Publications
401 results found
Moura RC, Fernandes LD, da Silva AFC, et al., 2024, Joint-mode diffusion analysis of discontinuous Galerkin methods: Towards superior dissipation estimates for nonlinear problems and implicit LES, Journal of Computational Physics, Vol: 505, ISSN: 0021-9991
We present a new linear eigensolution analysis technique that provides superior estimates of dissipation distribution in wavenumber space for the discontinuous Galerkin (DG) method. The technique builds upon traditional dispersion-diffusion analyses that have been applied to spectral/hp element methods, but in particular is an improvement upon the non-modal eigenanalysis approach proposed by Fernandez et al. in [1]. The present technique takes into account the indirect effects that dispersion may have on dissipation, as recently discussed by Moura et al. in [2], in order to better represent dissipation itself. Also, a concept often used with dynamic mode decomposition (DMD) techniques is invoked to weight the relative contribution of the multiple diffusion curves that stem from temporal eigenanalysis. This allows for obtaining a single dissipation profile in wavenumber space, so that the proposed technique is named joint-mode analysis. Although the non-modal approach also provides a single diffusion curve, the joint-mode dissipation curve is shown to correlate significantly better with the energy spectrum of Burgers' turbulence at large and intermediate scales, which is particularly relevant for implicit large-eddy simulation (LES). The proposed technique is readily extensible to other spectral/hp element methods.
Green MD, Kirilov KS, Turner M, et al., 2024, NekMesh: An open-source high-order mesh generation framework, Computer Physics Communications, Vol: 298, ISSN: 0010-4655
High-order spectral element simulations are now becoming increasingly popular within the computational modelling community, as they offer the potential to deliver increased accuracy at reduced cost compared to traditional low-order codes. However, to support accurate, high-fidelity simulations in complex industrial applications, there is a need to generate curvilinear meshes which robustly and accurately conform to geometrical features. This is, at present, a key challenge within the mesh generation community, with only a few open-source tools able to generate curvilinear meshes for complex geometries. We present NekMesh: an open-source mesh generation package which is designed to enable the generation of valid, high-quality curvilinear meshes of complex, three-dimensional geometries for performing high-order simulations. We outline the software architecture adopted in NekMesh, which uses a pipeline of processing modules to provide a flexible, CAD-independent high-order mesh processing tool, capable of both generating meshes for a wide range of use cases, as well as post-processing linear meshes from a range of input formats for use with high-order simulations. A number of examples in various application areas are presented, with a particular emphasis on challenging aeronautical and fluid dynamics test cases. Program summary: Program title: NekMesh (version 5.4.0) CPC Library link to program files: https://doi.org/10.17632/d82hjm4v6r.1 Licensing provisions: MIT Programming language: C++ External routines/libraries: Boost, TinyXML, OpenCASCADE, Triangle, TetGen, HDF5 Nature of problem: NekMesh is a high-order mesh generation framework with the goal of providing a robust framework to automate the process of generating valid meshes for complex three-dimensional CAD geometries. Solution method: Energy minimisation, solid body models and other techniques based around high-order finite element methods. Additional comments including restrictions and unusual features: The s
Gao AK, Cantwell CD, Son O, et al., 2023, Three-dimensional transition and force characteristics of low-Reynolds-number flows past a plunging airfoil, Journal of Fluid Mechanics, Vol: 973, ISSN: 0022-1120
The three-dimensional (3-D) transition of the leading-edge vortex (LEV) and the force characteristics of the plunging airfoil are investigated in the chord-based Strouhal number Stc range of 0.10 to 1.0 by means of experimental measurements, numerical simulations and linear stability analysis in order to understand the spanwise instabilities and the effects on the force. We find that the interaction pattern of the LEV, the LEV from a previous cycle (pLEV) and the trailing-edge vortex (TEV) is the primary mechanism that affects the 3-D transition and associated force characteristics. For Stc ≤ 0.16, the 3-D transition is dominated by the LEV-TEV interaction. For 0.16 < Stc ≤ 0.44, the TEV lies in the middle of the LEV and the pLEV and therefore vortex interaction between them is relatively weak; as a result, the LEV remains two-dimensional up to a relatively high Reynolds number of Re = 4000 at Stc = 0.32. For 0.44 < Stc ≤ 0.54, and at relatively low Reynolds numbers, the pLEV and the TEV tend to form a clockwise vortex pair, which is beneficial for the high lift and stability of the LEV. For 0.49 ≤ Stc, the pLEV and TEV tend to form an anticlockwise vortex pair, which is detrimental to the lift and flow stability. In the last Stc range, vortex interaction involving the LEV, the TEV and the pLEV results in an unstable period-doubling mode which has a wavelength of about two chord-lengths and the 3-D transition enhances the lift.
