10 . SPACECRAFJ T VOL1 . 23NO , Droplet Radiator Systems for Spacecraft Thermal Control Robert T. Taussig* Spectra Technology, Incorporated,^Bellevue, Washington and MattickT. A. J University of Washington, Seattle, Washington Liquid-droplet radiators (LDRs) can be as much as 5 to 10 times lighter than advanced heat pipe radiators. They are virtually immune to puncture, stow in a small volume, and are easily deployed. Systems studies show that they optimize in the 10- to 100-MW size for liquid lithium, tin, and aluminum and at several hundred kilowatts for NaK and vacuum oils. Larger radiators can be constructed from modules of these sizes. Power systems reoptimize lighmase R th tr sLD lowe d operatfo K 0 r10 rejec t ea t hea5 o t temperature3 e b y ma d san times lighter than those using conventional radiators. Recent collector tests have revealed a splash-free regime of operation promising high collection efficiencies testR spacn si LD . e shoul feasible d b neae th rn ei future . Nomenclature Introduction A = radiator sheet area (one side) MALL liquid droplets offe vera r y lightweigh rejeco t y ttwa Ar = radiator aspect ratio aste heat from space power systems becaus theif eo r high Bon= d numbe o f rotatinB o r g collector film surface area per unit mass. Lightweight radiators will become c = droplet liquid specific heat a necessity as the need for higher powers in space increases. C = evaporation rate function Missionundew no re consideratiosar n that will require rejec- d = separation distance between adjacent droplet tio f megawattno f wasto s e continuoua hea n o t s basisd an , streams future missions may need to reject hundreds to thousands of E3 = elliptic integral megawatts. The very feasibility of such missions is brought in- Froude= Fnumber f rotatino r g collector film doubo t t because conventional radiatoro heavo to to d e yan sar lengt= f radiatoho Lr r sheet difficult to deploy or assemble in space. drople= tm sheee t evaporation ratunir epe t area Liquid-droplet radiators (LDRs) have been investigatea y db thy = droplet sheet mass flow rate numbe authorsf ro havd 1"an 5 numbee a distinctivf ro e advan- M - total mass of droplet sheet radiator tage thin si s context: mas= f dropletso M ffligh n i s t 1) The radiating surface is invulnerable to puncture by P, Pr = radiated thermal power small particles and by directed energy weapons. r = droplet radius 2) They are lightweight because very little fluid mass is re- Re = Reynolds number of rotating collector film quired for a given radiating area and armoring against punc- drople= t shee s t thickness t requiredturno s ei . T0 = radiator inlet temperature 3) They can be deployed easily by using a mast that expands radiato= rT joutle t temperature to its full length in orbit. Te = effective mean radiator temperature 4) They can be stowed in a small volume, such as a canister ^peak = Peak thermal cycle temperature of liquid and a collapsible structure. drople= t velocitu y 5) The operatn ylona ca r gfo e perio f timdo - e oveap n a r ur = radial flow velocity of rotating collector film propriate temperature interval where evaporative losses are Ue = tip velocity of rotating collector minimal. w = droplet sheet width at droplet generator Droplet radiators are still in the conceptual stage of develop- We = relative droplet Weber number ment. Initial experiments exploring the formation of droplets, evaporate= 18d mass fraction splashing in simulated zero-G conditions, and radiative cool- e0 = intrinsic emissivity of droplet liquid ing from selected droplet materials have been carried outd an , t> €sheet = mean hemispherical emissivity of droplet sheet an investigation of droplet collector technology, described X = separation distance between droplets in a single below, has recently been completed. Preliminary systems stream analysis of the droplet radiator has accompanied these in- drople= t liquip d mass density vestigation guido st experimentae eth l endeavor modeo t d slan 2 pa = droplet sheet area density (kg/m ) the performance (e.g., total system weight, peak power, a = Stefan-Boltzmann constant radiator effectiveness) of various configurations. The systems T> Tmeashee= tn optical dept f dropleho t sheet model include majose eacth f hro radiator components, such optica= l dept70 droplef ho t shee t dropleta t generator as pumps, nozzle arrays, collectors structured an , s thae ar t radiato= rT Llifetim e needed to operate this type of radiator. A description of the angula= r velocitco f rotatinyo g collector systems model and a summary of the major conclusions of that analysis are discussed here. Presented as Paper 84-1797 at the AIAA 19th Thermophysics Con- ference, Snowmass , JunCO ,e 25-28, 1984; submitted Oct , 19841 . ; ConcepR LD e tTh revision received April 1, 1985. Copyright © American Institute of Mattick and Hertzberg have described the basic radiator Aeronautics and Astronautics, Inc., 1985. All rights reserved. 