Three-dimensional Incompressible Viscous Flow Research Articles

The Impact of Installation Angle on the Wind Load of Solar Photovoltaic Panels

In order to explore the wind load characteristics acting on solar photovoltaic panels under extreme severe weather conditions, based on the Shear Stress Transport (SST) κ-ω turbulence model, numerical calculations of three-dimensional incompressible viscous steady flow were performed for four installation angles and two extreme wind directions of the solar photovoltaic panels. The wind load characteristics on both sides of the photovoltaic panels were obtained, and the vortex structure characteristics were analyzed using the Q criterion. The results indicate that, under different installation angles, the windward side pressure of the solar photovoltaic panel is generally higher than the leeward side. The leeward side is prone to forming larger vortices, increasing the fatigue and damage risk of the material, which significantly impacts the solar photovoltaic panel. As the installation angle increases, the windward side pressure of the solar photovoltaic panel also gradually increases. Therefore, optimal installation methods include installing the panel facing the wind at angles of 30° and 45°, or installing it facing away from the wind at a 60° angle, to minimize the impact of wind load on the solar photovoltaic panel.

An analysis of the numerical stability of the immersed boundary method

We present a numerical stability analysis of the immersed boundary (IB) method for a special case which is constructed so that Fourier analysis is applicable. We examine the stability of the immersed boundary method with the discrete Fourier transforms defined differently on the fluid grid and the boundary grid. This approach gives accurate theoretical results about the stability boundary since it takes the effects of the spreading kernel of the immersed boundary method on the numerical stability into account. In this paper, the spreading kernel is the standard 4-point IB delta function. A three-dimensional incompressible viscous flow and a no-slip planar boundary are considered. The case of a planar elastic membrane is also analyzed using the same analysis framework and it serves as an example of many possible generalizations of our theory. We present some numerical results and show that the observed stability behaviors are consistent with what are predicted by the theory.

Characteristic-Based Fluid Flow Modeling between Two Eccentric Cylinders in Laminar and Turbulent Regimes

Determining the flow between eccentric cylinders is crucial in a wide range of industries. The governing equations for the flow between eccentric cylinders cannot be solved analytically. Therefore, three-dimensional incompressible viscous fluid flow between eccentric and concentric cylinders has numerically been simulated in this paper to investigate them using a characteristic-based approach. The first-order characteristic-based scheme is used to calculate convective terms, whereas the second-order averaging technique is used to calculate viscous fluxes. The Taylor number, eccentricity distance, Reynolds number, and radius ratio are considered the controlling parameters of fluid flow between the cylinders. The influence of flow between cylinders on flow patterns is presented in terms of velocity, pressure, and flow contours. It is found that at a constant Taylor number, the asymmetric centrifugal forces produce the Taylor vortices on the right of the internal rotating cylinder as the eccentric distance increases. When the eccentric distance increases, the magnitude of shear stress and its fluctuation on the cylinder wall, as well as the pressure on the cylinder wall, rise. The numerical results obtained were validated by comparing them to previously published experimental results, which showed a high level of agreement.

Effects of the Advance Ratio on the Evolution of Propeller Wake

This study numerically carried out the propeller open water test (POW) by solving Navier-Stokes equations governing the three-dimensional unsteady incompressible viscous flow with the turbulence closure model of the Κ-ω SST model. Numerical simulations were performed at wide range of advance ratios. A great difference of velocity magnitude between the inner region and the outer region of the slipstream tube forms the thick and large velocity gradient which originates from the propeller tip and develops along the downstream. Eventually, the strong shear layer appears and plays the role of the slipstream boundary. As the advance ratio increases, the vortical structures originated from the propeller tips quickly decay. The contraction of the vortices trace is considerable with decreasing the advance ratio.

