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The land speed record vehicle, Bloodhound, undertook testing at subsonic and low transonic speeds (up to Mach 0.8) at Hakskeen Pan, South Africa, during October and November of 2019. A decade of CFD-led aerodynamic design had been undertaken to produce a vehicle with the aim of minimised Mach number aerodynamic dependencies and minimised overall drag. This paper sets out and explains the measured pressure distributions with a focus on the highest speed run of Bloodhound up to a peak speed of 628 mile/h. It compares the measured aerodynamic performance with the various CFD model predictions used throughout the design process showing that, whilst localised discrepancies between CFD model and real behaviour exist, overall the Reynolds-averaged Navier–Stokes (RANS)-based CFD tools used to design the car did result in sufficiently accurate aerodynamic data to predict the overall vehicle performance to a high degree of accuracy. The work outlined in this paper, and the conclusions and recommendations drawn, form the basis for a future record attempt and the understanding of what will be required in principle to extend the World Land Speed Record to 1000 mile/h. It also provides guidance on how to effectively make use of RANS-based CFD modelling predictions for other complex, ground-interacting high-speed applications.

The standard Yee FDTD algorithm is widely used in computational electromagnetics because of its simplicity and divergence free nature. A generalization of this classical scheme to 3D unstructured co-volume meshes is adopted, based on the use of a Delaunay primal mesh and its high quality Voronoi dual. This circumvents the problem of accuracy losses, which are normally associated with the use of a staircased representation of curved material interfaces in the standard Yee scheme. The procedure has been successfully employed for modelling problems involving both isotropic and anisotropic lossy materials. Here, we consider the novel extension of this approach to allow for the challenging modelling of chiral materials, where the material parameters are frequency dependent. To adequately model the dispersive behaviour, the Z-transform is employed, using second order Padé approximations to maintain the accuracy of the basic scheme. To validate the implementation, the numerical results produced are compared with available analytical solutions. The stability of the chiral algorithm is also studied.

This work proposes a novel multi-output neural network for the prediction of the aerodynamic coefficients of wings in three dimensions using inviscid compressible flow data. Contrary to existing neural networks that are designed to predict the aerodynamic coefficients directly, the proposed network considers as output the pressure at a number of selected points on the aerodynamic shape. The performance of the proposed neural network is compared against the existing neural networks. The numerical results, involving high dimensional problems with flow and geometric parameters, show the benefits of the proposed approach.

This work proposes a novel multi-output neural network for the prediction of aerodynamic coefficients of aerofoils in two dimensions and wings in three dimensions. Contrary to existing neural networks that are often designed to predict aerodynamic quantities of interest, the proposed network considers as output the pressure at a number of selected points on the aerodynamic shape. The proposed multi-output neural network is compared with other approaches found in the literature. Furthermore, a detailed comparison of the proposed neural network with the popular proper orthogonal decomposition method is presented. The numerical results, involving high dimensional problems with flow and geometric parameters, show the benefits of the proposed approach.

Summary An excessive number of Steiner points may be inserted during the process of boundary recovery for constrained tetrahedral mesh generation, and these Steiner points are harmful in some circumstances. In this study, a new flip named shell transformation is proposed to reduce the usage of Steiner points in boundary recovery and thus to improve the performance of boundary recovery in terms of robustness, efficiency and element quality. Shell transformation searches for a local optimal mesh among multiple choices. Meanwhile, its recursive callings can perform flips on a much larger element set than a single flip, thereby leading the way to a better local optimum solution. By employing shell transformation properly, a mesh that intersects predefined constraints intensively can be transformed to another one with much fewer intersections, thus remarkably reducing the occasions of Steiner point insertion. Besides, shell transformation can be used to remove existing Steiner points by flipping the mesh aggressively. Meshing examples for various industrial applications and surface inputs mainly composed of stretched triangles are presented to illustrate how the improved algorithm works on difficult boundary constrained meshing tasks.

