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Comparisons of Predicted and Measured Aerodynamic Characteristics of the DLR LK6E2 Missile Airframe (Scale Resolving)
Abstract
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.
... LK6E2 was one of the research test cases developed to investigate vortex interactions on highly maneuverable transonic missiles. The initial collaborative analysis of the test case was published during special sessions at AIAA 2022 SciTech Conference [6,7]. It was shown that the flow solver and the turbulence model greatly impact the prediction of the flow field and aerodynamic coefficients of these missiles at high flow angles and transonic speeds. ...
... Apart from those, hybrid RANS-LES methods consume even more computational sources. Hence these methods are still considered impractical for simulation sets of multiple flow conditions, though they have been shown to compute better results [7,8]. For these reasons, the current study put effort into achieving improved RANS results within the bounds of the statistical turbulence models, which are considered more productive in practice. ...
In this study, we present our improved RANS results of the missile aerodynamic flow computation involving leading edge vortex separation. We have used our in-house tailored version of the open source finite volume solver FlowPsi. An ongoing study in the NATO STO Applied Vehicle Technologies Panel (AVT-316) has revealed that a highly maneuverable missile configuration (LK6E2) shows unusual rolling moment characteristics due to the vortex–surface interactions occurring during wing leading edge separation of vortices. We show the performance of the recently developed k-kL turbulence model for this test problem. This turbulence model is shown to have superior capabilities compared to other widely used turbulence models, such as Spalart–Allmaras and shear stress transport. With the k-kL turbulence model, it is possible to achieve more realistic computational results that agree better with the physical data. In addition, we propose improvements to this turbulence model to achieve even better predictions of rolling moment behavior. Modifications based on turbulence production terms in the k-kL turbulence model significantly improved the predicted rolling moment coefficient, in terms of accuracy and uncertainty.
... 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/10.2514/6.2022-3768.vid This paper is a sequel to a previous publication on the subject of CFD validation. Unlike its predecessor, which took a broad brush approach, this paper is more focused, limiting its scope to CFD model validation. By appealing to systems engineering principles, the evolutionary nature of model validation objectives throughout the development lifecycle is outlined. The concept of CFD model validation maturity is introduced to place these observations in context. CFD model development lifecycles are shown to be extended and federated across multiple stakeholders. This broad situational awareness allows the mutual dependencies between the various stakeholder communities to be re-interpreted in a manner that is consistent with the use of model validation metrics. The potential utility of such metrics in simultaneously monitoring and guiding the maturation of a CFD model’s development and use is outlined. Finally, in view of the acknowledged limitations of current set-based approaches to CFD validation and given the time that has elapsed since community-based guidance on CFD validation was last updated, it is recommended that the existing guidance be revised to reflect contemporary understanding and experience.
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.
Array programming provides a powerful, compact and expressive syntax for accessing, manipulating and operating on data in vectors, matrices and higher-dimensional arrays. NumPy is the primary array programming library for the Python language. It has an essential role in research analysis pipelines in fields as diverse as physics, chemistry, astronomy, geoscience, biology, psychology, materials science, engineering, finance and economics. For example, in astronomy, NumPy was an important part of the software stack used in the discovery of gravitational waves1 and in the first imaging of a black hole2. Here we review how a few fundamental array concepts lead to a simple and powerful programming paradigm for organizing, exploring and analysing scientific data. NumPy is the foundation upon which the scientific Python ecosystem is constructed. It is so pervasive that several projects, targeting audiences with specialized needs, have developed their own NumPy-like interfaces and array objects. Owing to its central position in the ecosystem, NumPy increasingly acts as an interoperability layer between such array computation libraries and, together with its application programming interface (API), provides a flexible framework to support the next decade of scientific and industrial analysis.
A study of the aerodynamic characteristics of two missile configurations has been performed using the data of an experiment, of a semi-empirical aerodynamic prediction code (Missile Datcom) and a RANS flow solver (TAU). The aerodynamic coefficients for different angles of attack and roll angles for Mach numbers of M= 0.85 and 1.2 are compared. Considering the design of the configurations one is rather unconventional with large aspect ratio wings. Whereas the other one has conventional wings with a small aspect ratio. The latter sustains large lift forces at high angles of attack due to the occurrence of vortices while the former performs better at low angles of attack. The comparison of the experimental data with the TAU predicted aerodynamic coefficients shows a good agreement for both configurations in the entire AoA-range. Regarding Missile Datcom, for the unconventional design the accuracy of the predicted data decreases with increasing angle of attack but remains almost constant for the conventional.
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.
A large-eddy simulation database of homogeneous isotropic decaying turbulence is used to assess four different LES quality
measures that have been proposed in the literature. The Smagorinsky subgrid model was adopted and the eddy-viscosity ‘parameter’
C < sub > S < /sub >CS and the grid spacing hh were varied systematically. It is shown that two methods qualitatively predict the basic features
of an error landscape including an optimal refinement trajectory. These methods are based on variants of Richardson extrapolation
and assume that the numerical error and the modelling error scale with a power of the mesh size. Hence they require the combination
of simulations on several grids. The results illustrate that an approximate optimal refinement strategy can be constructed
based on LES output only, without the need for DNS data. Comparison with the full error landscape shows the suitability of
the different methods in the error assessment for homogeneous turbulence. The ratio of the estimated turbulent kinetic energy
error and the ‘true’ turbulent kinetic energy error calculated from DNS is studied for different Smagorinsky parameters and
different grid sizes. The behaviour of this quantity for decreasing mesh size gives further insight into the reliability of
these methods.
