Presentation of OpenFOAM CFD results and methods for modeling nucleate boiling with customized solver.

1. Thermal Radiation Steam Thrust
Final Results
Mihai Pruna
ME632
For reference use only

2. Objectives
Develop analysis methodology to determine the thrust obtained from a
water tank heated by a radiative heat flux (solar concentrator or laser), with
a small opening for vapor to escape.
• System-level analysis system for preliminary design.
coupled with
• 3D Computational Fluid Dynamics analysis.
•Add boiling modeling to OpenFOAM 2.3.1
Determine optimal configuration for tank exhaust (that produces most
thrust for the fixed heat flux).
For reference use only

3. Review
Tank
Boiling
Water
Parabolic
Solar
Collector
Insulated
surface
Converging Nozzle
Accelerating Steam Exhaust
Radiation->Heat
Flux
Water boiled by solar concentrator
Problem Definition
Preliminary System-level Analysis in Excel /VBA
For reference use only

4. Tank overall dimensions (m)
For reference use only

5. • The open source CFD Toolbox OpenFOAM was used.
• A solver that can model phase changes (mainly used for cavitation), interPhaseChangeFoam has been selected
to model the problem.
• The solver was modified to account for the temperature field and thus be able to model boiling, based on the
work by Andersen(2011)
CFD Solver Additional Equations:
• Transport Equation to Model Temperature: Eqn 4 Andersen(2011)
• Where DT is the Thermal Diffusivity: Eqn 3 Andersen(2011)
• Roche-Magnus formula to get sat. pressure as a function of temp.(K)
Eqn 5 Andersen(2011)
• Phase change rate modeled with Kunz (1999) formulas, already
implemented in OpenFOAM
How do we pick the right Cc and Cv coefficients for our problem? Eqn 1 and 2 Andersen (2011)
CFD Analysis Method
For reference use only

6. Liquid volume fraction from system analysis
Alpha water from system analysis sensitivity study
Volumetric phase ratio at 0.15 seconds for Baseline case
For reference use only

7. 0.984
0.986
0.988
0.99
0.992
0.994
0.996
0.998
-0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1
Kunz phase change model sensitivity study
Alpha Value from System
Analysis
Alpha water from CFD analysis sensitivity study
Volumetric phase ratio at 0.15 seconds for Baseline case
Alpha water
versus Kunz
coefficients
Moving average trendline
Settled on Cc and Cv=0.69
Increasing Cc and Cv beyond
0.8 has shown rapid increase in
the phase change rate and
increase in Courant number to
unphysical values.
For reference use only

8. Boundary conditions
Mesh size reduction: ¼ of the tank is modeled
Symmetry
Plane
Symmetry
Plane
Mesh
Refinements
near
Walls
And
Exit
Plane
For reference use only

9. Boundary conditions
Wall
Outlet
P=Patm
Initial conditions (inside the tank)
Heated
bottom wall
T=377.86K
Calculated from
radiation heat flux, on
next slide
T (K) 373.15
Static pressure
(Pascals) 101325
Alpha liquid 1
Transport Properties
(assumed constant for T around 373.15K)
Thermal Diffusivity 0.000023m²/s
Surface Tension 0.07N/m²
Liquid Kinematic Viscosity 9.00E-07m2/s
Density 1000kg/m3
Vapor Kinematic Viscosity 4.27E-04m2/s
Density 0.02308kg/m3
For reference use only

10. Determining the bottom wall temperature
Equation 10.5 in Incropera DeWitt (2002)
• Radiative heat flux prescribed: 14739 W/m2 from El Ouederni et all (2009)
• Calculate wall temperature Ts with the system analysis spreadsheet:
• The surface temperature remains fairly constant through the iterative process, so the average value can be used
as a boundary condition in OpenFOAM: 377.8645K
Plot of Prandl Number vs Time from System Analysis
• Fluid properties remain constant due to the system achieving equilibrium pressure and temperature almost
immediately.
1.749
1.74905
1.7491
1.74915
1.7492
1.74925
1.7493
1.74935
0 0.05 0.1 0.15 0.2 0.25
Prandl Number (liquid) / timeFor reference use only

11. Water volume fraction animation, 0 to 1s.
1 Frame=0.01s Video at 5FPS X=0 cut
For reference use only

12. Nozzle velocity animation, 0 to 1s.
1 Frame=0.01s Video at 5FPS X=0
For reference use only

13. Validation (Baseline Configuration)
Figure 11 in Son,Dhir and Ramanujapu (1999)
Bubble diameter with time for wall superheat of 7.0K
Bubble departure timeline from CFD Results – at the wall
Time between frames is 0.01s:
0 0.01 0.02 0.03 0.04 0.05
Bubble departure diameter from CFD results.
Wall superheat is 4.7K
• Data was not available for the wall superheat determined
from the prescribed solar heat flux.
• The bubble departure time should decrease with
temperature difference increase.
• Overall the CFD solver appears to capture the phenomena
of bubble generation with sufficient accuracy.
For reference use only

