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Fluid Flow: Steady Flow. Objectives. Section 5 – Fluid Flow Module 4: Steady Flow Page 2. U nderstand steady flow. Identify the types of steady flow. Examine the considerations for steady flow. S tudy the Navier-Stokes Equation for steady flow. Learn from two examples:

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2. Objectives Section 5 – Fluid Flow Module4: Steady Flow Page 2 • 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

3. Steady Flow Section 5 – Fluid Flow Module4: Steady Flow Page 3 • 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.

4. Steady Flow Types Section 5 – Fluid Flow Module4: Steady Flow Page 4 • 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.

5. Considerations for Steady Flow Section 5 – Fluid Flow Module4: Steady Flow Page 5 • 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 out Flow in Flow out Flow out

6. Navier–Stokes Equation for Steady Flow Section 5 – Fluid Flow Module4: Steady Flow Page 6 The time derivative is set to zero, thus simplifying the calculation. 0 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.

7. Video Example: CFD Analysis of Couette Flow (Steady State) Section 5 – Fluid Flow Module4: Steady Flow Page 7 • 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. Y u0 Moving Plate X Stationary Plate

8. Additional Example:Flow Between Two Fixed Parallel Plates Section 5 – Fluid Flow Module4: Steady Flow Page 8 • 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 Y x Exact Solution These two exact solution equations can be used by students to verify results from CFD.

9. Summary Section 5 – Fluid Flow Module4: Steady Flow Page 9 • 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.

10. Summary Section 5 – Fluid Flow Module4: Steady Flow Page 10 • 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.

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