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The Influence of Adaptive Mesh Refinement on the Prediction of Vortex Interactions about a Generic Missile Airframe
Abstract
View Video Presentation: https://doi.org/10.2514/6.2022-1177.vid The complex interaction of forebody and wing vortices significantly impacts missile aerodynamics. The formation of these vortices involves smooth regions of the geometry or geometric discontinuities like leading edges, trailing edges, tips, and corners. Regions of supersonic flow and complex shock topologies interact with boundary layers and vortices. Smooth-body separation and 3D viscous effects strain current Reynolds-averaged Navier-Stokes (RANS) techniques. The quantification and control of discretization error is critical to obtaining reliable simulation results and often turbulence model assessments are made in the presence of unquantified (and potentially large) discretization errors. Two mesh adaptation schemes are applied to steady RANS simulations. Multiscale unstructured mesh adaptation is applied to control interpolation error estimates of the Mach field, which resolves boundary layers, vortices, and shocks. A dual-mesh approach with overset communication is applied between an expert-crafted near-body unstructured mesh and an adaptive off-body Cartesian mesh refined with Q-criterion scaled by the strain tensor magnitude. A generic missile configuration is examined in a supersonic flow field to show the interaction of mesh adaptation and turbulence model. Turbulence model modifications for rotational correction and a quadratic constitutive relationship show a strong influence on adaptive mesh refinement and predicted rolling moment.
... A similar work has been carried of using the NASA FUN3D code with the rene library. 18 The volume for the nal Mach adaptive mesh created with the Mach and distance sensors is shown in Figure 15, along with a horizontal y = 0 slice for both norms. Additionally, the complex shock and vortical structure are shown in Figure 15 with density contour from a slice where conical shocks are produced by the nose, leading edge of the wing, trailing edge of the wing, and n. Figure 16a and 16b and show the section through the n mid-chord of missile. ...
... A similar work has been carried of using the NASA FUN3D code with the rene library. 18 The volume for the nal Mach adaptive mesh created with the Mach and distance sensors is shown in Figure 15, along with a horizontal y = 0 slice for both norms. Additionally, the complex shock and vortical structure are shown in Figure 15 with density contour from a slice where conical shocks are produced by the nose, leading edge of the wing, trailing edge of the wing, and n. Figure 16a and 16b and show the section through the n mid-chord of missile. ...
... Other processes using CAD-based parameterizations for analysis or optimization have used automated meshing tools to generate a new mesh from the CAD model [8,9] or use adaptive meshing [10,11]. This process is not general as automated meshing tools are not adequate for use with structured computational fluid dynamics (CFD) solvers. ...
... The original element dimensions were 0.25 mm thick × 0.2 mm 2 in area. After the finite element meshing, the area of the projectile impacted on the target was refined to a ten-times higher density than others [38], as shown by the yellow circle in Figure 3. This meant that a single element was divided into ten elements in the J-direction. ...
The distribution and dissipation energies in fracture mechanisms were a critical challenge to derive, especially for this ultra-thin sample. The membrane failure, which is the end of the fracture mechanisms, is a result of the cone wave reflections from the backend membrane boundaries. These reflections delay the failure processes due to the shock impacts. To compare these results with the experimental work, a numerical simulation was conducted for these processes. The cylinder-shaped rigid projectile was impacted using a frictionless Lagrange solver. The target was a cartridge brass circle plate clamped at its perimeter, and its zone was refined to a ten-times higher meshing density for better analysis. The erosion and cut-off controls involved a zero-gap interaction condition and an instantaneous geometric erosion strain of 200%. Due to the maximum projectile velocity of 382 m/s having the slowest perforation, the target thickness was found to be 5.5 mm. The fracture mechanism phenomena, such as tensile, compressive, through-thickness, and growth in-plane delamination, propagating delamination, and local punch shear waves were observed. After deducting tensile and flexural strengths from the last experiment, a total residual membrane stress of 650 MPa was found. This result indicated a relationship between the fracture mechanisms and residual membrane stresses of metallic material.