In this paper, we develop numerical methods for modeling blast and fragments generated from explosive detonation and apply them to scenarios representing improvised explosive devices in confined spaces. The detonation of condensed phase explosives is modeled with a programmed burn method in a three-dimensional multimaterial flow solver. This solver has been coupled with a Lagrangian particle solver to model the acceleration of explosive-driven fragments. We first simulate an explosion in a long cylindrical tube to validate the fluid solver for a partially-confined blast. We then simulate explosions on a subway train platform for 10 kg and 30 kg C4 charges. The maximum shock overpressure and impulse are used to predict the risk of common blast injuries. To represent improvised explosive threats, we model C4 charges with spherical, cylindrical, and disk shapes that are surrounded by a layer of spherical fragments. We find that the explosive charge shape plays an important role in the acceleration of the spherical fragments. Finally, a realistic scenario of an improvised explosive detonation near a bomb technician is investigated to assess fragment trajectory and blast loads in the near field.

This paper presents an automated aerodynamic optimisation algorithm using a novel method of parameterising the search domain and geometry by employing user–defined control nodes. The displacement of the control nodes is coupled to the shape boundary movement via a ‘discrete boundary smoothing’. This is initiated by a linear deformation followed by a discrete smoothing step to act on the boundary during the mesh movement based on the change in its second derivative. Implementing the discrete boundary smoothing allows both linear and non-linear shape deformation along the same boundary dependent on the preference of the user. The domain mesh movement is coupled to the shape boundary movement via a Delaunay graph mapping. An optimisation algorithm called Modified Cuckoo Search (MCS) is used acting within the prescribed design space defined by the allowed range of control node displacement. In order to obtain the aerodynamic design fitness a finite volume compressible Navier-Stokes solver is utilized. The resulting coupled algorithm is applied to a range of case studies in two dimensional space including the optimisation of a RAE2822 aerofoil and the optimisation of an intake duct under subsonic, transonic and supersonic flow conditions. The discrete mesh–based optimisation approach outlined is shown to be effective in terms of its generalised applicability, intuitiveness and design space definition.

A methodology that combines the advantages of the vertex-centred finite volume (FV) method and high-order hybridisable discontinuous Galerkin (HDG) method is presented for the simulation of the transient inviscid two dimensional flows. The resulting method is suitable for simulating the transient effects on coarse meshes that are suitable to perform steady simulations with traditional low-order methods. In the vicinity of the aerodynamic shapes, FVs are used whereas in regions where the size of the element is too large for finite volumes to provide an accurate answer, the high-order HDG approach is employed with a non-uniform degree of approximation. The proposed method circumvents the need to produce tailored meshes for transient simulations, as required in a low-order context, and also the need to produce high-order curvilinear meshes, as required by high-order methods. Numerical examples are used to test the optimal convergence properties of the combined HDG-FV scheme and to demonstrate its potential in the context of simulating the wind gust effect on aerodynamic shapes.

The Yee finite difference time domain (FDTD) algorithm is widely used in computational electromagnetics because of its simplicity, low computational costs and divergence free nature. The standard method uses a pair of staggered orthogonal cartesian meshes. However, accuracy losses result when it is used for modelling electromagnetic interactions with objects of arbitrary shape, because of the staircased representation of curved interfaces. For the solution of such problems, we generalise the approach and adopt an unstructured mesh FDTD method. This co-volume method is based upon the use of a Delaunay primal mesh and its high quality Voronoi dual. Computational efficiency is improved by employing a hybrid primal mesh, consisting of tetrahedral elements in the vicinity of curved interfaces and hexahedral elements elsewhere. Difficulties associated with ensuring the necessary quality of the generated meshes will be discussed. The power of the proposed solution approach is demonstrated by considering a range of scattering and/or transmission problems involving perfect electric conductors and isotropic lossy, anisotropic lossy and isotropic frequency dependent chiral materials.

