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All sourcesNASA NTRSDOE OSTI
NASA NTRS2010

Challenges to Computational Aerothermodynamic Simulation and Validation for Planetary Entry Vehicle Analysis

Challenges to computational aerothermodynamic (CA) simulation and validation of hypersonic flow over planetary entry vehicles are discussed. Entry, descent, and landing (EDL) of high mass to Mars is a significant driver of new simulation requirements. These requirements include simulation of large deployable, flexible structures and interactions with reaction control system (RCS) and retro-thruster jets. Simulation of radiation and ablation coupled to the flow solver continues to be a high priority for planetary entry analyses, especially for return to Earth and outer planet missions. Three research areas addressing these challenges are emphasized. The first addresses the need to obtain accurate heating on unstructured tetrahedral grid systems to take advantage of flexibility in grid generation and grid adaptation. A multi-dimensional inviscid flux reconstruction algorithm is defined that is oriented with local flow topology as opposed to grid. The second addresses coupling of radiation and ablation to the hypersonic flow solver--flight- and ground-based data are used to provide limited validation of these multi-physics simulations. The third addresses the challenges of retro-propulsion simulation and the criticality of grid adaptation in this application. The evolution of CA to become a tool for innovation of EDL systems requires a successful resolution of these challenges.

Gnoffo, Peter A.↗
NASA NTRS2012

Extension of the Time-Spectral Approach to Overset Solvers for Arbitrary Motion

Forced periodic flows arise in a broad range of aerodynamic applications such as rotorcraft, turbomachinery, and flapping wing configurations. Standard practice involves solving the unsteady flow equations forward in time until the initial transient exits the domain and a statistically stationary flow is achieved. It is often required to simulate through several periods to remove the initial transient making unsteady design optimization prohibitively expensive for most realistic problems. An effort to reduce the computational cost of these calculations led to the development of the Harmonic Balance method [1, 2] which capitalizes on the periodic nature of the solution. The approach exploits the fact that forced temporally periodic flow, while varying in the time domain, is invariant in the frequency domain. Expanding the temporal variation at each spatial node into a Fourier series transforms the unsteady governing equations into a steady set of equations in integer harmonics that can be tackled with the acceleration techniques afforded to steady-state flow solvers. Other similar approaches, such as the Nonlinear Frequency Domain [3,4,5], Reduced Frequency [6] and Time-Spectral [7, 8, 9] methods, were developed shortly thereafter. Additionally, adjoint-based optimization techniques can be applied [10, 11] as well as frequency-adaptive methods [12, 13, 14] to provide even more flexibility to the method. The Fourier temporal basis functions imply spectral convergence as the number of harmonic modes, and correspondingly number of time samples, N, is increased. Some elect to solve the equations in the frequency domain directly, while others choose to transform the equations back into the time domain to simplify the process of adding this capability to existing solvers, but each harnesses the underlying steady solution in the frequency domain. These temporal projection methods will herein be collectively referred to as Time-Spectral methods. Time-Spectral methods have demonstrated marked success in reducing the computational costs associated with simulating periodic forced flows, but have yet to be fully applied to overset or Cartesian solvers for arbitrary motion with dynamic hole-cutting. Overset and Cartesian grid methodologies are versatile techniques capable of handling complex geometry configurations in practical engineering applications, and the combination of the Time-Spectral approach with this general capability potentially provides an enabling new design and analysis tool. In an arbitrary moving-body scenario for these approaches, a Lagrangian body moves through a fixed Eulerian mesh and mesh points in the Eulerian mesh interior to the solid body are removed (cut or blanked), leaving a hole in the Eulerian mesh. During the dynamic motion some gridpoints in the domain are blanked and do not have a complete set of time-samples preventing a direct implementation of the Time-Spectral method. Murman[6] demonstrated the Time-Spectral approach for a Cartesian solver with a rigid domain motion, wherein the hole cutting remains constant. Similarly, Custer et al. [15, 16] used the NASA overset OVERFLOW solver and limited the amount of relative motion to ensure static hole-cutting and interpolation. Recently, Mavriplis and Mundis[17] demonstrated a qualitative method for applying the Time-Spectral approach to an unstructured overset solver for arbitrary motion. The goal of the current work is to develop a robust and general method for handling arbitrary motion with the Time-Spectral approach within an overset or Cartesian mesh method, while still approaching the spectral convergence rate of the original Time-Spectral approach. The viscous OVERFLOW solver will be augmented with the new Time-Spectral algorithm and the capability of the method for benchmark problems in rotorcraft and turbomachinery will be demonstrated. This abstract begins with a brief synopsis of the Time-Spectral approach for overset grids and provides details of e current approach to allow for arbitrary motion. Model problem results in one and two dimensions are included to demonstrate the viability of the method and the convergence properties. Section IV briefly outlines the implementation into the OVERFLOW solver, and the abstract closes with a description of the benchmark test cases which will be included in the final paper.

