© 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. Education Community Fluid Flow: Establishing Boundary Conditions

© 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. Education Community Objectives  Understand the workflow to perform numerical analysis.  Identify system boundaries.  Examine types of boundary conditions (BCs).  Understand hydraulic diameter.  Learn how Initial conditions make an impact.  Identify regions of high gradients.  Understand grid independence.  Study the importance of correct boundary conditions.  Learn from an example: CFD analysis of Couette Flow (steady state) Section 5 – Fluid Flow Module 3: Boundary Conditions Page 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. Education Community Workflow  Once a user gets started with numerical analysis, the following steps will have to be taken:  Establish the flow characteristic (e.g., external, internal, steady, unsteady, laminar, turbulent, compressible, incompressible).  Establish boundaries of the flow domain as well as the objects inside the domain.  Determine the extent of the flow domain (hydraulic diameter and characteristic length) for external flows.  Identify regions with high gradients.  Achieve grid independence. Section 5 – Fluid Flow Module 3: Boundary Conditions Page 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. Education Community Types of Boundaries: Part I  Generally a CFD software application defines the following boundary conditions:  Inlet/Outlet  Wall  Fluid cannot pass through  No-slip  Wall roughness can be defined  Wall movement can be assigned  Porous Medium  Some fluid can pass through depending upon porosity  Periodic Boundary Condition  Can be applied for a regular geometrical pattern, such as flow across pipes Outlet Inlet Walls Section 5 – Fluid Flow Module 3: Boundary Conditions Page 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. Education Community Types of Boundaries: Part II  Fan Surface  Provides a sudden jump in velocity or pressure  Free Surface  Unbounded surface such as in open channel flows  Symmetric  Can reduce domain size to half or even a quarter if axis of symmetry exists  Axisymmetry  Flow in tanks, pipes and circular geometry can make use of axisymmetric boundary condition Wall Free Surface Wall Section 5 – Fluid Flow Module 3: Boundary Conditions Page 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. Education Community Identification of System Boundaries  In the case of internal flow, it is easier to determine system boundaries.  The fluid extent or physical wall determines the boundaries.  For an external flow system the extent of boundaries has to be identified, as the surrounding fluid is limitless.  In the case of external flow, system boundaries should be confined to the region of influence of the object with respect to the flow.  For external flow cases, hydraulic diameter and characteristic Length help us determine the system boundaries. Section 5 – Fluid Flow Module 3: Boundary Conditions Page 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. Education Community Understanding Boundaries  When selecting boundaries, consider that fluid entering the domain must be equal to the fluid exiting the domain.  Inlet and outlet boundary conditions must be selected for steady flow.  Conservation of mass and energy must be accounted for, or else divergence will result for steady flow / equilibrium problems.  Special cases include fluid confined inside a closed object (e.g., sloshing in tanks) where flow occurs due to movement of the object.  In such cases inlet and outlet conditions are not required.  Once the extent of a domain is worked out, geometry for the domain can be modeled in CAD software.  Simplification is sometimes required to eliminate small geometrical details that can increase mesh complexity. Section 5 – Fluid Flow Module 3: Boundary Conditions Page 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. Education Community Hydraulic Diameter and Characteristic Length  In fluid flow, hydraulic diameter is the estimated length of a non- circular conduit that would be equivalent to a circular duct in terms of influence on flow behavior.  Similarly, hydraulic diameter (HD) and characteristic length (CL) can also be used for external flow to determine the domain size.  A general rule of thumb is that for flow around a bluff body, 5 CL all around the body and 8 CL behind the bluff body should be added to the domain size.  Formulae are available to calculate the HD of various shapes.  For instance, the HD of a square is given as DH= 4 a b / (2 (a + b), where “a” is the length and “b” is the breadth of the rectangle. Section 5 – Fluid Flow Module 3: Boundary Conditions Page 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. Education Community Initial Conditions  Initial conditions may not have an effect on the outcome of the solution; however, a good initial estimate can reduce the number of iterations required.  At times, flow analysis from a separate simulation run can provide initial conditions for a subsequent simulation.  For instance, a flow simulation for steady state conditions inside a pipe with a fixed velocity of 5 m/s can provide initial conditions for a transient flow analysis for the same pipe for a case where velocity increases from 5m/s to 10m/s. Section 5 – Fluid Flow Module 3: Boundary Conditions Page 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. Education Community Regions of High Gradients  High pressure and velocity gradients can occur inside the flow domain.  Such regions become important because they can affect the outcome of the final result.  It is important to have a refined mesh in such regions so that the flow gradients are captured appropriately.  It is important that cells in this region should be regularly shaped and unskewed.  An experienced user can identify the regions of importance.  Fluid regions of converging, diverging or bending sections in internal flow and the near-wall and wake regions in external flow should have finer meshes. Section 5 – Fluid Flow Module 3: Boundary Conditions Page 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. Education Community Grid Independence  Grid independence is said to have been achieved when further refinement in a grid does not result in notable improvement in the accuracy of a solution.  Regions where high gradients exist are critical, and grid refinement in those regions can improve the accuracy of the results substantially.  If a problem setup has reached grid independence, it can act as a template for investigating what-if scenarios.  Pilot simulations can be run to identify regions of importance.  The meshes in these specific regions can then be refined. Section 5 – Fluid Flow Module 3: Boundary Conditions Page 11

© 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. Education Community Importance of Boundary Conditions  It is crucial for accurate analysis to identify the extent of the domain boundary and type of boundary.  For internal flows, the domain size is generally the size of the system.  Examples: pipes, pumps, mixing tanks  For external flow, domain boundaries are not distinctive and must be identified by the user.  Available computation resources and required accuracy are factors.  Examples: flow over a car, train, submarine or bluff body  Due to limitations in computing resources, simplifications are often made to geometry that affects boundaries.  Example: External geometry of an automobile may be simplified with small protrusions removed and depressions patched to save computation time. Section 5 – Fluid Flow Module 3: Boundary Conditions Page 12

© 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. 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 the application of boundary conditions.  The second part is about domain discretization and creation of algebraic equations and is relevant to this presentation. u0u0 X Stationary Plate Moving Plate Y Section 5 – Fluid Flow Module 3: Boundary Conditions Page 13

© 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. Education Community Summary  For any analysis, exact or numerical, Boundary Conditions must be defined.  In fluid flow, different types of boundary conditions are employed, of which the most common are inlet/outlet, wall and velocity.  Conservation of mass must be taken into account when selecting boundaries.  For instance, divergence in the numerical solution would occur with a system where only an inlet is defined without an outlet, with flow restricted inside by an impermeable and non-flexible wall. Section 5 – Fluid Flow Module 3: Boundary Conditions Page 14

© 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. Education Community Summary  For external flow systems, hydraulic diameter and characteristic length help establish domain extent.  Boundary conditions must be defined by the user.  The closer the boundary conditions are to real life cases, the better and more accurate the solution. Section 5 – Fluid Flow Module 3: Boundary Conditions Page 15