Simulation Solver Research Articles

Large Eddy Simulation of a Pistonless Constant Volume Combustor: A New Concept of Pressure Gain Combustion

Abstract Classical gas turbine thermodynamic cycle has undergone no change over the last decades. The most important efficiency improvements have been obtained by reducing thermal losses and raising the overall pressure ratio and peak temperature. Pressure gain combustion (PGC) represents an increasingly interesting solution to break out current technological limits. Indeed cycle models show that a pressure raise across the combustion process would reduce fuel consumption, increasing efficiency. Providing an efficiency close to the corresponding detonative technological concepts, constant volume combustion (CVC) represents a viable solution that still needs to be studied. In this work, the CV2 (constant-volume combustion vessel) installed at the Pprime laboratory (France) is numerically investigated using the high-fidelity compressible large eddy simulation (LES) solver AVBP. All the successive phases of the CVC cycle, i.e., air intake, fuel injection, spark-ignited combustion, and exhaust, are considered in the LES. Intake and exhaust valves are properly represented by novel boundary conditions able to mimic the valves impact on the flow without the need to directly consider their presence and dynamics during the simulation, reducing the computational costs. The spark ignition is modeled as an energy deposition term added to the energy equation. The combustion phase is treated by the dynamic version of the thickened flame model (DTFLES) extended to deal with nonconstant pressure combustion. Time-resolved particle imaging velocimetry (PIV) and pressure measurement inside the chamber reveal that cold and reactive turbulent flow are well captured in all the phases, showing the reliability of the approach and the models used.

A new residual distribution hydrodynamics solver for astrophysical simulations

ABSTRACT Many astrophysical systems can only be accurately modelled when the behaviour of their baryonic gas components is well understood. The residual distribution (RD) family of partial differential equation (PDE) solvers produce approximate solutions to the corresponding fluid equations. We present a new implementation of the RD method. The solver efficiently calculates the evolution of the fluid, with up to second order accuracy in both time and space, across an unstructured triangulation, in both 2D and 3D. We implement a novel variable time stepping routine, which applies a drifting mechanism to greatly improve the computational efficiency of the method. We conduct extensive testing of the new implementation, demonstrating its innate ability to resolve complex fluid structures, even at very low resolution. We can resolve complex structures with as few as 3–5 resolution elements, demonstrated by Kelvin–Helmholtz and Sedov blast tests. We also note that we find cold cloud destruction time scales consistent with those predicted by a typical PPE solver, albeit the exact evolution shows small differences. The code includes three residual calculation modes, the LDA, N, and blended schemes, tailored for scenarios from smooth flows (LDA), to extreme shocks (N), and both (blended). We compare our RD solver results to state-of-the-art solvers used in other astrophysical codes, demonstrating the competitiveness of the new approach, particularly at low resolution. This is of particular interest in large scale astrophysical simulations, where important structures, such as star forming gas clouds, are often resolved by small numbers of fluid elements.

Reconstruction of interfacial thermal transport mediated by hotspot in silicon-based nano-transistors

Transistors are typical multi-interface nanostructures, and the heat dissipation problem has become the bottleneck restricting size reduction and performance improvement of semiconductor devices. Local high-temperature hotspot generated by self-heating effects seriously affects the stability and reliability of the devices, and the interfaces further hinder the heat conduction. Thermal analysis is complicated by subcontinuum phenomena which reshapes the hotspot region and interface-mediating. There has been less description of device thermal transport mediated by hotspot coupling with the interfaces. In this paper, based on the phonon BTE (pBTE) thermal solver and electronic Monte Carlo (e-MC) simulation, we systematically study the thermal transport behavior of 1-D Si transistor and Si-based heterojunction interfaces under the hotspot effect. Also, the influence of other scattering events is investigated by modifying the relaxation time. Inside hard hotspot, the temperature and heat flux of different phonon modes are decomposed, which shows a strong non-equilibrium effect. The contributions of non-Fourier effects are separated and quantified based on split-flux model. In heterojunction structure, the interfacial thermal resistance further increases the hotspot temperature. Interestingly, on the side of hotspot near the interface, the direction of heat flux is opposite to the direction of the temperature drop, which violates Fourier's law. Through different substrate combinations, the heat dissipation effect of diamond, BN is not excellent due to the low interfacial thermal conductance (ITC), time-dependent BTE is used to study the heating rate. Mode-dependent temperature and heat flux reveal nonequilibrium phonon transport performance. Finally, the wave-resolved spectral heat flux is calculated to explore the predominant thermal transport channel and interface phonon transport characters. Above studies provide useful insights for further improving the accuracy of transistor-level thermal simulations.