Moxey D, Sherwin S, Lahoot M, et al., 2023, Nektar++ updates and future developments
Arshad M, Cheng S, van Reeuwijk M, et al., 2023, Modification of the swirling well cell culture model to alter shear stress metrics, BIOTECHNOLOGY AND BIOENGINEERING, Vol: 120, Pages: 1254-1268, ISSN: 0006-3592
Lyu G, Chen C, Du X, et al., 2023, Stable, entropy-pressure compatible subsonic Riemann boundary condition for embedded DG compressible flow simulations, Journal of Computational Physics, Vol: 476, Pages: 1-22, ISSN: 0021-9991
One approach to reducing the computational cost of simulating transitional compressible boundary layer flow is to adopt a near body reduced domain with boundary conditions enforced to be compatible with a computationally cheaper three-dimensional RANS simulation. In such an approach it is desirable to enforce a consistent pressure distribution which is not typically the case when using the standard Riemann inflow boundary conditions. We therefore revisit the Riemann problem adopted in many DG based high fidelity formulations.Through analysis of the one-dimensional linearized Euler equations it is demonstrated that maintaining entropy compatibility with the RANS simulation is important for a stable solution. It is also necessary to maintain the invariant for the Riemann outflow boundary condition in a subsonic flow leaving one condition that can be imposed at the inflow boundary. Therefore the entropy-pressure enforcement is the only stable boundary condition to enforce a known pressure distribution. We further demonstrate that all the entropy compatible inflow Riemann boundary conditions are stable providing the invariant compatible Riemann outflow boundary condition is also respected.Although the entropy-pressure compatible Riemann inflow boundary condition is stable from the one-dimensional analysis, two-dimensional tests highlight divergence in the inviscid problem and neutrally stable wiggles in the velocity fields in viscous simulations around the stagnation point. A two-dimensional analysis about a non-uniform baseflow assumption provides insight into this stability issue (ill-posedness) and motivates the use of a mix of inflow boundary conditions in this region of the flow.As a validation we apply the proposed boundary conditions to a reduced domain of a wing section normal to the leading-edge of the CRM-NLF model taken out of a full three-dimensional RANS simulation at Mach 0.86 and a Reynolds number of 8.5 million. The results show that the entropy-pressure
Slaughter J, Moxey D, Sherwin S, 2023, Large Eddy Simulation of an Inverted Multi-element Wing in Ground Effect, FLOW TURBULENCE AND COMBUSTION, ISSN: 1386-6184
Lindblad D, Sherwin SJ, Cantwell C, et al., 2023, Large Eddy simulations of isolated and installed jet noise using the high-order discontinuous Galerkin method, AIAA SCITECH 2023 Forum, Publisher: American Institute of Aeronautics and Astronautics, Pages: 1-21
A recently developed computational framework for jet noise is used to compute the noise generated by an isolated and installed jet. The framework consists of two parts. In the first part, the spectral/hp element framework Nektar++ is used to compute the near-field flow. Nektar++ solves the unfiltered Navier-Stokes equations on unstructured grids using the high-order discontinuous Galerkin method. The discrete equations are integrated in time using an implicit scheme based on the matrix-free Newton-GMRES method. In the second part, the Antares library is used to compute the far-field noise. Antares solves the Ffowcs Williams - Hawkings equation for a permeable integration surface in the time domain using a source-time dominant algorithm. The simulations are validated against experimental data obtained in the Doak Laboratory Flight Jet Rig, located at the University of Southampton. For the isolated jet, good agreement is achieved, both in terms of the flow statistics and the far-field noise. The discrepancies observed for the isolated jet are believed to be caused by an under-resolved boundary layer in the simulations. For the installed jet, the flow statistics are also well predicted. In the far-field, very good agreement is achieved for downstream observers. For upstream observers, some discrepancies are observed for very high and very low frequencies.
