Numerical Solution Of Navier-Stokes Equations Research Articles

Fluid-driven bacterial accumulation in proximity of laser-textured surfaces

In this work we investigated the role of fluid in the initial phase of bacterial adhesion on textured surfaces, focusing onto the approach of the bacterial cells towards the surface. In particular, stainless steel surfaces textured via femtosecond laser interaction have been considered. The method combined a simulation routine, based on the numerical solution of Navier-Stokes equations, and the use of a theoretical model, based on the Smoluchowski’s equation. Results highlighted a slowdown of the fluid velocity field in correspondence of the surface dales. In addition, a shear induced accumulation on the top of the surface protrusions was predicted for motile bacterial species, E. coli. In particular, we observed a role of the surface protrusions in increasing the range over which motile bacterial species are attracted towards the surface through a rheotactic mechanism. In other words, we found that, in certain conditions of fluid flow and textured surface morphology, surface protrusions act as a sort of “rheotactic antennas”.

Application of the combined CFD and swarm intelligence for optimization of baffles number in a mixer-settler

Process optimization in a mixer-settler is of great importance. Optimization algorithm of particle swarm optimization is one of the evolutionary algorithms to solve optimization problem which is used in many fields. In this study, the optimal condition is calculated in finite volume method in terms of the number of baffles, inlet velocity of fluid, and impeller speed in a mixer-settler with a specific dimension that can be extended to industrial dimensions using the PSO algorithm and the numerical solution of Navier-Stokes equations and k-ε standard.

Splitting Algorithms for Numerical Solution of Navier-Stokes Equations in Fluid Dynamics Problems

Splitting Algorithms for Numerical Solution of Navier-Stokes Equations in Fluid Dynamics Problems

Conjugate heat transfer due to conduction, natural convection, and radiation from a vertical hollow cylinder with finite thickness

A comprehensive numerical study is performed on a vertical hollow cylinder of finite thickness for natural convection with surface radiation effect. The prime aim is to find out the heat transfer rate due to both natural convection and radiation from both the inner and outer walls of the tube. Also, an attempt is made to estimate the cooling time, the time required to bring down the cylinder temperature from a prescribed temperature to atmospheric temperature. Numerical solution of Navier-Stokes equation, energy equation, and radiation equation is solved, taking the finite volume approach of ANSYS-Fluent 18 around a vertical tube for determining flow and heat transfer characteristics around it. Different relevant parameters are chosen for the numerical analysis, such as Rayleigh number (from 5.7 × 103 to 5.7 × 107), inner surface temperature (from 350 K to 550 K), and aspect ratio (L/D) of the tube (from 0.5 to 20). To catch the effect of surface radiation, emissivity (from 0 to 1) is also varied. A comparison is made for natural convection and fluid flow characteristics with and without surface radiation effect.

Finite Difference Analysis of Plane Couette Flow using MATLAB

Internal flow is a flow for which the fluid is confined by a surface. Hence, the boundary layer is unable to develop without eventually being constrained. An internal flow is constrained by the bounding walls, and the viscous effects will grow and meet and permeate the entire flow. Some examples of internal flows are: flow between two parallel horizontal plates, Couette flow, plane Poiseuille flow, flow through pipes, etc. In the present study, a plane Couette flow has been analyzed by a classical method (exact solution of Navier-Stokes equation) as well as by an approximate method using central difference scheme (numerical solution of Navier-Stokes equation). The flow domain has been divided into various nodes and the velocities are obtained at different nodes for various time intervals. The stability condition for the convergence of solution has been determined and further the convergence of solution has been obtained using a MATLAB program for Couette flow using Crank-Nicolson scheme.

