Method For Simulation Of Flows Research Articles

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.

Multi-objective optimization of guide vane closure scheme in clean pumped-storage power plant with emphasis on pressure fluctuations

In this study, multi-objective optimization was conducted for the guide vane closure scheme during the load-rejection process of a pump turbine, considering pressure fluctuation, maximum rotational speed, maximum pressure at the volute, and minimum pressure at the draft tube inlet to decrease the low-frequency high-amplitude pressure fluctuations at conditions near no-load. Two quantitative indicators, minimum discharge (Qmin) and the ratio of rotational speed to hydraulic head (NDH) of the pump turbine, were proposed to represent the backflow-induced pressure fluctuations. Two objective functions were defined to optimize the guide vane closure scheme and two optimized guide vane closure schemes, OPS-Q (based on Qmin) and OPS-NDH (based on NDH), were developed. The enhancements resulting from these vane closure schemes were verified using a one-dimensional–three-dimensional coupling flow simulation method. NDH was revealed to comprehensively represent backflow-induced pressure fluctuations, whereas Qmin partially represented the backflow. Consequently, OPS-NDH suppressed the pressure fluctuations by appropriately increasing the maximum pressure at the volute and the maximum vacuum at the draft tube inlet within the allowance ranges of the pumped-storage power plant. OPS-Q suppressed the pressure fluctuations; however, the minimum pressure at the draft tube inlet could not be controlled to satisfy the design requirements of the pumped-storage power plant. The findings of this study can be used as a theoretical reference for suppressing the pressure fluctuations in a clean pumped-storage power plant under near-no-load conditions.

Hybrid VOF–Lagrangian CFD Modeling of Droplet Aerobreakup

A hybrid VOF–Lagrangian method for simulating the aerodynamic breakup of liquid droplets induced by a traveling shock wave is proposed and tested. The droplet deformation and fragmentation, together with the subsequent mist development, are predicted by using a fully three-dimensional computational fluid dynamics model following the unsteady Reynolds-averaged Navier–Stokes approach. The main characteristics of the aerobreakup process under the shear-induced entrainment regime are effectively reproduced by employing the scale-adaptive simulation method for unsteady turbulent flows. The hybrid two-phase method combines the volume-of-fluid technique for tracking the transient gas–liquid interface on the finite volume grid and the discrete phase model for following the dynamics of the smallest liquid fragments. The proposed computational approach for fluids engineering applications is demonstrated by making a comparison with reference experiments and high-fidelity numerical simulations, achieving acceptably accurate results without being computationally expensive.

Formation pressure distribution and productivity prediction of fractured horizontal wells in stress sensitive reservoirs

Aiming at the problems of formation pressure distribution and productivity prediction after Horizontal Well Volume Fracturing in stress sensitive reservoirs, the methods of dynamic permeability and dynamic threshold pressure gradient are used to deal with the influence of stress sensitivity, a numerical simulation method of oil-water two-phase flow based on finite element method is established. History matching is performed on the basis of the prediction of formation pressure distribution after horizontal well volume fracturing of, which ensures high matching accuracy. Taking the ultra-low permeability sandy glutenite reservoir of Baikouquan Formation in M18 area of Aihu Oilfield as research object, the influence law of formation pressure level on productivity and stress sensitivity on formation pressure distribution is studied. Analysis of the calculation results shows that: the influence of formation pressure level on well productivity is mainly in the first year of production, and the effect of energy increasing by volume fracturing is clarified. Stress sensitivity mainly affects the middle and later stage of production. With the increase of sensitivity, the permeability loss of the formation tends to be concentrated in the low-pressure area near the artificial fracture, forming an isolation zone with high flow resistance, which make the development effect of far well zone worse.

