High-speed Aerodynamics Research Articles

Quantification analysis of high-speed train aerodynamics with geometric uncertainty of streamlined shape

Purpose This study aims to get a better understanding of the impact of streamlined high-speed trains (HSTs) with geometric uncertainty on aerodynamic performance, as well as the identification of the key parameters responsible for this impact. To reveal the critical parameters, this study creates a methodology for evaluating the uncertainty and sensitivity of drag coefficient induced by design parameters of HST streamlined shapes. Design/methodology/approach Bézier curves are used to parameterize the streamlined shape of HSTs, and there are eight design parameters required to fit the streamlined shape, followed by a series of steady Reynolds-averaged Navier–Stokes simulations. Combining the preparation work with the nonintrusive polynomial chaos method results in a workflow for uncertainty quantification and global sensitivity analysis. Based on this framework, this study quantifies the uncertainty of drag, pressure, surface friction coefficient and wake flow characteristics within the defined ranges of streamline shape parameters, as well as the contribution of each design parameter. Findings The results show that the change in drag reaches a maximum deviation of 15.37% from the baseline, and the impact on the tail car is more significant, with a deviation of up to 23.98%. The streamlined shape of the upper surface and the length of the pilot (The device is mounted on the front of a train’s locomotive and primarily serves to remove obstacles from the tracks, thereby preventing potential derailment.) are responsible for the dominant factors of the uncertainty in the drag for HSTs. Linear regression results show a significant quadratic polynomial relationship between the length of the pilot and the drag coefficient. The drag declines as the length of the pilot enlarges. By analyzing the case with the lowest drag, the positive pressure area in the front of pilot is greatly reduced, while the nose tip pressure of the tail is enhanced by altering the vortices in the wake. The counter-rotating vortex pair is significantly attenuated. Accordingly, exerts the impacts caused by geometric uncertainty can be found on the wake flow region, with pressure differences of up to 900 Pa. The parameters associated with the shape of the upper surface contribute significantly to the uncertainty in the core of the wake separation region. Originality/value The findings contribute to a better understanding of the impact of streamlined HSTs with geometric uncertainty on aerodynamic performance, as well as the identification of the key parameters responsible for this impact. Based on this study, future research could delve into the detailed design of critical areas in the streamlined shape of HSTs, as well as the direction of shape optimization to more precisely and efficiently reduce train aerodynamic drag under typical conditions.

Highly separated transitional shock-wave/boundary-layer interactions: A spatial modal study

At cruise altitudes, the Reynolds number may become sufficiently low to allow a laminar boundary layer to persist on the suction side of a transonic fan blade up to the shock-wave/boundary-layer interaction (SBLI). In such a transitional SBLI with sufficiently large shock-induced separation, a shock oscillation mechanism occurs, with the source at the upstream growth (until a critical length) and natural suppression (through shear layer instabilities) of the separation bubble. The oscillation cycle is characterized by a temporarily vanishing upstream laminar part of the separation bubble. The suppression of this laminar part is accompanied by downstream advection of turbulence and subsequent entrainment into the bulk separation bubble, affecting the reflected shock movement. In order to study the spatial behavior of the mechanism, particle image velocimetry of a highly separated transitional oblique SBLI at Mach 2.3 is conducted in the high speed aerodynamics laboratory of Delft University of Technology. Statistical quantities, including root mean square velocity fluctuations, phase averages, and spatial modes from proper orthogonal decomposition, are investigated. The entrainment strength varies depending on the phase of the oscillation, and the turbulent shear layer is not fully developed. The main growth and shrinking mode of the separation bubble were extracted, which affects the slip line region size and shock position. Secondary modes that affect the shear layer undulation and upstream effects were also extracted. The study provides quantitative analyses of an important shock oscillation type, with the focus on capturing the separation bubble size variation and upstream effects.

