Chapter 5: Radiant Coolers

Transcription

1 Chapter 5: Radiant Coolers L. CrawfordITT Industries, Fort Wayne, Indiana. Overview A radiant cooler is a passive thermal device used on spacecraft to cool components to cryogenic temperatures via radiative heat exchange to the space environment. The effective temperature of deep space is approximately 3 K, which makes it a very good radiative sink. Radiant coolers can be used on spacecraft instruments because those instruments operate in a high-vacuum environment that eliminates convective heat transfer. A radiant cooler is inherently a long-life device, because it requires no moving parts or stored refrigerants and consumes only the small amount of electrical power needed for maintaining stable temperatures. It can be turned off or warmed up by additional heaters or a cover over the emitting surface that can be closed. Traditionally "radiant cooler" has referred to a radiator that operates in the temperature range of 60 to 200 K (Fig. 5.1). The lower limit results from the T 4 nature of radiative heat transfer. Below 60 K, most instruments cannot afford the volume or mass of the radiant cooler. In simplistic terms, environmental and other parasitic heat loads cannot be minimized enough to allow operating temperatures less than 60 K.

2 Figure 5.1: (Fig. 1.1, reproduced here for convenience.) Operating temperature and cooling capacity of cryogenic cooling systems. Generally, radiant cooler designers are provided the temperature or temperature range at which a component must operate for a particular application. The most common application for a radiant cooler is to cool a detector in an instrument to a particular operating temperature. To sense radiation at a particular wavelength, λ, a quantum detector must be cooled to a temperature, T, at which the thermal (phonon) energy, kt, is much less than the energy of an incoming quantum, hc/λ. In these expressions, k refers to Boltzmann's constant, h refers to Planck's constant, and c is the speed of light. Computed temperatures that are required for a typical intrinsic HgCdTe quantum detector, at a variety of wavelengths, are shown in Table 5.1. For a comparison, consider that a wavelength of 0.56 μm corresponds to the human eye's maximum daylight sensitivity. Table 5.1: Temperature Required for Useful Sensitivity of a HgCdTe Detector Maximum Wavelength (μm) Temperature for Useful Sensitivity (K)

3 Table 5.1: Temperature Required for Useful Sensitivity of a HgCdTe Detector Maximum Wavelength (μm) Temperature for Useful Sensitivity (K) A notional form of a radiant cooler is shown in Fig The component to be cooled is typically mounted directly to the radiating surface (also called a "patch") or thermally coupled to it via a flexible strap. The patch (innermost cold stage) is mounted to the surrounding cooler housing by means of low-thermal-conductance supports. External inputs, such as Earth's (or another planet's) heat loads and views to warm spacecraft or instrument structure, result in a thermal load on the cone and the warm stages of the cooler. A radiant cooler can be designed for a planet-oriented spacecraft in a low, geostationary, or highly elliptical orbit. Figure 5.2: Simplified radiant cooler concept. In most applications, radiant coolers require a shield with highly specular (mirrorlike) surfaces. The shield's outward-sloping walls are designed such that cold space is the only external body seen by the emitter surface, either directly or by reflection on the walls. (Diffusely reflecting shield surfaces would not work, because they would reflect some energy down onto the patch.) The cone acts as a projection mirror or directional antenna that limits the view of the patch exclusively to cold space. The shield wall may be attached to the ambient-temperature cooler or instrument housing. This arrangement implies that the shield or cone temperature may be as high as 300 K.

4 To reduce the radiative heat load from the shield to the emitter surface, appropriate thermal control coatings white/black paint or OSR (optical solar reflector) tiles can be applied to a bib at the end of the cone to cool the shield (Fig. 5.2).The cone end can thus be designed to reject some of the energy conducted in from the warm structure to which it is mounted back out to space, thereby lowering the cone temperature. The cone end's emitter surface, however, is not allowed to have a radiative view to the patch; that would increase patch temperature. Radiant coolers operating in the K temperature range often comprise multiple stages. The emitter surface may be surrounded by an intermediate radiator stage, and/or an additional cooled housing. The addition of multiple stages reduces the overall parasitic load on the patch stage. [*] ITT Industries, Fort Wayne, Indiana. Radiant Cooler Thermal Balance Conceptual design of a radiant cooler or other cryogenic radiator system is performed using a steady-state energy balance equation. In such an expression, thermal inputs into a specific radiant cooler stage or radiator surface are balanced by the emission of energy to the space environment. Equation (5.1) is a typical thermal balance equation for a radiator surface, and Fig. 5.3 is a block diagram of the thermal balance for a single radiant cooler stage or cryogenic radiator. (5.1) Figure 5.3: Radiant cooler thermal inputs. where Q p is heat emitted by the radiator surface to space, Q ks is heat conducted in through structural supports, Q kw is heat conducted in through electrical leads, Q i is heat radiated in through insulation from surrounding stages that are at higher temperatures, Q w is heat radiated in from surrounding shields or walls, Q o is heat radiated in through optical openings, Q j is heat generated by a detector (or other component) being cooled, Q e is environmental heating

5 from planetary or solar loads on an emitter surface (direct or by reflection), Q c is heater power required for thermal control of the stage, and Q s/c is heat radiated from spacecraft structure with a direct or reflected view to the emitter surface. Depending upon the particular mission application, some or all of the terms on the right side of Eq. (5.1) may apply. For example, radiant coolers and cryogenic radiators all require structural supports and electrical leads to monitor temperature or operate control heaters. These components introduce heat transfer paths, as illustrated in Fig All radiators operating significantly below the temperature of surrounding spacecraft components (~300 K) will also require thermal isolation from the warm surroundings. Some of the terms in Eq. (5.1), however, including heat input from optical openings or detector dissipation, are applicable only to designs of radiant coolers used to cool detectors. Utilization of specular shields will minimize the terms associated with thermal loads that result from views to Earth, sun, or other spacecraft structure. Specific attention is required to minimize each of these terms to ensure the desired operating temperature is achieved.

6 Figure 5.4: Heat flow paths for a cryogenic radiator stage. Fixing the size and temperature of the emitter area determines the maximum amount of cooling that is potentially available from a particular stage. The power radiated to space is defined by the relationship shown in Eq. (5.2). To maintain a desired radiator temperature, the combination of thermal loads into a particular stage must not exceed the power radiated by the stage to space. (5.2) Get MathML where Q p is power (in watts) emitted by the radiator surface to space, η is radiator fin efficiency, ε is emitter surface emissivity, ς is the Stefan-Boltzmann constant ( W/m 2 K 4 ), A p is emitter surface area, and T p is emitter surface temperature.

7 For η, the term that accounts for radiator fin efficiency, values of less than 1.0 are required in the analysis of cryogenic radiators that must often spread heat out over large areas. Radiant coolers, however, are usually smaller and are located on a space-facing exterior surface of the spacecraft, with detectors mounted directly on the emitter stage. As a result, radiant cooler performance calculations can usually assume a fin efficiency of 1.0. Conceptual radiator design begins with selection of an initial emitter area and operating temperature based on mission constraints. Calculations of the input loads into a particular stage are then made, and the overall thermal balance equation is solved to determine if the desired operating temperature would be achieved. If the input loads exceed the power emitted to space, baseline design changes must be made or the emitter size must be increased to provide additional cooling. This process is iterated until the designer identifies a concept that satisfies metrics that usually include thermal performance, volume, mass, reliability, and cost. Orbital Considerations The solar illumination of a three-axis-stabilized spacecraft in a low Earth orbit (LEO) is shown in Figs. 5.5 and 5.6. Throughout a particular orbit, the vector from the spacecraft to the sun generates a cone whose half-angle equals the orbit-normal-to-sun angle, γ. (For a radiator on the side of the spacecraft that is parallel to the orbit plane and facing the sun, this cone will be centered about the radiator surface normal.) When γ > 90 Ω (the angle from nadir to Earth's tangent line), the spacecraft is in eclipse over part of the orbit, as in Fig Figure 5.5: LEO orbit solar illumination geometry.

