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Analytical Approach to LHP Condenser Modeling Using DeCoM at TFAWS 2011

This paper presents an analytical approach developed by Deepak Patel from NASA's Goddard Space Flight Center, focusing on the simulation of Loop Heat Pipe (LHP) condensers. The work aims to accurately model two-phase flow dynamics and heat transfer processes in condensers by creating a 1D computer code, DeCoM (Deepak Condenser Model). Key topics include governing equations, heat transfer calculations, and the implementation of the model using FORTRAN. The findings enhance understanding of condenser operations, benefiting future thermal engineering applications in spacecraft systems.

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Analytical Approach to LHP Condenser Modeling Using DeCoM at TFAWS 2011

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  1. TFAWS Paper Session Analytical Approach in DeCoM Presented ByDeepak Patel NASA/ Goddard Space Flight Center Thermal & Fluids Analysis WorkshopTFAWS 2011August 15-19, 2011 NASA Langley Research CenterNewport News, VA

  2. Acknowledgments • Hume Peabody • Matt Garrison • Dr. Jentung Ku • Tamara O'Connell • Thermal Engineering Branch at Goddard Space Flight Center TFAWS 2011 – August 15-19, 2011

  3. Outline • Introduction • Governing Equations • Develop 1D Computer Code • DeCoM • Conclusion • Summary TFAWS 2011 – August 15-19, 2011

  4. Introduction:Purpose • Purpose • To develop a model which efficiently and accurately simulates LHP Condenser • Understand basic principles of two-phase flow • Correlation method for two-phase convection value • Governing equations to obtain quality change TFAWS 2011 – August 15-19, 2011

  5. Introduction:Introduction to LHP • Compensation Chamber, QCC • Excess fluid is stored here, from which the LHP can increase its performance by accessing or storing the excess fluid. • Evaporator, QE • Liquid from the bayonet is flown into the wick where it is converted to vapor, from the heat that is conducted from the instrument. • Vapor Line • Vapor from evaporator is transferred to the condenser, adiabatically. Bayonet Tube • Liquid Line, LL • Subcooled liquid from the condenser is returned to the evaporator. • Condenser – QC (Condenser), QSC (Subcooled) • QC is the amount of heat rejected when the fluid is in two-phase, and QSC is for condensed Subcooled liquid section (1-phase fluid). TFAWS 2011 – August 15-19, 2011

  6. Introduction:Condenser Basics • Condenser: • Vapor generated travels from vapor transport line and enters the heat exchanger (condenser). • Vapor enters as saturated vapor and phase change occurs, after which it is condensed to liquid. Condenser and Subcooler TFAWS 2011 – August 15-19, 2011

  7. Outline • Introduction • Governing Equations • Develop 1D Computer Code • DeCoM • Conclusion • Summary TFAWS 2011 – August 15-19, 2011

  8. Governing Equations: Control Volume Analysis Node, Outlet Node, Inlet FLUID WALL T (oC) Control Volume for which Equations are formulated Superheated Vapor RADIATOR Subcooled Liquid Pressure = constant • The thermodynamic plot above describes the regions (arrows) that the equations are derived for. • A fluid is defined by its any two thermodynamic property (e.g. temperature and pressure) • Radiative Tsink T1 = T2 2 1 Two-Phase Envelope Sat’d Liquid and Sat’d Vapor • Conservation of Energy • Condenser source code is based on the Conservation of Energy equation. Applied on each node. v (m3/kg) TFAWS 2011 – August 15-19, 2011

  9. Governing Equations: Control Volume Analysis IF FLUID WALL TRADIATOR • Inlet conditions are known • Equations can vary depending upon the state of the fluid (2φ or SC), as shown above. • Lockhart-Martinelliequations are used to solve for the G2φvalue. • 2-Phase section • Subcooled section TFAWS 2011 – August 15-19, 2011

