External Aerodynamics Research Articles

The continuous adjoint to the incompressible (D)DES Spalart-Allmaras turbulence models

This article formulates the continuous adjoint method for the gradient-based shape optimization of fluid flows governed by the incompressible Detached Eddy Simulation (DES) and Delayed-DES (DDES) models, based on the Spalart-Allmaras turbulence model. As both flow models are inherently unsteady, challenges arise regarding the availability of flow fields during the backward in time integration of the unsteady adjoint equations. To minimize both the computational cost and the memory demands, the computed flow fields are compressed using the iPGDZ+ lossy compression technique, recently developed by the authors. Its application in the context of turbulence-resolving flows, where the compression of flow fields poses an intricate challenge, is a second original contribution of this article. Everything is implemented as an extension to the publicly available adjointOptimisation library of OpenFOAM, which is used to solve the flow and adjoint equations and conduct the optimization. Using two shape optimization problems in external aerodynamics, it is demonstrated that including the adjoint to the turbulence model equation is crucial for the computation of accurate sensitivity derivatives. In contrast to sensitivities computed under the “frozen turbulence” assumption, which neglects variations in turbulent viscosity due to changes in the design variables, the proposed adjoint method yields sensitivities that align with those obtained using Finite Differences. This is due to the Think-Discrete Do-Continuous adjoint method which, inspired by hand-differentiated discrete adjoint, gives rise to consistent discretization schemes of the terms involved in the equations derived by continuous adjoint. Furthermore, it is demonstrated that the proposed adjoint method can significantly benefit from the iPGDZ+ algorithm, by reducing memory requirements by more than two orders of magnitude, eliminating the need for flow recomputations, while maintaining the accuracy of the computed derivatives. Ways to handle large integration windows of the objective function with this type of flow models are beyond the scope of this article.

Eulerian–Lagrangian hybrid solvers in external aerodynamics: Modeling and analysis of airfoil stall

Hybrid computational solvers that integrate Eulerian and Lagrangian methods are emerging as powerful tools in computational fluid dynamics, particularly for external aerodynamics. These solvers rely on the strengths of both approaches: Eulerian methods efficiently handle boundary layers, while Lagrangian methods excel in reducing numerical diffusion in flow convection. Building on our prior development of a two-dimensional hybrid solver that combines OpenFOAM with vortex particle method, this paper extends its application to the complex phenomena of airfoil stall at low Reynolds numbers. Specifically, we examine both static and dynamic stall conditions of a National Advisory Committee for Aeronautics (NACA) airfoil series 0012 (NACA0012) across a wide range of attack angles and oscillation frequencies, comparing our results with established data. The findings demonstrate the accuracy of hybrid Eulerian–Lagrangian solvers in replicating known stall behaviors, underscoring their potential for advanced aerodynamic studies. This work not only confirms the capability of hybrid solvers in accurately modeling challenging flows but also paves the way for their increased involvement in the field of external aerodynamics.

Flow over traveling and rotating cylinders using a hybrid Eulerian–Lagrangian solver