Design of a Gas Permeation and Pervaporation Membrane Model for an Open Source Process Simulation Tool.

Gas permeation and pervaporation are technologies that emerged several decades ago. Even though they have discovered increasing popularity for industrial separation processes, they are not represented equally within process simulation tools except for commercial systems. The availability of such a numerical solution shall be extended due to the design of a membrane model with Visual Basic based on the solution-diffusion model. Although this works approach is presented for a specific process simulator application, the algorithm can generally be transferred to any other programming language and process simulation solver, which allows custom implementations or modeling. Furthermore, the modular design of the model enables its further development by operators through the integration of physical effects. A comparison with experimental data of gas permeation and pervaporation applications as well as other published simulation data delivers either good accordance with the results or negligible deviations of less than 1% from other data.

Computational realization of turbulent combustion in a scramjet combustor stabilized by a lobed strut

Currently, there are theoretical and technical challenges to organize stable flame in scramjet, especially for variable flight conditions. This paper applies the numerical simulation to investigate and analyze the combustion characteristics in a lobed strut-stabilized scramjet combustor under different conditions of Mach number (Ma). By comparing with the experiment date of hydrogen mole fraction, the reliability of large eddy simulation solver used in this paper is verified. On this basis, the simulations of mixing and combustion cases at Ma 1.5–3.0 are carried out separately. The numerical results show the streamwise vortices induced by the lobed strut enhance the mixing and are conducive to the subsequent stable combustion. The turbulent flame behaves lifted characteristics, and the auto-ignition provides the initial active radicals for its stabilization. There are two chemical reaction modes in the flow field, namely auto-ignition, and flame. Further comparison of the cases of different Mach numbers indicates that the lifted height of the flame depends on the Mach number. Analysis of probability density function (PDF) reveals that Mach number influent the competitive relationship between the auto-ignition mode and the flame mode. The auto-ignition and the flame coexist downstream in high ma cases, while the flame mode is the dominant in low Ma cases.

GPU simulation of wake effects at the Horns Rev 1 offshore wind farm using the CFD porous disk wake model

To verify the effectiveness of the GPU simulation of wake effects at a large-scale offshore wind farm, we ran an in-house large-eddy simulation (LES) solver with a CFD porous disk wake model for the Horns Rev 1 wind farm. For this numerical research, we prepared the latest workstation equipped with a Xeon W-2265 CPU and an NVIDIA RTX A6000 GPU. We clarified that the calculation speed of the single GPU of the NVIDIA RTX A6000 is approximately 10 times faster than the calculation speed of the Xeon W-2265. Careful data analysis and visualization of the unsteady turbulent flow fields obtained in the current LES study suggest that the mutual interference of the wakes developed by wind turbines may frequently form a local speed-up region around wind turbines, located on the downstream side of large offshore wind farms.

Using an Embedded Multi User Inverse Kinematic Solver for Intuitive Modeling and Simulation

Following the vision of Industry 4.0, manufacturers started to break down products into subsystems, each of which is developed and supplied by different suppliers to tackle the increasing complexity of product development (e.g., in vehicle, machine or plant construction). This process needs to be supported by intuitive Computer-Aided Design (CAD) tools and virtual modeling and simulation environments to effectively meet the challenges of increasingly complex product development. Therefore, in this paper, we present some outcoming of a research project called DisMoSim ( Dis tributed Mo deling and Sim ulation), which proposes an intuitive virtual environment for modeling and simulation that embeds a Multi User Inverse Kinematic Solver (MUKS). The MUKS allows (i) individual subsystems to be tested intuitively, i.e., Rapid Testing (RT), and (ii) people not yet familiar with a subsystem to understand it easily and quickly through simple kinematic actions, i.e., Rapid Understanding (RU), without unnaturally interrupting the modeling process. Finally, (iii) the MUKS enables subsystems to be easily assembled into complete systems, i.e., Rapid Assembling (RA), by means of a so-called snapping-point mechanism which supports the complex process of aligning and assembling different subsystems. To evaluate these capabilities, we present the results of a user study conducted with 20 participants. Special attention has been given to the embedded MUKS in contrast to existing approaches known from common CAD and simulation software. Thus, we demonstrate the practicability, usability, and versatility of our approach. • Finding modeling and simulation errors in CAD models is cumbersome with current tools. • CAD tools need intuitive means for testing during modeling. • Inverse kinematic solvers allow for rapid prototyping and testing in CAD systems. • New user interface and interaction paradigms ease interaction with CAD tools.