8 Figure 5.6: Solar illumination during a LEO orbit. The solar illumination of a three-axis-stabilized spacecraft in a geostationary Earth orbit (GEO) is illustrated in Fig The sun vector generates a cone with an elevation angle, θ s, that varies by 23.5 deg above and below the orbital (equatorial) plane during a 12-month period. During the summer solstice, θ s is deg, and during the winter solstice, θ s is 23.5 deg. An elevation angle of 0 deg corresponds to the autumnal and vernal equinoxes. During a 24-hour period (i.e., once a day), the sun completes a rotation about the azimuth (Δμ = 360 deg). Local midnight occurs when the azimuth is 0 deg, measured from nadir. Local noon occurs when the azimuth is 180 deg. Figure 5.7: Geostationary orbit geometry. The shield design for a radiant cooler located on the north or south face of a spacecraft in geosynchronous orbit can be simplified if the spacecraft performs a 180 deg yaw maneuver at equinox (Fig. 5.7). For half the year the radiant cooler will look south, and for the other half it will look north, thereby assuring that the sun is always shining on the opposite side of the vehicle from the one where the cooler is located. In practice, this maneuver can limit θ s to less than 5 deg, including margin for spacecraft attitude variations. As suggested by Fig. 5.7, the shield design of a GEO radiant cooler can be made symmetrical to ensure the shield is exposed to a constant solar load during the 24-hour orbital period.

9 Understanding the orbital environment is crucial for design of successful radiant coolers or cryogenic radiators for low Earth orbits. As Fig. 5.5 shows, the radiant cooler is, in general, not exposed to direct solar loads as long as γ 90 deg (or γ 90 deg). The operating temperature of the radiant cooler will determine the amount of shielding required from external heat sources (solar arrays, antennae, or other spacecraft structure). Radiant coolers designed to operate at temperatures less than 150 K will require minimizing or eliminating the view from all external heat sources to the cold stage. For orbits with γ < 90 deg, the radiant cooler may require a sun shield (cone) around the periphery of the patch to preclude direct or reflected solar illumination from illuminating the cold stage. An Earth shield will also be required to block the direct view of Earth to the patch. Preliminary Radiant Cooler Design and Analysis Environmental Heat Loads A number of computer programs calculate environmental heat loads on radiant cooler surfaces. Earth loads caused by planetary albedo and infrared (IR) emission, direct solar loads, and thermal loads from warm spacecraft surfaces are usually determined during the detailed design phase of the project by analysis tools such as THERMICA, IDEAS/TMG, or Thermal Desktop (see Chapter 15 of Vol. 1 for discussion of these codes). To speed up conceptual design of radiant coolers or cryogenic radiators, however, the designer can make initial estimates of shield geometry and the surface area of the patch or cold stage using simplified calculations of environmental heating rates. These calculations, discussed in detail in Chapter 20, provide insight into how various inputs will affect the radiator design; they therefore offer a good starting point for conceptual-design iterations. The remainder of this section assumes that the environmental heat loads on the cooler will be determined using one of these techniques. Specular Shields The single most important task during the design of a radiant cooler or cryogenic radiator is to decide what kind of shielding is necessary against external radiation heat sources. For LEO missions, shielding can be deployed to block a significant portion of environmental loads from Earth. For GEO orbiting spacecraft, shields can be designed to preclude the sun from illuminating the cold-patch stage. Shielding may also be required to block the view of cryogenic radiator stages to warm spacecraft surfaces such as solar arrays and antennae. These shields have highly specular surfaces. To generate a good starting design and to be able to synthesize optimum shield designs, knowledge of the multiple-image technique is crucial. Current computer analysis programs are useful for refining the final design of the shield, but they are not well suited to identifying its initial design. The multiple-image technique basically combines reflective optical design with standard thermal analysis practices. Radiative interchange between an emitter surface and a specular shield is characterized by the effective reflectivity of the shield as seen from the emitter (Eq. [5.3]). In this relation, ρ w refers to the reflectivity of the shield surface, and ε w refers to the shield surface emissivity. The term f n refers to the fraction of radiant flux from the emitter that reaches space after n specular reflections in a perfectly reflecting shield (ρ w = 1.0).

10 (5.3) Get MathML The effective reflectivity of the shield surface determines the fraction of radiant power emitted by the cold stage that reaches space. Using Kirchhoff's law, one can determine that the effective emissivity of the shield is equivalent to subtracting the reflectivity from unity. The effective emissivity can be related to the actual surface emissivity using the relation in Eq. (5.4). (5.4) Get MathML The effective emissivity determines the radiative thermal input from the shield to the emitter according to Eq. (5.5). The fraction f n is identical to the view factor (also called shape or configuration factor) used by conventional thermal analysis software. It is equal to the view factor F e m(n) from the emitter, e, to the shield mouth, m, as seen after n specular reflections in the shield walls. Forming the specular image array of the shield mouth in all the shield walls, one can approach the problem of determining the radiative input from the shield with conventional thermal analysis techniques. (5.5) Get MathML where Q shield is the thermal load on the emitter surface from the surrounding shield walls, ε e is the emissivity of the emitter surface (the IR absorptivity of the emitter surface), A e is the emitter surface area, ς is the Stefan-Boltzmann constant ( W/m 2 K 4 ), ε ew is the effective emissivity of the shield wall as seen by the emitter, T w is the temperature of the shield wall, ε w is the shield wall emissivity, and Fe m(n) is the view factor from the emitter to the shield mouth formed by n specular reflections in the shield walls. Departures from specular reflectance at the shield walls cause the effective shield-surface emissivity, ε ew, to exceed the surface's hemispherical emissivity, ε h. The difference between the effective and the hemispherical emissivities is a strong function of surface roughness and geometry of the cooler. Surface roughness converts part of the specular component of a perfectly smooth surface into a nonspecular component that increases the number of emitter reflections at the shield wall and increases effective emissivity. To achieve the highest possible ratio of the specular component reflectance at normal incidence to the specular reflectance of a perfectly smooth surface, one must use optically finished or mirrorlike shield surfaces. The emissivity values for optically polished, specular shield walls coated with a vacuumdeposited aluminum (VDA) have been reported by Estalote and Ramanathan [5.1] and are shown in Table 5.2. Shield wall emissivities that matched the Estalote and Ramanathan data were measured on radiant coolers for AVHRR/HIRS (Advanced Very High Resolution Radiometer/High-Resolution Infrared Radiation Sounder), a LEO mission, and InSat and GOES (Geostationary Operational Environmental Satellite), GEO missions. Shield wall emissivity depends upon surface finish, shield wall size, and the quality of the coating. Shield

11 emissivity values should always be verified through testing performed on flight-like hardware. Table 5.2: Emissivities for Shield Walls Coated with Vacuum-Deposited Aluminum Temperature (K) Lowest Emissivity Values Typical Emissivity Values As mentioned earlier, shields can be designed for a variety of applications with the design specifics depending upon the particular orbit, location on the spacecraft, and field-of-view to warm spacecraft or other instrument surfaces. Generally, cryogenic radiator surfaces are mounted on sides with a hemispherical view to space. No direct solar illumination is desired; however, shields can be designed to accommodate modest sun angles (e.g., ±23.5 deg from parallel to the radiator surface) and to reject radiant heat from the solar sails and astromasts encountered on some geostationary orbiting satellites such as the GOES K/L/M spacecraft. Figure 5.8 shows a cross section of a GOES radiant cooler that consists of three cooled stages. The first-stage housing, cooled using a bib emitter surface attached at the opening of the specular cone shield, operates at approximately 240 K at summer solstice. The radiator and patch emitter stages are mounted in a coplanar arrangement. The radiator surrounds the patch stage and serves as an intermediate state to reduce parasitic thermal load to the patch stage. The shield design is symmetric, to account for the apparent coning motion of the sun about the emitter surface normal. The radiator stage operates at approximately 144 K, and the patch stage is maintained at 99 K at summer solstice.