Hybrid Eulerian–Lagrangian solvers have gained increasing attention in the field of external aerodynamics, particularly when dealing with strong body–vortex interactions. This approach effectively combines the strengths of the Eulerian component, which accurately resolves boundary layer phenomena, and the Lagrangian component, which efficiently evolves the wake downstream. This study builds on our team’s previous work by enhancing the capabilities of a two-dimensional hybrid Eulerian–Lagrangian solver. We aim to upgrade our solver which was initially designed for static cases, to now also simulate cases involving moving objects. To ensure the reliability and applicability of a new solver, it is essential to validate its performance in complex cases. Here, the solver is validated across the case of a traveling cylinder and the case of a rotating cylinder in two different rotational speeds at low Reynolds numbers. In the realm of Eulerian solvers, such as OpenFOAM (utilized for the Eulerian component of this hybrid approach), traditional techniques include the use of morphing meshes, overset meshes, and Arbitrary Mesh Interfaces (AMI) to model body motion. The proposed methodology involves extending the Eulerian mesh up to a short distance from the solid boundary and moving it entirely as a solid entity. Then the Lagrangian solver is responsible for calculating the updated boundary conditions, thereby completing the hybrid solver’s functionality. This approach is very similar to the overset mesh technique. However, unlike the traditional method where an Eulerian mesh moves on top of a static one, our method involves the motion of an Eulerian mesh over a Lagrangian grid. We compared the results from our hybrid solver with those from a purely Eulerian solver, specifically OpenFOAM. The comparison demonstrates that our solver can replicate OpenFOAM’s results with high accuracy. Another interesting point highlighted in this study is the presence of high-frequency oscillations in the body forces in hybrid solvers that incorporate the redistribution of Lagrangian particles and do not utilize surface elements such as vortex panels, specifically when dealing with dynamic mesh simulations. When the Eulerian mesh travels on top of the Lagrangian grid of particles, the positions of the particles with respect to the Eulerian mesh continuously change. This results in a constant shift of particles near the solid body, where the highest vorticity is observed. Particles that are close to the solid boundary at one time step may find themselves inside the boundary at the next time step, leading to their removal. This pattern continuously changes during the simulation, causing fluctuations in the boundary conditions of the Eulerian solver and manifesting as oscillations in the forces acting on the body. It is shown that this issue can be alleviated either by increasing the spatial resolution of the Lagrangian solver or by synchronizing the movement of the Lagrangian grid with the motion of the Eulerian mesh. The results of the study make the solver trustworthy and pave the way for more demanding external aerodynamic simulations.

Effects of Race Car's Speed on the Aerodynamic Aspect Using Computational Fluid Dynamics Analysis

This research employs Computational Fluid Dynamics (CFD) methods to investigate the intricate relationship between race car speed and external aerodynamics during high-performance racing competitions. The primary objectives encompass the application of CFD in pre-processing and analyzing external aerodynamic aspects, coupled with a comprehensive examination of the external flow around a race car for a nuanced understanding of its aerodynamic performance. Various car speeds were considered with the RANS (k-ω SST) turbulent model. The results unveiled a direct correlation between inlet velocity and the maximum velocity attained by the race car. The aerodynamic design intricately directs the airflow, leading to higher velocities predominantly along the upper part of the car body. Noteworthy is the revelation that the highest recorded maximum velocity of 231.06 m/s coincides with a peak inlet velocity of 200 m/s, suggesting a consistent increase in maximum velocity with rising inlet velocity. This research emphasizes the pivotal role of inlet velocity in achieving peak car speed performance. It sheds light on the significance of turbulent model selection in capturing the complexities of external flow dynamics. This knowledge contributes to optimizing the external aerodynamics of race car body design, ultimately enhancing performance and competitiveness in the dynamic world of Formula 1 racing.

Computational Fluid Dynamics Analysis on the Road Bike Using Different Flow Models under Extreme Inlet Velocity

At high velocities, the aerodynamic forces acting on the road bike and rider become more pronounced, potentially affecting stability and control. Riders might experience increased resistance, requiring more effort to maintain balance and direction. This research employs Computational Fluid Dynamics (CFD) to thoroughly examine the external aerodynamics of road bikes, focusing on pre-processing techniques and their impact on overall aerodynamic performance. The research applies CFD methods for geometry preparation, meshing, and material property definition within a structured workflow using a road bike model representative of the cycling industry via SimFlow software. Through systematic variations in extreme inlet velocities (40, 70, and 100 m/s) and the utilization of diverse turbulent models, k-ω Shear-Stress Transport (SST) and Reynolds-Averaged Navier-Stokes (RANS) with k-ε and k-ω, the study reveals intricate airflow patterns around the road bike. The results explain the complicated connection between turbulent models and inlet velocities and provide new information on critical aerodynamic parameters, such as pressure and maximum velocity of the road bike model.

Flow around a pair of 2D cylinders using a hybrid Eulerian-Lagrangian solver

The field of external aerodynamics encompasses various engineering disciplines with a significant impact on wind energy technology. Aerodynamic investigations provide insights not only into the characteristics of individual blades or standalone wind turbines but also into entire wind farms. As advancements in wind turbine design continue, understanding the interactions between turbines in close proximity becomes crucial, presenting a multi-body problem. Researchers require efficient and accurate tools to comprehensively study such dynamics. This paper presents a hybrid Eulerian-Lagrangian solver designed to leverage the strengths of Eulerian solvers in resolving boundary layers and Lagrangian solvers in convecting wakes downstream without introducing significant numerical diffusion. The solver adeptly handles multi-body simulations, allowing the construction of independent Eulerian meshes that communicate seamlessly through Lagrangian particles. In this way, the computational study of multibody problems does not require very large and dense meshes. Validation in single-body cases has already been conducted, with this paper demonstrating the solver’s application to a pair of cylinders in different configurations. A comparative performance analysis is carried out against pure Eulerian solvers. The results highlight that the hybrid solver efficiently reproduces the accuracy of the Eulerian solver, demonstrating its effectiveness in handling complex aerodynamic simulations.

