3 assignmenttotal of 8 files should be doneMatlab, excel are requiredNeed space to upload 3 more matlab files for assignment but no space to upload, I will forward the rest with email
Microsoft Word - HW3 HW #3 REQUIRES MATLAB & SIMULINK 2020a or later CHEN 4570 Differential Equations (16 points) 1 Problem #1 (2 points) Download and open the Matlab 2019a Simulink file “tank.slx” You can run the file by pressing the large green button. You can inspect the outputs by typing the following instructions into the Matlab command line: >> close all;figure;plot(tout,states(:,1)) figure;plot(tout,states(:,2)) This Simulink simulation models a heated gravity drained tank AFTER you complete the necessary NONLINEAR differential equations. NEXT PAGES: Diagram of the system Definition of the variables (states, inputs, parameters) Expected Results (holdup or temperature versus time) Double click the “tank” in the Simulink file and complete the necessary fields. Do NOT adjust u, p, states, or the integrator. When you think your Simulink file replicates the behavior of a heated gravity drained tank, resave the file and upload “tank.slx” to the relevant Canvas dropbox. HW #3 REQUIRES MATLAB & SIMULINK 2020a or later CHEN 4570 Differential Equations (16 points) 2 Problem #1 continued (2 points) HW #3 REQUIRES MATLAB & SIMULINK 2020a or later CHEN 4570 Differential Equations (16 points) 3 Problem #1 continued (2 points) HW #3 REQUIRES MATLAB & SIMULINK 2020a or later CHEN 4570 Differential Equations (16 points) 4 Problem #1 continued (2 points) Expected holdup (moles) versus time (seconds) close all;figure;plot(tout,states(:,1)) Expected temperature (Kelvin) versus time (seconds) close all;figure;plot(tout,states(:,2)) 0 500 1000 1500 2000 2500 3000 3500 4000 3 3.5 4 4.5 5 5.5 10 4 0 500 1000 1500 2000 2500 3000 3500 4000 300 301 302 303 304 305 306 HW #3 REQUIRES MATLAB & SIMULINK 2020a or later CHEN 4570 Differential Equations (16 points) 5 Problem #2 (2 points) Download and open the Matlab 2019a Simulink file “HX.slx” You can run the file by pressing the large green button. You can inspect the outputs by typing the following instructions into the Matlab command line: >> close all;figure;plot(tout,states(:,1)) figure;plot(tout,states(:,2)) The Simulink simulation models a heat exchanger AFTER you complete the necessary NONLINEAR differential equations. NEXT PAGES: Diagram of the system Definition of the variables (states, inputs, parameters) Expected Results (holdup or temperature versus time) Double click the “HX” in the Simulink file and complete the necessary fields. Do NOT adjust u, p, states, or the integrator. When you think your Simulink file replicates the behavior of a heat exchanger, resave the file and upload “HX.slx” to the relevant Canvas dropbox. HW #3 REQUIRES MATLAB & SIMULINK 2020a or later CHEN 4570 Differential Equations (16 points) 6 Problem #2 continued (2 points) HW #3 REQUIRES MATLAB & SIMULINK 2020a or later CHEN 4570 Differential Equations (16 points) 7 Problem #2 continued (2 points) Matlab index state vector 1 T c time dependent Kelvin coolant outlet temperature 2 T h time dependent Kelvin cooled fluid outlet temperature Matlab index input vector 1 ṅc 20 mole/sec coolant flowrate 2 T c,in 300 Kelvin coolant inlet temperature 3 ṅh 15 mole/sec fluid flowrate 4 T h,in 500 Kelvin fluid inlet temperature Matlab index parameter vector 1 C p,c 125 J/(moleK) coolant heat capacity 2 C p,h 75 J/(moleK) fluid heat capacity 3 U 100 W/(m 2 K) heat transfer resistance 4 A 10 m 2 heat transfer area 5 M