Incompressible Navier-Stokes Research Articles

Hydrodynamic stability and turbulent transition with the Vreman LES SGS and a modified lattice Boltzmann equation

For the evaluation of a broad range of Re in incompressible flows, particularly unsteady and transition regimes, the Vreman subgrid scale model is studied within the framework of a modified lattice Boltzmann equation. A unique multiple relaxation time form which recovers the fully incompressible unsteady Navier-Stokes equations is derived for the D3Q19 lattice. Solutions to the 3D-driven cavity are compared to a number of lattice Boltzmann and Navier-Stokes solutions. Initial simulations demonstrate the vanishing nature of eddy viscosity in the steady laminar regime. Onset of unsteadiness is found between Re 1900 and 1950, matching well with the wealth of literature. At Re 6000, velocity history and complex vortex structures show a transition to turbulence near the domain bottom and front walls while the centre of the domain retains laminar characteristics. By Re 8000 intermittent turbulence has progressed to the domain centre. This range of Re for transition and the flow characteristics are in agreement with the general ranges in literature, with further observations being added here. The Vreman model with an incompressible lattice Boltzmann method is found to be a promising tool for laminarto- turbulent simulation.

Overview of the incompressible Navier–Stokes simulation capabilities in the MOOSE framework

The Multiphysics Object Oriented Simulation Environment (MOOSE) framework is a high-performance, open source, C++ finite element toolkit developed at Idaho National Laboratory. MOOSE was created with the aim of assisting domain scientists and engineers in creating customizable, high-quality tools for multiphysics simulations. While the core MOOSE framework itself does not contain code for simulating any particular physical application, it is distributed with a number of physics “modules” which are tailored to solving e.g. heat conduction, phase field, and solid/fluid mechanics problems. In this report, we describe the basic equations, finite element formulations, software implementation, and regression/verification tests currently available in MOOSE’s navier_stokes module for solving the Incompressible Navier-Stokes (INS) equations.

Hypocoercivity Based Sensitivity Analysis and Spectral Convergence of the Stochastic Galerkin Approximation to Collisional Kinetic Equations with Multiple Scales and Random Inputs

In this paper, we provide a general framework to study general class of linear and nonlinear kinetic equations with random uncertainties from the initial data or collision kernels, and their stochastic Galerkin approximations, in both incompressible Navier-Stokes and Euler (acoustic) regimes. First, we show that the general framework put forth in [C. Mouhot and L. Neumann, Nonlinearity, 19, 969-998, 2006, M. Briant, J. Diff. Eqn., 259, 6072-6141, 2005] based on hypocoercivity for the deterministic kinetic equations can be easily adopted for sensitivity analysis for random kinetic equations, which gives rise to an exponential convergence of the random solution toward the (deterministic) global equilibrium, under suitable conditions on the collision kernel. Then we use such theory to study the stochastic Galerkin (SG) methods for the equations, establish hypocoercivity of the SG system and regularity of its solution, and spectral accuracy and exponential decay of the numerical error of the method in a weighted Sobolev norm.

A numerical analysis of casing groove parameters on the performance of wave energy conversion device

Casing grooves in Wells turbine can enhance its performance. The present computational work has been carried out to understand the effect of casing-groove's width-to-chord (w/C) ratio on the performance of a wave energy conversion device. In this study, four different values of w/C ratio such as 0.24, 0.48, 0.64 and 0.96 were investigated. The circumferential casing groove depth (3% of the chord length) and tip clearance (1% of the chord length) were kept constant for all the cases. The flow field was analysed through discretisation of three-dimensional steady incompressible Reynolds-averaged Navier-stokes (RANS) equations with two-equation eddy viscosity turbulence closer model. The simulation results show that the w/C ratio has a significant impact on the turbine performance and the w/C = 0.64 was found to be the optimal one among the several values investigated in the present study.

Investigation of obstacle effect to improve conjugate heat transfer in backward facing step channel using fast simulation of incompressible flow

The current study investigates the conjugate heat transfer characteristics for laminar flow in backward facing step channel. All of the channel walls are insulated except the lower thick wall under a constant temperature. The upper wall includes a insulated obstacle perpendicular to flow direction. The effect of obstacle height and location on the fluid flow and heat transfer are numerically explored for the Reynolds number in the range of 10 ≤ Re ≤ 300. Incompressible Navier-Stokes and thermal energy equations are solved simultaneously in fluid region by the upwind compact finite difference scheme based on flux-difference splitting in conjunction with artificial compressibility method. In the thick wall, the energy equation is obtained by Laplace equation. A multi-block approach is used to perform parallel computing to reduce the CPU time. Each block is modeled separately by sharing boundary conditions with neighbors. The developed program for modeling was written in FORTRAN language with OpenMP API. The obtained results showed that using of the multi-block parallel computing method is a simple robust scheme with high performance and high-order accurate. Moreover, the obtained results demonstrated that the increment of Reynolds number and obstacle height as well as decrement of horizontal distance between the obstacle and the step improve the heat transfer.

