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NASA NTRS2006

Space-Time Error Representation and Estimation in Navier-Stokes Calculations

The mathematical framework for a-posteriori error estimation of functionals elucidated by Eriksson et al. [7] and Becker and Rannacher [3] is revisited in a space-time context. Using these theories, a hierarchy of exact and approximate error representation formulas are presented for use in error estimation and mesh adaptivity. Numerical space-time results for simple model problems as well as compressible Navier-Stokes flow at Re = 300 over a 2D circular cylinder are then presented to demonstrate elements of the error representation theory for time-dependent problems.

Barth, Timothy J.↗

NASA NTRS2006

3-D Navier-Stokes Analysis of Blade Root Aerodynamics for a Tiltrotor Aircraft In Cruise

The blade root area of a tiltrotor aircraft's rotor is constrained by a great many factors, not the least of which is aerodynamic performance in cruise. For this study, Navier-Stokes CFD techniques are used to study the aerodynamic performance in cruise of a rotor design as a function of airfoil thickness along the blade and spinner shape. Reducing airfoil thickness along the entire blade will be shown to have the greatest effect followed by smaller but still significant improvements achieved by reducing the thickness of root airfoils only. Furthermore, altering the shape of the spinner will be illustrated as a tool to tune the aerodynamic performance very near the blade root.

Romander, Ethan↗

NASA NTRS2007

Parametric Study of Flow Control Over a Hump Model Using an Unsteady Reynolds- Averaged Navier-Stokes Code

This is an expanded version of a limited-length paper that appeared at the 5th International Symposium on Turbulence and Shear Flow Phenomena by the same authors. A computational study was performed for steady and oscillatory flow control over a hump model with flow separation to assess how well the steady and unsteady Reynolds-averaged Navier-Stokes equations predict trends due to Reynolds number, control magnitude, and control frequency. As demonstrated in earlier studies, the hump model case is useful because it clearly demonstrates a failing in all known turbulence models: they under-predict the turbulent shear stress in the separated region and consequently reattachment occurs too far downstream. In spite of this known failing, three different turbulence models were employed to determine if trends can be captured even though absolute levels are not. Overall the three turbulence models showed very similar trends as experiment for steady suction, but only agreed qualitatively with some of the trends for oscillatory control.

Rumsey, Christopher L.↗

NASA NTRS2007

Nonlinear Aeroelastic Analysis Using a Time-Accurate Navier-Stokes Equations Solver

A method to simulate limit cycle oscillation (LCO) due to control surface freeplay using a modified CFL3D, a time-accurate Navier-Stokes computational fluid dynamics (CFD) analysis code with structural modeling capability, is presented. This approach can be used to analyze aeroelastic response of aircraft with structural behavior characterized by nonlinearity in the force verses displacement curve. A limited validation of the method, using very low Mach number experimental data for a three-degrees-of-freedom (pitch/plunge/flap deflection) airfoil model with flap freeplay, is also presented.

Kuruvila, Geojoe↗

NASA NTRS2007

Convergence Acceleration of Runge-Kutta Schemes for Solving the Navier-Stokes Equations

The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 can be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. This RK/implicit scheme is used as a smoother for multigrid. Fourier analysis is applied to determine damping properties. Numerical dissipation operators based on the Roe scheme, a matrix dissipation, and the CUSP scheme are considered in evaluating the RK/implicit scheme. In addition, the effect of the number of RK stages is examined. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. Turbulent flows over an airfoil and wing at subsonic and transonic conditions are computed. The effects of the cell aspect ratio on convergence are investigated for Reynolds numbers between 5:7 x 10(exp 6) and 100 x 10(exp 6). It is demonstrated that the implicit preconditioner can reduce the computational time of a well-tuned standard RK scheme by a factor between four and ten.

Swanson, Roy C., Jr.↗

NASA NTRS2006

Reynolds-Averaged Navier-Stokes Analysis of Zero Efflux Flow Control over a Hump Model

The unsteady flow over a hump model with zero efflux oscillatory flow control is modeled computationally using the unsteady Reynolds-averaged Navier-Stokes equations. Three different turbulence models produce similar results, and do a reasonably good job predicting the general character of the unsteady surface pressure coefficients during the forced cycle. However, the turbulent shear stresses are underpredicted in magnitude inside the separation bubble, and the computed results predict too large a (mean) separation bubble compared with experiment. These missed predictions are consistent with earlier steady-state results using no-flow-control and steady suction, from a 2004 CFD validation workshop for synthetic jets.

Rumsey, Christopher L.↗

NASA NTRS2006

Simulation of Synthetic Jets in Quiescent Air Using Unsteady Reynolds Averaged Navier-Stokes Equations

We apply an unsteady Reynolds-averaged Navier-Stokes (URANS) solver for the simulation of a synthetic jet created by a single diaphragm piezoelectric actuator in quiescent air. This configuration was designated as Case 1 for the CFDVAL2004 workshop held at Williamsburg, Virginia, in March 2004. Time-averaged and instantaneous data for this case were obtained at NASA Langley Research Center, using multiple measurement techniques. Computational results for this case using one-equation Spalart-Allmaras and two-equation Menter's turbulence models are presented along with the experimental data. The effect of grid refinement, preconditioning and time-step variation are also examined in this paper.

