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Towards certification of computational fluid dynamics as numerical experiments for rotorcraft applications
Abstract
Virtual Engineering (VE), also known as Model-Based Systems Engineering (MBSE), is necessary in both current operational engineering qualifications and to help reduce the costs of future vertical lift design and analysis. As computational power continues to provide increasing capability to the rotorcraft engineering community to perform simulations in both real time and off line, it is imperative that the community develop verification and validation protocols and processes to certify these methods so that they can be reliably used to help reduce engineering cost and schedule. Computational Fluid Dynamics (CFD) has become a major Computational Science and Engineering (CSE) tool in the fixed wing and vertical lift communities, but it has not been developed to the point where it is accepted as a replacement for testing in certification of new or existing systems or vehicles. Since the rise of modern CFD in the 1980s, the promise of CFD’s capabilities has been met or exceeded, but its role in certification arguably remains less prominent than projected. The ability to implement transformative technologies further drives the need for CFD in design. To meet CFD’s role in certification, several goals must be met to provide a true “numerical experiment” from which accuracies (error estimates), sensitivities, and consistent application results can be extracted. This paper discusses the progress and direction towards developing CFD strategies for certification.
A design methodology for mechatronic systems is proposed, relying on an integrated framework for engineering solutions with continuous interaction among different fields of knowledge. It incorporates the full life-cycle of mechatronic design, from the problem statement to the attainment of conditions for physical implementations. MBSE domains are addressed into a three dimensional cube shape model where each face is focused on a local analysis through individual and interacting V-models with their own time lines. The design is developed under a centralized tool framework with dependency conditions allowing traceability capabilities in multiple hierarchy levels of analysis for generation, updating and management of information among conceptual analysis, specifications, logical architecture, tasks, detailed design, and manufacturing conditions for production.
Dual-solver hybrid methodologies that couple fluid solvers in different regions of the flowfield have been developed to accelerate convergence with minimal compromises in accuracy. A new dual-solver hybrid analysis framework that addresses some of the major shortcomings of prior dual-solver hybrid methodologies has been developed through an academic–industry partnership. In this effort, one of the hybrid solvers, comprising of a computational fluid dynamics–computational structural dynamics (CFD-CSD) solver coupled with a Lagrangian wake-panel module, is assessed. The hybrid solver’s ability to replicate the accuracy of the more expensive CFD-CSD approach and its ability to capture the physics of the rotor system are presented. The criteria that have been evaluated include integrated aerodynamic performance quantities, structural loads and moments, and near-body wakes. If the best practices extracted from this analysis are applied, the analysis with a reduced off-body CFD mesh is able to predict forward-flight rotor behavior that is within 4% of a full CFD simulation with up to 70% cost savings. This accuracy has been assessed on both high-speed and high-thrust flight conditions and has been quantitatively verified for aerodynamic, structural, and hub variables of interest at a number of radial blade stations for a frequency range of 0–16/rev.
A new hybrid analysis framework that addresses some of the major shortcomings of prior hybrid solvers is being developed through an academic-industry partnership between the Georgia Institute of Technology and Continuum Dynamics, Inc. In this effort, one of the hybrid solvers, comprising of a Computational Fluid Dynamics - Computational Structural Dynamics (CFD-CSD) solver coupled with a wake-panel module, is assessed. The hybrid
solver’s ability to replicate the accuracy of the more expensive CFD-CSD approach and its ability to capture the physics of the system are described. The criteria that have been evaluated include integrated aerodynamic performance quantities, structural loads and moments, and near-body wakes. If the best practices extracted from this analysis are applied, the OVERFLOW+CHARM analysis with a reduced off-body mesh (contiguous mesh approach) is able to predict forward-flight rotor behavior that is as accurate as a full OVERFLOW simulation at 45%-50% of the cost. This accuracy has been assessed on both the high-speed and high-thrust flight conditions, and has been quantitatively verified for aerodynamic, structural, and hub variables of interest at a number of radial blade
stations for a frequency range of 0 – 16/rev.