Optimization and Analysis of Flow Field Simulations Across Different Mach Regimes Using Discrete Numerical Methods

This article explores the development of flow field models in steady-state environments utilizing Euler equations and potential flow equations, with verification processes conducted using Python. The models demonstrate stability and high accuracy in low-velocity scenarios, capturing essential dynamics effectively. However, as the conditions transition to supersonic speeds, the models begin to exhibit increased errors. This discrepancy highlights the challenges faced in simulating high-speed aerodynamics accurately. The research underscores the importance of improving model fidelity in diverse Mach regimes, particularly in supersonic conditions where traditional methods struggle. Future research directions identified include the development of unsteady flow field models, which are crucial for dynamic analyses, optimization of grid structures for three-dimensional complex fields to improve computational efficiency, and the creation of extensive model libraries. These advancements aim to enhance the accuracy, reliability, and practicality of flow field simulations, extending their applicability in both academic studies and industry applications, particularly in aerospace engineering where precise flow modeling is critical.

Event-Based Measurement of Aeroelastic Structure in High-Speed Flow

In high-speed aerodynamics research, point sensors are ideal for embedding in test models but lack spatial resolution, whereas high-speed cameras offer spatiotemporally resolved measurement but involve significant footprint, cost, and data size. To address these tradeoffs, this study explores the application of nascent event-based cameras for high-speed tests. Event-based cameras support continuous, data-sparse kilohertz-equivalent imaging at 720p resolution, on form factors as small as 36 mm and 40 grams in mass, combining the benefits of point sensors and high-speed cameras. However, these attributes come from asynchronous pixels that necessitate unique operating and postprocessing approaches. Here, the authors adapted event-based cameras for two-/three-dimensional photogrammetric tracking of aeroelastic structures, demonstrating an event-based workflow and two tracking algorithms (mean-shift filtering and circle fit). Bench-top validations achieved three-dimensional precision of 0.35 mm/s on 20 mm/s motion across a 259 mm field of view, while two-dimensional measurements of an aeroelastic titanium panel in Mach 0.76 transonic flow successfully identified millimeter-scale vibrations at 43.7, 120, and 270 Hz, validated against a laser displacement and high-speed camera. The transonic test’s raw data were 145.8 MB on the event-based camera, compared to 88.5 GB on the high-speed camera. The presented results demonstrated the viability of event-based techniques in high-speed aerodynamic testing, while highlighting challenges such as polarity switching and pixel latency.

Guest editorial: High-speed aerodynamics, from transonic to hypersonic

Guest editorial: High-speed aerodynamics, from transonic to hypersonic

Fighting wind with wind to improve high-speed train aerodynamics near mountains

A look at the acceleration effect of gale-force winds on high-speed trains reveals how mitigation efforts might be designed.

Kriging-based multi-objective optimization on high-speed train aerodynamics using sequential infill criterion with gradient information

For models with large numerical simulation costs, such as high-speed trains, using as few samples as possible to construct a high-precision surrogate model during aerodynamic multi-objective optimization is critical to improving optimization efficiency. This study proposes a sequential infill criterion (SIC) appropriate for the Kriging surrogate model to address this issue. Three multi-objective functions are employed to test the feasibility of constructing a surrogate model based on SIC, and the SIC surrogate model then performs multi-objective aerodynamic optimizations on the high-speed train. The findings indicate that the expected improvement infill criterion (EIC) in the first stage can enhance the global prediction accuracy of the SIC. An infill criterion based on EIC that fuses gradient information (PGEIC) in the second stage is proposed to seek samples in the Pareto front. The PGEIC surrogate model achieves the lowest generational distance and prediction error. The performance of EIC for global search, EIC for Pareto front search, and infill criterion for Pareto front search using only gradient information is poor. The final PGEIC–SIC surrogate model of train aerodynamics has less than 1% prediction error for the three optimization objectives. The optimal solution reduces the aerodynamic drag force of the head car and the aerodynamic drag and lift force of the tail car by 4.15%, 3.21%, and 3.56%, respectively, compared with the original model. Furthermore, sensitivity analysis of key parameters revealed that the nose height v1, cab window height v3, and lower contour line have a greater impact on aerodynamic forces. Moreover, the nose and cab window heights of the optimal model have been reduced, and the lower contour line is concave. Correspondingly, the streamlined shape appears more rounded and slender.