12 Figure 5.8: GOES radiant cooler shield concept. Location of hardware within the cooler's hemispherical field-of-view to space can significantly drive the design of the shield. On the GOES K/L/M instruments, increasing the shield angle from 25 to 32 deg reduces the thermal load on the patch stage from an astromast and solar sail. Thermal loads caused by the astromast and solar sail, however, still amount to 50% of the uncontrolled thermal load on the patch stage. The specular shield walls only contribute 30% of the uncontrolled thermal load on the patch. The remaining thermal load is caused by radiation from the radiator stage, structural support and electrical wire conductance, and detector thermal dissipation.

13 In low Earth orbits, radiant coolers or cryogenic radiators should be mounted on surfaces not exposed to direct sunlight. Earth will be the only heat source visible in the hemisphere above the cold emitter surface. The emitter surface can then be shielded by simply adding a semicircular shield that blocks the angle subtended by Earth (Fig. 5.9). The surface of the shield facing the emitter or patch stage has a highly specular, low-emittance surface finish. Sizing of the shield should account for the full dimensions of the emitter if the entire Earth disk is to be blocked from view. Sometimes simply adding vertical side extensions to the blocking surface minimizes the overall size of the shield, although this does slightly decrease the effective view to space, even with the shield's highly specular, low-emittance surface finishes. Figure 5.9: Shield concept for a low Earth orbiting radiant cooler. Radiative Heat Transfer Between Stages Radiation exchange between the stages of a radiant cooler or cryogenic radiator occurs in two forms. The first is direct radiative heat transfer between the surfaces of two stages that face each other. The second form is the radiative coupling caused by structural and electrical members connecting the two stages. (Both were illustrated in Fig. 5.4.) Radiative Exchange Between Facing Surfaces The net exchange of radiant energy between two surfaces can be represented as in Eq. (5.6). The insulation factor, S i, depends on the emissivity of the two surfaces (ε 1 and ε 2 ) and the

14 mode of reflection (specular or diffuse). The mode of reflection of the inner boundary does not matter because the radiation exchange between the enclosed and enclosing surface is assumed to form a two-surface enclosure. As a result, the view factor from the enclosed surface to the enclosing surface is equal to 1. The view factor from the enclosing surface to the enclosed surface is then, using reciprocity, the ratio of the enclosed area to the enclosing area, (A 1 /A 2 ). (5.6) Get MathML where ς is the Stefan-Boltzmann constant, W/m 2 K 4 ; A 1 is the surface area of the enclosed (inner or cold) boundary; T i is the temperature of boundary i (i = 2 for the warm or outer enclosing boundary and 1 for the cold, inner [enclosed] surface); and S i is the radiative insulation factor. Classic formulae for the insulation factor, S i, for three geometries and modes of reflection are listed in Table 5.3. Heat transfer for specular reflection is less than or equal to heat transfer for diffuse reflection. The formula provided for coaxial cylinders or concentric spheres is a good approximation for geometries such as short cylinders with elliptical or flat ends or other conservative shapes. In the case of diffuse reflection, surface areas A 1 and A 2 are the total surface areas of the two boundaries facing each other. Table 5.3: Formulae for Determining the Insulation Factor Based on Geometry [5.2] Geometry Specular Reflection Diffuse Reflection Infinite parallel plates ε ε ε ε Infinitely long, coaxial cylinders ε ε ε (A 1 /A 2 ) (ε 2 1 1) Concentric spheres ε ε ε (A 1 /A 2 ) (ε 2 1 1) [5.2] R. B. Scott, Cryogenic Engineering (D. Van Nostrand Co., Inc., Princeton, 1959), Chap. VI, "Insulation." The relationships shown in Table 5.3 indicate that, as long as both inner and outer surfaces have the same geometrical form and are closely spaced (A 1 ~ A 2 ), the insulation factor is independent of both the geometry and degree of specularity. Adding n intermediate shields between two stages increases the insulation factor between them as shown in Eq. (5.7). There is a diminishing return for the number of intermediate shields. The first intermediate shield reduces the radiative coupling between surfaces by a factor of 2, the second by a further factor of 1.5, the third by a further factor of 1.33, and so on. Multiple shields are most useful in the warmer stages of a radiant cooler, because the radiative input is dependent on temperature to the fourth power (T 4 ). (5.7) Get MathML

15 When multiple radiation shields are equally spaced on conductive supports, the radiative coupling and the conductive coupling between stages are independent of each other. Conduction between stages is determined by the summation of the n+1 conductors in series between the two stages. Emissivity values for two types of gold-plated surfaces are listed in Table 5.4. The uncertainty in emissivity for the values listed is ± Reduction in goldplating emissivity during the last 30 years has resulted in dramatic improvements in insulating capability. Table 5.4 indicates that using gold surfaces on each stage (one at 300 K, the other at 90) will result in an insulation factor of approximately 78 without any intermediate shields. Table 5.4: Emissivity Measurements for Gold Surfaces from Room Temperature to Cryogenic Temperature [5.3] Temperature (K) Standard Gold GSFC Vapor-Deposited Gold [5.3] J. G. Androulakis and L. Hemmerdinger, "Emissivity Measurements," Final Report, Contract NAS , 29 November Use of gold surfaces can be compared to multilayer blankets. Multilayer insulation (MLI) blankets used in the AVHRR radiant cooler provide an insulation factor between 50 and 65. The insulation factor using GSFC vapor-deposited gold surfaces in lieu of the blankets would be 63 for a 170 K surface viewing a 295 K surface. Radiative Exchange Resulting from Structural Members and Electrical Cables Structural supports and electrical cables can be surrounded with a thermal shield to help minimize the total heat transfer to the cold stages of a radiant cooler or cryogenic radiator. The radiative coupling between a conductive connection and its surrounding shield increases the total amount of heat transfer to a level greater than that caused by conduction alone. If the surrounding thermal shield is maintained at the temperature of the warmer stage, there is a radiative flow of heat from the shield to the mechanical or electrical element. Conversely, if the surrounding thermal shield is attached to the cold stage, there is a radiative flow of heat from the mechanical or electrical element to the shield. This radiative flow of heat causes a deviation in the linear temperature distribution caused by pure conductance, as illustrated in Fig

16 Figure 5.10: Effect of a radiative coupling on the temperature distribution across a conductive element. The increase in heat flow caused by the introduction of the radiative coupling can be expressed by a factor M. This factor (also referred to as the dual-mode factor) is defined as the ratio of the total heat flow through the support (conduction and radiation) to the heat flow caused by conductance alone. Defining the M factor in this way allows use of an effective thermal conductance MK, where K is the traditional conductance of the mechanical support or electrical connection. When performing initial sizing of radiant coolers, one typically uses a value of 1.2 to 1.3 for the M factor if the mechanical support is surrounded with a gold-plated shield. Conductive Heat Transfer Between Stages Conduction between stages of a radiant cooler or cryogenic radiator can be separated into two categories, conduction along mechanical supports and conduction along electrical cables. (Both were illustrated in Fig. 5.4.) Conductive Heat Transfer Through Mechanical Supports Structural support conductance depends upon the requirements that drive the overall structural design of a particular radiant cooler. These requirements may include launch loads, line-ofsight stability, coregistration of multiple channels, or minimum natural frequency. The allowable thermal load depends upon the particular stage of a radiant cooler or cryogenic

