Simulation Of Two-dimensional Flow Research Articles

Numerical Simulations of Shock Propagation Under Strong Nonequilibrium Conditions

A computational approach is developed to simulate high-enthalpy shock propagation under strong nonequilibrium conditions, such as reentry experiments at NASA’s Electric Arc Shock Tube (EAST) facility. Two-dimensional axisymmetric simulations of EAST flow are performed for Earth reentry at . An 11-species weakly ionized air model is used to capture the real-gas behavior with reaction rates from the literature. Species mass-diffusion fluxes are calculated assuming a self-consistent effective binary diffusion in conjunction with Gupta–Yos collision integral data. The unsteady, linearized system of conservation laws is solved in a moving frame of reference with active shock tracking to reduce the computational cost by three orders of magnitude relative to that of fixed-frame calculations on a uniform grid. This approach enables time-accurate yet computationally feasible predictions of gas behavior at the test section. Computational fluid dynamics predictions can be compared with the experimental data to gain an improved understanding of the flow physics. Additionally, useful quantities such as boundary-layer thickness and growth rate, and radial variation of gas properties can be computed, which are difficult to measure in experiments.

An immersed boundary formulation incorporating a two-layer wall model approach for RANS simulations with complex geometry

We propose an immersed boundary (IB) formulation incorporating a two-layer wall model approach for Reynolds-averaged Navier-Stokes (RANS) simulations with complex geometry. The main objective of the present study is to broaden the capability of the IB method to high-Reynolds number turbulent flows with non-equilibrium effects. A two-layer wall model is applied to the IB method by considering a thin boundary layer approximation near the wall in order to reduce the computational cost of resolving the turbulent boundary layer. Tangential pressure gradient and convective terms are included in the thin boundary layer equation to make the wall model suitable for non-equilibrium flows, in which cross-derivative terms are modeled along the wall-normal direction to maintain the ordinary differential form of the equation. Turbulent viscosity in the inner layer is determined using a simplified k−ϵ−fμ model, that performs better than the typical mixing-length model in the separation and reattachment regions, where the friction velocity uτ becomes zero. To impose the mass conservation constraint near the IB surface with marginal computational cost, the IB approximated domain method is applied. The proposed IB formulation is validated using numerical simulations of two-dimensional turbulent channel flow, backward-facing step flow, turbulent flow around a circular cylinder, and three-dimensional turbulent flow over a wall-mounted circular sphere with a relatively coarse grid near the IB surface. The results demonstrate that the proposed IB formulation captures the flow patterns well and accurately predicts wall shear stress for both equilibrium and non-equilibrium flows, even with a relatively coarse grid near the wall.

A generalized sphere function-based gas kinetic scheme for simulation of compressible viscous flows

In this paper, a generalized sphere function-based gas kinetic scheme (GKS) is developed for simulation of two-dimensional compressible viscous flows. This work aims to improve the existing simplified GKS, in which a simple two-dimensional/three-dimensional distribution function is used as the equilibrium state. The present scheme applies the finite volume method to discretize Navier–Stokes equations and the numerical flux at cell interface is evaluated by the local reconstruction of solution for the continuous Boltzmann equation with [Formula: see text]-dimensional sphere function. This local solution contains both the equilibrium part and nonequilibrium part, and the contribution of the nonequilibrium part is controlled by a switch function. It is found that the present scheme has the same expression as the circular function-based GKS for the two-dimensional case and the sphere function-based GKS for the three-dimensional case. Therefore, these two GKSs can be unified, and the developed method provides another way for the simple distribution function.