Heat transfer enhancement on the liquid side of an industrially designed flat-tube heat exchanger with passive inserts – Numerical investigation

Flow and heat transfer in a single tube of a flat-tube heat exchanger with passive inserts as means of heat transfer enhancement is numerically investigated. The tube geometry is taken from an industrial design with an elaborate pattern of passive inserts (bumps) distributed on the two walls of the channel. The channel is not symmetric in the spanwise direction, leaving a insert-free area on one side of the channel.In order to investigate the heat transfer in such a channel, the incompressible Navier-Stokes and energy equations are solved directly on a very fine computational mesh. These quasi-DNS simulations are carried out at three Reynolds numbers, spanning the threshold where laminar-turbulent regime transition is believed to occur based on previous experiments. Results suggest that turbulence does contribute to heat transfer enhancement at the highest Reynolds number. However, the boundary layer modification, which is the main heat transfer enhancement mechanism, is identically in action in both, laminar and turbulent, regimes. Results also show that the non-symmetric distribution of passive inserts is disadvantageous, particularly in the event of laminar-turbulence regime transition.

Investigation of DBD plasma actuator effect on the aerodynamic and thermodynamic performance of high solidity Wells turbine

Wells turbine is a promising self-rectifying device in the field of ocean wave energy conversion. This study, firstly offers a second law analysis of the isothermal flow through a Wells turbine. Numerical computations is carried out in OpenFOAM by solving steady, incompressible and three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations with Spalart-Allmaras turbulence model in a non-inertial reference frame rotating with the turbine rotor. Then local entropy generation rates due to the viscous dissipation around the rotor blades are added to the numerical code and accumulated with other irreversibilities to calculate the exergy efficiency. The results showed that separation and boundary layer interaction have a direct effect on the entropy generation and thus efficiency. The blade entropy generation increases from hub to tip at the leading edge and decreases from the leading edge to the trailing edge. Also, the point of maximum efficiencies coincides with the point of stall. The results proved that distribution of viscous entropy generation provides useful information about the causes of the flow irreversibilities for designers. Secondly, the equations of plasma actuator have been added to the numerical code and its effect on aerodynamics characteristics and first and second law efficiencies has been discussed. The results showed that by applying plasma, the average increase in torque coefficient is about 39.36% and average decrease of lift coefficient is about 30.53%. However, the second law efficiency increases about 39.16% without considering viscous dissipation term and decreases about 64.63% with considering viscous dissipation term. In order to reduce the negative effect of plasma on second law efficiency, it is suggested to apply it in pulsative manner. Also investigation of applying plasma on the leading edge can be useful.

An implicit potential method along with a meshless technique for incompressible fluid flows for regular and irregular geometries in 2D and 3D

We present the Implicit Potential (IPOT) numerical scheme developed in the framework of meshless point collocation. The proposed scheme is used for the numerical solution of the steady state, incompressible Navier-Stokes (N-S) equations in their primitive variable (u-v-w-p) formulation. The governing equations are solved in their strong form using either a collocated or a semi-staggered type meshless nodal configuration. The unknown field functions and derivatives are calculated using the Modified Moving Least Squares (MMLS) interpolation method. Both velocity-correction and pressure-correction methods applied ensure the incompressibility constraint and mass conservation. The proposed meshless point collocation (MPC) scheme has the following characteristics: (i) it can be applied, in a straightforward manner to: steady, unsteady, internal and external fluid flows in 2D and 3D, (ii) it equally applies to regular an irregular geometries, (iii) a distribution of points is sufficient, no numerical integration in space nor any mesh structure are required, (iv) there is no need for pressure boundary conditions since no pressure constitutive equation is solved, (v) it is quite simple and accurate, (vi) results can be obtained using collocated or semi-staggered nodal distributions, (vii) there is no need to compute the velocity potential nor the unit normal vectors and (viii) there is no need for a curvilinear system of coordinates. Simulations of fluid flow in 2D and 3D for regular and irregular geometries indicate the validity of the proposed methodology.

