Investigation into Fluid Velocity Field of Wedge-Shaped Gap in Grinding

2010 ◽  
Vol 37-38 ◽  
pp. 593-598 ◽  
Author(s):  
Chang He Li ◽  
Zhen Lu Han ◽  
Jing Yao Li
Keyword(s):  
Velocity Field ◽  
Fluid Velocity ◽  
Fluid Pressure ◽  
Surface Velocity ◽  
Navier Stokes ◽  
Coolant Fluid ◽  
Navier Stokes Equation ◽  
Part Surface ◽  
Peripheral Surface ◽  
Fluid Velocity Field

In the grinding process, grinding fluid is delivered for the purposes of chip flushing, cooling, lubrication and chemical protection of work surface. Hence, the conventional method of flood delivering coolant fluid by a nozzle in order to achieve high process performance purposivelly. However, hydrodynamic fluid pressure can be generated ahead of the grinding zone due to the wedge effect between wheel peripheral surface and part surface. In this paper, a theoretical fluid velocity field modeling is presented for flow of coolant fluid of wedge-shaped gap in flood delivery surface grinding, which is based on navier-stokes equation and continuous formulae. The numerical simulation results showed that the velocity in the x direction was dominant and the side-leakage in the y direction existed. The velocity in the z direction was smaller than the others because of the assumption of laminar flow. The smaller the gap is, the larger the velocity in the x direction. The magnitude of the velocity is also proportional to the surface velocity of the wheel.

scholarly journals Streamrate stagnation-point flow of a nanofluid on a stationary cylinder

2015 ◽  
Vol 3 (1) ◽  
pp. 124
Author(s):  
Vahid Amerian ◽  
Hamid Mohammadiun ◽  
Mohammad Mohammadiun ◽  
Iman Khazaee
Keyword(s):  
Velocity Field ◽  
Stagnation Point ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Constant Strain Rate ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Shear Stresses ◽  
Navier Stokes Equations ◽  
Fluid Velocity Field

<p>The steady-state, viscous flow of Nanofluid in the vicinity of an axisymmetric stagnation point of a stationary cylinder is investigated. The impinging free-stream is steady and with a constant strain rate . Exact solution of the Navier–Stokes equations is derived in this problem. A reduction of these equations is obtained by use of appropriate transformations introduced in this research. The general self-similar solution is obtained when the wall temperature of the cylinder is constant. All the solutions above are presented for Reynolds numbers ranging from 0.1 to 1000 and selected values of particle. For all Reynolds numbers, as the particle fraction increases, the depth of diffusion of the fluid velocity field in radial direction, the depth of the diffusion of the fluid velocity field in -direction, shear-stresses and pressure function decreases.<strong></strong></p>

Model and Simulation of Slurry Velocity and Hydrodynamic Pressure in Abrasive Jet Finishing with Grinding Wheel as Restraint

2008 ◽  
Vol 375-376 ◽  
pp. 449-453 ◽  
Author(s):  
Chang He Li ◽  
Ya Li Hou ◽  
Shi Chao Xiu ◽  
Guang Qi Cai
Keyword(s):  
Laminar Flow ◽  
Fluid Pressure ◽  
Three Dimensional ◽  
Hydrodynamic Pressure ◽  
Surface Velocity ◽  
Navier Stokes ◽  
Grinding Wheel ◽  
Maximum Pressure ◽  
Navier Stokes Equation ◽  
Model And Simulation

The models for three-dimensional velocity and hydrodynamic pressure of abrasive fluid in contact zone between wheel and workpiece on abrasive jet finishing with wheel as restraint were presented based on Navier-Stokes equation and continuous formulae. The emulational results shown that the hydrodynamic pressure was proportion to grinding wheel velocity, and inverse proportion to the minimum gap between wheel and workpiece and the maximum pressure was generated just in the minimum clearance region in which higher fluid pressure gradient occur. It can also be concluded the pressure distribution was uniform in the direction of width of wheel except at the edge of wheel because of the side-leakage. The velocity in the x direction was dominant and the side-leakage in the y direction existed. The velocity in the z direction was smaller than the others because of the assumption of laminar flow. The smaller the gap distance is, the larger the velocity in the x direction. The magnitude of the velocity is also proportional to the surface velocity of the wheel.