Natural fractures in soft coal seams and their effect on hydraulic fracture propagation: A field study

Natural fractures provide direct flow channels for coalbed methane (CBM) production and gas outburst control. However, in soft coal seams, the characteristics of natural fractures and their effect on hydraulic fractures are still unclear. In this study, a spatial system of visible natural fractures was established through underground dissection and measurement of ground joints from a case study of the Xinyuan Coal Mine in the northern Qinshui Basin, China. Our results show that the orientations of the subsurface exogenetic fractures of the coal seams are consistent with the macrostructural joints on the ground surface in the same tectonic setting. The exogenetic fractures of the coal seams have dominant orientations with approximately equal spacing. Next, a field test of a large-scale hydraulic fracturing project with a volume of up to 2000 m3 was conducted. The on-site observation of the underground coal seams revealed that the propagation orientation of the vertical propped fractures coincides with the predominant orientation of the natural fractures. Even at a high constant injection rate (12 m3/min), the corresponding injection pressure was not constant during the propagation of the hydraulic fractures, and this can be attributed to the effect of the depth of the coal seam, internal natural fracture network, and normal fault. Additionally, a two-dimensional (2D) particle flow simulation (PFC2D) showed that the propagation of the hydraulic fracture is controlled by the orientations of the natural fractures and the principal stresses. The orthogonal fracture network showed more sensitivity to joint spacing than the layered fracture network in controlling the hydraulic fractures. Finally, fluid detection of the coalbed demonstrated that the flow range of the fracturing fluid in the natural exogenetic fractures was up to a few hundred meters. The flow direction was consistent with that of the natural fractures. A comprehensive analysis of the natural fractures contributes to the identification of flow channels and helps in the design of hydraulic fracturing engineering in soft coal seams.

An immersed boundary method based on domain decomposition

A novel immersed boundary method based on a domain decomposition approach is proposed in the context of a finite element discretisation method. It is applicable to incompressible flows past rigid, deforming, or moving bodies. In this method, unlike most immersed boundary methods, strong boundary conditions are imposed in the regions of the computational domain that are occupied by the structure. In order to achieve this, the proposed formulation decomposes the computational domain by splitting the finite element test functions into solid and fluid parts. In the continuous Galerkin formulation, this produces a smeared representation of the fluid-structure interface. The absence of an immersed boundary forcing term implies that the method itself has no influence on the CFL stability criterion. Furthermore, the stiffness matrix in the momentum equation is sparser than compared with other forcing immersed boundary methods, and symmetry and positive-definiteness of the Laplacian operator in the pressure equation is preserved. As shown in this paper, stability and accurate imposition of boundary conditions make the method promising for high Reynolds number flows. The method is applied to the simulations of two-dimensional laminar flow over stationary and moving cylinders, as well as a moderately high Reynolds number flow past an aerofoil. Good results are obtained when compared with those from previous experimental and numerical studies.

The passage of a bubble or a drop past an obstruction in a channel

The passage of a fluid particle (bubble or a drop) past an obstruction in a rectangular channel is examined by numerical simulation, focusing on the disruption of the wake and the trajectory of the fluid particle. The flow is laminar, and the wake is initially steady. The obstruction is relatively large compared to the height of the channel. The problem is defined by the capillary number (Ca) and the Reynolds number (Re), the density (ηρ) and viscosity (ημ) ratios, and the relative size of the fluid particle (ηd). Simulations of three-dimensional flows are used to examine several combinations of these parameters. The results show that the motion of a drop is nearly independent of the wake downstream of the obstruction, but bubbles may get temporarily trapped in it. Drops also tend to block the background flow, while bubbles may accelerate it. It is found that a bubble of comparable or smaller size than the constriction can pass through the constriction intact without getting trapped. An increase in Ca and Re leads to bubbles passing through the constriction at a faster speed and move further downstream before being caught by the wake. Simulations of two-dimensional flows for a relatively larger range of Ca and Re are performed to obtain a flow regime diagram. The results show that relatively rigid particles (low Ca) tend to be temporarily trapped in the wake, while more deformable particles (higher Ca) pass without being trapped at lower Reynolds numbers but break up at higher Reynolds numbers. The influence of the obstruction geometry is also examined.

High-order least-square-based finite-difference-finite-volume method for simulation of incompressible thermal flows on arbitrary grids.