Experimental and numerical study on the flow characteristics of slug flow in a horizontal elbow

• Phase distribution of gas-liquid two-phase slug flow at the elbow was clarified. • Effects of elbow on flow characteristics at slug flow were analyzed. • A CFD simulation method for slug flow at the elbow was presented. Elbow is one of the most accident-prone locations in multiphase flow lines, and understanding the flow field is the key to manage the risk. In the meantime, the flow characteristics of slug flow are most complicated in the flow field. To clarify the flow characteristics of slug flow at the elbow, the influence and mechanism of the elbow on the flow characteristics of slug flow under different superficial gas-liquid velocities were studied with experiments and numerical simulations. A set of transparent loops with gas-liquid two phase flow was built. High-speed camera, pressure sensor, Doppler velocimeter and wire mesh sensor were used to collect flow pattern, pressure, slug velocity and gas-liquid distribution characteristics. In the meantime, the multi-fluid volume of fluid (VOF) model was used in the CFD simulations, and the simulation results were compared against the experimental results for verification. The results showed that the void fraction is highest at the inlet and lowest at the middle position, and the pressure and flow velocity at the extrados were higher than those at the intrados of the elbow. With the increase of the superficial liquid velocity and gas velocity, the number of bubbles accumulated inside the horizontal elbow increased, the slug flow liquid film velocity of the horizontal elbow increased, and the secondary flow phenomenon weakened.

Accurate conservative phase-field method for simulation of two-phase flows

In this work, we propose a novel phase-field model for the simulation of two-phase flows that is accurate, conservative, bounded, and robust. The proposed model conserves the mass of each of the phases, and results in bounded transport of the volume fraction. We present results from the canonical test cases of a drop advection and a drop in a shear flow, showing significant improvement in the accuracy over the commonly used conservative phase-field method.Moreover, the proposed model imposes a lesser restrictive Courant-Friedrichs-Lewy condition, and hence, is less expensive compared to other conservative phase-field models. We also propose improvements on computation of surface tension forces and show that the proposed improvement significantly reduces the magnitude of spurious velocities at the interface.We also derive a consistent and conservative momentum transport equation for the proposed phase-field model and show that the proposed model when coupled with the consistent momentum transport equation results in discrete conservation of kinetic energy, which is a sufficient condition for the numerical stability of incompressible flows, in the absence of dissipative mechanisms. To illustrate the robustness of the method in simulating high-density ratio turbulent two-phase flows, we present the numerical simulations of high-density ratio droplet-laden isotropic turbulence at finite and infinite Reynolds numbers.

Comparative study of the virtual flux method and immersed boundary method coupled with regularized lattice Boltzmann method for suspension flow simulations

Suspension flows are ubiquitous in many fields, and reducing computational costs for numerical simulations of suspension flows remains a great challenge. Numerical simulations of particle-laden flows were performed here using the regularized lattice Boltzmann method (RLBM). RLBM, coupled with the virtual flux method (VFM) or the immersed boundary method (IBM) with the multi-direct forcing approach, conducted a series of three simulations for stationary and moving boundaries. The VFM and IBM results were compared for validation, and the computational efficiency was evaluated. For the two simulations using stationary and moving boundaries (i.e., a steady flow past a stationary cylinder and a plane Poiseuille flow including a single moving circular particle), the results based on the VFM and IBM were qualitatively comparable. The computational time for IBM was longer than that for VFM due to the iterations in its scheme. The pressure-driven suspension flow simulations showed that a dilute suspension's (<5%) relative viscosity was almost equivalent. The difference between the results obtained by the VFM and IBM in the semidilute regime (>10%) was discussed in terms of particle rotational motion. Even though the scalability for parallel computing was comparable between the VFM and IBM, the computational time could be effectively reduced by using the VFM instead of the IBM because of the increased suspension concentration.

An implicit Cartesian cut-cell method for incompressible viscous flows with complex geometries

A versatile conservative three-dimensional Cartesian cut-cell method for simulation of incompressible viscous flows over complex geometries is presented in this paper. The present method is based on the finite volume method on a non-uniform staggered grid together with a consistent mass and momentum flux computation. Contrary to the commonly cut-cell methods, an implicit time integration scheme is employed in the present method, which avoids numerical instability without any additional small cut-cell treatment. Strict conservation of the mass and momentum for both fluid and cut cells is enforced through the PISO algorithm for the pressure–velocity coupling. The versatility and robustness of the present cut-cell method are demonstrated by simulating various two- and three-dimensional canonical benchmarks (flow over a circular cylinder, airfoil, sphere, pipe, and heart sculpture) and the computed results agree well with previous experimental measurements and various numerical results obtained from the boundary-fitted, immersed boundary/interface, and other cut-cell methods, verifying the accuracy of the proposed method.

