Unsteady Incompressible Viscous Flow Research Articles

Study on the integrated self-priming process of a vehicle-mounted self-priming pump

In order to explore the self-priming characteristics of the self-priming pump at the mobile pump truck, this paper established a complete three-dimensional circulatory piping system including the self-priming pump, tank, valves, inlet pipe and outlet pipe. The UDF(User Defined Functions) was used to realize the acceleration-constant speed operation process of the impeller, thus reflecting the actual changing state of the rotational speed. Based on the VOF(Volume Of Fluid) multiphase flow model and the Realizable k-ε turbulence model, a coupled numerical calculation of unsteady incompressible viscous flow was conducted for its self-priming process. The results show that the self-priming process of the pump can be roughly divided into four stages: the rapid suction stage, the shock exhaust stage, the rapid exhaust period and the pump residual gas discharge stage. The proportion of each stage in the total self-priming time showed an increasing trend. During the rapid suction stage, the water level in the vertical section of the inlet pipe showed a slow and then fast-rising pattern. During the shock exhaust stage, the average gas-phase volume fraction in the volute is lower than that of the impeller, and the gas content at the volute outlet is lower than that of the impeller inlet. The region at the inlet and outer edge of the impeller consistently experience significant energy losses.

Optimization of mass and heat flux of MHD viscous fluid flow with constant proportional Caputo derivative by using response surface methodology: Sensitivity analysis

The study of viscous dissipation in the context of unsteady incompressible magnetohydrodynamic viscous fluid flow over a moving plate is a complex and important topic in fluid dynamics and heat transfer. This scenario combines several physical phenomena and has practical applications in various engineering and scientific fields. The fractional mathematical model is proposed by considering the effect of viscous dissipation force of the flowing fluid. For this purpose, fluid is assumed to be lying over a vertical plate that is moving in its own plane. The governing equations are transformed into the dimensionless form and developed fractional model with a new operator Constant Proportional Caputo Derivative. We used the Laplace transform technique to find the solution of the dimensionless governing equation analytically. The transformed solutions for energy and momentum balances developed in terms of series. The validation of the present model comparison graphs is plotted for temperature. The sensitivity of different input parameters on output response are analyzed and displayed the sensitivity results in tabular and graphical form and found that the permeable parameter is most sensitive to skin friction coefficient, and the Eckert number is most sensitive parameter among others to Nusselt Number. The novelty of present work is to develop a correlation between input parameters and output responses by using Response Surface Methodology (RSM). As no such correlation has been developed for optimization of mass and heat flux of MHD viscous fluid flow with Constant Proportional Caputo derivative by using RSM. By using this correlation, we have performed sensitivity analysis for output responses.

Dual Solution with Heat Transfer through Moving Porous Plate of an Unsteady Incompressible Viscous Fluid

We examine graphically the behavior of the dual solution of an unsteady incompressible viscous flow with heat transfer due to a moving porous surface. The mathematical model is developed with the implementation of conservation laws which are then tackled numerically, and the simulations are performed through the Keller–Box technique. Application of the Keller–Box technique allows the non-linear differential equations to transform to a scheme of linear differential equations which are easier to illuminate. Outcomes of velocity and thermal behavior are shown graphically for certain values of the dimensionless parameters. It is obvious from the results that temperature of fluid decreases with the increasing values of dimensionless Prandtl number Pr, whereas the velocity enhances for blowing situations.

오일러리안 무격자법을 이용한 진동하는 2차원 원주주위 점성 유동 해석

In this study, a newly developed Eulerian gridless solver for the simulation of a two-dimensional unsteady incompressible viscous flow around a moving body is introduced. A moving domain method based on the Arbitrary Lagrangian Eulerian(ALE) technique is adopted to implement the moving body. The spatial derivatives of the governing equation are solved by weighted moving least square(WMLS) interpolation over the point cloud. The fractional time step method is adopted and the Poisson equation for pressure is solved successively in the WMLS sense. Simulations of flows around a cylinder moving with constant speed and in harmonic motion are solved for validation and the results are compared with experiments and other CFD simulations.<BR> For the constant speed cases, the drag, lift and pressure coefficients estimated by present method were well matched with other results. From the computational results under the harmonic motion with changing main parameters such as Keulegan-Carpenter and Reynolds numbers, the drag and inertial force coefficients using the Fourier series approach were obtained and compared with other results. Even small discrepancy exist, the coefficients were good agreement with other ones.