In this work, a high-order (HO) least-square-based finite difference-finite volume (LSFD-FV) method together with thermal lattice Boltzmann flux solver (TLBFS) is presented for simulation of two-dimensional (2D) incompressible thermal flows on arbitrary grids. In the present method, a HO polynomial based on Taylor series expansion is applied within each control cell, where the unknown spatial derivatives at each cell center are approximated by least-square-based finite difference (LSFD) scheme. Then the recently developed TLBFS is applied to evaluate the convective and diffusive fluxes simultaneously at the cell interface by local reconstruction of thermal lattice Boltzmann solutions of the density and internal energy distribution functions. The present HO LSFD-FV method is verified and validated by 2D incompressible heat transfer problems. Numerical results indicate that the present method can be effectively and flexibly applied to solve thermal flow problems with curved boundaries on arbitrary grids. Compared with the conventional low-order finite volume method, higher efficiency and lower memory cost make the present HO method more promising for practical thermal flow problems.

Flood Hazard, Vulnerability and Risk Assessment for Different Land Use Classes Using a Flow Model

This study is concerned with flood risk that can be assessed by integrating GIS, hydraulic modelling and required field information. A critical point in flood risk assessment is that while flood hazard is the same for a given area in terms of intensity, the risk could be different depending on a set of conditions (flood vulnerability). Clearly, risk is a function of hazard and vulnerability. This study aims to introducing a new approach of assessing flood risk, which successfully addresses this above-mentioned critical issue. The flood risk was assessed from flood hazard and vulnerability indices. Two-dimensional flood flow simulation was performed with Delft3D model to compute floodplain inundation depths for hazard assessment. For the purpose of flood vulnerability assessment, elements at risk and flood damage functions were identified and assessed, respectively. Then, finally flood risk was assessed first by combining replacement values assessed for the elements and then using the depth–damage function. Applying this approach, the study finds that areas with different levels of flood risk do not always increase with the increase in return period of flood. However, inundated areas with different levels of flood depth always increase with the increase in return period of flood. The approach for flood risk assessment adopted in this study successfully addresses the critical point in flood risk study, where flood risk can be varied even after there is no change in flood hazard intensity.

Numerical Characterization of Viscous Heat Dissipation Rate in Oscillatory Air Flow

Abstract The effect of viscous heat dissipation (VHD) in raising the temperature field of incompressible oscillatory air flow is studied numerically. A threshold is established for when the viscous heat dissipation term in the thermal energy equation changes or does not change the temperature field for the case of oscillatory air flow in a tube connecting two reservoirs. This new criterion has not been specified clearly in earlier oscillatory flow research. According to the defined threshold and when VHD is important, the effect of dissipative bulk heating can be described by a proposed correlation in terms of Womersley number (Wo) and axial tidal displacement (ΔZ) of the oscillatory fluid. These results are determined using two-dimensional (2D) numerical simulations of laminar oscillatory air flow (Pr = 0.7) for different adiabatic unconductive tube-reservoirs' systems configurations over a wide range of oscillatory frequencies and tidal displacements. It is found that the low amount of fluid kinetic energy, which is converted into internal energy, is not sufficient to significantly heat up the fluid at a low rate of the viscous work. Therefore, the effect of viscous heat dissipation in oscillatory air flow can be ignored only below a specific limit of unsteadiness depending on Womersley number and axial tidal displacement. Also, the results showed that the VHD becomes more significant with increasing (Wo) and (ΔZ).

Study of the ionizing gas flow in the channel of plasma accelerator with different ways of gas inflow at the inlet

Numerical studies of the ionization process are presented for various ways of the gas supplying at the inlet of the coaxial channel of the quasi-stationary plasma accelerator. Simulation of two-dimensional axisymmetric flows of ionizing gas was carried out on the basis of the equations of radiation magnetic gas dynamics taking into account radiation transport. The approximation of local thermodynamic equilibrium in three-component medium consisting of atoms, ions, and electrons was used in the MHD model. It was determined that non-uniform gas inflow at the channel inlet leads to even greater instability of the pulsating unsteady flows of the ionizing gas in the plasma accelerator. The method of long characteristics was used in the 3D model of radiation transport, including the basic mechanisms of emission and absorption for different portions of the spectrum. The radiation field in the ionizing gas flow was determined, including the integral radiation characteristics and the spectral radiation intensities in the narrow ranges of frequencies or photon energies.

