Development of a solar thermal thruster system

IAC-08- D1.1.01

DEVELOPMENT OF A SOLAR THERMAL THRUSTER SYSTEM

H.C.M. Leenders, B.T.C. Zandbergen

Chair of Space Systems Engineering, Faculty of Aerospace Engineering, Delft University of Technology, Delft, The Netherlands

Email corresponding author: B.T.C.Zandbergen@tudelft.nl

ABSTRACT

At the Delft University of Technology the use of solar radiation to heat a propellant to a high temperature is investigated as an alternative to resistance heating. The latter only allows for a solar power to heat conversion efficiency of about 25%, depending on the solar cells, whereas for solar heating 80% seems feasible. This paper addresses the theoretical and experimental investigations performed in the field of solar thermal propulsion at Delft University and more specific the solar thermal thruster development.

The work performed includes the development of a theoretical model that assists the designer in the design and prediction of the performances of the solar thermal thruster. Also a demonstration solar thermal thruster has been developed and tested at different mass flow rates to verify the model. These tests have been performed using the Delft Aerospace Rocket Test Stand. Measurement parameters included thrust, propellant temperature, mass flow and pressure. In this paper we will present an overview of the theoretical model developed, the demonstration thruster as well as the test results. Finally, we present the main conclusions and recommendations related to the outcomes of the work.

INTRODUCTION

Solar thermal propulsion (STP) is an advanced means of space propulsion wherein solar power is used to directly heat the propellant. This is in contrast to electro-thermal systems, like resistojets, wherein the solar energy is first converted in electrical energy before being used

for accelerating the propellant to a high exhaust velocity. Like for electro-thermal systems it offers specific impulse levels beyond 900 seconds. This is about twice that of the best performing chemical systems. A clear advantage to electro-thermal systems though is the much higher efficiency of converting solar power into heat. Values in the range of 80% seem feasible, whereas for solar-photovoltaic systems efficiencies are limited to approximately 25% depending on the type of solar cells used. As of this higher efficiency also higher thrust levels are feasible (10 - 100 N) than for electro-thermal propulsion which makes solar-thermal propulsion (STP) a promising option for orbit transfer and interplanetary missions. Since the 1970s various developments and mission studies have been made [1]-[6], leading to proof of concept, but so far STP has not been proven in space.

From 2000 onwards, in the frame of research on thermal space propulsion at the faculty of Aerospace Engineering at the Delft University of Technology a number of theoretical studies on STP have been performed [7]-[9] confirming the potential of STP. This paper addresses the design and testing of a technology demonstrator STP thruster producing a thrust in the range of 100 mN as a first step toward a STP demonstrator system suitable for a demonstration flight on a microsatellite. The study goal is to develop a low cost solar thermal propulsion technology demonstrator, suitable for ground testing in the TU-Delft DARTS test facility.

Hereafter, we first describe the starting points for the design. Next we discuss the thruster performances as envisaged. Thirdly the thruster is designed with focus on the receiver absorber cavity (RAC) as the most critical part of the design. Next we present the assembled

technology demonstrator thruster as well as the test set up of the thruster using an artificial light source. The test results and a discussion of these results including a comparison with the results of the theoretical model are discussed thereafter. Finally we present the main conclusions and recommendations resulting from the project.

STARTING POINTS

The following considerations and requirements were used in this thruster design and demonstration study:

• A thrust level was selected in the range of 100 mN. This corresponds to the thrust level specified for the TNO, UTwente and TU-Delft T3_{μPS [10], which is a cold gas}

propulsion system currently under development for flight on the second TU-Delft cubesat (Delfi-n3Xt) [11] in 2010; • System operating pressure shall be below

5 bar. This is the same maximum pressure level as selected for the T3μPS;

• To ensure safety as well as commonality with the T3μPS nitrogen is used as propellant. Using hydrogen would allow for reaching higher specific impulse levels to be reached, but this is not considered essential for demonstrating the technology.

• The thruster is of the indirect heating type this in agreement with the majority of thrusters developed in the world to date. In this type of thruster the (collected) solar energy heats up a receiver-absorber cavity (RAC) body to a high temperature. The propellant is forced through small channels in the RAC and heat is transferred to the propellant. Finally the high temperature propellant is exhausted through a nozzle. • To allow for the use of readily available

materials, propellant temperature is limited to a maximum of T = 1000 K.