Leffell, Joshua Isaac↗
NASA NTRS2017

Free-Flight Trajectory Simulation of the ADEPT Sounding Rocket Test Using CFD

A computational study of the Adaptive Deployable Entry and Placement Technology (ADEPT) Sounding Rocket (SR-1) Test is presented using the US3D flow solver. ADEPT SR-1 is intended, in part, to assess the dynamic stability of this entry vehicle architecture. Given that no dynamic stability data exists for the ADEPT geometry, a limited ballistic range campaign has been performed to characterize the vehicle's stability characteristics pre-flight for Mach numbers between 1.21 and 2.5. Here, this data is used to assess the accuracy of US3D's free-flight CFD capability. Computed trajectories from US3D and experimental data show that the flow solver compares well in vehicle oscillation frequency, downrange distance, and oscillatory amplitude during high Mach number flight (Mavg = 2.36). For Mach numbers below 1.5, the solver under predicts total angle-of-attack by an average of 16%, but compares well in oscillatory frequency and downrange distance. Additionally, a capability for simulating the trajectory of the flight article through the atmosphere using CFD is presented. This capability couples US3D's free-flight capability to an atmosphere model that accounts for changes in free-stream density and temperature as the vehicle descends. Two simulations for the purpose of demonstrating the capability and viability of this approach are applied to SR-1 flight article, and some unique challenges are discussed.

CFD↗
NASA NTRS1991

The design/analysis of flows through turbomachinery: A viscous/inviscid approach

The development of a design/analysis flow solver at NASA Lewis Research Center is discussed. The solver is axisymmetric and can be run inviscidly with assumed or calculated blockages, or with the viscous terms computed. The blade forces for each blade row are computed from blade-to-blade solutions, correlated data or force model, or from a full three dimensional solution. Codes currently under development can be separated into three distinct elements: the turbomachinery interactive grid generator energy distribution restart code (TIGGERC), the interactive blade element geometry generator (IBEGG), and the viscous/inviscid multi-blade-row average passage flow solver (VIADAC). Several experimental test cases were run to validate the VIADAC code. The tests, representative of typical axial turbomachinery duct axisymmetric wind tunnel body problems, were conducted on an SR7 Spinner axisymmetric body, a NASA Rotor 67 Fan test bed, and a transonic boatail body. The results show the computations to be in good agreement with test data.

Miller, D. P.↗
NASA NTRS2010

CFD Assessment of Aerodynamic Degradation of a Subsonic Transport Due to Airframe Damage

A computational study is presented to assess the utility of two NASA unstructured Navier-Stokes flow solvers for capturing the degradation in static stability and aerodynamic performance of a NASA General Transport Model (GTM) due to airframe damage. The approach is to correlate computational results with a substantial subset of experimental data for the GTM undergoing progressive losses to the wing, vertical tail, and horizontal tail components. The ultimate goal is to advance the probability of inserting computational data into the creation of advanced flight simulation models of damaged subsonic aircraft in order to improve pilot training. Results presented in this paper demonstrate good correlations with slope-derived quantities, such as pitch static margin and static directional stability, and incremental rolling moment due to wing damage. This study further demonstrates that high fidelity Navier-Stokes flow solvers could augment flight simulation models with additional aerodynamic data for various airframe damage scenarios.