Implementation of the HLL-GRP solver for multidimensional ideal MHD simulations based on finite volume method

The HLL solver for the generalized Riemann problem (HLL-GRP solver) is attractive because it is easy to implement for 1D hyperbolic problems and performs well. Based on the rotational invariance of multidimensional magnetohydrodynamics (MHD) equations, this paper provides a means of implementing the 1D HLL-GRP solver into the multidimensional ideal MHD simulations within the framework of the finite volume method. Furthermore, the Godunov-Powell source term and the locally divergence-free WLS-ENO reconstruction are adopted to constrain the divergence of the magnetic field. To maintain positive density and pressure, a positivity-preserving (PP) limiter is performed on the reconstructed polynomials of density and pressure. Some comparisons with other methods are listed in 1D, 2D and 3D MHD benchmark cases. The numerical results demonstrate that the scheme is stable and can well control the divergence of the magnetic field.

A Momentum-Conserving Weakly Compressible Navier–Stokes Solver for Simulation of Violent Two-Phase Flows with High Density Ratio

A consistent and conservative formulation for mass and momentum transport is proposed in the context of simulating incompressible two-phase flows by using weakly compressible method. Combined with the evolving pressure projection method to prevent oscillation of the solution induced by the acoustic wave, this solver aims at a robust and accurate computation of violent two-phase flows with a high density ratio, while taking advantage of fully explicit time integration of the weakly compressible Navier–Stokes equations. Coupled with the volume of fluid method for capturing interfaces, the mass and momentum fluxes are evaluated in a consistent manner using the finite volume method. In addition, a special implementation of the pressure projection is devised to avoid velocity-pressure decoupling on a collocated grid. The solver's accuracy and stability are demonstrated through various two-phase flow simulations, including dam break and liquid jet atomization scenarios, emphasizing its momentum-conserving properties.

Parameter identification and state estimation for nuclear reactor operation digital twin

Reactor Operation Digital Twin (RODT) is now receiving increasing attention and investment in nuclear engineering domain. A prototype of a RODT was first brought out by Gong et al. at Nuclear Power Institute of China. The RODT contains a forward solver for online real-time simulation and an inverse problem solver for parameter identification and state estimation. To further improve the efficiency and accuracy of RODT and promote the practical deployment of RODT (i) we first propose an advanced differential evolution algorithm to upgrade the inverse solver; (ii) then we bring out a systematical uncertainty quantification of RODT considering assimilation noisy observations. The accuracy and validity of the proposed RODT are tested along one cycle operating stage of HPR1000, at various operating temperatures, control rod steps, general power level and the inlet temperature of a practical nuclear reactor core. Numerous numerical results confirm its potential for practical engineering applications for on-line parameter identification and state estimation.

Experimental and numerical investigation into the effect of surface roughness on particle rebound

