1. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Fluid Flow: Steady Flow

2. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Objectives  Understand steady flow.  Identify the types of steady flow.  Examine the considerations for steady flow.  Study the Navier-Stokes Equation for steady flow.  Learn from two examples:  CFD Analysis of Couette Flow  Flow between two fixed parallel plates Section 5 – Fluid Flow Module 4: Steady Flow Page 2

3. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Steady Flow  A steady flow is one in which the conditions (velocity, pressure and cross-section) may differ from point to point but DO NOT change with time.  In steady flow, all time derivatives in the governing equations are removed.  Compared to unsteady flow, steady flow is computationally less expensive and therefore much faster to solve. Section 5 – Fluid Flow Module 4: Steady Flow Page 3

4. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Steady Flow Types  Steady flow can be further classified into steady uniform flow and steady non-uniform flow.  Steady uniform flow:  Conditions do not change with position in the stream or with time. An example is the flow of water in a pipe of constant diameter at constant velocity.  Steady non-uniform flow:  Conditions change from point to point in the stream but do not change with time. An example is flow in a tapering pipe with constant velocity at the inlet. Velocity changes as fluid moves along the length of the pipe toward the exit. Section 5 – Fluid Flow Module 4: Steady Flow Page 4

5. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Considerations for Steady Flow  For all steady state flow cases, the total amount of flow entering into the system must have an outlet boundary that would allow the same amount of fluid out.  If this is not done, the solution will either fail to converge or circulation will occur at the inlet boundary.  Mass flow conservation as well as energy conservation should be ensured for the domain. Flow inFlow out Section 5 – Fluid Flow Module 4: Steady Flow Page 5

6. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Navier–Stokes Equation for Steady Flow 0 The time derivative is set to zero, thus simplifying the calculation. The most simplified cases of CFD are incompressible steady state flow with no body forces, as the terms inside the Navier–Stokes Equation are reduced. Section 5 – Fluid Flow Module 4: Steady Flow Page 6

7. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Video Example: CFD Analysis of Couette Flow (Steady State)  The CFD analysis of Couette flow using Autodesk Simulation Multiphysics has been described in a two-part video:  The first part explains the problem, setting up of the flow domain, meshing and application of boundary conditions.  The second part explains the analysis and post processing, covering the details of equation solving in the background and display of the analysis results. u0u0 X Stationary Plate Moving Plate Y Section 5 – Fluid Flow Module 4: Steady Flow Page 7

8. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Additional Example: Flow Between Two Fixed Parallel Plates  Flow between two fixed parallel plates  Couette flow case can be used  Setting up geometry and walls can be fixed  Distance between the plates is 2Y  The velocity can be defined as:  Maximum Velocity will occur at the center, i.e., at y =0 y x Y Exact Solution These two exact solution equations can be used by students to verify results from CFD. Section 5 – Fluid Flow Module 4: Steady Flow Page 8

9. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Summary  Steady flow is when flow behavior (velocity, pressure) does not change with the passage of time.  Many real life studies are carried out assuming steady flow.  Even when studying unsteady flow, it is a common practice to carry out a steady state analysis first. Section 5 – Fluid Flow Module 4: Steady Flow Page 9

10. © 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the original, and must attribute source content to Autodesk. www.autodesk.com/edcommunity Education Community Summary  For example, study of flow across a vehicle is carried out in steady state to evaluate the drag coefficient.  It is important that the boundary conditions are set up for steady flow such that the continuity is maintained and changes with time inside the domain are zero.  Otherwise, the numerical analysis may diverge. Section 5 – Fluid Flow Module 4: Steady Flow Page 10