• The receiver shall be designed to allow light to be received from a direction perpendicular to the thrust axis. This is in agreement with most other such thruster concepts currently under study in the world. • The technology demonstrator thruster is to

be tested on the Delft Aerospace Rocket Test Stand (DARTS), see also later in this paper.

• Power source. A 1000 W electrical power incandescent theatre lamp is available to act as a light source. It is expected that at least 10% of this power will be available for heating the receiver-absorber, which results in a radiated power received of 100 W.

THRUSTER PERFORMANCE

To determine thruster performance, it is essential to know the amount of power needed to heat a given mass flow rate to a given temperature and to know the resulting exhaust velocity.

To determine the power P needed to heat a certain mass flow rate m to a certain temperature the following relation is used:

H

m

P

=

Δ

(1)

Here ΔH refers to the enthalpy change related to

a change in temperature. Enthalpy values for a range of species including nitrogen and temperatures can be obtained from [14]. Figure 1 presents the mass flow rate of nitrogen that can be heated to a certain temperature as a function of the power input assuming that 80% of the received power is used for the heating of the propellant. 0 10 20 30 40 50 60 0 50 100 150 200 250 300 350 400 Power [W] M a s s fl o w [m g /s ] T_c = 373 K T_c = 400 K T_c = 450 K T_c = 500 K Tc = 1000 K

Figure 1: Required power versus mass flow rate for nitrogen propellant; an efficiency of 80% is

taken in account

The velocity with which the propellant leaves the thruster can be determined using ideal rocket theory [12] provided that the nozzle dimensions are known. The Table 1 presents ideal thruster performance that can be achieved using a nozzle with a throat diameter of 0.58 mm and an exit diameter of 0.68 mm for a propellant

temperature of 1000 K at different mass flow rates. The nozzle dimensions have been taken from an existing nozzle used in another program. It is intended to use this nozzle also for our technology demonstrator. It is made of copper and has a mass of 5 grams. Its low area ratio of ~1.38 ensures a sufficiently high pressure in the nozzle exit at the low chamber pressures envisaged (in excess of 2 bar) to prevent flow separation. For space application of course a nozzle with a much larger area ratio can be used thereby allowing for significantly higher specific impulse (i.e. lower propellant consumption). m [mg/s] 50 75 100 150 200 300 pc[bar] 1.5 2.3 3.0 4.5 6.0 9.0

F [mN] 18 46 73 128 182 292

Table 1: Ideal thruster performance (propellant temperature is 1000 K)

RAC DESIGN

Material

Various materials are used for the RAC. For instance in [1] materials such as graphite, boron, tungsten, silicon carbide, alumina and beryllium are mentioned. These materials are all characterised by a high melting temperature. However, as during this project temperatures of the RAC are limited to 1000 K much less costly and readily available materials, such as copper, aluminium or steel can be considered. For this project copper is selected as the RAC material, as it offers good thermal conductivity, see Table 2, which ensures that the heat is transferred well through the receiver wall. Furthermore copper has a low heat capacity, which means that less energy is required to heat the RAC to a certain temperature than in the case of steel and aluminium. Material Heat capacity [J/kg-K] Thermal conductivity [W/m-K] Copper 373 386 Stainless steel 502 16 Aluminium 896 235

Table 2: Material properties

A further advantage of copper is that, when oxidized it has a good absorption coefficient (in the range of 0.77 – 0.87 [17]).

Layout

The general idea of a RAC is that it receives radiation, heats up and transfers the heat to a propellant. Three different RAC concepts have been considered in this study see also Figure 2 and Figure 3:

• Cylindrical without cavity • Cylindrical with cavity • Conical with cavity

For a given size of the focal spot (from the concentrator) and propellant temperature, each shape leads to a different size of the RAC in terms of length of the flow channels, total length, diameter, cone angle, etc.

Figure 2: Conical RAC (cross-sectional view)

Figure 3: Cylindrical RAC (cross-sectional view)

The Table 3 presents a trade-off table used to determine the most suitable concept. The three concepts are each graded for 4 criteria including convection and radiation heat transfer loss, temperature distribution in the RAC, mass and reflection losses. The grades are given by colours:

• green: exceed requirements • blue: satisfies requirements

• yellow: partly satisfies requirements • red: does not satisfy requirements.