Prediction of effect of small local surface irregularities on natural transition to turbulence based on Global Stability Analysis

Reliable prediction of the effect of surface irregularities on laminar-turbulent transition (LTT) is of great importance for many industrial applications. At low levels of free-stream turbulence typical of external aerodynamics, the primary mechanism of LTT is associated with the so-called convective instability of the Tollmien-Schlichting waves. In this paper, a non-empiric methodology based on Global Stability Analysis, which has been developed and validated previously to predict the evolution of these waves and the location of the LTT on a smooth flat plate, is applied to evaluation of this effect for backward- and forward- facing steps of different heights and locations. The results obtained are analyzed and compared with results of 2D time-accurate unsteady Navier-Stokes simulations, as well as with available experimental data and with the semi-empiric “variable N-factor” method.

Large-scale graph-machine-learning surrogate models for 3D-flowfield prediction in external aerodynamics

The article presents the application of inductive graph machine learning surrogate models for accurate and efficient prediction of 3D flow for industrial geometries, explicitly focusing here on external aerodynamics for a motorsport case. The final aim is to build a surrogate model that can provide quick predictions, bypassing in this way the unfeasible computational burden of traditional computational fluid dynamics (CFD) simulations. We investigate in this contribution the usage of graph neural networks, given their ability to smoothly deal with unstructured data, which is the typical context for industrial simulations. We integrate an efficient subgraph-sampling approach with our model, specifically tailored for large dataset training. REV-GNN is the chosen graph machine learning model, that stands out for its capacity to extract deeper insights from neighboring graph regions. Additionally, its unique feature lies in its reversible architecture, which allows keeping the memory usage constant while increasing the number of network layers. We tested the methodology by applying it to a parametric Navier–Stokes problem, where the parameters control the surface shape of the industrial artifact at hand, here a motorbike.

An adaptive sampling algorithm for reduced‐order models using Isomap

AbstractThe use of reduced‐order models (ROMs) in physics‐based modeling and simulation is a popular tool for drastically lowering the computational cost associated with high‐fidelity simulations. ROMs use training data from a set of computed high‐fidelity simulations with different design parameters that control physical and geometric properties of the full‐order model. The quality of the training data dictates the performance of the ROM, making the choice of training design parameters important. A widely used method for generating training parameters for ROMs is Latin hypercube sampling (LHS), a statistical method that aims to maximize the distance and minimize the correlation amongst produced samples. However, LHS fails to account for the physics of the full‐order model and can lead to an over‐representation of some physical regimes in the training data while neglecting others. In this work, we present a computationally efficient adaptive sampling method for ROMs using Isomap, a versatile algorithm for nonlinear dimensionality reduction. Using an initial number of samples, the adaptive sampling algorithm iteratively generates samples based on a low‐dimensional manifold of the training data. When applied to two external aerodynamics problems, the proposed adaptive sampling algorithm offers significantly improved performance in predicting physical fields and coefficients of lift and drag for a given computational budget for both non‐intrusive and projection‐based ROMs.

Аэродинамика плохообтекаемых тел на примере конвективного теплообменного аппарата

