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The Influence of Modelling in Predictions of Vortex Interactions About a Generic Missile Airframe: RANS
Abstract
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.
... The turbulence models estimate excessive turbulent viscosity and, therefore, tend to dissipate the vortex rapidly. Therefore, the dissipation characteristics of the numerical model are also important [5,6,31]. ...
... We have also refined the RC correction for our k-kL turbulence model implementation. It has already been shown that the vorticity corrections are able to provide better vortex predictions via compensation of the over-dissipative character of Boussinesq hypothesis-based turbulence models [31,37]. The present test case, however, will give the opportunity for the performance evaluation of the RC correction in the context of the prediction of the formation of a leading edge vortex. ...
... As shown in several recent studies on external aerodynamic flow with vortex development [31,[45][46][47][48], the RANS models result in inaccurate predictions of vortex dynamics, as a result of over-prediction of turbulent quantities. Spalart suggests that this shortcoming arises since the vortex effects were not included in the development and calibration procedures of turbulence models [45]. ...
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 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. ...
... At this point there arose a need for dissociation of these multiple effects on the different aspects of predicted flow field characteristics. For this purpose, more focused studies were planned for RANS [15] and Scale Resolving Simulations (SRS) [16]. As widely known, computational requirements for SRS is still substantial so the physical time required for this type of analyses would be much weightier. ...
... The discussion of computational results within the common mesh study is not in the scope of this paper. They are comparatively discussed with a focus on modeling effects in another paper of the current AVT-316 special session [15]. ...
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.
... Promising results have been shown, e.g., for the prediction of aeronautical flows. 11,[13][14][15][16][17][18][19][20][21][22][23] However, improvement is still required with respect to separating flows, 24 and research on adverse-pressure gradient flows with and without separation is still ongoing, e.g., Refs. 25-33. ...
Turbulence equilibrium state is analyzed for the modeled Reynolds-stress transport equation, assuming the most general formulation of pressure-strain correlation. In a two-dimensional mean flow at a high-Reynolds number, an algebraic equation system is obtained, providing Reynolds-stress anisotropies as functions of pressure-strain model coefficients. Conversely, the equations provide calibration conditions for the model coefficients to predict specified equilibrium anisotropies. The predicted von-Kármán constant depends on the predicted equilibrium anisotropies and, hence, the pressure-strain model coefficients. Identical equilibrium anisotropies can be obtained with different sets of model coefficients. Identical equilibrium values of invariants of the Reynolds-stress anisotropy tensor can be achieved, despite the differing anisotropy components. Numerical simulations with the Speziale-Sarkar-Gatski (SSG) model, using different sets of model coefficients, confirm the results of the theoretical analysis. They show that the predicted equilibrium value of the Reynolds-shear stress anisotropy determines the predicted skin friction of a boundary layer as well as the predicted spreading rate of a plane mixing layer. However, different values and, hence, different sets of model coefficients are required for achieving good agreement with experimental data for both flows. Therefore, for general improvement of turbulence models, the set of model coefficients probably needs to be adapted to the local type of flow. The required classification is supposed to be suitable for machine learning methods.
... 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.
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.
High-speed aircraft often develop separation-induced leading-edge vortices and vortex flow aerodynamics. In this paper, the discovery of separation-induced vortex flows and the development of methods to predict these flows for wing aerodynamics are reviewed. Much of the content for this article was presented at the 2017 Lanchester Lecture and the content was selected with a view towards Lanchester’s approach to research and development.