Yan ZG, Pan Y, Peiró J, et al., 2023, Eigenspectral Analysis of Preconditioners in an Adaptive Compressible Flow Solver, Pages: 521-532, ISSN: 1439-7358
An implicit-in-time discontinuous Galerkin (DG) solver has been developed for compressible flows, which adopts an adaptive time stepping strategy balancing different discretization errors. To study the effects of preconditioning for further speed-up, preconditioners based on Jacobi iteration, Gauss-Seidel iteration, incomplete LU factorization, and p-multigrid are studied using eigenspectral analysis and numerical experiments. The condition number and eigenvalue distributions are studied based on a lid-driven flow. The preliminary results show that the eigenspectral analysis can correctly reflect preconditioning effects and the p-multigrid method is highly dependent on the smoother adopted.
Marioni YF, Adami P, Montomoli F, et al., 2023, MACHINE-LEARNT TURBULENCE CLOSURES FOR AXIAL COMPRESSOR CASCADE WITH CORNER SEPARATION
Corner separation in axial compressors is a complex phenomenon, which is hardly well captured by traditional steady RANS calculations, primarily because of the deficiencies of the Reynolds stress tensor formulations. In this work a Machine Learning (ML) framework is applied to Large-Eddy Simulation (LES) data to develop non-linear turbulence stress closures. Two linear compressor cascade LES calculations are run with the Rolls-Royce solver HYDRA: one at nominal incidence condition, for which no corner separation is observed, and one at high incidence, where more complex secondary flow structures and recirculation appear. The two cases are validated against experiments performed in the linear cascade facility at LMFA, Lyon. A transitional variant of Wilcox's k−ω SST is used as baseline turbulence model and traditional closures are found to perform well at nominal conditions, but poorly at higher incidence, as they strongly over-predict losses and secondary flows. The coefficients of an Explicit Algebraic Reynolds Stress Model (EARSM) are trained using Artificial Neural Networks (ANN) on the high incidence dataset. When tested in HYDRA, improvements are observed in the prediction of end-wall losses, as well as vorticity and Reynolds stress contours downstream of the separation region. The model also performs well at nominal incidence. The importance of a near-wall coefficient damping is discussed. Finally, end-wall loss polars are computed and compared for different non-linear constitutive relationships.
Isler J, Vivarelli G, Montomoli F, et al., 2023, High Fidelity Compressible and Incompressible Flow Simulations of an Engine Intake Pressure Distribution
In this work, we investigated the impact of compressibility of an engine intake pressure distribution at high Reynolds numbers in absence of transonic effects and under strong adverse pressure gradients on a flate plate by means of computational simulations. In order to assess the compressibility effects in the vicinity and over the flat plate surface, compressible and incompressible high-order Implicit Large Eddy Simulations (iLES) of the Navier-Stokes (NS) equations were performed using the Nektar++ framework. With this methodology, we were able to assert what are the physical mechanisms behind the turbulent transition processes. In addition, and crucially, what role the compressibility is playing in this flow configuration, in order to promote the design of improved geometries using high-order methods. Therefore, a consistent investigation of the density variation effects and boundary layer behaviours of the compressible and incompressible solutions provided the necessary understanding of the viscous driven separation that governs the flow in an engine intake at moderate fan speed.