Variable thickness flow over a rotating disk under the influence of variable magnetic field: An application to parametric continuation method

The present work explores the behavior of three-dimensional incompressible viscous fluid flow and heat transfer over the surface of a non-flat stretchable rotating disk. A variable thickness fluid is subjected under the influence of an external variable magnetic field and heat transfer. Navier–Stokes equation is coupled with Maxwell equations to examine the hydrothermal properties of fluid. The basic governing equations of motion are diminished to a system of nonlinear ordinary differential equations using appropriate similarity framework, which are further treated with numerical scheme known as parametric continuation method. The parametric continuation method has combined interesting characteristics of both shooting and implicit finite difference methods. For validity of the present numerical scheme, a comparison with the published work is performed and it is found that the results are in excellent agreement with each other. Numerical and graphical results for the velocity, temperature, and magnetic strength profiles as well as skin fractions and Nusselt number are presented and discussed in detail for various physical parameters. The heat transfer process is reduced with positive increment of no-flatness parameter [Formula: see text], while Prandtl number increases the heat transfer rate at the surface of the disk.

A three-dimensional gas-kinetic flux solver for simulation of viscous flows with explicit formulations of conservative variables and numerical flux

A truly three-dimensional (3D) gas-kinetic flux solver for simulation of incompressible and compressible viscous flows is presented in this work. By local reconstruction of continuous Boltzmann equation, the inviscid and viscous fluxes across the cell interface are evaluated simultaneously in the solver. Different from conventional gas-kinetic scheme, in the present work, the distribution function at cell interface is computed in a straightforward way. As an extension of our previous work (Sun et al., Journal of Computational Physics, 300 (2015) 492–519), the non-equilibrium distribution function is calculated by the difference of equilibrium distribution functions between the cell interface and its surrounding points. As a result, the distribution function at cell interface can be simply calculated and the formulations for computing the conservative flow variables and fluxes can be given explicitly. To validate the proposed flux solver, several incompressible and compressible viscous flows are simulated. Numerical results show that the current scheme can provide accurate numerical results for three-dimensional incompressible and compressible viscous flows.

A parallel nonlinear multigrid solver for unsteady incompressible flow simulation on multi-GPU cluster

A nonlinear multigrid solver for solutions of unsteady three-dimensional incompressible viscous flow working on multi-GPU cluster is developed. The solver consists of a full approximation scheme (FAS) V-cycle scheme to accelerate the computation, in which the artificial compressibility method based Navier-Stokes solver is used as a smoother. Multi-stream overlapping strategies are designed to assist multi-GPU computations. The numerical procedure is validated by computing 3D laminar and turbulent flows within a lid-driven cubic cavity. The predicted results compare favorably with previous benchmark solutions and measurements, both in mean and turbulent quantities. For the performance of the FAS V-cycle scheme, up to two orders of magnitude speedups are reported, and the relationship between work unit (WU) and total grid number N is O(N0.3) under the deepest FAS V-cycle. A detailed evaluation of the GPU implementation is carried out employing the Roofline model and the scalability analysis.

Highly accurate simplified lattice Boltzmann method

In this paper, we present a highly accurate simplified lattice Boltzmann method (HSLBM) which can achieve the third-order of accuracy in space. By introducing virtual streaming nodes and decoupling the streaming distance from the mesh spacing, HSLBM effectively combines the local second-order simplified and highly stable lattice Boltzmann method (SHSLBM) and the overall high order scheme. The correlation between the streaming distance and the mesh spacing is accomplished by a high-order Lagrange interpolation algorithm. Through a series of tests, it is found that using 5 interpolation points and setting streaming distance as 1/5 of the mesh spacing can give optimal results. In general, HSLBM improves the accuracy of SHSLBM from the second order to the third order, while maintaining its merits like low memory cost, convenient implementation of physical boundary conditions, and good numerical stability. To match the accuracy of the flow solver, a linear extrapolation scheme with the third-order of accuracy is also proposed to determine the boundary values of the non-equilibrium distribution functions. Various benchmark tests are performed to demonstrate the robustness of HSLBM in simulating two- and three-dimensional incompressible viscous flows as well as its flexibility in problems with curved boundaries and on body-fitted meshes.

