Thickness Allocation Between Two Fused Silica Filters Brian Vick And J. Robert Mahan Mechanical Engineering Department Virginia Tech Kory Priestley CERES & RBI Project Scientist NASA Langley Research Center
Typical Earth radiation budget instrument Objectives To analyze the performance and effectiveness of filters used to block LW radiation in the SW channel of detectors in earth radiation budget instruments (CERES and RBI). To investigate the design improvements obtained by replacing a single filter with a split filter. To meet stringent design requirements.
Incident radiation I λ,0 Radiation exchange ε, T sur Motivation Design criteria: Analysis of the noise equivalent power level indicated that the temperature rise of the surface facing the detector should be no more than 9 mk. Front surface Back surface L z z ε, T sur Detector L r r Contact with walls h L, T sur Using a single filter, the back surface becomes too hot, resulting in too much re-emitted LW radiation, interpreted by the detector as LW leak through the filter. One way to reduce the unwanted reemitted radiation is to divide the filter into two segments.
Incident LW radiation at the front surface of filter-1 is absorbed. Heat is conducted to the sides and to the back surface of filter-1 Front surface of filter-2 is heated by radiation exchange with the back surface of filter-1 Heat is conducted to the sides and to the back surface of filter-2 Unwanted secondary radiation causes an error in the signal from the detector Mathematical Model Incident LW radiation I λ,0 L z,1 z Radiation exchange between filters L z,2 z Filter-1 Filter-2 Radiation exchange ε, T sur Radiation exchange ε, T sur L r r Contact with walls h L, T sur Contact with walls h L, T sur Detector
Mathematical Model Filter-1 Filter-2
Radiative Coupling Between Filters A critical link in the two-filter model is the radiation exchange between the two filters. For an enclosure of N-black surfaces, the transient energy balance at a typical surface node-i is NN ρρρρρρ ii TT ii = qq ii = jj=1 FF iiii AA ii EE bb,ii EE bb,jj NN = FF iiii AA ii σσ TT 4 4 ii TT jj jj=1 Linearize and discretize in a stable, implicit fashion TT pp+1 pp NN ii TT ii pp ρρρρρρ ii = FF tt iiii AA ii h rrrrrr,iiii jj=1 TT ii pp+1 TT jj pp+1 In matrix form II + WW TT pp+1 = TT pp
Absorption of LW Earth-emitted Radiation This is the most critical input to the thermal model. Monte-Carlo ray-trace (MCRT) method is used. Distribution of absorbed LW Earth-emitted radiation in the fused silica SW filter.
Numerical Solution Using the Modified Cellular Automata Method Basic Idea Split complex processes into simpler, elementary processes. Develop rules to advanced each elementary process in a discrete manner in time using a physically correct, computationally explicit, and numerically stable rule. Assemble complex processes by applying each elementary rule in a cascading, sequential manner.
An Approximate Analysis Define the thermal effectiveness ε of a filter as the fraction of the absorbed radiation that fails to pass on through.
Filter Properties
Surface Temperatures A typical temperature distribution.
Effect of Scanning A constant Earth view only is considered, since that produces the highest temperatures and is the worst case scenario.
Surface Temperatures Figure 9a: Steady state temperature rise at the surfaces of the split filter. Figure 9b: Transient temperature rise at the center of the back surface of the split filter.
Single Filter vs. Split Filter Steady state temperature rise over the back surface for one filter and split filters Transient temperature rise at the center of the back surface for one filter and split filters.
Single Filter vs. Split Filter
Thickness Allocation
Summary A thermal model of a two-filter system is formulated. Important components include The distribution of the absorbed LW radiation, obtained using the MCRT method The radiative coupling between the filters A Modified Cellular Automata technique is used to build complex models from simple processes. This technique is being extended to build a compete end-to-end model of the telescope. Results indicate that A single standard thickness filter allows far too much unwanted radiation to be reemitted to the detector. A thicker, single filter helps but is still unable to meet design criteria. A split filter is necessary to meet the stringent design requirements associated with Earth radiation budget applications.
Thank You Questions?