A pressure compensation method for lattice Boltzmann simulation of particle-laden flows in periodic geometries

A simple and efficient boundary treatment is proposed for periodic boundary conditions in a lattice Boltzmann method for simulating fully developed, pressure driven particle-laden flows in a complex geometry. The pressure driven effect is implemented by a simple pressure compensation method (PCM) using the pressure difference between the inlet and outlet boundaries. It eliminates the exchange of nonequilibrium distribution functions between inlet and outlet boundary nodes. It also eliminates the nonphysical oscillations of particle trajectory produced by a nonequilibrium extrapolation method when particles cross the periodic boundary. Simulation results show that the present PCM is equivalent to the body force method (BFM) for flow in a periodic straight channel with a uniform cross section. However, the BFM would significantly underestimate the fluid velocity for a flow and, hence, cannot accurately predict the particle trajectory in a periodic complex channel with a nonuniform cross section, especially at high Reynolds numbers.

Wall model‐based diffuse‐interface immersed boundary method for simulation of incompressible turbulent flows

AbstractIn this work, a method is proposed to simulate the high Reynolds number turbulent flows by combining the diffuse‐interface immersed boundary method (IBM) with different wall models. In this method, two auxiliary layers (a series of Lagrangian points) are set outside the wall: the reference layer and the enforced layer. The wall model is applied at the reference layer to calculate the wall shear stress and the boundary condition is implemented at the enforced layer. When implementing the boundary condition, the implicit velocity correction‐based IBM is used. This process requires the velocity at the enforced layer. To calculate the velocity at the enforced layer, the momentum equation is integrated along the normal direction of the wall to link the tangential component of the velocity to the wall shear stress predicted by the wall models, and the normal component of the velocity is approximately reconstructed by the parabolic distribution. In addition, the Reichardt's law combined with Spalding's formula is utilized to determine the integral length. Numerical experiments for the turbulent flows around the flat plate, the NACA0012 airfoil and the NACA23012 airfoil are carried out to verify the feasibility of this method.

Turbulent flow simulations of the common research model on Cartesian grids using recursive fitting approach

In this study, we propose a new method that uses the recursive fitting method and wall function for the three-dimensional turbulent flow simulation. The recursive fitting method based on the Cartesian grid method is employed for the automatic generation around two- and three-dimensional geometries. The grid approximately represents the concave and convex features, i.e., a wing–fuselage juncture and wing trailing edges. The wall boundary conditions can be imposed on the wall faces; thus, the conservation laws are strictly satisfied. Meanwhile, using the wall function allows turbulent boundary layers to be accurately reproduced. The turbulent flow simulation using the wall function is straightforward because the flow variables at the first cell centroid are employed for friction velocity estimation. However, the distance between the body surface and the first cell centroid varies since cells with different shapes are generated. Therefore, the simulation using the proposed method is validated through turbulent flow simulations in two dimensions. The results show the accurate predictions of the turbulent boundary layers. To investigate the capacity of the proposed method, three-dimensional simulation around aircraft at a transonic cruise condition is conducted. The automatically generated grids by the proposed method approximately represent the geometric features. The results of flow simulation show that the surface pressure and skin friction coefficient distributions agree with those of the reference simulation on a conventional body-fitted grid. Further, predicted pressure and viscous drag coefficients are reasonable compared with those of the reference simulation.