... The Missile Facet was established to (i) Assess the current capabilities of CFD to predict missile aerodynamic characteristics for flows containing multiple vortex interactions; (ii) Share and seek to learn from comparable experience of applying CFD to other classes of NATO vehicles (combat aircraft, in particular); and (iii) Consolidate lessons learned and any attendant future requirements [1]. This paper is one of a series being presented at this conference to provide a technical overview of the activities and accomplishments of the AVT-316 Missile Facet [2][3][4][5][6][7][8][9][10][11]. The work is still ongoing: a final output, constituting a more detailed and consolidated technical record, will be published by NATO STO towards the end of 2022. ...
View Video Presentation: https://doi.org/10.2514/6.2022-1686.vid Predicting the flowfield around a supersonic store at a high incidence angle is challenging due to the presence of vortices and shocks that interact with each other. The complexity of the problem is further increased by the presence of wing-body and wing-tail junctions giving rise to secondary flows. Given that the flow is turbulent, linear eddy-viscosity turbulence models are unable to account for the secondary flows and are often more dissipative than their non-linear counterparts. The high incidence angle further increases the complexity. This work investigates the effect of grid refinement and turbulence modelling on three store configurations - one with wings and fins, one without fins and wings, and one with wings only. The in-house CFD solver of the University of Glasgow is used to perform simulations at different angles of incidence and roll. Grids consisting of approximately 80 × 10e6 cells or less were found to be inadequate to capture the flow features. This shows that even if a high-order spatial method is employed, a grid of sufficient density must be used to accurately capture the aerodynamic loads of the store. In addition, grid converged results were difficult to obtain for the full configuration due to the interaction of the wing vortices with the store’s fins. Improved convergence was observed for the simplified store configurations. This further showed that the difficulty in grid convergence is related to the wing vortex interactions with the store’s fins.
... The Missile Facet was established to (i) Assess the current capabilities of CFD to predict missile aerodynamic characteristics for flows containing multiple vortex interactions; (ii) Share and seek to learn from comparable experience of applying CFD to other classes of NATO vehicles (combat aircraft, in particular); and (iii) Consolidate lessons learned and any attendant future requirements [1]. This paper is one of a series being presented at this conference to provide a technical overview of the activities and accomplishments of the AVT-316 Missile Facet [2][3][4][5][6][7][8][9][10][11]. The work is still ongoing: a final output, constituting a more detailed and consolidated technical record, will be published by NATO STO towards the end of 2022 [68]. ...
View Video Presentation: https://doi.org/10.2514/6.2022-0416.vid Within the framework of the NATO Science and Technology Organization Applied Vehicle Technology Task Group AVT316 calculations have been made of the supersonic flow around a slender body with wings and fins. In this paper a synthesis of the results obtained using the Reynolds Averaged Navier-Stokes equations are presented. The results show significant sensitivity to the choice of turbulence model. Whilst the gross features of the flow are similar, details of the development of the leeward wake are different. Simple linear eddy viscosity models predict vortices that rapidly decay, resulting in weak interactions with the downstream fins and relatively small rolling moments. This is attributed to an over production in turbulence quantities that results in excessive effective turbulent viscosity. Interventions that limit the production of turbulence, for example the SST limiter or curvature corrections, results in vortices that grow more slowly, changing the nature of the downstream interactions resulting in increased rolling moment. The use of more complex formulations, such as Reynolds stress models, that are inherently more capable for highly strained flows, further limits the rate of growth of the vortex cores leading to rolling moment predictions that are 2-3 times greater than those obtained with the simplest models.
View Video Presentation: https://doi.org/10.2514/6.2022-2308.vid Time-accurate, turbulence scale resolving simulations of a transonic missile at high incidence and roll angle were performed and compared to simulations using standard Reynolds-Averaged Navier-Stokes turbulence models. The scale resolving simulations showed improved prediction of the total roll moment observed in wind tunnel tests compared to the RANS simulations, but still did not accurately predict the trend in roll moment with incidence angle in the range 15.0°≤σ≤17.5°. The scale resolving simulations predicted less turbulence energy in the vortex structures and larger separation regions over the wings. Spectral analysis of the roll moment signal showed dominant frequency modes consistent with a leading-edge vortex breakdown over two wings.