14. Limitations
Method
• Diffuse Interface (A feature of the VOF method without interface sharpening)
• Simulations on nucleate boiling require special treatment at the wall (micro region)
Figure 2(a) in Yohei and Bojan (2011)
• Thermal Diffusivity modeled as a constant
• Phase change model more suitable for cavitation rather than temperature driven evaporation
Computational Power / Time
• Each simulation of 1s took 12 hours. Phenomena beyond 1s were not captured.
• Mesh was rather coarse, finer mesh would help with a sharper interface and more accuracy,
For reference use only

15. Geometry variations
Baseline Wide nozzle intake Narrow nozzle exhaust
For reference use only

16. Baseline
Wide nozzle intake
Narrow nozzle
exhaust
Nozzle velocity plots at 0.63s
For reference use only

17. Thrust variation with nozzle geometry
Baseline Wide nozzle intake Narrow nozzle exhaust
4.43*10-3N 4.06*10-3N 6.47*10-3N
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008 0.009 0.01 0.011 0.012 0.013 0.014 0.015 0.016
Thrust vs Avg. Nozzle Diam
Thrust was averaged over the first second , ignoring
the first tenth of a second, in order to allow the flow
to adjust from the initial conditions to a more
natural exhaust.
For reference use only

18. Summary of project accomplishments
Developed a hybrid analysis method for computing thrust of a
nozzle-equipped vessel heated from below with a radiation
flux.
Iterative system analysis in Excel:
• Radiative heat flux converted to temperature difference for easy application of CFD BC
• Estimate of liquid volume fraction with time used to tweak CFD phase change model.
CFD Analysis in OpenFOAM
• Extended the work of Andersen(2011) to add evaporation to a newer version of OpenFOAM,
2.3.1
• Performed sensitivity studies to determine the best Kunz phase change model coefficients
• Shared insights gained on the cfd-online.com forums so that others can continue to refine the
solver
• Determined the trend of thrust increasing with smaller overall nozzle dimensions. (more
simulation runs for different configurations will help refine the trend)
For reference use only

19. References
• Hill, Philip G., and Carl R. Peterson. Mechanics and Thermodynamics of Propulsion. Reading, MA: Addison-
Wesley Pub., 1992. Print.
• Incropera, Frank P., and David P. DeWitt. Fundamentals of Heat and Mass Transfer. New York: Wiley, 2002.
Print.
• Brennen, Christopher E. Fundamentals of Multiphase Flow. Cambridge: Cambridge UP, 2005. Print.
• Michta, Edouard. Modeling of Subcooled Nucleate Boiling with OpenFOAM. Master of Science Thesis. Royal
Institute of Technology. Stockholm, Sweden, 2011.
• CFD Online." CFD Online. N.p., n.d. Web. 10 Feb. 2015. cfd-online.com
• El Ouederni A.R. , Salah M. Ben , Askri F. , Nasrallah M. Ben and Aloui F. Experimental Study of a Parabolic
Solar Concentrator. Revue des Energies Renouvelables Vol. 12 N°3 (2009) 395 – 404
• "The OpenFOAM Foundation." OpenFOAM®. N.p., n.d. Web. 10 Feb. 2015.openfoam.org
• Yohei Sato, Bojan Ničeno. A New Conservative Phase Change Model for Nucleate Boiling. Proceedings of the
International Conference Nuclear Energy for New Europe. Bovec, Slovenia, 2011
• Andersen, Martin. CFD with OpenSource software. Chalmers University of Technology. Sweden, 2011.
• Kunz, Robert F., Boger, David A., Chyczewski, Thomas S., Stinebring, David R. and Gibeling, Howard J. Multi-phase
CFD Analysis of Natural And Ventilated Cavitation About Submerged Bodies. 3rd ASME/JSME Joint Fluids
Engineering Conference. San Francisco, California, 1999.
• Son, G., Dhir, V. and Ramanujapu, N. “Dynamics and Heat Transfer Associated With a Single Bubble During Nucleate
Boiling on a Horizontal Surface”. Journal of Heat Transfer, Vol 121. Los Angeles, CA, 1999.
For reference use only

20. Appendix 1: CFD Analysis Equation Details
• Andersen (2011) eqn. 3: Thermal Diffusivity
• Andersen (2011) eqns. 1 and 2 or Kunz and all (1999) eqn. 3: Evaporation / CondensationFor reference use only

21. Appendix 2: Auxiliary equations details
Equation 10.5 in Incropera DeWitt (2002)
Csf is the surface fluid combination; Cpl is the specific heat of the liquid. L suffix means liquid and v
suffix means vapor; hfg is the latent heat of vaporization; Ts is the temperature of the heated surface ;
Tsat is the temperature of saturated vapor.
Prandl Number is the ratio of viscous diffusion rate to thermal diffusion rate
Equation 6.46 in Incropera DeWitt (2002)
For reference use only

22. Appendix 3: Determining thrust with Paraview
Exhaust surface patch (top)Calculate thrust/area for each
cell cell
Integrate by multiplying with
cell area and summing over
surface
For reference use only

23. Appendix 4: Thrust versus time
(Baseline configuration)
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0 0.2 0.4 0.6 0.8 1 1.2
Thrust(N) vs Time(s) for Baseline
Averaging thrust over the first 0.7s (0.1-0.7 in 0.1s increments) appears to be sufficient to calculate a value.
Thrust might decrease later on but a longer analysis will require computational resources currently unavailable.
For reference use only