Preconditioned characteristic boundary conditions based on artificial compressibility method for solution of incompressible flows

The preconditioned characteristic boundary conditions based on the artificial compressibility (AC) method are implemented at artificial boundaries for the solution of two- and three-dimensional incompressible viscous flows in the generalized curvilinear coordinates. The compatibility equations and the corresponding characteristic variables (or the Riemann invariants) are mathematically derived and then applied as suitable boundary conditions in a high-order accurate incompressible flow solver. The spatial discretization of the resulting system of equations is carried out by the fourth-order compact finite-difference (FD) scheme. In the preconditioning applied here, the value of AC parameter in the flow field and also at the far-field boundary is automatically calculated based on the local flow conditions to enhance the robustness and performance of the solution algorithm. The code is fully parallelized using the Concurrency Runtime standard and Parallel Patterns Library (PPL) and its performance on a multi-core CPU is analyzed. The incompressible viscous flows around a 2-D circular cylinder, a 2-D NACA0012 airfoil and also a 3-D wavy cylinder are simulated and the accuracy and performance of the preconditioned characteristic boundary conditions applied at the far-field boundaries are evaluated in comparison to the simplified boundary conditions and the non-preconditioned characteristic boundary conditions. It is indicated that the preconditioned characteristic boundary conditions considerably improve the convergence rate of the solution of incompressible flows compared to the other boundary conditions and the computational costs are significantly decreased.

On effects of viscosity and magnetic fields on the largest growth rate of linear Rayleigh–Taylor instability

In this article, we investigate the effect of viscosity on the largest growth rate in the linear Rayleigh–Taylor (RT) instability of a three-dimensional nonhomogeneous incompressible viscous flow in a bounded domain. By adapting a modified variational approach and careful analysis, we show that the largest growth rate in linear RT instability tends to zero as the viscosity coefficient goes to infinity. Moreover, the largest growth rate increasingly converges to one of the corresponding inviscid fluids as the viscosity coefficient goes to zero. Applying these analysis techniques to the corresponding viscous magnetohydrodynamic fluids, we can also show that the largest growth rate in linear magnetic RT instability tends to zero as the strength of horizontal (or vertical) magnetic field increasingly goes to a critical value.

다공성 매질이 존재하는 용광로 내부 이상유체 경계면의 특성

The present study numerically investigated the deformation of the interface of two-phase fluids flow in a blast furnace. To simulate three-dimensional(3D) incompressible viscous two-phase flow in the furnace filled with the air and molten iron, the volume of fluid(VOF) method based on the finite volume method has been utilized. In addition, the porous medium with the porosity has been considered as the bed of the particles such as cokes and char etc. For the comparison, the single phase flow and the two-phase flow without the porosity have been simulated. The two-phase flow without porosity condition revealed the smooth parabolic profile of the free surface near the outlet. However, the free surface under the porosity condition formed the viscous finger when the free surface was close to the outlet. This viscous finger accelerated the velocity of the free surface falling and the outflow velocity of the fluids near the outlet.

Numerical Investigation of Transient Flow in a Prototype Centrifugal Pump during Startup Period

AbstractTransient performance of pumps during transient operating periods, such as startup and stopping, has drawn more and more attentions recently due to the growing engineering needs. During the startup period of a pump, the performance parameters such as the flow rate and head would vary significantly in a broad range. Therefore, it is very difficult to accurately specify the unsteady boundary conditions for a pump alone to solve the transient flow in the absence of experimental results. The closed-loop pipe system including a centrifugal pump is built to accomplish the self-coupling calculation. The three-dimensional unsteady incompressible viscous flow inside the passage of the pump during startup period is numerically simulated using the dynamic mesh method. Simulation results show that there are tiny fluctuations in the flow rate even under stable operating conditions and this can be attributed to influence of the rotor–stator interaction. At the very beginning of the startup, the rising speed of the flow rate is lower than that of the rotational speed. It is also found that it is not suitable to predict the transient performance of pumps using the calculation method of quasi-steady flow, especially at the earlier period of the startup.

