This experiment is aimed at computing the average face temperatures of small satellites. It is divided into two parts. To conduct the analysis it is important to understand the environment satellites operate in. The external loads incident on the satellite include solar radiaition from the sun, radiation to outer space, heat dissipation terms from the electronic components. Apart from these the faces radiate to each other and conduction also takes place. All the loads except the solar radiation from the sun can be calculated using simple formulae. The focus of the first part of the experiment is to estimate these loads. The second part actually computes the face average temperatures for the given orbit and satellite parameters. Reference values user are that of Pratham- The student satellite project of IIT Bombay for the convenience of the user.

The first part of the experiment aims at computing the solar radiaiton incident on the satellite for typical orbits. The inputs from the user include the altitude of the orbit, measured from the surface of the earth in kms, and the inclination of the orbit in degrees. In case of an equitorial orbit the inclination is the angle made by the plane of the orbit and the equitorial plane. In case of the polar orbit, it is the angle between the plane of the orbit and the polar plane. Using these parameters the position of the satellite can be obtained as a function of time. The orientation of the satellite is another parameter that needs to be determined in order to compute the solar radiaiton incident on the satellite. For simplicity, it has been assumed that the satellite is always oriented such that one of the faces has its normal aligned with the tangent of the satellite and one face has its normal aligned with the normal to the orbit in the plane of the orbit. The nomenclature of the faces are:

  • Nadir Side – Side pointing towards Earth

  • Zenith Side – Side pointing away from Earth

  • Leading Side – Side pointing towards the direction of Velocity

  • Lagging Side – Side pointing away from the direction of Velocity

  • Sun Side – Side that always faces the Sun

  • Antisun Side – Side that never faces the Sun

With these assumptions, the normals of all the faces can be determined and the angle made by the faces with the solar rays can be determined and hence the solar radiation can be estimated. The Solar flux constant which the solar radiation incident on a square meter of area is assumed to be 1353 W/m2 which is a very good approximation from low earth orbits. The effect of shadowing has also been accounted for. Shadowing means that the Satellite is eclipsed by the Earth.

The user can download this data and also view it in a graphical format. An animation is provided which helps in visualizing the orbit in space and also gives an estimation of the relative orientation of faces. With this all the load incident on the satellite are known.

The second part of the experiment aims at computing the face average temperatures for a particular orbit and given satellite parameters. This sections is further divided into the following sub-sections:

  • Geometry

  • Meshing

  • Material Properties

  • Loads

  • Numerical Method

  • Results

Geometry:
Typical micro satellites are cubes of the size 10 cm. This code is meant to compute average face temperatures for cube satellites only. For simplicity, the size of the satellite in can be modified in steps on 5 cms and can go upto only 30 cms. Pratham is a cube satellite of size approximately 25 cms. The constraint of 5 cms shall be explained in the meshing section. The size cannot exceed 30 cms because it increases the computation time beyond 15 mins. The code automatically generates 6 faces of the satellite in the form of 2-D plates having a finite thickness which can be inputted by the user. The thickness of Pratham is 3 mm. Small satellites generally have a thickness to size ratio of the order of 100. This code only computes the temperatures of an empty cube. It does not have any solar panels. Though a very crude approximation, it helps one understand the effect of changing various parameters on the temperatures of the faces. These parametric studies can used as a tool later on in the design stages of the thermals sub-system of satellites.

Meshing:
The code automatically generates a orthogonal hex mesh. The size of each element is 5 cm x 5 cm x thickness. It is assumed that properties do not across the thickness of the satellite. The size of the element puts a constraint on the size of the satellite. It is preferable to choose the largest possible mesh size in order to minimize the computation time. But as the mesh size is increased the accuracy of the result goes on decreasing. The value of 5 cms is not an optimized value but its just for convenience considering the typical size of cube satellites. Satisfactory results have been obtained for such coarse meshes.

Material Properties:
Next comes definfing the material properties. The relevant properties are the Conductivity of the material, K(W/m-K), Specific heat capacity C,(J/kg-K) and the density of the material, r, (kg/m3). The typical values for aluminium 6061 which is the material used for pratham are 200, 800 and 2000 approximately. The material is assumed to be isotropic and the satellite is assumed to be made of the same material.

One also needs to specify the surface properties for the determination of all kinds of radiation fluxes. External surface absorptivity(alpha-e) and emissivity(eplison-e) are required for computing the exact loads on the satellite. Internal surface absorptivity(alpha-i) and emissivity(epsilon-i) are required to compute the internal radiation terms. All the four mentioned values lie between 0 and 1.

The internal surface for pratham has been planned to be painted black which is alpha-i=0.8 and epsilon-i=0.8. The external surface properties of the chosen material are, alpha-e=0.2 and epsilon-e=0.031. They are dependent on the manufacturing processes used to manufacture the material.

Loads:
The default loads assumed to be incident on the satellite are:

  • Solar Radiation incident on the satellite

  • Conduction

  • Radiation to free space

  • Internal Radiation

  • Initial Temperature

The initial temperature of the satellite is assumed to be 300 K. Apart from that a functionality is provided so that the user can enter a average flux value (W/m2) which is to account for the heat dissipation for all the electronic components. The user can specify one such value for each face.

Numerical Method:
The problem at hand is a coupled transient conduction radiation problem. The numerical method implemented is a finite difference method. The derivatives have been approximated to the first order. Conduction has also been modeled by thier corresponding first order numerical derivatives. All the other loads have been treated as source terms in the equation. The time step of the simulation is chosen to be 5 seconds .It has been obseved that the numerical method is stable for the given mesh size and a range of material properties. Non-physical values of material properties may lead to arbitary results. The code computes the temperatures of all elements for 5 cycles.

Results:
The results obtained have been averaged face wise to obtain the face average temperatures as a function time. For convenience, the face average values have been exported for every 30 seconds only. These can be viewed in a graphical form.

In case any such problem is encountered, do mail the input data to manasrachh@aero.iitb.ac.in.