tfaws interdisciplinary paper sessionfluid properties shell inlet fluid properties control volume...
TRANSCRIPT
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
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• Problem Statement
• Project ObjectiveMotivation
• Mass Balance
• Energy BalanceDynamic Modeling
• State Space
• PID TuningControls
O2 Production System with Pre-Heater
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O2 Production System with Heat Recovery
TFAWS 2018 – August 20-24, 2018 4Addition of Heat
Recovery Unit
Simple HX Model
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Outlet
Outlet
Well
Mixed
Well
Mixed
Design Constraints and Assumptions
• Treat shell and tube sides as two separate control volumes
• Well-insulated heat exchanger
• Well–mixed control volumes = Control Volume temperature
is the same as outlet temperature.
• Fully developed flows.
• No mass accumulation in control volume = Steady state
mass flows.
• Constant and low conduction resistance.
• Uniform, constant fluid properties on shell and tube sides.
• No external work on the system.
• Hot fluid in the tubes.
• Counter current flow configuration.
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Mass Balance
• General Mass Balance
𝑑𝑚
𝑑𝑡= ሶ𝑚1 − ሶ𝑚2
• Mass Flow Rate of Shell = ሶ𝑚𝑠
ሶ𝑚𝑠 = 3.95𝑥10−4𝑘𝑔
𝑠• Mass Flow Rate of Tube = ሶ𝑚𝑡
ሶ𝑚𝑡 = 9.86𝑥10−5𝑘𝑔
𝑠
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Fluid Properties
Shell Inlet Fluid
Properties
Control Volume Fluid
Properties
Specific Heat (Cp) [kJ/kgK] 1.006 1.089
Temperature (T) [℃] 25 117
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Tube Inlet Fluid
Properties
Control Volume Fluid
Properties
Specific Heat (Cp) [kJ/kgK] 1.154 1.089
Temperature (T) [℃] 519 117
Shell Inlet Fluid
Properties
Control Volume Fluid
Properties
Specific Heat (Cp) [kJ/kgK] 1.006 1.089
Temperature (T) [℃] 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
• General Energy Balance
• Heat Transfer Rate ( ሶ𝑸)
– ሶ𝑸=UA(AMTD)
– Arithmetic Mean Temperature Difference (AMTD)
𝐴𝑀𝑇𝐷 =𝑇𝑡1 + 𝑇𝑡
2−𝑇𝑠1 + 𝑇𝑠
2
• Enthalpy rate ( ሶ𝑚ℎ)
– ሶ𝑚ℎ = ሶ𝑚𝐶𝑝Δ𝑇
• External Work ( ሶ𝑾)
– ሶ𝑊 =0
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d(𝑚𝐶𝑝(𝑇 − 𝑇𝑟𝑒𝑓))
𝑑𝑡= ሶ𝑚1 ∙ ℎ1 − ሶ𝑚2 ∙ ℎ + ሶ𝑄 − ሶ𝑊
Energy Balance
• Shell and Tube Dynamic Model (DM)
– Tube Energy Balance
𝑑𝑇𝑡𝑑𝑡
=ሶ𝑚𝑡 ∙ 𝐶𝑝𝑡1𝑚𝑡 ∙ 𝐶𝑝𝑡
𝑇𝑇1 − 𝑇𝑟𝑒𝑓 −ሶ𝑚𝑡
𝑚𝑡𝑇𝑡 − 𝑇𝑟𝑒𝑓 −
𝑈𝑜𝐴𝑜𝑚𝑡 ∙ 𝐶𝑝𝑡
𝑇𝑡1 + 𝑇𝑡2
−𝑇𝑠1 + 𝑇𝑠
2
– Shell Energy Balance
𝑑𝑇𝑠𝑑𝑡
=ሶ𝑚𝑠 ∙ 𝐶𝑝𝑠1𝑚𝑠 ∙ 𝐶𝑝𝑠
𝑇𝑆1 − 𝑇𝑟𝑒𝑓 −ሶ𝑚𝑠
𝑚𝑠𝑇𝑠 − 𝑇𝑟𝑒𝑓 +
𝑈𝑜𝐴𝑜𝑚𝑠 ∙ 𝐶𝑝𝑠
𝑇𝑡1 + 𝑇𝑡2
−𝑇𝑠1 + 𝑇𝑠
2
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Steady State
• Shell and Tube Steady State Model (SM)