The weight factor for each of the criteria is indicated by the width of the cells in the table

with wider cells carrying more weight.

The table shows that the conical cavity RAC is the best option. Some of the main reasons are that:

• the conical cavity allows for the incoming radiation to be more evenly distributed over the cavity wall and hence results in a more even temperature distribution than for the other two configurations;

• the conical shape allows for the propellant channels to run straight through (no bends needed), which reduces manufacturing problems.

Dimensioning

To dimension and size the conical shaped RAC in detail we first need to dimension the propellant flow channels. Next we dimension the cavity of the RAC.

As design conditions for the RAC were chosen a mass flow rate of 300 mg/s to be heated to a temperature of 373 K (100 degrees centigrade) with the RAC having a temperature of 400 K. Moreover it was decided to divide the propellant flow through the RAC over 8 identical flow channels. For the cross-sectional radius Rc of

these channels we selected a value of 0.3 mm, thereby ensuring a sufficiently high flow velocity to guarantee a high degree of heat transfer by convection, while limiting the flow mach number in the channels to less than 0.15.

Propellant flow path

To heat up the nitrogen propellant to 373 K the RAC should transfer about 32 W of power to the propellant. The length of the flow channel to accomplish the heating of the propellant to the required temperature is estimated using a traditional approach based on Newton’s law of cooling, see equation

(2) and assuming a constant wall temperature for the RAC walls of the flow channels.

(

_lm

)

2

_{c c}

(

_lm

Q

=

hA

Δ

T

=

h

π

R L

Δ

T

)

(

)

2

c c lm

Q

L

h

π

R

T

=

Δ

(2)

Here Q is the required power, h is the coefficient of convective heat transfer, A the channel wall surface area, Rc the cross-sectional radius of the

flow channel, Lc the length of the flow channel,

and ΔTlm is the log-mean temperature difference.

The convective heat transfer coefficient is determined using:

Nu k

h

D

⋅

=

(3)

Here Nu is the Nusselt number, k the thermal conductivity of the fluid and D a representative length scale here taken equal to the diameter of Model Convection

and radiation Temperature loss

distribution Mass Reflection loss Without cavity Outer surface

loss green Light on front yellow High mass 100% yellow yellow Cylindrical cavity Outer surface

and cavity surface loss blue Light partially on cavity wall blue Low mass 13% green blue

Conical cavity Outer surface and cavity surface loss

blue

Light on all cavity wall green

Low mass 20%

green blue

the flow channel. Nu is calculated using the Gnielinski correlation taken from [15].

(

)

( )

(

Pr

1

)

7

.

12

1

Pr

1000

Re

3 / 2 2 / 1 8 8

−

+

−

=

f f

Nu

(4) 4 / 1

Re

1

316

.

0

⎟

⎠

⎞

⎜

⎝

⎛

=

f

(5)

Here Re is the Reynolds number and Pr is the Prandtl number. The fluid properties needed to estimate Re and Pr are taken from [14]. Calculations showed a length of the flow channels of approximately 5 cm.

Cavity

To limit the size of the light inlet of the RAC the focal point of the concentrating lens is positioned in the inlet. As preliminary testing with the light source and concentrator lens showed that a focal spot of ~2 cm could be obtained, we selected for the diameter of the receiver inlet a value of 2.5 cm. As straight flow channels were selected, this lead to a half cone angle of the conical RAC of ~14o. The equally spaced propellant channels (8 in total) are running through the wall of the conical cavity. They run from the base of the cone, see Figure 4 (left hand side) to the top of the cone where they join and connect to the nozzle inlet.

Figure 4: Complete RAC

Since drilling such small holes for such a length is costly it was decided to use two cones (an inner and an outer), see Figure 5. The propellant channels are milled in the inner cone with the outer cone acting as the closure of the channels.