An improved result on Rayleigh–Taylor instability of nonhomogeneous incompressible viscous flows

In [F. Jiang, S. Jiang, On instability and stability of three-dimensional gravity driven viscous flows in a bounded domain, Adv. Math., 264 (2014) 831--863], Jiang et.al. investigated the instability of Rayleigh--Taylor steady-state of a three-dimensional nonhomogeneous incompressible viscous flow driven by gravity in a bounded domain $\Omega$ of class $C^2$. In particular, they proved the steady-state is nonlinearly unstable under a restrictive condition of that the derivative function of steady density possesses a positive lower bound. In this article, by exploiting a standard energy functional and more-refined analysis of error estimates in the bootstrap argument, we can show the nonlinear instability result without the restrictive condition.

On instability and stability of three-dimensional gravity driven viscous flows in a bounded domain

We investigate the instability and stability of some steady-states of a three-dimensional nonhomogeneous incompressible viscous flow driven by gravity in a bounded domain Ω of class C2. When the steady density is heavier with increasing height (i.e., the Rayleigh–Taylor steady-state), we show that the steady-state is linear unstable (i.e., the linear solution grows in time in H2) by constructing a (standard) energy functional and exploiting the modified variational method. Then, by introducing a new energy functional and using a careful bootstrap argument, we further show that the steady-state is nonlinear unstable in the sense of Hadamard. When the steady density is lighter with increasing height, we show, with the help of a restricted condition imposed on steady density, that the steady-state is linearly globally stable and nonlinearly asymptotically stable in the sense of Hadamard.

An efficient boundary condition-implemented immersed boundary-lattice Boltzmann method for simulation of 3D incompressible viscous flows

An efficient boundary condition-implemented immersed boundary-lattice Boltzmann method (IB-LBM) is presented in this paper. In this work, no-slip boundary condition is directly used to modify velocities at boundary-dependent points through the second-order Lagrange interpolation. As a consequence, flow penetration is avoided and more accurate results are acquired. The boundary-dependent points can be easily identified from intersection points between Cartesian mesh lines and the immersed boundary. Another important contribution of this work is to use Newton’s second law to compute forcing terms at the boundary-dependent points. Due to presence of the solid boundary, velocity change between pre-modified velocity and post-modified velocity will generate acceleration. This acceleration can be used to compute force given from the boundary. Numerical experiments show that present solver has the second-order of overall accuracy. To validate the present method, three-dimensional (3D) incompressible viscous flow over a sphere is first simulated. Then simulations of complicated 3D moving boundary flows are conducted. Numerical results show that the flow penetration of conventional IB-LBM is completely eliminated, and the results obtained agree very well with available data in the literature.

프로펠러 회전류에서 작동하는 방향타의 받음각 특성 연구

This study aims at numerically investigating the angle of attack characteristics of the rudder behind a rotating propeller. The rotating propeller of 5 blades and the full spade rudder are placed in the numerical water tunnel with a uniform flow condition to consider propeller-rudder interaction. The turbulence closure model is employed to simulate the three-dimensional unsteady incompressible viscous turbulent flow around the propeller and the rudder. The present numerical method are well verified by comparing with the experimental results. In order to identify the dependence of the angle of attack of the rudder on the rudder angle, a wide range of rudder angles is considered. The present study carried out the quantitative and qualitative analysis of the angle of attack in terms of the pressure distribution, streamlines and the evaluation of the flow incidence, resulting in that the angle of attack increases as we move from the root and the tip to the center of the rudder, regardless of the rudder angle. The distribution of the angle-of-attack along the span is strongly affected by rotating propeller flow and rudder angle. Consequently, the distribution of the angle-of-attack of the oncoming flow against the rudder leading edge plays a role in determination of rudder performance.

