scholarly journals Numerical Modeling of Jet at the Bottom of Tank at Moderate Reynolds Number Using Compact Hermitian Finite Differences Method

Fluids ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 63
Author(s):  
Mohammed Loukili ◽  
Kamila Kotrasova ◽  
Denys Dutykh
Keyword(s):  
Finite Differences ◽  
Stokes Equations ◽  
Flow Direction ◽  
Numerical Code ◽  
Navier Stokes ◽  
Computational Domain ◽  
Numerical Resolution ◽  
Moderate Reynolds Number ◽  
Finite Differences Method ◽  
High Reynolds

In this manuscript, the injection of a homogeneous jet in a numerical tank is considered to revolve around discussing the limitation of the direct numerical simulation (DNS), to resolve the equations governing the problem of a jet emitted from the bottom of a numerical tank. The investigation has been made in the context of an unsteady, viscous, and incompressible fluid. The numerical resolution of the equations governing the problem is made by the compact Hermitian finite differences method (HFDM) high accuracy Oh2,h4 First, the numerical code used in this work is validated by comparing the profiles of the velocity components at the median of the lid-driven cavity with the results of the literature. Furthermore, to confirm the validity of the present numerical code, an evaluation of mesh domain sensitivity is assessed by comparing the numerical vertical velocity profiles for different steps of y-direction (flow direction) with the analytical solution. Afterward, the aim is to perform the nonlinear simulations of the Navier–Stokes equations in a large computational domain. Next, the goal is to characterize the instabilities associated with high Reynolds numbers when a jet is emitted from the bottom of the numerical tank.

scholarly journals Modeling the 3-d flow around a cylinder using the SAS hybrid model

2014 ◽  
Vol 16 (5) ◽  
pp. 901-918 ◽  
Keyword(s):  
Turbulence Modeling ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Cross Flow ◽  
Numerical Code ◽  
Navier Stokes ◽  
Computational Domain ◽  
Mean Flow ◽  
Unstable Flow ◽  
Vortex Size

<div> <p>Three-dimensional calculations were performed to simulate the flow around a cylindrical vegetation element using the Scale Adaptive Simulation (SAS) model; commonly, this is the first step of the modeling of the flow through multiple vegetation elements. SAS solves the Reynolds Averaged Navier-Stokes equations in stable flow regions, while in regions with unstable flow it goes unsteady producing a resolved turbulent spectrum after reducing eddy viscosity according to the locally resolved vortex size represented by the von Karman length scale. A finite volume numerical code was used for the spatial discretisation of the rectangular computational domain with stream-wise, cross-flow and vertical dimensions equal to 30D, 11D and 1D, respectively, which was resolved with unstructured grids. Calculations were compared with experiments and Large Eddy Simulations (LES). Predicted overall flow parameters and mean flow velocities exhibited a very satisfactory agreement with experiments and LES, while the agreement of predicted turbulent stresses was satisfactory. Calculations showed that SAS is an efficient and relatively fast turbulence modeling approach, especially in relevant practical problems, in which the very high accuracy that can be achieved by LES at the expense of large computational times is not required.</p> </div> <p>&nbsp;</p>

Drag Coefficients of Viscous Spheres at Intermediate and High Reynolds Numbers

2001 ◽  
Vol 123 (4) ◽  
pp. 841-849 ◽  
Author(s):  
Zhi-Gang Feng ◽  
Efstathios E. Michaelides
Keyword(s):  
Drag Coefficient ◽  
Viscosity Ratio ◽  
Stokes Equations ◽  
Hydrodynamic Force ◽  
Density Ratio ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Uniform Grid ◽  
Computational Domain ◽  
High Reynolds

