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Lecture Objectives

Lecture Objectives. Review for exam Course overview Example questions from previous exams Discuss midterm project. Course Masterial Review. Navier-Stokes equations and RANS Turbulence modeling Discretization and equation solver Boundary conditions Numerical properties.

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Lecture Objectives

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  1. Lecture Objectives • Review for exam • Course overview • Example questions from previous exams • Discuss midterm project

  2. Course Masterial Review • Navier-Stokes equations and RANS • Turbulence modeling • Discretization and equation solver • Boundary conditions • Numerical properties

  3. Conservation Equations Navier Stokes Equations

  4. Reynolds Averaged Navier Stokes equations Continuity: 1) Momentum: 2) 3) 4) Similar is for STy and STx 4 equations 5 unknowns → We need to model

  5. Modeling of Turbulent Viscosity Fluid property – often called laminar viscosity Flow property – turbulent viscosity MVM: Mean velocity models TKEM: Turbulent kinetic energy equation models Additional models: LES: Large Eddy simulation models RSM: Reynolds stress models

  6. Discretization and equation solver SIMPLE algorithm Discretization of RANS Guess p* p=p* Step1: solve V* from momentum equations Step2: introduce correction P’ and express V = V* + f(P’) Step3: substitute V into continuity equation solve P’ and then V Step4: Solve T , k , e equations no Converged (residual check) yes end

  7. momentum sources Boundary Conditions • Surfaces (wall functions) • Velocity • Temperature • Concentration • Inlets and outlets • Supply diffusers and • Outlets Surface cell Velocity profile Laminar sub-layer

  8. Numerical properties that affect the solutions • Grid distribution - Grid dependent/independent solution • Differencing scheme - Numerical diffusion • Convergence - Residual and Number of iterations • Stability - Relaxation • Tests the solution - Check the conservation of mass, concentration, and energy

  9. Exam • Open book, open notes • 120 minutes • 25% of your final grade • Comprehensive • Several short problems and • Several questions Examples are posted on the course website !

  10. Example of short questions (yes no or very short answer) • Reynolds stresses describe the property of fluid or flow? • What is the difference between the shear stresses and Reynolds stresses? • Is the relaxation is necessary for the system of linear equations? • Is the SIMPLE algorithm explicit method for solving of system of equations? • Why do we use QUICK discretization scheme? • How many Reynolds stresses we have in two dimensional flow?

  11. Explanation questions • Describe the difference between explicit and implicit method. Which are the advantages and disadvantages of both? • Explain how the dispersion of contaminant in the boundary layer depends on velocity field. • Describe how the temperature field affects the airflow. Identify the term in conservation equation that link energy and velocity equation, and describe which assumption we used to get this term.

  12. outlet inlet outlet T1=30C T1 inlet outlet inlet T2 T2=20C Project 1 Pat a) Numerical diffusion The purpose of this project part is to analyze how mesh size and orientation affects the accuracy of result. Pat b) Learn how to: 1) Model: geometry, heat sources, concentration sources, diffusers, 2) Select important simulation parameters 3) Generate appropriate mesh 4) Check the results 5) Present the results

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