The rotor hub system is recognized as one of the primary contributors to helicopter parasite drag and is one of the inherent limiters to maximum helicopter forward-flight speed. Despite its importance for the performance of rotorcraft, complex bluff-body flows of the rotor hub have received only intermittent attention since the first studies in the 1950s. This work presents a comprehensive review of experimental and computational research over the past 60 years on rotor hub flows and describes the challenges associated with component and interference drag, effect of the hub near wake on pylon and fuselage flows, and the long-age wake of rotor hubs at high Reynolds number with the associated size and strength of flow structures that interact with the empennage. Computational technology is assessed as an emerging design tool for hub/pylon design, and, with its ability to capture downstream flow unsteadiness, empennage/tail surface aeroelasticity and controllability. The work concludes with recommendations of future experimental and computational evaluations to advance the community's understanding of rotor hub flows and mitigation of its adverse effects for future rotorcraft.
The ability to accurately and rapidly predict tethered load instabilities and behavior is required if expensive flight test qualification flights are to be minimized. Tethered or slung loads are complex systems of systems, wherein the system and each constituent must be carefully classified, quantified, and modeled. A physics-based six degree-of-freedom simulation model, the Georgia Tech Aerodynamic Model for Bluff Bodies (GTABB), is under development, and has been adopted by the U.S. Army AMRDEC to support Army slung load simulations (FlightLab). An innovative feature of the GTABB model is that it can be informed using quasi-steady experimental test data, high-fidelity computations, or aerodynamic theory. This model is coupled with empirically-determined unsteady aerodynamic characteristics to provide a flexible, accurate, and extensible modeling and simulation framework. In this effort, unsteady aerodynamic refinements and computational cost reductions are demonstrated. A rigorous uncertainty quantification framework at both the system and component level, necessary for model certification, is established, along with examples. Model validation is extended to include correlations of full-scale flight test with a CONEX container, and comparisons with a complex configuration (truck) evaluated in a wind tunnel. The ramifications of predicting slung load behavior with and without helicopter degrees of freedom and wind are presented.
This paper presents an approach for the rapid implementation of an adjoint solver for the Reynolds- Averaged Navier-Stokes equations with a Spalart-Allmaras turbulence model. Automatic differentiation is used to construct the partial derivatives required in the adjoint formulation. The resulting adjoint implementation is computationally efficient and highly accurate. The assembly of each partial derivative in the adjoint formulation is discussed. In addition, a coloring acceleration technique is presented to improve the adjoint efficiency. The RANS adjoint is verified with complex-step method using a flow over a bump case. The RANS-based aerodynamic shape optimization of an ONERA M6 wing is also presented to demonstrate the aerodynamic shape optimization capability. The drag coefficient is reduced by 19% when subject to a lift coefficient constraint. The results are compared with Euler-based aerodynamic shape optimization and previous work. Finally, the effects of the frozenturbulence assumption on the accuracy and computational cost are assessed.
We introduce a procedure to generate metric-orthogonal anisotropic volume meshes. These meshes are obtained when most of the edges are aligned with the eigenvectors of a provided input metric field. The goal is to generate locally structured meshes in an anisotropic context and in the presence of complex geometries. The algorithm relies on two local mesh modification operators. The first one is used to quickly coarsen volume meshes. From a coarse volume mesh, the second operator is used to insert iteratively points in a frontal manner. The local alignment and orthogonality are naturally inherited from the eigenvectors and eigenvalues of an input metric field. We show on several 3D numerical examples that this procedure is robust and can generate anisotropic locally structured meshes.
The primary objective of the insteady aerodynamics experiment was to provide information needed to quantify the full-scale, three-dimensional aerodynamic behavior of horizontal-axis wind turbines. This report is intended to familiarize the user with the entire scope of the wind tunnel test and to support the use of the resulting data.
A transport equation for the turbulent viscosity is assembled, using empiricism and arguments of dimensional analysis, Galilean invariance, and selective dependence on the molecular viscosity. It has similarities with the models of Nee and Kovaszany, Secundov et al., and Baldwin and Barth. The equation includes a non-viscous destruction term that depends on the distance of the wall.
Adjoint methods are a computationally inexpensive way of deriving sensitivity information where there are fewer dependent (cost) variables than there are independent (input) variables. Automatic differentiation (AD) software makes it possible to create discrete adjoint codes with minimal human effort, an issue that had previously restricted acceptance of adjoint CFD codes. In terms of computational performance, automatic code is often assumed to be inferior to hand code. The structure of the underlying code is critical to the performance of the transformed code. This paper reviews the implementation of AD on Fortran CFD codes and gives details of how small rearrangements can be used to produce competitive tangent and adjoint code using source transformation AD. Copyright © 2005 John Wiley & Sons, Ltd.