A range of turbulence models is exercised in the problem of a mature two-dimensional isolated vortex with high circulation Reynolds number, mature meaning that the core size has grown to many times its initial value, and the vortex reaches a self-similar state in which all quantities scale with its outside circulation Γ and its age t. The reasoning closely follows the landmark papers of Govindaraju and Saffman (Phys. Fluids 14, 2074–2080, 1971) (GS) and Zeman (Phys. Fluids A 7, 135–143, 1995), and we call this the GSZ flow. The models produce radically different outcomes, and this simple problem clearly places each model into one of two classes, in terms of its predictions in vortices. Some reach a turbulent state, including the circulation overshoot first predicted by GS, whereas others reach a laminar state free of overshoot. We have no evidence of non-unique solutions or bifurcations for a given model. The overshoot consists in the circulation, as a function of radius r, rising from zero on the axis at r = 0 to values that exceed the outside circulation Γ, and then falling back down. This happens within the turbulent region, and it is associated with the creation by turbulence of mean vorticity of sign opposite to the core vorticity. We consider the second (i.e., the laminar) response as the correct one, the circulation overshoot appearing to us unphysical, a thought which was clear in both of the original papers and is supported by experimental and simulation results. The laminar state is given by eddy-viscosity models only when they include a rotation/curvature correction. A Reynolds-stress transport model and an Explicit Algebraic Reynolds-Stress Model return turbulent solutions but with weak turbulence, which we consider a positive result, although Zeman’s Reynolds-stress model prevented any overshoot and led to a laminar mature flow. We believe this flow can become a relevant, well-defined, standard test case for turbulence models.
It is noted that the eddy–viscosity turbulence models often rely on constitutive and transport equations. These models are generally validated and tested through their predictions for certain test cases and their outputs are compared to experimental or direct numerical simulation (DNS) data. This whole procedure is known as a posteriori analysis. It is observed that the direct tests of the basic hypothesis which belongs to a priori analysis are applied. This in turn, helps to better discriminate the fundamental hypothesis behind constitutive and transport equations, independently of parameter tuning. This chapter illustrates the constitutive equation, using databases that provide the Reynolds stress tensor and the mean velocity gradient tensor. The classical K-transport equation is also tested using large eddy simulation (LES) data, thus providing the kinetic energy gradient vector, and the pressure and instantaneous kinetic energy vector fluxes. For each database a degree of validity of the basis hypothesis is plotted. The results so obtained indicate that these simplifying hypotheses are badly verified for all parts of the flow that ranges from vanishing shears to complex flow regions.
The results of a numerical investigation of the interaction between an aircraft vortex wake (vortex pair) and the ground during the takeoff and landing phases are presented. The calculations were performed within the framework of the time-dependent two-dimensional Reynolds-averaged Navier-Stokes equations using the Spalart-Shur turbulence model generalizing the turbulent viscosity transport model of Spalart and Allmaras to the case of the flows with curved streamlines and rotation. Similar calculations were carried out on the basis of the original Spalart-Allmaras model and the k-? model of Menter. Some new qualitative and quantitative data on the distinctive features of the phenomenon under consideration are obtained.
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.
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.
Detached-eddy simulation (DES) was first proposed in 1997 and first used in 1999, so its full history can be surveyed. A DES community has formed, with adepts and critics, as well as new branches. The initial motivation of high– Reynolds number, massively separated flows remains, for which DES is con-vincingly more capable presently than either unsteady Reynolds-averaged Navier-Stokes (RANS) or large-eddy simulation (LES). This review dis-cusses compelling examples, noting the visual and quantitative success of DES. Its principal weakness is its response to ambiguous grids, in which the wall-parallel grid spacing is of the order of the boundary-layer thickness. In some situations, DES on a given grid is then less accurate than RANS on the same grid or DES on a coarser grid. Partial remedies have been found, yet dealing with thickening boundary layers and shallow separation bubbles is a central challenge. The nonmonotonic response of DES to grid refinement is disturbing to most observers, as is the absence of a theoretical order of accuracy. These issues also affect LES in any nontrivial flow. This review also covers the numerical needs of DES, gridding practices, coupling with different RANS models, derivative uses such as wall modeling in LES, and extensions such as zonal DES and delayed DES.