A finite-difference scheme is used to solve the Navier-Stokes equations for the steady flow inside and outside viscous spheres in a fluid of different properties. Hence, the hydrodynamic force and the steady-state drag coefficient of the spheres are obtained. The Reynolds numbers of the computations range between 0.5 and 1000 and the viscosity ratio ranges between 0 (inviscid bubble) and infinity (solid particle). Unlike the numerical schemes previously implemented in similar studies (uniform grid in a stretched coordinate system) the present method introduces a two-layer concept for the computational domain outside the sphere. The first layer is a very thin one [ORe−1/2] and is positioned at the interface of the sphere. The second layer is based on an exponential function and covers the rest of the domain. The need for such a double-layered domain arises from the observation that at intermediate and large Reynolds numbers a very thin boundary layer appears at the fluid-fluid interface. The computations yield the friction and the form drag of the sphere. It is found that with the present scheme, one is able to obtain results for the drag coefficient up to 1000 with relatively low computational power. It is also observed that both the Reynolds number and the viscosity ratio play a major role on the value of the hydrodynamic force and the drag coefficient. The results show that, if all other conditions are the same, there is a negligible effect of the density ratio on the drag coefficient of viscous spheres.

scholarly journals NUMERICAL SOLUTION OF FLUID-STRUCTURE INTERACTION PROBLEMS WITH CONSIDERING OF CONTACTS

2021 ◽  
Vol 61 (SI) ◽  
pp. 155-162
Author(s):  
Petr Sváček
Keyword(s):  
Stokes Equations ◽  
Fluid Motion ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Computational Domain ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
Computational Mesh ◽  
Arbitrary Lagrangian Eulerian Method ◽  
High Reynolds

This paper is interested in the mathematical modelling of the voice production process. The main attention is on the possible closure of the glottis, which is included in the model with the concept of a fictitious porous media and using the Hertz impact force The time dependent computational domain is treated with the aid of the Arbitrary Lagrangian-Eulerian method and the fluid motion is described by the incompressible Navier-Stokes equations coupled to structural dynamics. In order to overcome the instability caused by the dominating convection due to high Reynolds numbers, stabilization procedures are applied and numerically analyzed for a simplified problem. The possible distortion of the computational mesh is considered. Numerical results are shown.

Numerical Modeling of Evolution of Boundary Between Incompressible Gas and Liquid in Two-Dimensional Region

2006 ◽  
Vol 4 ◽  
pp. 224-236
Author(s):  
A.S. Topolnikov
Keyword(s):  
Numerical Modeling ◽  
Interphase Boundary ◽  
Incompressible Liquid ◽  
Stokes Equations ◽  
Numerical Code ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Incompressible Media ◽  
Good Agreement

The paper is devoted to numerical modeling of Navier–Stokes equations for incompressible media in the case, when there exist gas and liquid inside the rectangular calculation region, which are separated by interphase boundary. The set of equations for incompressible liquid accounting for viscous, gravitational and surface (capillary) forces is solved by finite-difference scheme on the spaced grid, for description of interphase boundary the ideology of Level Set Method is used. By developed numerical code the set of hydrodynamic problems is solved, which describe the motion of two-phase incompressible media with interphase boundary. As a result of numerical simulation the solutions are obtained, which are in good agreement with existing analytical and experimental solutions.

Simulation of the Transitional Flow in a Low Pressure Gas Turbine Cascade With a High-Order Discontinuous Galerkin Method

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
A. Ghidoni ◽  
A. Colombo ◽  
S. Rebay ◽  
F. Bassi
Keyword(s):  
Discontinuous Galerkin ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Time Integration ◽  
High Order ◽  
Transitional Flow ◽  
Navier Stokes ◽  
Implicit Time ◽  
Turbine Cascade ◽  
High Reynolds

In the last decade, discontinuous Galerkin (DG) methods have been the subject of extensive research efforts because of their excellent performance in the high-order accurate discretization of advection-diffusion problems on general unstructured grids, and are nowadays finding use in several different applications. In this paper, the potential offered by a high-order accurate DG space discretization method with implicit time integration for the solution of the Reynolds-averaged Navier–Stokes equations coupled with the k-ω turbulence model is investigated in the numerical simulation of the turbulent flow through the well-known T106A turbine cascade. The numerical results demonstrate that, by exploiting high order accurate DG schemes, it is possible to compute accurate simulations of this flow on very coarse grids, with both the high-Reynolds and low-Reynolds number versions of the k-ω turbulence model.