Figure 5: Exploded view of conical RAC

Because of the milling, it was decided to opt for channels with a square cross-section of side length 0.6 mm thus providing a hydraulic diameter slightly larger than used for the determination of the length of the flow channels. On the inlet side of the conical cavity a propellant manifold is included. This manifold distributes the propellant to the eight individual flow channels in the RAC. To ensure proper filling of these channels, the cross-sectional area of the flow channel in the manifold is set at 12 times the cross-sectional area of each of the individual propellant channels. Initially the manifold was considered to also thermally insulate the hot RAC from the cold propellant inlet. But during some preliminary tests, it turned out that the material selected was too brittle, therefore a copper replacement was designed. As now the propellant inlet is no longer insulated, a longer propellant inlet tube was used which also functions as a cooling fin.

RAC with nozzle

The Figure 6 presents the final design of thruster showing the RAC and the nozzle assembled.

Figure 6: Final RAC design with nozzle

This nozzle has a length of approximately 2 cm and is solder joined to a bended tube. The latter is to ensure that the light enters the receiver along an axis perpendicular to the thrust axis. On the other end, the bended tube is solder joined to a perforated nut. This nut allows the nozzle to be

screw mounted on to the RAC via the threaded nozzle interface.

As a last step in the design, to ensure that the cavity absorbs enough light, it was decided to oxidize the RAC cavity to obtain a high absorption coefficient of the cavity wall.

Thermal modelling

Following the design of the RAC a thermal model was made that would allow for predicting the RAC performances at a given power input while also taking into account heat loss to the environment as well as the effect of thermal insulation. For illustration, the Figure 7 shows the heat flow in case of absence of propellant flow.

Figure 7: Energy balance insulated RAC (no propellant flow)

The figure shows the power input to the RAC as well as the heat loss through radiation and (free) convection that occurs at the inner cavity wall and at the insulated outer wall. The reason for also taking into account free convection is that testing is conducted in a non-vacuum environment. Not shown in the figure are the power needed to heat up the RAC and conduction heat loss via the thruster mounts. The only conduction that is taken into account is the conduction through the insulation material. The following relation forms the basis of the thermal model.

in RAC rad conv cond prop

Q

=

Q

+

Q

+

Q

+

Q

+

Q

(6)

Here Qin represents the input power, QRAC the

energy that heats up the RAC, Qconv the free

convection loss, Qcond the heat conducted

through the insulation to the outer surface of the RAC, Qrad the heat loss due to radiation and Qprop the heat that flows to the propellant.

Input power to the RAC depends on the power P collected, the absorption coefficient of the cavity material (for copper α = 0.8 [17]) and that portion of the light reflected (represented by the reflection factor r) by the cavity onto itself that is still absorbed by the cavity wall:

(

1

+

1−1

)

=

P

rF

Q

_in

ηα

(7)

r

h

H

H

F

=

+

−

=

−

;

1

1

1

2 1 1 (8)

Here F1-1 is the geometric view factor indicating

the portion of the radiation coming from a surface 1 (the cavity surface) that falls onto it self, h is the height of the cone and r is the radius of the base of the cone. In addition, an efficiency factor η is introduced allowing taking into account further losses.

Convection losses are calculated using:

(

−

∞

)

⋅

=

A

T

T

L

k

Nu

Q

_{conv w} (9)

In this relation k is the thermal conductivity of air, A the RAC surface area in contact with the surrounding air (e.g. cavity area or insulation area) and L a characteristic length. For the free convection loss occurring at the inner surface of the RAC Nu is determined using [16]:

447 . 0

00324

.

0

Ra

Nu

=

(10)

Here Ra is the Rayleigh number. For the outer surface of the RAC two situations are distinguished, with and without insulation. With insulation, the RAC is treated as a short circular cylinder rather than a cone. For a short circular cylinder Nu is determined using the following relations taken from [15].

(

_m

)

m t m l

Nu

Nu

Nu

=

+

1/ ₍₁₁₎

(

)

( )

(

_n

)

n T n COND l

Nu

Nu

Nu

=

+

1/ ₍₁₂₎ 3 / 1

Ra

C

Nu

t

=

t (13) 4 / 1

Ra

C

G

Nu

T

=

_l (14) 9 / 4 16 / 9

Pr

492

.

0

1

671

.

0

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟

⎠

⎞

⎜

⎝

⎛

+

=

l

C

(15)

Here G,

C

_t, m, n , are constants whose values are given in the

COND

Nu

Table 4.