Vivarelli G, Isler JA, Williams TS, et al., 2023, ON THE EFFECT OF CURVATURE AND COMPRESSIBILITY IN LAMINAR BOUNDARY LAYERS OVER FAN BLADES
During the early phases of the turbomachinery design process, it is often the case that various simplifications and assumptions are made to understand boundary layer behaviour subject to pressure gradients. For example, simplified boundary-layer models can be employed to appreciate losses incurred in flows over gas turbine components. These neglect the effect of surface curvature and/or density, while retaining the surface pressure distribution. This paper's objective is to assess the implication of those simplifications by studying a realistic fan loading and the status of the boundary layer just upstream of a shock. A set of 2D aerofoils, representing the pressure distribution found at 70% and 90% span of a modern low-speed fan, are analysed at cruise conditions. In order to investigate compressibility, the two profiles were redesigned to achieve exactly the same pressure loading at incompressible conditions. On the other hand, curvature effects were studied by means of a comparison of incompressible flow over the symmetric aerofoil and a convergent-convergent nozzle, once again with the same loading. The resulting laminar boundary layer quantities were compared explaining the necessary scaling required along with the reasons behind the discrepancies, such as the effect of density and curvature variations. All test-cases were analysed deploying Nektar++. This is a high-order spectral h/p element solver having both compressible and incompressible formulations.
Marioni YF, Adami P, Montomoli F, et al., 2023, MACHINE-LEARNT TURBULENCE CLOSURES FOR AXIAL COMPRESSOR CASCADE WITH CORNER SEPARATION, ISSN: 2313-0067
Corner separation in axial compressors is a complex phenomenon, which is hardly well captured by traditional steady RANS calculations, primarily because of the deficiencies of the Reynolds stress tensor formulations. In this work a Machine Learning (ML) framework is applied to Large-Eddy Simulation (LES) data to develop non-linear turbulence stress closures. Two linear compressor cascade LES calculations are run with the Rolls-Royce solver HYDRA: one at nominal incidence condition, for which no corner separation is observed, and one at high incidence, where more complex secondary flow structures and recirculation appear. The two cases are validated against experiments performed in the linear cascade facility at LMFA, Lyon. A transitional variant of Wilcox's k−ω SST is used as baseline turbulence model and traditional closures are found to perform well at nominal conditions, but poorly at higher incidence, as they strongly over-predict losses and secondary flows. The coefficients of an Explicit Algebraic Reynolds Stress Model (EARSM) are trained using Artificial Neural Networks (ANN) on the high incidence dataset. When tested in HYDRA, improvements are observed in the prediction of end-wall losses, as well as vorticity and Reynolds stress contours downstream of the separation region. The model also performs well at nominal incidence. The importance of a near-wall coefficient damping is discussed. Finally, end-wall loss polars are computed and compared for different non-linear constitutive relationships.
Isler J, Vivarelli G, Montomoli F, et al., 2023, High Fidelity Compressible and Incompressible Flow Simulations of an Engine Intake Pressure Distribution, ISSN: 2313-0067
In this work, we investigated the impact of compressibility of an engine intake pressure distribution at high Reynolds numbers in absence of transonic effects and under strong adverse pressure gradients on a flate plate by means of computational simulations. In order to assess the compressibility effects in the vicinity and over the flat plate surface, compressible and incompressible high-order Implicit Large Eddy Simulations (iLES) of the Navier-Stokes (NS) equations were performed using the Nektar++ framework. With this methodology, we were able to assert what are the physical mechanisms behind the turbulent transition processes. In addition, and crucially, what role the compressibility is playing in this flow configuration, in order to promote the design of improved geometries using high-order methods. Therefore, a consistent investigation of the density variation effects and boundary layer behaviours of the compressible and incompressible solutions provided the necessary understanding of the viscous driven separation that governs the flow in an engine intake at moderate fan speed.