РОЗРАХУНОК АЕРОДИНАМІЧНИХ ХАРАКТЕРИСТИК НАДЗВУКОВИХ ОПЕРЕНИХ ОСЕСИМЕТРИЧНИХ ТІЛ ОБЕРТАННЯ

The subject of research in the article is the aerodynamic forces arising from the flight of supersonic feathered rotation bodies such as unguided rockets. The aim of the work is to develop a method for calculating the aerodynamic coefficients of the resultant forces and moments of supersonic feathered bodies of revolution such as unguided missiles when flown around at an angle of attack with pre-, trans- and supersonic speeds according to drawings of their external contours. Tasks: using modern software systems and flight experiments, develop a method for calculating the distribution of normal and tangential stresses over the surface of a supersonic feathered body of rotation, their equivalent and aerodynamic coefficients at up-, trans- and supersonic flow velocities at an angle of attack. The applied methods are the numerical solution of the Navier-Stokes equations, the use of two-parameter differential models of near-wall turbulent viscosity, verification of the methodology by comparing the results of calculations with the data of flight experiments and known data on the aerodynamic resistance of the object of research. The following results were obtained. Based on the numerical solution of the Navier-Stokes equations in the ANSYS CFX software package using the γ-ReΘt SST–model of Menter’s near-wall turbulence, a method is developed for calculating the aerodynamic characteristics of supersonic axially symmetric rotation bodies of uncontrollable missiles according to drawings of the external contours in the presence of a counter-flow angle. Using the developed technique it is possible to calculate the aerodynamic coefficients of friction resistance, pressure resistance and bottom resistance at sub-, trans- and supersonic speeds. Characteristics include the coefficients of the longitudinal aerodynamic force, transverse aerodynamic force, aerodynamic stabilizing moment and the coordinate of the center of pressure of the feathered body of rotation. For the calculations, were applied the external contours of the unguided missile M–21OФ. Calculations were performed for the counter-flow Mach numbers within0,1 £ M∞ £ 2,5. The aerodynamic coefficients were calculated as functions of the Mach number M∞. In order to determine the Reynolds number of the beginning of the laminar-turbulent transition in the boundary layer for this type of aircraft the characteristics of the friction resistance were calculated and compared with the flight data for two samples of research aerophysical complexes. Conclusions. The scientific novelty of the results is as follows: a pilot test was created and involved the results of flight experiments on Reynolds numbers of the start of a laminar-turbulent transition in the boundary layers of a method for calculating the aerodynamic drag coefficients of supersonic axially rotated bodies of rotation like uncontrollable missiles according to the drawings of their external contours during turning angle of attack based on the numerical solution of the Reynolds-averaged Navier-Stokes equations in the framework of the programme product ANSYS CFX using γ-ReΘt SST–Menter turbulence model. Verification of the calculation results was carried out on the basis of their comparison with the known values of the aerodynamic characteristics of the object of research with the axisymmetric flow.

物理のための計算機実験(2) : ナビエ・ストークス方程式の数値解

物理のための計算機実験(2) : ナビエ・ストークス方程式の数値解

An efficient shock-capturing scheme for simulating compressible homogeneous mixture flow

This work is devoted to the development of a procedure for the numerical solution of Navier-Stokes equations for cavitating flows with and without ventilation based on a compressible, multiphase, homogeneous mixture model. The governing equations are discretized on a general structured grid using a high-resolution shock-capturing scheme in conjunction with appropriate limiters to prevent the generation of spurious solutions near shock waves or discontinuities. Two well-known limiters are examined, and a new limiter is proposed to enhance the accuracy and stability of the numerical scheme. A sensitivity analysis is first conducted to determine the relative influences of various model parameters on the solution. These parameters are adopted for the computation of water flows over a hemispherical body, conical body and a divergent/convergent nozzle. Finally, numerical calculations of ventilated supercavitating flows over a hemispherical cylinder body with a hot propulsive jet are conducted to verify the capabilities of the numerical scheme.

An Algorithm for the Numerical Solution of the Pseudo Compressible Navier-stokes Equations Based on the Experimenting Fields Approach

Abstract In this work, the experimenting fields approach is applied to the numerical solution of the Navier-Stokes equation for incompressible viscous flow. In this work, the solution is sought for both the pressure and velocity fields in the same time. Apparently, the correct velocity and pressure fields satisfy the governing equations and the boundary conditions. In this technique a set of predefined fields are introduced to the governing equations and the residues are calculated. The flow according to these fields will not satisfy the governing equations and the boundary conditions. However, the residues are used to construct the matrix of coefficients. Although, in this setup it seems trivial constructing the global matrix of coefficients, in other setups it can be quite involved. This technique separates the solver routine from the physics routines and therefore makes easy the coding and debugging procedures. We compare with few examples that demonstrate the capability of this technique.

