Method For Simulation Of Flows Research Articles

One-dimensional turbulence modeling of compressible flows: II. Full compressible modification and application to shock–turbulence interaction

One-dimensional turbulence (ODT) is a simulation methodology that represents the essential physics of three-dimensional turbulence through stochastic resolution of the full range of length and time scales on a one-dimensional domain. In the present study, full compressible modifications are incorporated into ODT methodology, based on an Eulerian framework and a conservative form of the governing equations. In the deterministic part of this approach, a shock capturing scheme is introduced for the first time. In the stochastic part, one-dimensional eddy events are modeled and sampled according to standard methods for compressible flow simulation. Time advancement adjustments are made to balance comparable time steps between the deterministic and stochastic parts in compressible flows. Canonical shock–turbulence interaction cases involving Richtmyer–Meshkov instability at Mach numbers 1.24, 1.5, and 1.98 are simulated to validate the extended model. The ODT results are compared with available reference data from large eddy simulations and laboratory experiments. The introduction of a shock capturing scheme significantly improves the performance of the ODT method, and the results for turbulent kinetic energy are qualitatively improved compared with those of a previous compressible Lagrangian ODT method [Jozefik et al., “Simulation of shock–turbulence interaction in non-reactive flow and in turbulent deflagration and detonation regimes using one-dimensional turbulence,” Combust. Flame 164, 53 (2016)]. For the time evolution of profiles of the turbulent mixing zone width, ensemble-averaged density, and specific heat ratio, the new model also yields good to reasonable results. Furthermore, it is found that the viscous penalty parameter Z of the ODT model is insensitive to compressibility effects in turbulent flows without wall effects. A small value of Z is appropriate for turbulent flows with weak wall effects, and the parameter Z serves to suppress extremely small eddy events that would be dissipated instantly by viscosity.

Numerical study on the hydrodynamic properties of bentonite slurries with Herschel-Bulkley-Papanastasiou rheology model

During the construction of slurry shield tunnels, bentonite slurries play a significant part in maintaining excavation face stability where suitable slurries infiltrate into the stratum to form an impermeable filter cake. To enhance filter cake quality, accurate prediction of the hydrodynamic properties of bentonite slurries is always required during slurry parameters design. The main purpose of this study is to investigate the flow characteristics of bentonite slurries with different polymer contents using computational fluid dynamics (CFD) simulation. Mixtures of sodium bentonite powder, carboxymethyl cellulose (CMC), and water in different ratios were prepared, and a series of indoor rheological tests were conducted. Then an optimized numerical method for slurry flow simulation was developed by incorporating the Herschel- Bulkley-Papanastasiou (HBP) rheology model with the finite volume method (FVM). The proposed model was implanted in OpenFOAM, and then applied to theoretical cases of non-Newtonian plane-Poiseuille flow for model verification. Results show the theoretical and simulation results were in good accordance, with a successful description of the shear thinning characteristics of fluids and no divergency during the numerical solution procedure. Based on it, CFD simulations were implemented to investigate pipe flow characteristics of bentonite slurries with different CMC contents. Results indicate when the inlet velocity is constant, the decrease of pipe diameter can cause a more inhomogeneous flow and the growth of pressure drop; rises in rheological parameters can all increase the energy consumption and reduce the infiltration distance. When the yield stress is 25 Pa, the pressure drop reaches a maximum value of 5.47 kPa, compared with 2.69 kPa for slurries with a yield stress of 5 Pa. Furthermore, the infiltration law of bentonite slurries in pipes essentially conforms to a non-Darcy infiltration with an initial hydraulic gradient i0, which has a positive relationship with yield stress of fluids. i0 increases from 0.082 to 0.414 after adding 0.3% CMC into bentonite slurries. This research can provide significant guidance for the establishment of slurry infiltration theories and relevant numerical simulations.

Efficient Parallel Dynamic Overset Unstructured Grid for Flow Simulation with Moving Bodies

The overset grid method for simulation of unsteady flow with moving bodies faces several issues, including low assembly efficiency for a large number of bodies, difficult parallel implementation, and the requirement of manual intervention. To address these issues, in this paper, we develop an efficient, automatic, and robust parallel dynamic overset-unstructured-grid assembly method. It is achieved by parallelizing its two main steps: hole cutting, and identification of interpolation stencils. The hole cutting is simply implemented in parallel by identifying the active zone of each grid with a criterion of the global minimum wall distance. The global minimum wall distance is efficiently calculated on each process with the oriented-bounding-box-based -dimensional (-D) trees of the wall surface grids. For identification of the interpolation stencil, we use the results of the first step, optimally define the interpolation boundary nodes, and determine their candidate donor partitions in each process. This efficiently minimizes the number of query nodes and their donor cell candidates. The donor cell search is efficiently performed in parallel in each candidate donor partition by using the oriented-bounding-box-based -D tree of the field volume grid. Several cases are adopted to test the efficiency and capability of the proposed parallel dynamic overset-unstructured-grid assembly approach.