Without insulation the same convection equations can be used as for the short circular cylinder, but the value of the constants differs, see again the Table 4.

Short cylinder Cone

G 0.889 1.057 NuCOND 1.59 2.1 n 1.11 1.43 m 8 10 t

C

0.103 0.10 Ls [m] 0.53 A [m2_{] 0.083}

Table 4: Convection parameters [15]

The radiation loss is calculated using the following simple relation.

(

4 4

)

∞

−

=

FA

T

T

Q

rad

εσ

w (16)

In this relation ε is the emission coefficient, σ the Stefan-Boltzmann constant, A the surface area of the radiating body and F is the view factor [12]. The radiation loss is multiplied with the view factor because it is assumed that only the fraction of radiation directly radiated to the surroundings is lost.

The heat conducted through the insulation to the outer surface is calculated with the following relation valid for a cylindrical geometry.

(

)

(

)

2

ln

cond i o o i

kL

Q

T

r r

T

π

=

−

(17) The inner radius is ri = 14.8 mm and the outer

radius is equal to the inner radius plus insulation thickness ro = 54.8 mm. To calculate the

insulation outer temperature that is required for the radiation, convection and also for the conduction is done as follows. The conduction through the insulation is set equal to the power that is lost due to convection and radiation at the outside of the insulation.

rad conv

cond

Q

Q

Q

=

+

(18)

When the relation for conduction, convection and radiation are substituted in equation (18) a relation for the RAC temperature as function of

the outer insulation temperature can be obtained. Because the RAC temperature is known, the outer insulation temperature can be found by solving the relation numerically.

The power that goes to the propellant is calculated using the equation (1).

The power remaining in the RAC is calculated using:

RAC in rad conv cond prop

Q

=

Q

−

Q

−

Q

−

Q

−

Q

(19) The energy in the RAC is found by multiplying the power in the RAC with a certain time increment. From the energy the temperature increase of the RAC is found for that time increment, by dividing the energy by the heat capacity and the mass of the RAC.

RAC

Q

t

T

cM

Δ

Δ =

(20)

To calculate the temperature increase of the RAC per time step the calculation is performed a great number of times.

Typical outputs of the model for an RAC mass of 86 grams are presented in Table 5 (no propellant flow).

Power [W] 50 100 150

RAC with insulation

Temp [K] 720 920 1050

Time [min] 40 27 20

RAC without insulation

Temp [K] 508 622 700

Time [min] 20 16 13

Table 5: Thermal model outputs for heating the RAC

DEMONSTRATOR THRUSTER

An overview of the layout of the actual thruster can be obtained from the Figure 8 to Figure 10. The Table 6 provides an overview of its main characteristics.

Figure 8 shows the inner and outer cone separately (left) with the inner cone showing the milled out propellant flow channels. On the right we see the assembled RAC clearly showing the propellant distribution channel (without top). The Figure 9 shows the copper ring closure ring which closes the distribution flow channel and connects to the propellant feed system. Not

shown is a steel tube that is soldered in the inlet hole and which connects to the feed system.

Figure 8: Inner and outer cone

Figure 9: Copper closure ring with RAC

Propellant Nitrogen (N2)

RAC material Copper

Propellant channel Shape (cross-section) Area (cross-section) Length Number of channels Squared A = 0.36 mm2 L = 5 cm 8 Propellant distribution channel Shape (cross-section)

Area (cross-section) Squared A = 4.41 mm2

RAC

Inlet hole diameter Half cone angle Cavity length RAC wall thickness

D = 2.5 cm

α

= 14o L = 50.1 mm t = 2.5 mm Nozzle Throat diameter Exit diameter DDtt = 0.58 mm = 0.68 mm System mass RAC: Outer cone Inner cone Copper seal ring

Inlet tube Bolt with hole Bended tube Nozzle Total mass M = 36 g M = 30 g M = 20 g M = 2 g M = 8 g M = 1 g M = 5 g M = 107 g

Table 6: Thruster specifications

Figure 10 shows the nozzle with an end cap. The latter is used to close off the system for leak testing.

Figure 10: Nozzle

TEST PLAN AND SETUP

It is planned to characterize the thruster at different mass flow rates using an artificial light source and a concentrating lens. Since the power output of the artificial light source is not know, it is first planned to perform irradiance tests to determine the emitted power of the light source, i.e. the power in the focal plane of the concentrating lens.

