Analytical Approach in DeCoM

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