Numerical method for gas-liquid two-phase flow with phase change heat transfer considering compressibility using OpenFOAM

The numerical simulation of phase change heat transfer is important for predicting the gas-liquid two-phase flow and heat transfer characteristics and optimizing the phase change heat dissipation system. For the isovolumetric phase change heat transfer process, the compressibility of the gas phase has a significant impact on the simulation accuracy. A numerical simulation method of flow and phase change heat transfer considering gas-liquid two-phase compressibility is established based on VOF method using OpenFOAM in this paper. This method introduces a generalized phase change source term and a compressible source term to improve the isoAdvector geometric reconstruction algorithm and establishes a method for capturing the phase interface of a compressible two-phase flow. The phase change flux based on the phase interface is converted into a phase change source term based on the unit volume by calculating the phase interface density. The compressible term of the governing equation is constructed and its implicit discrete method is proposed. The coupling between velocity and pressure is realized based on the PISO algorithm. A numerical calculation method for phase change heat transfer of compressible two-phase flow is established. The effectiveness and accuracy of the proposed numerical method for predicting the heat transfer characteristics of phase change flows are verified by the simulation of vertical flat film condensation and film boiling. The numerical simulation results are in good agreement with the experiment. Compared with the other numerical simulation methods, the proposed method considering the influence of the compressibility of the gas phase on the flow and heat transfer characteristics in the heat pipe has high accuracy in predicting the gas-liquid two-phase flow, capturing the evolution characteristics of the phase interface and predicting the phase change heat transfer. The numerical simulation method can provide algorithm support for the numerical simulation of compressible two-phase flow phase change heat transfer and the design of a phase change heat dissipation system.

High-order implicit RBF-based differential quadrature-finite volume method on unstructured grids: Application to inviscid and viscous compressible flows

This paper exploits the potential of a high-order implicit radial basis function-based differential quadrature-finite volume (IRBFDQ-FV) method for effective simulation of inviscid and viscous compressible flows using unstructured grids. The framework of IRBFDQ-FV method is based on finite volume discretization which can guarantee conservation of mass, momentum and energy. The flow field variables within each control cell are represented by a fourth-order approximation constructed by a Taylor series expansion to the cell center with spatial derivatives as the undetermined coefficients. All spatial derivatives are computed by the meshless and highly converged RBF-based differential quadrature (RBFDQ) technique. Regarding flux evaluation, the discrete gas-kinetic flux solver is applied to evaluate inviscid and viscous fluxes simultaneously for compressible viscous flows. Resultantly, the special mathematical treatment for the viscous flux, which is usually adopted in other high-order methods, can be avoided. A point extrema-based extended bounds (PEEB) shock-capturing limiter is introduced to eliminate spurious numerical oscillations near discontinuities. Due to the implicit nature of the proposed method, implicit time-stepping schemes compatible with the spatial accuracy are devised to efficiently solve the resulting discretized equations. Representative compressible flow problems are simulated to verify the high-order accuracy, excellent efficiency and robustness of the present method. Comparison with two other high-order finite volume methods further shows competitiveness of the present method in solving compressible flow problems on unstructured grids.

Emergency evacuation time model of nuclear power plant pedestrians

The construction of nuclear power plant is usually multi-phase. In the coexisting period of operation and construction, the types of pedestrian in nuclear power plant are complicated. Like Fukushima accident, nuclear power plant accident is dangerous and easy to cause mass panic. In order to improve the efficiency of emergency evacuation in nuclear power plant and accurately obtain the evacuation time of nuclear power plant pedestrians, a pedestrian evacuation time model is established. Firstly, by studying the general layout characteristics of nuclear power plant, nuclear power plant is divided into three areas, protected area, management area and construction area. Secondly, the pedestrian flow movement monitoring data of nuclear power plant are analyzed to obtain the pedestrian movement characteristics and speed-density curves of different locations(facilities) in different areas of the plant, which will provide data support for establishing the pedestrian evacuation time model of nuclear power plant. Thirdly, the evacuation time of nuclear power plant is divided into three parts: pedestrian reaction time, pedestrian walking time and pedestrian waiting time. The evacuation time model of nuclear power plant pedestrian is obtained by analyzing and modeling these three parts respectively. Finally, taking a nuclear power plant as an example, three types of evacuation areas are set up according to the layout characteristics and construction status of nuclear power plant. The model was used to calculate the evacuation time of different types of areas. Based on multi-agent pedestrian flow simulation method, emergency pedestrian flow simulation of three types of evacuation areas is obtained. The results of the model are compared with the simulation results, and it is found that the model has good matching in different nuclear power plant areas, which verifies the rationality and accuracy of the model.