Vivarelli G, Isler JA, Williams TS, et al., 2023, ON THE EFFECT OF CURVATURE AND COMPRESSIBILITY IN LAMINAR BOUNDARY LAYERS OVER FAN BLADES, ISSN: 2313-0067
During the early phases of the turbomachinery design process, it is often the case that various simplifications and assumptions are made to understand boundary layer behaviour subject to pressure gradients. For example, simplified boundary-layer models can be employed to appreciate losses incurred in flows over gas turbine components. These neglect the effect of surface curvature and/or density, while retaining the surface pressure distribution. This paper's objective is to assess the implication of those simplifications by studying a realistic fan loading and the status of the boundary layer just upstream of a shock. A set of 2D aerofoils, representing the pressure distribution found at 70% and 90% span of a modern low-speed fan, are analysed at cruise conditions. In order to investigate compressibility, the two profiles were redesigned to achieve exactly the same pressure loading at incompressible conditions. On the other hand, curvature effects were studied by means of a comparison of incompressible flow over the symmetric aerofoil and a convergent-convergent nozzle, once again with the same loading. The resulting laminar boundary layer quantities were compared explaining the necessary scaling required along with the reasons behind the discrepancies, such as the effect of density and curvature variations. All test-cases were analysed deploying Nektar++. This is a high-order spectral h/p element solver having both compressible and incompressible formulations.
Lahooti M, Bao Y, Scott D, et al., 2023, LES/DNS fluid-structure interaction simulation of non-linear slender structures in<i> Nektar plus plus </i> framework, COMPUTER PHYSICS COMMUNICATIONS, Vol: 282, ISSN: 0010-4655
Moura RC, Fernandes LD, Silva AFC, et al., 2022, Spectral/hp element methods' linear mechanism of (apparent) energy transfer in Fourier space: Insights into dispersion analysis for implicit LES, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 471, ISSN: 0021-9991
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- Citations: 2
Weinberg P, Kandangwa P, Torii R, et al., 2022, Influence of right coronary artery motion, flow pulsatility and non-Newtonian rheology on wall shear stress metrics, Fontiers in Bioengineering and Biotechnology, Vol: 10, Pages: 1-14, ISSN: 2296-4185
The patchy distribution of atherosclerosis within the arterial system is consistent with a controlling influence of hemodynamic wall shear stress (WSS). Patterns of low, oscillatory and transverse WSS have been invoked to explain the distribution of disease in the aorta. Disease of coronary arteries has greater clinical importance but blood flow in these vessels may be complicated by their movement during the cardiac cycle. Previous studies have shown that time average WSS is little affected by the dynamic geometry, and that oscillatory shear is influenced more. Here we additionally investigate effects on transverse WSS. We also investigate the influence of non-Newtonian blood rheologyas it can influence vortical structure, on which transverse WSS depends; Carreau-Yasuda models were used. WSS metrics were derived from numerical simulations of blood flow in a model of a moving right coronary artery which, together with a subject-specific inflow waveform, was obtained by MR imaging of a healthy human subject in a previous study. The results confirmed that time average WSS was little affected by dynamic motion, and that oscillatory WSS was more affected. They additionally showed that transverse WSS and its non-dimensional analogue, the Cross Flow Index, were affected still further. This appeared to reflect time-varying vortical structures caused by the changes in curvature. The influence of non-Newtonian rheology was significant with some physiologically realistic parameter values, and hence may be important in certain subjects. Dynamic geometry and non-Newtonian rheology should be incorporated into models designed to produce maps of transverse WSS in coronary arteries.