Frink, Neal T.↗
NASA NTRS1999

Practical Aerodynamic Design Optimization Based on the Navier-Stokes Equations and a Discrete Adjoint Method

Compressible and incompressible versions of a three-dimensional unstructured mesh Reynolds-averaged Navier-Stokes flow solver have been differentiated and resulting derivatives have been verified by comparisons with finite differences and a complex-variable approach. In this implementation, the turbulence model is fully coupled with the flow equations in order to achieve this consistency. The accuracy demonstrated in the current work represents the first time that such an approach has been successfully implemented. The accuracy of a number of simplifying approximations to the linearizations of the residual have been examined. A first-order approximation to the dependent variables in both the adjoint and design equations has been investigated. The effects of a "frozen" eddy viscosity and the ramifications of neglecting some mesh sensitivity terms were also examined. It has been found that none of the approximations yielded derivatives of acceptable accuracy and were often of incorrect sign. However, numerical experiments indicate that an incomplete convergence of the adjoint system often yield sufficiently accurate derivatives, thereby significantly lowering the time required for computing sensitivity information. The convergence rate of the adjoint solver relative to the flow solver has been examined. Inviscid adjoint solutions typically require one to four times the cost of a flow solution, while for turbulent adjoint computations, this ratio can reach as high as eight to ten. Numerical experiments have shown that the adjoint solver can stall before converging the solution to machine accuracy, particularly for viscous cases. A possible remedy for this phenomenon would be to include the complete higher-order linearization in the preconditioning step, or to employ a simple form of mesh sequencing to obtain better approximations to the solution through the use of coarser meshes. An efficient surface parameterization based on a free-form deformation technique has been utilized and the resulting codes have been integrated with an optimization package. Lastly, sample optimizations have been shown for inviscid and turbulent flow over an ONERA M6 wing. Drag reductions have been demonstrated by reducing shock strengths across the span of the wing. In order for large scale optimization to become routine, the benefits of parallel architectures should be exploited. Although the flow solver has been parallelized using compiler directives. The parallel efficiency is under 50 percent. Clearly, parallel versions of the codes will have an immediate impact on the ability to design realistic configurations on fine meshes, and this effort is currently underway.

Grossman, Bernard↗
DOE OSTI2022

Hybrid RANS-LES of the Atmospheric Boundary Layer for Wind Farm Simulations: Preprint

Wind farm simulations often do not accurately represent wake-atmospheric boundary layer (ABL) interactions, blade boundary layer (BL) dynamics, and turbine-turbine interactions. In this work, we use Active Model Split (AMS), a new hybrid Reynolds-Averaged Navier Stokes (RANS)-large eddy simulation (LES) model, which is well suited to capture these effects because the model can (i) accurately simulate the ABL with the Coriolis effect, (ii) is accurate in adverse pressure gradients such as those near wind turbine blades, and (iii) has sufficiently low computational cost to simulate multiple turbines while resolving the blade BL. For simplicity and consistency we develop AMS to be used throughout the domain rather than in a zonal method. We implement our work in the massively parallel flow solver, Nalu-Wind, so that our model can access the compute resources needed for blade-resolved simulations of multiple wind turbines. To accomplish these aims, we modify the baseline AMS by changing the RANS contribution to SST k - omega with a length scale limiter, adding the Coriolis effect, and developing an appropriate wall treatment. We show that AMS of the ABL with the Coriolis effect matches LES reference results better than those obtained with RANS. We describe our plans to add buoyancy effects and wind turbines to our AMS simulations.

atmospheric boundary layer↗
NASA NTRS2014

Computational Investigation of Novel Tip Leakage Mitigation Methods for High Pressure Turbine Blades