Comparison between variable forcing techniques of the lattice Boltzmann method for turbulent flow simulations

Comparison between variable forcing techniques of the lattice Boltzmann method for turbulent flow simulations

Development of Surface Smoothing Method for Blood Flow Simulation

Development of Surface Smoothing Method for Blood Flow Simulation

Overtopping-Induced breaching process of concrete-faced rockfill dam: A case study of Upper Taum Sauk dam

The back analysis of the dam breaching process based on reported failure case data is of great significance for understanding dam breaching mechanisms and the ability to predict breach flow hydrograph during emergencies. According to the essential information and post-failure investigation report of the Upper Taum Sauk dam, the first pumped storage power station in the United States, the most probable failure mechanism for dam breach is studied. Furthermore, a detailed physically-based numerical model is developed to simulate the overtopping-induced breach process of the concrete-faced rockfill dam (CFRD). Highlights of the model include the establishment of a simulation method of the dam-break flow based on the actual three-dimensional terrain considering the water-retaining characteristics of concrete face slabs, and the times and lengths of failure for each concrete face slab under water load and self-weight, as well as the adoption of different transportation modes for the widely graded rockfill materials. The breach side slope sliding mechanism is considered during the dam breach process. It is worth noting that the hydraulic features of dam-break flow and breach morphology can be well described with a combination of renormalization group (RNG) k-ε turbulence model and volume of fluid (VOF) method. The calculated results of the Upper Taum Sauk dam breaching parameters agree with the measured values, which testify to the rationality of the proposed model. The obtained time-varying dynamic dam breach process of CFRD can be divided into three stages. Moreover, the sensitivity analysis indicated that, the presence and absence of concrete face slabs affect the breach process of the Upper Taum Sauk dam significantly. The performance comparison with the existing dam breach models also verifies the advancement of the detailed physically-based model. Hence, the addressed numerical method can be used as an effective tool for simulating the CFRD breach process.

A Novel Equivalent Numerical Simulation Method for Non-Darcy Seepage Flow in Low-Permeability Reservoirs

The low permeability and submicron throats in most shale or tight sandstone reservoirs have a significant impact on microscale flow. The flow characteristics can be described with difficultly by the conventional Darcy flow in low-permeability reservoirs. In particular, the thickness of the boundary layer is an important factor affecting the formation permeability, and the relative permeability curve obtained under conventional conditions cannot accurately express the seepage characteristics of porous media. In this work, the apparent permeability and relative permeability were calculated by using non-Darcy-flow mathematical modeling. The results revealed that the newly calculated oil–water relative permeability was slightly higher than that calculated by the Darcy seepage model. The results of the non-Darcy flow based on the conceptual model showed that the area swept by water in non-Darcy was smaller than that in Darcy seepage. The fingering phenomenon and the high bottom hole pressure in the non-Darcy seepage model resulted from the larger amount of injected water. There was a large pressure difference between the injection and production wells where the permeability changed greatly. A small pressure difference between wells resulted in lower variation of permeability. Consequently, the non-Darcy simulation results were consistent with actual production data.

A Multifidelity Simulation Method for Internal and External Flow of a Hypersonic Airbreathing Propulsion System

As hypersonic vehicles are highly integrated, a multifidelity simulation method based on a commercial solver is developed to reduce simulation time for such vehicles and their propulsion systems. This method is characterized by high-level fidelity numerical analysis of external flow and low-level fidelity numerical analysis of internal flow. The external flow of a propulsion system is solved by RANS equations. The internal flow is modeled by a quasi-one-dimensional equation. The interaction between external and internal flow is governed by a CFD solver through a user-defined function (UDF). The static pressure distribution acquired from the multifidelity simulation method is in agreement with the experimental data, indicating that this simulation method can be used to study the flow physics of hypersonic propulsion systems at a reasonable cost. From a design perspective, the results indicate that the horizontal force increases with the fuel equivalence ratio, and the thrust balance is realized at φ = 0.35. The positive net thrust is maintained throughout the flight regime from Ma 4 to Ma 7, whether the combustor operates in ramjet or scramjet mode.

