Effect of outer insulating porous plastic foam layer on target thermal response during injection

Transcription

1 University of California, San Diego UCSD-ENG-096 Effect of outer insulating porous plastic foam layer on target thermal response during injection A. R. Raffray, J. Pulsifer, M. S. Tillack and X. Wang October 31, 2002 Fusion Division Center for Energy Research University of California, San Diego La Jolla, CA

2 Effect of Outer Insulating Porous Plastic Foam Layer on Target Thermal Response during Injection A. R. Raffray, J. Pulsifer, M. S. Tillack and X. Wang Jacobs School of Engineering and the Center for Energy Research University of California, San Diego Introduction Technical report UCSD-ENG-096 October 31, 2002 Recent analyses have confirmed that the lifetime of an injected direct-drive target is a major issue that could severely constrain the target chamber conditions prior to each shot (e.g. [1]). This lifetime is based on thermal (or thermo-mechanical) constraints at the DT interface with the outer plastic shell arising from the physics requirement on target symmetry and uniformity. One of the measures envisaged to address this issue is the inclusion of an empty plastic foam layer on the outside of the target to provide thermal insulation that would delay the heat transfer to the DT region of the target and help extend its lifetime during injection. This is being assessed as part of the UCSD/GA target/chamber interface effort and preliminary results are presented here. Configuration and Material Properties The target configuration assumed in the analysis is shown in Figure 1. The assumption based on earlier discussion (July 2002) with Steve Obenschain (NRL) was to replace some of the DTfoam region by this outer (and empty) porous foam layer. The properties of the cryogenic foam were based on those of fully dense polystyrene. The density was adjusted based on the assumed porosity of the foam region. For simplicity, the thermal conductivity of the porous foam was similarly adjusted and then further scaled by a factor of 2/3 to account for possible optimization of the porous micro-structure to minimize the conductivity. The thermal diffusivity (k/rcp) of the insulating foam is a key factor in retarding the temperature rise of the DT interface. Since both k and r change in proportion with the density of the foam, it is expected that increasing the foam porosity for a given thickness will increase the maximum temperature of the foam but not much affect the DT thermal behavior. This is what was found out for constant properties of the

3 fully dense foam (density ~1050 kg/m 3 ). However, Cp of polystyrene increases quite dramatically with temperature between K as shown in Figure 2. The thermal conductivity also increases with temperature but not as much apparently. There seem to be a large scatter in the polystyrene thermal conductivity data and few data at the cryogenic temperatures of interest (e.g. see Figure 3 for polystyrene with different densities [5]), indicating the need for measurement of cryogenic properties for the plastic of interest. Figure 3 suggests a thermal conductivity of about 0.01 W/m-K for fully dense polystyrene at 10 K, while Hartwig [3] suggests a value of 0.03 W/m-K, and the SOMRERO[4] study utilized a value of W/m-K. As a conservative measure, the higher values were used in this study consistent also with those used by Siegel [5], with k ranging from W/m-K at 19 K to 0.13 W/m-K at 40 K. x ~ mms (0.289-x) mm Insulating foam DT + foam Au or Pd Dense plastic coat 0.19 mm DT solid DT gas 1.5 mm Figure 1 Target configuration assumed in the present analysis

4 Figure 2 Figure 3 Polystyrene heat capacity as a function of temperature (from Refs. [2-4]) Polystyrene thermal conductivity as a function of temperature [5]

5 Results (i) Initial Configuration The transient analyses were performed using ANSYS and included the solid to liquid phase change effect at the triple point. The results are illustrated in Figure 4 for a heat flux distribution corresponding to convection in a chamber with 10 mtorr, 4000 K Xe (q max = 2.2 W/cm 2 )[1]. The figure shows the DT interface temperature history during injection for a target with a 25% dense outer foam layer of various thicknesses. In this case a thickness of about 130 microns would be sufficient to prevent the DT interface temperature from reaching the triple point (and, thus, from undergoing a change of phase) after s (corresponding to a target velocity of 400 m/s in a chamber of radius 5 m). This corresponds to about 32 microns of solid polystyrene used as insulating layer and it remains to be seen whether this would be acceptable based on target physics requirements. 21 Thermal Response for DT Target with 25% Dense of Polystyrene Layer(q max =2.21 W/cm 2 ) DT Interface Temperature, K micron 140 micron 120 micron 100 micron 80 micron 0 micron T.P.(19.79 K) Figure E E E E E E E E E E E E-03 Injection Time, S 7.20E E E E E E E E E E E E E E-02 DT interface temperature history for various thicknesses of a 25% dense outer foam insulating layer.

6 Figure 5 shows the DT interface temperature histories for different densities of the outer foam layer and for a fixed thickness of 100 microns. The time for DT to reach the triple point is increasingly retarded as the foam density is decreased due in good part to the large increase in Cp as the temperature of the foam increases. This indicates a preference for the highest porosity foam which can still accommodate the target physics and structural integrity requirements. 20 Thermal Response for DT Target with 100 Micron Polystyrene(q" max =2.21 W/cm 2 ) DT INTERFACE TEMPERATURE (K) % dense 25% dense 50% dense E E E E E E E E E E E E-03 INJECTION TIME (S) 7.20E E E E E E E E E E E E % dense 1.44E E-02 Figure 5 DT interface temperature history for various densities of a 100 micron-thick outer foam insulating layer.