This document describes the current formulation of the SST turbulence models, as well as a number of model enhancements. The model enhancements cover a modified near wall treatment of the equations, which allows for a more flexible grid generation process and a zonal DES formulation, which reduces the problem of grid induced separation for industrial flow simulations. Results for a complete aircraft configuration with and without engine nacelles will be shown.
The paper presents a new model of turbulence in which the local turbulent viscosity is determined from the solution of transport equations for the turbulence kinetic energy and the energy dissipation rate. The major component of this work has been the provision of a suitable form of the model for regions where the turbulence Reynolds number is low. The model has been applied to the prediction of wall boundary-layer flows in which streamwise accelerations are so severe that the boundary layer reverts partially towards laminar. In all cases, the predicted hydrodynamic and heat-transfer development of the boundary layers is in close agreement with the measured behaviour.
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/10.2514/6.2022-1685.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.
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.
Recent work which aims to explain the nature of three-dimensional separation, to predict its occurrence, and to represent the behaviour of separated flow is reviewed. An attempt is made to present a unified view which leads from a consideration of the structure of the problem and the role of modelling, through the partial solutions which have been found, to some illustrations of the application of three-dimensional flow separation in aircraft design.
A computational study of the aerodynamics of vane type micro-vortex generators has been performed. Solutions of the incompressible Reynolds -Averaged Navier-Stokes equations have been obtained for a rectangular vane type micro-vortex generator mounted on a flat plate at a Reynolds number of 81,000 based upon vortex generator length. The study demonstrates the importance of resolving the detailed flow around the vortex generator. Simulations which ignore the finite thickness of the device or improperly resolve the device boundary layer are shown to produce results that are in poor agreement with the available experimental data. Comparisons of results obtained using conventional one- and two-equation turbulent closures with full Reynolds stress models highlight inherent weaknesses of conventional turbulence modeling for boundary layers containing discrete vortical structures. © 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
A comparison of two differential Reynolds-stress models for aeronautical flows is presented. The model herein combines the Speziale-Sarkar-Gatski pressure-strain model with the Launder-Reece-Rodi model toward the wall, where the length scale is supplied by Menter's baseline equation. The epsilon h model from Jakirli and Hanjali has been particularly designed for representing the correct near-wall behavior of turbulence and has been adapted to aeronautical needs. Its length scale is provided by a transport equation for the homogeneous part of the dissipation rate. The models are applied to a series of test cases relevant to aeronautics, showing improved predictions compared to eddy-viscosity models particularly in case of axial vortices.
The results of an investigation into the structure of slender missile body vortices are described. It was found that existing potential flow vortex models do not always correctly reproduce the real flow. Particularly at the base, the vorticity was found to be distributed rather than concentrated, as is usually assumed. Vortex strengths, positions, and induced velocities were predicted with only fair accuracy by the various techniques used to calculate them. It is concluded that considerable upgrading of existing models will be necessary before the strengths, locations, andinduced velocities of body vortices can be predicted with certainty at high angles of attack. © 1977 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.
This paper presents a reformulated version of the author's k-ω model of turbulence. Revisions include the addition of just one new closure coefficient and an adjustment to the dependence of eddy viscosity on turbulence properties. The result is a significantly improved model that applies to both boundary layers and free shear flows and that has very little sensitivity to finite freestream boundary conditions on turbulence properties. The improvements to the k-ω model facilitate a significant expansion of its range of applicability. The new model, like preceding versions, provides accurate solutions for mildly separated flows and simple geometries such as that of a backward-facing step. The model's improvement over earlier versions lies in its accuracy for even more complicated separated flows. This paper demonstrates the enhanced capability for supersonic flow into compression corners and a hypersonic shock-wave/boundary-layer interaction. The excellent agreement is achieved without introducing any compressibility modifications to the turbulence model.
