1. Phoebus 2A, Nuclear Thermal Element
Thermal Fluids Modeling
By Mishaal Ashemimry
December 12, 2006
MAE 5130: Viscous Flows
Dr. Kirk

2. Overview:
The Phoebus 2A is a nuclear thermal propulsion system which was tested back in the 1960s.
CFD Modeling was not as readily available then as it is now.
Most of these fuel elements cracked during testing due to thermal stresses.
To analyze this further, modeling a single element is necessary.

3. Basic NTP Rocket
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4. NTP rocket details

5. Closer look:
Hydrogen flows through each coolant channel as seen on the left.
Hydrogen comes in at a temperature of 300 K and comes out at ~ 2500 K
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6. NTP Specifications Total number of Elements: 4,789
Total number of Cooling holes per hexagon=19
Total power of reactor: 5000MW
Total power per element: MW
Total power per cooing hole: kW ~55 kW

7. Analytical Model
Modeling a single cooling hole analytically using MATLAB is critical to assess the validity of the fluent model.
Two MATLAB codes were written, one with a constant power profile, the other using a sine power profile.
Due to some complexities, the sine power profile was not used to model the element in fluent as of this time but will be integrated soon enough.

8. Power Profiles Q=55 kW Sine Power Profile
Constant Power, Power profile

9. Finding Tf, and TW For Sine power profile: For Constant power profile:
Then, from the Nusselt number
Then Tw may be found, as

10. Temperature Distributions
Sine power profile, Temperature Distributions in a single tube
Constant power, Temperature Distributions in a single tube

11. Pressure Drops Sine power profile, Pressure drop along a single tube
Constant power, Pressure drop along a single tube

12. Velocity Sine power profile, velocity along a single tube
Constant power, Velocity along a single tube

13. Thermal Fluids Modeling
Used Gambit to create and mesh 1/6 the fuel element geometry. Made use of periodic boundary conditions
Used half the length of the real element for simplicity and to reduce the size of the mesh
Set up boundary condition in fluent
Inlet temperature: 300 K
Inlet pressure: MPa
Mass flow rate: kg/s per cooling channel
Outer walls: Adiabatic
Heat generation, q’’’: 3.41x109 W/m3
Outlet condition: set to outflow (match the mass flow)

14. Cross-sectional view of 1/6th of the element
Outer wall
Solid, Tungsten
Periodic left wall, same for right wall
Coolant Channel
Extra walls placed to help mesh, but are not part of the actual element geometry

15. Meshing
The cooling channels were meshed using an O-grid, with a quad map scheme
The inner face of the geometry had to be cut into parts to allow meshing and to achieve a coarser mesh in the solid than in the channels
Tungsten properties were used for the solid, by modifying the aluminum properties in fluent.
Hydrogen was used as the fluid flowing through the coolant channels

16. Meshed Face or Cross-section

17. Meshed volume Hex/wedge Cooper mesh was used to mesh the volume
Volume extends to m, which is half the length of the actual NTP element

18. Fluent properties
In reality, the solid part of element has a sine power profile along the axial direction, which in turn affects the heat generation rate along the axial direction and hence the temperature.
For this case, a constant heat generation rate was used rather than the use of a user defined function, which is more complex.
A 3D, segregated, implicit steady model was used, with a K-Epsilon viscous model
SIMPLE Pressure-velocity coupling model was used
Discretization was all set to second order

19. Convergence
After many runs, the converged solution, predicted temperature within 20%, however for velocity magnitude this solution did not do so well.
For a different run, where continuity only reached a magnitude of 10-2, the velocity magnitude at the inlet was predicted, however the temperatures were too high and hence velocity along the tube was higher than desired

20. Residuals Plot:

21. Fluent Results: Temperature distribution at Inlet surface

22. Temperature Distribution, at half the length of the modeled element

23. Temperature Distribution at the outlet

24. Temperature Distribution at the outer walls

25. Temperature results for Const PP
Property
MATLAB Results
Fluent Results
Percent Difference
Tf(L/4)
1,102 K
1,344 K
18%
Tf(L/2)
1,794 K
2,268 K
21%
Tw(L/4)
1,459 K
1,772 K
Tw(L/2)
2,096 K
2,688 K
22%

26. Velocity magnitude at the inlet
invalid

27. Velocity magnitude, at half the length of the modeled element

28. Velocity magnitude at the outlet

29. Velocity results for Const pp
Property
MATLAB Results
Fluent Results
Percent Difference
u(0)
m/s
301.4 m/s
59.5%
u(L/4)
m/s
m/s
75%
u(L/2)
m/s
2,917 m/s
77.4%

30. Future work, and design Nuclear Thermal disk elements
With Triangular grooves
New proposal of semi-circular grooves
4 in
1 in
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31. Current Standing and Future Progress
Must modify Phoebus 2A fluent model to converge.
Need super computer (Thank you Dr. Kirk)
Attempt to include chemical reaction inside tubes (not high priority right now)
Create analytical and CFD models of Two disk designs: one triangular and the other half circle.
Currently working on code for straight triangular tubes within disk design. (90% complete)
Must continue to finish 6 cases of triangular design
Must implement a half circle design and compare to the 6 cases of the triangle design