Vatsa, Veer N.↗

NASA NTRS2000

Navier-Stokes Analysis of a High Wing Transport High-Lift Configuration with Externally Blown Flaps

Insights and lessons learned from the aerodynamic analysis of the High Wing Transport (HWT) high-lift configuration are presented. Three-dimensional Navier-Stokes CFD simulations using the OVERFLOW flow solver are compared with high Reynolds test data obtained in the NASA Ames 12 Foot Pressure Wind Tunnel (PWT) facility. Computational analysis of the baseline HWT high-lift configuration with and without Externally Blown Flap (EBF) jet effects is highlighted. Several additional aerodynamic investigations, such as nacelle strake effectiveness and wake vortex studies, are presented. Technical capabilities and shortcomings of the computational method are discussed and summarized.

Slotnick, Jeffrey P.↗

NASA NTRS2009

Nearly Interactive Parabolized Navier-Stokes Solver for High Speed Forebody and Inlet Flows

A system of computer programs is being developed for the preliminary design of high speed inlets and forebodies. The system comprises four functions: geometry definition, flow grid generation, flow solver, and graphics post-processor. The system runs on a dedicated personal computer using the Windows operating system and is controlled by graphical user interfaces written in MATLAB (The Mathworks, Inc.). The flow solver uses the Parabolized Navier-Stokes equations to compute millions of mesh points in several minutes. Sample two-dimensional and three-dimensional calculations are demonstrated in the paper.

Benson, Thomas J.↗

NASA NTRS2009

Navier-Stokes Simulation of a Heavy Lift Slowed-Rotor Compound Helicopter Configuration

Time accurate numerical simulations were performed using the Reynolds-averaged Navier-Stokes (RANS) flow solver OVERFLOW for a heavy lift, slowed-rotor, compound helicopter configuration, tested at the NASA Langley 14- by 22-Foot Subsonic Tunnel. The primary purpose of these simulations is to provide support for the development of a large field of view Particle Imaging Velocimetry (PIV) flow measurement technique supported by the Subsonic Rotary Wing (SRW) project under the NASA Fundamental Aeronautics program. These simulations provide a better understanding of the rotor and body wake flows and helped to define PIV measurement locations as well as requirements for validation of flow solver codes. The large field PIV system can measure the three-dimensional velocity flow field in a 0.914m by 1.83m plane. PIV measurements were performed upstream and downstream of the vertical tail section and are compared to simulation results. The simulations are also used to better understand the tunnel wall and body/rotor support effects by comparing simulations with and without tunnel floor/ceiling walls and supports. Comparisons are also made to the experimental force and moment data for the body and rotor.

Allan, Brian G.↗

NASA NTRS2003

Coherent Anti-Stokes Raman Spectroscopic Thermometry in a Supersonic Combustor

An experiment has been conducted to acquire data for the validation of computational fluid dynamics codes used in the design of supersonic combustors. The flow in a supersonic combustor, consisting of a diverging duct with a single downstream-angled wail injector, is studied. Combustor entrance Mach number is 2 and enthalpy nominally corresponds to Mach 7 flight. The primary measurement technique is coherent anti-Stokes Raman spectroscopy, but surface pressures and temperatures have also been acquired. Modern design of experiment techniques have been used to maximize the quality of the data set (for the given level of effort) and to minimize systematic errors. Temperature maps are obtained at several planes in the flow for a case in which the combustor is piloted by injecting fuel upstream of the main injector and one case in which it is not piloted. Boundary conditions and uncertainties are characterized.

Cutler, A. D.↗

NASA NTRS2003

Dual-Pump Coherent Anti-Stokes Raman Scattering Temperature and CO2 Concentration Measurements

Measurements of temperature and CO2 concentration using dual-pump coherent anti-Stokes Raman scattering, (CARS) are described. The measurements were performed in laboratory flames,in a room-temperature gas cell, and on an engine test stand at the U.S. Air Force Research Laboratory, Wright-Patterson Air Force Base. A modeless dye laser, a single-mode Nd:YAG laser, and an unintensified back-illuminated charge-coupled device digital camera were used for these measurements. The CARS measurements were performed on a single-laser-shot basis. The standard deviations of the temperatures and CO2 mole fractions determined from single-shot dual-pump CARS spectra in steady laminar propane/air flames were approximately 2 and 10% of the mean values of approximately 2000 K and 0.10, respectively. The precision and accuracy of single-shot temperature measurements obtained from the nitrogen part of the dual-pump CARS system were investigated in detail in near-adiabatic hydrogen/air/CO2 flames. The precision of the CARS temperature measurements was found to be comparable to the best results reported in the literature for conventional two-laser, single-pump CARS. The application of dual-pump CARS for single-shot measurements in a swirl-stabilized combustor fueled with JP-8 was also demonstrated.