Erosion damage and particle deposition are crucial wear phenomena in gas turbine engines. As a result, compressor efficiency decreases, stability margin reduces, and maintenance cost increases. Hence, predicting these phenomena in an accurate manner is of paramount importance for a cost-efficient, safe, and sustainable operation. Erosion and particle deposition in the annulus are affected by particle transportation in the fluid and particle-wall interaction. The latter involves the particle impact, the potential damage of the surface and/or the particle, and the particle rebound. Particle rebounds are statistical in nature due to the target surface roughness, the variability in particle sizes, and superimposed effects caused by particle shapes as well as particle rotation and particle break-up during contact. Multiple studies investigated the statistics of particle rebound, providing empirical-based models for median and spread. However, modeling the particle-wall interaction and its data spread on a transparent physical basis allows separating the effect of target roughness from superimposed effects. The presented article pursues this objective by assessing the statistical spread of particle rebound data through multiple techniques and utilizing their interdependencies. It combines experimental, numerical, and analytical considerations. For the first time, coherent boundary conditions for the experimental, numerical and analytical setup allow the distinction of the effect of roughness from the integral effect of the superimposed phenomena. A sandblast test rig equipped with laser measurement equipment was used to measure particle rebound from flat titanium and stainless steel plates at different angles. The numerical setup is developed under OpenFOAM 6 using a RANS solver for transient simulations with compressible media in combination with one-way coupled particle flows. The numerical model includes the rebound spread model proposed by Altmeppen et al. combined with the quasi-analytical rebound model proposed by Bons et al. The statistical spread of particle rebound is investigated for roughness levels that are similar to the ones of deteriorated high-pressure compressor blades as discussed by Gilge et al. The measured surface roughness of the experimentally investigated targets is used as input parameters to the numerical framework. The rebound statistics obtained in the numerical simulation are compared to the rebound data measured in the experiment. Based on this study, conclusions are drawn about which part of the rebound spread is attributable to surface roughness and which is caused by superimposed effects. It was found that the effect of surface roughness as characterized by Altmeppen et al. contributes in the order of 46 % to the rebound spread for small impact angles. However, the share in spread due to roughness gradually decreases with increasing global impact angles to a level of 13 % for angles close to 90°. The remaining percentage of rebound spread is attributed to superimposing phenomena. In addition to the rolling and sliding of aspherical particles, further phenomena such as plastic deformation and erosion of the roughness peaks during contact and the associated dissipation of energy gain in importance for steeper impact angles. Therefore, the effect of surface roughness should not be neglected in numerical simulations of particle-laden flows. Modeling the superimposed phenomena which are observed to be dominating at high impact angles opens up a further field of research.

A high-order scheme based on lattice Boltzmann flux solver for viscous compressible flow simulations

A high-order scheme based on lattice Boltzmann flux solver for viscous compressible flow simulations

Development of a 3D Eulerian/Lagrangian Aircraft Icing Simulation Solver Based on OpenFOAM

A 3D icing simulation code is developed in the open-source CFD toolbox OpenFOAM. A hybrid Cartesian/body-fitted meshing method is used to generate high-quality meshes around complex ice shapes. Steady-state 3D Reynolds-averaged Navier-Stokes (RANS) equations are solved to provide the ensemble-averaged flow around the airfoil. Considering the multi-scale nature of droplet size distribution, and more importantly, to represent the less uniform nature of the Super-cooled Large Droplets (SLD), two droplet tracking methods are realized: the Eulerian method is used to track the small-size droplets (below 50 m) for the sake of efficiency; the Lagrangian method with random sampling is used to track the large droplets (above 50 m); the heat transfer of the surface overflow is solved on a virtual surface mesh; the ice accumulation is estimated via the Myers model; finally, the final ice shape is predicted by time marching. Limited by the availability of experimental data, validations are performed on 3D simulations of 2D geometries using the Eulerian and Lagrangian methods, respectively. The code proves to be feasible and accurate enough in predicting ice shapes. Finally, an icing simulation result of the M6 wing is presented to illustrate the full 3D capability.

A novel high-order solver for simulation of incompressible flows using the flux reconstruction method and lattice Boltzmann flux solver

In this paper, a novel high-order solver using the flux reconstruction (FR) method and the lattice Boltzmann flux solver (LBFS) is proposed for accurately and efficiently simulating nearly incompressible flows. The existing LBFSs are all based on the finite volume (FV) scheme. The present work extends the application of the LBFS for the first time by combining the high-order FR scheme. Compared with the traditional high-order incompressible Navier-stokes (N-S) solvers, no particular techniques are needed for the current FR-LBFS to overcome the difficulty of the pressure-velocity coupling since the present method is a weakly compressible model. Moreover, unlike the traditional N-S solvers where the inviscid and viscous terms are treated separately, the inviscid and viscous fluxes in the current scheme are coupled and computed uniformly in FR-LBFS. In the present method, the common inviscid and viscous fluxes at the cell interface of the FR scheme are evaluated simultaneously by the local reconstruction of lattice Boltzmann equation (LBE) solution from macroscopic flow variables at solution points. Thus the discretization of the second-order partial derivative term is avoided. Compared with the high-order off-lattice Boltzmann methods (OLBM), the FR-LBFS is more stable, efficient and low-storage. No special techniques are needed to remove the stiffness of the governing equations which existing in the discrete velocity Boltzmann equation (DVBE). Compared with the high-order FV-LBFS, the FR-LBFS is compact for parallel computing by avoiding wide stencils on meshes. In addition, the present scheme has lower dissipation and can be more flexible to increase accuracy order. Numerical validations of the proposed method are implemented by simulating (a) Taylor-Green vortex problem, (b) steady plane Poiseuille flow, (c) lid-driven cavity flow, (d) laminar boundary layer and (e) flow past a square cylinder.