Reducing Drag by Optimizing the Underbody with Ride Height in Formula 1

This study investigates the aerodynamic interaction between wheel wakes and the underbody of Formula 1 cars, focusing on the effect of varying ride heights on drag reduction and ground effect optimization. With the reintroduction of ground effect principles in the 2022-2026 Formula 1 regulations, the potential for enhanced vehicle performance through improved aerodynamic design is significant. However, the efficiency of venturi tunnels, essential for generating effective downforce, is compromised by turbulent airflows produced by the wheels, known as wheel wakes. This research utilizes computational fluid dynamics (CFD) simulations to model these interactions at different ride heights, aiming to pinpoint optimal configurations that minimize aerodynamic drag while maximizing downforce. Initial findings suggest a delicate balance between ride height adjustment and tunnel geometry optimization, offering potential pathways to achieve aerodynamic efficiency in modern Formula 1 vehicles. This paper contributes to the evolving discourse on high-speed vehicle aerodynamics, providing insights that could inform future vehicle design and regulatory frameworks in motorsports.

High-order implicit shock tracking boundary conditions for flows with parametrized shocks

High-order implicit shock tracking (fitting) is a class of high-order, optimization-based numerical methods to approximate solutions of conservation laws with non-smooth features by aligning elements of the computational mesh with non-smooth features. This ensures the non-smooth features are perfectly represented by inter-element jumps and high-order basis functions approximate smooth regions of the solution without nonlinear stabilization, which leads to accurate approximations on traditionally coarse meshes. In this work, we introduce a robust implicit shock tracking framework specialized for problems with parameter-dependent lead shocks (i.e., shocks separating a farfield condition from the downstream flow), which commonly arise in high-speed aerodynamics and astrophysics applications. After a shock-aligned mesh is produced at one parameter configuration, all elements upstream of the lead shock are removed and the nodes on the lead shock are positioned for new parameter configurations using the implicit shock tracking solver. The proposed framework can be used for most many-query applications involving parametrized lead shocks such as optimization, uncertainty quantification, parameter sweeps, “what-if” scenarios, or parameter-based continuation. We demonstrate the robustness and flexibility of the framework using a one-dimensional space-time Riemann problem, and two- and three-dimensional supersonic and hypersonic benchmark problems.

High-speed aerodynamics control using energy injection of pulsed discharges

We present a novel method of high-speed aerodynamic control that relies on active energy injection of pulsed discharges characterized by a high power density and long pulse width. The control principle, which is based on the manipulation of a shock wave by the energy injection, is investigated and verified via M5 wind tunnel experiments and a numerical simulation. The test model is a cone-shaped model with two compression ramps, and we organize four discharges which are connected in series and located on the surface of the model. We use high-resolution schlieren imaging and a fiber optic balance to analyze the control effects of these discharges on the flow topology and the aerodynamic force. Schlieren imaging reveals a notable change in the flow topology and a weakening of the attached shock wave due to the discharge plasma layer creating a virtual wedge that diverts the incoming flow and reducing the local Mach number. The quantitative balance data show a significant force reduction in the presence of the pulsed discharges, and reveals that the force reduction rate is associated with the energy ratio, which increases with an increase in the pulse energy and a decrease in the dynamic pressure. A larger energy ratio of discharge leads to a higher penetration depth of the plasma layer, which is more conducive to aerodynamic control. The simulation results show similar flow topologies and consistent variation tendency in the aerodynamic force to the experimental results.