On the Accelerated Settling of Fine Particles in a Bidisperse Slurry

An estimation of increasing the volume average sedimentation velocity of fine particles in bidisperse suspension due to their capturing in the circulation zone formed in the laminar flow of incompressible viscous fluid around the spherical coarse particle is proposed. The estimation is important for an explanation of the nonmonotonic shape of the separation curve observed for hydrocyclones. The volume average sedimentation velocity is evaluated on the basis of a cellular model. The characteristic dimensions of the circulation zone are obtained on the basis of a numerical solution of Navier-Stokes equations. Furthermore, these calculations are used for modelling the fast sedimentation of fine particles during their cosedimentation in bidisperse suspension. It was found that the acceleration of sedimentation of fine particles is determined by the concentration of coarse particles in bidisperse suspension, and the sedimentation velocity of fine fraction is proportional to the square of the coarse and fine particle diameter ratio. The limitations of the proposed model are ascertained.

Vortex Formation for Different Geometry of Cavities Using High Reynolds Number

A preliminary study of Computational Fluid Dynamics (CFD) on the effect of high Reynolds numbers in the cavity has been carried out. Two dimensional model analysis of the flow characteristics were conducted using the numerical solution of Navier-Stokes equations based on the finite difference method. The flow characteristics in the cavity and the driven flow were modeled via turbulence equation modelling. This paper focuses on the effects of different high Reynolds number on the flow pattern of contaminant removal in the cavity. Different types of geometry and aspect ratio of the geometry were used as the parameters of the cavity in this study. Based on visualization of flows between each model with the different parameters used, the results of a comparison analysis focusing on the behavior of the flow were reported.

Accuracy analysis of a mesh refinement method using benchmarks of 2-D lid-driven cavity flows and finer meshes

Lid-driven cavity flows have been widely investigated and accurate results have been achieved as benchmarks for testing the accuracy of computational methods. This paper verifies the accuracy of a mesh refinement method numerically using two-dimensional steady incompressible lid-driven flows and finer meshes. The accuracy is shown by comparing the coordinates of centres of vortices located by the mesh refinement method with the corresponding benchmark results. The accuracy verification shows that the mesh refinement method provides refined meshes that all centres of vortices are contained in refined grids based on the numerical solutions of Navier-Stokes equations solved by finite volume method except for one case. The well known SIMPLE algorithm is employed for pressure–velocity coupling. The accuracy of the numerical solutions is shown by comparing the profiles of horizontal and vertical components of velocity fields with the corresponding components of the benchmarks and also streamlines. The mesh refinement method verified in this paper can be applied to find the accurate numerical solutions of any mathematical models containing continuity equations for incompressible fluid or steady state fluid flows or heat transfer.

Numerical Methods for Solving Turbulent Flows by Using Parallel Technologies

Parallel implementation of algorithm of numerical solution of Navier-Stokes equations for large eddy simulation (LES) of turbulence is presented in this research. The Dynamic Smagorinsky model is applied for sub-grid simulation of turbulence. The numerical algorithm was worked out using a scheme of splitting on physical parameters. At the first stage it is supposed that carrying over movement amount takes place only due to convection and diffusion. Intermediate field of velocity is determined by method of fractional steps by using Thomas algorithm (tridiaginal matrix algorithm). At the second stage found intermediate field of velocity is used for determination of the field of pressure. Three dimensional Poisson equation for the field of pressure is solved using upper relaxation method. Moreover various ways of geometrical decomposition for parallel numerical solution of three dimensional Poisson equations are investigated.