View Video Presentation: https://doi.org/10.2514/6.2022-1685.vid Hybrid Reynolds Average Navier-Stokes (RANS) - Large Eddy Simulations (LES) have been applied to predict the rolling moment coefficient of a generic missile at high angle of incidence in supersonic flow. The missile airframe was rolled which generated unsymmetrical vortices affecting the downstream tail fin section. Traditional RANS indicated difficulties predicting the rolling moment. This challenge was accepted by the NATO Science and Technology Organization (STO), Applied Vehicle Technology (AVT) panel forming a devoted Task Group AVT-316 “Vortex Interaction Effects Relevant To Military Air Vehicle Performance”. The paper describes the Missile Facets work on scale resolving simulations with spatial and temporal resolution strategy, quality index for LES and comparison with industry standard RANS methods. The hybrid RANS-LES results provided additional insights into the nature of the complex vortex interactions, including shocks, associated with slender body aerodynamics not detected with RANS. Scale resolving simulations drastically reduced vortex dissipation and resulted in significant shift of rolling moment magnitude.
View Video Presentation: https://doi.org/10.2514/6.2022-1178.vid Vortex dominated flows provide a challenge for modern computational fluid dynamics (CFD) solvers to accurately predict and capture the true physics of the flow. Modeling the formation and propagation of vortices downstream, as well as interactions with other vortices and shocks, are affected by a number of decisions including but not limited to the mesh generated, numerical scheme employed, and modelling assumptions. A research program has been underway for four years to study vortex interaction aerodynamics that are relevant to military air vehicle performance. The program has been conducted under the auspices of the NATO Science and Technology Organization (STO), Applied Vehicle Technology (AVT) panel by a Task Group with the identification of AVT-316. The paper at hand will look at the OTC1 test case [1], which is comprised of a generic missile configuration in supersonic flow, and the influence of the numerical scheme on the predicted results. The decision of the spatial discretization scheme, order of the turbulent flux, and choice of limiter were all shown to have strong influence on the predicted rolling moment of the OTC1 test case.
View Video Presentation: https://doi.org/10.2514/6.2022-0002.vid A research program has been underway for four years to study vortex interaction aerodynamics that are relevant to military air vehicle performance. The program has been conducted under the auspices of the NATO Science and Technology Organization (STO), Applied Vehicle Technology (AVT) panel by a Task Group with the identification of AVT-316. The Task Group was split into two facets: an aircraft facet and a missile facet, each focusing on the vortex interactions associated with airframes of direct interest to NATO. This paper is one of a series being presented at this conference to provide a technical overview of the activities and accomplishments of the AVT-316 missile facet. A substantial body of work has been established pertaining to two generic missile airframes: OTC1 and LK6E2. The test cases studied incorporate multiple vortices and associated interactions and pose a variety of challenges for CFD. Significant progress has been made in consolidating understanding of these challenges and in assessing the current capabilities of CFD to simulate such flows. In so doing, the importance of solution verification has been reinforced, with fine resolution of the flow being required to avoid excessive dissipation. The use of multi-fidelity analysis has also afforded various insights into the physical models being used: for instance, this has allowed compelling demonstrations of the limitations of linear eddy viscosity turbulence models to be provided without recourse to physical test data. As a result of the progress made in these fundamental areas with OTC1, it has been possible to identify features of the overall aerodynamic characteristics of LK6E2 that had been obscured in previous CFD analyses and to subject them to better informed – and therefore more incisive – analysis. The work of the missile facet is ongoing: a final output, constituting a more detailed and consolidated technical record, will be published by NATO STO towards the end of 2022.
View Video Presentation: https://doi.org/10.2514/6.2022-0001.vid A research program has been underway for four years to study vortex interaction aerodynamics that are relevant to military air vehicle performance. The program has been conducted under the auspices of the NATO Science and Technology Organization (STO), Applied Vehicle Technology (AVT) panel by a Task Group with the identification of AVT-316. The Task Group was split into two facets: an aircraft facet and a missile facet, each focusing on the vortex interactions associated with airframes of direct interest to NATO. This paper, one of a series being presented at this conference to provide a technical overview of the activities and accomplishments of the AVT-316 missile facet, provides an overview of its formation, objectives and manner of working. The work of the missile fact is still ongoing: a final output, constituting a more detailed and consolidated technical record, will be published by NATO STO towards the end of 2022.