Chun S, Marcon J, Peiro J, et al., 2022, Reducing errors caused by geometrical inaccuracy to solve partial differential equations with moving frames on curvilinear domain, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, Vol: 398, ISSN: 0045-7825
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Lyu G, Chen C, Du X, et al., 2022, Open-source Framework for Transonic Boundary Layer Natural Transition Analysis over Complex Geometries in Nektar++, AIAA Aviation 2022 Forum
Xu H, Tu G, Sherwin SJ, 2022, Theoretical advances and applications of high-fidelity computation and modelling in fluid dynamics, COMPUTERS & FLUIDS, Vol: 241, ISSN: 0045-7930
Lindblad D, Sherwin S, Cantwell C, et al., 2022, Aeroacoustic analysis of a subsonic jet using the discontinuous Galerkin method, 28th AIAA/CEAS Aeroacoustics 2022 Conference, Publisher: American Institute of Aeronautics and Astronautics, Pages: 1-21
In this work, the open-source spectral/hp element framework Nektar++ is coupled with the Antares library to predict noise from a subsonic jet. Nektar++ uses the high-order discontinuous Galerkin method to solve the compressible Navier-Stokes equations on unstructured grids. Unresolved turbulent scales are modeled using an implicit Large Eddy Simulation approach. In this approach, the favourable dissipation properties of the discontinuous Galerkin method are used to remove the highest resolved wavenumbers from the solution. For time-integration, an implicit, matrix-free, Newton-Krylov method is used. To compute the far-field noise, Antares solves the Ffowcs Williams - Hawkings equation for a permeable integration surface in the time-domain using a source-time dominant algorithm. The simulation results are validated against experimental data obtained in the Doak Laboratory Flight Jet Rig, located at the University of Southampton.
Son O, Gao A, Gursul I, et al., 2022, Leading-edge vortex dynamics on plunging airfoils and wings, Journal of Fluid Mechanics, Vol: 940, Pages: 1-30, ISSN: 0022-1120
The vortex dynamics of leading-edge vortices on plunging high-aspect-ratio (AR = 10) wings and airfoils were investigated by means of volumetric velocity measurements, numerical simulations, and stability analysis in order to understand the deformation of the leading-edge vortex filament and spanwise instabilities. The vortex filaments on both the wing and airfoilexhibit spanwise waves, but with different origins. The presence of a wing tip causes the leg of the vortex to remain attached to the wing upper surface, while the initial deformation of the filament near the wing-tip resembles a helical vortex. The essential features can be modelled as the deformation of initially L-shaped semi-infinite vortex column. In contrast, the instabilityof the vortices is well captured by the instability of counter-rotating vortex pairs, which are formed either by the trailing-edge vortices or the secondary vortices rolled-up from the wing surface. The wavelengths observed in the experiments and simulations are in agreement with the stability analysis of counter-rotating vortex pairs of unequal strength.
Pan Y, Yan Z-G, Peiro J, et al., 2022, Development of a balanced adaptive time-stepping strategy based on an implicit JFNK-DG compressible flow solver, Communications on Applied Mathematics and Computation, Vol: 4, Pages: 728-757, ISSN: 2661-8893
A balanced adaptive time-stepping strategy is implemented in an implicit discontinuous Galerkin solver to guarantee the temporal accuracy of unsteady simulations. A proper relation between the spatial, temporal and iterative errors generated within one time step is constructed. With an estimate of temporal and spatial error using an embedded Runge-Kutta scheme and a higher order spatial discretization, an adaptive time-stepping strategy is proposed based on the idea that the time step should be the maximum without obviously influencing the total error of the discretization. The designed adaptive time-stepping strategy is then tested in various types of problems including isentropic vortex convection, steady-state flow past a flat plate, Taylor-Green vortex and turbulent flow over a circular cylinder at Re=3900. The results indicate that the adaptive time-stepping strategy can maintain that the discretization error is dominated by the spatial error and relatively high efficiency is obtained for unsteady and steady, well-resolved and under-resolved simulations.
