Guidelines for Modeling Capillary Two Phase Loops At the System Level

1. Guidelines for Modeling Capillary Two Phase Loops At the System Level Aerospace Thermal Control Workshop 2003 Jane Baumannjane.baumann@crtech.com

2. The Need for Analysis • The user’s confidence in any technology is based in part on its predictability • The ability to model predictable behavior • The ability to bound unpredictable behavior • Must have compatibility with industry standard thermal analysis tools, including radiation/orbital analyzers • Should be able to integrate with concurrent engineering methods such as CAD and structural/FEM

3. LHP Modeling • LHPs are not difficult to simulate provided the engineer • has access to relevant performance metrics from the LHP vendor (wick properties, conductivity, etc.) • possesses a basic understanding of the technology • LHPs and CPLs require a sufficiently detailed two-phase thermohydraulic code • Must contain at least rudimentary capillary modeling components • Modeling of LHPs using thermal networks is inappropriate • Accurate simulation of two-phase flow and condensation processes is critical to successful LHP performance predictions

4. The Unpredictable • Analyst must capture predictable behavior and bound unpredictable behavior • Bounding analyses may be necessary to capture effects of unpredictable behavior • LHP core status (relative amount of back-conduction, etc.) • Temperature spike associated with the start up transient and vapor line clearing • NCG and evaporator mass effects • Separate detailed loop model, not system level

5. The Predictable • Evaporator and compensation chamber energy balance • Capture wick back-conduction • Axial wall conduction • Fluid heat transfer • Wall superheat • Loop pressure drop (diameters, lengths, elevation, etc.) • Detailed condenser modeling is necessary to accurately predict subcooling production • Ability to capture the variable film coefficient along the length of the condenser, and flow splits in parallel legs (including static pressure recovery) • Transport line environment parasitic losses/gains

6. LHP and CPL Modeling • Must accurately predict seemingly minor heat gains or losses in the liquid line and the compensation chamber especially at low powers • Must accurately predict condenser performance (specifically, the subcooling production) Qback = DTwick/Rwick ≈ Qsubcool Qsubcool = m*Cp,liq*DTsubcoolwhere m is the loop mass flow rate

7. Evaporator/CC Modeling Model network representing the evaporator and compensation chamber within SINDA/FLUINT

8. Wick Back-conduction • Simplified back- conduction through a wet wick • Treat wick as effective solid, using • From Dunn & Reay: • Sintered wicks, where g= Kliq /Kwick • Correcting for heat transfer with counter-flowing liquid in a tubular wick G = KA/ L or G = 2p Keff L / ln( Ro /Ri ) [ ] Keff = Kwick* 2 + g –2 e( 1 – g ) 2 + g –2 e( 1 – g ) Gcorrected = (FRliq *Cpliq ) / [ (Ro /Ri )**{ FRliq *Cp /( ln(Ro/Ri )* Guncorrected )} - 1 ]

9. Condenser Modeling • Must accurately predict subcooling production • Import CAD geometry for condenser layout • Requires sufficient resolution to capture thermal gradients for accurate subcooling prediction (thermal cross-talk between condenser lines) • Capture variable heat transfer coefficient in the condenser line based on flow regime • Model flow splits in parallel leg condenser

10. Condenser Modeling • New tools easily convert CAD lines, arcs, or polylines to fluid pipes for quick model development

11. LHP Modeling Evaporator Serpentine 1D Condenser Compensation Chamber

12. CPL Modeling • CPL GAS condenser temperature profile

13. Hints and Tricks • Keep fluid model simple, apply detail where necessary on the thermal side • Use zero volume and time independent components (JUNCTIONS and STUBES in SINDA/FLUINT) • The liquid side of the evaporator/cc should be a tank • Possibly vapor side as tank with artificially high vapor volume for stability or in the presence of an IFACE • Take advantage of symmetry to simplify models when feasible • Fluid models require reasonable initial conditions • Use PTEST logic and FASTIC (user control of solution) to create initial conditions for a STDSTL solution • LHP Prebuilt available for C&R Technologies

14. Conclusions • New CAD methods are available for modeling LHPs, CPLs, and heat pipes • Focus LHP modeling on condenser/transport details and bracketing unknown behaviors • Evaporator and compensation chamber energy balance • Model condenser detail for subcooling production • Bracket unpredictable behavior for core status, NCG, start up etc.

15. References • 1) D. Johnson et al, “CAD-based Methods for Thermal Modeling of Coolant Loops and Heat Pipes”, ITherm 2002 • 2) J. Ku, “Operating Characteristics of Loop Heat Pipes,” SAE 1999-01-2007, July 1999. • 3) J. Baumann et al, “Steady State and Transient Loop Heat Pipe Modeling,” SAE 2000-ICES-105, July 2000. • 4) J. Baumann et al: “Noncondensible Gas, Mass, and Adverse Tilt Effects on the Start-up of Loop Heat Pipes,” SAE 1999-01-2048. • 5) J. Baumann et al, “An Analytical Methodology for Evaluating Start-up of Loop Heat Pipes,” AIAA 2000-2285.