PH508: Spacecraft Power generation

Solar cells, fuel cells and RTGs.

Payload mass, mp = 5 tons ms1 = 140 tons (given in table) ms2 = 35 tons “ ms3 = 10 tons “ mf1 = 2160 tons “ mf2 = 420 tons “ mf3 = 100 tons “

mo1 =ms1 + mf1 + ms2 + mf2 + ms3 + mf3 + mp

=2870 tons

mo2 =ms2 + mf2 + ms3 + mf3 + mp

=570 tons

mo3 =ms3 + mf3 + mp

=115 tons

Homework – Week 15, Q2, part 1.

Now calculate ‘R’ for each stage

Recall:

∴

Homework – Week 15, Q2, part 1.

fioi

oii mm

mR

67.7110115

115

80.3420570

570

04.421602870

2870

3

2

1

R

R

R

Now we have R1, R2, and R3 can calculate the final rocket velocity, vfinal via:

Homework – Week 15, Q2, part 1.

1-

332211

s km 3.17

66.874.524.3

67.7ln25.480.3ln10.404.4ln32.2

lnlnln

RvRvRvv eeefinal

This wasn’t easy – my apologies. From definition of R we have:

Homework – Week 15, Q2, part 2.

6

25.410.432.2

16

25.410.432.2

25.410.432.2

321

332211

321

10886.810

110

145

565

705

2865

10

110

145

565

705

2865ln16

10

110ln

145

565ln

705

2865ln16

10

110ln25.4

145

565ln10.4

705

2865ln32.216

ln25.4ln10.4ln32.216

0.16lnlnln

10

110,

145

565,

705

2865

p

p

p

p

p

p

p

p

p

p

p

p

p

p

p

p

p

p

p

p

p

p

p

p

eeefinal

p

p

p

p

p

p

m

m

m

m

m

me

m

m

m

m

m

m

m

m

m

m

m

m

m

m

m

m

m

m

RRR

RvRvRvv

m

mR

m

mR

m

mR

ANALYTICALLY INTRACTABLE!?!?

Homework – Week 15, Q2, part 2: graphical solution

Solve by plotting, vfinal versus mp

PH508: Spacecraft Power generation

Solar cells, fuel cells and RTGs.

The Glast Satellite, source NASA/Sonoma State University (Aurore Simonnet) 

Solar Cells: I

These use solar radiant energy and convert it directly into electricity, via the photovoltaic effect.

An array is made up of thousands of individual cells (2 cm x 4 cm typically), connected in series to provide DC power (28 V typical, 120 V can be found today).

Power levels can be in range of a few Watts to 100’s of kW.

An individual cell is just a semiconductor p-n junction.

Solar cells: II

Solar Cells: IV

Solar cells: IISolar panels on ISS

Silicon was typical, today (Gallium Arsenide) GaAs has been used but is not universal.

 Silicon is doped with boron to produce p-type (electron deficient) material and phosphorous for n-type (electron excess) material.

In dark conditions an equilibrium is reached where no significant current flows. If illuminated, by photons of sufficient energy, electron-hole pairs are created, these flow creating a potential difference across the device.

Solar cells: V

Solar cells: III

Schematic showing photoconduction of an electron

Solar cells: II

To cause the hole-electron production the photon energy has to exceed the band-gap energy. If photons have excess energy this can be deposited as heat.

We can define hf Eg where h is Planck’s constant, f is the frequency of the radiation and Eg is the band gap in Joules.

You can characterise a solar cell by its I-V curve. The best operating point is the maximum power point, given by Vmp and Imp

Solar cells: VI

Typical solar-cellI-V characteristic

Solar cells: VII

You can also define:◦ Open circuit voltage (i.e. no current drawn) Voc

◦ Short circuit current Isc

◦ A fill factor (FF) which says how “square” the I-V curve is. The “squarer” the better. FF is defined as:

FF = (Vmp Imp)/(Voc Isc)

The closer to 1 this is the “squarer” it is.

Solar cells: VIII

For a silicon cell Voc is typically 0.5 to 0.6 V, Isc depends on the illumination level, and FF can be 0.7 to 0.85.

To find the peak power, you draw output power vs. output voltage. A clear peak can be found, which defines Vmp and hence Imp

can be determined. If you heat a solar cell you will find its

performance changes. Its efficiency falls as its temperature increases.

Solar cells: IX

There is a packing factor for a solar panel, which describes how much of its surface area is really solar cells, 0.9 is good. The rest is structure, edges, gaps etc. So the effective area is less than the actual surface area of a solar panel.

Solar panels need to be face on to the Sun for maximum efficiency. If they are tilted then a geometric correction has to be applied to give the cross-section projected orthogonal to the solar direction. If the angle between the normal to the surface of the panel and the solar direction is θ, then there is a factor cos θ that has to be applied when finding the effective surface area illuminated and hence the power output.