DARCY-FORCHHEIMER TANGENT HYPERBOLIC NANOFLUID FLOW THROUGH A VERTICAL CONE WITH NON-UNIFORM HEAT GENERATION

The convective flows through different geometries have numerous applications in high-speed aerodynamics, nuclear cooling systems, fiber technology, and polymer engineering. In the present paper, we investigate the non-linear, mixed convective, boundary-driven, tangent hyperbolic nanofluid flow through a cone. The flow takes place under nonuniform heat sink/source. Darcy-Forchheimer effects have also been taken into account in mathematical modeling and analysis. The Buongiorno model is implemented to examine the effects of thermophoresis and Brownian motion parameters. The governing equations are constructed through the laws of conservation. The modeled flow problem is converted into a set of ordinary differential equations with the help of proposed similarity transformations. To interpret the modified system of equations, the homotopy analysis method (HAM) is applied. The roles of versatile parameters of interest are analyzed and sketched for better understanding. The velocity profile increases by increasing the Darcy number, and converse behavior is found by giving rise to the Forchheimer inertial drag parameter. The rise in temperature profile occurs by increasing a non-uniform heat source variable. The concentration profile enhances when the value of the thermophoresis parameter increases, and shows inverse behavior for the Brownian motion parameter. In the Buongiorno model, nanoparticle concentration has an inverse relation with the Brownian motion parameter. So, the concentration profile declines for greater Brownian motion parameter. To understand the behavior of flow through a cone, the values of Nusselt number and Sherwood numbers are examined.

Impact assessment of new generation high-speed agricultural tractor aerodynamics on transportation fuel consumption and related phenomena.

New generation agricultural tractors contribute to transportation by increased travel speeds. There is not any available aerodynamic data on the authentic agricultural tractor form. On-road transportation by tractors is between 8 and 30% of their operational time. In this work, two agricultural tractors are modelled via computational fluid dynamics for nine different speeds to determine aerodynamic resistances. Constant speed travel scenarios are analyzed. Corresponding speeds are 5 and 10 to 80km/h with 10km/h increments. Reynolds number changes between 1.6 × 105 and 2.98 × 106. The characteristic lengths are taken as the square root of the streamwise projected area of the tractor geometries. Aerodynamic forces exerted on the tractors change between 3 and 746N. The calculated drag coefficients are found as independent from Reynolds number and are 0.6 and 0.78 for the two different types of driver compartments. The approximated aerodynamic related fuel consumptions for 1-h changes between 0.002 and 8.28 lt/s which correspond to 0.001 to 5.76kg/s carbon emission. A potential improvement in decreasing aerodynamic resistance about 20% is discussed by spatial data. Since the conducted work is being regarded as the first instance in the literature, it is estimated that several consecutive reports will be triggered.

600 km/h moving model rig for high-speed train aerodynamics

A maglev train with a speed of 600 km/h or higher can fill the speed gap between civil aircrafts and wheel rail trains to alleviate the contradiction between the existing transportation demand and actual transport capacity. However, the aerodynamic problems arising due to trains running at a higher speed threaten their safety and fuel efficiency. Therefore, we developed a newly moving model rig with a maximum speed of 680 km/h to evaluate aerodynamic performance of trains, thus determining the range of the aerodynamic design parameters. In the present work, a launch system with a mechanical efficiency of 68.1% was developed, and a structure of brake shoes with front and rear overlapping was designed to increase the friction. Additionally, a device to suppress the pressure disturbances generated by the compressed air, as well as a double track with the function of continuously adjusting the line spacing, were adopted. In repetitive experiments, the time histories of pressure curves for the same measuring point are in good agreement. Meanwhile, the moving model test and full-scale experimental result of maglev trains passing each other in open air are compared, with an error less than 4.6%, proving the repeatability and rationality of the proposed moving-model.

Research@ZaB: Study of FDS Capabilities to Assess the High-Speed Train Impact on Pressure Pattern Within a\xa0Railway Tunnel

