynolds stress in the boundary layers and wakes is simulated with eddy viscosity models for the various flow zones. The viscous calculations are carried into the wake of the airfoil where the drag is found from the defect in the wake momentum.

Olson, L. E.↗

NASA NTRS2015

Aerodynamic Shape Optimization Benchmarks with Error Control and Automatic Parameterization

Results are presented for four optimization benchmark problems posed by the AIAA Aerodynamic Design Optimization Discussion Group. The benchmarks are intended to exercise optimization frameworks on representative airfoil and wing design problems. All problems involve drag minimization subject to geometric and aerodynamic constraints. Our design approach involves two forms of adaptation. First, the shape parameterization is gradually and automatically enriched from an initially coarse search space. Second, adjoint solutions are used to drive adaptive mesh refinement to control discretization error. The error threshold is tailored so that the nest meshes, with the greatest accuracy, are used only when nearing the optimum. On the inviscid airfoil design problem, while reducing the drag by a factor of 10, we show how the combination of progressive parameterization and tiered discretization error control can dramatically accelerate the optimization. On the viscous airfoil design problem, we use inviscid analysis-driven optimization to reduce the total drag by a factor of two. Next, we improve the span efficiency factor of a wing by performing twist optimization. Finally, we optimize the Common Research Model wing, managing to hold drag roughly fixed, while targeting an initially-violated pitching moment constraint. Our approach aims to introduce greater complexity and accuracy only when necessary to improve the design, and also support a greater degree of automation.

Anderson, George R.↗

NASA NTRS1994

Self-gravity and dissipation in polar rings

Studies of inclined rings inside galaxy potentials have mostly considered the influence of self-gravity and viscous dissipation separately. In this study, we construct models of highly inclined ('polar') rings in an external potential including both self-gravity and dissipation due to a drag force. We do not include pressure forces and thus ignore shock heating that dominates the evolution of gaseous rings inside strongly nonspherical potentials. We adopt an oblate spheroidal scale-free logarithmic potential with axis ratio q = 0.85 and an initial inclination of 80 deg for the self-gravitating rings. We find that stellar (dissipationless) rings suffer from mass loss during their evolution. Mass loss also drives a secular change of the mean inclination toward the poles of the potential. As much as half of the ring mass escapes in the process and forms an inner and an outer shell of precessing orbits. If the remaining mass is more than approximately 0.02 of the enclosed galaxy mass, rings remain bound and do not fall apart from differential precession. The rings precess at a constant rate for more than a precession period tau(sub p) finding the configuration predicted by Sparke in 1986 which warps at larger radii toward the poles of the potential. We model shear viscosity with a velocity-dependent drag force and find that nuclear inflow dominates over self-gravity if the characteristic viscous inflow time scale tau(sub vi) is shorter than approximately 25(tau(sub p)). Rings with (tau(sub vi))/(tau(sub p)) less than or approximately equal to 25 collapse toward the nucleus of the potential within one precession period independent of the amount of self-gravity. Our results imply that stars and gas in real polar rings exhibit markedly different dynamical evolutions.

Dubinski, John↗

NASA NTRS1980

Separation region on boattail nozzles

Computer subroutine package VISCUS offers flow analyst practical engineering computational procedure to model viscous effects of separated reverse flow on afterbody pressures and drag. Program is written in FORTRAN IV.

Buteau, J. D.↗

NASA NTRS1986

Viscous pumping and the spin-down of thermospheric gyres and jets

Strong gyres and jets can be generated at auroral latitudes in the thermosphere by enhanced electric fields during geomagnetic substorms. Typical height profiles of ion density suggest that the ion drag force should generate large curvature in the vertical profile of the winds in the highly viscous region of the thermosphere above about 200 km. It is proposed that the poststorm spin-down of these gyres and jets proceeds via Ekman circulations driven by the curvatures in the height profiles of the winds. Analytic and numerical calculations of the ageostrophic winds forced by curvature in model geostrophic wind profiles show that the ageostrophic wind speeds and directions depend mainly on the kinematic viscosity in the region of curvature and the total change in shear in the geostrophic wind. Ageostrophic wind speeds for typical thermospheric jets can exceed 200 m/s (about 50 percent of the jet winds). Spin-down times of thermospheric jets and cyclonic gyres by the Ekman pumping mechanism are estimated at less than about 6 hours.