This paper presents preliminary findings on a possible approach to reducing tip leakage losses. In this paper a computational study was conducted on the Energy Efficient Engine (EEE) High Pressure Turbine (HPT) rotor tip geometry using the commercial numerical solver ANSYS FLUENT. The flow solver was validated against aerodynamic data acquired in the NASA Transonic Turbine Blade Cascade facility. The scope of the ongoing study is to computationally investigate how the tip leakage and overall blade losses are affected by (1) injection from the tip near the pressure side, (2) injection from the tip surface at the camber line, and (3) injection from the tip surface into the tip separation bubble. The objective is to identify the locations on the tip surface at which to place appropriately configured blowing keeping in mind the film cooling application of tip blowing holes. The validation was conducted at Reynolds numbers of 85,000, 343,000, and 685,000 and at engine realistic flow conditions. The coolant injection simulations were conducted at a Reynolds number of 343,000 based on blade chord and inlet velocity and utilized the SST turbulence model in FLUENT. The key parameters examined are the number of jets, jet angle and jet location. A coolant to inlet pressure ratio of 1.0 was studied for angles of +30 deg, -30 deg, and 90 deg to the local free stream on the tip. For the 3 hole configuration, 3 holes spaced 3 hole diameters apart with length to diameter ratio of 1.5 were used. A simulation including 11 holes along the entire mean camber line is also presented (30 deg toward suction side). In addition, the effect of a single hole is also compared to a flat tip with no injection. The results provide insight into tip flow control methods and can be used to guide further investigation into tip flow control. As noted in past research it is concluded that reducing leakage flow is not necessarily synonymous with reducing losses due to leakage.

Ibrahim, Mounir↗
NASA NTRS2014

Computational Investigation of Novel Tip Leakage Mitigation Methods for High Pressure Turbine Blades

This paper presents preliminary findings on a possible approach to reducing tip leakage losses. In this paper a computational study was conducted on the EEE (Energy Efficient Engine) HPT (High Pressure Turbine) rotor tip geometry using the commercial numerical solver ANSYS FLUENT. The flow solver was validated against aerodynamic data acquired in the NASA Transonic Turbine Blade Cascade facility. The scope of the ongoing study is to computationally investigate how the tip leakage and overall blade losses are affected by 1. injection from the tip near the pressure side, 2. injection from the tip surface at the camber line, and 3. injection from the tip surface into the tip separation bubble. The objective is to identify the locations on the tip surface at which to place appropriately configured blowing keeping in mind the film cooling application of tip blowing holes. The validation was conducted at Reynolds numbers of 85,000, 343,000 and 685,000 and at engine realistic flow conditions. The coolant injection simulations were conducted at a Reynolds number of 343,000 based on blade chord and inlet velocity and utilized the SST turbulence model in FLUENT. The key parameters examined are the number of jets, jet angle and jet location. A coolant to inlet pressure ratio of 1.0 was studied for angles of +30 deg., -30 deg. and 90 deg. to the local free stream on the tip. For the 3 hole configuration, 3 holes spaced 3 hole diameters apart with length to diameter ratio of 1.5 were used. A simulation including 11 holes along the entire mean camber line is also presented (30 degrees toward suction side). In addition, the effect of a single hole is also compared to a flat tip with no injection. The results provide insight into tip flow control methods and can be used to guide further investigation into tip flow control. As noted in past research it is concluded that reducing leakage flow is not necessarily synonymous with reducing losses due to leakage.

Ibrahim, Mounir↗
NASA NTRS1991

The study of PDF turbulence models in combustion

In combustion computations, it is known that the predictions of chemical reaction rates are poor if conventional turbulence models are used. The probability density function (pdf) method seems to be the only alternative that uses local instantaneous values of the temperature, density, etc., in predicting chemical reaction rates, and thus is the only viable approach for more accurate turbulent combustion calculations. The fact that the pdf equation has a very large dimensionality renders finite difference schemes extremely demanding on computer memories and thus impractical. A logical alternative is the Monte Carlo scheme. Since CFD has a certain maturity as well as acceptance, it seems that the use of a combined CFD and Monte Carlo scheme is more beneficial. Therefore, a scheme is chosen that uses a conventional CFD flow solver in calculating the flow field properties such as velocity, pressure, etc., while the chemical reaction part is solved using a Monte Carlo scheme. The discharge of a heated turbulent plane jet into quiescent air was studied. Experimental data for this problem shows that when the temperature difference between the jet and the surrounding air is small, buoyancy effect can be neglected and the temperature can be treated as a passive scalar. The fact that jet flows have a self-similar solution lends convenience in the modeling study. Futhermore, the existence of experimental data for turbulent shear stress and temperature variance make the case ideal for the testing of pdf models wherein these values can be directly evaluated.