c 300000 moles coolant on cold side of HX 6 M h 400000 moles fluid on hot side of HX HW #3 REQUIRES MATLAB & SIMULINK 2020a or later CHEN 4570 Differential Equations (16 points) 8 Problem #2 continued (2 points) Expected cold outlet temperature (Kelvin) versus time (seconds) close all;figure;plot(tout,states(:,1)) Expected hot outlet temperature (Kelvin) versus time (seconds) close all;figure;plot(tout,states(:,2)) HW #3 REQUIRES MATLAB & SIMULINK 2020a or later CHEN 4570 Differential Equations (16 points) 9 Problem #3 (4 points) Download and open the Matlab 2019a Simulink file “CSTR.slx” You can run the file by pressing the large green button. You can inspect the outputs by typing the following instructions into the Matlab command line: >> close all;figure;plot(tout,states(:,1)) figure;plot(tout,states(:,2)); figure;plot(tout,states(:,3)) figure;plot(tout,states(:,4)) The Simulink simulation models a CSTR AFTER you complete the necessary NONLINEAR differential equations. NEXT PAGES: Diagram of the system Definition of the variables (states, inputs, parameters) Expected Results (holdup, temperature, jacket temperature or mole fraction versus time) Double click the “CSTR” in the Simulink file and complete the necessary fields. Do NOT adjust u, p, states, or the integrator. When you think your Simulink file replicates the behavior of a CSTR, resave the file and upload “CSTR.slx” to the relevant Canvas dropbox. HW #3 REQUIRES MATLAB & SIMULINK 2020a or later CHEN 4570 Differential Equations (16 points) 10 Problem #3 continued (4 points) HW #3 REQUIRES MATLAB & SIMULINK 2020a or later CHEN 4570 Differential Equations (16 points) 11 Problem #3 continued (4 points) Matlab index state vector 1 M time dependent moles tank inventory 2 x time dependent unitless component a in tank UNPACK LAST 3 T time dependent Kelvin temperature of tank 4 T c time dependent Kelvin temperature of exiting coolant Matlab index input vector 1 ṅa 5 mole/sec pure a into tank 2 T a 300 Kelvin temperature of stream ṅa 3 x a 1 unitless mole fraction a of stream ṅa 4 ṅr 15 mole/sec recycled material into tank (from elsewhere) 5 T r 300 Kelvin temperature of stream ṅr 6 x r 0.5 unitless mole fraction a of stream ṅr 7 ṅ 20 mole/sec material out of tank 8 ṅc 20 mole/sec coolants through tank jacket 9 T c.in 300 Kelvin coolant temperature into tank jacket Matlab index parameter vector 1 C p 75 J/moleK heat capacity of reactants and products 2 C p,c 125 J/moleK heat capacity of the coolant 3 k f 0.03 mole/(mole*sec) rate constant of the forward reaction 4 E f 9888.37 J activation energy of the forward reaction 5 k b 1310204.37 mole/(mole*sec) rate constant of the reverse reaction 6 E b 100000 J activation energy of the reverse reaction 7 ΔH 20000 J/mole enthalpy of reaction 8 U 200 W/(m 2 K) heat transfer resistance 9 A 1 m 2 heat transfer area 10 M c 20000 moles inventory of coolent in tank jacket 11 R 8.314 J/mole gas constant HW #3 REQUIRES MATLAB & SIMULINK 2020a or later CHEN 4570 Differential Equations (16 points) 12 Problem #3 continued (4 points) Expected holdup (moles) versus time (seconds) close all;figure;plot(tout,states(:,1)) Expected mole fraction (mol/mol) versus time (seconds) close all;figure;plot(tout,states(:,2)) HW #3 REQUIRES MATLAB & SIMULINK 2020a or later CHEN 4570 Differential Equations (16 points) 13 Problem #3 continued (4 points) Expected reactor temperature (Kelvin) versus time (seconds) close all;figure;plot(tout,states(:,3)) Expected jacket temperature (Kelvin) versus time (seconds) close