1 2 * Directo f Energo r y Technology. Member AIAA. physics of the liquid-droplet radiator. ' In their model the tFormerly Mathematical Sciences Northwest, Inc. droplets form a thin sheet with variable optical thickness, ^Research Associate Professor, Aeronautics & Astronautics. dependin droplee th n go t number density, droplet sized an , JAN.-FEB. 1986 RADIATOR SYSTEM SPACECRAFR SFO T THERMAL CONTROL 11 sheet thickness. The radiative transfer equation was solved LDR Systems Model assuming isotropic scattering and a constant temperature from preliminarA y systems mode triangulaa f o l r liquid droplet top to bottom of the sheet. The only temperature variation sheet radiator has been developed which incorporates in- considered was in the direction of the droplet velocity due to dividual models of each of the major components and radiative coolin collectore routn gth e o et . Figur showe1 sa calculates self-consistentl liquie yth d flow rate, pressured an , triangular droplet sheet radiator wit rotatinha g collectot a r component mass at each station in the system. As a conse- the focal point. quence e componenth , t sized operatinan s g conditione ar s extreme th t A dropleew limilo f o tt densit vera r yy(o thi n matched throughout the system. sheet), the droplets radiate their heat independently of each initiae Th l radiator configuratio majod an n r components other; this is the lightest-weight version of the droplet radiator showe ar Fign ni heae . 3Th .t exchange t beeno ns incorha r - but als largese oth arean i tr hig Fo .h droplet densities- op e th , porate modee th n di l sinc t dependei specifie th n so c mission tical thickness increases and radiation from the droplets near powed an r system used. the center of the sheet is occluded by neighboring droplets so e tharadiativth t e effectivenes f o individuas l droplets Droplet Sheet Model .decreases. However equivalene th , t emissivit droplee th f yo t The main assumptions underlying the droplet sheet calcula- sheet increases so that the required sheet area decreases. For tion thae sar t 1) materia loss li t primarily through evaporation optical depths much greate poina , r 5 diminishinf tha tr o o n4 g aimind an g inaccuracies radiatoe th ) 2 ; r retains s 100it f %o return s reachei s d wher e sheeeth t becomes heavier without load capacit givea r yfo n lifetime Tliquie L th (years) ) d3 d an ; real gain in emissivity. The optical depth r is defined as droplet temperatur collectoe th t ea vers i r y clos freezingo et . T=irr2S/(d2\). In the case of liquid metal droplets, the sheet The input parameter e totaar s l radiated powe r pea(o r k emissivit largee b n ry ca tha intrinsie nth c material emissivity temperature), droplet material properties (i.e., density, sur- (i.e., infraree 0. 0.1o 1th t near-infrared n 5i an d d spectrum) face tension, viscosity, specific heat, and intrinsic emissivity), because radiation from the interior droplets escapes via multi- optica le sheetth dept f ,o h sheet aspect ratio (i.e.,= ple reflections from neighboring droplets case f th oils eo n I ., width/length), radiator lifetime, aiming accuracy, droplet the droplet emissivity is already high (i.e., 0.5 to 0.85) so that radius, and number of radiators operating in parallel. If the even though radiation fro interioe mth occludeds ri sheee th , t total power radiated and number of parallel radiators are in- higa stils h lha effectiv e intrinsiemissivite th o t e c yemissivdu - put data, a separate calculation must be made of the peak droplee th itf yo t material. (inlet) temperatur e dropletsth f e evaporatioo e Th . n rate basiconcepe R Th cLD tformatio e relieth n so f uniforno m depend radiatoe th n so r temperature opticae th n o l deptd san h droplets using technolog printerst y je relate k in o d.t Uniform- sheete o th f- 2E :1 m3[ (ee= 0f)]C( 7^,7^), wher factoe eth n i r itf dropleyo t sizvelocitied ean s ensures equal cooling during square brackets represent e reabsorptioth s f evaporateo n d droplet travel. Although droplet e outeth rn e o sedgth f o e material by neighboring droplets in the sheet. The factor sheet will cool faster than inside e thosth preliminar r n eo ou , y r( 0C , 7\) increases rapidly with temperatur dependd ean n so calculations indicate that this effec modests i t . Analysie th f so the droplet material chosen.8 Each liquid can be used only electric charge induce droplete space th th n do y e sb plasm a over a specific range of peak temperatures before evaporation and by solar photon bombardment show that deflection of severely limits the lifetime of the radiator.