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## Couette Flow

Computational Science Stack Exchange is a question and answer site for scientists using computers to solve scientific problems. It only takes a minute to sign up. I am currently following J. Anderson Jr. As the title suggests I am solving an incompressible Couette flow using an explicit finite difference approach. How can I increase the steps without it blowing up? Oh and the B. I realized where I went wrong This is not perfect still though I think the fact that I nondimensionalized my equation is messing with my solution, but nonetheless for small value of reynolds number it seems to generate the graph I want.

Explicit scheme have a stability condition, which requires that the amplification factor of the whole scheme be below 1 in order to ensure stability of the scheme. If you wish to use a larger time step, you need to use an implicit scheme. This will lead to the resolution of a linear system of equations. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Asked 3 years, 2 months ago. Active 3 years, 2 months ago.

Viewed times. K 33 4 4 bronze badges. Active Oldest Votes. BlaB BlaB 5 5 silver badges 16 16 bronze badges. K Feb 8 '17 at To get to it, you need to run the code long enough so that the solution to the unsteady flow problem you are solving approaches the steady-state solution. Is this a typo? Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. The Overflow Blog. The Overflow How many jobs can be done at home?

Socializing with co-workers while social distancing. Featured on Meta. Community and Moderator guidelines for escalating issues via new response…. Feedback on Q2 Community Roadmap.Tiegang Fang, Chia Fon F. In this work, the transient incompressible Couette flow and steady-state temperature profiles between two porous parallel plates for slightly rarefied gases are solved exactly. The first-order approximation of slip velocity at the boundaries is used in the formulation.

The solution is also applicable for Couette flow in micro-channels under certain circumstances.

The influences of mass transfer and a nondimensional slip parameter on slip velocities are discussed. It is also found that the transient slip velocities at the walls are greatly different from the steady-state velocity slips. The influences of velocity slip and temperature slip parameters on the temperature distribution and heat transfer at the walls are analyzed and discussed. It is shown that the slip parameters can greatly change the temperature profiles and heat transfer characteristics at the walls.

Exact solutions of incompressible Couette flow with porous walls for slightly rarefied gases. T1 - Exact solutions of incompressible Couette flow with porous walls for slightly rarefied gases. N2 - In this work, the transient incompressible Couette flow and steady-state temperature profiles between two porous parallel plates for slightly rarefied gases are solved exactly. AB - In this work, the transient incompressible Couette flow and steady-state temperature profiles between two porous parallel plates for slightly rarefied gases are solved exactly.

Mechanical Science and Engineering.

Abstract In this work, the transient incompressible Couette flow and steady-state temperature profiles between two porous parallel plates for slightly rarefied gases are solved exactly. Incompressible flow. Couette flow. Heat transfer. Mass transfer. Temperature distribution. Access to Document Incompressible Couette Flow. Recommend Documents. Computational Turbulent Incompressible Flow Oct 20, Couette Flow of Two-Dimensional Foams. Optimal Taylor-Couette flow: direct numerical simulations.

Instabilities in magnetized spherical Couette flow. Nonlinear instability of viscous plane Couette flow. Unsteady Couette Flow through a Porous Medium. Operated by New Jersey Institute of Technology. On the other hand, flows which are stable can become unstable. AP] 30 Jan Scalars convected by a 2D incompressible flow. Diego Cordoba. Department of Mathematics. Numerical simulation of incompressible viscous flow Large Scale Parallel Solution of Incompressible Flow mulation to simulate heat, mass, and momentum transport in react- ing flows.

PETSc users manual. Heat transfer to objects in pool fires, in transport phenomena. Unsteady Incompressible Stokes Flow through Linear instability of magnetic Taylor-Couette flow with Hall effect. Ex vivo evaluation of a Taylor-Couette flow, immobilized heparinase Contributed by Robert Langer, December 14, A schematic of the reactor, referred to as the vortex The well known analytical solution to the problem of incompressible couette is compared with a numerical solution.