Despite significant advancements on computational fluid dynamics and their coupling with computa-
tional structural dynamics (CSD, widely just called comprehensive codes) for rotorcraft applications,
comprehensive codes with their engineering type of modeling the rotor blade dynamics, unsteady section aerodynamics and the vortical wake are still the workhorse for the majority of applications. In this paper, the capabilities of such codes will be demonstrated at the example of the HART II International
Workshop data base, which includes strong blade-vortex interactions. The challenge is to correctly predict the physics behind and thus, all the dynamics, aerodynamics and aeroacoustics coming with it.
Results of the Third AIAA Drag Prediction Workshop (DPW-III) are summarized. The workshop focused on the prediction of both absolute and differential drag levels for wing-body and wing-alone configurations that are representative of transonic transport aircraft. The baseline DLR-F6 wing-body geometry, previously used in DPW-II, is augmented with a side-of-body fairing to help reduce the complexity of the flow physics in the wing-body juncture region. In addition, two new wing-alone geometries have been developed for DPW-III. Numerical calculations are performed using industry-relevant test cases that include lift-specific and fixed-alpha flight conditions, as well as full drag polars. Drag, lift, and pitching-moment predictions from numerous Reynolds-averaged Navier-Stokes computational fluid dynamics methods are presented, focused on fully turbulent flows. Solutions are performed on structured, unstructured, and hybrid grid systems. The structured grid sets include point-matched multiblock meshes and overset grid systems. The unstructured and hybrid grid sets are composed of tetrahedral, pyramid, and prismatic elements. Effort was made to provide a high-quality and parametrically consistent familiy of grids for each grid type about each configuration under study. The wing-body families are composed of a coarse, medium, and fine grid, whereas the wing-alone families also include an extra-fine mesh. These mesh sequences are used to help determine how the provided flow solutions fare with respect to asymptotic grid convegence, and are used to estimate an absolute drag for each configuration.
Engineering computational fluid dynamics (CFD) analysis and design applications focus on output functions (e.g., lift, drag). Errors in these output functions are generally unknown and conservatively accurate solutions may be computed. Computable error estimates can offer the possibility to minimize computational work for a prescribed error tolerance. Such an estimate can be computed by solving the flow equations and the linear adjoint problem for the functional of interest. The computational mesh can be modified to minimize the uncertainty of a computed error estimate. This robust mesh-adaptation procedure automatically terminates when the simulation is within a user specified error tolerance. This procedure for estimating and adapting to error in a functional is demonstrated for three-dimensional Euler problems. An adaptive mesh procedure that links to a Computer Aided Design (CAD) surface representation is demonstrated for wing, wing-body, and extruded high lift airfoil configurations. The error estimation and adaptation procedure yielded corrected functions that are as accurate as functions calculated on uniformly refined grids with ten times as many grid points.
This work couples a computational fluid dynamics (CFD) code and rotorcraft computational structural dynamics (CSD) code to calculate helicopter rotor airloads across a range of flight conditions. An iterative loose (weak) coupling methodology is used to couple the CFD and CSD codes on a per revolution, periodic basis. The CFD uses a high fidelity, Navier-Stokes, overset grid methodology with first principles-based wake capturing. Modifications are made to the CFD code for aeroelastic analysis. For a UH-60A Blackhawk helicopter, four challenging level flight conditions are computed: 1) low speed (u = 0.15) with blade-vortex interaction, 2) high speed (u = 0.37) with advancing blade negative lift, 3) high thrust with dynamic stall (u = 0.24), and 4) hover. Results are compared with UH-60A Airloads Program fight test data. Most importantly, for all cases the loose coupling methodology is shown to be stable, convergent, and robust with full coupling of normal force, pitching moment, and chord force. In comparison with flight test data, normal force and pitching moment magnitudes are in good agreement. For the high speed and dynamic stall cases a phase lag in comparison with the data is seen, nonetheless, the shapes of the curves are very good. Overall, the results are noteworthy improvement over lifting line aerodynamics used in rotorcraft comprehensive codes.