This article deals with the interaction of co-rotating vortices, in configurations similar to those found in the extended near-wake of typical transport aircraft. The fundamental process of vortex merging is analyzed and modeled in detail in a two-dimensional context, giving insight into the conditions for merging and its physical origin, and yielding predictions for the resulting flow. Three-dimensional effects, in the form an elliptic short-wave instability arising in the initial co-rotating vortex flow, are described and analyzed theoretically. They are found to cause significant changes in the merging process, such as earlier merging and larger final vortex cores. Illustrations from recent experimental, numerical and theoretical studies are given, and the relevance of the results for applications to real aircraft wakes is discussed. To cite this article: P. Meunier et al., C. R. Physique 6 (2005).
The near-field behavior of a wingtip vortex flow has been studied computationally and experimentally in an interactive fashion, The computational approach involved using the method of artificial compressibility to solve the three-dimensional, incompressible, Navier-Stokes equations with experimentally determined boundary conditions and a modified Baldwin-Barth turbulence model. Inaccuracies caused by the finite difference technique, grid resolution, and turbulence modeling have been explored. The complete geometry case was computed using 1.5 million grid points and compared with mean velocity measurements on the suction side of the wing and in the near wake. Good agreement between the computed and measured flowfields has been obtained. The velocity distribution in the vortex core compares to within 3% of the experiment.
The principal subject of this paper is analysis and modeling of turbulent wing tip vortex flows in a far-field region of the vortex evolution. The choice of a Reynolds stress closure (RSC) to model the vortex turbulence is shown to be indispensable for representation of the flow rotation effects on turbulence. The principal result reported is the model–experiment comparison of the vortex growth rates for different vortex Reynolds numbers. The mean vortical flow generated by the wing tip very effectively suppresses the Reynolds shear stress, which mediates the extraction of energy from the mean flow by turbulence. In consequence, the vortex-core growth rate is controlled only by molecular viscosity and the vortex turbulence decays since the turbulence production rate is very nearly zero. This rather unexpected result is shown to be supported by experiments. Finally, it is shown that the computed turbulence structure is consistent with experimental data at the NASA Ames Research Center.
An ogive-cylinder body of revolution having a nose section 3 diameters long, tangent to a cylindrical body 7.7 diameters long was tested at angles of attack from 5 to 24 degrees at Mach numbers of 0.3 to 0.95 (Reynolds number of 0.44 x 10 to the 6th power). The effects of a large increase in Reynolds number at a low subsonic Mach number were also studied. These subsonic results supplement those reported in NACA Report 1371 for a similar body at Mach number 1.98 and the same test Reynolds number.
Streamline curvature in the plane of the mean shear produces large changes in the turbulence structure of shear layers, usually an order of magnitude more important than normal pressure gradients and other terms in the mean-motion equations for curved flows. The effects on momentum and heat transfer in boundary layers are noticeable on typical wing sections and are very important on highly-cambered turbomachine blades: turbulence may be nearly eliminated on highly-convex surfaces, while on highly-concave surfaces momentum transfer by quasi-steady longitudinal vortices dominates the ordinary turbulence processes. The greatly enhanced mixing rates of swirling jets and the characteristic non-turbulent cores of trailing vortices are also consequences of the effects of streamline curvature on the turbulence structure. A progress report, comprises a review of current knowledge, a discussion of methods of predicting curvature effects, and a presentation of principles for the guidance of future workers.
The attenuation of skew-induced longitudinal vortices by turbulent or
viscous stresses is studied for the case of pure, artificially-generated
longitudinal vortices entrained into initially two-dimensional boundary
layers in nominally zero pressure gradients. Three types of
vortex-boundary interactions are studied in detail: (1) an isolated
vortex in a two-dimensional boundary layer; (2) a vortex pair in a
turbulent boundary layer with the common flow between the vortices
moving away from the surface; (3) a vortex pair in a boundary layer with
the common flow moving towards the surface. Detailed mean flow and
turbulence measurements are made, showing that the eddy viscosities
defined for the different shear-stress components behave in different
and complicated ways. Terms in the Reynolds stress transport equations,
notably the triple products that effect turbulent diffusion of Reynolds
stress, also fail to obey simple rules.