all;figure;plot(tout,states(:,4)) HW #3 REQUIRES MATLAB & SIMULINK 2020a or later CHEN 4570 Differential Equations (16 points) 14 Problem #4 (3 points) Download and open the Matlab 2019a Simulink file “trays.slx” You can run the file by pressing the large green button. You can inspect the outputs by typing the following instructions into the Matlab command line: >> close all;figure;plot(tout,states) The Simulink simulation models trays AFTER you complete the necessary differential equations. NEXT PAGES: Diagram of the system Definition of the variables (states, inputs, parameters) Expected Results (stage compositions versus time) Double click the “trays” in the Simulink file and complete the necessary fields. Do NOT adjust u, p, states, or the integrator. When you think your Simulink file replicates the behavior of a trays, resave the file and upload “trays.slx” to the relevant Canvas dropbox. HW #3 REQUIRES MATLAB & SIMULINK 2020a or later CHEN 4570 Differential Equations (16 points) 15 Problem #4 continued (3 points) HW #3 REQUIRES MATLAB & SIMULINK 2020a or later CHEN 4570 Differential Equations (16 points) 16 HW #3 REQUIRES MATLAB & SIMULINK 2020a or later CHEN 4570 Differential Equations (16 points) 17 Problem #4 continued (3 points) Expected tray compositions temperature (mol/mol) versus time (seconds) close all;figure;plot(tout,states) 0 200 400 600 800 1000 0 0.2 0.4 0.6 0.8 1 HW #3 REQUIRES MATLAB & SIMULINK 2020a or later CHEN 4570 Differential Equations (16 points) 18 Problem #5 (5 points) Download and open the Matlab 2019a Simulink file “bioreactor.slx” You can run the file by pressing the large green button. You can inspect the outputs by typing the following instructions into the Matlab command line: >> close all;figure;plot(tout,states(:,1)); figure;plot(tout,states(:,2));figure;plot(tout,states(:,3) figure;plot(tout,states(:,4));figure;plot(tout,states(:,5)) The Simulink simulation models a reboiler AFTER you complete the necessary differential equations. NEXT PAGES: Diagram of the system Definition of the variables (states, inputs, parameters) Expected Results (mass concentrations, % bubble O2, or volume in liters) Double click the “bioreactor” in the Simulink file and complete the necessary fields. Do NOT adjust u, p, states, or the integrator. When you think your Simulink file replicates the behavior of a bioreactor, resave the file and upload “bioreactor.slx” to the relevant Canvas dropbox. HW #3 REQUIRES MATLAB & SIMULINK 2020a or later CHEN 4570 Differential Equations (16 points) 19 Problem #5 continued (5 points) Due to metabolic complexity, bacterial fermentation is highly empirical. Models are often written on a mass basis, versus a mole basis, to capture macroscopic behavior. The goal is usually maximal organism proliferation, because more organism means more product. The Monod Model herein is based on: 1) Roeva O and Tzonkov S. (2006) “Modelling of Escherichia coli Cultivations: Acetate Inhibition in a Fed-batch Culture.” Bioautomation, vol. 4, pg. 1. 2) Strandberg L, Andersson L, and Enfors SO (1994) “The use of fed batch cultivation for achieving high cell densities in the production of a recombinant protein in E. coli.” FEMS Microbiology Reviews, vol. 21, pg. 53. 3) Harrison DEF. (1972) “Physiological Effects of Dissolved Oxygen Tension & Redox Potential on Growing Populations of Micro-organisms.” J. Applied Chemical Biotechnology, vol 22, pg 417. ‘ aerobic metabolism hypoxic metabolism CO 2 acetic acid (inhibits growth) C 2 H 3 OOH “A” glucose C 6 H 12 O 6 “G” O 2, “O” X G x A O V