Mission Design for the CubeSat OUFTI-1
Mission Design for the CubeSat OUFTI-1 Mission Design for the CubeSat OUFTI-1
CHAPTER 9We have now all the parameters to connect the nodes: we only need thesurfaces parameters and the conductivity.If the structure’s and coating’s parameters are fixed, the solar cells opticalparameters vary as a function of the temperature.The goal of a solar cell is in fact to collect the sun’s flux and to convert it intoelectrical power: not all the energy collected becomes heat. The absorptionfactor of a solar cell varies following the relation:α(T ) = α 0 (1 − η(T )) (9.14)where α 0 is the absorption at 28 ◦ C and η(T ) the efficiency.This formula shows an important conclusion: higher is the efficiency, and so thepower produced, lower is the percent of collected energy converted into heat.We have so a double interest in having an efficiency as higher as possible.Then, the efficiency varies in function of temperature:η(T ) = η 0 + dηdT (T − 28◦ C) (9.15)where η 0 is the efficiency at 28 ◦ C.As the efficiency is defined as the maximum percent of incident power convertedinto electrical energy (see formula 8.10 ), we define its derivate respectto temperature as:dηdT = ddT( )Pmax= 1 ()dI maxV maxC s S C s S dT+ I dV maxmaxdT(9.16)Using the values indicated in table 8.2, we can calculate the absorption factorof the solar cells.Concerning the infrared emissivity ɛ, we need to point out that each solarcell is usually covered by a transparent tape and by a so-called cover glass whichis transparent for the visible wavelength but determine the infrared emissivity:ɛ is usually between 0.8 and 0.85. We used ɛ = 0.8.The dimension of solar cells are indicated in table 8.1.Concerning the structure, it’s an aluminium alloy with the following properties:Table 9.3: Structure propertiesConductivity k [ W mK ] 138Thickness [mm] 1.27Galli Stefania 92 University of Liège
CHAPTER 9.THERMAL-CONTROL SYSTEM9.3.3 Hot and cold caseWe are dealing with a simplified model: we are not expecting to have a detailedthermal description of our CubeSat. The goal of this preliminary study is toidentify the maximum and minimum temperatures reached during lifetime inorder to avoid the overpass of the imposed limits.We identify therefore three possible cases:• the hot case: the satellite is in sunlight and the solar arrays do not produceany power but only cumulate solar heat flux. The solar flux is injected ona face and the absorption coefficient is α 0 as the efficiency is null.• the operating case: the satellite is in sunlight and the solar arrays areproviding the necessary power. The payload is on and we need to radiate0.5 W corresponding to the losses in the communication system convertedinto heat. In this case, the absorption factor of solar cells needs to beupdated as a function of the solar cell temperature• the cold case: the satellite is in eclipse and the payload is off. In this casethe solution seems to be trivial: the equilibrium temperature is practicallythe T cold but it doesn’t respect the reality. Furthermore in this case thehypothesis of steady-state cannot be applied integrally. We added thereforea flux of 847W/m2, which is the solar flux weighed on the averagetime of eclipse.For the operating case, we needed to add a worksheet to Thermal-Excel inorder to update the solar cells properties as a function their temperatures.9.4 Thermal results for OUFTI-1Once decided the kind of model to study and identified the material properties,we passes to the implementation into the software Thermal-Excel.As above mentioned, a starting guess temperature is demanded and for eachcase we calculated it as explained in section 9.2 respecting the characteristicsof each case.At the beginning, we had some problems as the final results depended on thestarting temperature, which is impossible for the static case. With an accuratereflection we find out the reason: the standard algorithm used by the softwarehas a really slow convergence when the number of radiative exchange is importantrespect to the conductive. As the criterion of convergence is the differencebetween successive temperatures, the software thought to have converged evenif it was not true. We needed therefore to strongly reduce the convergence criterionin order to have the good solution.Galli Stefania 93 University of Liège
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CHAPTER 9We have now all <strong>the</strong> parameters to connect <strong>the</strong> nodes: we only need <strong>the</strong>surfaces parameters and <strong>the</strong> conductivity.If <strong>the</strong> structure’s and coating’s parameters are fixed, <strong>the</strong> solar cells opticalparameters vary as a function of <strong>the</strong> temperature.The goal of a solar cell is in fact to collect <strong>the</strong> sun’s flux and to convert it intoelectrical power: not all <strong>the</strong> energy collected becomes heat. The absorptionfactor of a solar cell varies following <strong>the</strong> relation:α(T ) = α 0 (1 − η(T )) (9.14)where α 0 is <strong>the</strong> absorption at 28 ◦ C and η(T ) <strong>the</strong> efficiency.This <strong>for</strong>mula shows an important conclusion: higher is <strong>the</strong> efficiency, and so <strong>the</strong>power produced, lower is <strong>the</strong> percent of collected energy converted into heat.We have so a double interest in having an efficiency as higher as possible.Then, <strong>the</strong> efficiency varies in function of temperature:η(T ) = η 0 + dηdT (T − 28◦ C) (9.15)where η 0 is <strong>the</strong> efficiency at 28 ◦ C.As <strong>the</strong> efficiency is defined as <strong>the</strong> maximum percent of incident power convertedinto electrical energy (see <strong>for</strong>mula 8.10 ), we define its derivate respectto temperature as:dηdT = ddT( )Pmax= 1 ()dI maxV maxC s S C s S dT+ I dV maxmaxdT(9.16)Using <strong>the</strong> values indicated in table 8.2, we can calculate <strong>the</strong> absorption factorof <strong>the</strong> solar cells.Concerning <strong>the</strong> infrared emissivity ɛ, we need to point out that each solarcell is usually covered by a transparent tape and by a so-called cover glass whichis transparent <strong>for</strong> <strong>the</strong> visible wavelength but determine <strong>the</strong> infrared emissivity:ɛ is usually between 0.8 and 0.85. We used ɛ = 0.8.The dimension of solar cells are indicated in table 8.1.Concerning <strong>the</strong> structure, it’s an aluminium alloy with <strong>the</strong> following properties:Table 9.3: Structure propertiesConductivity k [ W mK ] 138Thickness [mm] 1.27Galli Stefania 92 University of Liège