Transient internal characteristic study of a centrifugal pump during startup process

The transient process of a centrifugal pump existed in a variety of occasions. There were a lot of researches in the external characteristic in startup process and stopping process, but internal characteristics were less observed and studied. Study of the internal flow field had significant meanings. The performance of a pump could be evaluated and improved by revealing the flow field. In the other hand, the prediction of external characteristic was based on the correct analysis of the internal flow. In this paper, theoretical method and numerical simulation were used to study the internal characteristic of a centrifugal pump. The theoretical study showed that the relative flow in an impeller was composed of homogeneous flow and axial vortex flow. The vortex intensity was mainly determined by angular velocity of impeller, flow channel width and blade curvature. In order to get the internal flow field and observe the evolution of transient internal flow in the impeller, Computational Fluid Dynamics(CFD) were used to study the three-dimensional unsteady incompressible viscous flows in a centrifugal pump during starting period. The Dynamic Mesh (DM) method with non-conformal grid boundaries was applied to get the external characteristic and internal flow field. The simulate model included three pumps with different blade numbers and the same blade curvature. The relative velocity vector showed that there was a big axial vortex in impeller channel. At the beginning, the vortex was raised in the pressure side of the impeller outlet and with time went on, it shifted to the middle flow channel of the impeller and the vortex intensity increased. When the speed and flow rate reached a definite value, the influence of the axial vortex began to get smaller. The vortex developed faster when the flow channel got narrower. Due to the evolution of axial vortex, the slip factor during starting period was smaller than that in quasi-steady condition. As a result, transient head was lower than quasi-steady head in startup process.

Solution of three-dimensional viscous flows using integral velocity–vorticity formulation

In this paper, a numerical approach is presented to solve the velocity–vorticity integro-differential formulations for three-dimensional incompressible viscous flow. Both the velocity and pressure are solved in integral formulations and the general numerical method is based on standard finite volume scheme. The velocities needed at the vertexes of each control volume are calculated by a so-called generalized Biot–Savart formula combined with a fast multipole algorithm, which makes the velocity boundary conditions implicitly satisfied by maintaining the kinematic compatibility of the velocity and vorticity fields. The well-known fractional step approaches are used to solve the vorticity transport equation. No-flux boundary conditions on solid objects are satisfied as vorticity Helmholtz equation is solved. The diffusion term in the transport equation is treated implicitly using a conservative finite update. The diffusive fluxes of vorticity into flow domain from solid boundaries are determined by an iterative process in order to satisfy the no tangential-flow boundary condition. As an application example, the impulsively started flow through a sphere with different Reynolds numbers is computed using the method. The calculated results are compared with the experimental data and other numerical results and show good agreement.

Double-diffusive convection in a cubical lid-driven cavity with opposing temperature and concentration gradients

A numerical study of three-dimensional incompressible viscous flow inside a cubical lid-driven cavity is presented. The flow is governed by two mechanisms: (1) the sliding of the upper surface of the cavity at a constant velocity and (2) the creation of an external gradient for temperature and solutal fields. Extensive numerical results of the three-dimensional flow field governed by the Navier-Stokes equations are obtained over a wide range of physical parameters, namely Reynolds number, Grashof number and the ratio of buoyancy forces. The preceding numerical results obtained have a good agreement with the available numerical results and the experimental observations. The deviation of the flow characteristics from its two-dimensional form is emphasized. The changes in main characteristics of the flow due to variation of Reynolds number are elaborated. The effective difference between the two-dimensional and three-dimensional results for average Nusselt number and Sherwood number at high Reynolds numbers along the heated wall is analyzed. It has been observed that the substantial transverse velocity that occurs at a higher range of Reynolds number disturbs the two-dimensional nature of the flow.

프로펠러 후류의 총와도 수식모델 연구

This study numerically carried out the propeller open water test(POW) by solving Navier-Stokes equations governing the three-dimensional unsteady incompressible viscous flow with the turbulence closure model of the <TEX>${\kappa}-{\omega}$</TEX> SST model. Numerical simulations are performed at various range of advance ratios. Corresponding to Reynolds numbers of <TEX>$5.89{\times}105{\sim}6.47{\times}105$</TEX> based on free stream velocity and the chord length at 0.7 propeller radius. The present results give a good agreement with those of the experiment. The propeller induced vortical structures have been analyzed by visualizing the resultant vorticity. As the advance ratio increases, the magnitude and length of the resultant vorticity decrease significantly. As the main focus of present study, the numerical model to present the (<TEX>$r-{\theta}$</TEX>) plane-averaged resultant vorticity along the streamwise direction for various advance ratios has been suggested.