Investigation on the Performance of Forward Bending Fan

Abstract The forward bending centrifugal fan features long vanes and narrow passages, and the internal flow is apt to be affected by wall boundary layer of the blade surfaces. An aerodynamic investigation on the forward bending centrifugal fan is presented in this paper. The performances of the unsteady flow field in the centrifugal fan is predicted by solving the incompressible Reynolds-averaged Navier-Stokes (RANS) equations based on the Shear Stress Transport (SST) – Scale Adaptive Simulation (SAS) turbulence model. And three-dimensional (3-D) flow phenomenon of non-uniform fluid flow is discussed through observing the flow separation and vortex distribution in the impeller region. The installation location of inlet nozzle is finally adjusted based on the calculated results, and the centrifugal fan with eccentric inlet nozzle is proposed. From the results, the eccentric inlet nozzle with L=3 mm, θ=120° could improve the internal flow of the forward bending centrifugal fan and enhance its aerodynamic performance.

A high-order Discontinuous Galerkin solver for unsteady incompressible turbulent flows

In this work we investigate the use of adaptive linearly implicit Rosenbrock-type Runge–Kutta and Explicit Singly Diagonally Implicit Runge–Kutta schemes to integrate in time high-order Discontinuous Galerkin space discretizations of the incompressible Navier–Stokes (INS) and Reynolds Averaged Navier–Stokes (URANS) equations. The objective of this activity is to assess the efficiency and accuracy of the considered schemes coupled with a time-step adaptation technique for incompressible URANS simulations. The schemes have been first investigated for the computation of the laminar travelling waves and of the turbulent flow around a circular cylinder at a Reynolds number Re=5×104, verifying the convergence order, a simple relation to set the system tolerance starting from the tolerance of the adaptation strategy, and their computational efficiency. Finally, the best scheme resulting from our analysis has been applied to the URANS simulation of the flow through a vertical axis wind turbine, comparing the results with CFD and experimental data available in literature.

On transient hybrid Lattice Boltzmann–Navier-Stokes flow simulations

We investigate one- and two-way coupled schemes combining Lattice Boltzmann (LB) and incompressible Navier-Stokes (NS) solvers. The one-way coupled simulation maps information from a coarse-grained NS system onto LB boundaries which allows for arbitrarily complex fluid flow boundary conditions on LB side. We find that this produces accurate velocity, pressure and stress predictions in Couette, Taylor–Green and Karman vortex scenarios. The two-way coupled simulation decomposes the computational domain into overlapping LB and NS domains. We point out that the weak compressibility of LB can have a major impact on the coupled system. Although very good agreement is found for Couette scenarios, this is not achieved to same extent in Taylor–Green flows.

Development of a High-Resolution Scheme for Solving the PNP-NS Equations in Curved Channels

AbstractA high-order finite difference scheme has been developed to approximate the spatial derivative terms present in the unsteady Poisson-Nernst-Planck (PNP) equations and incompressible Navier-Stokes (NS) equations. Near the wall the sharp solution profiles are resolved by using the combined compact difference (CCD) scheme developed in five-point stencil. This CCD scheme has a sixth-order accuracy for the second-order derivative terms while a seventh-order accuracy for the first-order derivative terms. PNP-NS equations have been also transformed to the curvilinear coordinate system to study the effects of channel shapes on the development of electroos-motic flow. In this study, the developed scheme has been analyzed rigorously through the modified equation analysis. In addition, the developed method has been computationally verified through four problems which are amenable to their own exact solutions. The electroosmotic flow details in planar and wavy channels have been explored with the emphasis on the formation of Coulomb force. Significance of different forces resulting from the pressure gradient, diffusion and Coulomb origins on the convective electroosmotic flow motion is also investigated in detail.