Hambli W, Slaughter J, Buscariolo FF, et al., 2022, Extension of Spectral/hp Element Methods towards Robust Large-Eddy Simulation of Industrial Automotive Geometries, FLUIDS, Vol: 7
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Cassinelli A, Mateo Gabín A, Montomoli F, et al., 2022, Reynolds sensitivity of the wake passing effect on a LPT cascade using spectral/hp element methods, International Journal of Turbomachinery, Propulsion and Power, Vol: 7, Pages: 8-8, ISSN: 2504-186X
Reynolds-Averaged Navier–Stokes (RANS) methods continue to be the backbone of CFD-based design; however, the recent development of high-order unstructured solvers and meshing algorithms, combined with the lowering cost of HPC infrastructures, has the potential to allow for the introduction of high-fidelity simulations in the design loop, taking the role of a virtual wind tunnel. Extensive validation and verification is required over a broad design space. This is challenging for a number of reasons, including the range of operating conditions, the complexity of industrial geometries and their relative motion. A representative industrial low pressure turbine (LPT) cascade subject to wake passing interactions is analysed, adopting the incompressible Navier–Stokes solver implemented in the spectral/hp element framework Nektar++. The bar passing effect is modelled by leveraging a spectral-element/Fourier Smoothed Profile Method. The Reynolds sensitivity is analysed, focusing in detail on the dynamics of the separation bubble on the suction surface as well as the mean flow properties, wake profiles and loss estimations. The main findings are compared with experimental data, showing agreement in the prediction of wake traverses and losses across the entire range of flow regimes, the latter within 5% of the experimental measurements.
Liu B, Cantwell CD, Moxey D, et al., 2022, VECTORISED SPECTRAL/HP ELEMENT MATRIX-FREE OPERATOR FOR ANISOTROPIC HEAT TRANSPORT IN TOKAMAK EDGE PLASMA
A highly efficient matrix-free Helmholtz operator with single-instruction multipledata (SIMD) vectorisation is implemented in Nektar++ [1] and applied to the simulation of anisotropic heat transport in tokamak edge plasma. A tokamak is currently the leading candidate for a practical fusion reactor using the magnetic confinement approach to produce electricity through controlled thermonuclear fusion. Predicting the transport of heat in magnetized plasma is important to designing a safe tokamak design. Due to the ionized nature of plasma, the heat conduction of the magnetized plasma is highly anisotropic along the magnetic field lines. In this study, a variational form is proposed to simulate the anisotropic heat transport in magnetized plasma and the details of its mathematical derivation and implementation are presented. To accurately approximate the thermal load of plasma deposition on the wall of tokamak chamber, highly scalable and efficient algorithms are crucial. To achieve this, a matrix-free Helmholtz operator is implemented in the Nektar++ framework, utilising sum-factorisation to reduce the operation count and increase arithmetic intensity, and leveraging SIMD vectorisation to accelerate the computation on modern hardware. The performance of the implementation is assessed by measuring throughput and speed-up of the operators using deformed and regular quadrilateral and triangular elements.
Marioni YF, Cassinelli A, Adami P, et al., 2022, DEVELOPMENT OF MACHINE-LEARNT TURBULENCE CLOSURES FOR WAKE MIXING PREDICTIONS IN LOW-PRESSURE TURBINES
In this work, a DNS – Machine Learning (ML) framework is developed for low-pressure turbine (LPT) profiles to inform turbulence closures in Reynolds-Averaged Navier–Stokes (RANS) calculations. This is done by training the coefficients of Explicit Algebraic Reynolds Stress Models (EARSM) with shallow artificial neural networks (ANN) as a function of input flow features. DNS data are generated with the incompressible Navier–Stokes solver in Nektar++ and validated against experiments. All calculations include moving bars upstream of the profile to capture the effect of incoming wakes. The resulting formulations are then implemented in the Rolls-Royce solver HYDRA and tested a posteriori. The aim is to improve mixing predictions in LPT wakes, compared to the baseline model, Wilcox’s k− ω SST, in terms of velocity profiles, turbulent kinetic energy (TKE) production and mixing losses. LPT calculations are run at Reynolds numbers spanning from ≈ 80k to ≈ 300k, to cover the range of aircraft engine applications. Models for the low and high Reynolds datasets are trained separately and a method is developed to merge the two together. The resulting model is tested on an intermediate Reynolds case. This process is followed for two computational domains: one starting downstream of the profile trailing edge and one including the last portion of the profile. Finally, the developed closures are tested on the entire profile, to confirm the validity of the improvements when the additional effect of transition is included in the simulation. This work explains the methodology used to develop ML-driven closures and shows how it is possible to combine models trained on different datasets.
