Initial sizing of 8.5 kN solar thermal propulsion system
(Version 1.1)
Delft University of Technology
Faculty of Aerospace Engineering
Date
Authors:
22 July 2008
B.T.C. Zandbergen
Document Change Record
Revision
1.0
Effective Date
July 2008
1.1
July 2008
Description of Changes
Original document.
Alternative solution option added
Problem statement
You are asked to size a solar thermal propulsion (STP) system to provide the required power to
drive a thermal rocket engine with a thrust (F) of 8.5 kN (8500 N), a specific impulse (I sp ) of
1
1000 s , and a thrust efficiency (η F ) of 85%. You should take into account a thrust period of 10
seconds once every 24 minutes. Given is that the vehicle is always in full sun light and that the
solar flux equals 600 W/m 2 . Values given in this problem have been taken from the work of
[Arshad], who designed a solar thermal propulsion module suitable for performing a capture
maneuver at Mars.
Solution
For the design, we use the simple method as outlined in [Zandbergen]. Zandbergen considers as
main system elements, see figure 1, a concentrator that collects and focuses the incident solar
radiation, a receiver/absorber chamber that absorbs the concentrated solar radiation, a thruster
that generates the thrust, and a radiation heat shield (not shown in the figure) to prevent heat
loss.
Figure 1: Block diagram of solar thermal propulsion (STP) system (absorber includes receiver and thermal energy storage
and heat exchanger)
For background information on STP, see SSE propulsion web pages (www.sse.lr.tudelft.nl)
Starting points
For the technology used, we select:
o Inflatable solar collector/concentrator with a reflective efficiency (η coll ) of 85% and a
2
mass density (ρ coll ) of 0.5 kg/m ; Typical technologies available include:
o Conventional rigid panel concentrators 10 kg/m 2
2
o Advanced concentrator, Spline Radial Panel (SRP): 2 kg/m
2
o Future: Inflatable concentrator 0.5-0.2 kg/m
o
A graphite receiver/absorber chamber with a receiver efficiency (η rec ) of 95%, a storage
efficiency of 95%, an allowable temperature range (ΔT TES ) of 400K, a mass density
3
(ρ graph )of 2240 kg/m , and a heat capacity (c graph ) of 2240 J/Kg-K [Arshad];
1
A specific impulse of 1000 seconds can for instance be realised when using hydrogen as propellant. To
make it true, we should design the thruster to be able to attain a hydrogen temperature of about 3000 K at a
nozzle pressure ratio of 20,000:1. Note that by increasing the pressure ratio the required hydrogen
temperature can be reduced to some extent.
3
o
Thermal blanket insulation or MLI, see figure, with a mass density (ρ ins ) of 0.8 kg/m 2
(including allowance for attachments) to provide for thermal insulation, thereby limiting
the thermal loss to 5% or less (see storage
efficiency). The relatively high loss is also
because for small objects effective emittanc e is
higher than for small objects [SMAD].
Figure 2: Example of Multi-Layer Insulation (MLI)
Calculations
T hruster input power
E stimate jet power:
P j = 0.5 * F * I sp * g o = 0.5 * 8500 * 1000 * 9.80665 = 41.7 MW t
S ubscript ”t” refers to thermal power in contrast to electric power.
T hermal input power thruster:
P in = P j /η F = 41.7/0.85 = 49.0 MW t
R eceiver/absorber chamber design
P ower required from absorber/energy storage is equal to thermal input power thruster: P ab = P in
= 49.0 MW t .
Po wer required from receiver:
P rec = P ab / η ab = 49.0 MW t *1/0 .95 = 51.6 MW t
E stimate energy storage requirement:
E ab = (P ab t b ) / η ab
E ab = 49.0 MW t x 10 sec / 0.95 ≈ 516 MJ
D etermine receiver/absorber chamber mass and volume:
M ab = E ab / (c graph ΔT TES )
M ab = 516 MJ / (2240 J/Kg -K x 400 K) = 576 kg
V ab = f 1 x M ab / ρ graph = 1.2 x 642 kg / 2240 kg/m 3 = 0.309 m 3
It is assumed here that the mass and volume of the receiver/absorber/thermal storage chamber
are fully determined by the storage requirement. The factor f 1 takes into account that cavities
exist in the graphite material, which lead to a larger size/volume.
C ollector/concentrator design
E stimate energy required from collector/concentrator:
E coll = E ab /η rec = 543 MJ
E stimate power required from collector/concentrator
P coll = E coll / t load
P coll = 543 MJ / [2 4 min x 60 sec] = 377 kW t
D etermine collector area A coll and diameter D Coll :
4
2
2
A Coll = P Coll / (η coll S) = 377 kW t / (0.85 x 600 W/m ) = 740 m
1/2
D coll = (4/π A coll ) = 30.7 m (or two collectors with a diamete r of 21.7 m each)
D etermine collector mass M coll :
M coll = A coll x f 2 x ρ coll = 740 m x 1.3 x 0.5 kg/m = 481 kg
2
2
T he factor f 2 takes into account the difference between surface and frontal area, that we need
some structure to hold the collector (concentrator), and that we need some means of articulatio n
of the collector. I have selected a value of 1.3. Later studies must allow for determining a more
precise value depending on the shape of the collector.