Hsu, Andrew T.↗
NASA NTRS2000

Single Airfoil Gust Response Problem

An unsteady aerodynamic code, called GUST3D, has been developed to solve the single, non-constant coefficient, inhomogeneous convective wave equation for flows with periodic vortical disturbance. The code uses a frequency-domain approach with second-order central differences and a Sommerfeld radiation condition in the far field. It has been extensively validated on model problems with analytical solutions. GUST3D requires as input certain mean flow quantities which are calculated separately by a potential flow solver. This solver calculates the mean flow using a Gothert's Rule approximation. On the airfoil surface, it uses the solution calculated by the potential code FL036. A figure shows the mean pressure along the airfoil surface. To calculate the unsteady pressure, GUST3D was run oil systematically refined grids to obtain a converged solution at each frequency. It was found that 24 points per wavelength was sufficient for convergence. The location of the outer grid boundary was also varied to check for sensitivity to the far-field boundary condition.

Scott, James R.↗
NASA NTRSDate not supplied

USM3D-ME Analyses Performed in Support of a Wind Tunnel Test of a Boundary-Layer Ingestion Configuration

Boundary Layer Ingestion (BLI) has been proposed as a technology with the potential to decrease fuel burn. However, one major concern for BLI configurations is the potential degradation of the flow quality, both on the airframe and at the fan face, resulting from the tightly integrated propulsor. A wind tunnel test was performed in the National Transonic Facility (NTF) at the NASA Langley Research Center to investigate the flow quality ingested by a tail cone thruster configuration, similar to the Single Aisle Turboelectric Aircraft Concept with Aft Boundary Layer Ingestion (STARC-ABL). The wind tunnel model was a modified version of the Common Research Model (CRM) to include an aft-mounted, flow-through propulsor. The experimental data obtained from the wind tunnel test provide insight into the flow and enables an assessment of the accuracy of the USM3D-ME flow solver for predicting the flow at the fan face, which will be crucial for fan design purposes. Both grid refinement and turbulence model studies were performed for the Clean and Cruise MFP configurations at the condition corresponding to ReMAC = 5 million, Mach = 0.8, and alpha = 2 deg. The selected grid refinement level and turbulence model were then used to perform simulations over the range of conditions considered in the NTF wind tunnel test. The condition sweep comparisons illustrate favorable agreement with the experimental data over the entire range of conditions and for all Mass Flow Plug (MFP) configurations. The largest differences were observed for the Idle MFP configuration, with approximately 3% difference observed between USM3D-ME and the experimental data. Future work should investigate the impact of higher fidelity turbulence models and grid adaptation on the USM3D-ME predictions.

CRM↗
NASA NTRSDate not supplied

USM3D-ME Analyses Performed in Support of a Wind Tunnel Test of a Boundary-Layer Ingestion Configuration

Boundary Layer Ingestion (BLI) has been proposed as a technology with the potential to decrease fuel burn. However, one major concern for BLI configurations is the potential degradation of the flow quality, both on the airframe and at the fan face, resulting from the tightly integrated propulsor. A wind tunnel test was performed in the National Transonic Facility (NTF) at the NASA Langley Research Center to investigate the flow quality ingested by a tail cone thruster configuration, similar to the Single Aisle Turboelectric Aircraft Concept with Aft Boundary Layer Ingestion (STARC-ABL). The wind tunnel model was a modified version of the Common Research Model (CRM) to include an aft-mounted, flow-through propulsor. The experimental data obtained from the wind tunnel test provide insight into the flow and enables an assessment of the accuracy of the USM3D-ME flow solver for predicting the flow at the fan face, which will be crucial for fan design purposes. Both grid refinement and turbulence model studies were performed for the Clean and Cruise MFP configurations at the condition corresponding to ReMAC = 5 million, Mach = 0.8, and alpha = 2 deg. The selected grid refinement level and turbulence model were then used to perform simulations over the range of conditions considered in the NTF wind tunnel test. The condition sweep comparisons illustrate favorable agreement with the experimental data over the entire range of conditions and for all Mass Flow Plug (MFP) configurations. The largest differences were observed for the Idle MFP configuration, with approximately 3% difference observed between USM3D-ME and the experimental data. Future work should investigate the impact of higher fidelity turbulence models and grid adaptation on the USM3D-ME predictions.