A 3D fully‐nonlinear potential‐flow solver for efficient simulations of large‐scale free‐surface waves

AbstractIn the quest for a numerical method for surface waves and wave‐induced effects applicable when linear or weakly nonlinear methods are insufficient, a three‐dimensional numerical wave tank assuming fully‐nonlinear potential‐flow theory is proposed. When viscous‐flow effects, breaking waves or other violent flow‐phenomena are not of primary importance, potential‐flow methods may have similar capability in capturing the involved physics as Navier–Stokes solvers while being potentially more accurate in handling wave‐propagation mechanism and more computationally efficient. If made sufficiently accurate, efficient and numerically robust, fully‐nonlinear potential flow models can therefore represent a powerful tool in the study of ocean waves and their interaction with marine structures, which is the main motivation behind the present work. The governing Laplace equation for the velocity potential is solved using the harmonic polynomial cell method, which is a field method giving high‐order accuracy provided that the cells used to describe the water domain have no stretching or distortion. This can only be achieved in a grid with cubic cells, which leads to poor numerical efficiency unless measures are introduced to refine the grid locally. Here, to improve the efficiency using strictly cubic cells, an adaptive grid refinement technique is introduced. It is shown that this has the ability to improve the computational speed with a factor of up to 20 without sacrificing accuracy. Numerical results are shown to be in good agreement with highly accurate nonlinear reference solutions for regular and irregular waves of various steepness up to the limit of theoretical wave breaking. For long‐crested irregular waves, significant discrepancies with a second‐order theory for the crest‐height distribution are identified, while the second‐order theory appears to provide a better description of the crest height for the single short‐crested irregular sea state simulated. Having demonstrated that the proposed numerical method accurately models nonlinear wave phenomena up to the limit of wave breaking, future work should seek to implement wave‐body interaction capabilities. The adaptive grid refinement technique, which refines the grid dynamically depending on the position of boundaries of interest, is developed with this application in mind. Except from providing a robust way of dealing with wave‐body intersection points, extending the method to account for wave‐body interactions should therefore involve limited difficulty.

Phase-field-lattice Boltzmann flux solver for simulations of solid-liquid phase change

<p indent="0mm">A phase-field-lattice Boltzmann flux solver (PF-LBFS) is proposed in this paper for numerical simulations of the solid-liquid phase change in a pure material. LBFS serves as a flow solver, which globally resolves the Navier-Stokes equations and reconstructs numerical fluxes with local solutions to the lattice Boltzmann equation on the cell interface. Being a physical reconstruction strategy, the LBFS simultaneously reconstructs the inviscid and viscous numerical fluxes and ensures consistency between the local equation resolved on the cell interface and the global governing equations. Another key module of the PF-LBFS is the phase-field equation, which updates the order parameter for identifying the solid-liquid interface. The phase-field method allows a smooth transition between phases and is consolidated into the energy conservation law. The convergence, accuracy, and physical robustness of the proposed method, as well as its flexibility on a nonuniform mesh, are numerically validated through three representative benchmark tests.

Numerical simulation method of a circulating fluidized bed reactor using a modified MP-PIC solver of OpenFOAM

There are some previous works for simulating a bubbling fluidized bed (BFB) reactor using OpenFOAM's MPPICFoam solver, but those for circulating fluidized bed (CFB) reactors are few. In this study, the MPPICFoam solver was verified with a BFB reactor by comparing the solver's simulation results with the experiment and simulation results from the literature. By introducing the inter-boundary particle circulation function and a new module for setting sand particle size distribution, simulations were performed for a 0.1 MW th pilot-scale CFB combustor under isothermal conditions. The modified solver for the CFB reactor gives similar results as the experiment and commercial computational fluid dynamics (CFD) tool, well-predicting the pressure distribution and solid volume fraction in the riser. • MPPICFoam solver reliability for lab-scale bubbling fluidized-bed reactor verified. • Accurate solver prediction of solid volume fraction (horizontal) distribution. • Model used for numerical simulation to study riser hydrodynamics of a CFB combustor. • Particle size distribution module and new circulating boundary conditions added. • Improved solver shows superior predicted experimental results in dense bed region.

