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You may receive emails, depending on your notification preferences. How to get the Couette Flow? Veronica Stuckey on 28 Jan Vote 0. Commented: Peter Dieter on 15 May The purpose of the assignment is to create a movie that shows the couette flow.Couette flow is viscous laminar flow between two parallel plates, one of which is moving relative to the other. Due to its simple nature and the existance of an analytical solution, it is a common validation case for CFD codes.
An example validation case is shown in Hirsch . Couette flow results in a constant shear stress which has a linear velocity profile and a parabolic temperature profile as shown below. Three of the newer features in Aither are periodic boundary conditions, moving walls, and isothermal walls.
A couette flow simulation can make use of all of these features, so it makes a great addition to the test cases suite. The parallel plates are placed a distance of 0. The bottom plate is held at a temperature of K and is stationary. The top plate is held at a temperature of K and is moving at For this setup, the product of the Prandtl and Eckert numbers is 4. This means that for the temperature profile, the maximum temperature will not be at the plate, but in the flow instead.
The exact solution dictates that the maximum temperature should be three fourths of the way between the cold and hot plates. Isothermal walls can be specified in Aither by adding the temperature parameter to the boundary state list. Similarly moving walls can be specified by adding the velocity parameter. Periodic boundary conditions are specified by indicating which boundary condition tags should be paired as periodic. This is done through the startTag and endTag parameters.
For each periodic boundary condition a transformation must be done to get from one periodic face to the other. Currently a translation can be specified by adding the translation parameter which is a vector specifying how the boundary at the startTag should be translated to get to the boundary at the endTag. Alternatively a rotation can be specified by using the axispointand rotation parameters. The axis parameter is a vector defining the axis of rotation.
The point parameter is a vector defining a point about which to rotate. The rotation parameter is a scalar defining the rotation angle in radians. An example of these new boundary condition options is shown below. The results from Aither show a linear velocity profile and a parabolic temperature profile as expected. The results agree very well with the exact solution. These results can be reproduced by running the Aither code.
The grid and input file for the couette flow case can be found in the testCases directory of the repository. Couette Flow Couette flow is viscous laminar flow between two parallel plates, one of which is moving relative to the other.
Problem Setup The parallel plates are placed a distance of 0.Objective: To obtain the velocity profile of a non-Newtonian fluid flowing between two infinitely long parallel plates, with one plate being stationary and the other moving with a constant velocity Couette flow. The viscosity of the fluid is variable and the necessary adjustment has to be made while solving the governing equation. However, in this problem statement, the viscosity itself varies with the velocity gradient, given by the equation:.
Where k and n are constants that depend on the fluid. Here, the velocity for one of the nodes in this case the south node, denoted by S is already known by a boundary condition, i. The velocities at the middle point P and the north node N have to be calculated by using the finite difference method, while the Gauss-Seidel method is used to calculate the value of the velocity at those points.
The corresponding values of C1, C2 and C3 are given as follows:. This follows similar to the process done in the first calculation, with the exception that the loop is written for a general case to calculate all the velocity values. Here, v is the number of CVs. Furthermore, all the C1s obtained in each calculation is found from the same formula of C1 as mentioned above. The various graphs obtained vary with the number of CVs given as the input, and more the number, better the accuracy of the plot.
Sources of error and their correction. The absolute function to specify the velocity gradient is very important, as for negative differences between the velocities at the nodes, the value becomes imaginary when raised to an even power.
This error must be corrected by including the absolute function. Some functions in the createfigure. This can be easily modified by using the appropriate syntax for the version being used. Thus, the velocity vs. This project can also be used as a base for further investigations in more complex problems, such as addition of turbulence in non-Newtonian flow etc.
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Couette Flow in Matlab using Pressure Correction Method
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Sign up. Go back. Launching Xcode If nothing happens, download Xcode and try again. Latest commit. Git stats 5 commits. Failed to load latest commit information. View code. Example usage: couette 1, 10, 1, 0. Topics computational-fluid-dynamics.
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Analytics cookies We use analytics cookies to understand how you use our websites so we can make them better, e. Save preferences.February 16,Problem in modeling 2D Couette flow. Join Date: Feb Hey guys, this was my first attempt at modeling incompressible flow.
I've been studying J. Anderson's "CFD Basics and applications" and took up the Couette flow problem described in chapter 9 and tried writing code for it in Matlab. I've used a finite difference scheme and a pressure correction method that is explained in the book. Also, I've tried keeping the implementation as identical to what is described in the text. The matlab script file has been attached for reference.
The test runs for a couple of iterations but then the x-velocity near the top moving wall and the inlet oscillates and soon the program crashes with the velocity developing inordinate values. Thank you, Shantanu. Last edited by shantanu; February 18, at February 23, Aeronautics El. Try reducing your dt see also at the bottom of page of the book you mentioned.
March 11, Lefteris: I tried decreasing the time step and it really worked. Of course, there was also a small change that had to be made in the for loops. Thanks a ton for bringing that to my notice. And it's funny how the value of dt used by the author, himself, did not work!
Regards, Shantanu. October 14,couette 2D flow ploting of u,v,p vs y. October 28,help needed.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.
Number of iterations also depends upon the convergence criteria set for pressure correction i. Hence it depends upon the application, the kind of accuracy is required. Lower the value of d, higher are the number of iterations required. 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. Thanks for choosing to leave a comment. Please keep in mind that all comments are moderated according to our comment policyand your email address will NOT be published.
Let's have a personal and meaningful conversation. Comments 0. 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.
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. 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 known, aninevitable and difficult test case for any numerical… 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, results for the two different fluids- Air and Hydrogen… Read more.
2D Couette Flow ( SIMPLE Algorithm )
Arrayrow X 5-columns. Array: 5-rows X 1-column. And we cannot multiply two… Read more. Boundary and initial condition saurabh updated on Aug 04,pm IST Boundary conditions and initial conditions dictate particular solutions to be obtained from Partial differential equations.Updated 09 Apr This app will plot the variation of velocity with distance for different values of non Dimensional pressure gradient P.
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How to get the Couette Flow?
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Couette Flow Between Parallel Plates version 1.
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