Walterscheid, R. L.↗

NASA NTRS1978

An improved analytical model of the separated region on nozzle boattails

A viscous flow calculation is formulated for modelling the effects of separated, reverse flow regions on nozzle afterbody pressures and drags at subsonic Mach numbers. A discriminating streamline approach is used. Effects of skin friction, axial pressure gradient, and nozzle jet entrainment on the separated discriminating streamline shape are included. The viscous flow calculation is coupled to a potential flow calculation. The combined analysis is found to accurately predict both the magnitude of the measured afterbody pressures and drag, and also their variation with Reynolds number, Mach number and afterbody shape.

Presz, W. M., Jr.↗

NASA NTRS1988

The fix for tough spots

Modern turbulence-control techniques are discussed. Particular atention is given to retrofit techniques such as riblets and large-eddy breakup (LEBU) devices which use passive elements suitable for a variety of existing vehicles with minimum added complexity. Riblets are small flow-aligned grooves in the aircraft skin that damp turbulence and reduce skin friction; the mechanism of riblet drag reduction derives from the enhancement of turbulence-altering, transverse viscous forces by strong spanwise surface geometry gradients. LEBUs are thin plates or ribbons suspended in a turbulent boundary layer to sever or break up the large vortices that form the convoluted outer edge of the layer. Other turbulence-control techniques are discussed, including one that involves the injection of control vortices into the turbulent boundary layer to modify or substitute for large-eddy structures.

Anders, John B.↗

NASA NTRS1990

Prospects for drag prediction using computational fluid dynamics

An account is given of CFD methods deemed likely to yield aerodynamic drag prediction improvements. Improvements in drag prediction are noted to largely proceed from improvements in viscous-layer resolution. Geometric modeling and grid generation are acknowledged to be major pacing items, and may be more important than turbulence modeling. The use of upwind differencing has led to improved solution accuracy due to the nature of the artificial viscosity in cases involving shocks and nonphysical dissipation across viscous layers. Multiblock algorithms will allow more complex geometries to be treated.

Roberts, Thomas W.↗

NASA NTRS2003

1100 to 1500 K Slow Plastic Compressive Behavior of NiAl-xCr Single Crystals

The compressive properties of near <001> and <111> oriented NiAl-2Cr single crystals and near <011> oriented NiAl-6Cr samples have been measured between 1100 and 1500 K. The 2Cr addition produced significant solid solution strengthening in NiAl, and the <111> and <001> single crystals possessed similar strengths. The 6Cr crystals were not stronger than the 2Cr versions. At 1100 and 1200 K plastic flow in all three Cr-modified materials was highly dependent on stress with exponents > 10. The <011> oriented 6Cr alloy exhibited a stress exponent of about 8 at 1400 and 1500 K; whereas both <001> and <111> NiAl-2Cr crystals possessed stress exponents near 3 which is indicative of a viscous dislocation glide creep mechanism. While the Cottrell-Jaswon solute drag model predicted creep rates within a factor of 3 at 1500 K for <001>-oriented NiAl-2Cr; this mechanism greatly over predicted creep rates for other orientations and at 1400 K for <001> crystals.