The thruster characterization tests aim to determine the maximum RAC temperature with and without propellant flow as well as thrust, chamber pressure, pressure drop in the thruster and effective exhaust velocity. Essentially three different types of tests are planned:

1. without propellant flow without insulation 2. without propellant flow with insulation 3. with propellant flow with insulation

Set up for irradiance testing

The light source used is a 1000 W incandescent theatre lamp, see Figure 11. This source has a slightly diverging beam with a diameter of approximately 20 cm at the outlet of the lamp. A converging lens system (consisting of multiple lenses) is used to focus the beam.

Figure 11: 1000 W lamp and combined lens

The Table 7 gives the lens specifications. Notice that the lens diameter is 10 cm, meaning that only part of the light that the source emits is concentrated. However, the irradiance tests show that the power output increases with the lens present. For the actual thruster characterization a

shutter is used to restrict the diameter of the light beam that leaves the lamp to 10 cm.

Lens diameter [cm] 10

Focal length [cm] 2

Magnification [-] 0.23 Focal spot diameter [cm] 2

Table 7: Combined lens specifications

The irradiance of the light source is measured using a pyranometer and a multi-meter. The pyranometer is specified in [19]. The measurement is performed by moving the pyranometer through the light beam (at a fixed distance from the lamp) and taking measurements at different points in the beam at 5 cm interval both along the x- and y-axis.

Set up for thruster characterization

testing

The thruster characterisation tests are performed in the Delft Aerospace Rocket Stand (DARTS), see Figure 12.

Figure 12: DARTS test facility

It consists of a single-axis thrust bench, a propellant feed and control system, an instrumentation system and a data acquisition and control system. It allows for ambient (sea level) testing of small thrusters with a thrust level in the range 20-1000 mN. The feed and control system allows for extended duration testing and is capable of providing a range of gaseous propellants, including nitrogen, helium and carbon-dioxide to the test object. Maximum flow rate is 41.3 standard normal

litres with control accuracy better than 1% full scale output (FSO). The instrumentation system allows for extensive measurements of thrust, mass flow rate, gas pressure, and temperature. The data acquisition and control system allows for the control of the experiment in time and for the acquisition of measurement data for analysis purposes. Signal sampling rate is 100.000 samples/(sec-channel).In Figure 13 the (insulated) thruster is shown mounted on the test stand.

Figure 13: Test setup

The theatre lamp with shutter and lens aligned with the RAC inlet are shown on the right. To prevent conductive heat loss from the thruster to the environment, the thruster is mounted using ceramic insulators in between.

During testing the following measurements are made in time: thrust produced, chamber pressure (at nozzle inlet), thruster inlet pressure, propellant temperature, RAC temperature and mass flow rate. The latter actually is to check the mass flow settings. All measurements are performed at a rate of 1 Hz.

RAC temperatures are measured at four different locations on the RAC, see Figure 14. This is to find out if the assumption of a constant wall temperature made in our model holds. During testing thermocouple 1 to 3 are located on the top and 4 on the bottom.

Figure 14: RAC with four thermocouples

Before the actual testing is performed a leak check is performed in order to ensure the proper mass flow rate through the nozzle. This is done by closing the system with the nozzle cap and pressurizing it with the propellant feed system.

TEST RESULTS AND

DISCUSSION

Light source power output

Two types of measurements have been made: with and without lens.

The measurement data of the irradiance test without lens are plotted in a 3D graph, see Figure 15. These data were obtained at a distance of 148 cm from the lamp. This was done to remain within the limits of the pyranometer used. -0.5 0 0.5 -0.5 0 0.5 0 500 1000 1500 2000 2500 x [m]

Spectral irradiance of the Sylvania theater lamp at a distance of 148 cm from the lamp

y [m]

I [

W

/m

2]

Figure 15: Irradiance pattern of light source

The figure clearly shows that the pattern is symmetrical, that the centre of the beam is the most intense part with a maximum intensity of ~2350 W/m2, and that the intensity decreases to towards the beam edges. Integration gives for the total power emitted by the light source a value of approximately 240 W. This is 24% of the input

power of the light source. Assuming that the intensity increases with decreasing distance squared and neglecting losses to the surrounding air, it was estimated that approximately 40 W of power would be available for heating the RAC with the lamp at a close distance from the RAC. With the lens, it was found that this power level increased to about 61 W.