Powder metallurgy (PM) refers to a range of engineering techniques whereby net shape or near-net shape bodies are produced through the aggregation of a powder substrate. Specifically, the emergence of Additive Layer Manufacturing (ALM) is an exciting development in this field. However, the quality of any product produced by ALM is highly dependent upon the quality of the powder used. Gas atomisation is a specialised processing route in the PM field for the production of fine, spherical powders directly from a molten metal melt. The close-coupled gas atomisation process involves a melt stream being impacted by high velocity, under-expanded gas jets which initiate its break-up in two distinct phases; the second critical in determining the final particle size distribution (PSD) of the powder produced. However, fully understanding the mechanisms at work and exerting a high level of control over any produced powder is a challenge faced by the powder manufacturing industry; highlighted by the stringent requirements of the new ALM manufacturing technique. Utilising Ansys Fluent v14.5 computational fluid dynamics (CFD) software, a 3D axi-symmetric simulation has been developed of a close-coupled atomising gas jet nozzle configuration utilised by a powder manufacturer. Through the two-way coupling of the CFD with a Discrete Particle Model (DPM) using the Euler–Lagrange approach, an assessment has been made of the effect of process parameters on the final PSD of the metal powders produced. The most appropriate model for the simulation of the secondary break-up phase has been identified from the Kelvin–Helmholtz (KH), Kelvin–Helmholtz Rayleigh-Transport (KHRT) and Taylor Analogy Break-up (TAB) models. Subsequently, the validated simulation approach has been used for the qualitative assessment of the effect of altering the atomising nozzle geometry and process conditions on the average size of powders produced i.e. finer or coarser. It was also established that there is potential for the model to be used as a quantitative predictive tool of powder size; useful for quality control especially when manufacturing powder for use in ALM. However, further development and validation is required for confirmation of this function.

The Modified Cuckoo Search was used to customise the design of a pre-mixer for use in a pressure let-down station heater. This is a true industrial test application for this novel optimisation algorithm. A commercial-off-the-shelf (COTS) mixer was used as a bench mark to assess the impact of Modified Cuckoo Search. In addition to customisation of the pre-mixer’s design using Modified Cuckoo Search, the commercial Ansys Design Exploration v16.0 software was applied to the problem. This package utilises the Non-Dominated Sorted Genetic Algorithm-II (NSGA-II). The results of our study showed that by using these optimisation algorithms at least a 30% improvement in the performance as compared to the COTS design could be achieved. Further to this, it was found that the free and open source Modified Cuckoo Search performed comparatively to the commercial package Ansys. This will be significant for small to medium sized enterprises who are often limited by budget constraints to using off the shelf devices.

We propose an unstructured mesh adaptation approach for unsteady high speed compressible Navier–Stokes applications involving blasts and explosions with the presence of strong shock waves propagating in three dimensional complex domains. The idea is to identify the locations of critical physics locally and then re-mesh these regions based on solution derived metrics. The approach ensures both geometry fidelity and mesh validity, especially for areas near complex geometries, a task that is always a challenge in mesh adaptation. The proposed adaptivity is applied for simulations of blast wave propagations and compared with available data in literature. The results show that the proposed method is fully robust and efficient for computational fluid dynamics (CFD) problems in complex three-dimensional domains.

Summary In this paper, a method is proposed for modeling explosive-driven fragments as spherical particles with a point-particle approach. Lagrangian particles are coupled with a multimaterial Eulerian solver that uses a three-dimensional finite volume framework on unstructured grids. The Euler–Lagrange method provides a straightforward and inexpensive alternative to directly resolving particle surfaces or coupling with structural dynamics solvers. The importance of the drag and inviscid unsteady particle forces is shown through investigations of particles accelerated in shock tube experiments and in condensed phase explosive detonation. Numerical experiments are conducted to study the acceleration of isolated explosive-driven particles at various locations relative to the explosive surface. The point-particle method predicts fragment terminal velocities that are in good agreement with simulations where particles are fully resolved, while using a computational cell size that is eight times larger. It is determined that inviscid unsteady forces are dominating for particles sitting on, or embedded in, the explosive charge. The effect of explosive confinement, provided by multiple particles, is investigated through a numerical study with a cylindrical C4 charge. Decreasing particle spacing, until particles are touching, causes a 30–50% increase in particle terminal velocity and similar increase in gas impulse. Copyright © 2015 John Wiley & Sons, Ltd.

