1 / 27

Lecture 6: Feedback Systems of Reactors

Lecture 6: Feedback Systems of Reactors. CE 498/698 and ERS 685 Principles of Water Quality Modeling. W 1. W 2. Q 01 c 0. Q 12 c 1. Q 23 c 2. Q 21 c 2. k 2 V 2 c 2. k 1 V 1 c 1. Feedback. 1. W 1. 2. W 2. Q 01 c 0. Q 12 c 1. Q 23 c 2. Q 21 c 2. Lake 1:. k 2 V 2 c 2.

jania
Télécharger la présentation

Lecture 6: Feedback Systems of Reactors

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 6: Feedback Systems of Reactors CE 498/698 and ERS 685 Principles of Water Quality Modeling Lecture 6

  2. W1 W2 Q01c0 Q12c1 Q23c2 Q21c2 k2V2c2 k1V1c1 Feedback Lecture 6

  3. 1 W1 2 W2 Q01c0 Q12c1 Q23c2 Q21c2 Lake 1: k2V2c2 k1V1c1 Lake 2: Lecture 6

  4. Steady-state: Lake 1: and Lake 2: Lecture 6

  5. system parameters unknowns loadings LINEAR ALGEBRAIC EQUATIONS Matrix algebra Lecture 6

  6. Lecture 6

  7. 33 identity matrix: augmented matrix: Gauss-Jordan method To compute the matrix inverse Identity matrix Lecture 6

  8. Gauss-Jordan method To compute the matrix inverse 1) Normalize 2) Elimination Lecture 6

  9. Divide by a11 Gauss-Jordan method 1) Normalize Lecture 6

  10. Gauss-Jordan method 2) Elimination Lecture 6

  11. Gauss-Jordan method 2) Elimination Lecture 6

  12. Gauss-Jordan method 1) Normalization Lecture 6

  13. Matrix inverse Gauss-Jordan method Lecture 6

  14. augmented matrix Gauss-Jordan method example Lecture 6

  15. Divide by 3 (normalize) Gauss-Jordan method example Lecture 6

  16. Divide by 7.003 (normalize) Gauss-Jordan method example Lecture 6

  17. Gauss-Jordan method example Lecture 6

  18. Gauss-Jordan method example Lecture 6

  19. Gauss-Jordan method • Can also be used to solve for concentrations Lecture 6

  20. Excel - MINVERSE • Enter your [A] matrix • Block an area the same size • Type =MINVERSE(block location of [A]matrix)and press CNTL+SHIFT+ENTER Lecture 6

  21. Multiply both sides by [A]-1 Definitions of identity matrix We want to solve for {C} Lecture 6

  22. Homework Problem 6.2(a) • Use both Gauss-Jordan method and Excel MINVERSE function Lecture 6

  23. Unit change in loading of reactor 2 Response of reactor 1 {C} = response {W} = forcing functions [A]-1 = parameters {response} =[interactions]{forcing functions} Lecture 6

  24. Matrix Multiplication (Box 6.1) # columns in matrix 1 = # rows in matrix 2 Lecture 6

  25. Terminology SUPERDIAGONAL Effects of d/s loadings on u/s reactors DIAGONAL Effect of direct loading SUBDIAGONAL Effects of u/s loadings on d/s reactors Lecture 6

  26. where Time-variable response for two reactors Lecture 6

  27. ’s are functions of ’s c’s are coefficients that depend on eigenvalues and initial concentrations where f= fast eigenvalue s = slow eigenvalue f >>s Time-variable response for two reactors General solution if c1=c10 at t = 0 see formulason page 111 Lecture 6

More Related