Hybrid Dynamic Mesh Redistribution - Immersed Boundary Method for Acoustic Simulation of Flow Around a Propeller

A novel hybrid dynamic mesh redistribution – immersed boundary method for simulation of turbulent flows around rotating obstacles of complex geometry and analysis of tonal acoustics is proposed. The feasibility of the approach is demonstrated by considering a drone propeller problem. The results of three-dimensional Reynolds-averaged Navier–Stokes simulations using the proposed approach are compared to the results of body-fitted unstructured simulations in noninertial reference frame. The dynamic mesh redistribution method allows the reposition of mesh points taking into account the shape of the moving body while retaining the mesh topology. The cell size and quality of the dynamically redistributed mesh strongly depend on the curvature of the body surface. The position and shape of the moving obstacle is prescribed by a distance function defined on an adaptive octree. The results of simulations using the proposed method are in good agreement with both the results of body-fitted simulations and the experimental data.

Volume Flux Free SPH Approach for Multiphase Fluids

Aiming at the numerical issue at the interface during multiphase flow simulation with high density ratio and resulting unreasonable effect of convective motion, an implicit pressure algorithm based on volumetric flux free condition is proposed. Firstly, the causes of density approximation errors in the traditional multiphase flow simulation methods are analyzed. Secondly, the correlation calculation of "volume-compression ratio" is proposed to construct the linear relationship between fluid compression state and pressure. Thirdly, the constant volume solver and the volume flux free solver are designed respectively to realize the incompressibility of fluid volume and the divergence free of velocity field. In order to verify the performance of the proposed algorithm, the advanced fluid simulation method DFSPH is taken as comparison. And the rationality of simulation effect, numerical stability and convergence are taken as the qualitative and quantitative evaluation factors respectively. Experiments such as two-phase dam break and thermal convection are carried out under multiphase flow condition. The results show that the proposed method can achieve efficient and stable multiphase flow interaction. Under the same multiphase flow conditions, it can consume less calculation time and achieve convergence faster than DFSPH. It has good robustness, effectiveness and scalability in various complex simulation scenarios, especially suitable for simulating fluids with high density ratio.

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

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

A cut finite element method for two-phase flows with insoluble surfactants

We propose a new unfitted finite element method for simulation of two-phase flows in presence of insoluble surfactant. The key features of the method are 1) discrete conservation of surfactant mass; 2) the possibility of having meshes that do not conform to the evolving interface separating the immiscible fluids; 3) accurate approximation of quantities with weak or strong discontinuities across evolving geometries such as the velocity field and the pressure. The new discretization of the incompressible Navier-Stokes equations coupled to the convection-diffusion equation modeling the surfactant transport on evolving surfaces is based on a space-time cut finite element formulation with quadrature in time and a stabilization term in the weak formulation that provides function extension. The proposed strategy utilizes the same computational mesh for the discretization of the surface Partial Differential Equation (PDE) and the bulk PDEs and can be combined with different techniques for representing and evolving the interface, here the level set method is used. Numerical simulations in both two and three space dimensions are presented including simulations showing the role of surfactant in the interaction between two drops.

Sharp Interface Methods for Simulation and Analysis of Free Surface Flows with Singularities: Breakup and Coalescence

A common feature of many free surface flows—drop/bubble breakup or coalescence and film/sheet rupture—is the occurrence of hydrodynamic singularities. Accurately computing such flows with continuum mechanical, multidimensional free surface flow algorithms is a challenging task given these problems’ multiscale nature, which necessitates capturing dynamics occurring over disparate length scales across 5–6 orders of magnitude. In drop breakup, the thinning of fluid threads that form and eventually pinch-off must be simulated until the thread's radius is about 10 nm. When two drops approach one another, the thickness of the fluid film separating them must fall below 10 nm before coalescence is said to have occurred. If the initial drop radii are 1 mm, simulations must remain faithful to the physics as thread radius or film thickness falls from 10−3 m to below 10−8 m. Here we review significant findings in interfacial flows with hydrodynamic singularities spearheaded by sharp interface algorithms. These multidimensional algorithms can achieve resolution that to date has only been possible with the use of simple 1D evolution equations.