Issues related to the research and study of regularities and features of external aerodynamics of various designs of thermal (including heat exchange) equipment, which are weakly streamlined bodies, remain uncovered and insufficiently studied. However, it is the control of the aerodynamic resistance of a design (aerodynamic imperfection) that can be a convenient criterion for both the thermal efficiency assessment and the optimisation of convective heat exchanger designs. The work is devoted to the study of the aerodynamics of poorly streamlined bodies using the example of a single section of a convective heat exchanger with a developed external surface. The single section is an assembly of two flat six-channel elements with non-standard external finning placed parallel to each other at a small distance, which leads to the formation of lattices in the inner space of the section. A numerical study of the influence of the structural parameters of the cross-section on the air flow regime and its local peculiarities has been carried out. The numerical solution is constructed in a quasi-stationary formulation based on the solution of the conservation equations of compressible continuous media by the control volume method. Due to the geometrically driven turbulence of the flow, the conservation equations were Favre and Reynolds averaged, followed by the closure of the averaged system of equations by the SST turbulence model. A counter-flow scheme of 2nd order accuracy is used to resolve non-viscous flows, and a central difference scheme of 2nd order accuracy is used for viscous flows. The conjugate gradient method is used to accelerate convergence. Significant non-uniformity of the flow both in the section channel and after the airflow exits to free space is shown, described and substantiated. The jet-like nature of the air flow after leaving the section is identified and shown. The essential non-uniformity and asymmetry of velocity and pressure profiles, and gradual pressure decrease along the length of the region are shown. At the same time, the peak values of the flow velocity maxima are 5 and more times higher than the velocity values in the middle section of the channel. It should also be noted that the formation of peripheral attached currents near symmetry planes with a local increase in the velocity modulus is observed. The analysis of the revealed peculiarities of the flow aerodynamics has allowed to designate constructive elements, the improvement of which will allow to optimise the design of the oil cooler in order to increase the efficiency of its operation. The possibility of the constructive optimisation of the external fin design is shown.

Towards a High Quality Shrink Wrap Mesh Generation Algorithm Using Mathematical Morphology

Various computational fluid dynamic simulations in engineering, such as external aerodynamics, only need the silhouette of an input geometry. Often, it is a laborious process that can take up many human hours. In addition, the CAD geometries are too complex and contain intricate features and topological holes. We showcase an effortless way to shrink-wrap triangulated surfaces with the sole intent of topology and surface simplification. Building upon the concepts of mathematical morphology and newer advancements in geometry processing, we present a straightforward and robust algorithm that can guarantee genus-zero surfaces. Our techniques are equally applicable to general polyhedral meshes and well-suited for handling both oriented and unoriented point clouds. We provide examples using unoriented point clouds to demonstrate the versatility of our algorithms. We have designed our algorithms with a wide variety of applications in mind. However, we specifically highlight their capability for aerodynamic simulations, fluid volume extraction, and surface simplification. Additionally, we emphasize the practicality and ease of implementing the proposed algorithms, and we chain additional algorithms to develop variants of our wrap algorithm.

A Zero-Equation Model for External Aerodynamics

The zero-equation model (ZEM) has been generalized for aerodynamic applications by eliminating the thickness of boundary-layer (BL) dependency to construct the stress length parameter . The SED (Structural Ensemble Dynamics) postulate evaluates the using the order function based on universal multi-layer structures for wall turbulence. The SED concept is further employed to optimize the profiles of the turbulent kinetic energy and dissipation rate with turbulent BL flows. Results demonstrate that the multi-layer ZEM receives a remarkable achievement in the prediction of wall-bounded turbulence and thus, prevails over the drawbacks encountered in most algebraic turbulence models.

Numerical analysis of unsteady flow features around a realistic Estate vehicle with hybrid RANS/LES methods

A comparative study is conducted to analyze the flow around a realistic Peugeot Estate car (308 SW) using RKE and SST RANS models, as well as DDES hybrid RANS/LES approach. The authors used previous work on 25° Ahmed bodies to establish the best grid and DDES parameters for external aerodynamics prediction. The aim of this work is to extend and transpose the numerical methodology to a realistic car. Numerical and physical characteristics related to the simulation of this complex flow are therefore carefully investigated. The numerical results are compared to in-house experiments carried out in S2A Stellantis Wind Tunnel. Two grids with 115 and 185 million elements, based on 20 prism layers cells near the wall, are used to compare the three turbulence models. Even with a smaller grid size in the wake and underbody, the predictions of drag and lift coefficients are almost identical. Moreover, refining the near-wall region from 20 to 30 prism layers has no effect on drag coefficient and flow prediction. Consequently, the grid with 20 prism layers and 115M cells is used as reference grid in this work. Then, the flow features between RKE, SST and SST DDES models are compared to two-dimensional (2D) and three-dimensional (3D) experimental results. RANS gives better agreement on aerodynamics forces. However, DDES reproduces accurately the specific three-dimensional topology of the flow around the car, in the wake and the underbody when RANS results are globally wrong.