Numerical study of the flow of a mixture of reacting gases in an inhomogeneous catalyst layer

2003 ◽  
Vol 3 ◽  
pp. 246-254
Author(s):  
C.I. Mikhaylenko ◽  
S.F. Urmancheev
Keyword(s):  
Velocity Field ◽  
Chemical Reactions ◽  
Porous Layer ◽  
Computational Experiment ◽  
Numerical Study ◽  
Fluid Velocity ◽  
Catalyst Layer ◽  
Granular Catalyst ◽  
Fluid Velocity Field

The behavior of a liquid flowing through a fixed bulk porous layer of a granular catalyst is considered. The effects of the nonuniformity of the fluid velocity field, which arise when the surface of the layer is curved, and the effect of the resulting inhomogeneity on the speed and nature of the course of chemical reactions are investigated by the methods of a computational experiment.

Coriolis force influence on the AKA effect

2021 ◽  
Author(s):  
Peter Rutkevich ◽  
Georgy Golitsyn ◽  
Anatoly Tur
Keyword(s):  
Steady State ◽  
Stokes Equation ◽  
Nonlinear Equations ◽  
Coriolis Force ◽  
Large Scale ◽  
Fluid Velocity ◽  
Navier Stokes ◽  
Basic Solution ◽  
Navier Stokes Equation ◽  
Alpha Effect

&lt;p&gt;Large-scale instability in incompressible fluid driven by the so called Anisotropic Kinetic Alpha (AKA) effect satisfying the incompressible Navier-Stokes equation with Coriolis force is considered. The external force is periodic; this allows applying an unusual for turbulence calculations mathematical method developed by Frisch et al [1]. The method provides the orders for nonlinear equations and obtaining large scale equations from the corresponding secular relations that appear at different orders of expansions. This method allows obtaining not only corrections to the basic solutions of the linear problem but also provides the large-scale solution of the nonlinear equations with the amplitude exceeding that of the basic solution. The fluid velocity is obtained by numerical integration of the large-scale equations. The solution without the Coriolis force leads to constant velocities at the steady-state, which agrees with the full solution of the Navier-Stokes equation reported previously. The time-invariant solution contains three families of solutions, however, only one of these families contains stable solutions. The final values of the steady-state fluid velocity are determined by the initial conditions. After account of the Coriolis force the solutions become periodic in time and the family of solutions collapses to a unique solution. On the other hand, even with the Coriolis force the fluid motion remains two-dimensional in space and depends on a single spatial variable. The latter fact limits the scope of the AKA method to applications with pronounced 2D nature. In application to 3D models the method must be used with caution.&lt;/p&gt;&lt;p&gt;[1] U. Frisch, Z.S. She and P. L. Sulem, &amp;#8220;Large-Scale Flow Driven by the Anisotropic Kinetic Alpha Effect,&amp;#8221; Physica D, Vol. 28, No. 3, 1987, pp. 382-392.&lt;/p&gt;

Wave Motion of a Compressible Viscous Fluid Contained in a Cylindrical Shell

1993 ◽  
Vol 115 (3) ◽  
pp. 302-312 ◽  
Author(s):  
J. H. Terhune ◽  
K. Karim-Panahi
Keyword(s):  
Velocity Field ◽  
Viscous Fluid ◽  
Imaginary Part ◽  
Fluid Velocity ◽  
Wave Number ◽  
Mode Shapes ◽  
Infinite Length ◽  
Complex Frequency ◽  
Compressible Viscous Fluid ◽  
Fluid Velocity Field