An efficient method for the simulation of compressible multimaterial flows with a general form of equation of state is presented for explosive detonation and airblast applications. Multimaterial flows are modeled with a volume-fraction type approach for immiscible fluids governed by the compressible Euler equations on three-dimensional unstructured grids. The five-equation quasi-conservative system is discretized in space using an edge-based finite volume approach with a second-order accurate HLLC approximate Riemann solver and temporal discretization with an explicit multistage Runge–Kutta method. The computational model is robust enough to handle flows with strong shocks, while being general enough to model materials with different equations of state and physical states. Numerical tests demonstrate the accuracy of the method for strong shock and interface interactions. A program burn method is implemented to describe the conversion of solid unreacted explosive to reacted gases in condensed phase detonations. The accuracy of the burn model is validated by comparison with published numerical results of flow profiles during detonation and for near-field airblast. Numerical simulations of hemispherical and plate-shaped explosive charge detonations are performed to investigate the influence of charge shape on airblast. The predicted pressure and impulse from simulation compare well with published experimental data.

A novel parallel technique that couples the lattice–Boltzmann method and a finite volume scheme for the prediction of concentration polarisation and pore blocking in axisymmetric cross-flow membrane separation process is presented. The model uses the Lattice–Boltzmann method to solve the incompressible Navier–Stokes equations for hydrodynamics and the finite volume method to solve the convection–diffusion equation for solute particles. Concentration polarisation is modelled for micro–particles by having the diffusion coefficient defined as a function of particle concentration and shear rate. The model considers the effect of an incompressible cake formation. Pore blocking phenomenon is predicted for filtration membrane fouling by using the rate of particles arriving at the membrane surface. The simulation code is parallelised in two ways. Compute Unified Device Architecture (CUDA) is used for a cluster of graphical processing units (GPUs) and Message Passing Interface (MPI) is utilised for a cluster of central processing units (CPUs), with various parallelisation techniques to optimise memory usage for higher performance. The proposed model is validated by comparing to analytical solutions and experimental result.

This paper introduces developments in modified techniques for the generation of unstructured, non-uniform, dual orthogonal meshes which are suitable for use with co-volume solution schemes. Two new mesh generation techniques, a modified advancing front technique and an octree-Delaunay algorithm, are coupled with a mesh optimisation algorithm. When using a Delaunay–Voronoi dual, to construct mutually orthogonal meshes for co-volume schemes, it is essential to minimise the number of Delaunay elements which do not contain their Voronoi vertex. These new techniques provide an improvement over previous approaches, as they produce meshes in which the number of elements that do not contain their Voronoi vertex is reduced. In particular, it is found that the optimisation algorithm, which could be applied to any mesh cosmetics problem, is very effective, regardless of the quality of the initial mesh. This is illustrated by applying the proposed approach to a number of complex industrial aerospace geometries.

SUMMARY A new mesh optimisation scheme, reduced order mesh optimisation, is introduced. The technique uses proper orthogonal decomposition to reduce the number of dimensions in a mesh optimisation problem. This reduction in dimensionality allows the expression of the optimisation problem globally rather than the more traditional local mesh optimisation or smoothing algorithms. To perform the optimisation, the recently developed gradient-free technique modified cuckoo search is applied. The effectiveness of the algorithm is shown by considering the problem of optimising meshes for use in co-volume techniques. Co-volume techniques require the existence of two mutually orthogonal meshes; this is achieved by utilising the Delaunay–Voronoi dual. A combination of considering the problem globally and the use of a gradient-free technique results in a scheme that significantly outperforms previous methods in solving this particular problem. Although the examples presented in this paper are specific to optimising dual meshes, the technique is general and can be simply modified to any mesh optimisation problem. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, an alternative approach to the traditional continuum analysis of flow problems is presented. The traditional methods, that have been popular with the CFD community in recent times, include potential flow, Euler and Navier–Stokes solvers. The method presented here involves solving the governing equation of the molecular gas dynamics that underlies the macroscopic behaviour described by the macroscopic governing equations. The equation solved is the Boltzmann kinetic equation in its simplified collisionless and BGK forms. The algorithm used is a discontinuous Taylor–Galerkin type and it is applied to the 2D problems of a highly rarefied gas expanding into a vacuum, flow over a vertical plate, rarefied hypersonic flow over a double ellipse, and subsonic and transonic flow over an aerofoil. The benefit of this type of solver is that it is not restricted to continuum regime (low Knudsen number) problems. However, it is a computationally expensive technique.