High-resolution cerebral blood flow simulation with a domain decomposition method and verified by the TCD measurement

Background: An efficient and accurate blood flow simulation can be useful for understanding many vascular diseases. Accurately resolving the blood flow velocity based on patient-specific geometries and model parameters is still a major challenge because of complex geomerty and turbulence issues. In addition, obtaining results in a short amount of computing time is important so that the simulation can be used in the clinical environment. In this work, we present a parallel scalable method for the patient-specific blood flow simulation with focuses on its parallel performance study and clinical verification.Methods: We adopt a fully implicit unstructured finite element method for a patient-specific simulation of blood flow in a full precerebral artery. The 3D artery is constructed from MRI images, and a parallel Newton–Krylov method preconditioned with a two-level domain decomposition method is adopted to solve the large nonlinear system discretized from the time-dependent 3D Navier-Stokes equations in the artery with an integral outlet boundary condition. The simulated results are verified using the clinical data measured by transcranial Doppler ultrasound, and the parallel performance of the algorithm is studied on a supercomputer.Results: The simulated velocity matches the clinical measured data well. Other simulated blood flow parameters, such as pressure and wall shear stress, are within reasonable ranges. The results show that the parallel algorithm scales up to 2160 processors with a 49% parallel efficiency for solving a problem with over 20 million unstructured elements on a supercomputer. For a standard cerebral blood flow simulation case with approximately 4 million finite elements, the calculation of one cardiac cycle can be finished within one hour with 1000 processors.Conclusion: The proposed method is able to perform high-resolution 3D blood flow simulations in a patient-specific full precerebral artery within an acceptable time, and the simulated results are comparable with the clinical measured data, which demonstrates its high potential for clinical applications.

Modeling drainage in porous media considering locally variable contact angle based on pore morphology method

The pore morphology method (PMM) has been widely applied to simulate the quasi–static drainage process of porous media, which requires less computational time and computer memory compared to other two–phase flow simulation methods. However, most of the existing pore morphology simulations were restricted to totally wetting systems (i.e., contact angle is equal to zero). Here, we propose a new pore morphology method (Lvca–PMM) enhanced by considering locally variable contact angles, which now enables a reproduction of the primary drainage process for porous media under different wettability conditions featuring the full range of contact angle for wetting phase for various spatial distribution. A series of simulations are performed by using the Lvca–PMM to a porous medium under different uniform and mixed wettability conditions. The proposed Lvca–PMM presents a better result compared to the method by Schulz et al. (2014) for different wettability conditions. The capillary pressure–saturation relations as well as the pore–scale fluid distributions can be well captured by the proposed Lvca-PMM.

An accurate and stable alternating directional moving particle semi-implicit method for incompressible flow simulation

As a Lagrangian mesh free method, Moving Particle Semi-implicit (MPS) method can easily handle complex incompressible flow with free surface. However, some deficiencies of MPS method such as inaccurate results, unphysical pressure oscillation and particle thrust near free surface still required to be further resolved. In this paper, an improved MPS method based on Crank-Nicolson time scheme, named Alternating Direction Moving Particle Semi-implicit (ADMPS) method, is proposed. In addition, a time integral source term (TIS) is developed to suppress unphysical pressure oscillation and a free-surface revise (FR) technique is proposed to avoid particle thrust near free surface. Enhancement of accuracy and stability by these improvements is proved by hydrostatic and dam breaking benchmarks, and the numerical results of the ADMPS-FR-TIS model show good agreement with the hydrostatic analytical solution and the dam breaking experiment data.

A three-dimensional particle finite element model for simulating soil flow with elastoplasticity

Soil flow is involved in many earth surface processes such as debris flows and landslides. It is a very challenging task to model this large deformational phenomenon because of the extreme change in material configurations and properties when soil flows. Most of the existing models require a two-dimensional (2D) simplification of actual systems, which are however three-dimensional (3D). To overcome this issue, we develop a novel 3D particle finite element method (PFEM) for direct simulation of complex soil flows in 3D space. Our PFEM model implemented in a fully implicit solution framework based on a generalised Hellinger–Reissner variational principle permits the use of a large time step without compromising the numerical stability. A mixed quadratic-linear element is used to avoid volumetric locking issues and ensure computational accuracy. The correctness and robustness of our 3D PFEM formulation for modelling large deformational soil flow problems are demonstrated by a series of benchmarks against analytical or independent numerical solutions. Our model can serve as an effective tool to support the assessment of catastrophic soil slope failures and subsequent runout behaviours.