The “wind tunnel” approach is applied to study high-speed train aerodynamics in a railway tunnel using FDS software. The main focus of the research is on the pressure distribution along the tunnel. Proven analytical dependencies based on the experimental observations for air jet centerline velocity and flow entrainment are used to evaluate the model setup. A model verification is carried out based on the pressure drop calculations due to viscous effects where the impact of the surface roughness and the tunnel length are also considered. A sensitivity analysis is performed to evaluate changes in input FDS parameters and to explore interactions between them. It is proposed to use the standard deviation, obtained from the calculated time-averaged pressure values, to specify the appropriate numeric parameter combinations, e.g. DT and PRESSURE_TOLERANCE, considering the desired results consistency and the computational time consumed. The simulated cases with and without a train inside a tunnel provide data on the aerodynamic characteristics of the models. The obtained volumetric and cross-sectional profiles for pressure and airflow velocity distribution form the basis for an informed decision regarding the tunnel design or safety solutions, for example, defining areas under maximal and minimal pressure loads. The analysis displays the necessity to carefully manage each investigated case considering the FDS features and limitations that largely affect a model setup and calculations.

On the implementation of flux limiters in algebraic frameworks

The use of flux limiters is widespread within the scientific computing community to capture shock discontinuities and are of paramount importance for the temporal integration of high-speed aerodynamics, multiphase flows and hyperbolic equations in general.Meanwhile, the breakthrough of new computing architectures and the hybridization of supercomputer systems pose a huge portability challenge, particularly for legacy codes, since the computing subroutines that form the algorithms, the so-called kernels, must be adapted to various complex parallel programming paradigms. From this perspective, the development of innovative implementations relying on a minimalist set of kernels simplifies the deployment of scientific computing software on state-of-the-art supercomputers, while it requires the reformulation of algorithms, such as the aforementioned flux limiters.Equipped with basic algebraic topology and graph theory underlying the classical mesh concept, a new flux limiter formulation is presented based on the adoption of algebraic data structures and kernels. As a result, traditional flux limiters are cast into a stream of only two types of computing kernels: sparse matrix-vector multiplication and generalized pointwise binary operators. The newly proposed formulation eases the deployment of such a numerical technique in massively parallel, potentially hybrid, computing systems and is demonstrated for a canonical advection problem.

Numerical solution of compressible Euler and Magnetohydrodynamic flow past an infinite cone

A numerical scheme is developed for systems of conservation laws on manifolds which arise in high speed aerodynamics and magneto-aerodynamics. The systems are presented in an arbitrary coordinate system on the manifold and involve source terms which account for the curvature of the domain. In order for a numerical method to accurately capture the behavior of the system it is solving, the equations must be discretized in a way that is not only consistent in value, but also models the appropriate character of the system. Such a discretization is presented in this work which preserves the tensorial transformation relationships involved in formulating equations in a curved space. A numerical method is then developed and applied to the conical Euler and Ideal Magnetohydrodynamic equations. To the authors’ knowledge, this is the first demonstration of a numerical solver for the conical Ideal MHD equations. Along with the curvature of the domain, is the added challenge that both systems of equations are of mixed type. Both systems change between elliptic and hyperbolic type throughout the domain, which had to be accommodated by the numerical method.

Space–Time Conservation Element and Solution Element Method and Its Applications

This paper reviews the development of the space–time conservation element and solution element (CESE) method and summarizes its applications in various research areas. The CESE method is a special finite-volume-type method that provides an alternative approach to numerical solutions of fluid-dynamic equations and conservation laws in various physical systems. Based on a unified treatment of time and space, this method solves the integral form of the governing equations by discretization of the space–time domain. Recent progress in CESE schemes mainly includes the construction of a family of upwind CESE schemes, the extended definitions of conservation elements and solution elements for arbitrary meshes, and a new approach to developing high-order CESE schemes. Selected applications of the CESE method (including high-speed aerodynamics, multifluid flows, detonations, and aeroacoustics) are presented. Features of the CESE method are described.

