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Lecture Objectives:

Lecture Objectives:. 1) Discuss HW3 problems 2) Define Relaxation (example) 3) Define boundary conditions for CFD Model Boundary conditions . Residual calculation for CFD. Residual for the cell R F ijk = F k ijk - F k-1 ijk Total residual for the simulation domain

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Lecture Objectives:

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  1. Lecture Objectives: 1) Discuss HW3 problems 2) Define Relaxation (example) 3) Define boundary conditions for CFD • Model Boundary conditions

  2. Residual calculation for CFD • Residual for the cell RFijk=Fkijk-Fk-1ijk • Total residual for the simulation domain RFtotal=S|RFijk| • Scaled (normalized) residual RF=S|RFijk|/FF iteration cell position Variable: p,V,T,… For all cells Flux of variable F used for normalization Vary for different CFD software

  3. Relaxation Relaxation with iterative solvers: When the equations are nonlinear it can happen that you get divergency in iterative procedure for solving considered time step divergence variable solution convergence Solution is Under-Relaxation: Y*=f·Y(n)+(1-f)·Y(n-1) Y – considered parameter , n –iteration , f – relaxation factor For our example Y*in iteration101=f·Y(100)+(1-f) ·Y(99) f = [0-1] – under-relaxation -stabilize the iteration f = [1-2] – over-relaxation - speed-up the convergence iteration Value which is should be used for the next iteration Under-Relaxation is often required when you have nonlinear equations!

  4. Example of relaxation(example from homework 3 assignment) Example: Advection diffusion equation, 1-D, steady-state, 4 nodes 1) Explicit format: 4 3 1 2 2) Guess initial values: 3) Substitute and calculate: Substitute and calculate: 4) Substitute and calculate: ………………………….

  5. Relaxation example in Excel

  6. Boundary Conditions CFD ACCURACYDepends on airflow in the vicinity of Boundary conditions 1) At air supply device 2) In the vicinity of occupant 3) At room surfaces • Detailed modeling • limited by • computer power

  7. Define Boundary Conditions at: • Surfaces (wall functions) • Velocity • Temperature • Concentration • Inlets and outlets • Diffusers and outlets • Windows and cracks

  8. Diffuser Types Valve diffuser swirl diffusers ceiling diffuser wall or ceiling floor

  9. Diffuser Types Grill (side wall) diffusers Linear diffusers Vertical Horizontal one side

  10. Displacement ventilationdiffusers

  11. momentum sources Diffuser modeling Complex geometry - Δ~10-4m We can spend all our computing power for one small detail Momentum method

  12. Diffuser Modeling Fine mesh or box method for diffuser modeling

  13. Diffuser modeling High Aspiration diffuser D D L L Jet through one opening only

  14. Jet parameters A0 - effective area of the diffuser V0 – initial jet velocity X - distance from the diffuser Vm – maximum jet velocity at distance x from the diffuser K – property of diffuser

  15. 20.4 ASHRAE method: Diffuser properties (ASHRAE) Fig. 1 Airflow patterns of different diffusers

  16. Examples in AirpakDiffuser’s Macro

  17. Surface boundary conditionstemperatureand velocity

  18. Surface boundarieswall functions Wall surface Use wall functions to model the micro-flow in the vicinity of surface Using relatively large mesh (cell) size.

  19. Surface boundary conditions and log-wall functions E is the integration constant and y* is a length scale y*- thickness of boundary layer The assumption of ‘constant shear stress’ is used here. Constants k = 0.41 and E = 8.43 fit well to a range of boundary layer flows. Surface cell Turbulent profile Laminar sub-layer

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