View Video Presentation: https://doi.org/10.2514/6.2022-0025.vid A research program has been underway for four years to study vortex interaction aerodynamics that are relevant to military air vehicle performance. The program has been conducted under the auspices of the NATO Science and Technology Organization (STO), Applied Vehicle Technology (AVT) panel by a Task Group with the identification of AVT-316. Seven special sessions have been established to highlight accomplishments from the AVT-316 research. An overview of the AVT-316 program is presented in this paper.
View Video Presentation: https://doi.org/10.2514/6.2022-0160.vid The NATO Science and Technology Organization Applied Vehicle Technology Task Group AVT316 study vortical flow for missiles and combat aircraft. RANS and DDES simulations were performed for both cases and show similar physics of vortical development between the two cases. CFD simulations are compared to averaged aircraft experimental data showing that DDES better captures the details of the flow than RANS. When increasing the Reynolds number, the boundary layer flow become complex and interacts with the shear layer feeding the primary vortex in a nonlinear way creating steady substructures. In return, the primary vortex interacts with the boundary layer creating a closed feedback loop. In the missile case, the coefficients are directly impacted by the unsteadiness created at the wing travelling downstream within the vortical structure before hitting the fins.
A unified approach to system-rotation and streamline-curvature effects in the framework of simple eddy-viscosity turbulence models is exercised in a range of rotating and curved channel flows. The Spalart-Allmaras (SA) one-equation turbulence model (Spalart, P.R., and Allmaras, S. R., "A One-Equation Turbulence Model For Aerodynamic Flows," AIAA Paper 92-0439, 1992) modified in this manner is shown to be quite competitive with advanced nonlinear and Reynolds-stress models and to be much more accurate than the original Sri model and other eddy-viscosity models that are widely used for industrial flow computations. The new term adds about 20% to the computing cost, but does not degrade convergence.
In FY2008, the U.S. Department of Defense (DoD) initiated the Computational Research and Engineering Acquisition Tools and Environments (CREATE) program, a $360M program with a two-year planning phase and a ten-year execution phase. CREATE will develop and deploy three computational engineering tool sets for DoD acquisition programs to use to design aircraft, ships and radio-frequency antennas. The planning and execution of CREATE are based on the 'lessons learned' from case studies of large-scale computational science and engineering projects. The case studies stress the importance of a stable, close-knit development team; a focus on customer needs and requirements; verification and validation; flexible and agile planning, management, and development processes; risk management; realistic schedules and resource levels; balanced short- and long-term goals and deliverables; and stable, long-term support by the program sponsor. Since it began in FY2008, the CREATE program has built a team and project structure, developed requirements and begun validating them, identified candidate products, established initial connections with the acquisition programs, begun detailed project planning and development, and generated the initial collaboration infrastructure necessary for success by its multi-institutional, multidisciplinary teams.
Several numerical schemes for the solution of hyperbolic conservation laws are based on exploiting the information obtained by considering a sequence of Riemann problems. It is argued that in existing schemes much of this information is degraded, and that only certain features of the exact solution are worth striving for. It is shown that these features can be obtained by constructing a matrix with a certain “Property U.” Matrices having this property are exhibited for the equations of steady and unsteady gasdynamics. In order to construct thems it is found helpful to introduce “parameter vectors” which notably simplify the structure of the conservation laws.
