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Presented By
Kevin Fuentes
Thermal & Fluids Analysis Workshop
TFAWS 2018
August 20-24, 2018
NASA Johnson Space Center
Houston, TX
Temperature Controller Design of a Heat Exchanger
within a High Temperature Oxygen Production System
using a Lumped Thermal Modeling approach
Kevin Fuentes, Samuel Ogletree and M. A. Rafe Biswas
Department of Mechanical Engineering, Houston Engineering Center, University of
Texas at Tyler
TFAWS Interdisciplinary Paper Session
General Overview
TFAWS 2018 β August 20-24, 2018 2
β’ Problem Statement
β’ Project ObjectiveMotivation
β’ Mass Balance
β’ Energy BalanceDynamic Modeling
β’ State Space
β’ PID TuningControls
O2 Production System with Pre-Heater
TFAWS 2018 β August 20-24, 2018 3
O2 Production System with Heat Recovery
TFAWS 2018 β August 20-24, 2018 4Addition of Heat
Recovery Unit
Simple HX Model
TFAWS 2018 β August 20-24, 2018 5
Outlet
Outlet
Well
Mixed
Well
Mixed
Design Constraints and Assumptions
β’ Treat shell and tube sides as two separate control volumes
β’ Well-insulated heat exchanger
β’ Wellβmixed control volumes = Control Volume temperature
is the same as outlet temperature.
β’ Fully developed flows.
β’ No mass accumulation in control volume = Steady state
mass flows.
β’ Constant and low conduction resistance.
β’ Uniform, constant fluid properties on shell and tube sides.
β’ No external work on the system.
β’ Hot fluid in the tubes.
β’ Counter current flow configuration.
TFAWS 2018 β August 20-24, 2018 6
Mass Balance
β’ General Mass Balance
ππ
ππ‘= αΆπ1 β αΆπ2
β’ Mass Flow Rate of Shell = αΆππ
αΆππ = 3.95π₯10β4ππ
π β’ Mass Flow Rate of Tube = αΆππ‘
αΆππ‘ = 9.86π₯10β5ππ
π
TFAWS 2018 β August 20-24, 2018 7
Fluid Properties
Shell Inlet Fluid
Properties
Control Volume Fluid
Properties
Specific Heat (Cp) [kJ/kgK] 1.006 1.089
Temperature (T) [β] 25 117
TFAWS 2018 β August 20-24, 2018 8
Tube Inlet Fluid
Properties
Control Volume Fluid
Properties
Specific Heat (Cp) [kJ/kgK] 1.154 1.089
Temperature (T) [β] 519 117
Shell Inlet Fluid
Properties
Control Volume Fluid
Properties
Specific Heat (Cp) [kJ/kgK] 1.006 1.089
Temperature (T) [β] 25 117
Constants
Convection Coefficient (Uo) [W/m2K] 0.12
Surface Area (Ao) [m2] 0.58
Mass of Fluid in Shell (ms) [kg] 0.0049
Mass of Fluid in Tubes (mt) [kg] 0.0014
Energy Balance - Heat
β’ General Energy Balance
β’ Heat Transfer Rate ( αΆπΈ)
β αΆπΈ=UA(AMTD)
β Arithmetic Mean Temperature Difference (AMTD)
π΄πππ· =ππ‘1 + ππ‘
2βππ 1 + ππ
2
β’ Enthalpy rate ( αΆπβ)
β αΆπβ = αΆππΆπΞπ
β’ External Work ( αΆπΎ)
β αΆπ =0
TFAWS 2018 β August 20-24, 2018 9
d(ππΆπ(π β ππππ))
ππ‘= αΆπ1 β β1 β αΆπ2 β β + αΆπ β αΆπ
Energy Balance
β’ Shell and Tube Dynamic Model (DM)
β Tube Energy Balance
πππ‘ππ‘
=αΆππ‘ β πΆππ‘1ππ‘ β πΆππ‘
ππ1 β ππππ βαΆππ‘
ππ‘ππ‘ β ππππ β