17 radiator under consideration. The importance of structural support conductance increases as the temperature decreases. This implies that a robust structural support can be designed for the warmest stage of the radiant cooler without significantly impacting the temperature of the coldest stage. Structural support conductance is governed by Fourier's Law of Heat Conduction (one dimension) as shown in Eq. (5.8). The term Q x represents the heat transfer rate (in watts) in the x direction. The coefficient k, which refers to the thermal conductivity of a material, varies with temperature as well as composition of the material. Heat flow is always perpendicular to the cross-sectional area of the material, A. The negative sign in Eq. (5.8) implies heat is transferred from the warm (T 2 ) to the cold (T 1 ) body (i.e., in the direction of decreasing temperature). The temperature distribution is assumed to be linear through a particular section of the material defined by a characteristic length, L. The grouping of terms k, A, and L in Eq. (5.8) defines the thermal conductance through the support, K s. (5.8) Get MathML The multiple structural supports typically used in design of radiant coolers introduce parallel conduction paths. The details of parallel or series thermal conductance are discussed in basic heat transfer textbooks. For radiant coolers, it is often convenient to use thermal conductance (as opposed to thermal resistance) in calculations, as parallel conductances are summed together to achieve the total conductance of the material in question. The thermal effectiveness of mechanical supports can be determined using a ratio of the thermal conductance per emitter area, thermal conductance per unit mass, or thermal conductance per insulation area. These groupings are very helpful during the conceptual design phase, when trades are performed to determine the required cooler size for a particular application. Grouping of the terms in such a manner allows for the scaling of structural support conductance. Table 5.5 contains a summary of HIRS (a LEO example) and GOES (a GEO example) structural support conductance for various stages. Care should be exercised when using these values for radiant cooler designs. They depend upon specific design features of asbuilt units and are only included to provide an indication of the allowable thermal conductance. Table 5.5: Radiant Cooler Structural Support Characteristics Instrument Thermal Conductance (W/K) per Radiator Patch HIRS/2I emitter area (cm 2 ) mass (g) GOES-K emitter area (cm 2 ) mass (g) A variety of structural support concepts are used in radiant-cooler design. The evolution of structural supports has been geared toward providing more efficient support (thermal conductance per unit area or mass) at higher natural frequencies. Initial radiant cooler designs featured use of a bicycle spoke or wire suspension supports made from titanium. This type of

18 isolation scheme gave way to support concepts that used low-thermal-conductivity, highstrength composite materials (epoxy glass or synthane). These hollow tube or rod supports isolated a relatively small cold stage from the warm stage using a cantilever configuration. As the size of emitter areas grew, the cantilever support design was changed to a table-leg configuration that provided stiffness in two directions. The table-leg configuration was superseded by a center-of-mass configuration, a mechanical support concept that uses multiple posts or rods to provide support in all three directions and uncouple vibration modes. The GOES-K, HIRS, and AVHRR radiant coolers use the multiple-post support design (Fig. 5.11). When combined with multiple radiation shields, the multiple-post configuration can support several stages (three stages, in the case of the GOES-M radiant cooler). Figure 5.11: The GOES-K radiant cooler uses a mechanical support concept that includes rods with wires wrapped around them. The conductance of mechanical supports is calculated using Eq. (5.8). Usually, the most complicated part of Eq. (5.8) is determining the conductivity of the support material at cryogenic temperature. Fortunately, numerous reports and technical papers in the open literature address thermal conductance of synthane and other support materials. Thermal conductivity data for synthane (G-10) and epoxy glass support materials from several sources are shown in Fig Testing of synthane used for radiant cooler supports on the GOES program indicates the thermal conductivity data matched the data discussed in the Foster report. [5.4]

19 Figure 5.12: Thermal conductivity data for G-10 and epoxy glass structural supports. [5.4] [5.7] Flexure supports are another type of structural support used in radiant cooler design. Flexure supports reintroduce the concept of separating structural and electrical connections. Mounted around the periphery of a radiant cooler stage, these supports free up internal volume that can be used for adding more channels or simplifying the fabrication, because the electrical leads have been decoupled. Conductive Heat Transfer Through Electrical Cables Heat conducted along electrical wires between stages can be calculated with the same equation (Eq. [5.8]) used for conduction along structural supports. Electrical connections in radiant coolers followed much the same evolutionary path as mechanical supports. Initial radiant cooler designs featured separate, flying leads. Flying leads, however, did not contain sufficient length to provide adequate thermal isolation; as a result, the leads were combined and coiled around structural supports. The structural supports provided a means for supporting the wires and also allowed for increased wire length needed for adequate conductive insulation. Initially, the wires were passed through the center of the supports; later, though, the wires were wrapped around the outside of the supports (Fig. 5.11). Combining the mechanical and electrical connections has drawbacks, however. It complicates the assembly and increases the time required to repair the radiant cooler. In addition, the glass transition temperature of synthane mechanical supports is approximately 120 C. Analysis is therefore required to ensure that decomposition of the structural support material does not occur in vacuum because of wire heating during outgassing or other high-power, nonoperational modes.

20 The increasing complexity of focal-plane arrays (FPA) has reintroduced the concept of separate flying leads into radiant cooler design. Routing of wires from the FPA to the exterior of the radiant cooler is now accomplished using multilayer flex cables, which are basically flat cables that combine the necessary signal, ground, and shielding in one layer. (An early concept for a multilayer flex cable is shown in Fig ) The layer is separated from additional layers via polyimide insulation. Flex cables in radiant coolers generally have constantan traces, which are separated from one another by an adhesive. If required, the flex cable may also contain layers to provide electromagnetic interference (EMI) protection and an exterior gold layer that will minimize radiative heat transfer with the warm surroundings. Figure 5.13: Multilayer flex cable concept for the GOES Multi-channel Imager. An example showing the results of calculations based on Eq. (5.8) for determining the thermal conductance of electrical connections is summarized in Table 5.6. This example shows the total conductance between the ambient instrument and the vacuum housing (first stage) of a GOES radiant cooler. Table 5.6: Sample Calculation of Wire Conductance Between Stages of a Radiant Cooler Material Conductivity (W/cm K) Quantity of Wire Diameter of Wire (cm) Free Length, L (cm) Conductance (W/K) Copper Constantan

21 Table 5.6: Sample Calculation of Wire Conductance Between Stages of a Radiant Cooler Material Conductivity (W/cm K) Quantity of Wire Diameter of Wire (cm) Free Length, L (cm) Conductance (W/K) Total The conductance of flex cables is calculated by means of the same technique shown in Table 5.6. In the case of flex cables, the overall conductance of each constituent of the cable is determined based upon the total cross-sectional area of each material. Contact with flex cable vendors or the supplier of the focal-plane assembly is required to obtain thermal properties of materials at cryogenic temperatures. In some instances, the flex cable may be delivered as part of the focal-plane assembly. Separate calculations for the effect of radiative heat transfer will determine the benefit of adding a gold shield to the outer layer of the cable. Adding gold plating directly to the exterior of the cable reduces radiative heat transfer from the warm stage but also increases overall cable thermal conductance. Detector Heat Dissipation The single factor that will most likely determine whether a radiant cooler can be packaged within the allowable sensor envelope is detector heat dissipation. Detector heat dissipation and the radiative heat load into the optical port (discussed in the next section) constitute the useful cooling obtained from a radiant cooler. In general, these loads remain fixed and do not scale as a function of cooler size. The optical port load is dependent on the aperture opening, but this input usually remains constant once the optical design has been selected. Detector heat dissipation has grown from 4 mw (four-element detectors used on GOES-M, Imager IR channels) to 100 mw (for present-day detectors cooled to 70 K). The patch stage of the GOES-M radiant cooler, capable of dissipating 136 mw of power to space, requires an emitter area of approximately 290 cm 2 at an uncontrolled patch temperature of 96.2 K. Of the 136 mw, the detector heat dissipation and the optical port radiative heat load only account for 6 mw (approximately 4.4%) of the total load. The remaining load on the patch stage is caused by radiative back-loads from an astromast and solar sail (48.7%), input from shield walls (32.1%), radiative exchange with the radiator stage (5.1%), and conductive input from the radiator stage (9.7%). During the conceptual design of a radiant cooler, the designer should maintain close contact with the detector supplier to obtain a good estimate for the detector amplifier power dissipation. In the event the fixed cooling loads exceed 100 mw and the required operating temperature drops below 80 K, the trade of a passive radiant cooler for an active refrigerator may be warranted. Fixed cooling loads on the order of 100 mw may result in a passive radiant cooler design that exceeds the allowable sensor envelope.