Solar cells: X

Typical bandgap energies for solar cell materials

Solar cells: XI

nnn

Solar cells: XII

Solar cells in orbit do suffer degradation with time. Due to:◦Accumulation of micrometeorite impact damage,◦Attack by atomic oxygen on the wiring◦Radiation damage to the semi-conductor.

There is thus a factor for loss of efficiency with time – power output falls slowly with time.

Estimating this loss rate, and over-sizing the solar array at the Beginning of Life (BOL) so it over-produces power but produces the correct power at the End of Life (EOL). Solar panels at the BOL in Earth orbit can produce 30 – 50 W/kg of mass.

Current state-of-the-art Multi-Junction (MJ) solar cells have efficiencies approaching 50%.

Solar cells: XIII

Fuels Cells [F & S Chapter 10, p. 337] The basic idea is to generate electricity from

chemical reactions. They are used on the Shuttle, and were used in

the Mercury, Gemini and Apollo space missions. An oxidation reaction is used. It has a high energy

density (typical o/p Gemini: 33W/kg, Apollo: 25 W/kg, STS: 275 W/kg). This is available on demand and continuous when running (although the start up time of early cells was long). But you need to carry fuel (oxygen and hydrogen).

Fuel cells: I

A hydrogen/oxygen fuel cell is typical and produces water (a useful output).

In an ideal cell the voltage (Er) produced is given by:

Where ΔG is the Gibbs free energy in the reaction, n is the number of electrons transferred and F is the Faraday constant (9.65× 104 C/mol).

Fuel cells: II

nF

GEr

In the hydrogen/oxygen cell the reaction transfers 2 electrons per molecule of water formed and ΔG = -273.2 kJ/mol at 25 °C. This gives 1.416 V. In reality this is the ideal potential, as there are losses in the system.

Early cells could take 24 hrs to start and 17 hrs to stop (Apollo), but for the Shuttle start up times is 15 min and shut down is immediate.

Fuel cells: III

Fuel cells: IV

v

Radioisotope Thermal Generators (RTGs) are used to generate power on space missions where solar energy is at a low flux or not available for long periods (mainly unmanned missions).

They generate heat. They then use the thermoelectric effect whereby a voltage is generated between two materials (semi-conductors or conductors) if a temperature difference is maintained between the two ends (think of a thermocouple). 

Here the cold end is achieved by exposure to space. The hot end by waste heat from nuclear decay.

RTGs: I

RTGs: II

A practical device is shown in F&S page 340

Isotope Fuel form Decay product

Power density (W/g)

τ½ (years)

Polonium 210 Gd Po α 82 0.38

Plutonium 238 Pu O2 α 0.41 86.4

Curium 242 Cm2 O3 α 98 0.4

Strontium 90 SrO β 0.24 28.0

RTGs: III

Various radioactive materials for possible use in a RTG.

RTGsPellet of glowing 238PuO2 – generating 62 watts of heat

RTGs: IV

Cassini RTG – source, NASA

RTGsCassini’s RTG? Doesn’t look like a clean room!

RTGsMuch better…..New Horizons’ RTG (mission to Pluto)[Cassini flight spare, using 11 kg of Plutonium pellets]

When considering a design, care has to be made to ensure that in the event of an accident during launch, the radioactive material does not escape into the environment. Clean-up costs would be expensive in terms of money, and public support!

The power generated by a RTG is not constant with time, the material decays so there is less as time goes on and hence less power can be generated.

RTGs: V

You need: 

Where Pt is power at time t, and P0 is the initial power at t = 0.

τ½ (years) is given in the table above.

RTGs: VI

tPP ot

2/1

693.0exp

So you have to calculate what power you need for the mission and start the mission (Beginning Of Life - BOL) with too much power. Then as the source decays, the RTG’s output falls and you plan it so you have just the right amount of power at the end of the mission lifetime (End Of Life – EOL)

RTGs: VII

Pros:◦ You are not reliant on the spacecraft pointing at

the Sun or not being in eclipse.◦ You are not dependent on radial distance from the

Sun◦ Power levels can be sustained for periods of years

(depending on τ½). Voyager’s RTG has been running for almost 30 years.

◦ Aside: Congress has just agreed to the start-up of plutonium production to fulfil NASA’s requirement for RTG material – at NASA’s expense it would seem!

RTGs: VIII

 Cons:◦ Radiation is emitted and may affect instruments on the

spacecraft.◦ The material is radioactive and often highly poisonous – it

needs careful handing during construction and spacecraft integration at the launch.

◦ By definition the hotter the better, but this may not be good for spacecraft components so may need to shield the heat from the spacecraft interior.

◦ The public does not like the word radioactive and rockets do fail during launch, so extra care has to be taken in packaging the RTG to prevent disassembly during an explosion or crash.

RTGs: IX

Should now have an understanding of the different mechanisms available to power a spacecraft:◦ Solar Panels◦ Fuel Cells◦ RTGs

You should also understand the advantages and disadvantages of each.

The power source you choose is dependent on the mission requirements.

Conclusions