Transient Behavior of a Prototype Centrifugal Pump with Abrupt Decreasing Flow Rate

Centrifugal pump often operates at different working flow rates to meet engineering requirement. To better reveal the transient behavior of centrifugal pump in the process of decreasing flow rate, the finite volume method (FVM), RNG k-ε turbulence model, sliding mesh technology, and user-defined functions (UDF) were employed to simulate the three-dimensional unsteady viscous incompressible flow in a low-specific-speed centrifugal pump during the abrupt valve-off period. The results show that the differences are very obvious between transient and quasi-steady calculations. The velocity is maximum on the wall of hub and shroud, while the velocity is minimum and uniform distribution at middle positions. The transient flow field lags behind the quasi-steady flow field, which may be related to the reasons; namely, kinetic energy cannot convert pressure energy in time.

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.

Comparative study by DTM for unsteady viscous flow between the jet engines combustion unit subjected to inclined magnetic field

Purpose The purpose of this study to analyze the unsteady magneto hydrodynamic incompressible viscous fluid flow along the porous parallel plates in which constant periodic suction/injection takes place at lower and upper plate, respectively. By the proper choice of stream function, they obtained exact solution analytically. Velocity components are obtained from exact solution. Design/methodology/approach Emissions of the pollutants from the aviation sectors are doubled compared to 2000. There are many recent developments that are actively developed to combat the emission by increasing the performance of the Jet engines. The role of the computational fluid dynamics and the numerical approaches are crucial in terms of research and development. Findings Velocity profiles like axial and radial have been drawn for various values of M, D, α and θ. The exact solutions have been solved by differential transformation method. The closed form analytical solutions are obtained for the stream function, axial and radial velocities and flow velocity. Originality/value The effects of Darcy parameter, magnetic parameter, Suction Reynolds number and frequency parameter on lower and upper plates are discussed through graphs.

Unsteady MHD Couette viscous fluid flow through silver metallic parallel plates with an inclined magnetic field and angular velocity subjected to constant suction at lower plate

Abstract In this paper, we discussed unsteady magneto hydrodynamic incompressible viscous couette flow along the silver metallic parallel plates in which constant periodic suction takes place at the bottom porous silver metallic shield subjected to the magnetic field with inclination along with the rotation of system. By means of appropriate choice of stream function we obtained exact solution analytically. Axial Velocity component and radial Velocity component are obtained from the analytical solution. Velocity profiles like axial and transverse are examined for different parameters α , K r , M a n d ω t . The effects of Magnetic parameter, Suction Reynolds number and Rotation parameter on the plates are discussed and illustrated graphically.

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.

Penalty and characteristic-based operator splitting with multistep scheme finite element method for unsteady incompressible viscous flows

Penalty and characteristic-based operator splitting with multistep scheme finite element method for unsteady incompressible viscous flows

Penalty and characteristic-based operator splitting with multistep scheme finite element method for unsteady incompressible viscous flows

The penalty and characteristic-based operator splitting with multistep scheme (penalty-MCBOS) has been developed for the unsteady incompressible Navier-Stokes N-S equations. At each time step, the N-S equations are split into the diffusive part, the convective part by adopting the operator splitting method and the pressure part by applying the penalty method with low penalty parameters. For the diffusive part, the temporal discretisation is based on backward difference method and is solved by preconditioned conjugate gradient (PCG) method. For the convective part, the temporal discretisation is performed by characteristic-Galerkin method. It is solved explicitly and the multistep technique is used. The pressure can be calculated from the pressure part without necessitating the solution of the pressure Poisson equation. The plane Poisseuille flow, the lid-driven cavity flow, the lid-driven triangular cavity flow and the backward-facing step flow are investigated to validate the present model. It is shown that the numerical results are in good agreement with the previously published data, and the present model has high efficiency. For the backward-facing step problem at Re = 3,000, the flow becomes periodical in time and dynamic evolution process of vortex can be simulated.