Numerical Simulation on End Suction Centrifugal Pump Running in Inverse Flow for Microhydro Applications

The initial capital cost for most microhydro projects has always been an overriding issue for self-funded remote communities. The cost will escalate significantly in the absence of local microhydro electromechanical manufacturers. The application of end suction centrifugal pump as turbine will reduce the overall cost, which renders microhydro systems feasible for self-funded projects and are therefore suitable for rural communities. The goal of this study is to design and develop a pump as turbine (PAT) which serves as a substitute to commercial electromechanical components. Numerical analysis of an inverse flow for an end suction centrifugal pump is presented in this paper, which includes the performance curves and hydraulic characteristics of the pump. ANSYS CFX, a commercial CFD software is used to simulate the performance of the pump with specific speed, Ns of 70 units (Euroflo EU50-20). The computational flow domain inside the pump is comprises of impeller, volute and draft tube. Unstructured tetrahedral mesh is used to maintain good surface mesh due to complex flow domain geometries. The governing equations used in the simulations are three-dimensional, incompressible Navier-Stokes and k-ϵ turbulence model under steady-state condition. The simulation results are compared with pump performance curve supplied by the pump manufacturer. The verification results show good agreement for flow rates between 0.7 and 1.3 QBEP. The best efficient point (BEP) for inverse flow is attained at a higher head and flow rate compared to pump mode, whereby the value is found to be 21.55 m and 14.0 l/s, respectively. It is believed that the findings of this study will be useful to predict hydraulic characteristics and performance curves of PAT and the model may be used to identify poor flow characteristics inside the pump. It is recommended that optimization process is carried out using CFD tools in future studies.

МОДЕЛЮВАННЯ ШВИДКОСТІ РОЗПОДІЛУ ПОВІТРЯ У ВІДСІКУ ВИПАРНИКА ХОЛОДИЛЬНОЇ УСТАНОВКИ РЕФРИЖЕРАТОРНОГО КОНТЕЙНЕРА

The study is aimed at solving the problem of convective heat transfer calculating in the tubular evaporator unit of refrigerating container, which is equipped with fan forced convection. The mathematical model of the problem as a differential equation that establishes the energy conservation law in the air cells through the surface of which its movement is carried out is given. Inthe process of the convective heat transfer around the evaporator problem calculating the link between the basic physical quantities in the air − temperature fields and velocity of its movement was considered. Close relationship of obtained temperature values and air velocity at the outlet from evaporator unit as boundary conditions for further calculation of temperature field in the refrigerator compartment of refrigerating container was proved. Statement of the problem and its simulation wereperformed in a two-dimensional coordinate system, and software environment COMSOL Multiphysics, Femlab 3.0, Fluid Dynamics - Incompressible Navier-Stokes - Convection and Conduction was applied for its solution. he accomplished calculations have shown that the integral temperature value at the outlet of the evaporator unit, was calculated taking into account air velocity, which is lower than its values obtained without air movement consideration. The results of the study should be useful during the research of the convective heat transfer phenomenon in the different refrigerating devices, allow to choose evaporator and fan capacity morereasonably under conditions of obtaining the desired cooling mode for perishable products as well asin the learning process

МОДЕЛЮВАННЯ ЗАДАЧІ КОНВЕКТИВНОГО ТЕПЛООБМІНУ В ХОЛОДИЛЬНІЙ ШАФІ РЕФРИЖЕРАТОРНОГО КОНТЕЙНЕРА

Materials of the study are directed on the solving the problem of air velocity calculating in a confined volume of refrigerating chamber of 20 foot refrigerated container with forced air convection from Carrier Transicold producer firm and on this basis –of convective heat transfer. Problem simulation has been performed in a two-dimensional coordinate system using COMSOL Multiphysics, Femlab 3.0, Fluid Dynamics - Incompressible Navier-Stokes - Convection and Conduction software. As an object of research differential equations of air movement impulse and transfer of energy with it were applied. As a subject of research was selected thermal physical phenomena inside and around the net volume of empty and loaded refrigerated container at air movement. Significant impact of the air movement on the temperature distribution inside the refrigerating container chamber has been established.The obtained results allow to get closer to the theoretical evaluation of the refrigerating machine efficiency in an ordered mode during changes of thermophysical parameters of cargo volume and the environment during perishable products transportation. Tested method is useful for application by scientists and post-graduate students engaged in theoretical simulation of heat transfer problems in the field of refrigeration engineering.

Simulation of a Cantilevered Thin-Elastic Plate with Large Deformation Subjected to Axial Flow

The instability and dynamics behavior of a cantilevered thin-elastic plate with large deformation subjected to axial flow is studied numerically. The structural dynamics equation is discretized by isoparametric displacement-based finite, and the motion of a continuous fluid domain is governed by two-dimensional incompressible viscous Navier-Stokes equations, which discretized by finite volume method. The two-dimensional numerical model of two-way fluid-structure coupling is established combined with moving mesh technology, realizing the interaction of thin-elastic plate and axial fluid. Firstly, under given different flow velocity, the stability of limit-cycle oscillations has been studied through Hopf bifurcation, time trace, vibration responses. Secondly, the fluid domain features are analyzed qualitatively by separately comparing with vorticity under given different flow velocity, and cloud diagram of pressure and velocity are also analyzed at U=3.6m/s.