Whittenberger, J. Daniel↗

NASA NTRS1995

Aerodynamic Performance Predictions of Single and Twin Jet Afterbodies

The multiblock three-dimensional Navier-Stokes method PAB3D was utilized by the Component Integration Branch (formerly Propulsion Aerodynamics Branch) at the NASA-Langley Research Center in an international study sponsored by AGARD Working Group #17 for the assessment of the state-of-the-art of propulsion-airframe integration testing techniques and CFD prediction technologies. Three test geometries from ONERA involving fundamental flow physics and four geometries from NASA-LaRC involving realistic flow interactions of wing, body, tail, and jet plumes were chosen by the Working Group. An overview of results on four (1 ONERA and 3 LaRC) of the seven test cases is presented. External static pressures, integrated pressure drag and total drag were calculated for the Langley test cases and jet plume velocity profiles and turbulent viscous stresses were calculated for the ONERA test case. Only selected data from these calculations are presented in this paper. The complete data sets calculated by the participants will be presented in an AGARD summary report. Predicted surface static pressures compared favorably with experimental data for the Langley geometries. Predicted afterbody drag compared well with experiment. Predicted nozzle drag was typically low due to over-compression of the flow near the trailing edge. Total drag was typically high. Predicted jet plume quantities on the ONERA case compared generally well with data.

Carlson, John R.↗

NASA NTRS1990

Grid generation and flow computation about a Martian entry vehicle

A number of vehicles are currently being proposed for a manned mission to Mars. One of these vehicles has a modified blunt-nosed cone configuration. Experimental results were obtained for this vehicle in 1968. They show lift-over-drag ratios comparable to those needed for Mars entry. Computations are performed to verify the earlier results and to further describe the flight characteristics of this vehicle. An analytical method is used to define the surface of this vehicle. A single-block volume grid is generated around the vehicle using the algebraic Two-Boundary Grid Generation algorithm (TBGG) and transfinite interpolation. Euler solutions are then obtained from a Langley Aerodynamic Upward Relaxation Algorithm (LAURA) at Mach 6.0 and angles of attack of 0, 6, and 12 deg. The lift coefficient determined from the LAURA code agree very well with the experimental results. The drag and pitching moment coefficients, however, are underestimated by the code since viscous effects are not considered. Contour plots of the flowfield show no evidence of separation for angles of attack up to 12 deg.

Stewart, J. E.↗

NASA NTRS1992

Ablative subduction - A two-sided alternative to the conventional subduction model

The plausibility of a two-sided fluid-based model of lithospheric subduction that is based upon current views of lithospheric structure is examined. In this model the viscous lower lithosphere flows downward, and the brittle upper lithosphere deforms in passive response. This process is potentially double-sided, since it is found that even a buoyant plate can be dragged downward by a dense descending neighbor. Thus an apparent overriding plate may be worn away by a process of viscous ablation, with the rate of ablation a function of plate buoyancy. This process, called 'ablative subduction,' makes it possible to simply interpret observations concerning slab profiles, interplate seismicity, back arc tectonics, and complex processes such as double subduction and subduction polarity reversal. When experiments modeling the evolution of simple fluid 'slabs' are performed, slab profile is found to be strongly influenced by ablation in the overriding plate. When ablation is weak, as when a buoyant continent borders the trench, deformable slabs adopt shallow Andean-style profiles.

Tao, Winston C.↗

NASA NTRS1999

HSCT Ref-H Transonic Flap Data Base: Wind-Tunnel Test and Comparison with Theory

In cooperation with personnel from the Boeing ANP Laboratory and NASA Langley, a performance test was conducted using the Reference-H 1.675% model ("NASA Modular Model") without nacelles at the NASA Langley 16-Ft Transonic Tunnel. The main objective of the test was to determine the drag reduction achievable with leading-edge and trailing-edge flaps deflected along the outboard wing span at transonic Mach numbers (M = 0.9 to 1.2) for purpose of preliminary design and for comparison with computational predictions. The obtained drag data with flap deflections for Mach numbers of 1.07 to 1.20 are unique for the Reference H wing. Four leading-edge and two trailing-edge flap deflection angles were tested at a mean-wing chord-Reynolds number of about 5.7 million. An outboard-wing leading-edge flap deflection of 81 provides a 4.5 percent drag reduction at M = 1.2 A = 0.2), and much larger values at lower Mach numbers with larger flap deflections. The present results for the baseline (no flaps deflected) compare reasonably well with previous Boeing and NASA Ref-H tunnel tests, including high-Reynolds number NTF results. Viscous CFD simulations using the OVERFLOW thin-layer N.S. method properly predict the observed trend in drag reduction at M = 1.2 as function of leading-edge flap deflection. Modified linear theory properly predicts the flap effects on drag at subsonic conditions (Aero2S code), and properly predicts the absolute drag for the 40 and 80 leading-edge deflection at M = 1.2 (A389 code).