ANALYSIS OF A HETEROGENEOUS DOMAIN DECOMPOSITION FOR COMPRESSIBLE VISCOUS FLOW

2001 ◽  
Vol 11 (04) ◽  
pp. 565-599 ◽  
Author(s):  
CRISTIAN A. COCLICI ◽  
WOLFGANG L. WENDLAND
Keyword(s):  
Domain Decomposition ◽  
Stokes Equations ◽  
Domain Decomposition Method ◽  
Near Field ◽  
Outer Region ◽  
Navier Stokes ◽  
Far Field ◽  
Computational Domain ◽  
Linearized Euler Equations ◽  
Naca0012 Airfoil

We analyze a nonoverlapping domain decomposition method for the treatment of two-dimensional compressible viscous flows around airfoils. Since at some distance to the given profile the inertial forces are strongly dominant, there the viscosity effects are neglected and the flow is assumed to be inviscid. Accordingly, we consider a decomposition of the original flow field into a bounded computational domain (near field) and a complementary outer region (far field). The compressible Navier–Stokes equations are used close to the profile and are coupled with the linearized Euler equations in the far field by appropriate transmission conditions, according to the physical properties and the mathematical type of the corresponding partial differential equations. We present some results of flow around the NACA0012 airfoil and develop an a posteriori analysis of the approximate solution, showing that conservation of mass, momentum and energy are asymptotically attained with the linear model in the far field.

Parameter Extension Simulation of Turbulent Flows in a Compressor Cascade With a High Reynolds Number

2020 ◽  
Author(s):  
Yan Jin
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Simulation Method ◽  
Potential Method ◽  
Navier Stokes ◽  
Reference Solution ◽  
Compressor Cascade ◽  
High Reynolds

Abstract The turbulent flow in a compressor cascade is calculated by using a new simulation method, i.e., parameter extension simulation (PES). It is defined as the calculation of a turbulent flow with the help of a reference solution. A special large-eddy simulation (LES) method is developed to calculate the reference solution for PES. Then, the reference solution is extended to approximate the exact solution for the Navier-Stokes equations. The Richardson extrapolation is used to estimate the model error. The compressor cascade is made of NACA0065-009 airfoils. The Reynolds number 3.82 × 105 and the attack angles −2° to 7° are accounted for in the study. The effects of the end-walls, attack angle, and tripping bands on the flow are analyzed. The PES results are compared with the experimental data as well as the LES results using the Smagorinsky, k-equation and WALE subgrid models. The numerical results show that the PES requires a lower mesh resolution than the other LES methods. The details of the flow field including the laminar-turbulence transition can be directly captured from the PES results without introducing any additional model. These characteristics make the PES a potential method for simulating flows in turbomachinery with high Reynolds numbers.

On Offset Placement of a Compound Droplet in a Channel Flow

2021 ◽  
Author(s):  
Jagannath Mahato ◽  
Dhananjay Kumar Srivastava ◽  
Dinesh Kumar Chandraker ◽  
Rajaram Lakkaraju
Keyword(s):  
Viscosity Ratio ◽  
Stokes Equations ◽  
Temporal Dynamics ◽  
Flow Direction ◽  
Navier Stokes ◽  
Volume Of Fluid Method ◽  
Lateral Migration ◽  
Navier Stokes Equations ◽  
Deformation Patterns ◽  
Compound Droplet

Abstract Investigations on flow dynamics of a compound droplet have been carried out in a two-dimensional fully-developed Poiseuille flow by solving the Navier-Stokes equations with the evolution of the droplet using the volume of fluid method with interface compression. The outer droplet undergoes elongation similar to a simple droplet of same size placed under similar ambient condition in the flow direction, but, the inner droplet evolves in compressed form. The compound droplet is varied starting from the centerline towards the walls of the channel. The simulations showed that on applying an offset, asymmetric slipper-like shapes are observed as opposed to symmetric bullet-like shapes through the centerline. Temporal dynamics, deformation patterns, and droplet shell pinch-off mode vary with the offset, with induction of lateral migration. Also, investigations are done on the effect of various parameters like droplet size, Capillary number, and viscosity ratio on the deformation magnitude and lateral migration.

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