September 24-25, 2003 HAPL Program Meeting, UW, Madison 1 Report on Target Action Items A.R. Raffray and B. Christensen University of California, San Diego Target Survival Workshop HAPL Program Meeting University of Wisconsin, Madison September 24-25, 2003

HAPL Program Meeting, UW, Madison 2 Action Items from Last Target Survival Workshop (see 4.Evaluate how much temperature drop there is to keep the insulated target cold (with beta decay heat) and determine how beneficial this temperature drop is with respect to survival estimates. 5(a).Evaluate the effect of asymmetric heating in particular on local phase change behavior. 5(b).Summarize phase change results from new model for the thermo- mechanical behavior of the target. I II III

September 24-25, 2003 HAPL Program Meeting, UW, Madison 3 Coupled Thermo-Mechanical Model of Target 1-D heat conduction equation with variable properties DT vapor (if present)is modeled as a thermal resistance (neglect capacitance) DT solid assumed rigid initially Evaporation/sublimation increase the pressure of the vapor but latent heat effects are negligible Plastic shell deformation behavior modeled (limiting cases: fully rigid and membrane behavior) Plastic Shell Vapor Gap Rigid DT Solid Simplified Target Cross Section DT Vapor Core Phase change analysis assumes a pre- existing vapor micro-gap -Vapor bubbles/gap insulate the DT -Vapor growth could result in the destruction of the target -Pre-existing “small” vapor bubbles/defects could be eliminated through density change

September 24-25, 2003 HAPL Program Meeting, UW, Madison 4 Deflection of the Plastic Shell due to DT Vapor Pressure Two Possible Cases: Membrane theory (valid for r/t > 10) for a sphere with a uniform internal pressure From bending theory, max. deflection under the center of the load* Uniform Internal Pressure, P r t -Where A is a numerical coefficient =f (r o, R, t,  ) -This equation is valid for any edge support positioned 3 degrees or more from the center of the load *Roark’s Formulas for Stress & Strain, 6 th Edition, p. 546 t roro R P

September 24-25, 2003 HAPL Program Meeting, UW, Madison 5 Comparison of the Calculated Deflection of the Plastic Shell by Membrane and Bending Theory for a Pressure of 10 4 Pa for Several Vapor Bubble Sizes, r o roro R Bubble size for which bending theory approaches membrane theory is independent of pressure, ~ 37  m in this case Would need much smaller bubble size in target to avoid large “membrane-like” deflections

September 24-25, 2003 HAPL Program Meeting, UW, Madison 6 Model Results Show Unacceptable High Vapor Region Thickness Based on Membrane Theory Even for Heat Fluxes ~ 1 W/cm 2 The Model Correctly Predicts that for Large Bubble Radius (37  m), the Maximum Deflection Using Bending Theory is Equal to the Deflection Predicted by Membrane Theory tv_o=pre-existing vapor gap thickness

September 24-25, 2003 HAPL Program Meeting, UW, Madison 7 Pre-existing Vapor Bubbles Could Close if the Bubble Size is Below a Critical Size and the Heat Flux is Above a Critical Value time = s T init = 18 K e.g. for bubble size, r o =5  m, vapor gap will close for initial thicknesses, t v,o, of 3  m and minimum heat fluxes of ~1.7 W/cm 2 Plastic Shell Local Vapor Bubble Rigid DT Solid t v,o roro

September 24-25, 2003 HAPL Program Meeting, UW, Madison 8 The Critical Bubble Size, r o,crit Depends on Initial Vapor Region Thickness and Initial Bubble Size q’’ = 5.5 W/cm 2, Plastic Thickness = 2  m

September 24-25, 2003 HAPL Program Meeting, UW, Madison 9 The Heat Flux Into the Target is Limited by Homogeneous Nucleation (0.8T c ~ 32 K) DT temperature as a function of heat flux for original target

September 24-25, 2003 HAPL Program Meeting, UW, Madison 10 Example Case with Insulating Foam Showing the Combined Effect of Including an Insulating Foam and Allowing for Phase Change 100 microns of 10% Dense Insulating Foam r o = 5e-6 m, tv_o = 1e-6 m Low heat fluxes may not be self healing The heat flux can be increased substantially For this example, the gap closes and the heat flux is limited by T DT for homogeneous nucleation (q’’>>20 W/cm 2 ) Max. DT temperature as a f(q’’) (<0.8T c for q’’ considered)

September 24-25, 2003 HAPL Program Meeting, UW, Madison 11 Temperature Drop through Foam due to Beta Decay Heat MeV  decay with half life of yr -q’’’ from beta decay in DT small ~ 1.3 x 10 5 W/m 3 -q’’ through outer insulating layer ~ 50 W/m 2 -  T through 100  m 10% dense insulating layer(k~0.01 W/m-K) ~ 0.5 K -  T though DT ice even lower ~ 1 K DT Vapor Core Foam Plastic Shell DT Ice DT/Foam Would need to maintain target surface at a lower temperature (~1 K) than DT bulk

September 24-25, 2003 HAPL Program Meeting, UW, Madison 12 Effect of 2-D Heat Flux Distribution to Account for Relative Velocity Effect on Flux on Xe Atoms Impacting the Target Perimeter from Front to Back During Flight 1-D ANSYS results very close to 2-D ANSYS results for typical cases considered -Reasonably conservative to use 1-D analysis V

September 24-25, 2003 HAPL Program Meeting, UW, Madison 13 2-D ANSYS Model Used to Study the Effects of Local Vapor Bubble Formation on Heat Transfer 3  m thick vapor bubble Bubble arc length varied and results compared to 1-D case Plastic Shell Local Vapor Bubble Rigid DT DT Vapor Core 3  m

September 24-25, 2003 HAPL Program Meeting, UW, Madison 14 Comparison of the Results For a Small Bubble to those Obtained for a Continuous Vapor Gap Show that a 2-D Heat Transfer Model may be Important for Small Bubbles Entire arc length Time (s) 15  m arc length Time (s) Outer Surface of the Plastic Shell Vapor-Plastic Interface Vapor-DT Interface

September 24-25, 2003 HAPL Program Meeting, UW, Madison 15 Comparison of the Results For a Bubble to those Obtained for a Continuous Vapor Gap Show that a 1-D Heat Transfer Model is Sufficient for Large Bubbles (15-50  m arc length for 3  m gap) Entire arc length Time (s) 50  m arc length Time (s) Outer Surface of the Plastic Shell Vapor-Plastic Interface Vapor-DT Interface