7 (ii) Modified Configuration A recent communication (September 2002) from John Sethian (NRL) provided additional guidelines as to how to adjust the foam thickness and porosity. The insulated outer foam layer would have to be: (1) of the same density as the DT+foam layer; and (2) to a first approximation, the total mass should be less than 25% of the mass of the DT+foam. The original thickness assumed for the DT+foam layer is 289 microns (see Fig. 1) and consists mostly of DT whose density is about 25% as that of 100% dense polystyrene. Thus, the outer foam density should be about 25% of fully dense polystyrene to fulfill condition (1) and the thickness of the layer should be about 72 microns to fulfill condition (2). In addition, the insulating effect of increasing the dense plastic coating from 2 to 10 microns was investigated. The calculations were done for a target configuration similar to that shown in Fig. 1 but with the above-described outer foam replacing the original 289mm-thick DT+foam layer. Note that the results for the temperature at the DT/plastic coating interface will essentially be the same even if the DT+foam layer is maintained except that the region of interest will then be at the interface of the DT+foam and plastic coating. Two convection heat flux cases were considered: a lower heat flux case with 10 mtorr/2000k Xe and a high heat flux case with 100 mtorr/2000k Xe, as shown in Table 1 [1]. Table 1. Heat flux cases based on convection from Xe gas [1] Xe Pressure at RT (mtorr) Xe Temperature (K) Maximum Heat Flux on Target (W/cm 2 ) Minimum Heat Flux on Target (W/cm 2 ) The results of the analysis are summarized in Table 2. Clearly adding only a 72 mm, 25% dense outer foam insulating layer is not sufficient as the time for DT to reach its triple point is about 0.01 s (as compared to a flight time of s for an assumed 400 m/s target in a 5 m radius chamber). Increasing the plastic coating thickness from 2 mm to 10 mm only marginally retards the time for DT to reach its triple point. However, if this plastic coating thickness increase (8

8 mm) could be used instead to further increase the outer foam thickness (i.e. up to 104 mm for a 25% dense foam), then DT would not reach the triple point after s for the 10 mtorr/ 2000 K Xe case. The effectiveness of the outer foam region would be much enhanced if a lower density foam can be used. For example, a 152 mm thick, 10% dense outer foam layer would prevent DT from reaching its triple point before ~0.015 s even for the higher heat flux case (100 mtorr/2000 K Xe). It would be very interesting to obtain a clearer picture of the constraints on reducing the outer foam density based on target physics considerations. Table 2. Summary of results with different configurations of outer foam and fully-dense plastic coating regions Foam Density Foam Thickness (mm) Plastic coating thickness (mm) Maximum q on Target (W/cm 2 ) Time for DT to Reach Triple Point (s) > > Summary Thermal analyses were performed for a direct drive target with an insulating foam outer layer. The foam thermo-physical properties were based on those of polystyrene. The substantial increase in the polystyrene heat capacity with temperature at these cryogenic temperatures is beneficial for the insulating layer effectiveness and was incorporated in the

9 analysis. Polystyrene thermal conductivity data are scarce and scattered and higher values were conservatively used (consistent also with Siegel [6]). The results from the analysis indicate that in order to markedly delay the DT interface from reaching the triple point, the outer foam density must be reduced as much as possible for an acceptable thickness. For example, preventing DT from reaching the triple point after s requires: - ~100 mm of 25% dense foam for a 10 mtorr/2000k Xe convection heat flux case; - ~130 mm of 25% dense foam for a 10 mtorr/4000k Xe convection heat flux case; and - ~152 mm of 10% dense foam for a 100 mtorr/2000k Xe convection heat flux case. The equivalent fully dense foam thickness required in the above cases ranges from 15 to 32 mm. Alternatively, increasing the fully dense plastic coating from 2 to 10 mm does not help much. It is important to obtain clearer guidelines from the target physics requirements as to the combination of foam minimum density and maximum thickness that could be used for such an outer insulating layer. The heat fluxes assumed in the calculations do not include radiation from the chamber wall (which is being modeled in more detail as part of the ongoing effort in this area) and possible ion recombination at the target surface due to the presence of cold plasma remaining during target injection. Other possibility of accommodating the heat flux on the target are being investigated including the possibility of allowing phase change to an extent compatible with target physics requirements. These are being investigated. However, even if the presence of an outer insulating foam layer does not completely resolve the target thermo-mechanical problem it will certainly help and should be considered further.

10 References 1. A. R. Raffray, M. S. Tillack and J. Pulsifer, Target Thermal Response and Gas Interactions, Fusion Program Technical Report, UCSD-ENG-092, June Wunderlich and Baur, Heat Capacities of Linear High Polymers, Advances in polymer science, Vol Hartwig, Polymer Properties at Room and Cryogenic Temperatures, W. R. Meier, et al., OSIRIS and SOMBRERO Inertial Fusion Power Plant Designs: Final Report, WJSA (DOE/ER/ ) March Proceedings of the 7th Symposium on Thermophysical Properties, Vol. 7, N. P. Siegel, Thermal Analysis of Inertial Fusion Energy Targets, Master of Science Thesis, San Diego State University, May 2000.