Power minimization and vortex shedding elimination of a circular cylinder by moving surface mechanism

A two-dimensional simulation of the laminar flow past a circular cylinder is investigated, in this study. To control the boundary layer growth, a pair of moving surfaces with streamwise (positive) motion is mounted on different locations of the upper and lower surfaces of the cylinder. The effects of the surface locations on the power and drag coefficients and the vortex shedding state are studied at several moving surface speeds. The Reynolds number based on the cylinder diameter is varied between 60 and 180. The flow simulation is performed by a solution of the unsteady Navier-Stokes equations using a pressure-velocity coupling method. To integrate the momentum equations, a four-stage Runge–Kutta scheme with second-order accuracy in time and space is used. Some results are compared with previous experimental and numerical data. The results from this study indicate that the moving surfaces can eliminate the vortex shedding so that the flow achieves a steady state for the above-mentioned range of Reynolds number. It is also found that some of these surfaces reduce the drag coefficient and the total power requirements of the system motion. Moreover, the optimum location and the speed of the surfaces corresponding to the minimum power coefficient are obtained.

連続性と時間刻み依存性を考慮したDiffusion wave 法による２次元土石流解析

連続性と時間刻み依存性を考慮したDiffusion wave 法による２次元土石流解析

Numerical simulations of the pulsatile blood flow in narrowing small vessels using different rheological models

The study of the blood flow through the circulatory system vessels depends on the rheological properties of the blood, the pulsatile nature of the blood flow and the vessel diameter. Blood behaves as a non-Newtonian fluid in small vessels, in situations of complex geometry and in certain cardiovascular diseases such as hypertension, coronary artery diseases, etc.In this article, we present two-dimensional computational simulation of blood flow in an axisymmetric narrowed small vessels (stenosis artery) taking into consideration the non-Newtonian fluid properties. The study is based on the numerical solution of the Navier-Stokes equations for Pulsatile flow using three constitutive relations for modeling the rheological blood behavior, ie; the Cross law; the Generalized power law; Gpl, and the Herschel-Bulkley law. We examined the flow characteristics particularly the velocity, shear rate distribution, wall shear stress and time-dependent vortex structures with respect to critical flow conditions in small vessels. Results indicate that the instantaneous flow characteristics are significantly affected by the blood rheological models considered, especially, in zones of important shear rate.

Characteristics of Flood Flow with Active Sediment Transport in the Sozu River Flood Hazards at the Severe Rainfall Event in July 2018

This study reveals the characteristics of flood flow with active sediment transport that caused the Sozu River flood disaster in July 2018. The results of field surveys revealed that the basin contains steep mountains and flat areas, facilitating the rapid transport of sediment produced in the mountains to downstream areas during the disaster. Two-dimensional numerical simulations of flood flow with sediment transport are conducted to realize the flood flow characteristics. As a result of the simulation, a huge amount of sediment deposition in the channel near the top of the alluvial fan increases the inundation damage at downstream areas. The results indicate that within two flood peaks during the disaster, the inundation in the second flood peak is more severe than that in the first peak, whereas the discharge of the second peak is much less than that in the first peak, caused by the reduction in the capacity of the original channel owing to the sand deposition during the first and second flood peaks.

Method of Evaluating Exhaust Characteristics of High-Voltage Circuit Breaker

The exhaust characteristics at high current duty of a breaker terminal fault for a gas circuit breaker are evaluated. A method of designing the exhaust chamber so that the exhaust temperature is less than the threshold temperature is then proposed. The threshold temperature is the value at which the maximum electric field of the exhaust chamber coincides with the critical electric field. In the design, the initial value of the structure is determined so as to decrease the number of trials in the development process. The calculation time of the numerical analysis is reduced by combining a one-dimensional (1-D) arc simulation with a two-dimensional (2-D) gas flow simulation of only the exhaust parts. An optimal design of an exhaust chamber using this design method is described as an example. In the interruption test of 63 kA using the optimal structure, dielectric strength was ensured and no flashovers occurred in any opening area.

