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Simulations of flows around complex and simplified supersonic store geometries at high incidence angles using statistical and scale-resolving turbulence models
Abstract
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 classe s of NATO vehicles (combat aircraft, in particular); and (iii) Consolidate lessons learned and an y attendant future requirements [11]. 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 [12][13][14][15][16][17][18][19][20][21][22]. 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/10.2514/6.2022-1176.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 Missile Facet of this group has concentrated their work on the vortical flow field around a generic missile airframe and its prediction via computational methods. This paper focuses on mesh-related effects and RANS simulations. Simulated vortex characteristics were found to depend strongly on the properties of the employed mesh, in terms of both resolution and topology. Predictions of missile aerodynamic coefficients show a great dependence on mesh properties as they are sensitive to computed vortex dynamics. Key suggestions about the desired mesh characteristics have been made. Based on these, a shared mesh was constructed to perform common analyses between the AVT-316 Missile Facet members. Mesh based uncertainties of the aerodynamic coefficient predictions were estimated via Richardson Extrapolation method.
... 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/10.2514/6.2022-0160.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 method of second-order accuracy is described for integrating the equations of ideal compressible flow. The method is based on the integral conservation laws and is dissipative, so that it can be used across shocks. The heart of the method is a one-dimensional Lagrangean scheme that may be regarded as a second-order sequel to Godunov's method. The second-order accuracy is achieved by taking the distributions of the state quantities inside a gas slab to be linear, rather than uniform as in Godunov's method. The Lagrangean results are remapped with least-squares accuracy onto the desired Euler grid in a separate step. Several monotonicity algorithms are applied to ensure positivity, monotonicity and nonlinear stability. Higher dimensions are covered through time splitting. Numerical results for one-dimensional and two-dimensional flows are presented, demonstrating the efficiency of the method. The paper concludes with a summary of the results of the whole series “Towards the Ultimate Conservative Difference Scheme.”
A method of second-order accuracy is described for integrating the equations of ideal compressible flow. The method is based on the integral conservation laws and is dissipative, so that it can be used across shocks. The heart of the method is a one-dimensional Lagrangean scheme that may be regarded as a second-order sequel to Godunov's method. The second-order accuracy is achieved by taking the distributions of the state quantities inside a gas slab to be linear, rather than uniform as in Godunov's method. The Lagrangean results are remapped with least-squares accuracy onto the desired Euler grid in a separate step. Several monotonicity algorithms are applied to ensure positivity, monotonicity and nonlinear stability. Higher dimensions are covered through time splitting. Numerical results for one-dimensional and two-dimensional flows are presented, demonstrating the efficiency of the method. The paper concludes with a summary of the results of the whole series “Towards the Ultimate Conservative Difference Scheme.”
In search of reliable computational methods for cosmic flow problems, we apply several commonly used algorithms and one new algorithm, to a representative problem in galactic gas dynamics. A careful choice of the algorithm used in a calculation is found to be of the utmost importance in obtaining reliable results. Two methods most commonly employed in astronomy (the Beam scheme and FCT methods) prove to be highly unsuitable for our test problem. The penalty in programming effort and computer time per grid point required for the best second-order accurate codes tested is more than offset by the improvement in accuracy obtained and the possibility to reduce the number of points in a grid.
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/10.2514/6.2022-2308.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/10.2514/6.2022-2307.vid In this study, the influence of the turbulence model, grid resolution and flow solvers on the results of RANS simulations is investigated. The work is part of the NATO AVT Task Group AVT-316 (Vortex Interaction Effects Relevant to Military Air Vehicle Performance). Simulations have been carried out for a generic transonic missile configuration by various organizations and compared with data from wind tunnel experiments for a Mach number of M = 0.85, a roll angle of and total incidences in the range of . In the first part of the study each organization used their own computational mesh and best practice for the grid generation. In the second part a common mesh family (three grids) were used for the simulations. It was shown that even for the common mesh family, the results of the different flow solvers in some cases showed large variations. This applies in particular to the rolling moment. Here, the accurate flow solver-dependent prediction of the complicated flow topology on the large wings and the accurate prediction of the location of the leeward vortices have a particularly strong effect. Only one flow solver predicted this flow in a form that gave good agreement with the wind tunnel results over the entire angular range ().
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/10.2514/6.2022-0160.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.
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.
View Video Presentation: https://doi.org/10.2514/6.2022-1176.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 Missile Facet of this group has concentrated their work on the vortical flow field around a generic missile airframe and its prediction via computational methods. This paper focuses on mesh-related effects and RANS simulations. Simulated vortex characteristics were found to depend strongly on the properties of the employed mesh, in terms of both resolution and topology. Predictions of missile aerodynamic coefficients show a great dependence on mesh properties as they are sensitive to computed vortex dynamics. Key suggestions about the desired mesh characteristics have been made. Based on these, a shared mesh was constructed to perform common analyses between the AVT-316 Missile Facet members. Mesh based uncertainties of the aerodynamic coefficient predictions were estimated via Richardson Extrapolation method.
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.
Preface Acknowledgements 1. Direct solution methods 2. Theory of matrix eigenvalues 3. Positive definite matrices, Schur complements, and generalized eigenvalue problems 4. Reducible and irreducible matrices and the Perron-Frobenius theory for nonnegative matrices 5. Basic iterative methods and their rates of convergence 6. M-matrices, convergent splittings, and the SOR method 7. Incomplete factorization preconditioning methods 8. Approximate matrix inverses and corresponding preconditioning methods 9. Block diagonal and Schur complement preconditionings 10. Estimates of eigenvalues and condition numbers for preconditional matrices 11. Conjugate gradient and Lanczos-type methods 12. Generalized conjugate gradient methods 13. The rate of convergence of the conjugate gradient method Appendices.