M LI design
C alculate receiver surface area (S rec ):
We assume that the receiver/absorber h as a cylindrical shape and that only the surface of the
cylinder (not the end caps) is insulated. Taking a length to diameter ratio of 5, it follows:
S rec = 3.18 m 2 (diameter of cylinder is 0.43 m and length is 2.14 m).
C alculate MLI surface area (S MLI )
Taking the MLI surface equal to th e receiver surface gives an insulator mass (M ins ):
2
2
M ins = S ins x ρ ins = 3.18 m x 0.8 kg/m = 2.5 kg
Summary results
M ass summary
S ummarizing, we have:
Collector mass:
Receiver/absorbe r mass :
Insulator mass
Total dry system mass:
481 kg
576 kg
3 kg
1060 kg
Remarks
T he total dry system mass given above is about twice the value reported in [Arshad]. This is
attributed to Arshad using a more advanced concentrator design, reduced margins, and highe r
efficiencies. Hence, it is advised that all numbers used in the previous are verified in more detai l
for instance by comparing with ‘real’ data, i.e. data used in other solar-thermal design studies or
by detailed design (e.g. efficiencies used, the factors f 1 and f 2 , mass of radiation shield, etc.).
Sensitivity analysis must be performed to find out which parameters have largest effect on
design result (in terms of size, mass).
Storage device (receiver/absorber) is m ost heavy component. It is advised to consider the
possibility of leaving out the storage device, thereby accepting a much lower thrust level.
Note that in the above no attention has been given to the propellant storage and feed syste m,
the selection of an appropriate propellant, and the specifics of the thruster (absorber
temperature and nozzle specifics). The latter can be dealt with once a suitable propell ant has
been selected. Also the total amount of propellant on board has not been considered (depends
on the time the system is operational, i.e. the total velocity change (Δv) to be accomplished).
For a simple method to quickly estimate the propellant mass (given propellant) and the mass o f
the propellant storage and feed system, see [Zandbergen].
Alternative solution option
In the foregoing it is assumed that we have a thrusting period of 10 seconds and a recharging period of 24
minutes. Instead we might opt for a lower thrust level of about 59 N and than opt for continuous thrusting.
This would greatly reduce the mass (and the size) of the receiver/absorber as in that case there would be no
need for thermal energy storage. It also would limit the losses associated with the storage of the heat.
The results obtained are summarized in the table 1.
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Table 1: Results for continuous thrust STP system for Mars capture manoeuvre
Parameter
Jet power
Input power
Power from receiver/absorber
Power from collector
Power from Sun on to collector
Collector area
Diameter of collector
Mass of collector
Mass of receiver/absorber
Mass of insulation
Total dry system mass
Symbol
Pj
P in
P re c
P coll
Psun
A Coll
D coll
M coll
M rec/ ab
M ins
Value
289.4 kWt
340.5 kWt
340.5 kWt
358.4 kWt
421.6 kWt
702 m 2
29.9 m
456.3 kg
0.6 kg
negligible
457 kg
Remarks
See below table for explanation
In the table also the mass of the receiver/absorber is included. For this we assumed that the mass is
comparable to the mass of a monopropellant thruster with the same thrust. For these thrusters [Zandbergen]
gives:
y = 0.0046x + 0.2985,
with thruster mass (y, in kg) and thrust (x, in N). For a thrust of 59 N we than find a thruster mass of 0.6 kg,
which is much less than the earlier given receiver/absorber mass of 576 kg.
We find that in that case the total dry system mass is about half of the earlier calculated value with thermal
store. On the other hand, however, we must reckon with an increase in propellant mass due to “gravity
losses”. Whether the increase in propellant mass outweighs the reduction in dry system mass is still to be
studied.
References
1. Arshad A. M., High Thrust – Solar Thermal Propulsion, MSc. Thesis, TU-Delft, The
Netherlands, October 2007.
2. Zandbergen B.T.C., Space engineering & Technology II, part A1, Course notes ae2-S02, TUDelft/LR, 2005.
3. Wertz J.R. and Larson W.J., SMAD or Space Mission Analysis and Design, 3rd ed.,
Microcosm Press, 1999.
4. Zandbergen B.T.C., Propulsion Concept Design & Selection for a Coplanar LEO-to-GEO
transfer mission, TU-Delft, Aerospace Engineering, January 2005.
5. Zandbergen B.T.C., Thruster mass estimation, SSE propulsion web pages, TU-Delft/LR/DEOS/SSE,
2008.
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