  10. Governing Equations: Fluid flow regimes • Flow regimes of the fluid inside a tube • Two-Phase Lockhart-Martinelli calculations are based on an Annular Flow regime • This is a general case in all simple condensers, and a safe assumption TFAWS 2011 – August 15-19, 2011

  11. Governing Equations: 2φ Lockhart-Martinelli Calculations • Calculate , two-phase heat transfer coefficient multiplier. • Lockhart – Martinelli correlation • An empirically formulated two-phase multiplier equation • X – Lockhart-Martinelli parameter Wall Fluid Vapor • Lockhart-Martinelli correlation is based upon an annular flow regime. TFAWS 2011 – August 15-19, 2011

  12. Background Theory / Governing Equations: 2φ Heat Transfer Calculations • Solving for the convection value using Lockhart-Martinelli multiplier T (oC) • Thermodynamic Plot highlights the region being analyzed (arrow). • The plot on the right shows behavior of the convection value in relation to the fluid quality for saturation temperature at -4 degC @ 216W. Superheated Vapor Subcooled Liquid 99.5 Pressure = constant T1 = T2 2 1 Two-Phase Envelope Sat’d Liquid and Sat’d Vapor v (m3/kg) TFAWS 2011 – August 15-19, 2011

  13. Background Theory / Governing Equations: Liquid Phase Heat Transfer Calculations T (oC) • Equations here are based upon 1-phase, subcooled liquid. Using the flow characteristics, either turbulent or laminar, the heat transfer coefficient is calculated. • Thermodynamic plot above shows (the blue arrow) section being analyzed. Superheated Vapor Subcooled Liquid Pressure = constant T1 = T2 2 1 Two-Phase Envelope Sat’d Liquid and Sat’d Vapor v (m3/kg) TFAWS 2011 – August 15-19, 2011

  14. Outline • Introduction • Governing Equations • Develop 1D Computer Code • DeCoM • Conclusion • Summary TFAWS 2011 – August 15-19, 2011

  15. DECOM Implementation • DeCoM (Deepak Condenser Model) Implementation • Code based on FORTRAN language. • Model works for transient and steady state conditions • Response time to transient is part of future work. • Calculate condenser fluid quality, temperature values, and fluid – wall convection value. • Radiator and wall temperatures are calculated by SINDA. • Input DECOM in VAR 1 of SINDA, in order for the logic to be executed at every time step. • **Equations based on Governing Theory from previous slides. TFAWS 2011 – August 15-19, 2011

  16. DECOM Implementation: Nodal network These temperatures and conductor values are calculated by EXCEL/DECOM Fluid Boundary Nodes Fluid – Wall Conductor Wall Nodes Wall – Rad Conductor Radiator Nodes Nodal Network • DECOM Internal • The above diagram shows the network of nodes in the solution (code). TFAWS 2011 – August 15-19, 2011

  17. DECOM Implementation: Calculations Flow Chart Initial Conditions i= 1 , N Read Input Values YES NO Determine Fluid Stage 2-Phase Fluid Subcooled Liquid Calculate Fluid to Wall Heat Transfer Value Solve for, φi (as shown in Equation Slides) Calculate Fluid Parameters Output Fluid Parameters TFAWS 2011 – August 15-19, 2011

  18. Outline • Introduction • Governing Equations • Develop 1D Computer Code • DeCoM • Conclusion • Summary TFAWS 2011 – August 15-19, 2011

  19. Summary • Alternative LHP Condenser modeling method • Purpose of explicit condenser modeling • Understand condenser governing equation • Implement two-phase correlation method • Fluid to Wall interaction modeling • Developed FORTRAN code based on governing equations. TFAWS 2011 – August 15-19, 2011

  20. BACKUPSymbols & Acronyms Subscripts Superscripts Acronyms SINDA: Systems Improved Numerical Differencing Analyzer) FLUINT: Fluid Integrator) SC: SubCooled LL: Liquid Line LHP: Loop Heat Pipe STOP: Structural-Thermal-Optical Performance TFAWS 2011 – August 15-19, 2011

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