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

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.

Basic NTP Rocket http://my.fit.edu/~dkirk/MARS_NTP.ppt#599,2,GOING TO MARS WITH NUCLEAR THERMAL ROCKET PROPULSION

NTP rocket details

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 http://my.fit.edu/~dkirk/MARS_NTP.ppt#599,2,GOING TO MARS WITH NUCLEAR THERMAL ROCKET PROPULSION

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: 1.044 MW Total power per cooing hole: 54.95 kW ~55 kW

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.

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

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

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

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

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

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: 3.45 MPa Mass flow rate: 0.00152 kg/s per cooling channel Outer walls: Adiabatic Heat generation, q’’’: 3.41x109 W/m3 Outlet condition: set to outflow (match the mass flow)

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

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

Meshed Face or Cross-section

Meshed volume Hex/wedge Cooper mesh was used to mesh the volume Volume extends to 0.6985m, which is half the length of the actual NTP element

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

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

Residuals Plot:

Fluent Results: Temperature distribution at Inlet surface

Temperature Distribution, at half the length of the modeled element

Temperature Distribution at the outlet

Temperature Distribution at the outer walls

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%

Velocity magnitude at the inlet invalid

Velocity magnitude, at half the length of the modeled element

Velocity magnitude at the outlet

Velocity results for Const pp Property MATLAB Results Fluent Results Percent Difference u(0) 122.03 m/s 301.4 m/s 59.5% u(L/4) 400.55 m/s 1609.43 m/s 75% u(L/2) 659.16 m/s 2,917 m/s 77.4%

Future work, and design Nuclear Thermal disk elements With Triangular grooves New proposal of semi-circular grooves 4 in 1 in http://my.fit.edu/~dkirk/MARS_NTP.ppt#599,2,GOING TO MARS WITH NUCLEAR THERMAL ROCKET PROPULSION

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