An immersed boundary/multi-relaxation time lattice Boltzmann method on adaptive octree grids for the particle-resolved simulation of particle-laden flows

We present an immersed boundary/multi-relaxation time lattice Boltzmann method for the particle-resolved simulation of particle-laden flows. The no-slip boundary condition is handled by an explicit feedback immersed boundary method for fixed and moving particles with arbitrary shape. Two special treatments are applied to improve the simulation stability and accuracy: (i) a smoothed discrete delta function (Yang et al. (2009) [47]) is adopted to suppress the spurious force oscillations and (ii) a multi-relaxation time collision operator is utilized to fix the viscosity-dependent numerical slip error of the immersed boundaries. To further reduce the computational effort, we extend the method from fixed and uniform Cartesian grids to adaptive quadtree/octree grids by implementing it in the open-source software Basilisk. A Lax-Wendroff streaming operator is adopted in our method to retain second-order accuracy in both space and time on non-uniform grids, as well as to maintain a unified time scale over the entire computational domain. Consequently, one collision-streaming operation only is required per time step at all grid levels. We test our proposed method on a set of validation cases corresponding to assorted incompressible flows with fixed and moving rigid particles in both 2D and 3D. The accuracy and robustness of our method are demonstrated via thorough comparison with the analytical, experimental and numerical data provided in the literature.

An explicit particle method for simulation of multiphase flows

Weakly-compressible Moving particle simulation (WCMPS) is a Lagrange meshless method that is advantageous in solving complex fluid problems. Although the accuracy can be addressed in WCMPS, instability arises due to pressure fluctuations from particle clustering. Weakly Compressible Moving Particle Explicit (WCMPE) method improved the pressure calculation and stability of WCMPS while preserving its coding system with high computational efficiency. In this study, the multiphase WCMPE method is developed with a simple density smooth technique and interface detection procedure. Several numerical cases were investigated by the multiphase WCMPE method, including Rayleigh-Taylor (R-T) instability cases with various density and viscosity ratio conditions, oil spill and oil-water sloshing experiments. In general, good agreements with analytical solutions or from experimental data were obtained in multiphase WCMPE results with negligible unphysical pressure oscillation and pressure noise points.

ColESo: Collection of exact solutions for verification of numerical algorithms for simulation of compressible flows

ColESo is a set of subroutines that evaluate particular solutions of the Euler equations, the Navier – Stokes equations, and their linearized versions. These solutions were used by the author for the verification of high-order methods for the compressible flow simulation. It is convenient to use an exact solution when it is available for each point of the computational domain, accurate enough, and quick to evaluate. A solution given by a composition of elementary functions is usually a good choice, but the set of such solutions is too limited. ColESo adds to this set several solutions in integral form and provides their quick calculation with a good accuracy. Program summaryProgram Title: ColESoCPC Library link to program files:https://doi.org/10.17632/z7mypchgfz.1Developer's repository link:https://github.com/bahvalo/ColESoCode Ocean capsule:https://codeocean.com/capsule/0365245Licensing provisions: GPLv2.1Programming language: C++ (C++03 standard)Nature of problem: Verification of high-order methods for the simulation of compressible gas dynamics on curvilinear or unstructured grids.Solution method: Change of variables, Fourier transformation, Gauss–Legendre and Gauss–Jacobi quadrature rules.Additional comments including restrictions and unusual features: ColESo uses several special functions provided by Cephes Math Library and GNU LibQuadMath (for the quadruple precision). To define the Gauss – Jacobi quadrature rules, ColESo uses a code written by S. Elhay, J. Kautsky, J. Burkadrt. These libraries are open-access and distributable with compatible licenses.

A data‐driven memory model for solving turbulent flows with the pseudo‐direct numerical simulation method

ABSTRACTIt is well known that the inherent three‐dimensional and unsteady nature of turbulent flows is a stumbling block for all approaches aimed at resolving their spatial and temporal variability. The pseudo‐direct numerical simulation (P‐DNS) method for turbulent flows, proposed by the authors in a previous publication, focused on resolving the spatial variability, leaving the task of solving the temporal evolution to a highly simplified, parameter dependent model, to be adjusted in a case by case basis. Although some auspicious results were obtained, the applicability of P‐DNS for problems of industrial interest required a more sophisticated method to deal with the temporal variability. In this sense, the present work proposes a new, parameter free, data‐driven memory model for P‐DNS. The model is based on the study of off‐line DNS solutions of turbulent flows transitioning between statistically steady states in simple domains. The new P‐DNS model is tested and successfully compared against existing methods in selected three‐dimensional turbulent flows.