Methane gas transport in unconfined aquifers: A numerical sensitivity study of a controlled release experiment at CFB Borden

Subsurface leakage of natural gas from petroleum wells can impact freshwater aquifers. Accurate prediction of gas migration in the subsurface will depend on knowledge of permeability, porosity, and flow system conditions. A series of two-dimensional numerical multi-phase flow simulations (CFbio) were conducted to investigate the role of multi-phase parameters (relative permeability and air entry pressure), flow system conditions (intrinsic permeability, anisotropy, and groundwater velocity), and geometric properties (layer thickness and layer lateral continuity) on the flow of gas-phase methane emanating from two variable-rate point sources in an unconfined sandy aquifer. Numerical simulations showed that for a homogeneous, weakly anisotropic aquifer, gas migrates almost exclusively vertically due to buoyancy, before venting to the vadose zone and atmosphere. As vertical migration became restricted through increased anisotropy, inclusion of lower-permeable layers, or increased horizontal groundwater velocity, an increase in the lateral component of gas migration was observed. This led to the formation of a broader lateral migration of the gas-phase plume and establishment of variably distributed vertical preferential flow paths, ultimately resulting in increased gas retention in the aquifer with relatively less methane reaching the vadose zone or atmosphere. The inclusion of a thin layer with moderately lower permeability (1–2 orders of magnitude) and increased air entry pressure was used to depict a fine-grained sand lens within a uniform aquifer. This subtle feature led to the formation of thin gas pools extending up- and down-gradient beneath the lens, allowing methane to travel much farther and faster than by groundwater advection alone, which is consistent with field observations during the experiment. In all scenarios investigated gas-phase methane was shown to migrate predominantly vertically due to buoyancy, until the aquitard permeability was <30% of the aquifer permeability. Our modelling demonstrates that even subtle permeability contrasts, together with capillary pressure changes demarcating grain-scale bedding, will lead to extensive lateral free-phase gas migration, and development of a more extensive and complex zone of impacted aquifer than presupposed.

Insights into design of mobility control for chemical enhanced oil recovery

This study compares two methods of mobility-control design for chemical enhanced oil recovery processes. Method 1 matches the total relative fluid mobility upstream and downstream of the shock front. In method 2 the viscosity of the displacing agent is selected such that the total mobility at the shock water saturation is equal to or less than the minimum mobility across the saturation range. The two methods are based on fractional flow analysis of one-dimensional flow and they are validated against two-dimensional simulations of flow through heterogeneous permeable media. Our results emphasize the key role of the water/oil relative permeability curves for the design of mobility control in polymer and surfactant/polymer flooding. The polymer viscosity obtained by setting the shock-front mobility ratio to one (method 1) is the minimum viscosity to ensure a stable displacement front. Design by method 2 results in a larger viscosity than method 1. This shifts the shock water saturation to larger values and hence more oil is displaced. Moreover, we find that for surfactant-polymer (SP) solutions with ultra-low interfacial tension (IFT) reduction (Winsor type III), the required polymer viscosity is always greater than the oil viscosity (at low shear rates). However, for Winsor type I solutions, for oils with medium and large viscosity the non-linear shape of the relative permeability function leads to polymer viscosities that are less than that of the oil. For light oils the viscosity of the ASP solution should be significantly larger than the oil viscosity.

Evaluating Curb Inlet Efficiency for Urban Drainage and Road Bioretention Facilities