Computational Study on the Influence of jet on Reduction of Drag Over Cone Flare Bodies in Hypersonic Turbulent Flow

Recently, Nhypersonic research activities around the universe have been in major focus because of the milestone developments in hypersonic reentry vehicles, orbital transfer vehicles, reusable launch vehicles and space recovery experimental modules. One of the major problems in hypersonic flight is drag and with the tremendous progress in computational powers it can be analysed. In this work, the effects of counter flow jet on reduction of drag around two blunt cone flare bodies in the hypersonic turbulent flow are investigated through a numerical study. Flow field around the blunt bodies is calculated numerically for the free stream Mach number of 6.5. Numerical solutions of Navier-Stokes equation and energy equation governing the turbulent flow of compressible fluid are obtained by adopting Finite Volume Method (FVM) through an industry standard CFD code, FLUENT 6.3.26 package. Shear Stress Transport (SST) model was used in the computation of pressure drag, skin friction drag and total drag for both the absence of jet and the presence of jet cases for both the configuration. Contours of Mach number are presented to describe the flow patterns. It is clear that the reduction of drag was greatly influenced by the jet conditions and body shapes.

Numerical simulation of supersonic flows in a channel

An algorithm for numerical solution of Navier-Stokes equations for two-dimensional motion of a viscous heat-conducting gas is proposed in the paper. The discretization of the equations is performed by a combination of the method of trajectories for the substantive derivative and the finite element method with piecewise-bilinear basis functions for other summands. Results of numerical study of the supersonic flow structure are presented for a flat channel in its step expansion zone for a wide range of Mach and Reynolds numbers. Velocity and pressure fields are investigated, the vortex structure of the circulation flow is studied in the domain after the step

Large eddy simulation of turbulent mixing by using 3D decomposition method

Parallel implementation of algorithm of numerical solution of Navier-Stokes equations for large eddy simulation (LES) of turbulence is presented in this research. The dynamic Smagorinsky model is applied for sub-grid simulation of turbulence. The numerical algorithm was worked out using a scheme of splitting on physical parameters. At the first stage it is supposed that carrying over of movement amount takes place only due to convection and diffusion. Intermediate field of velocity is determined by method of fractional steps by using Thomas algorithm (tridiagonal matrix algorithm). At the second stage the determined intermediate field of velocity is used for determination of the field of pressure. Three dimensional Poisson equation for the field of pressure is solved using over relaxation method.

Wavelets with differential relation

Divergence-free wavelets are successfully applied to numerical solutions of Navier-Stokes equation and to analysis of incompressible flows. They closely depend on a pair of one-dimensional wavelets with some differential relations. In this paper, we point out some restrictions of those wavelets and study scaling functions with the differential relation; Wavelets and their duals are discussed; In addition to the differential relation, we are particularly interested in a class of examples with the interpolatory property; It turns out there is a connection between our examples and Micchelli’s work.

Numerical investigation of heat transfer on the surface of experimental models in the test chamber of an induction plasmatron

An axisymmetric flow of a subsonic jet of air plasma past experimental models in the test chamber of a radio-frequency induction plasmatron is considered. The simulation is performed using the numerical solution of Navier-Stokes equations describing the flow of a nonequilibrium chemically reacting mixture of gases. The effect is investigated, which is made by the configuration of model and catalycity of its surface on the profiles of concentrations of chemical components in the boundary layer and on the distribution of heat fluxes.

Flow-induced permeation of non-occlusive blood clots: an MRI study and modelling

The success of clot thrombolysis very much depends on efficient clot permeation with blood plasma carrying the thrombolytic agent. In this paper clot permeation was studied by dynamic magnetic resonance imaging (MRI) on artificial non-occlusive blood clots inserted in an artificial circulation system filled with blood plasma to which an MRI contrast agent was added. The MRI results revealed that clot permeation is much faster and more efficient at the entrance of the flow channel across the clot. Clot permeation with fluid was simulated numerically as well. The simulation was based on numerical solution of Navier-Stokes equations for the flow in the channel and within the clot. The clot was considered as a porous material with known permeability and porosity. Based on the calculated velocity profiles, concentration profiles of fluid in the clot were modelled. These agreed well with the MRI results. The presented model of clot permeation with fluid may also serve as a useful extension to numerical modelling of dissolution of non-occlusive blood clots during thrombolytic therapy.

Numerical simulation of a viscous separation flow around a rotating circular cylinder

Results of numerical solution of Navier-Stokes equations in stream function-vortex variables for a nonstationary laminar flow around a circular cylinder with a rotational degree of freedom are presented. The cases of definite, free, and inertial rotation of the indicated cylinder were considered.