22 Optical Port Radiative Heat Load The optical port heat load (Q o in Eq. [5.1]) accounts for radiative thermal interchange through the optical ports that separate the cooled optics and detectors from the warm optics housed in the ambient instrument. The goal of the radiant cooler designer is to minimize this radiative heat transfer without adversely affecting the input signal flux. To minimize the optical port load, the input aperture size should be minimized. Use of a separate optical port for each spectral band helps minimize both spectral content (optical bandpass) and physical size of the optical port. The emissivity of the optical ports can be minimized by using reflective bandpass filters (i.e., selecting band-pass filters and optical substrates with high reflectivity outside their required transmission bands). A final recommendation for reducing the optical port load is to limit the spectral band of the cold optical elements to the warm elements. Placing bandpass filters on the warmer stages will limit thermal load on the coldest stage of the radiant cooler. Cooled optical elements, or windows, used in radiant coolers act as barriers that prevent molecular contaminants from depositing onto surfaces. Windows also attenuate out-of-band spectral response, and this reduces background noise. Optical port load for a particular radiant cooler stage is calculated using Eq. (5.9). In this expression, Q ij refers to the radiative input from the source, i, absorbed by the receiver, j. The summations include all optical port sources that are visible from the window (Q i -window) or the adjacent gap (Q i -gap) on a particular stage. Use of the fraction 1/2 indicates that half the radiation input incident on the gap is absorbed by the cold stage in question. The other half of the energy incident on the gap is absorbed by the warmer stage. If j refers to the radiator stage (middle stage) of a three-stage radiant cooler, then half the radiative input into the gap is absorbed by the radiator stage and the remaining portion is absorbed by the vacuum-housing stage (the warmer stage surrounding the radiator). Figure 5.14 shows a representation of the terms required to calculate the optical port load for the GOES three-stage radiant cooler. (5.9) Get MathML

23 Figure 5.14: Representation of the terms needed to calculate the optical port load for the GOES radiant cooler. 1: the ambient portion of the instrument, which is maintained at 295 K; 2, 3: windows mounted on the vacuum housing (2) and radiator stages (3); 4: the opening in the patch stage where the detectors are located; 5, 6, 7: the physical gaps separating stages. An individual input for one energy term used in Eq. (5.9) is determined by Eq. (5.10). (The parameters in Eq. [5.10] are illustrated in Fig ) Equation (5.10) is considered a conservative estimate for the radiative exchange of energy as multiple reflections between a receiver and a source are accounted for, based upon the use of closely spaced geometry. (5.10) Get MathML Figure 5.15: Parameters needed for calculating an individual optical port heat load term.

24 where A j is the receiving area (window), ς is the Stefan-Boltzmann constant ( W/m 2 K 4 ), F ji is the view factor from receiver j to source i, ε ij is the emissivity of source i as seen by receiver j, α ji is the absorptivity of j for emission from i, ρ j is the reflectivity of j for emission from i, ρ i is the reflectivity of i for emission from j, P ij is the fraction of blackbody emission from i that is transmitted by the windows/filter to j, and T i is the temperature of source i. Window materials are selected to cover a particular spectral band. Optical substrates are selected with a cutoff beyond the spectral band in question. An optical bandpass filter is added to the substrate that has a cut-on wavelength below the desired band and a cutoff wavelength above the desired spectral band. The bandpass filter must reject radiation by reflection to minimize the emissivity of the window. The typical wavelength separating the cut-on and cutoff to the desired spectral band is 0.5 μm. Cutoff wavelengths for commonly used window substrates are shown in Table 5.7. Table 5.7: Cutoff Wavelengths for Window Substrates Substrate Cutoff Wavelength (μm) Sapphire 5.5 ZnS 14 ZnSe 20 CdTe 25 Thermal properties for window substrates are available in the open literature. Excellent sources for emissivity and absorptivity data for various materials are Touloukian et al. [5.8],[5.9] When calculating optical port loads, one assumes the absorptivity and emissivity for all gaps are both 1.0. In-band energy from the instrument ambient that has a clear view to the patch is not absorbed in the windows. It passes through the radiant cooler and is fully absorbed in the coldest stage (or is reflected back out the window). For gray-body radiation exchange, the absorptivity of j for an emission from i is the emissivity of j at the temperature of i. Windows do not behave as gray bodies; as a result, absorptivity and reflectivity are estimated using the emissivity value and the cutoff wavelength of the optical element. To estimate these values, one first determines the fraction of blackbody emission at a temperature that lies beyond the cutoff wavelength of the substrate. The ratio of the actual emissivity (ε) to the fraction of blackbody emission beyond the cutoff (P) determines the effective absorptivity at wavelengths beyond the cutoff. Because nothing is transmitted beyond the optical element at these wavelengths, the effective reflectivity is determined by subtracting the effective absorptivity from unity. A sample calculation for determining the effective absorptivity of a window above the cutoff wavelength can be performed using a ZnS substrate. ZnS has an emissivity of 0.57 at a temperature of 150 K. In Table 5.7, one sees that the approximate cutoff wavelength of the ZnS substrate is 14 μm. The fraction of blackbody emission at 150 K beyond 14 μm is 0.92 (calculated using blackbody radiation functions). This implies the effective absorptivity is 0.57/0.92, or According to Kirchhoff's Law, the emissivity is equal to the absorptivity;

25 hence ε = (Using this technique for ZnSe windows deserves a cautionary note, however, because the cutoff wavelength for ZnSe is a strong function of the thickness.) Calculation of all terms required for the optical port load using the techniques described in this section can be time-consuming and frustrating. Current thermal analysis tools or optical design software may be able to perform this calculation, but in the initial phases of a program the optical design is usually not defined to a point where optical elements and coatings have been selected. Estimates for the optical port load can be generated by assuming blackbody radiation exchange with the surroundings (the adjacent warm stage) and using Eq. (5.11). To perform this calculation, one obtains an estimate for the aperture size from the optical designer; from the estimate, one can determine the surface area of the opening. The view factor from the warm to the cold surface is assumed equal to 1.0, and all incoming energy is assumed to be absorbed. Equation (5.11) refers to the net heat transfer from a cold stage (T j ) with view to a warm stage (T i ). (5.11) Get MathML The optical port load estimated using Eq. (5.11) can be compared to values generated using a detailed model of the GOES-Imager radiator and patch stage (Table 5.8). The aperture area for the radiator window and opening into the patch is cm 2. The temperature of the vacuum housing stage is maintained at K, the radiator stage at K, and the patch stage at 96.2 K. Table 5.8 indicates that the estimated port load for the patch stage agrees quite closely with the detailed thermal model results, and thus Eq. (5.11) is a good first-order tool for estimating optical port load. The table also shows how the magnitude of optical port load decreases as function of temperature to the fourth power. If the allowable fixed load on a 96 K radiant cooler stage is 100 mw, only 3 mw needs to be allocated for optical port load; the remaining 97 mw can be allocated to detector dissipation. Table 5.8: Estimated Optical Port Thermal Loads vs. Model-Generated Optical Port Thermal Loads Optical Port Aperture (cm 2 ) Stefan-Boltzmann Constant (W/cm 2 K 4 ) T i (K) T j (K) Estimated Optical Port Load (mw) Actual Optical Port Load (mw) Radiator E Patch E [5.1] E. A. Estalote and K. G. Ramanathan, "Low Temperature Emissivities of Copper and Aluminum," J. Opt. Soc. Am. 67, (1977). [5.4] W. G. Foster et al., "Thermal Conductivity Measurements of Fiberglass/Epoxy Structural Tubes from 4 K to 320 K," AIAA 10th Thermophysics Conference (Denver, CO, May 1975).