A splitting method for the numerical simulation of free surface flows with sediment deposition and resuspension

AbstractWe present a numerical model for the simulation of 3D sediment transport in a Newtonian flow with free surfaces. The Navier–Stokes equations are coupled with the transport, deposition, and resuspension of the particle concentrations, and a volume‐of‐fluid approach to track the free surface between water and air. The numerical method relies on operator splitting to decouple advection and diffusion phenomena, and a two‐grid method. An appropriate combination of characteristics, finite volumes, and finite elements methods is advocated. The numerical model is validated through comparisons with numerical experiments, sediment flushing, shear flow erosion, and the formation of dunes.

Simulation of the effects of high shares of electric vehicles on voltage unbalance in the distribution grid level

Due to increasing shares of electric vehicles and thus of charging facilities, a multitude of issues and challenges arise for the operation and planning of distribution grids. In this context, voltage quality and in particular the impact on voltage unbalance is gaining more and more attention. For this reason, this paper addresses the impact of high penetration rates of electromobility on voltage unbalance in the low-voltage grid and the related question of whether current limits for the maximum customer-side unbalanced load need to be adjusted. For this purpose, different technological scenarios and exemplary grids are analyzed by a phase-accurate Monte-Carlo-based load flow simulation method. The results show a noticeable influence of unbalanced EV charging power on the voltage unbalance in the considered grids.

Multiscale Modeling of Gas–Solid Surface Interactions Under High-Temperature Gas Effect

The high-temperature gas effect is critical to the design of high-speed aircraft in terms of the thermal protection at their surfaces. However, studies on this topic are challenging for both experiments and numerical simulation. To cope with the breakdown of continuum methods and the extremely high cost of molecular methods, a multiscale model and simulation method for flow, diffusion, adsorption/desorption, reaction, and heat transfer is developed to understand the gas effect based on hard-sphere/pseudo-particle modeling (HS-PPM). The model was first used to describe the catalytic reactions of high-temperature gas without flow on the surface of copper, tungsten, platinum, nickel, silicon dioxide, etcetera. The recombination coefficients of oxygen and nitrogen atoms obtained at different temperatures are in good agreement with the existing simulation and experimental results, which verified the effectiveness and accuracy of the approach. The approach is also capable of simulating the complex physical and chemical processes in the gas flow near the silicon dioxide surface, with the critical flow velocity slip and temperature jump reasonably reproduced. These studies demonstrated that HS-PPM can be a comprehensive virtual experimental tool for the study of surface catalytic characteristics of thermal protection materials in a hypersonic environment and accurate prediction of the aerodynamic thermal behavior there.

A method for pore-scale simulation of single-phase shale oil flow based on three-dimensional digital cores with hybrid mineral phases

The mineral properties of the pore walls have a great influence on the single-phase shale oil flow at the pore scale. In this paper, a new method is proposed for pore-scale simulation of single-phase shale oil flow based on digital cores with hybrid mineral phases. This method can identify each mineral pore wall and correspondingly consider the adsorption layer and slippage boundary condition. First, three-dimensional (3D) digital cores with hybrid mineral phases are reconstructed from two-dimensional (2D) scanning electron microscope images of a shale sample, and correspondingly the pore space is divided with computational grids. Second, a mathematical model of shale fluid flow is established based on the Navier–Stokes (N–S) equation, combined with the slip length and viscosity formula. Finally, the equations are discretized on the mesh by the finite volume method and solved by the semi-implicit method for pressure-linked equations for flow simulation of shale oil in the 3D digital cores. By applying the method, we analyze effects of total organic carbon in volume, slippage, and adsorption on the single-phase shale oil flow based on 3D digital cores with hybrid mineral phases.