Adaptative finite element simulation of unsteady turbulent compressible flows on unstructured meshes

The simulation of high-speed turbulent compressible flows using Large Eddy Simulation (LES) combined with the Characteristic-Based Split scheme (CBS) and a mesh adaptation strategy is presented in this work. A compressible dynamic Smagorinsky model is employed for the compressible LES model and the CBS scheme is employed in a Finite Element Method (FEM) context for space and time discretization using unstructured meshes. An accurate mesh adaptation scheme is frequently applied along the simulation including mesh refinement, mesh coarsening, edge or face swapping and a vertex smoothing technique in order to control the interpolation error and the mesh size. A feature-based error estimation is employed considering multi-scale and multi-metric intersection in order to capture turbulence effects. Two and three-dimensional applications are evaluated in order to investigate the capabilities of the present approach for evaluating external turbulent and compressible aerodynamics problems. The turbulent transonic flow around a circular cylinder in 2D and 3D domains and the turbulent supersonic flow past a blunt cylinder-flare model are investigated. Aerodynamic coefficients, frequency analysis and pressure distributions are compared against experimental data and other numerical simulations.

Effect of modifications to island shape and geometrical configuration on the external aerodynamics of a generic aircraft carrier

The external aerodynamics of an aircraft carrier plays a vital role in the safe landing of aircraft during take-off and recovery. The hull, flight deck, and the island create a turbulent disturbance behind the aircraft carrier, leading to a simultaneous reduction in forward velocity and a downwash, which together create a sinking effect on the aircraft along its glideslope path. This phenomenon is known as the burble effect. It could potentially increase the pilot’s workload and strain their mental and physical faculties. Any design change that obviates or reduces the burble effect would potentially increase the probability of safely landing the aircraft on an aircraft carrier. There are only a few studies on the external aerodynamics of an aircraft carrier. The primary motivation of this study is to evaluate the effect of modifications to the island structure on the external aerodynamics of a generic aircraft carrier, especially the burble behind the carrier. The first part of the study pertains to the parametric changes to the aspect ratio of the island, that is, its length to width ratio and the consequent impact on the aerodynamics behind the carrier along the flight glide path. The second part of the study focuses on changing the geometry of the island by rounding the assumed cuboid island’s sharp corners, and evaluating its effect on the burble along the glideslope path of the aircraft. For the study, computational fluid dynamics (CFD) analysis on a generic aircraft carrier model has been carried out using the commercially available CFD solver Ansys FLUENT. The CFD studies have been validated by results of experiments conducted in a wind tunnel on the same generic aircraft carrier model. From the studies, it is seen that the aspect ratio of the island greater than one and rounding the sharp edges of the island have beneficial effects in reducing the impact of the burble behind the carrier.

Determination of Aerodynamic Losses of Electric Motors

The energy efficiency of machines is nowadays an intensively studied problem. The efficiency of the induction motor is dominantly influenced by the rotor’s and stator winding’s temperature. The main goal of the research presented in this paper is to develop a methodology based on Computational Fluid Dynamics (CFD) analysis of internal and external aerodynamics, which is necessary for the optimisation of cooling of the induction motors. In this paper, the theoretical, as well as the numerical study of the internal and external aerodynamics of the induction motor, is described and verified by the experimental measurements. In the CFD-based numerical study, the Reynolds-averaged Navier–Stokes (RANS) turbulence modelling approach was applied to the flow field simulations inside and outside the induction motor. The complexity of the solved problem is increased not only by the geometric asymmetry but also by the flow’s asymmetric character caused by the fan’s rotation to cool the motor casing. This increases demand, especially on computational resources, as it is impossible to create a simplified numerical model incorporating symmetry. The volume flow of the cooling air and velocity between ribs was measured for the experimental study. Comparing the results of the Computational Fluid Dynamics (CFD) simulations and data obtained from the experimental measurement, we concluded that the results of CFD simulations are in good relationship with the results of experimental measurement and analytical approximations. An experimentally validated CFD model of the induction motor, the so-called digital twin, will be in the future used for virtual optimisation of the new designs concerning minimising losses and maximising efficiency, respectively.