A finite volume method for the simulation of compressible aerodynamic flows is de- scribed. Stabilisation and shock capturing is achieved by the use of an HLLC consistent numerical flux function, with acoustic wave improvement. The method is implemented on an unstructured hybrid mesh in three dimensions. A solution of higher order accuracy is obtained by reconstruc- tion, using an iteratively corrected least squares process, and by a new limiting procedure. The numerical performance of the complete approach is demonstrated by considering its application to the simulation of steady turbulent transonic flow over an ONERA M6 wing and to a steady inviscid supersonic flow over a modern military aircraft configuration.

This paper presents a fully coupled three-dimensional solver for the analysis of time-dependent fluid-structure interaction. A partitioned time marching algorithm is employed for the solution of the time-dependent coupled discretised problem, enabling the use of highly developed, robust and well-tested solvers for each field. Conservative transfer of information at the fluid-structure interface is combined with an effective block-Gauss-Seidel iterative scheme to enable implicit coupling of the interacting fields at each time increment. The three-dimensional unsteady incompressible fluid is solved using a powerful implicit dual time stepping technique with explicit multi-stage Runga-Kutta time stepping in pseudo-time and an ALE formulation for moving boundaries. A finite element dynamic analysis of the highly deformable structure is carried out with a numerical strategy combining the implicit Newmark time integration algorithm with a Newton-Raphson second-order optimisation method. Test cases are presented to benchmark the algorithm and to demonstrate the potential applications of this method.

The BLOODHOUND SSC project was publicly announced in October 2008, with a primary engineering objective of designing, constructing and running a vehicle capable of achieving a speed of 1000 mph on land. The aerodynamic design of this vehicle is to be accomplished using computational simulation only and this paper describes the development and application of the approach adopted. The computational model employs a cell vertex finite volume algorithm for the solution of compressible viscous flow problems on unstructured hybrid meshes. A one equation turbulence model is adopted and the solution of the steady flow equations is obtained by explicit relaxation. For the combination of high Mach number, complex geometry and complex boundary conditions, involving rotating surfaces and a rolling ground, a consistent HLLC numerical flux function is adopted to ensure a stable procedure. To illustrate the impact of the approach upon the final configuration, a number of simulations undertaken to aid the aerodynamic design are described. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010

The Yee algorithm is a highly efficient time domain co-volume method for computational electromagnetics using a pair of staggered orthogonal cartesian meshes. An equivalent unstructured mesh process is readily implemented on a primal Delaunay tetrahedral mesh and its orthogonal Voronoi dual. The difficulty, for practical applications, is ensuring that both the Delaunay and the Voronoi meshes possess the necessary properties to enable an accurate and efficient solution to be obtained by this approach. This is a mesh generation problem and it is addressed here by using a combination of a point distribution provided by an ideal tetrahedral mesh, a constrained centroidal Voronoi tessellation method and a mesh quality optimization procedure. For the selected application area of electromagnetic wave scattering problems, the computational efficiency is enhanced by using a hybrid primal mesh, consisting of tetrahedral elements in the vicinity of the scatterer and hexahedral elements elsewhere. Three examples are included to demonstrate the viability of the proposed approach and to indicate the numerical performance that can be achieved. Copyright © 2010 John Wiley & Sons, Ltd.