πππ΄πππ‘ β πΆππ‘
ππ‘1 + ππ‘2
βππ 1 + ππ
2
β Shell Energy Balance
πππ ππ‘
=αΆππ β πΆππ 1ππ β πΆππ
ππ1 β ππππ βαΆππ
ππ ππ β ππππ +
πππ΄πππ β πΆππ
ππ‘1 + ππ‘2
βππ 1 + ππ
2
TFAWS 2018 β August 20-24, 2018 10
Steady State
β’ Shell and Tube Steady State Model (SM)
β Tube Energy Balance
0 =αΆππ‘ β πΆππ‘1ππ‘ β πΆππ‘
ππ‘1 β ππππ βαΆππ‘
ππ‘ππ‘ β ππππ β
πππ΄πππ‘ β πΆππ‘
ππ‘1 + ΰ΄₯ππ‘2
βππ 1 + ΰ΄₯ππ
2
β Shell Energy Balance
0 =αΆππ β πΆππ 1ππ β πΆππ
ππ 1 β ππππ βαΆππ
ππ
ΰ΄₯ππ β ππππ +πππ΄π
ππ β πΆππ
ππ‘1 + ΰ΄₯ππ‘2
βππ 1 + ΰ΄₯ππ
2
TFAWS 2018 β August 20-24, 2018 11
Linearization and State Variables
β’ Shell and Tube DM β SM
β Deviation State Variables
β Tube Energy Balance
ππ2ππ‘
=αΆππ‘ β πΆππ‘1ππ‘ β πΆππ‘
π1 βαΆππ‘
ππ‘π2 β
πππ΄πππ‘ β πΆππ‘
π1 + π22
βπ3 + π4
2
β Shell Energy Balance
ππ4ππ‘
=αΆππ β πΆππ 1ππ β πΆππ
π3 βαΆππ
ππ π4 +
πππ΄πππ β πΆππ
π1 + π22
βπ3 + π4
2
TFAWS 2018 β August 20-24, 2018 12
π1 = ππ‘1 β ππ‘1 β ππππ π3 = ππ 1 β ππ 1 β ππππ
π2 = ππ‘ β ΰ΄₯ππ‘ β ππππ π4 = ππ β ΰ΄₯ππ β ππππ
State Space (MISO)
αΆπ₯ = π΄π₯ + π΅π’
π¦ = πΆπ₯ + π·π’
αΆπ½παΆπ½2=
βπππ΄π2ππ πΆππ
βαΆππ
ππ
πππ΄π2ππ πΆππ
πππ΄π2ππ‘πΆππ‘
βπππ΄π2ππ‘πΆππ‘
βαΆππ‘
ππ‘
π½ππ½π
+
βπππ΄π2ππ πΆππ
+αΆππ πΆππ 1ππ πΆππ
πππ΄π2ππ πΆππ
πππ΄π2ππ‘πΆππ‘
βπππ΄π2ππ‘πΆππ‘
+αΆππ‘ πΆππ‘1ππ‘πΆππ‘
π½ππ½π
π¦ = π½π = [1 0]π½ππ½π
+ ππ½3π½π
TFAWS 2018 β August 20-24, 2018 13
Open Loop Response
TFAWS 2018 β August 20-24, 2018 14
Control Design Requirements
β’ No overshoot.
β’ 2% Steady State Error or less.
β’ No rapid change in temperature.
β’ Steady State in less than 3 hours
TFAWS 2018 β August 20-24, 2018 15
Closed Loop Response
TFAWS 2018 β August 20-24, 2018 16
Controller Value
P 50
I 0
D 0
Closed Loop Response
TFAWS 2018 β August 20-24, 2018 17
Controller Value
P 0.747
I 0.042
D 0
Closed Loop Response
TFAWS 2018 β August 20-24, 2018 18
Controller Value
P 0
I 0.00137
D 0
Closed Loop Response
TFAWS 2018 β August 20-24, 2018 19
Controller Value
P 8.86
I 0.603
D 0.39
Conclusion
β’ A Heat Exchanger designed for Heat Recovery
in High Temperature Oxygen Production System
was analyzed
β’ A Simplified Dynamic model was developed to
approximate the outlet shell temperature
β’ PID Controller is designed to ensure outlet shell
temperature is maintained at given setpoint
β’ Based on the tuning, desired requirements
including settling time can be achieved.
TFAWS 2018 β August 20-24, 2018 20
References
β’ Janna, William S., and Raj P. Chhabra. Design of Fluid
Thermal Systems. Cengage Learning, 2015.
β’ Ogata, Katsuhiko. System Dynamics. Prentice Hall,
1998.
β’ Engineering ToolBox, (2005). Dry Air Properties. [online]
Available at: https://www.engineeringtoolbox.com/dry-air-
properties-d_973.html
TFAWS 2018 β August 20-24, 2018 21
Thank you
TFAWS 2018 β August 20-24, 2018 22
Appendix β Steady State Temperature
TFAWS 2018 β August 20-24, 2018 23