26 [5.7] Thermal Conductivity Measurements of Glass Epoxy and Boron Epoxy Specimens, 30 September 1998, measurements performed by Precision Measurement Instruments, Inc. for ITT. [5.8] Y. S. Touloukian et al., Thermal Radiative Properties, Vol. 8 of Thermophysical Properties of Matter (IFI Plenum Press, New York and Washington, 1972). [5.9] Y. S. Touloukian et al., "Nonmetallic Solids," Part 3 of Thermal Radiative Properties, Vol. 8 of Thermophysical Properties of Matter (IFI Plenum Press, New York and Washington, 1972) Contamination Control Guidelines Radiant cooler or cryogenic radiator external surfaces act as cold traps that condense contaminants in the atmosphere surrounding the spacecraft and instrument. Because radiant coolers and some nonblack cryogenic radiator surfaces operate below 150 K, condensation of contaminants on these sensitive surfaces cannot be eliminated; therefore, the contaminants must be controlled. Optical elements used within radiant coolers tend to be much more susceptible to contamination than emitter surfaces or internal surfaces facing each other, because transmissive elements generally are more sensitive to contamination than reflective elements. Moderate contamination has negligible effect on the IR reflectivity (and emissivity) of metals, but it significantly reduces the transmission of IR windows or lenses. For this reason, a refractive (transmitting) element should never be exposed to an atmosphere warmer than itself. Every instrument carries its own atmosphere into orbit, and the dominant constituent of this atmosphere is water vapor. Water vapor has a lower vapor pressure at a given temperature than most common gases. As a result, it is usually the first contaminant to condense on sensitive surfaces (emitter surface, specular shields, or cryogenic thermal strap surface) as ice or frost. Ice tends to absorb in the IR wavelengths and scatters in visible wavelengths. The atmosphere surrounding the instrument decays slowly. On-orbit measurements of the spacecraft and instrument atmosphere, made using the OGO mass spectrometer, are shown in Table 5.9. The temperatures reflect the temperatures at which condensation of ice occurs as predicted by Eq. (5.12), the Antoine equation. The saturated water vapor pressure of water at 100 K is approximately torr (Table 5.10). This means that ice will always condense upon the portion of the cold emitter surface facing space. (5.12) Days in Orbit Get MathML Table 5.9: Condensation Temperature of Water Versus Time in Orbit No MLI Present MLI Present Pressure (torr) Temperature (K) Pressure (torr) Temperature (K)

27 Table 5.10: Vapor Pressure of Water Vapor Over Ice as Predicted by the Antoine Equation Temperature (K) Pressure (torr) Usually, emitter surfaces that operate at or below 150 K are painted black to maximize the radiative emission to space (emissivity of 0.92 or higher). Therefore formation of ice on an emitter surface does not significantly alter the thermal properties of the emitter. The temperature increase across the ice layer is also negligible. The thermal conductivity of ice actually increases as the temperature decreases. For an emitter surface at 100 K, the thermal conductivity of ice is approximately W/cm K. For a 40 μm thickness of ice, the temperature drop through the layer is only K. Most of the water vapor that condenses on cryogenic surfaces was carried into orbit with the instrument and spacecraft; however, it can also be produced as a propellant by-product. Another common propellant by-product is ammonia. Fortunately, the pressure required to condense ammonia on a surface at 150 K is approximately torr. Such a high vapor pressure is not likely in the proximity of a radiant cooler, so ammonia is not a likely contamination source. Because the contamination environment within or around a radiant cooler cannot be completely eliminated, control methods are required to minimize the susceptibility of the radiant cooler to contamination. Contaminants should be controlled so that they are kept from reaching optical surfaces where they could condense and degrade instrument performance. The simplest action that can control the contamination environment after launch is to provide for outgassing or decontamination of all optical elements. After launch, optical elements

28 should be maintained at or above the surrounding instrument's ambient temperature until the surrounding spacecraft atmosphere has had adequate time to decay. Typically, the time allotted for initial on-orbit outgassing is 30 days, which is usually adequate for allowing the spacecraft atmosphere time to decay to the point where it will not condense on sensitive surfaces. In addition, the radiant cooler should contain provisions for a decontamination mode to drive off contaminants that accumulate after the initial outgassing period. Outgassing or decontamination should not be viewed as the primary means of controlling contamination; rather, it should be thought of as a back-up solution. The primary means of controlling contamination is properly designing the radiant cooler so decontamination is not necessary. External thermal control surfaces such as OSR tiles, white paint, silvered Teflon, and specular shields should all be maintained at temperatures sufficiently high to preclude water vapor condensation from the external atmosphere. As discussed previously, a practical lower limit is 150 K. Selection of this limit implies that during the initial on-orbit outgassing, all nonblack, external radiator emitter surfaces (including specular shield surfaces) should be maintained at temperatures at or above 150 K. All cooled optical elements within the radiant cooler should never be exposed to an atmosphere warmer than the element itself. An optical element colder than the surrounding atmosphere acts as a cold trap on which contaminants condense, and this condensation results in reduced optical transmission. One way to protect the cooled optical element is to implement a cold trap that reduces the condensation temperature below the temperature of the optical element. Another method is to heat the optical elements (passively or actively) to the temperature of the surrounding atmosphere or higher. Vent paths within the radiant cooler should be designed so that outgassing products vent directly to space. Optical windows should be used between radiant cooler stages and on the warm stage of the radiant cooler that faces the ambient instrument. Once the initial on-orbit outgassing period is completed, and the radiant cooler has cooled down, vent paths will become entrances for contamination. Cold traps can be added around the periphery of the optical element to reduce the temperature of incoming water vapor to the temperature of the cold optic. The outer window between the radiant cooler and the ambient instrument serves as a barrier to keep contaminants from the instrument from entering the radiant cooler. The use of MLI blankets and polyimides within the radiant cooler should be avoided if at all possible. MLI is a prime source of water vapor. Polyimides, known to retain water, have a saturation temperature of 152 K. As a result, they should not be used where they have a view of optical elements below 152 K. Vacuum baking of polyimides is generally ineffective, because this material tends to reabsorb water from the surrounding atmosphere. The atmosphere surrounding the radiant cooler is usually maintained at a relatively high humidity to prevent electrostatic discharge. A good material that can be used within all stages of a radiant cooler is synthane G-10 (epoxy glass), because it does not retain water. Radiant cooler performance can also be degraded if organic material is allowed to polymerize on emitter surfaces. Polymerization results in an increase in the solar absorptivity of external, nonblack thermal control surfaces such as OSR tiles and specular shields. Once polymerization occurs, the contamination is permanent and cannot be removed by heating (decontamination). Organics (hydrocarbons) that result in polymerization are generated from bulk diffusion of material within the spacecraft and instrument. The electrostatic return process is also responsible for organic material that results in polymerization. Electrostatic

