Results

With the aforementioned modifications to THROHPUT the calculated response to heat pipe transients has been greatly improved. In particular, the liquid return to the evaporator section has been enhanced to the extent that during reasonable transients it is no longer a consideration.

THROHPUT has been used to model the transient operation of a SPAR-8 heat pipe which was fabricated and tested at Los Alamos National Laboratory (##merr86 ##merr86). This heat pipe had an evaporator section of 0.4 m, an adiabatic section of 0.09 m, and an overall length of 4.0 m. It had an annular wick design and used lithium as a working fluid. The initial condition was a frozen solid state at 300 K.

Unfortunately, there is a fundamental problem associated with modeling this experiment: the only available data from the experiment is the heat output, rather than the heat input. Heat pipe modeling codes in general, and THROHPUT in particular, need the heat input as a boundary condition. There is no way to use the heat output, which has been integrated over the entire condenser section, as a boundary condition for the code - for one thing the distribution in space is unknown. For the heat input boundary condition, it is assumed that the heat flux is evenly distributed over the evaporator section, which is a reasonable assumption. However, a constant heat flux assumption in the condenser section would be gravely wrong, since partial length operation, with distinctly nonconstant temperature profiles, is the standard start-up behavior.

The approach taken in this paper is to use the experimental heat output as the heat input boundary condition for modeling purposes. This is certainly wrong, but short of multiple runs with guessed inputs iterating to match the known output, it is the best option available. In the following, both raw and ``cooked'' results from this methodology are shown.

Figure 1: SPAR-8 Experimental Comparison (##merr86 ##merr86) to THROHPUT Model Results at 2400 s, 7230 s, and 12060 s. The THROHPUT Model used the experimental heat output as a heat input boundary condition.

Figure 1 shows a comparison of the experimental measurements of the external wall temperature and the raw model results at three different times during the transient. At 2400 s, there is very good agreement between the experimental and calculated values. At later times, the calculated values seem to lag behind the experimental values. The probable cause for this behavior is the problem mentioned above, namely that the values used for the heat input to the THROHPUT code were actually the experimentally measured heat output values. Since there is a time lag between heat input and output, a corresponding time lag is caused by using the output values instead of the real input values.

One way to deal with the time lag problem in a heuristic manner is as follows: for both the experimental and THROHPUT model situations, calculate a time-integrated total heat output,

$$\scriptsize int \left(\vphantom{ t }\right. \left.\vphantom{ t }\right) \int_{0}^{t} \scriptsize out \left(\vphantom{ t^\prime }\right. \prime \left.\vphantom{ t^\prime }\right) \prime$$ (17)

Then, for a given experimental time, determine the time in the THROHPUT model when the two Q_{$\scriptsize int$}$\left(\vphantom{ t }\right.$t$\left.\vphantom{ t }\right)$ values are equal. This technique assures that both experiment and calculation have output the same amount of heat from the condenser section of the heat pipe, but it is still fundamentally incorrect due to the different lengths of time seen by the model and the experiment. Using this heuristic technique, model-experiment agreement later in the transient is significantly improved (see Figure 2), but the good agreement early in the transient degrades.

Figure 2: SPAR-8 Experimental Comparison (##merr86 ##merr86) to Time-Adjusted THROHPUT Model Results at 6030 s, 8430 s, and 10860 s. The THROHPUT Model used the experimental heat output as a heat input boundary condition, and output times were adjusted (denoted as ``eff'') to match experimental time-integrated heat output.

Figure 3(a): SPAR-8 THROHPUT Model Results at 13,260 s: Liquid and Vapor Pressure Distributions.

Figure 3(b): SPAR-8 THROHPUT Model Results at 13,260 s: Liquid and Vapor Velocity Distributions.

Figure 3(a) shows the liquid and vapor pressures at the end of the modeled transient, 13,260 s (3.68 hrs). At this time in the model, the melt front is located roughly halfway down the length of the heat pipe, which is in partial length operation. On the condenser side of the melt front, all of the pressures are nearly zero, as the saturation pressure is almost zero at low temperatures. On the evaporator side of the melt front, a complete heat pipe cycle is in operation, with adequate liquid return to replenish the evaporative losses. Note that the liquid pressure gradient (and consequently liquid flow) would be non-existent without the ability to put the liquid in tension. The maximum tension in the liquid obtained here is -150 Pa. During transients that have been modeled to date, the liquid pressure values have been calculated to be as low as -10,000 Pa, well within experimental observations and theoretical predictions.

The velocities of the liquid (multiplied by 10,000) and the vapor at 13,260 s are shown in Figure 3(b). The liquid velocity is negative, representing return flow toward the evaporator section. The vapor velocity curve is typical for heat pipes, increasing roughly linearly through the evaporator section, and then decreasing through the condenser section. The liquid velocity distribution is also consistent with expectations. Assuming that there is an approximate equilibrium in the mass flow rates of the vapor and liquid leads to a velocity ratio of 53,000, which is indeed the case.