Vijgen, Paul M.↗

NASA NTRS1988

Viscous shock-layer solutions for the low-density hypersonic flow past long slender bodies

Results are obtained for the surface pressure, drag, heat-transfer, and skin-friction coefficients for hyperboloids and sphere cones. Body half angles from 5 to 22.5 degrees are considered for various low-density flow conditions. Recently obtained surface-slip and shock-slip equations are employed to account for the low-density effects. The method of solution employed for the viscous shock-layer (VSL) equations is a partially coupled spatial-marching implicit finite-difference technique. The flow cases analyzed include highly cooled long slender bodies in high Mach number flows. The present perfect-gas VSL calculations compare quite well with available experimental data. Results have also been obtained from the steady-state Navier-Stokes (NS) equations by successive approximations. Comparison between the NS and VSL results indicates that VSL equations even with body and shock-slip boundary conditions may not be adequate in the stagnation region at altitudes greater than about 75 km for the cases analyzed here.

Gupta, R. N.↗

NASA NTRS1977

Low Reynolds number flow past a blunt axisymmetric body at angle of attack

Low Reynolds number flow of an ideal gas over a blunt axisymmetric body of large half-angle at small angles of attack is investigated, for the case of laminar hypersonic flow. Time-varying viscous shock layer equations describing the flowfield are obtained from the full Navier-Stokes system by keeping terms to second order in the inverse square root of Re in both viscous and inviscid regions; the equations are valid for moderate to high Re. Drag, skin friction, and heating rates were obtained at small (or zero) angles of attack. Conditions experienced by planetary entry probes during the high-altitude (early) legs of an atmospheric entry trajectory are pertinent to the problem.

Kumar, A.↗

NASA NTRS1992

A turbulence model for iced airfoils and its validation

A turbulence model based on the extension of the algebraic eddy viscosity formulation of Cebeci and Smith developed for two dimensional flows over smooth and rough surfaces is described for iced airfoils and validated for computed ice shapes obtained for a range of total temperatures varying from 28 to -15 F. The validation is made with an interactive boundary layer method which uses a panel method to compute the inviscid flow and an inverse finite difference boundary layer method to compute the viscous flow. The interaction between inviscid and viscous flows is established by the use of the Hilbert integral. The calculated drag coefficients compare well with recent experimental data taken at the NASA-Lewis Icing Research Tunnel (IRT) and show that, in general, the drag increase due to ice accretion can be predicted well and efficiently.

Shin, Jaiwon↗

NASA NTRS1992

A turbulence model for iced airfoils and its validation

A turbulence model based on the extension of the algebraic eddy viscosity formulation of Cebeci and Smith developed for two-dimensional flows over smooth and rough surfaces is described for iced airfoils and validated for computed ice shapes obtained for a range of total temperatures varying from 28 to -15 F. The validation is made with an interactive boundary layer method which uses a panel method to compute the inviscid flow and an inverse finite difference boundary layer method to compute the viscous flow. The interaction between inviscid and viscous flows is established by the use of the Hilbert integral. The calculated drag coefficients compare well with recent experimental data taken at the NASA-Lewis Icing Research Tunnel (IRT) and show that, in general, the drag increase due to ice accretion can be predicted well and efficiently.

Shin, Jaiwon↗