29 return permits a non-line-of-site transport of contaminants that could ultimately deposit and polymerize on emitter or shield surfaces. The amount of material available for polymerization depends upon the proximity to vent paths and outgas sources. Location of vent paths within the instrument or spacecraft should be checked to ensure there is no direct line of sight to a critical optical element or sensitive thermal control surface. The presence of an atmosphere containing potential contaminants near a surface in the presence of solar ultraviolet light will result in the deposition of polymerized products onto the surface. The polymerization of material is independent of the vapor pressure of contaminants or the temperature of the surface in question. Deposition of contaminants onto a surface occurs under conditions where condensation may not normally occur. Solar illumination of a surface tends to darken and permanently fix previously condensed contaminants onto the surface. When a surface is not exposed to ultraviolet light, the contamination is not permanent and can be removed by heating. Heating the surface above 200 K tends to result in a very short residence time for molecules on the surface. The largest amount of contaminants present in the surrounding spacecraft/instrument atmosphere occurs during the first few months of the mission. An important process to consider during initial on-orbit outgassing is shading sensitive surfaces from sunlight exposure. Shading can be accomplished using deployable or reclosable covers. Some radiant coolers contain covers as a result of envelope constraints required during launch. Covers actually reduce the amount of electrical power needed for outgassing or allow a higher outgas temperature to be achieved. In addition, reclosable covers also prevent the cooler from becoming a solar furnace during initial orbit acquisition or upon entering safe or survival modes. No matter what kind of clean-room environment and procedures are used to assemble radiant coolers, cleaning of external surfaces will be required upon completion of assembly, systemlevel testing, and integration with the launch vehicle. Sensitive surfaces (e.g., emitter surfaces, OSR tiles, specular shields) should be cleaned as close as possible to the launch date to ensure optimal system performance. Particulate and molecular contaminants act as scattering centers for incident sunlight. When scatter centers reside on specular shield surfaces visible from the cold stages (typically stages below 160 K), they produce an additional thermal load not normally accounted for in the thermal balance of the stage. Fortunately, the measures used to control condensation and polymerization of contaminants also serve to control sunlight scatter. Cleaning surfaces as close as possible to the launch date and maintaining surfaces at temperatures that preclude condensation reduce the amount of scatter. When specular shields are subject to direct solar illumination, the shield configuration should be designed with high scatter angles to the cold stages. Designing the shields in such a manner minimizes the thermal load on cold stages caused by scattered sunlight. For the purposes of design, a single limit can be allocated for the combination of particulate and molecular contaminants. The contamination limit defined by scatter prior to polymerization is much lower than the limit imposed after polymerization occurs; as a consequence, it is possible to determine a combined limit on particulate and molecular contamination in terms of the scatter that limit produces. This limit is specified as a scatter

30 coefficient (Bidirectional Reflectance Distribution Function, BRDF) for given incidence and scatter angles and can also be related to a cleanliness level. Tribble et al. [5.10] contains excellent descriptions of contaminants and their effects on thermal control surfaces. [5.10] A. C. Tribble et al., "Contamination Control Engineering Design Guidelines for the Aerospace Community," NASA Contractor Report 4740, May Radiant Cooler Sizing Guidelines To generate a successful design for a radiant cooler or cryogenic radiator, one must determine the configuration or geometry of the specular shield for the patch and radiator emitter stages. The geometry of the shielding surface is impacted by limitations on the view to cold space as defined by the Earth, sun, and spacecraft/instrument structural interfaces. In general, the aspect ratio of the patch or radiator emitter surface (length/width) needs to be constrained to a reasonable value. This aspect ratio is often influenced by an ambient optical interface external to the radiant cooler. A broad range of near-optimum configurations is usually available for a firststage emitter surface, and a specific choice does not dramatically affect the firststage temperature. For coolers exposed to direct sunlight, first-stage emitter surfaces are often finished in OSR tiles for GEO applications and white paint for LEO applications. Once the initial geometry of the radiant cooler is determined, scaling factors need to be established. The conceptual development of a radiant cooler is performed using an iterative process. The designer must often change the geometry to fit the radiant cooler within the allotted envelope of the instrument. One way of performing this is to first identify which inputs are fixed and which scale with cooler size. Generally, the detector dissipation, electrical connections, and optical port inputs are fixed loads and are not impacted by cooler size. Inputs such as structural supports, radiative insulation, and shield loads scale with cooler size. Scaling of the radiant cooler size is often accomplished using a ratio of conductance or radiative coupling as a function of emitter area, insulation area, or mass. To a first order, once a conductive coupling is initially determined, scaling this coupling according to emitter area has proven to be adequate. All external inputs to the radiant cooler should be expressed in terms of power per unit area absorbed in the surface in question from all external sources. When using shields that completely surround the emitter surface, the designer can divide external inputs between the shield mouth (entrance into specular shield cavity and cold stages) and the first-stage emitter area. A first-order estimate of the radiative coupling between the shield walls and cold emitter surfaces can also be determined. These couplings are used in thermal balance equations to determine thermal loads on the patch (cold) and radiator (intermediate) stages of the radiant cooler. An initial understanding of the coupling between warm shield walls and the cold stages is important for determining whether this input is the dominant thermal load on these stages. Usually, a significant change in the shield design is necessary to significantly impact the shield-to-emitter coupling.

31 Interstage support conductance can be scaled on a per-area basis, as mentioned previously. Typically, the first stage of the radiant cooler is scaled using a sum of areas including the emitter area, the shield wall area, and the first-stage housing area. The first-stage housing area can be estimated by multiplying the sum of cold-stage emitter areas (second-and third-stage emitter areas added together) by 1.2. Interstage support conductance for an intermediate stage is determined by adding the emitter areas of cold stages. The sum of cold stages is used because the supports mounted to an intermediate stage support all other cold stages. For the final cold stage, structural supports can be scaled using the emitter area of the cold stage, because this is the only stage supported from these supports. Interstage radiative couplings are also scaled on a per-unit-area basis similar to the interstage support conductance. In the case of a cooled first stage, it is important to include the insulation area from the emitter surface, shield walls, and vacuum-housing surface area. In the event the first-stage emitter and specular shield include external radiative insulation, only the vacuum-housing area needs to be included. For intermediate stages, one must multiply the sum of all cold-stage and the intermediate-stage emitter areas by a small factor on the order of 1.2. This factor accounts for side surfaces and the fact that the intermediate stage surrounds nested cold stages (separated by a gap). The insulation area of the final cold stage is determined by multiplying the cold-stage emitter area by a small factor (1.2) to account for side surfaces and the gap between the cold stage and the surrounding warm stage. Iteration of the cooler size is often required to increase or decrease radiant cooler size based upon instrument envelopes and mandatory cooling requirements for each stage. As the cooler size changes, it may be necessary to update wire conductance estimates if wire routing lengths have changed. Also, it may be necessary to recalculate the radiative coupling of shields that surround interstage structural supports or wires if the size of the cooler changed significantly. The iteration of radiant cooler size may often be limited to reapportioning emitter areas to balance thermal margins on the various stages. During the initial phase of radiant cooler design, parametric studies will often determine how the temperature of stages depends upon specific parameters. For example, the temperature of a cold stage (patch) is more sensitive to changes in the temperature of the adjacent stage than to the first-stage temperature. Studies will also reveal how cold-stage temperature depends upon shield mouth or adjacent emitter area size. These studies may indicate a modification to the geometry that is beneficial to cooler performance. The final step in iterating the size of the radiant cooler is to check volume constraints imposed by the instrument or spacecraft. The radiant cooler emitter needs to include sufficient area to package detectors and adjustment mechanisms and sufficient aperture in the optical port elements. Discussions with the manufacturing personnel responsible for assembly of the radiant cooler may also lead to changes to the configuration that result in a design that is easier to build and repair. Design Example: Three-Stage Radiant Cooler, Geosynchronous Orbit The Geostationary Operational Environmental Satellite (GOES) includes both imager and sounder instruments. The imager instrument, which consists of five spectral channels and a two-axis scanning radiometer, provides imagery and radiometric information on Earth's

32 surface and cloud cover. The radiant cooler designed for the GOES-M instrument consists of three stages and provides the capability to cool four IR channels (Fig. 5.16). Figure 5.16: GOES-M Imager radiant cooler configuration. The first stage of the GOES-M radiant cooler is cooled to approximately 235 K during the summer season and 170 K during the winter season at beginning-oflife. Over the five-year operational life of the radiant cooler, the first-stage temperature will not exceed 254 K. The radiant cooler is mounted to the imager instrument maintained at approximately K. During the summer season, the first-stage emitter and the specular shield attached to the first stage are exposed to direct sunlight as the sun is inclined 23.5 deg above the plane of the emitter surface. OSR tiles are used on this surface to minimize absorption of direct solar energy. Heat conducted into the first stage is attributed to structural supports attaching the first stage to the instrument, wires routed to the ambient instrument, and a window isolator. The purpose of the window isolator is to maintain an optical element attached to the first stage at or above the instrument's ambient temperature. This is required to preclude the deposition of contaminants on this window. Vacuum Housing (First Stage) Equation (5.13) is the thermal balance equation for the first stage. The first-stage temperature is determined by solving Eq. (5.13) for T v (using the terms in Table 5.11), which results in a first-stage temperature of K. Heat load inputs from each thermal balance term are given in the rightmost column of Table 5.11; these values clearly show that the thermal load on the first stage is dominated by the input from direct sunlight that illuminates the first-stage emitter and shield during the summer season. Slight changes in conductive or radiative insulation terms will not significantly alter the first-stage temperature. (5.13) Get MathML Table 5.11: Thermal Balance, First Stage of the GOES-M Radiant Cooler