The current effort develops and demonstrates the application of high resolution turbulence modeling to flight mechanics and aeroelasticity of air vehicles at flight conditions where the vehicle is experiencing massively separated flow fields. The effort has both a basic research component to aid in developing the method and an applied component where the method is used to demonstrate an ability to simulate current DoD aircraft issues in flight mechanics and aeroelasticity. The high resolution turbulence method is a hybrid Reynolds averaged Navier-Stokes (RANS)-large eddy-simulation (LES) method introduced by Spalart et al. in 1997 called detached-eddy simulation (DES) implemented in an unstructured Navier-Stokes solver, Cobalt. In the basic research component, DES has been applied to an Aerospatiale-A airfoil at an angle of attack of 13.3 degrees and a Reynolds number of 2 million. The project is called DESFOIL and simulates laminar-to-turbulent transition, adverse pressure gradients, streamline curvature, and boundary layer separation of a 3D airfoil strip. This study is in the early stages of developing a baseline for RANS and DES computations. DES has also been applied to flight mechanic and aeroelasticity problems of DoD air vehicles to demonstrate the utility of DES and also discover some of the nonlinear mechanisms causing these flight issues. The applications studied include the F/A-18E forced motion about the roll axis and one degree of freedom simulation of abrupt wing stall (AWS), the F/A-18C at conditions of tail buffet, and the ARGUS missile at conditions where it experiences coning motion.
Despite significant advancements in computational fluid dynamics (CFD) and their coupling with computational structural dynamics (CSD, or comprehensive codes) for rotorcraft applications, CSD codes with their engineering level of modeling the rotor blade dynamics, the unsteady sectional aerodynamics and the vortical wake are still the workhorse for the majority of applications. This is especially true when a large number of parameter variations is to be performed and their impact on performance, structural loads, vibration and noise is to be judged in an approximate yet reliable and as accurate as possible manner. In this article, the capabilities of such codes are evaluated using the HART II International Workshop data base, focusing on a typical descent operating condition which includes strong blade-vortex interactions; a companion article addresses the CFD/CSD coupled approach. Three cases are of interest: the baseline case and two cases with 3/rev higher harmonic blade root pitch control (HHC) with different control phases employed. One setting is for minimum blade-vortex interaction noise radiation and the other one for minimum vibration generation. The challenge is to correctly predict the wake physics - especially for the cases with HHC - and all the dynamics, aerodynamics, modifications of the wake structure and the aero-acoustics coming with it. It is observed that the comprehensive codes used today have a surprisingly good predictive capability when they appropriately account for all of the physics involved. The minimum requirements to obtain these results are outlined.
An overview of new capabilities recently included in the HPCMP CREATE TM -AV Helios high-delity rotorcraft simulation code is presented. These include a new implicit obody Cartesian solver to support both steady solutions and time-accurate RANS/DES in the wake, a new body hierarchy formulation to support coupled wing/rotor aeroelastics and maneuvering ight, a new strand-based near-body solver intended to support enhanced automation and accuracy, the inclusion of two new unstructured near-body solvers { FUN3D from NASA and kCFD from CREATE-AV Kestrel. New unsteady particle tracing and moving contour plane capability have been added to runtime-based in situ visualization. Example application of these capabilities are presented.
The work carries out coupled computational fluid dynamics and comprehensive analysis (Helios/Rotorcraft Comprehensive Analysis System (RCAS)) of a full-scale UH-60A rotor slowed down to 40% of nominal RPM, operating at advance ratios up to 1.0. The objectives of the work are to (1) validate the analysis with detailed aerodynamic measurements under loading conditions unique to this regime and (2) use the analysis to complement testmeasurements and expand fundamental understanding of slowed rotor and high advance ratio physics. Airloads validation shows excellent agreement with normal force, but pitching moments are poorly predicted on both the advancing (negative lifting) and retreating (reversed flow) blades. Fundamental understanding is gained of the physics of the reversed flow region, wake interactions, advancing and retreating blade moment impulses, differential span loading, and blade deformations-as influenced by RPM and advance ratio. Flow field visualizations show in exceptional detail the unconventional wake patterns, the reversed flow dynamic stall vortex progression, blade-on-blade interactions, reversed-flow-edge vortex, and root vortices. Comparisons of rotor performance and trim controls are documented, showing reasonable trend agreement.