Physics-informed neural networks for high-speed flows

In this work we investigate the possibility of using physics-informed neural networks (PINNs) to approximate the Euler equations that model high-speed aerodynamic flows. In particular, we solve both the forward and inverse problems in one-dimensional and two-dimensional domains. For the forward problem, we utilize the Euler equations and the initial/boundary conditions to formulate the loss function, and solve the one-dimensional Euler equations with smooth solutions and with solutions that have a contact discontinuity as well as a two-dimensional oblique shock wave problem. We demonstrate that we can capture the solutions with only a few scattered points clustered randomly around the discontinuities. For the inverse problem, motivated by mimicking the Schlieren photography experimental technique used traditionally in high-speed aerodynamics, we use the data on density gradient ∇ρ(x,t), the pressure p(x∗,t) at a specified point x=x∗ as well as the conservation laws to infer all states of interest (density, velocity and pressure fields). We present illustrative benchmark examples for both the problem with smooth solutions and Riemann problems (Sod and Lax problems) with PINNs, demonstrating that all inferred states are in good agreement with the reference solutions. Moreover, we show that the choice of the position of the point x∗ plays an important role in the learning process. In particular, for the problem with smooth solutions we can randomly choose the position of the point x∗ from the computational domain, while for the Sod or Lax problem, we have to choose the position of the point x∗ from the domain between the initial discontinuous point and the shock position of the final time. We also solve the inverse problem by combining the aforementioned data and the Euler equations in characteristic form, showing that the results obtained by using the Euler equations in characteristic form are better than that obtained by using the Euler equations in conservative form. Furthermore, we consider another type of inverse problem, specifically, we employ PINNs to learn the value of the parameter γ in the equation of state for the parameterized two-dimensional oblique wave problem by using the given data of the density, velocity and the pressure, and we identify the parameter γ accurately. Taken together, our results demonstrate that in the current form, where the conservation laws are imposed at random points, PINNs are not as accurate as traditional numerical methods for forward problems but they are superior for inverse problems that cannot even be solved with standard techniques.

Review of research on high-speed railway aerodynamics in China

AbstractHigh-speed railway aerodynamics is the key basic science for solving the bottleneck problem of high-speed railway development. This paper systematically summarizes the aerodynamic research relating to China’s high-speed railway network. Seven key research advances are comprehensively discussed, including train aerodynamic drag-reduction technology, train aerodynamic noise-reduction technology, train ventilation technology, train crossing aerodynamics, train/tunnel aerodynamics, train/climate environment aerodynamics, and train/human body aerodynamics. Seven types of railway aerodynamic test platform built by Central South University are introduced. Five major systems for a high-speed railway network—the aerodynamics theoretical system, the aerodynamic shape (train, tunnel, and so on) design system, the aerodynamics evaluation system, the 3D protection system for operational safety of the high-speed railway network, and the high-speed railway aerodynamic test/computation/analysis platform system—are also introduced. Finally, eight future development directions for the field of railway aerodynamics are proposed. For over 30 years, railway aerodynamics has been an important supporting element in the development of China’s high-speed railway network, which has also promoted the development of high-speed railway aerodynamics throughout the world.

Test Facility for High-Speed Probe Calibration

A new test facility was built up as a part of a closed-loop transonic wind tunnel in VZLU´s High-speed Aerodynamics Department. The wind tunnel is driven by a twelve stage radial compressor and Mach and Reynolds numbers can be changed by the compressor speed and by the total pressure in the wind tunnel loop by a set of vacuum pumps, respectively. The facility consists of an axisymmetric subsonic nozzle with an exit diameter de = 100 mm. The subsonic nozzle is designed for regimes up to M = 1 at the nozzle outlet. At the nozzle inlet there is a set of a honeycomb and screens to ensure the flow stream laminar at the outlet of the nozzle. The subsonic nozzle can be supplemented with a transonic slotted nozzle or a supersonic rigid nozzle for transonic and supersonic outlet Mach numbers. The probe is fixed in a probe manipulator situated downstream of the nozzle and it ensures a set of two perpendicular angles in a wide range (±90°). The outlet flow field was measured through in several axial distances downstream the subsonic nozzle outlet. The total pressure and static pressure was measured in the centreline and the total pressure distribution in the vertical and horizontal plane was measured as well. Total pressure fluctuations in the nozzle centreline were detected by a FRAP probe. From the initial flow measurement in a wide range of Mach numbers the best location for probe calibration was chosen. The flow field was found to be suitable for probe calibration.