A weak coupling between a near-wall Eulerian solver and a Vortex Particle-Mesh method for the efficient simulation of 2D external flows

We introduce and validate a weak coupling approach between a body-fitted velocity-pressure solver and a Vortex Particle-Mesh (VPM) method in 2D for the simulation of incompressible external aerodynamics. The approach does not involve inner iterations, conserves circulation up to interpolation accuracy without resorting to a panel method, and accommodates different time steps across the solvers. It also utilizes a mixed boundary condition for the body-fitted solver that ensures the continuity of the vorticity field across the solvers. The second order convergence of the methodology is first demonstrated. We then assess it on the flow past a cylinder at various Reynolds numbers (from Re=550 to 9500), and we finally apply it to the flow past an airfoil at Re=5000.

Aerodynamic design and evaluation of an open-nose supersonic drone

The objective of this paper is to investigate the efficiency of a proposed supersonic drone configuration, in terms of drag, ram recovery, and fundamental flight performance factors. Sustainable supersonic cruise at Mach 1.6 is the major segment of the mission profile which affects the overall geometry resulting from the conceptual design phase, a tailless delta drone with an open-nose forebody, lofted around the inlet which consists of an analytical compression surface and a S-duct diffuser. Because the aerodynamics of this unconventional configuration is unknown, a series of CFD simulations using the ANSYS Fluent solver is coupled to the design process to predict both internal and external aerodynamics as a proof of the concept. The simulations indicate that the drone’s overall drag is significantly lower than the other configurations with side or underside integrated inlets while the inlet pressure recovery is adjusted to maximize the engine thrust. The parasite drag at design speed is about 0.022 which is considerably lower than conventional configurations and the pressure recovery more than 0.96 is possible by applying the boundary layer bypass. A comparative study, with a developed thrust model, shows that the configuration satisfies mission requirements and exceeds them at transonic and supersonic flight phases.

Numerical investigation of a plunging flat-plate airfoil using a diffuse interface immersed boundary method

This study investigates the capabilities of a diffuse interface immersed boundary method in the simulation of fluid flow over an oscillating flat-plate airfoil at moderately high Reynolds numbers where interacting unsteady vortical flows control the flow behavior. The recently developed and modified Smoothed Profile Method (SPM) is adopted as a diffuse interface immersed boundary solver to model the fluid-structure interaction (FSI) problem. While in general diffuse interface methods are simpler to implement relative to sharp-interface methods (SIMs), they have been thought to lose accuracy in the simulation of moderate Reynolds number flows. The simulation results show that the lift coefficient and vorticity contours from SPM match well with experiments. Moreover, our detailed analysis of the vorticity fluxes at the airfoil leading edge and the comparison with experiments also show that SPM can be used for moderate Reynolds number external aerodynamics problems applicable to micro-air vehicles.

Modeling of Air Flow Over a Generic Aircraft Carrier With and Without Island Structure

The study of external aerodynamics of an aircraft carrier is of utmost importance in ensuring the safety of aircraft and pilots during take-off and recovery. The velocity deficit in the forward direction and the downwash together combine to give a sinking effect to the aircraft, along its glideslope path and is known as the ‘burble’ in naval aviation parlance. This phenomenon is primarily responsible for the potential increase in pilot workload on approach to the aircraft carrier. There is little literature in the open domain regarding ways and means to alleviate the burble effect. Unlike in the case of the automobile industry, which has the generic ‘Ahmed body’ and for the frigates/destroyers, for which there is the Simplified Frigate Ship (SFS), on which experiments and validation through CFD could be carried out, by researchers from all over the world, there is no generic Aircraft Carrier model for carrying out experiments and validation of CFD codes. The aim of this study is to define the Generic Aircraft Carrier Model (GAC), as developed at IIT Delhi, and to carry out numerical studies on the GAC and a variant of GAC without the island, BGAC (Baseline GAC), to assess the contribution of the island to the burble behind an Aircraft Carrier. This study gives a quantitative estimation of the effect and contribution of individual components of an Aircraft Carrier (like flight deck, island, etc.) to the burble behind the carrier, and would give a Naval Ship Designer an understanding of the effect of the geometrical configuration of the flight deck and the island on generation of the burble behind the carrier, which could aid the designer in potentially reducing the pilot workload.