Anisotropic, adaptive meshing for flows around complex, three-dimensional bodies remains a barrier to increased automation in computational fluid dynamics. Two specific advances are introduced in this thesis. First, a finite-volume discretization for tetrahedral cut-cells is developed that makes possible robust, anisotropic adaptation on complex bodies. Through grid refinement studies on inviscid flows, this cut-cell discretization is shown to produce similar accuracy as boundary-conforming meshes with a small increase in the degrees of freedom. The cut-cell discretization is then combined with output-based error estimation and anisotropic adaptation such that the mesh size and shape are controlled by the output error estimate and the Hessian (i.e. second derivatives) of the Mach number, respectively. Using a parallel implementation, this output-based adaptive method is applied to a series of sonic boom test cases and the automated ability to correctly estimate pressure signatures at several body lengths is demonstrated starting with initial meshes of a few thousand control volumes. Second, a new framework for adaptation is introduced in which error estimates are directly controlled by removing the common intermediate step of specifying a desired mesh size and shape. As a result, output error control can be achieved without the adhoc selection of a specific field (such as Mach number) to control anisotropy, rather anisotropy in the mesh naturally results from both the primal and dual solutions. Furthermore, the direct error control extends naturally to higher-order discretizations for which the use of a Hessian is no longer appropriate to determine mesh shape. The direct error control adaptive method is demonstrated on a series of simple test cases to control interpolation error and discontinuous Galerkin finite element output error. This new direct method produces grids with less elements but the same accuracy as existing metric-based approaches.
For the full or isenthalpic Euler equations combined with the ideal-gas law, the flux-vector splitting presented here is, by a great margin, the simplest means to implement upwind differencing. For a polytropic gas law, with γ > 1, closed formulas have not yet been derived.
The scheme produces steady shock profiles with two interior zones. There is evidence [10] that, among implicit versions of upwind methods, those with a two-zone steady-shock representation give faster convergence to a steady solution than those with a one-zone representation.
A disadvantage in using any flux-vector splitting is that it leads to numerical diffusion of a contact discontinuity at rest. This diffusion can be removed; present research is aimed at achieving this with minimal computational effort.
Numerical solutions by first- and second-order schemes including the above split fluxes can be found in Refs. [6], [7] (one-dimensional) and [8], r91 (two-dimensional).
View Video Presentation: https://doi.org/10.2514/6.2021-2992.vid The control of discretization error is critical to obtaining reliable simulation results. Recent progress has matured anisotropic mesh adaptation, which automates discretization error control for complex geometries. However, the meshing process can fail when geometric model Boundary REPresentation (BREP) tolerances are larger than boundary layer surface normal and tangential spacing requirements. Geometry sources are often created in Mechanical Computer-Aided Design (MCAD) systems, which are designed to produce models for manufacturing and not the stricter requirements of viscous flow analysis. BREP tolerances are strained by three factors: the inherent complexity of the model (e.g., large range of scales and complex topology), the numerical difficulties arising from surface/surface intersections, and the omission of crucial data during export and translation. Manual preparation of geometry is commonly employed to enable expert-guided mesh generation, which severely inhibits workflow automation. Accommodation of loose BREP tolerances is required for automated mesh processes, because barrier issues may not be detected until well into the solution process. To raise awareness of this class of geometry issues and their impact on simulation, a survey of these barrier issues is presented with example mitigation techniques. This awareness may also impact geometry creation workflows to prevent the introduction of these artifacts.
In the context of scientific computing, the mesh is used as a discrete support for the considered numerical methods. As a consequence, the mesh greatly impacts the efficiency, the stability and the accuracy of numerical methods. The goal of anisotropic mesh adaptation is to generate a mesh which fits the application and the numerical scheme in order to achieve the best possible solution. It is thus an active field of research which is progressing continuously. This review article proposes a synthesis of the research activity of the INRIA Gamma3 team in the field of anisotropic mesh adaptation applied to inviscid flows in computational fluid dynamics since 2000. It shows the evolution of the theoretical and numerical results during this period. Finally, challenges for the next decade are discussed.
TetGen is a C++ program for generating good quality tetrahedral meshes aimed to support numerical methods and scientific computing. The problem of quality tetrahedral mesh generation is challenged by many theoretical and practical issues. TetGen uses Delaunay-based algorithms which have theoretical guarantee of correctness. It can robustly handle arbitrary complex 3D geometries and is fast in practice. The source code of TetGen is freely available.
This article presents the essential algorithms and techniques used to develop TetGen. The intended audience are researchers or developers in mesh generation or other related areas. It describes the key software components of TetGen, including an efficient tetrahedral mesh data structure, a set of enhanced local mesh operations (combination of flips and edge removal), and filtered exact geometric predicates. The essential algorithms include incremental Delaunay algorithms for inserting vertices, constrained Delaunay algorithms for inserting constraints (edges and triangles), a new edge recovery algorithm for recovering constraints, and a new constrained Delaunay refinement algorithm for adaptive quality tetrahedral mesh generation. Experimental examples as well as comparisons with other softwares are presented.