This paper presents an overview of the Rotorcraft Comprehensive Analysis System (RCAS) capabilities, recent enhancements, and validations and also demonstrates RCAS' application to practical rotorcraft problems. More than 10 years have passed since a similar paper was presented. During this time RCAS has been continually enhanced and there have been several significant developments. This paper summarizes these developments, which include new structural elements and improvement of exiting ones, addition of new wake and airloads options, addition of coupling with external wake modules, expansion of coupling with CFD modules, and development of a graphical user interface. This paper surveys and adds to the body of RCAS validation, which has greatly expanded since the last paper. RCAS validations now include detailed work on RCAS' vortex wake models, blade element momentum inflow models, and RCAS/CFD coupling capabilities to name a few. By summarizing RCAS' capabilities, recent developments, and validations, while also demonstrating RCAS applications, this paper provides the rotorcraft technical community with an up-to-date and consolidated resource on the state of RCAS comprehensive analysis.
A complete mesh generation or mesh adaptation process usually requires a large number of operators : Delaunay insertion, edge-face-element point insertion, edge collapse, point smoothing, face/edge swaps, etc. Independently of the complexity of the geometry, the more operators are involved in a remeshing process, the less robust the process may become. In addition, deriving a parallel version of the process may involve a large number of modifications for each operator. Consequently, the multiplication of operators implies additional difficulties in maintaining, improving and parallelizing a code. The scope of this paper is to address these issues by introducing a unique cavity-based operator. As it embeds all aforementioned operators, it can be used as the unique operator at each step of the process from surface and volume remeshing to boundary layer extrusion. In addition, we show that a coarse grain parallelization is possible by using a surface-constrained version of the operator.
Two fundamental models of the flow (static and dynamic) over airfoils in the reverse How region of a helicopter in forward flight are investigated experimentally and computationally at Reynolds numbers of O(105). The first model examines the time-averaged and unsteady flow resulting from a two-dimensional NACA 0012 airfoil held at a static angle of attack. Computational tools successfully predict the presence of three unsteady wake regimes and time-averaged airloads measured experimentally at the University of Maryland (UMD). A second model is investigated by pitching a NACA 0012 airfoil through deep dynamic stall in reverse flow. Both experimental and computational results reveal flow separation at the sharp leading edge for shallow angles of attack, leading to the early formation of a reverse flow dynamic stall vortex. Subsequent flow features in the pitching cycle (trailing edge vortex, secondary dynamic stall vortex) are also captured by the numerical simulation, although the timing and strength of some of these features do not align completely with experiment. This work gives fundamental insight of the aerodynamic behavior of airfoils in reverse flow towards a better understanding of the complex nature of the reverse flow region as well as promising new computational tools to be used in the simulation of this unique flow regime.
This paper describes and analyzes the measurements from a full-scale, slowed revolutions per minute (rpm), UH-60A rotor tested at the National Full-Scale Aerodynamics Complex 40- by 80-ft wind tunnel up to an advance ratio of 1.0. A comprehensive set of measurements that includes performance, blade loads, hub loads, and pressures/airloads makes this data set unique. The measurements reveal new and rich aeromechanical phenomena that are unique to this exotic regime. These include reverse chord dynamic stall, retreating side impulse in torsion load, large inboard-outboard elastic twist differential, diminishing rotor forces and yet a dramatic buildup of blade loads, and high blade loads and yet benign levels of vibratory hub loads. The objective of this research is the fundamental understanding of these unique aeromechanical phenomena. The intent is to provide useful knowledge for the design of high-speed, high-efficiency, slowed rpm rotors of the future and a database for validation of advanced analyses.
Discretization error is usually the largest and most difficult numerical error to estimate in a Computational Fluid Dynamics (CFD) simulation. Development and evaluation of discretization error estimators ideally requires exact solutions to the PDEs which are only available for relatively simple cases. An alternative is to use numerical benchmarks which require a verified code and numerical solutions on a mesh which is sufficiently fine so that the discretization error in the benchmark solution is (essentially) negligible. The focus of this work is to use several numerical benchmark solutions to evaluate residual-based discretization error estimation methods which include defect correction and error transport equations for the Euler equations. This class of discretization error estimation methods requires accurate estimation of a residual/truncation error which will also be evaluated because the residual is the primary factor affecting the accuracy of the discretization error estimate, (i.e., an exact residual results in an exact discretization error estimate). The benchmark solutions include a supersonic inlet and a blunted hypersonic cone.