This paper reviews the studies undertaken on vortex breakdown over the past 45 years. The paper is structured such that the area is considered in three sections — experimental, numerical and finally theoretical, and provides a ‘guide’ to the literature and where necessary directs the reader to more indepth reviews in the specific areas.
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/10.2514/6.2022-1685.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/10.2514/6.2022-0002.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/10.2514/6.2022-0160.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/10.2514/6.2022-1686.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.
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.
Cette thèse est principalement dédiée à la simulation des écoulements massivement décollés dans le domaine spatial. Nous avons restreint notre étude aux écoulements d'arrière-corps, pour lesquels ces décollements sont imposés par des changements brutaux de la géométrie. Dans le domaine spatial, le caractère fortement compressible des écoulements rencontrés impose l'utilisation de schémas numériques robustes. D'un autre coté, la simulation fine de la turbulence impose des schémas d'ordre élevé et peu dissipatifs. Ces deux spécifications, apparemment contradictoires, doivent pourtant coexister au sein d'une même simulation. Les modèles de turbulence ainsi que les schémas de discrétisation sont indissociables et leur couplage doit impérativement être considéré. Les schémas numériques doivent garder leur précision formelle dans des géométries complexes et des maillages très irréguliers imposés par le contexte industriel. Cette étude analyse le schéma de discrétisation utilisé dans le code de calcul FLUSEPA développé par Airbus Defence & Space. Ce schéma est robuste et précis pour des écoulements avec chocs et il présente une faible sensibilité au maillage (l'ordre 3 étant conservé même sur des maillages fortement perturbés). Malheureusement, le schéma possède une trop faible résolvabilité liée à un niveau de dissipation trop élevé pour envisager des simulations hybrides RANS/LES. Pour pallier à cet inconvénient, nous nous sommes penchés vers une solution basée sur un recentrage conditionnel et local : dans les zones dominées par des structures tourbillonnaires, une fonction analytique assure un recentrage local lorsque la stabilité numérique le permet. Cette condition de stabilité assure le couplage entre le schéma et le modèle. De cette manière, les viscosités laminaire et tourbillonnaire sont les seules à jouer un rôle dans les régions dominées par la vorticité et servent aussi à stabiliser le schéma numérique. Cette étude présente de plus une comparaison qualitative et quantitative de plusieurs modèles hybrides RANS/LES, à égalité de maillage et de schéma utilisés Pour cela, un certain nombre d'améliorations (notamment de leur capacité à résoudre les instabilités de Kelvin-Helmohlotz sans retard), proposées dans la littérature ou bien introduites dans cette thèse, sont prises en compte. Les applications numériques étudiées concernent des géométries allant de la marche descendante au lanceur spatial complet à échelle réduite.
A wide range of unsteady phenomena relevant to vortex flows over stationary and maneuvering delta wings is reviewed. The origin, characteristics, and physical mechanisms of these unsteady phenomena are discussed. Dynamic response of leading-edge vortices for maneuvering wings and mechanisms of hysteresis and time-lag effects are reviewed. Issues and challenges for unsteady vortex flows over delta wings are outlined.
Aircraft aerodynamics have been predicted using computational fluid dynamics for a number of years. While viscous flow computations for cruise conditions have become commonplace, the non-linear effects that take place at high angles of attack are much more difficult to predict. A variety of difficulties arise when performing these computations, including challenges in properly modeling turbulence and transition for vortical and massively separated flows, the need to use appropriate numerical algorithms if flow asymmetry is possible, and the difficulties in creating grids that allow for accurate simulation of the flowfield. These issues are addressed and recommendations are made for further improvements in high angle of attack flow prediction. Current predictive capabilities for high angle of attack flows are reviewed, and solutions based on hybrid turbulence models are presented.
Two new versions of the kappa-omega two-equation turbulence model will be presented. The new Baseline (BSL) model is designed to give results similar to those of the original kappa-omega model of Wilcox, but without its strong dependency on arbitrary freestream values. The BSL model is identical to the Wilcox model in the inner 50% of the boundary-layer but changes gradually to the standard kappa-epsilon model (in a kappa- omega formulation) towards the boundary-layer edge. The free shear layers. The second version of the model is called Shear-Stress Transport (SST) model. It is a variation of the BSL model with the additional ability to account for the transport of the principal turbulent shear stress in adverse pressure gradient boundary-layers. The model is based on Bradshaw's assumption that the principal shear-stress is proportional to the turbulent kinetic energy, which is introduced into the definition of the eddy-viscosity. Both models are tested for a large number of different flowfields. The results of the BSL model are similar to those of the original kappa-omega model, but without the undesirable freestream dependency. The predictions of the SST model are also independent of the freestream values but show better agreement with experimental data for adverse pressure gradient boundary-layer flows.
Improvement of Physical Modeling for Vortex-Dominated Flows
- V Togiti
- A Krumbein
- A Probst