Junction flows may suffer from secondary flows such as horseshoe vortices and corner separations that can dramatically impair the performances of aircrafts. The present article brings into focus the unsteady aspects of the flow at the intersection of a wing and a flat plate. The simplified junction flow test case is designed according to a literature review to favor the onset of a corner separation. The salient statistical and fluctuating properties of the flow are scrutinized using large eddy simulation and wind tunnel tests, which are carried out at a Reynolds number based on the wing chord c and the free stream velocity U∞ of Rec=2.8×105. As the incoming boundary layer at Reθ=2100 (θ being the boundary layer momentum thickness one-half chord upstream the junction) experiences the adverse pressure gradient created by the wing, a three dimensional separation occurs at the nose of the junction leading to the formation of a horseshoe vortex. The low frequency, large scale bimodal behavior of the horseshoe vortex at the nose of the junction is characterized by multiple frequencies within f.δ/U∞=[0.05−0.1] (where δ is the boundary layer thickness one-half chord upstream the wing). Downstream of the bimodal region, the meandering of the core of the horseshoe vortex legs in the crossflow planes is scrutinized. It is found that the horseshoe vortex oscillates around a mean location over an area covering almost 10% of the wing chord in the tranverse plane at the trailing edge at normalized frequencies around f.δ/U∞=0.2–0.3. This so-called meandering is found to be part of a global dynamics of the horseshoe vortex initiated by the bimodal behavior. Within the corner, no separation is observed and it is shown that a high level of anisotropy (according to Lumley’s formalism) is reached at the intersection of the wing and the flat plate, which makes the investigated test case challenging for numerical methods. The conditions of apparition of a corner separation are eventually discussed and we assume that the vicinity of the horseshoe vortex suction side leg might prevent the corner separation. It is also anticipated that higher Reynolds number junction flows are more likely to suffer from such separations.
Three-dimensional real-life simulations are generally unsteady and involve moving geometries. Industry is currently very far from performing such body-fitted simulations on a daily basis, mainly due to the robustness of the moving mesh algorithm and their extensive computational cost. The proposed approach is a way to improve these two issues. This paper introduces two new ideas. First, it demonstrates numerically that moving three-dimensional complex geometries with large displacements is feasible using only vertex displacements and mesh-connectivity changes. This is new and presents several advantages over usual techniques for which the number of vertices varies in time. Second, most of the CPU time spent to move the mesh is due to solving the mesh deformation algorithm to propagate the body displacement inside the volume. Thanks to the use of high-order vertex trajectory and advanced meshing operators to optimize the mesh, we can drastically reduce the required number of solutions and CPU time. The efficiency of this new methodology is illustrated on numerous 3D problems involving large displacements.
Automatic mesh generation and adaptive refinement methods for complex three-dimensional domains have proven to be very successful tools for the efficient solution of complex applications problems. These methods can, however, produce poorly shaped elements that cause the numerical solution to be less accurate and more difficult to compute. Fortunately, the shape of the elements can be improved through several mechanisms, including face- and edge-swapping techniques, which change local connectivity, and optimization-based mesh smoothing methods, which adjust mesh point location. We consider several criteria for each of these two methods and compare the quality of several meshes obtained by using different combinations of swapping and smoothing. Computational experiments show that swapping is critical to the improvement of general mesh quality and that optimization-based smoothing is highly effective in eliminating very small and very large angles. High-quality meshes are obtained in a computationally efficient manner by using optimization-based smoothing to improve only the worst elements and a smart variant of Laplacian smoothing on the remaining elements. Based on our experiments, we offer several recommendations for the improvement of tetrahedral meshes.
An adaptive mesh refinement strategy that couples feature detection with local error estimation is presented. The strategy first selects vortical regions for refinement using feature detection, and then terminates refinement when an acceptable error level has been reached. The feature detection scheme uses a local normalization of the Q-criterion, which allows it to properly identify regions of swirling flow without requiring case-specific tuning. The error estimator relies upon a Richardson extrapolation-like procedure to compute local solution error by comparing the solution on different grid levels. Validation of the proposed approach is carried out using a theoretical advecting vortex and two practical cases, namely, tip vortices from a NACA 0015 wing and the wake structure of a quarter-scale V22 rotor in hover.