Unsteady Preconditioned Characteristic Boundary Conditions for Direct Numerical Simulation of Incompressible Flows

The unsteady preconditioned characteristic boundary conditions (UPCBCs) based on the artificial compressibility (AC) method are formulated and applied at artificial boundaries for the direct numerical simulation (DNS) of incompressible flows. The compatibility equations including the unsteady terms are mathematically derived in the generalized curvilinear coordinates and then incorporated as boundary conditions (BCs) in a high-order accurate incompressible flow solver. The spatial derivative terms of the system of equations are discretized using the fourth-order compact finite difference (FD) scheme, consistent with the high-order accuracy required for the DNS. The time integration is carried out using an implicit dual time-stepping method, and the robustness and performance of the numerical algorithm are enhanced by applying the preconditioning technique and calculating the automated AC parameter based on the local flow conditions. At first, the steady viscous incompressible flow for a two-dimensional plane jet is computed to assess the accuracy and performance of the solution method by applying the UPCBCs in comparison with the simplified BCs. Then, the simulation of the unsteady incompressible viscous flow around a two-dimensional NACA0012 airfoil at the Reynolds number 800 and the angle of attack 20° is performed, and it is indicated that the computational cost of the solution is considerably decreased by implementing the UPCBCs at the artificial far-field boundary compared with the simplified BCs, which is remarkably valuable for the DNSs. Finally, the computation of the transition to unsteady for the incompressible flow around a three-dimensional NACA0012 wing at the same conditions of the two-dimensional case is successfully performed, and the results obtained are compared with those of previous studies that exhibit good agreement. Indications are that the present solution method by applying the UPCBCs at the artificial far-field boundary can be effectively used for the DNSs of the incompressible flows.

The three-dimensional hydrodynamics of tadpole model’s solitary swimming and parallel schooling

Tadpole swimming, including a solitary tadpole swimming and schooling side-by-side in an in-phase mode, is investigated numerically in the present paper. The three-dimensional Navier-Stokes equations for the unsteady incompressible viscous flow are solved. A dynamic mesh fitting the tadpole’s deforming body surface is adopted. The results showed that for a solitary tadpole swimming, two vortex rings are shed in each undulating period. However, as the resultant force on the tadpole is drag, the vortex rings are obviously asymmetric, shaped like “C”. When the resultant force in the swimming direction approaches zero, the axes of the vortex rings are nearly vertical to the swimming direction. Distorted vortex rings are found when the resultant force on the tadpole is thrust. When the tadpole model obtains the optimum propulsive efficiency, its swimming speed and undulating frequency are close to the values observed in nature. For tadpoles swimming side-by-side in an in-phase mode, the vortex structures in the wake may merge, split and recombine. Compared with a solitary tadpole swimming, only a small hydrodynamic advantage occur with schooling in parallel, which may be one of the reasons why tadpoles rarely, if ever swim, side by side for any amount of time or distance in nature. The effect of the undulating frequency on the tadpoles schooling is similar to that on a solitary tadpole. In addition, with an increase in the Reynolds number, the thrust force and the propulsive efficiency both increase, while the power consumption decreases. We also found that the tadpole benefits from the vortex pair shedding from its blunt snout, which can strengthen the vortex intensity in the wake and improve the pressure distribution.

Wave number selection under the action of accelerated rotation

Unsteady viscous incompressible flows in a spherical layer due to an increase in the rotation velocity of the inner sphere with constant acceleration are investigated. The acceleration starts at the Reynolds numbers Re corresponding to a stationary flow and ends at Re higher than the stability limit of the stationary flow, whereupon the rotation velocity of the inner sphere remains constant. The outer sphere is fixed and the spherical layer thickness is equal to the inner sphere radius. The inner sphere acceleration effect is studied on both the formation of one of two possible secondary-flow structures after the acceleration has been stopped, namely, traveling azimuthal waves with wavenumbers of 3 or 4, and on the change in the flow structure during the action of the acceleration. It is shown that not only an increase in the acceleration but also a decrease in Re corresponding to the acceleration onset can lead to an increase in the deviation of the instantaneous velocity profiles from their stationary values and can be accompanied by a variation in the secondary flow wavenumber.