– Tube Energy Balance
0 =ሶ𝑚𝑡 ∙ 𝐶𝑝𝑡1𝑚𝑡 ∙ 𝐶𝑝𝑡
𝑇𝑡1 − 𝑇𝑟𝑒𝑓 −ሶ𝑚𝑡
𝑚𝑡𝑇𝑡 − 𝑇𝑟𝑒𝑓 −
𝑈𝑜𝐴𝑜𝑚𝑡 ∙ 𝐶𝑝𝑡
𝑇𝑡1 + ഥ𝑇𝑡2
−𝑇𝑠1 + ഥ𝑇𝑠
2
– Shell Energy Balance
0 =ሶ𝑚𝑠 ∙ 𝐶𝑝𝑠1𝑚𝑠 ∙ 𝐶𝑝𝑠
𝑇𝑠1 − 𝑇𝑟𝑒𝑓 −ሶ𝑚𝑠
𝑚𝑠
ഥ𝑇𝑠 − 𝑇𝑟𝑒𝑓 +𝑈𝑜𝐴𝑜
𝑚𝑠 ∙ 𝐶𝑝𝑠
𝑇𝑡1 + ഥ𝑇𝑡2
−𝑇𝑠1 + ഥ𝑇𝑠
2
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Linearization and State Variables
• Shell and Tube DM – SM
– Deviation State Variables
– Tube Energy Balance
𝑑𝜃2𝑑𝑡
=ሶ𝑚𝑡 ∙ 𝐶𝑝𝑡1𝑚𝑡 ∙ 𝐶𝑝𝑡
𝜃1 −ሶ𝑚𝑡
𝑚𝑡𝜃2 −
𝑈𝑜𝐴𝑜𝑚𝑡 ∙ 𝐶𝑝𝑡
𝜃1 + 𝜃22
−𝜃3 + 𝜃4
2
– Shell Energy Balance
𝑑𝜃4𝑑𝑡
=ሶ𝑚𝑠 ∙ 𝐶𝑝𝑠1𝑚𝑠 ∙ 𝐶𝑝𝑠
𝜃3 −ሶ𝑚𝑠
𝑚𝑠𝜃4 +
𝑈𝑜𝐴𝑜𝑚𝑠 ∙ 𝐶𝑝𝑠
𝜃1 + 𝜃22
−𝜃3 + 𝜃4
2
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𝜃1 = 𝑇𝑡1 − 𝑇𝑡1 − 𝑇𝑟𝑒𝑓 𝜃3 = 𝑇𝑠1 − 𝑇𝑠1 − 𝑇𝑟𝑒𝑓
𝜃2 = 𝑇𝑡 − ഥ𝑇𝑡 − 𝑇𝑟𝑒𝑓 𝜃4 = 𝑇𝑠 − ഥ𝑇𝑠 − 𝑇𝑟𝑒𝑓
State Space (MISO)
ሶ𝑥 = 𝐴𝑥 + 𝐵𝑢
𝑦 = 𝐶𝑥 + 𝐷𝑢
ሶ𝜽𝟒ሶ𝜽2=
−𝑈𝑜𝐴𝑜2𝑚𝑠𝐶𝑝𝑠
−ሶ𝑚𝑠
𝑚𝑠
𝑈𝑜𝐴𝑜2𝑚𝑠𝐶𝑝𝑠
𝑈𝑜𝐴𝑜2𝑚𝑡𝐶𝑝𝑡
−𝑈𝑜𝐴𝑜2𝑚𝑡𝐶𝑝𝑡
−ሶ𝑚𝑡
𝑚𝑡
𝜽𝟒𝜽𝟐
+
−𝑈𝑜𝐴𝑜2𝑚𝑠𝐶𝑝𝑠
+ሶ𝑚𝑠𝐶𝑝𝑠1𝑚𝑠𝐶𝑝𝑠
𝑈𝑜𝐴𝑜2𝑚𝑠𝐶𝑝𝑠
𝑈𝑜𝐴𝑜2𝑚𝑡𝐶𝑝𝑡
−𝑈𝑜𝐴𝑜2𝑚𝑡𝐶𝑝𝑡
+ሶ𝑚𝑡 𝐶𝑝𝑡1𝑚𝑡𝐶𝑝𝑡
𝜽𝟑𝜽𝟏
𝑦 = 𝜽𝟒 = [1 0]𝜽𝟒𝜽𝟐
+ 𝟎𝜽3𝜽𝟏
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Open Loop Response
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Control Design Requirements
• No overshoot.
• 2% Steady State Error or less.
• No rapid change in temperature.
• Steady State in less than 3 hours
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Closed Loop Response
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Controller Value
P 50
I 0
D 0
Closed Loop Response
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Controller Value
P 0.747
I 0.042
D 0
Closed Loop Response
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Controller Value
P 0
I 0.00137
D 0
Closed Loop Response
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Controller Value
P 8.86
I 0.603
D 0.39
Conclusion
• A Heat Exchanger designed for Heat Recovery
in High Temperature Oxygen Production System
was analyzed
• A Simplified Dynamic model was developed to
approximate the outlet shell temperature
• PID Controller is designed to ensure outlet shell
temperature is maintained at given setpoint
• Based on the tuning, desired requirements
including settling time can be achieved.
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References
• Janna, William S., and Raj P. Chhabra. Design of Fluid
Thermal Systems. Cengage Learning, 2015.
• Ogata, Katsuhiko. System Dynamics. Prentice Hall,
1998.
• Engineering ToolBox, (2005). Dry Air Properties. [online]
Available at: https://www.engineeringtoolbox.com/dry-air-
properties-d_973.html
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Thank you
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Appendix – Steady State Temperature
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