The numerical solution of Maxwell's curl equations in the time domain is achieved by combining an unstructured mesh finite element algorithm with a cartesian finite difference method. The practical problem area selected to illustrate the application of the approach is the simulation of three-dimensional electromagnetic wave scattering. The scattering obstacle and the free space region immediately adjacent to it are discretized using an unstructured mesh of linear tetrahedral elements. The remainder of the computational domain is filled with a regular cartesian mesh. These two meshes are overlapped to create a hybrid mesh for the numerical solution. On the cartesian mesh, an explicit finite difference method is adopted and an implicit/explicit finite element formulation is employed on the unstructured mesh. This approach ensures that computational efficiency is maintained if, for any reason, the generated unstructured mesh contains elements of a size much smaller than that required for accurate wave propagation. A perfectly matched layer is added at the artificial far field boundary, created by the truncation of the physical domain prior to the numerical solution. The complete solution approach is parallelized, to enable large-scale simulations to be effectively performed. Examples are included to demonstrate the numerical performance that can be achieved.

The development of a hybrid high order time domain finite element solution procedure for the simulation of two dimensional problems in computational electromagnetics is considered. The chosen application area is that of electromagnetic scattering. The spatial approximation adopted incorporates both a continuous Galerkin spectral element method and a high order discontinuous Galerkin method. Temporal discretisation is achieved by means of a fourth order Runge–Kutta procedure. An exact analytical solution is employed initially to validate the procedure and the numerical performance is then demonstrated for a number of more challenging examples.

PurposeThe purpose of this paper is to present an adaptive finite element procedure that improves the quality of convection dominated mid‐ocean ridge (MOR) and subduction zone (SZ) simulations in geodynamics.Design/methodology/approachThe method adapts the mesh automatically around regions of high‐solution gradient, yielding enhanced resolution of the associated flow features. The approach utilizes an automatic, unstructured mesh generator and a finite element flow solver. Mesh adaptation is accomplished through mesh regeneration, employing information provided by an interpolation‐based local error indicator, obtained from the computed solution on an existing mesh.FindingsThe proposed methodology works remarkably well at improving solution accuracy for both MOR and SZ simulations. Furthermore, the method is computationally highly efficient.Originality/valueTo date, successful goal‐orientated/error‐guided grid adaptation techniques have, to the knowledge, not been utilized within the field of geodynamics. This paper presents the first true geodynamical application of such methods.

The standard Yee algorithm is widely used in computational electromagnetics because of its simplicity and divergence free nature. A generalization of the classical Yee scheme to 3D unstructured meshes is adopted, based on the use of a Delaunay primal mesh and its high quality Voronoi dual. This allows the problem of accuracy losses, which are normally associated with the use of the standard Yee scheme and a staircased representation of curved material interfaces, to be circumvented. The 3D dual mesh leapfrog-scheme which is presented has the ability to model both electric and magnetic anisotropic lossy materials. This approach enables the modelling of problems, of current practical interest, involving structured composites and metamaterials.

This paper outlines a new computational aerodynamic design optimisation algorithm using a novel method of parameterising a computational mesh using ‘control nodes’. The shape boundary movement as well as the mesh movement is coupled to the movement of user–defined control nodes via a Delaunay Graph Mapping technique. A Modified Cuckoo Search algorithm is employed for optimisation within the prescribed design space defined by the allowed range of control node displacement. A finite volume compressible Navier–Stokes solver is used for aerodynamic modelling to predict aerodynamic design ‘fitness’. The resulting coupled algorithm is applied to a range of test cases in two dimensions including aerofoil lift–drag ratio optimisation intake duct optimisation under subsonic, transonic and supersonic flow conditions. The discrete (mesh–based) optimisation approach presented is demonstrated to be effective in terms of its generalised applicability and intuitiveness.

A review of a procedure for the simulation of time-dependent, inviscid and turbulent viscous, compressible flows involving geometries that change in time is presented. The adopted discretization technique employs unstructured meshes and both explicit and implicit time-stepping schemes. A dual time-stepping procedure and an ALE formulation enable flows involving moving boundary components to be included. Techniques that have been developed to maintain the validity of the unstructured mesh and to allow for the capture of moving flow features are also reviewed. Using the in-house developed techniques, some examples are included to demonstrate the use of the approach for the simulation of a number of flows of practical industrial interest.