Topology optimization method for unsteady state incompressible viscous flow based on a level set immersed boundary method

Topology optimization method for unsteady state incompressible viscous flow based on a level set immersed boundary method

A New Approximate Analytical Solutions for Two- and Three-Dimensional Unsteady Viscous Incompressible Flows by Using the Kinetically Reduced Local Navier-Stokes Equations

In this work, the kinetically reduced local Navier-Stokes equations are applied to the simulation of two- and three-dimensional unsteady viscous incompressible flow problems. The reduced differential transform method is used to find the new approximate analytical solutions of these flow problems. The new technique has been tested by using four selected multidimensional unsteady flow problems: two- and three-dimensional Taylor decaying vortices flow, Kovasznay flow, and three-dimensional Beltrami flow. The convergence analysis was discussed for this approach. The numerical results obtained by this approach are compared with other results that are available in previous works. Our results show that this method is efficient to provide new approximate analytic solutions. Moreover, we found that it has highly precise solutions with good convergence, less time consuming, being easily implemented for high Reynolds numbers, and low Mach numbers.

2차원 비압축성 점성 열유동 해석을 위한 WMLS 기반 무격자 해법의 개발

In this study, a newly-developed Eulerian gridless solver for simulating two-dimensional unsteady incompressible viscous thermal flows in low Reynolds number is introduced. The Boussinesq approximation is applied to deal with heat transfer and spatial derivatives of governing equations are solved by WMLS(Weighted Moving Least Square) interpolations on a cloud of points. A fractional time step method is adopted and the Poission equation for pressure are solved by successively in a WMLS sense. Some heat transfer problems are solved by the developed solver for the validation and the results are compared with analytic solution and those from other CFD simulations.

Numerical simulations of unsteady viscous incompressible flows using general pressure equation

In fluid dynamics, an important problem is linked to the knowledge of the fluid pressure. Recently, another approach to study incompressible fluid flow was suggested. It consists in using a general pressure equation (GPE) derived from compressible Navier–Stokes equation. In this paper, GPE is considered and compared with the Chorin's artificial compressibility method (ACM) and the Entropically damped artificial compressibility (EDAC) method. The three methods are discretized in a staggered grid system with second order centered schemes in space and a third order Runge–Kutta scheme in time. Three test cases are realized: two-dimensional Taylor–Green vortex flow, the traveling wave and the doubly periodic shear layers. It is demonstrated that GPE is accurate and efficient to capture the correct behavior for unsteady incompressible flows. The numerical results obtained by GPE are in excellent agreement with those obtained by ACM, EDAC and a classical finite volume method with a Poisson equation. Furthermore, GPE convergence is better than ACM convergence. The proposed general pressure equation (GPE) allows to solve general, time-accurate, incompressible Navier–Stokes flows. Finally, the parametric study realized in terms of Mach and Prandtl numbers shows that the velocity divergence can be limited by an arbitrary maximum and that acoustic waves can be damped.

Free Convective Unsteady MHD Flow in Slip-Flow Regime Past A Vertical Plate with A Convective Surface Boundary Condition

This paper examines the unsteady free convective viscous incompressible MHD flow past a vertical porous flat plate with convective surface boundary condition in slip flow regime under the influence of uniform magnetic field acting perpendicular to the porous surface. Assuming time dependent variable suction velocity at the porous plate, analytical expressions for the flow characteristics are obtained by using perturbation technique which converts the non-linear partial differential equations into ordinary differential equations. The effect of various parameters such as Prandtl number, Grashoff number, the Magnetic field parameter, Suction parameter and Convective heat change parameter on the transient velocity, transient temperature, skin friction coefficient and the rate of heat transfer are discussed with the help of graphs.

A numerical study of tadpole swimming in the wake of a D-section cylinder

The vortex structure and the hydrodynamic performance of a tadpole undulating in the wake of a D-section cylinder are studied by solving the Navier-Stokes equations for the unsteady incompressible viscous flow. A dynamic mesh fitting the tadpole's deforming body surface is used in the simulation. It is found that three main factors can contribute to the thrust of the tadpole behind a D-cylinder: the backward jet in the wake, the local reverse flows on the tadpole surface and the suction force caused by the passing vortices. The tadpole's relative undulating frequency and the distance between the D-cylinder and the tadpole have a great influence on both the vortex structure and the hydrodynamic performance. At some undulating frequency, a tadpole may break or dodge vortices from the D-cylinder. When the vortices are broken, the tadpole can gain a great thrust but will consume much energy to maintain its undulation. When the vortices are dodged, the tadpole is subject to a small thrust or even a drag. However, it is an effective way to save much energy in the undulating swimming, as the Kármán gait does. As the tadpole is located behind the D-cylinder at different distances, three typical kinds of wake are observed. When an incomplete Kármán vortex street forms between the D-cylinder and the tadpole, the tadpole is subject to the highest thrust.