An immersed boundary-material point method for shock-structure interaction and dynamic fracture

As a class of extreme fluid-structure interaction (FSI), shock-structure interaction problems are always accompanied with dynamic fracture phenomena in solid structure. During the dynamic fracture process, small fragments of thin geometry and fresh FSI interfaces will be generated, which makes the FSI interface difficult to be reconstructed. An immersed boundary-material point method (IBMPM) is proposed in this paper for simultaneous simulations of shock-structure interaction and accompanied dynamic fracture. The finite volume method (FVM) is employed as fluid solver and specifically a TVD Riemann solver is adopted for shock simulation, while the material point method (MPM) is employed as solid solver for simulation of extreme deformation problem. The FVM and MPM are then coupled by our improved immersed boundary method (IBM) which is named as Lagrangian continuous-forcing IBM (lg-CFIBM). The lg-CFIBM is proposed in the frame of continuous forcing approach with a compact support area for the immersed boundary conditions. It can guarantee the boundary velocity conditions strictly at each time step and has no need to reconstruct FSI interfaces. Several numerical examples, including shock-cylinder obstacle interaction, flexible panel deformation induced by shock wave and fragmentation driven by detonation, are studied to verify and validate the proposed method, and numerical results are in good agreement with experiments.

High Order Wall-Modeled Large-Eddy Simulation on Mixed Unstructured Meshes

In the present study, an algebraic equilibrium wall model previously developed for hexahedral elements is extended to handle mixed meshes including prismatic, tetrahedral, and pyramidal elements in the context of a discontinuous high-order method. This extension is needed for complex geometries, for which high-order mixed elements (e.g., tetrahedral and pyramidal elements) are often necessary near solid walls to avoid meshing challenges. Various design decisions are discussed to achieve the best performance on massively parallel CPU/GPU architectures for a production-level high-order large-eddy simulation solver based on the flux reconstruction/correction procedure via reconstruction method, hpMusic. The extension to other elements is first evaluated using a benchmark channel flow problem at various Reynolds numbers. After that, flow over the NASA high-lift Common Research Model (CRM-HL) from the 4th AIAA High-lift Prediction Workshop is computed to further test the new implementation. Computational results at the third- and fourth-order accuracies are compared with experimental data.

A combined flux reconstruction and lattice Boltzmann flux solver for inviscid compressible flow simulation

AbstractA numerical method, which combines the high order flux reconstruction (FR) and the lattice Boltzmann flux solver (LBFS), has been developed to solve inviscid compressible flows in this article. Extensive research has shown that LBFS has absorbed the advantages of both finite volume method (FVM) and lattice Boltzmann method (LBM). On one hand, compared with FVM, FR can achieve arbitrary high order accuracy and is compact for parallel computing by avoiding wide stencils on meshes, which shows FR is a better choice than FVM. On the other hand, different from the discrete velocity Boltzmann equation based methods, the present method, that is, FR‐LBFS, solves the Euler equations essentially, and then the calculation efficiency can be improved. In FR‐LBFS, the common inviscid flux at the cell interface is evaluated by the local reconstruction of the lattice Boltzmann equation (LBE) solution from macroscopic flow variables at solution points. Unlike the traditional flux solution at the interface where the nonlinear convective terms have to be considered in the computation, the feature of linear convection term in LBE can make it easier to calculate flux in the current method. Furthermore, by considering real physical effects in LBM, the positive density and pressure can be achieved in the case of strong shocks and discontinuities. Some typical inviscid problems, including the advection of density perturbation, sod shock tube, Riemann problem for two‐dimensional gas dynamics, supersonic flow in a convergent nozzle with a ramp, subsonic flow around a cylinder, and transonic flow over a NACA0012 airfoil, are simulated to demonstrate the accuracies and robustness of the proposed FR‐LBFS.