Thruster characterization

During thruster characterization essentially two types of tests are performed: with and without propellant flow.

Without propellant flow

Figure 16 shows typical RAC temperatures obtained for the insulated (M-FIL insulation) thruster. The result indicates that it takes about 30 minutes before the temperature reaches a stable condition. Here a stable situation is considered to be reached when the propellant temperature changes less than 1 degree per minute. After switching off the light source it takes about the same time for the thruster to cool off. From the figure we also learn that the temperature along the RAC is reasonably constant and that the maximum temperature reached is in the range of 700-750 K.

0 10 20 30 40 50 60 70 80 90 100 250 300 350 400 450 500 550 600 650 700 750 Time [min] T e m p er a tur e [ K ] T1 T2 T3 T4

Figure 16: Test results: heating RAC with M-FIL insulation without propellant flow

The highest temperature that the RAC attained during our tests was 750 K using rock wool as insulation. It must however be noted that the rock wool cannot withstand such high temperatures. Without insulation used similar results are obtained, but the RAC temperature

only reaches 550 K which is between 150 and 200 K lower than when insulation is used.

With propellant flow

Measurements have been obtained of thrust, RAC and propellant temperature, and pressure at thruster and nozzle inlet for various mass flow rates.

Typical test results with propellant flow are presented in Figure 17 to Figure 19.

0 5 10 15 20 25 30 35 40 45 250 300 350 400 450 500 550 600 650 700 time [min] T em per at ur e [ K ] 0 5 10 15 20 25 30 35 40 450 50 100 150 200 250 300 M a s s fl o w [m g \s ] RAC T1 RAC T2 T_prop Mass flow

Figure 17: RAC temperature and propellant temperature with mass flow

The Figure 17 shows the measured mass flow rate, and RAC and propellant temperature versus time. Note that for clarity only two RAC temperatures have been included. During the first part (up to approximately 23 minutes) the thruster heats up to a stable temperature in the range 630-650 K. The slight increase in propellant temperature is because of the air inside the heater being heated and is of no real significance here. Once a stable temperature is reached, propellant mass flow is started. This figure shows subsequently the results for two different mass flow rates (77 mg/s and 103 mg/s) with in between a period of about 90 seconds with no mass flow. Upon starting the mass flow rate, we see a fast rise in propellant temperature and after some time a slow decrease. At the same time we see that RAC temperature decreases. The latter is because heat is transferred to the propellant. It is because of the decrease in RAC temperature that after some point also the propellant temperature decreases until after some time the propellant temperature stabilizes. In between the two mass flow rates at mass flow rate is zero, we see the temperature of the RAC

increasing again. Highest stable propellant temperature attained during all the experiments was 525 K at the lowest mass flow rate tested of 50 mg/s.

Figure 18 shows the pressure at the nozzle inlet (nozzle pressure) as well as at the thruster inlet (inlet pressure) measured during the two periods of mass flow rate shown in the Figure 18.

15 20 25 30 35 40 45 50 0.5 1 1.5 2 2.5 3 3.5 4 Time [min] P re ssu re [ b a r] Nozzle pressure Inlet pressure

Figure 18: Pressure measurement

Each increase/decrease in pressure corresponds with an increase/decrease in mass flow rate. The figure clearly shows that only a small pressure drop occurs. The slight decrease in pressure, at constant mass flow rate is attributed to the slowly decreasing temperature of the propellant, see the Figure 17.

The Figure 19 shows typical thrust data measured during the tests with propellant mass flow rate of 77 and 103 mg/s, respectively. Like for the pressure, we see that thrust increases from zero to a more or less stable value when the propellant flow is started and decreases to zero when there is no mass flow. We also see that the thrust remains about constant when the mass flow rate is constant.