FSI Numerical Simulation for Wind-Induced Dynamic Response of Tension Membrane Structures

In this paper, systemic FSI numerical simulations for wind-induced dynamic response of saddle-shaped tension membrane structures are performed using ADINA software, and the effects of some parameters such as inlet velocity, wind direction, span, rise-span ratio, tension stiffness and pre-stress of tension membrane are considered. The flow is modeled with the incompressible viscous Navier-Stokes equations and the standard κ-ω turbulence model, and the membrane is assumed as isotropic-linear-elastic material with large displacement and small strain. The rules of FSI numerical simulation for wind-induced dynamic responses of saddle-shaped tension membrane structures are summarized and the wind-induced dynamic coefficients and the wind pressure distribution coefficients are obtained which can be used in the design of membrane structures.

On a Wavenumber Optimized Streamline Upwinding Method for Solving Steady Incompressible Navier-Stokes Equations

A stabilized upwind finite-element model is developed to solve the three-dimensional incompressible steady Navier-Stokes equations. The test function is constructed to have a larger weight on the upstream side. This has been achieved by adding a stabilized term to the shape function so as to optimize the numerical wavenumber for convection terms. To avoid Lanczos or pivoting breakdown while solving the resulting unsymmetric and indefinite mixed finite-element matrix equations iteratively, the finite-element equation has been modified by pre-multiplying it with its transpose. The resulting normalized matrix equation becomes symmetric and positive-definite. We can therefore apply a computationally efficient conjugate gradient Krylov iterative solver to get an unconditionally convergent solution. However, the condition number of the new system becomes the square of the original unsymmetric indefinite system. To fully exploit excellent convergence nature of the conjugate gradient iterative solver, an element-by-element strategy is adopted to avoid assembling of all the stiffness matrices obtained at element level. We alleviate the drawback of slower convergence of the conjugate gradient method due to the increased condition number by preconditioning the positive-definite matrix. The resulting preconditioned matrix equation is solved in a matrix-free manner using the preconditioned conjugate gradient iterative solver. The developed finite-element code is first verified by solving a problem amenable to analytical solution. The benchmark lid-driven cavity problem is also solved in a cube for assessing the three chosen iterative solvers.

Nonhomogeneous boundary value problem for "Equation missing" similar solutions of incompressible two-dimensional Euler equations

Abstract In this paper we introduce the ( I , J ) similar method for incompressible two-dimensional Euler equations, and obtain a series of explicit ( I , J ) similar solutions to the incompressible two-dimensional Euler equations. These solutions include all of the twin wave solutions, some new singularity solutions, and some global smooth solutions with a finite energy. We also reveal that the twin wave solution and an affine solution to the two-dimensional incompressible Euler equations are, respectively, a plane wave and constant vector. We prove that the initial boundary value problem of the incompressible two-dimensional Euler equations admits a unique solution and discuss the stability of the solution. Finally, we supply some explicit piecewise smooth solutions to the incompressible three-dimensional Euler case and an example of the incompressible three-dimensional Navier-Stokes equations which indicates that the viscosity limit of a solution to the Navier-Stokes equations does not need to be a solution to the Euler equations. MSC:35Q30, 76D05, 76D10.

The aerodynamic performance of flexible wing in plunge

Inspired by the fact that flexible wing in nature possesses advance aerodynamic performance, a numerical experiment is applied to investigate the aerodynamic performance of flexible wing in plunge motion, where the incompressible Navier-Stokes (N-S) equations coupled with the structural dynamic equation for the motion of the wing is solved. A two-dimensional, elastic and inextensible beam model wing is considered at Re = 1256. The harmonic plunge motion is specified at the leading edge of wing, and the other part of wing is responded passively deforming by the aerodynamic force. By analyzing the flow field, aerodynamic force and energy efficiency of different flexibility wings, it is found that the flexibility influences the aerodynamic characteristics of the plunge wing greatly and when the plunge frequency is less than the structural frequency the flexibility can increase the thrust force and the energy efficiency of the wing, and the maximum energy efficiency is obtained when the wing plunge near the resonance. Moreover, a lighter wing possesses larger energy efficiency than a heavier wing, but it may not be functioning for too light wing. The results obtained in this study will provide physical insight into the understanding of fluid and structure interaction problem.