Lecture Objectives Review for exam Discuss midterm project 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

Conservation Equations Navier Stokes Equations

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

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

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

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

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

Exam Open book, open notes 90 minutes 30% of your final grade Comprehensive Several short problems and Several questions Examples are posted on the course website !

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?

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.

IAQ parameters Number of ACH quantitative indicator ACH - for total air - for fresh air Ventilation effectiveness qualitative indicator takes into account air distribution in the space Exposure takes into account air distribution and source position and intensity

IAQ parameters Age-of-air air-change effectiveness (EV) Specific Contaminant Concentration contaminant removal effectiveness e

Single value IAQ indicators Ev and ε Contaminant removal effectiveness (e) concentration at exhaust average contaminant concentration Contamination level 2. Air-change efficiency (Ev) shortest time for replacing the air average of local values of age of air Air freshness

Air-change efficiency (Ev) Depends only on airflow pattern in a room We need to calculate age of air (t) Average time of exchange What is the age of air at the exhaust? Type of flow Perfect mixing Piston (unidirectional) flow Flow with stagnation and short-circuiting flow

Air exchange efficiency for characteristic room ventilation flow types Flow pattern Air-change efficiency Comparison with average time of exchange Unidirectional flow 1 - 2 tn < texc < 2tn Perfect mixing 1 texc = tn Short Circuiting 0 - 1 texc > tn

Contaminant removal effectiveness (e) Depends on: position of a contaminant source Airflow in the room Questions 1) Is the concentration of pollutant in the room with stratified flow larger or smaller that the concentration with perfect mixing? 2) How to find the concentration at exhaust of the room?

Differences and similarities of Ev and e Depending on the source position: - similar or - completely different air quality Ev = 0.41 e = 0.19 e = 2.20