The first airloads measurements were made in the 1950s at NACA Langley on a 15.3-ft-diameter model rotor, stimulated by the invention of miniaturized pressure transducers. The inability to predict higher harmonic loads in those early years led the U. S. Army to fund airloads measurements
on the CH-34 and the UH-1A aircraft. Nine additional comprehensive airloads tests have been done since that early work, including the recent test of an instrumented UH-60A rotor in the 40- × 80-ft Wind Tunnel at NASA Ames. This historical narrative discusses the 12 airloads tests and
how the results were integrated with analytical efforts. The recent history of the UH-60A Airloads Workshops is presented, and it is shown that new developments in analytical methods have transformed our capability to predict airloads that are critical for design.
The adjoint method, among other sensitivity analysis methods, can fail in
chaotic dynamical systems. The result from these methods can be too large,
often by orders of magnitude, when the result is the derivative of a long time
averaged quantity. This failure is known to be caused by ill-conditioned
initial value problems. This paper overcomes this failure by replacing the
initial value problem with the well-conditioned "least squares shadowing (LSS)
problem". The LSS problem is then linearized in our sensitivity analysis
algorithm, which computes a derivative that converges to the derivative of the
infinitely long time average. We demonstrate our algorithm in several dynamical
systems exhibiting both periodic and chaotic oscillations.
Schemes for anisotropic grid adaptation for dynamic overset simulations are presented. These approaches permit adaptation over a periodic time window in a dynamic flowfield so that an accurate evolution of the unsteady wake may be obtained, as demonstrated on an unstructured flow solver. Unlike prior adaptive schemes, this approach permits grid adaptation to occur seamlessly across any number of grids that are overset, excluding only the boundary layer to avoid surface manipulations. A demonstration on a rotor/fuselage-interaction configuration includes correlations with time-averaged and instantaneous fuselage pressures, and wake trajectories. Additionally, the effects of modeling the flow as inviscid and turbulent are reported. The ability of the methodology to improve these predictions is confirmed, including a vortex/fuselage-impingement phenomenon that has before now not been captured by computational simulations. The adapted solutions exhibit dependency based on the choice of the feature to form the adaptation indicator, indicating that there is no single best practice for feature-based adaptation across the spectrum of rotorcraft applications.
Parasite drag on rotorcraft can become a crucial factor in forward flight, especially for high speed flight. Prior evaluations of the ability of computational methods to predict hub drag have focused on the ability of these solvers to match model scale experimental data, but the codes have not been examined for full scale conditions. Using an unstructured computational method, the sources of hub drag on a moderately complex model are deconstructed and examined for model and full scale configurations and flight conditions. Correlations with a model-scale wind tunnel test and theoretical data are provided to confirm the appropriateness of the initial grid. Unlike prior efforts, grid adaptation across the overset meshes permits grid refinement where needed and minimizes the grid cost. It has been observed that for the moderately complex hub evaluated that grids developed for the model scale analysis can not be applied directly to a full-scale analysis. Deconstruction of the drag illustrates that evaluation of the Reynolds number for each component to evaluate its impact on drag, as well as consideration of changes in the interference effects, are required when scaling results from model to full scale, even for static (nonrotating) configurations. Velocity scaling for rotating hubs must also be considered; scaling to similar advance ratio rather than rotor angular velocity appears to be more appropriate. Estimation of the interference drag for rotating hubs must consider the Magnus effect, which appear to directly influence the nonlinearities observed in scaling the drag.
The Onera elsA CFD software is both a software package capitalizing the innovative results of research over time and a multi-purpose tool for applied CFD and multi-physics. The research input from Onera and other laboratories and the feedback from aeronautical industry users allow enhancement of its capabilities and continuous improvement. The paper presents recent accomplishments of varying complexity from research and industry for a wide range of aerospace applications: aircraft, helicopters, turbomachinery...