Vivarelli G, Isler JA, Montomoli F, et al., 2022, HIGH-ORDER SPECTRAL/HP COMPRESSIBLE AND INCOMPRESSIBLE COMPARISON OF TRANSITIONAL BOUNDARY-LAYERS SUBJECT TO A REALISTIC PRESSURE GRADIENT AND HIGH REYNOLDS NUMBER
Within the literature, there are limited high-order results concerning large Reynolds number flows under the influence of strong adverse pressure gradients, mainly due to the computational expense involved. The main advantage in employing high-order methodologies over standard second-order finite-volume solvers, relates to their ability to increase accuracy with a significantly lower number of degrees of freedom. In theory, this would permit Direct Numerical Simulation sort of analysis. Yet, there is still a significant computational cost involved. For this reason, an efficient approach to analyse such flows by means of a Nektar++ high-order Implicit Large Eddy Simulation is proposed. The flow conditions considered in this case cause a separation bubble to form with consequent turbulent transition. In particular, Tollmien-Schlichting instabilities trigger Kelvin-Helmholtz behaviour, which in turn cause the turbulent transition. The bulk of the study will be carried out with the incompressible flow solver, as it is assumed that compressibility effects are negligible within the boundary layer. An initial 2D analysis will be conducted to determine the necessary spatial resolution and whether it is possible to consider a subset of the overall simulation domain to reduce the computational expense. Once this will have been established, the 3D results will be achieved by Fourier expansion in the cross-flow direction. These results will prove the cost-effectiveness of the methodology, that could be used within an industrial setting with a limited turn-around time. Additionally, a comparison between the results achieved by means of the Nektar++ compressible flow solver in 2D and 3D will be provided, to assess any differences that may be present.
Gao AK, Sherwin SJ, Cantwell CD, 2022, THREE-DIMENSIONAL TRANSITION OF A LOW REYNOLDS NUMBER FLOW PAST A PLUNGING NACA 0012 AIRFOIL AT POST-STALL ANGLE OF ATTACK
The two-dimensional to three-dimensional transition of a flow past a plunging NACA 0012 airfoil at a Reynolds number of Re = 400, based on the chord length c, and an angle of attack of 15 degrees was investigated using global linear stability analysis and spanwise-homogeneous direct numerical simulation (DNS). The peak-to-peak plunging amplitude was fixed at A/c = 0.5 and the Strouhal number was varied from Stc = 0.10 to Stc = 1.00. This parameter regime encompasses flow phenomena of leading-edge vortex (LEV) dominated flow (0.10 ≤ Stc ≤ 0.19), almost vanishing LEV-trailing-edge vortex (TEV) interaction (0.22 ≤ Stc < 0.5), strong previous cycle LEV-TEV interaction (0.49 ≤ Stc ≤ 0.95) and aperiodic flow (Stc ≥ 0.99). For the periodic baseflow, Floquet stability analysis was conducted. Below a Strouhal number of 0.5, the Floquet multiplier is smaller than the static airfoil which indicates the plunging motion stabilises the two-dimensional baseflow. For higher frequencies, a period-doubling mode appears, which has a peak Floquet multiplier around a spanwise wavelength of 2c. This unstable mode also dominates in three-dimensional direct numerical simulations (DNS). Finally, a short-wave mode becomes unstable at Stc = 0.95, which generates more small-scale vorticies in the DNS result.
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