1 / 14

Lecture Objectives:

Lecture Objectives:. Review discretization methods for advection diffusion equation Accuracy Numerical Stability Unsteady-state CFD Explicit vs. Implicit method Boundary conditions and Airpak Example. Advection diffusion equation 1-D, steady-state. D x. D x. P. E. W. D x. e. w.

raleigh
Download Presentation

Lecture Objectives:

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lecture Objectives: • Review discretization methods for advection diffusion equation • Accuracy • Numerical Stability • Unsteady-state CFD • Explicit vs. Implicit method • Boundary conditions and Airpak • Example

  2. Advection diffusion equation 1-D, steady-state Dx Dx P E W Dx e w y Q Example: Equation for temperature of water flowing through hot pipe Assume that diffusion in y direction ins negligible: This is incorrect assumption introduced jut to simplify example to 1-D problem! Temperature is changing along x x Q model Vx T1 T2 T3 T4 … Tn

  3. Advection diffusion equation 1-D, steady-state Dx Dx N N+1 N-1 Different notation: Dx General equation

  4. Advection equation 1-D, steady-state Dx Dx P E W Dx Vx>0 1) Upwind scheme: Vx<0 2) Central differencing scheme: 3) Hybrid of upwind and central differencing scheme Higher order differencing scheme: Quadratic upwind differencing Scheme (QUICK) N+1 N+2 N-1 N N-2 P WW E EE W We need to find coefficients aP, aW, aE, aWW, aEE,

  5. Quadratic upwind differencing Scheme (QUICK) Coefficients: Advection coefficient: Source: Diffusion coefficients : For advection only:

  6. General Transport Equationunsteady-state H N Equation in the algebraic format: W E P S L We have to solve the system matrix for each time step ! Transient term: Are these values for step  or + ? If: -  - explicit method - + - implicit method Unsteady-state 1-D

  7. General Transport Equationunsteady-state 1-D Fully explicit method: Implicit method: Value form previous time step (known value) • Make the difference between • - Calculation for different time step • - Calculation in iteration step

  8. Boundary conditionsin CFD application in indoor airflow Real geometry Model geometry Where are the boundary Conditions?

  9. CFD ACCURACY Depends 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

  10. Surface boundaries thickness 0.01-20 mm for forced convection Wall surface W use wall functions to model the micro-flow in the vicinity of surface Using relatively large mesh (cell) size.

  11. momentum sources Airflow at air supply devices Complex geometry - Δ~10-4m We can spend all our computing power for one small detail

  12. Diffuser jet properties High Aspiration diffuser D D L L How small cells do you need? We need simplified models for diffusers

  13. Simulation of airflow in the vicinity of occupants How detailed should we make the geometry?

  14. AIRPAK Software

More Related