For discrete problem formulation, implicit Figure 1: Schematic representation of Couette Flow Crank-Nicolson method was used. Finally, the sys- Problem tem of equation tridiagonal is solved with both Thomas and simple Gauss Method. Results of both 2 Fundamental Equations methods are compared. Departament of Physics and Astronomy. We will also use a continuity equation, which can be written as follows 1 : 1I assume constans density of the fluid.

That is now a governing problem of incompressible couette flow analysis. Mathematical Formulation of the Couette Problem Incompressible couette problem is not needed to 3. That equation is a vector type where c1 and c2 are integration constans.In this project, Couette flow flow of a viscous fluid in the space between two surfaces, one of which is moving tangentially relative to the other is being studied.

The main objective of the project is to discretize the Navier-Stokes equation using Finite Difference method, and solve them numerically using SIMPLE Semi-Implicit Method for Pressure Linked Equationsto analyse the flow of viscous fluid between two surfaces, in which the top surface is moving relative to the bottom plate.

The second part of the project is to analyse the flow over 2D Planar Backward Facing step using same Matlab code, only just changing the boundary conditions and initial conditions in the code.

Project Part1: Couette FlowIn fluid dynamics, Couette flow is defined as the flow of viscous fluid in the space between to surfaces, one of which is moving relative to the other, tangentially. The flow is driven by the viscous drag force acting on the fluid. This configuration can model certain practical problems, like flow in lightly loaded journal bearings, in viscometry and to demonstrate approximation of reversibility. This type of flow is named in the honour of Maurice Couette, a Professor of Physics at French University of Angers in late 19th century.

Project Part 2: Backward Facing StepFor the second part of project, we will be solving fully developed laminar channel flow on a backward facing step as given in the below given figure:. Project: Part1Starting from the assumed conditions for pressure and velocities at all points, variables are iterated to the correct values which satisfy the mass imbalance equation i.

In the below given curve, velocity component in x direction is plotted as function of vertical distance across the duct. Profiles are shown for various iteration numbers from 4 to iteration steps.

As we can see in the above given graph, with increase in iteration step, values for x component of velocity-U reaches convergence to the actual physical value. With increase in iteration, velocity magnitude increases with each iteration near the middle region, as the effect of upper plate moving reaches towards the bottom plate.

The hydraulic domain at the lower part of inflow shows negative magnitudethat means the direction of flow reverses at the lower part, below inflow which illustrates the effect of backward facing step. This can also be verified in the velocity vector diagram.

For instance in case of grid 51X21for Reynold number, number of iterations for main loop is 89, but for Reynold number, number of iterations shoots to about iterations. Where is an animation? Create an animation and upload it on Youtube link and paste the link in the project page. Marks here are deducted for the above mentioned reasons. In the current project a Shock wave tube or a Riemann tube problem is being studied. This is aparticularly useful case as it simulates a shock wave, expansion wave and discontinuity.

From a numerical point of view, this problem constitutes, since the exact solution is kno Read more. The main objective of this project is to design a 4-stage- Axial compressor with inlet guide vane, having constant tip diameter and using free vortex distribution i. Also, for the same volume flow rate and inlet conditions Read more. This projects summarizes the CFD simulation carried out for a shocktube problem using Converge Studio Package and post-processingi in Paraview.

In this simulation, we have used this feature- "Events" used in converge package. This feature help us to simulate the simila Read more. Flow simulation was setup up using Converge Studio, and post processing was carried out in Paraview. In sup Read more.

Project Part 2: Backward Facing StepFor the second part of project, we will be solving fully developed laminar channel flow on a backward facing step as given in the below given figure: Project Approach: SIMPLE method is employed for solving Navier-Stokes equation: Staggered Grid setting: Results and Discussion: Project: Part1Starting from the assumed conditions for pressure and velocities at all points, variables are iterated to the correct values which satisfy the mass imbalance equation i.

Projects by saurabh pargal. The End.

**Description and Derivation of the Navier-Stokes Equations**

Have an awesome project idea?In fluid dynamicsCouette flow is the flow of a viscous fluid in the space between two surfaces, one of which is moving tangentially relative to the other.