CRM↗
NASA NTRS1993

Three-dimensional unstructured grid method applied to turbomachinery

This work has three objectives: to develop a three-dimensional flow solver based on unstructured tetrahedral meshes for turbomachinery flows; to validate the solver through comparisons with experimental data; and to apply the solver for better understanding of the flow through turbomachinery geometries and design improvement. The work followed three different approaches: an existing external flow solver/grid generator (USM3D/VGRID) was extensively modified for internal flows; a three-dimensional, finite-volume solver based on Roe's flux-difference splitting and explicit Runge-Kutta time stepping; and three-dimensional unstructured tetrahedral mesh generation using an advancing-front technique. A discussion of these topics is presented in viewgraph form.

Oh Joon Kwon↗
NASA NTRS1993

Calculation methods for rotor wake formation in forward flight

The primary focus of this research centered on improving the vorticity-capturing properties of Eulerian flow solvers in convection-dominated flows. The work was motivated by the fact that excessive numerical diffusion observed in current Euler solvers on grids of feasible size is a major obstacle to accurately computing the flow about helicopter rotors, especially in the forward flight case. The work was originally supported by NASA Grant NAG2-421 for two years. The research then continued for four more years under an ONR contract. The research goal of reduction of numerical diffusion in Euler solvers remained the same, although the target application was now the prediction of internal vortical secondary flows. This was part of a larger ONR-sponsored research program at MIT aimed at reducing the noise of turbopumps. The research work culminated in the PhD thesis titled 'A Coupled Eulerian/Lagrangian Method for the Solution of Three-Dimensional Vortical Flows'.

Drela, Mark↗
NASA NTRSDate not supplied

Flow Characterization of the NASA Langley Unitary Plan Wind Tunnel, Test Section 2: Computational Results