Currently, wind turbine designers rely on safety factors to compensate for the effects of unknown loads acting on the turbine structure. This results in components that are overdesigned because precise load levels and load paths are unknown. To advance wind turbine technology, the forces acting on the turbine structure must be accurately characterized because these forces translate directly into loads imparted to the wind turbine structure and resulting power production. Once these forces are more accurately characterized, we will better understand load paths and can therefore optimize turbine structures. To address this problem, the National Renewable Energy Laboratory (NREL) conducted the Unsteady Aerodynamics Experiment (UAE), which was a test of an extensively instrumented wind turbine in the giant NASA-Ames 24.4-m (80 feet) by 36.6-m (120 feet) wind tunnel. To maximize the benefits from testing, NREL formed a Science Panel of advisers comprised of wind turbine aerodynamics and modeling experts throughout the world. NREL used the Science Panel's guidance to specify the conditions and configurations under which the turbine was operated in the wind tunnel. The panel also helped define test priorities and objectives that would be effective for wind turbine modeling tool development and validation.
Error estimation and control are critical ingredients for improving the reliability of computational simulations. Ad joint-based techniques can be used to both estimate the error in chosen solution outputs and to provide local indicators for adaptive refinement. This article reviews recent work on these techniques for computational fluid dynamics applications in aerospace engineering. The definition of the adjoint as the sensitivity of an output to residual source perturbations is used to derive both the adjoint equation, in fully discrete and variational formulations, and the adjoint-weighted residual method for error estimation. Assumptions and approximations made in the calculations are discussed. Presentation of the discrete and variational formulations enables a side-by-side comparison of recent work in output-error estimation using the finite volume method and the finite element method. Techniques for adapting meshes using output-error indicators are also reviewed. Recent adaptive results from a variety of laminar and Reynolds-averaged Navier Stokes applications show the power of output-based adaptive methods for improving the robustness of computational fluid dynamics computations. However, challenges and areas of additional future research remain, including computable error bounds and robust mesh adaptation mechanics.
An overview of a comprehensive framework is given for estimating the predictive uncertainty of scientific computing applications. The framework is comprehensive in the sense that it treats both types of uncertainty (aleatory and epistemic), incorporates uncertainty due to the mathematical form of the model, and it provides a procedure for including estimates of numerical error in the predictive uncertainty. Aleatory (random) uncertainties in model inputs are treated as random variables, while epistemic (lack of knowledge) uncertainties are treated as intervals with no assumed probability distributions. Approaches for propagating both types of uncertainties through the model to the system response quantities of interest are briefly discussed. Numerical approximation errors (due to discretization, iteration, and computer round off) are estimated using verification techniques, and the conversion of these errors into epistemic uncertainties is discussed. Model form uncertainty is quantified using (a) model validation procedures, i.e., statistical comparisons of model predictions to available experimental data, and (b) extrapolation of this uncertainty structure to points in the application domain where experimental data do not exist. Finally, methods for conveying the total predictive uncertainty to decision makers are presented. The different steps in the predictive uncertainty framework are illustrated using a simple example in computational fluid dynamics applied to a hypersonic wind tunnel.
An algorithm to construct boundary-conforming, isotropic clouds of points with variable density in space is described. The input required consists of a specified mean point distance and an initial triangulation of the surface. Borrowing a key concept from advancing front grid generators, one point at a time is removed and, if possible, surrounded by admissible new points. This operation is repeated until no active points are left. Timings show that the scheme is about an order of magnitude faster than volume grid generators based on the advancing front technique, making it possible to generate large (>106) yet optimal clouds of points in a matter of minutes on a workstation. Several examples are included that demonstrate the capabilities of the technique. Copyright © 1998 John Wiley & Sons, Ltd.
This article develops a general framework for identifying error and uncertainty in computational simulations that deal with the numerical solution of a set of partial differential equations (PDEs). A comprehensive, new view of the general phases of modeling and simulation is proposed, consisting of the following phases: conceptual modeling of the physical system, mathematical modeling of the conceptual model, discretization and algorithm selection for the mathematical model, computer programming of the discrete model, numerical solution of the computer program model, and representation of the numerical solution. Our view incorporates the modeling and simulation phases that are recognized in the systems engineering and operations research communities, but it adds phases that are specific to the numerical solution of PDEs. In each of these phases, general sources of uncertainty, both aleatory and epistemic, and error are identified. Our general framework is applicable to any numerical discretization procedure for solving ODEs or PDEs. To demonstrate this framework, we describe a system-level example: the flight of an unguided, rocket-boosted, aircraft-launched missile. This example is discussed in detail at each of the six phases of modeling and simulation. Two alternative models of the flight dynamics are considered, along with aleatory uncertainty of the initial mass of the missile and epistemic uncertainty in the thrust of the rocket motor. We also investigate the interaction of modeling uncertainties and numerical integration error in the solution of the ordinary differential equations for the flight dynamics.