The configuration often takes the form of two parallel plates or the gap between two concentric cylinders. The flow is driven by virtue of viscous drag force acting on the fluid, but may additionally be motivated by an applied pressure gradient in the flow direction. The Couette configuration models certain practical problems, like flow in lightly loaded journal bearingsand is often employed in viscometry and to demonstrate approximations of reversibility.

Couette flow is frequently used in undergraduate physics and engineering courses to illustrate shear-driven fluid motion. Neglecting pressure gradients, the Navier—Stokes equations simplify to. This equation reflects the assumption that the flow is uni-directional. The exact solution. A notable aspect of the flow is that shear stress is constant throughout the flow domain. This is implied by the straight-line profile in the figure.

According to Newton's Law of Viscosity Newtonian fluidthe shear stress is the product of this expression and the constant fluid viscosity. In reality, the Couette solution cannot be reached instantaneously. The startup problem is given by. The problem can be converted to a homogeneous problem by subtracting steady solution and using separation of variablesthe solution is given by. This problem was studied by H.

Rowell and U. Finlayson [6] [7]. The Navier—Stokes equations, in this case, simplify to. Integrating the above equation twice and applying the boundary conditions same as in the case of Couette flow without pressure gradient to yield the following exact solution. The pressure gradient can be positive adverse pressure gradient or negative favorable pressure gradient.

This problem was first addressed by C.Couette Flow is drag-induced flow either between parallel flat plates or between concentric rotating cylinders. Drag-induced flow is thus distinguished from pressure-induced flow, such as Poiseuille Flow. Flow between parallel flat plates is easier to analyze than flow between concentric cylinders. The upper plate is of infinite length and infinite width; it moves at constant speed U in its own plane in the direction of the length of the lower plate.

There is no variation in pressure p anywhere in the flow. Because of the geometry, Couette flow is analyzed using rectangular or Cartesian coordinates x, y.

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The volumetric flow rate per unit width between the plates is given by:. Practical realization of Couette flow between parallel flat plates is difficult. A good approximation can, however, be obtained in the annular gap between two rotating concentric cylinders of slightly differing radii. Thus, if the inner cylinder has an outer radius R 1 and the outer cylinder has an inner radius R 2the flow between them is very similar to that given by Eq.

Flow between rotating concentric cylinders forms the basis of the Couette viscometer. In order to avoid the Taylor instability, it is usual to rotate the outer cylinder and keep the inner cylinder stationary. Then, if there is a torque or moment F x r on the inner cylinder, it can be shown that [see Fredrickson ]:. Note, incidentally, that Eq. Chandrasekhar, S. Drazin, P. Fredrickson, A. Richardson, S. Library Subscription: Guest.

Couette Flow Richardson, S. DOI: References Chandrasekhar, S.Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. Jain Published Physics. The present paper investigates a closed form solution for the transient free convection flow of a viscous fluid between 2 infinite vertical parallel plates in the presence of radiation.

The flow is set up due to free convective currents occurring as a result of application of constant heat flux CHF at one wall and constant temperature on the other wall. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. View PDF. Save to Library. Create Alert. Launch Research Feed. Share This Paper. Figures from this paper. Citations Publications citing this paper.

SarkarR. Jana Physics References Publications referenced by this paper. Fully developed laminar free convection between vertical plates heated asymmetrically Win Thanda Aung Physics Transient free convective flow in a vertical channel with constant temperature and constant heat flux on walls Thomas S. PaulBasant K.

JhaAshutosh Kumar Singh Physics Krishnakanta SinghThomas S. Paul Physics RaptisC. Perdikis Physics Effects of radiation in an optically thin gray gas flowing past a vertical infinite plate in the presence of a magnetic field A. PerdikisAlexandros Leontitsis Physics Thermal radiation of an optically thin gray gas A. Transient free-convective flow in a vertical channel due to symmetric heating Basant K. JhaA. Krishnakanta SinghHarmindar S. Takhar Physics SachetiA.

Krishnakanta Singh Physics Radiation and free convection flow past a moving plate A. Perdikis Materials Science

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