This is an abstract for an invited paper at the AIAA Aviation Conference, June 2021. The work described here is part of an effort of coordinated experiments in the Unitary Plan Wind Tunnel (UPWT) facility at the NASA Langley Research Center (LaRC) and matching CFD simulations. The primary goal of the work is to assess the productivity and true predictive accuracy of CFD, absent any guidance from experiment, in the high supersonic speed range as compared to experiments performed at the NASA LaRC’s UPWT facility. This report concerns CFD simulation of the primary flow-path in the empty wind tunnel, including the settling chamber, nozzle, test section, and some of the tunnel downstream of the test section. The Mach number in the test section ranges from M~2.4 to M~4.6, and the required area ratio variation is achieved by translation of a nozzle block which constricts the area of a loosely S-shaped throat. Flow past protuberances in the settling chamber and into this S-bend throat are predicted by CFD to generate streamwise vorticity that may, or may not, persist through the throat and into the test section as coherent vortices. Some flow conditions are notably unsteady at frequencies well below those of turbulence, due to unsteady separated flow ahead of the nozzle block. The bulk flow moves at velocities ranging from 'walking speed' in the settling chamber to M~4.6 in the test section. Heat transfer to the settling chamber walls and buoyancy are significant at high Mach number. Subtle variations in surface curvature in the nozzle generate Mach waves that propagate into the test section. CFD of the empty tunnel serves two purposes. Firstly, the full-tunnel simulations are used to provide upstream boundary conditions for CFD of vehicle aerodynamics which are generally performed in a domain confined to the wind tunnel test section; these companion studies are addressed in other papers. Secondly, it is a challenging test for CFD to resolve all of the empty tunnel flow phenomena relevant to flow in the test section. It requires a more complete definition of geometry than was originally anticipated. In addition, it requires good spatial and temporal accuracy, and turbulence modeling that performs well on specific phenomena such as corner flows. The boundary conditions and solution algorithms must perform well from incompressible to almost hypersonic speeds. The final state of the pre-test CFD was a product of an iterative self-improvement process. The initial simulations of the empty tunnel were deficient in many respects, but hints to those deficiencies were recognized in the solutions, and remedies were implemented. Possible further improvements will be studied in the post-test phase when comparisons with experimental data are possible. The CFD was performed by five separate collaborative teams using four different flow solvers: FUN3D, Overflow, Star-CCM+ and USM3D. The level of effort of these teams varied significantly, but each made important contributions to the goals of the work. A concerted effort to use uncertainty quantification methods (UQ) in CFD is also a goal of this work. To this end, variations in CFD results due to grid refinement, turbulence modeling, and boundary conditions have been characterized. Code-to-code variation is another means of assessing CFD uncertainty. All CFD solvers predict similarity among the primary flow features; these include the variation of Mach number due to changes in Reynolds number, and the bulk flow angularity due to tunnel-wall curvature. All CFD solvers also predict similar trends in secondary flows, such as the downwash in the side-wall boundary layers. Three of the high-spatial resolution simulations give similar predictions of a complex secondary flow phenomena, streamwise vortices generated in the S-bend throat that persist into the side-wall boundary layers of the test section. Two of the highest-resolution simulations, run with the same turbulence model in different CFD solvers, gave encouragingly similar predictions of a complex tertiary flow phenomenon, small transient "sprites" of upwash flows, resulting from vortices that presumably originate in the separated flow near the leading edge of the nozzle block. While the CFD was done in a "blind pre-test" mode, requests from the experimental team for CFD results pertaining to unsteadiness and total temperature variations in the test section resulted in CFD runs that included a cooled wall in settling chamber. This then led to a change in the standard practice for running the Overflow results, which would not have occurred without this "release" of this experimental information. CFD was also used to guide some measurements. The paper will focus on establishing the consensus among CFD results and understanding differences among those results. Initial findings from the efforts to characterize CFD uncertainty have been done and will be included in the paper.

Robert Edward Childs↗
NASA NTRS1999

Practical Aerodynamic Design Optimization Based on the Navier-Stokes Equations and a Discrete Adjoint Method

The technical details are summarized below: Compressible and incompressible versions of a three-dimensional unstructured mesh Reynolds-averaged Navier-Stokes flow solver have been differentiated and resulting derivatives have been verified by comparisons with finite differences and a complex-variable approach. In this implementation, the turbulence model is fully coupled with the flow equations in order to achieve this consistency. The accuracy demonstrated in the current work represents the first time that such an approach has been successfully implemented. The accuracy of a number of simplifying approximations to the linearizations of the residual have been examined. A first-order approximation to the dependent variables in both the adjoint and design equations has been investigated. The effects of a "frozen" eddy viscosity and the ramifications of neglecting some mesh sensitivity terms were also examined. It has been found that none of the approximations yielded derivatives of acceptable accuracy and were often of incorrect sign. However, numerical experiments indicate that an incomplete convergence of the adjoint system often yield sufficiently accurate derivatives, thereby significantly lowering the time required for computing sensitivity information. The convergence rate of the adjoint solver relative to the flow solver has been examined. Inviscid adjoint solutions typically require one to four times the cost of a flow solution, while for turbulent adjoint computations, this ratio can reach as high as eight to ten. Numerical experiments have shown that the adjoint solver can stall before converging the solution to machine accuracy, particularly for viscous cases. A possible remedy for this phenomenon would be to include the complete higher-order linearization in the preconditioning step, or to employ a simple form of mesh sequencing to obtain better approximations to the solution through the use of coarser meshes. . An efficient surface parameterization based on a free-form deformation technique has been utilized and the resulting codes have been integrated with an optimization package. Lastly, sample optimizations have been shown for inviscid and turbulent flow over an ONERA M6 wing. Drag reductions have been demonstrated by reducing shock strengths across the span of the wing.

Grossman, Bernard↗