Background discussion, definitions, and descriptions are given for some terms related to confidence building in computational fluid dynamics. The two principal distinctions made are between verification vs validation and between verification of codes vs verification of individual calculations. Also discussed are numerical errors vs conceptual modeling errors; iterative convergence vs grid convergence (or residual accuracy vs discretization accuracy); confirmation, calibration, tuning, and certification; error taxonomies; and customer illusions vs customer care. Emphasis is given to rigorous code verification via systematic grid convergence using the method of manufactured solutions, and a simple method for uniform reporting of grid convergence studies using the Grid Convergence Index (GCI). Also discussed are surrogate single-grid error indicators.
This paper proposes the use of a Grid Convergence Index (GCI) for the uniform reporting of grid refinement studies in Computational Fluid Dynamics. The method provides an objective asymptotic approach to quantification of uncertainty of grid convergence. The basic idea is to approximately relate the results from any grid refinement test to the expected results from a grid doubling using a second-order method. The GCI is based upon a grid refinement error estimator derived from the theory of generalized Richardson Extrapolation. It is recommended for use whether or not Richardson Extrapolation is actually used to improve the accuracy, and in some cases even if the conditions for the theory do not strictly hold. A different form of the GCI applies to reporting coarse grid solutions when the GCI is evaluated from a ''nearby'' problem. The simple formulas may be applied a posterior by editors and reviewers, even if authors are reluctant to do so.
The development and preliminary validation of a new k-omega turbulence model based on explicit algebraic Reynolds-stress modeling are presented. This new k-omega model is especially designed for the requirements typical in high-lift aerodynamics. Attention is especially paid to the model behavior at the turbulent/laminar edges, to the model sensitivity to pressure gradients, and to the calibration of the model coefficients for appropriate flow phenomena. The model development is based on both analytical studies and numerical experimenting. The developed;model is assessed and validated for a set of realistic flow problems including high-lift airfoil flows.
The paper addresses issues related to the resolution of turbulent structures in technical CFD simulations. Some important aspects related to URANS, LES and DES techniques are discussed. The alternative concept of Scale-Adaptive Simulation (SAS) turbulence models is introduced and its viability is demonstrated for a number of testcases. It is shown that the SAS modeling approach allows to formulate turbulence models, which can operate in RANS and LES mode without an explicit grid dependency.
The study of rotor–fuselage interactional aerodynamics is central to the design and performance analysis of helicopters. However, regardless of its significance, rotor–fuselage aerodynamics has so far been addressed by very few authors. This is mainly due to the difficulties associated with both experimental and computational techniques when such complex configurations, rich in flow physics, are considered. In view of the above, the objective of this study is to develop computational tools suitable for rotor–fuselage engineering analysis based on computational fluid dynamics (CFD).
To account for the relative motion between the fuselage and the rotor blades, the concept of sliding meshes is introduced. A sliding surface forms a boundary between a CFD mesh around the fuselage and a rotor-fixed CFD mesh which rotates to account for the movement of the rotor. The sliding surface allows communication between meshes. Meshes adjacent to the sliding surface do not necessarily have matching nodes or even the same number of cell faces. This poses a problem of interpolation, which should not introduce numerical artefacts in the solution and should have minimal effects on the overall solution quality. As an additional objective, the employed sliding mesh algorithms should have small CPU overhead. The sliding mesh methods developed for this work are demonstrated for both simple and complex cases with emphasis placed on the presentation of the inner workings of the developed algorithms. Copyright
The article gives an overview of the Scale-Adaptive Simulation (SAS) method developed by the authors during the last years.
The motivation for the formulation of the SAS method is given and a detailed explanation of the underlying ideas is presented.
The derivation of the high-Reynolds number form of the equations as well as the calibration of the constants is provided.
The concept of SAS is explained using several generic examples and test cases. In a companion article, the model is applied
to more complex industrial-type applications.
KeywordsTurbulence model-Scale-adaptive simulation-SAS-Hybrid RANS–LES
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.
A unified treatment of several upwind shock capturing algorithms is presented. Each algorithm has a Riemann initial value problem as its basis. The treatment of boundaries involves solving the associated Riemann initial-boundary value problem. The first author's algorithm, applied to multidimensional Euler equations in general geometries, is then presented. Its worth is verified by various calculations, which include Mach 8 supersonic flow past a circular cylinder.
A framework is described and demonstrated for CFD analysis of helicopter rotors in hover and forward flight. Starting from the Navier-Stokes equations, the paper describes the periodic rotor blade motions required to trim the rotor in forward flight (blade flapping, blade lead-lag and blade pitching) as well as the required mesh deformation. Throughout, the rotor blades are assumed to be rigid and the rotor to be fully articulated with separate hinges for each blade. The employed method allows for rotors with different numbers of blades and with various rotor hub layouts to be analysed. This method is then combined with a novel grid deformation strategy which preserves the quality of multi-block structured, body-fitted grids around the blades. The coupling of the CFD method with a rotor trimming approach is also described and implemented. The complete framework is validated for hovering and forward flying rotors and comparisons are made against available experimental data. Finally, suggestions for further development are put forward. For all cases, results were in good agreement with experiments and rapid convergence has been obtained. Comparisons between the present grid deformation method and transfinite interpolation were made highlighting the advantages of the current approach.
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.