33 Input Thermal Balance Expression [a] Thermal Load (W) Conductance Q k = (T f T v ) 2.86 (9.8% of load) Radiative insulation Q i = (T f 4 T v 4 ) (3.3% of load) Direct sun Q s = W (86.9% of load) Output: firststage emitter Q e = (T v ΔT e ) (total load emitted to space) [a] T f = main instrument temperature (= K); T v = first-stage temperature or vacuum housing temperature (K); Δ T e = temperature drop from the first stage housing the emitter surface located at plane of the shield mouth (= 4.3 K). Radiator (Second Stage) The second-stage emitter of the GOES-M radiant cooler is mounted coplanar with the thirdstage patch. The second-stage radiator that surrounds the patch is uncontrolled and achieves an intermediate temperature of K during the summer season. The shield configuration mounted to the first stage is designed to preclude sunlight from hitting the radiator or patch stages directly or by reflection in the shield walls. In addition, both the radiator and patch emitters have a view to an astromast and solar sail mounted on the north face of the spacecraft. The second stage cools optical elements that transmit the incoming scene to the detectors mounted to the third stage. Equation (5.14) is the thermal balance equation for the second-stage radiator. The term Q a+b refers to the thermal load on the second- and third-stage emitter areas from the astromast and solar sail. Results from the thermal balance calculation are shown in Table The dominant thermal loads on the second stage (64%) are the conductive and radiative insulation terms. If decreasing the temperature of the radiator stage is desired to improve the performance of the third stage by reducing the parasitic thermal load, then one should consider reduction of the heat load caused by the radiative and conductive loads. (5.14) Get MathML Table 5.12: Thermal Balance, Second Stage (Radiator) of the GOES-M Radiant Cooler Input Thermal Balance Expression [a] Therma l Load (mw) Conductance Q k = (T v T r ) (37.0% of load)

34 Radiative insulation Q i = (T v 4 T r 4 ) (37.1% of load) Shield wall Q w = (T w 4 T 4 r ) (5.5% of load) Optical port load Q o = T f T v T r (7.1% of load) Astromast/sail Q a+b = 46.2 mw 46.2 (13.3% of load) Output: second-stage emitter (radiator) Q r = T r 4 = ε A r ς T r (total load emitted to space) [a] T f = ambient instrument temperature = K; T v = first-stage temperature = K; T r = second-stage (radiator) temperature = K; T w = shield wall temperature = T v K = K; ε = 0.97 (black-painted honeycomb surface); A r = cm 2. Patch (Third Stage) All four of the detectors for the IR channels are mounted on the patch stage, and the total power dissipated from these devices is 4 mw. Openings for the detector result in an optical port load that is incident on the third stage. This input results from radiation exchange with the other stages of the radiant cooler as well as the ambient instrument. Specular shield walls surrounding the patch and radiator stages are cooled to approximately K; this results in a radiative coupling to the cold stage. Equation (5.15) is the thermal balance equation for the patch. (5.15) Get MathML The thermal balance for the patch stage is shown in Table The largest single heat input is the astromast and solar sail load. The next highest load results from the shield walls. The biggest improvement in radiant cooler performance would be, potentially, the reduction of both shield wall and astromast/sail thermal loads. Table 5.13: Thermal Balance, Third Stage (Patch) of the GOES-M Radiant Cooler Input Thermal Balance Expression [a] Thermal Load (mw) Conductance Q k = (T r T p ) (9.7% of load) Radiative insulation Q i = (T r 4 T p 4 ) 6.91 (5.1% of load)

35 Table 5.13: Thermal Balance, Third Stage (Patch) of the GOES-M Radiant Cooler Input Thermal Balance Expression [a] Thermal Load (mw) Shield wall Q w = (T w 4 T p 4 ) (32.1% of load) Optical port load Q o = T f T v T r T p (1.5% of load) Detector dissipation Q j = 4 mw 4.0 (2.9% of load) Astromast/sail Q a+b = mw (48.7% of load) Output: third-stage emitter (patch) Q p = T p 4 = ε A p ς T p (total load emitted to space) [a] T f = ambient instrument temperature = K; T v = first-stage temperature = K; T r = second-stage (radiator) temperature = K; T p = third-stage (patch) temperature (uncontrolled) = 96.2 K; T w = shield wall temperature = T v K = K; ε = 0.97 (black-painted honeycomb emitter surface); A p = patch emitter area = cm 2. The uncontrolled temperature for the patch stage during the summer season at beginning-oflife is 96.2 K and 99.6 K at end-of-life. To maintain thermal control of the patch stage, the control point should be higher than the temperature predicted at end-of-life. Using MIL-STD- 1540C as a guideline, one should consider, at these temperature levels, a thermal margin of 9 K prior to qualification of a radiant cooler design. The minimum recommended thermal margin after completion of qualification testing is 5 K. Applying these guidelines to the patch stage of the GOES-M radiant cooler implies the minimum control point for the patch stage is 99.6 K + 5 K, or approximately 105 K. The total power emitted to space for a 105 K patch temperature is 193 mw, which is 57 mw more than will be radiated to space by the uncontrolled patch at 99.6 K. This means that approximately 57 mw of heater power must be applied to the third-stage patch during the beginning-of-life summer season to maintain a control point of 105 K. Design Example: Two-Stage Radiant Cooler, Low Earth Orbit The HIRS/3 radiant cooler provides cryogenic cooling for two IR detectors mounted to the patch stage. This particular radiant cooler is designed for a sunsynchronous orbit at an altitude of 833 km. The vacuum housing stage is maintained at instrument ambient temperature and is not cooled. As a result, the only cooled stages are the radiator and patch. Sunshades are used to shadow the instrument at orbit-normal-to-sun angles greater than 68 deg. Once the initial on-orbit outgassing period is completed, the Earth shield is deployed and remains open for the duration of the mission. The Earth shield is attached directly to the radiator housing. Earth shield surfaces that face emitter surfaces are specular, and the surfaces facing Earth are covered with silver Teflon. A portion of the radiator is exposed to Earth loads and direct sunlight, because side extensions on the Earth shield were only sized to completely block the patch emitter from direct Earth and sun exposure. An exploded view of the HIRS/3 radiant cooler is shown in Fig

36 Figure 5.17: HIRS/3 radiant cooler configuration. Radiator Thermal Balance The steady-state thermal balance for the radiator is described by Eq. (5.16). Solving this equation yields an uncontrolled radiator temperature of K. (5.16) Get MathML where Q r is power emitted to space from the radiator (= ε ς A r T radiator 4 ), Qe is direct input from the sun, Qd is direct input from Earth, Q k is input from structural and electrical connections, Q i is interstage radiative exchange, Q c is radiative and conductive input from the Earth shield cover, and Q o is radiative load from optical ports. For calculation of Q r, ε is emissivity of the emitter (= 0.97, black-painted honeycomb), and A r is radiator emitter area (= cm 2 ). The deployable Earth shield attaches directly to the radiator housing (Fig. 5.17). The external cover facing Earth is thermally isolated from the radiator stage by means of G-10 supports, and gold surfaces are used to reduce the radiative exchange with the radiator housing. As a result, the external cover temperature, T c, achieves an equilibrium temperature of K for an orbit beta angle of 80 deg. This implies that the specular shield surfaces facing the radiator and patch emitters and the emitters themselves are at the same temperature, and no radiation exchange takes place between these surfaces. Thermal balance results for the radiator stage are shown in Table 5.14.