The turbulence model equations of Saffman have been applied to the
prediction of flows with significant mean streamline curvature. Two
problems were considered: (1) fully turbulent flow between concentric
rotating cylinders for various ratios of inner and outer cylinder
velocities and radii, and (2) the decay of an isolated turbulent line
vortex. In the former case, good agreement is obtained with measured
torque and velocity profiles. In the latter case, only qualitative
comparison is possible, as direct quantitative comparison with existing
experimental results for turbulent trailing vortices is shown to be
inappropriate.
Detailed mean flow and turbulence measurements have been made in a low-speed turbulent boundary layer in zero pressure gradient with an isolated, artificially generated vortex pair imbedded in it. The vortices, generated by two half-delta wings on the floor of the wind-tunnel settling chamber, rotate in opposite directions such that the ‘common flow’ between the vortices is away from the surface, and the vortex pair draws boundary-layer fluid upwards. The distance of the vortex cores above the surface grows downstream, and is roughly twice the local boundary-layer thickness. The cancellation of circulation by mixing of fluid from the two vortices is slow, and the vortices are identifiable down the full length of the test section. As in the case of the single vortex investigated in Part 1 of this series, large changes in structural parameters of the turbulence occur.
Detailed mean-flow and turbulence measurements have been made in a low-speed turbulent boundary layer in zero pressure gradient with an isolated, artificially generated vortex imbedded in it. The vortex was generated by a half-delta wing on the floor of the wind-tunnel settling chamber, so that the vortex entering the working section had the same circulation as that originally generated, while axial-component velocity variations were very much reduced, relative to the local mean velocity, from values just behind the generator. The measurements show that the circulation around the vortex imbedded in the boundary layer is almost conserved, being reduced only by the spanwise-component surface shear stress. Therefore the region of flow affected by the vortex continues to grow downstream, its cross-sectional dimensions being roughly proportional to the local boundary-layer thickness. The behaviour of the various components of eddy viscosity, deduced from measured Reynolds stresses, and of the various triple products, suggests that the simple empirical correlations for these quantities used in present-day turbulence models are not likely to yield flow predictions which are accurate in detail.
Some new developments of explicit algebraic Reynolds stress turbulence models
(EARSM) are presented. The new developments include a new near-wall treatment
ensuring realizability for the individual stress components, a formulation for
compressible flows, and a suggestion for a possible approximation of diffusion terms in
the anisotropy transport equation. Recent developments in this area are assessed and
collected into a model for both incompressible and compressible three-dimensional
wall-bounded turbulent flows. This model represents a solution of the implicit ARSM
equations, where the production to dissipation ratio is obtained as a solution to a
nonlinear algebraic relation. Three-dimensionality is fully accounted for in the mean
flow description of the stress anisotropy. The resulting EARSM has been found to
be well suited to integration to the wall and all individual Reynolds stresses can be
well predicted by introducing wall damping functions derived from the van Driest
damping function. The platform for the model consists of the transport equations for
the kinetic energy and an auxiliary quantity. The proposed model can be used with
any such platform, and examples are shown for two different choices of the auxiliary
quantity.
We calculate the flow induced by a vortex pair in a viscous fluid, which is otherwise at rest, in the presence of a plane boundary. This may be either a no-slip or a stress-free boundary. The phenomenon of rebound of the vortices from the boundary occurs for either type of boundary, and an explanation for this is offered in terms of viscous effects.