The free vibration of cylindrical shells filled with a compressible viscous fluid has been studied by numerous workers using the linearized Navier-Stokes equations, the fluid continuity equation, and Flu¨gge ’s equations of motion for thin shells. It happens that solutions can be obtained for which the interface conditions at the shell surface are satisfied. Formally, a characteristic equation for the system eigenvalues can be written down, and solutions are usually obtained numerically providing some insight into the physical mechanisms. In this paper, we modify the usual approach to this problem, use a more rigorous mathematical solution and limit the discussion to a single thin shell of infinite length and finite radius, totally filled with a viscous, compressible fluid. It is shown that separable solutions are obtained only in a particular gage, defined by the divergence of the fluid velocity vector potential, and the solutions are unique to that gage. The complex frequency dependence for the transverse component of the fluid velocity field is shown to be a result of surface interaction between the compressional and vortex motions in the fluid and that this motion is confined to the boundary layer near the surface. Numerical results are obtained for the first few wave modes of a large shell, which illustrate the general approach to the solution. The axial wave number is complex for wave propagation, the imaginary part being the spatial attenuation coefficient. The frequency is also complex, the imaginary part of which is the temporal damping coefficient. The wave phase velocity is related to the real part of the axial wave number and turns out to be independent of frequency, with numerical value lying between the sonic velocities in the fluid and the shell. The frequency dependencies of these parameters and fluid velocity field mode shapes are computed for a typical case and displayed in non-dimensional graphs.

scholarly journals Experimental and Numerical Investigation of Preferential Flow in Fractured Network with Clogging Process

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Xiaobing Chen ◽  
Jian Zhao ◽  
Li Chen
Keyword(s):  
Velocity Field ◽  
Cross Sections ◽  
Preferential Flow ◽  
Pressure Head ◽  
Fracture Network ◽  
Navier Stokes ◽  
Single Fracture ◽  
Navier Stokes Equation ◽  
Physical Experiments ◽  
Fractured Network

In this study, physical experiments and numerical simulations are combined to provide a detailed understanding of flow dynamics in fracture network. Hydraulic parameters such as pressure head, velocity field, Reynolds number on certain monitoring cross points, and total flux rate are examined under various clogging conditions. Applying the COMSOL Multiphysics code to solve the Navier-Stokes equation instead of Reynolds equation and using the measured data to validate the model, the fluid flow in the horizontal 2D cross-sections of the fracture network was simulated. Results show that local clogging leads to a significant reshaping of the flow velocity field and a reduction of the transport capacity of the entire system. The flow rate distribution is highly influenced by the fractures connected to the dominant flow channels, although local disturbances in velocity field are unlikely to spread over the whole network. Also, modeling results indicate that water flow in a fracture network, compared with that in a single fracture, is likely to transit into turbulence earlier under the same hydraulic gradient due to the influence of fracture intersections.

scholarly journals Closed-Form Non-Stationary Solutionsfor Thermo and Chemovibrational Viscous Flows

Fluids ◽  
2019 ◽  
Vol 4 (3) ◽  
pp. 175 ◽  
Author(s):  
Dmitry Bratsun ◽  
Vladimir Vyatkin
Keyword(s):  
Viscous Flow ◽  
Closed Form ◽  
General Procedure ◽  
Fluid Velocity ◽  
Fluid Motion ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Chemical Transformations ◽  
Navier Stokes Equation ◽  
Harmonic Vibrations

A class of closed-form exact solutions for the Navier–Stokes equation written in the Boussinesq approximation is discussed. Solutions describe the motion of a non-homogeneous reacting fluid subjected to harmonic vibrations of low or finite frequency. Inhomogeneity of the medium arises due to the transversal density gradient which appears as a result of the exothermicity and chemical transformations due to a reaction. Ultimately, the physical mechanism of fluid motion is the unequal effect of a variable inertial field on laminar sublayers of different densities. We derive the solutions for several problems for thermo- and chemovibrational convections including the viscous flow of heat-generating fluid either in a plain layer or in a closed pipe and the viscous flow of fluid reacting according to a first-order chemical scheme under harmonic vibrations. Closed-form analytical expressions for fluid velocity, pressure, temperature, and reagent concentration are derived for each case. A general procedure to derive the exact solution is discussed.

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