An adaptive mesh procedure for improving the quality of steady state solutions of the Euler equations in two dimensions is described. The procedure is implemented in conjunction with a finite element solution algorithm, using linear triangular elements, and an explicit time-stepping scheme. The mesh adaptation is accomplished by regeneration using information provided by the computed solution on the current mesh. The meshes produced are characterised by the appearance of stretched elements in the vicinity of one-dimensional flow features and can exhibit a large variation in element size. This allows solutions of enhanced quality to be produced in a computationally efficient manner.
This is an attempt to clarify and size up the many levels possible for the numerical prediction of a turbulent flow, the target being a complete airplane, turbine, or car. Not all the author's opinions will be accepted, but his hope is to stimulate reflection, discussion, and planning. These levels still range from a solution of the steady Reynolds-Averaged Navier–Stokes (RANS) equations to a Direct Numerical Simulation, with Large-Eddy Simulation in between. However recent years have added intermediate strategies, dubbed “VLES”, “URANS” and “DES”. They are in experimental use and, although more expensive, threaten complex RANS models especially for bluff-body and similar flows. Turbulence predictions in aerodynamics face two principal challenges: (I) growth and separation of the boundary layer, and (II) momentum transfer after separation. (I) is simpler, but makes very high accuracy demands, and appears to give models of higher complexity little advantage. (II) is now the arena for complex RANS models and the newer strategies, by which time-dependent three-dimensional simulations are the norm even over two-dimensional geometries. In some strategies, grid refinement is aimed at numerical accuracy; in others it is aimed at richer turbulence physics. In some approaches, the empirical constants play a strong role even when the grid is very fine; in others, their role vanishes. For several decades, practical methods will necessarily be RANS, possibly unsteady, or RANS/LES hybrids, pure LES being unaffordable. Their empirical content will remain substantial, and the law of the wall will be particularly resistant. Estimates are offered of the grid resolution needed for the application of each strategy to full-blown aerodynamic calculations, feeding into rough estimates of its feasibility date, based on computing-power growth.
An adaptive mesh procedure for computing steady state solutions of the compressible Euler equations in three dimensions is presented. The method is an extension of previous work in two dimensions. The approach requires the coupling of a surface triangulator, an automatic tetrahedral mesh generator, a finite element flow solver and an error estimation procedure. An example involving flow at high Mach number is included to demonstrate the numerical performance of the proposed approach. The example shows that the use of this form of adaptivity in three dimensions offers the potential of even greater computational savings than those attained in the corresponding two-dimensional implementation.
An implicit, Navier-Stokes solution algorithm is presented for the computation of turbulent flow on unstructured grids. The inviscid fluxes are computed using an upwind algorithm and the solution is advanced in time using a backward-Euler time-stepping scheme. At each time step, the linear system of equations is approximately solved with a point-implicit relaxation scheme. This methodology provides a viable and robust algorithm for computing turbulent flows on unstructured meshes. Results are shown for subsonic flow over a NACA 0012 airfoil and for transonic flow over an RAE 2822 airfoil exhibiting a strong upper-surface shock. In addition, results are shown for 3- and 4-element airfoil configurations. For the calculations, two 1-equation turbulence models are utilized. For the NACA 0012 airfoil a pressure distribution and force data are compared with other computational results as well as with the experiment. Comparisons of computed pressure distributions and velocity profiles with experimental data are shown for the RAE airfoil and for the 3-element configuration. For the 4-element case, comparisons of surface pressure distributions with the experiment are made. In general, the agreement between the computations and the experiment is good.