The accuracy of tip vortex flow prediction in the near-field region is investigated numerically by attempting to quantify the shortcomings of the turbulence models and the flow solver. In particular, some turbulence models can produce a ‘numerical diffusion’ that artificially smears the vortex core. Low-order finite differencing techniques of the convective and pressure terms of the Navier–Stokes equations and inadequate grid density and distribution can also produce the same adverse effect. The flow over a wing and the near-wake with the wind tunnel walls included was simulated using 2.5 million grid points. Two subset problems, one using a steady, three-dimensional analytical vortex, and the other, a vortex obtained from experiment and propagated downstream, were also devised in order to make the study of vortex preservation more tractable. The method of artificial compressibility is used to solve the steady, three-dimensional, incompressible Navier–Stokes equations. Two one-equation turbulence models (Baldwin–Barth and Spalart–Allmaras turbulence models), have been used with the production term modified to account for the stabilizing effect of the nearly solid body rotation in the vortex core. Finally, a comparison between the computed results and experiment is presented. Published in 1999 by John Wiley & Sons, Ltd.
Detailed measurements with hot-wires and pressure probes are presented for the interaction between a turbulent longitudinal vortex pair with common flow down, and a turbulent boundary layer. The interaction has a larger value of the vortex circulation parameter, and therefore better represents many aircraft/vortex interactions, than those studied previously. The vortices move down towards the boundary layer, but only the outer parts of the vortices actually enter the it. Beneath the vortices the boundary layer is thinned by lateral divergence to the extent that it almost ceases to grow. Outboard of the vortices the boundary layer is thickened by lateral convergence. The changes in turbulence structure parameters in the boundary layer appear to be due to the effects of extra-rate-of-strain produced by lateral divergence (or convergence) and by free-stream turbulence. The effect of the interaction on the vortices (other than the inviscid effect of the image vortices below the surface) is small. The flow constitutes a searching test case for prediction methods for three-dimensional turbulent flows.
An in-depth review of boundary-layer flow-separation control by a passive method using low-profile vortex generators is presented. The generators are defined as those with a device height between 10% and 50% of the boundary-layer thickness. Key results are presented for several research efforts, all of which were performed within the past decade and a half where the majority of these works emphasize experimentation with some recent efforts on numerical simulations. Topics of discussion consist of both basic fluid dynamics and applied aerodynamics research. The fluid dynamics research includes comparative studies on separation control effectiveness as well as device-induced vortex characterization and correlation. The comparative studies cover the controlling of low-speed separated flows in adverse pressure gradient and supersonic shock-induced separation. The aerodynamics research includes several applications for aircraft performance enhancement and covers a wide range of speeds. Significant performance improvements are achieved through increased lift and/or reduced drag for various airfoils—low-Reynolds number, high-lift, and transonic—as well as highly swept wings. Performance enhancements for non-airfoil applications include aircraft interior noise reduction, inlet flow distortion alleviation inside compact ducts, and a more efficient overwing fairing. The low-profile vortex generators are best for being applied to applications where flow-separation locations are relatively fixed and the generators can be placed reasonably close upstream of the separation. Using the approach of minimal near-wall protuberances through substantially reduced device height, these devices can produce streamwise vortices just strong enough to overcome the separation without unnecessarily persisting within the boundary layer once the flow-control objective is achieved. Practical advantages of low-profile vortex generators, such as their inherent simplicity and low device drag, are demonstrated to be critically important for many applications as well.
The discovery of coherent structures in turbulence has fostered the hope
that the study of vortices will lead to models and an understanding of
turbulent flow, thereby solving or at least making less mysterious one
of the great unresolved problems of classical physics. Vortex dynamics
is a natural paradigm for the field of chaotic motion and modern
dynamical system theory. The emphasis in this monograph is on the
classical theory of inviscid incompressible fluids containing finite
regions of vorticity. The effects of viscosity, compressiblity,
inhomogeneity, and stratification are enormously important in many
fields of application, from hypersonic flight to global environmental
fluid mechanics. However, this volume focuses on those aspects of fluid
motion that are primarily controlled by the vorticity and are such that
the effects of the other fluid properties are secondary. This book will
be of interest to students of fluid mechanics, turbulence, and vortex
methods as well as to applied mathematicians and engineers.