An updated two-dimensional flow simulation program, FullSWOF-ZG, which fully (Full) solves shallow water (SW) equations for overland flow (OF) and includes submodules modeling infiltration by zones (Z) and flow interception by grate-inlet (G), was tested with 20 locally depressed curb inlets to validate the inlet efficiency (Eci), and with 80 undepressed curb inlets to validate the inlet lengths (LT) for 100% interception. Previous curb inlet equations were based on certain theoretical approximations and limited experimental data. In this study, 1000 road-curb inlet modeling cases from the combinations of 10 longitudinal slopes (S0, 0.1–1%), 10 cross slopes (Sx, 1.5–6%), and 10 upstream inflows (Qin, 6–24 L/s) were established and modeled to determine LT. The second 1000 modeling cases with the same 10 S0 and 10 Sx and 10 curb inlet lengths (Lci, 0.15–1.5 m) were established to determine Eci. The LT and Eci regression equations were developed as a function of input parameters (S0, Sx, and Qin) and Lci/LT with the multiple linear regression method, respectively. Newly developed regression equations were applied to 10,000 inlet design cases (10 S0, 10 Sx, 10 Qin, and 10 Lci combinations) and comprehensively compared with three equations in previous studies. The 100% intercepted gutter flow (Qg100) equations were derived, and over-prediction of Qg100 from previous methods was strongly correlated to smaller S0. Newly developed equations gave more accurate estimations of LT and Eci over a wide range of input parameters. These equations can be applied to designing urban drainage and road bioretention facilities, since they were developed using a large number of simulation runs with diverse input parameters, but previous methods often overpredict the gutter flow of total interception when the longitudinal slope S0 is small.

Evaluation of force term in lattice Boltzmann method with discrete external boundary force for flow over an immersed body

In this paper, lattice Boltzmann method is used for the simulation of two-dimensional flow over an immersed solid body using external boundary force. Fluid simulation is performed using the Eulerian grid for the entire computational domain, while the domain of solid body is discretized using a boundary-fitted Lagrangian grid, imposed on the uniform Eulerian grid. Fluid–solid interaction is modeled using external boundary force (EBF) technique. Two different methods of implementing boundary force are discussed including modification in (a) collision step of LBM and (b) both collision and computation of macroscopic velocity steps. Computations are performed for flow over a stationary circular object as well as particle sedimentation. Results of drag force and sedimentation velocity show good correspondence with previously published ones at Re =1.0 for both methods. No discrepancy in results was observed between two methods for higher Reynolds numbers. Results obtained for sedimentation of an elliptical object show that the type of implementation of boundary force has no significant effect on the predicted location and angular position of the elliptical object. Furthermore, it is observed that more accurate results are obtained by introducing a modification in EBF for which solutions were independent of the number of nodes on the surface boundary.

Prediction of water velocities in circular aquaculture tanks using an axisymmetric CFD model

Computational fluid dynamics (CFD) software was used to construct two-dimensional axisymmetric simulations of the turbulent flow inside 1.5, 5, 9.15 and 10 m tanks containing rotating water. The water rotation was induced mathematically by either placing a rotating cover on the surface of the water or locating a tangential water inlet near the top of the side wall. Central and side drains evacuated the water from the tank when using an inlet. The rotating cover produced a forced vortex in the tanks similar to the one observed in actual rearing tanks when the majority of the flow is leaving via the side drain. The predicted flow structure in tanks with an inlet can be divided into three regions: a narrow region along the side wall where the rotating water is moving down toward the floor, a thin boundary layer along the floor where the rotating water is moving radially inward, and a large region in the bulk of the tank where radial and axial velocities are small and the tangential velocity is independent of elevation but varies with radial position. Calculations were performed with the k-ε (RNG) and Reynolds stress turbulence models. Converged solutions were easier to obtain with the k-ε (RNG) model but only the Reynolds stress model could predict the strong vortex which is experimentally observed to form in the central portion of the tank as the flow leaving via the center drains is increased. The simulations predict that the thickness of the floor boundary layer is proportional to the tank diameter and that the radial velocity within the floor boundary layer is maximum at an elevation equal to about 10% of the boundary layer thickness. At any given radial position, the maximum value of the radial velocity next to the floor is between 15 and 45% of the tangential velocity in the bulk of the tank. Predicted shear stresses along bounding surfaces were used to obtain correlations for the side-wall and floor friction coefficients in terms of the Reynolds number. These correlations were in turn substituted in an overall moment balance to obtain an analytical model for predicting the maximum tangential velocity Vθw near the side wall of multi-drain rearing tanks. The predictions of the analytical model are in excellent agreement with Vθw values reported in the literature for tanks with diameters ranging from 1.5–15 m and indicate that the drag from inlet structures is non-negligible. The results demonstrate that the axisymmetric CFD model can simulate the main features of the rotating flow inside circular tanks and provide valuable boundary-layer information that is difficult to obtain experimentally.