We present two error estimation approaches for bounding or correcting the error in functional estimates such as lift or drag. Adjoint methods quantify the error in a particular output functional that results from residual errors in approximating the solution to the partial differential equation. Defect methods can be used to bound or reduce the error in the entire solution, with corresponding improvements to functional estimates. Both approaches rely on smooth solution reconstructions and may be used separately or in combination to obtain highly accurate solutions with asymptotically sharp error bounds. The adjoint theory is presented for both smooth and shocked problems; numerical experiments confirm fourth-order error estimates for a pressure integral of shocked quasi-1D Euler flow. By employing defect and adjoint methods together and accounting for errors in approximating the geometry, it is possible to obtain functional estimates that exceed the order of accuracy of the discretization process and the reconstruction approach. Superconvergent drag estimates are obtained for subsonic Euler flow over a lifting airfoil.
An anisotropic, unstructured grid adaptive method is presented for improving the accuracy of functional outputs of viscous, compressible flow simulations for general discretizations. The procedure merges output error control with Hessian-based anisotropic grid adaptation. An adjoint formulation is used to relate the estimated functional error to the local residual errors of both the primal and adjoint solutions. This relationship allows local error contributions to be used as indicators in a grid adaptive method designed to produce specially tuned grids for accurately estimating the chosen functional. Element stretching and orientation information is obtained from interpolation error estimates for linear triangular finite elements. The proposed adaptive method is implemented using a standard second-order upwind finite volume discretization, although the procedure is applicable to other types of discretizations such as the finite element method. A series of airfoil test cases, including separated, high-lift flows, are presented to demonstrate the approach; the functionals considered are the lift and drag coefficients. The proposed adaptive method is shown to be superior in terms of reliability and output accuracy relative to pure Hessian-based adaptation.
The verification and validation (V & V) in computational fluid dynamics was presented. The methods and procedures for assessing V & V were presented. The issues such as code verification versus solution verification, model validation versus solution validation, the distinction between error and uncertainity, conceptual sources of error and uncertainity, and the relationship between validation and prediction was discussed. Methods for determining the accuracy of numerical solutions were presented and the importance of software testing during verification activities were emphasized.
This paper presents an output-based adaptive algorithm for unsteady simulations of convection-dominated flows. A space–time discontinuous Galerkin discretization is used in which the spatial meshes remain static in both position and resolution, and in which all elements advance by the same time step. Error estimates are computed using an adjoint-weighted residual, where the discrete adjoint is computed on a finer space obtained by order enrichment of the primal space. An iterative method based on an approximate factorization is used to solve both the forward and adjoint problems. The output error estimate drives a fixed-growth adaptive strategy that employs hanging-node refinement in the spatial domain and slab bisection in the temporal domain. Detection of space–time anisotropy in the localization of the output error is found to be important for efficiency of the adaptive algorithm, and two anisotropy measures are presented: one based on inter-element solution jumps, and one based on projection of the adjoint. Adaptive results are shown for several two-dimensional convection-dominated flows, including the compressible Navier–Stokes equations. For sufficiently-low accuracy levels, output-based adaptation is shown to be advantageous in terms of degrees of freedom when compared to uniform refinement and to adaptive indicators based on approximation error and the unweighted residual. Time integral quantities are used for the outputs of interest, but entire time histories of the integrands are also compared and found to converge rapidly under the proposed scheme. In addition, the final output-adapted space–time meshes are shown to be relatively insensitive to the starting mesh.
Some past developments and current examples of computational aerodynamics are briefly reviewed. An assessment is made of the requirements on future computer memory and speed imposed by advanced numerical simulations, giving emphasis to the Reynolds averaged Navier-Stokes equations and to turbulent eddy simulations. Experimental scales of turbulence structure are used to determine the mesh spacings required to adequately resolve turbulent energy and shear. Assessment also is made of the changing market environment for developing future large computers, and of the projections of micro-electronics memory and logic technology that affect future computer capability. From the two assessments, estimates are formed of the future time scale in which various advanced types of aerodynamic flow simulations could become feasible. Areas of research judged especially relevant to future developments are noted.
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