An implicit algorithm for solving the discrete adjoint system based on an unstructured-grid discretization of the Navier–Stokes equations is presented. The method is constructed such that an adjoint solution exactly dual to a direct differentiation approach is recovered at each time step, yielding a convergence rate which is asymptotically equivalent to that of the primal system. The new approach is implemented within a three-dimensional unstructured-grid framework and results are presented for inviscid, laminar, and turbulent flows. Improvements to the baseline solution algorithm, such as line-implicit relaxation and a tight coupling of the turbulence model, are also presented. By storing nearest-neighbor terms in the residual computation, the dual scheme is computationally efficient, while requiring twice the memory of the flow solution. The current implementation allows for multiple right-hand side vectors, enabling simultaneous adjoint solutions for several cost functions or constraints with minimal additional storage requirements, while reducing the solution time compared to serial applications of the adjoint solver. The scheme is expected to have a broad impact on computational problems related to design optimization as well as error estimation and grid adaptation efforts.
This paper gives a status on anisotropic mesh gradation. We present two 3D anisotropic formulations of mesh gradation. The metric at each point defines a well-graded smooth continuous metric field over the domain. The mesh gradation then consists in taking into account at each point the strongest size constraint given by all these continuous metric fields. This is achieved by a metric intersection procedure. We apply it to several examples involving highly anisotropic meshes.
This paper presents an accurate approach to simulate the sonic boom of supersonic aircrafts. The near-field flow is modeled by the conservative Euler equations and is solved using a vertex-centered finite volume approach on adapted unstructured tetrahedral meshes. A metric-based anisotropic mesh adaptation is considered to control the interpolation error in Lp norm. Then, from the CFD solution, the pressure distribution under the aircraft is extracted and used to set up the initial conditions of the propagation algorithm in the far-field. The pressure distribution is propagated down to the ground in order to obtain the sonic boom signature using a ray tracing algorithm based upon the Thomas waveform parameter method. In this study, a sonic boom sensitivity analysis is carried out on several aircraft designs (low-drag and low-boom shapes).
We develop locally normalized feature-detection methods to guide the adaptive mesh refinement (AMR) process for Cartesian grid systems to improve the resolution of vortical features in aerodynamic wakes. The methods include: the Q-criterion [1], the lambda2 method [2], the lambdaci method [3], and the lambda+ method [4]. Specific attention is given to automate the feature identification process by applying a local normalization based upon the shear-strain rate so that they can be applied to a wide range of flow-fields without the need for user intervention. To validate the methods, we assess tagging efficiency and accuracy using a series of static vortex-dominated flow-fields, and use the methods to drive the AMR process for several theoretical and practical simulations. We demonstrate that the adaptive solutions provide comparable accuracy to solutions obtained on uniformly refined meshes at a fraction of the computational cost. Overall, the normalized feature detection methods are shown to be effective in driving the AMR process in an automated and efficient manner.
A searching algorithm is presented for determining which members of
a set of n points in an N dimensional space lie inside a prescribed
space su bregion. The algorithm is then extended to handle finite
size objects as well as points. In this form it is capable of solving
problems such as that of finding the objects from a given set which
intersect with a prescribed object. The suita bility of the algorithm
is demonstrated for the problem of three dimensional uns tructured
mesh generation using the advancing front method.
The symmetric and asymmetric leeward-side flowfields on an inclined ogive cylinder have been investigated using a number of experimental techniques. Naturally occurring and perturbed flowfields were studied at a moderate Reynolds number and at many incidence angles. By close examination of the steady side-force behavior at different roll orientations of the tip, it has been established that microvariations in the tip geometry of the model have a large influence on the downstream development of the flowfield. Under certain conditions a bistable flowfield was observed.
Two new two-equation eddy-viscosity turbulence models will be presented. They combine different elements of existing models that are considered superior to their alternatives. The first model, referred to as the baseline (BSL) model, utilizes the original k-omega model of Wilcox In the inner region of the boundary layer and switches to the standard k -epsilon model in the outer region and in free shear flows. It has a performance similar to the Wilcox model, but avoids that model's strong freestream sensitivity. The second model results from a modification to the definition of the eddy-viscosity in the BSL model, which accounts for the effect of the transport of the principal turbulent shear stress. The new model is called the shear-stress transport-model and leads to major improvements in the prediction of adverse pressure gradient flows.
28632 Roadside Drive
- Metacomp Technologies
- Inc
SAMRAI Concepts and Software Design
- R Anderson
- W Arrighi
- N Elliott
- B Gunney
- R Hornung