The Table 8 shows the final results.

m [mg/s] 77 103 128 154 167 Fmeas[mN] 28.9 43.3 59.7 74.5 81.3 Tprop[K] 494 480 466 452 445 TRAC[K] 545 514 490 470 460 pinlet[bar] 1.97 2.53 3.07 3.61 3.92 pnozzle [bar] 1.94 2.48 3.02 3.55 3.87

Table 8: Test results of solar thermal thruster

The results show that thrust and pressure increase with increasing mass flow rate, whereas propellant and RAC temperature decrease. The

results also show that the pressure drop is maximum 0.05 bar, which is quite reasonable. The results have also been compared to the results following from theory. For thrust this comparison is given in the Figure 19.

15 20 25 30 35 40 45 50 0 10 20 30 40 50 60 Time [min] Th ru s t [ m N ] Theory

Experiment (drift compensated)

Figure 19: Theoretical and measured thrust (drift compensated)

Theoretical thrust has been calculated using the measured propellant temperature and chamber pressure as inputs. Comparison shows that the theoretical thrust agrees fairly well with the experimental values obtained see also the Table 9. m [mg/s] 77 103 128 154 167 Ueq[m/s] 375 420 466 484 487 Fmeas[mN] 28.9 43.3 59.7 74.5 81.3 Ftheory [mN] 33.5 53.1 72.6 91.8 103. 4

Table 9: Experimentally determined equivalent velocity and measured and theoretical thrust at various mass flow rates

The data shows measured thrust is about 80-85% of the thrust from theory. This is due to losses occurring in the thruster and possible thrust misalignment.

Table 9 also shows the equivalent exhaust velocity that follows from the test. We find a fairly strong increase with mass flow rate. This is mostly attributed to the increase in nozzle exit pressure that results from the increase in chamber pressure that accompanies the increase in mass flow rate.

The Figure 20 presents a comparison of the temperature of the RAC as determined from

theory and an averaged RAC temperature as determined from the measurements for the case.

0 20 40 60 80 100 120 200 300 400 500 600 700 800 900 Time [min] T e m p er at u re [ K ] Theory Measurement

Figure 20: Heating RAC with insulation and with flow compared with theory

From the figure we find that the theoretical model shows the same behaviour as found in the experiment. Only the first peak is slightly more pronounced than in the real case (about 23% higher).

Further comparisons were made for the situation wherein the thruster was heated but without propellant flow (both with and without insulation present). The agreement was found to be almost perfect in the case of no insulation. In case of insulation present, the model tends to over-predict the temperature from about 9% for short duration tests up to about 20% for long duration tests. This is attributed to an increase of the emitted power by the lamp with time due to the heating of the lamp itself [20].

As a final parameter, we discuss the thermal efficiency of the system. It is determined by the ratio between the output power and the input power: thermal in

m H

Q

η

=

Δ

(21)

The thermal efficiency obtained at 6 different mass flow rates is shown in Table 10.

m [mg/s] 78 103 128 154 167 205

η

[%] 32 40 45 50 52 60

Table 10: Thermal efficiency

The results show that the efficiency increases with increasing mass flow. So the thermal efficiency can be increased by increasing the mass flow, but then also the thrust level

increases. Another way is to increase the length of the flow channels and/or to decrease the hydraulic radius of the flow channels, thereby enhancing the heat transfer from the RAC to the propellant.

CONCLUSIONS AND

RECOMMENDATIONS

In this study a technology demonstrator of a solar thermal thruster has been designed, built and tested. Thrusts have been measured in the range from 20-100 mN with effective exhaust velocities up to 500 m/s. Results show that there is good agreement between the performances predicted and measured. Because of this good agreement, we are confident that the theoretical model developed can be used for the optimization of the current design and/or for the design of other solar thermal thrusters with different thrust levels and mass flow rates. As such this study is a good first step to a space qualified STP thruster.

To reach higher performances, it is recommended to increase the power input in the system so that higher propellant temperatures can be reached up to the initially defined goal of 1000 K. Also the design of the thruster can be further improved and/or optimized. This can for instance be accomplished by selecting other RAC materials allowing for higher propellant temperatures to be achieved. It is also recommended to investigate improving the heat transfer by changing the diameter of the flow channels and/or the length of the flow channels. The latter could be for instance by spiralling the propellant channels over the cone surface in stead of the straight channel shape now selected. Finally, it is recommended to perform further testing to allow for better characterizing the contribution of the various thruster elements in the total thruster performances.

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