FIGURE 4-2 Comparison of computational fluid dynamics (CFD) model predictions with experimental results for thermocouples 4 and 6 on projectile 14 with CFD predictions. SOURCE: Jonathon Berkoe, Manager, Bechtel Advanced Simulation and Analysis Group, “Blue Grass MPT CFD Modeling Comparison to Pasco TRRP Experiment Measurements,” presentation to the committee, September 5, 2007.

general-purpose finite-element-based incompressible flow solver. The code is based on a nonlinear solver that (1) is accurate to second order in space and time; (2) globally and locally conserves mass, momentum, and energy; and (3) allows a choice of finite-element shape function. The model handles multimode heat transfer, including graybody radiation with view factor computation.

The model includes the coupled effects of (1) convective heat transfer rates between the injected steam and the projectiles, (2) conduction within the projectiles, and (3) radiative transfer rates between the inductively heated chamber surfaces and the projectiles, and between the projectiles themselves. These rates are used to predict the local projectile temperature-time profiles while the projectiles are in the chamber. The model is complex because the instantaneous heat transfer rate depends on the following:

  • The temperature difference between the local steam and the projectile surface temperatures at any time;

  • The radiative transfer rate, which depends on the difference between the fourth power of the absolute temperature of each element on the inductively heated surface and a projectile element;

  • The emissivities of all the surfaces; and

  • Reflected and emitted radiation from the adjacent projectiles and other structures inside the MPT chamber.

These effects must be summed over all surface elements at each time interval. A typical set of parameters used in the model for the TRRP MPT is given in Table 4-1, and typical boundary conditions are shown in Table 4-2. The model is highly nonlinear in temperature, and it includes first- and fourth-power temperature dependences and their effect on the heat-up rates.

The present CFD model uses constant values for the projectile emissivity and for the specific heat of the projectiles. Because of the variety of coatings used on the projectiles and the unknown change that occurs during coating pyrolysis, it is probably not possible to model the emissivity more accurately. However, measured values of temperature-dependent specific heat cp were obtained by the BPBGT (Figure 4-4), but these were not used in the CFD model except to extract a representative constant value. The specific heat nearly doubles between room temperature and 700°C. The increasing values of cp with temperature will tend to cause the heat-up rate to be slower at higher temperatures. This may contribute to the difference in behavior between the

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