Lucht, Robert P.↗

NASA NTRS2009

Hypersonic Navier Stokes Comparisons to Orbiter Flight Data

Hypersonic chemical nonequilibrium simulations of low earth orbit entry flow fields are becoming increasingly commonplace as software and computational capabilities become more capable. However, development of robust and accurate software to model these environments will always encounter a significant barrier in developing a suite of high quality calibration cases. The US3D hypersonic nonequilibrium Navier Stokes analysis capability has been favorably compared to a number of wind tunnel test cases. Extension of the calibration basis for this software to Orbiter flight conditions will provide an incremental increase in confidence. As part of the Orbiter Boundary Layer Transition Flight Experiment and the Hypersonic Thermodynamic Infrared Measurements project, NASA is performing entry flight testing on the Orbiter to provide valuable aerothermodynamic heating data. An increase in interest related to orbiter entry environments is resulting from this activity. With the advent of this new data, comparisons of the US3D software to the new flight testing data is warranted. This paper will provide information regarding the framework of analyses that will be applied with the US3D analysis tool. In addition, comparisons will be made to entry flight testing data provided by the Orbiter BLT Flight Experiment and HYTHIRM projects. If data from digital scans of the Orbiter windward surface become available, simulations will also be performed to characterize the difference in surface heating between the CAD reference OML and the digitized surface provided by the surface scans.

Campbell, Charles H.↗

NASA NTRS2009

Comment on Modified Stokes Parameters

It is common practice in passive microwave remote sensing (microwave radiometry) to express observables as temperatures and in the case of polarimetric radiometry to use what are called "Modified Stokes Parameters in Brightness Temperature" to describe the scene. However, definitions with slightly different normalization (with and without division by bandwidth) have appeared in the literature. The purpose of this manuscript is to present an analysis to clarify the meaning of terms in the definition and resolve the question of the proper normalization.

Le Vine, D.M.↗

NASA NTRS2010

Width-Increased Dual-Pump Enhanced Coherent Anti-Stokes Raman Spectroscopy (WIDECARS)

WIDECARS is a dual-pump coherent anti-Stokes Raman Spectroscopy technique that is capable of simultaneously measuring temperature and species mole fractions of N2, O2, H2, C2H4, CO, and CO2. WIDECARS is designed for measurements of all the major species (except water) in supersonic combustion flows fueled with hydrogen and hydrogen/ethylene mixtures. The two lowest rotational energy levels of hydrogen detectable by WIDECARS are H2 S(3) and H2 S(4). The detection of these lines gives the system the capability to measure temperature and species concentrations in regions of the flow containing pure hydrogen fuel at room temperature.

Tedder, Sarah A.↗

NASA NTRS2010

Application of the FUN3D Unstructured-Grid Navier-Stokes Solver to the 4th AIAA Drag Prediction Workshop Cases

FUN3D Navier-Stokes solutions were computed for the 4th AIAA Drag Prediction Workshop grid convergence study, downwash study, and Reynolds number study on a set of node-based mixed-element grids. All of the baseline tetrahedral grids were generated with the VGRID (developmental) advancing-layer and advancing-front grid generation software package following the gridding guidelines developed for the workshop. With maximum grid sizes exceeding 100 million nodes, the grid convergence study was particularly challenging for the node-based unstructured grid generators and flow solvers. At the time of the workshop, the super-fine grid with 105 million nodes and 600 million elements was the largest grid known to have been generated using VGRID. FUN3D Version 11.0 has a completely new pre- and post-processing paradigm that has been incorporated directly into the solver and functions entirely in a parallel, distributed memory environment. This feature allowed for practical pre-processing and solution times on the largest unstructured-grid size requested for the workshop. For the constant-lift grid convergence case, the convergence of total drag is approximately second-order on the finest three grids. The variation in total drag between the finest two grids is only 2 counts. At the finest grid levels, only small variations in wing and tail pressure distributions are seen with grid refinement. Similarly, a small wing side-of-body separation also shows little variation at the finest grid levels. Overall, the FUN3D results compare well with the structured-grid code CFL3D. The FUN3D downwash study and Reynolds number study results compare well with the range of results shown in the workshop presentations.

Lee-Rausch, Elizabeth M.↗

NASA NTRS2010

Navier-Stokes Dynamics by a Discrete Boltzmann Model

This work investigates the possibility of particle-based algorithms for the Navier-Stokes equations and higher order continuum approximations of the Boltzmann equation; such algorithms would generalize the well-known Pullin scheme for the Euler equations. One such method is proposed in the context of a discrete velocity model of the Boltzmann equation. Preliminary results on shock structure are consistent with the expectation that the shock should be much broader than the near discontinuity predicted by the Pullin scheme, yet narrower than the prediction of the Boltzmann equation. We discuss the extension of this essentially deterministic method to a stochastic particle method that, like DSMC, samples the distribution function rather than resolving it completely.

Rubinstein, Robet↗

NASA NTRS2010

Width-Increased Dual-Pump Enhanced Coherent Anti-Stokes Raman Spectroscopy (WIDECARS)

Tedder, Sarah A.↗