SP2016_3125194

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SPACE PROPULSION 2016, MARRIOTT PARK HOTEL, ROME, ITALY / 2–6 MAY 2016

ELECTRIC PROPULSION SYTEM TRADE-OFF ANALYSIS BASED ON ALTERNATIVE PROPELLANT SELECTION

V. Giannetti(1), T. Andreussi(2), A. Leporini(3), S. Gregucci(4), M. Saravia(5), A. Rossodivita(6), M.

Andrenucci(7), D. Estublier(8), C. Edwards(9)

(1)(2)(3)(4)(6)(7) SITAEL S.p.A., Via A. Gherardesca 5, 56121 Pisa, Italy,

Email: vittorio.giannetti@gmail.com

tommaso.andreussi@sitael.com andrea.leporini@sitael.com stefan.gregucci@sitael.com

angela.rossodivita@sitael.com mariano.andrenucci@sitael.com

(5) University of Pisa, Largo Lucio Lazzarino, 56121 Pisa, Italy,

Email: manuel.saravia@ing.unipi.com

(8)(9) European Space Agency, ESTEC, 2200 AG Noordwijk, The Netherlands,

Email: Denis.Estublier@esa.int Clive.Edwards@esa.int

KEYWORDS: Hall Effect Thruster, Alternative Propellants, System Trade-off.

ABSTRACT:

Recent mission analyses have shown a need for higher power electric propulsion (EP) systems for both Earth orbit raising and deep space applications. Therefore, the development of high power EP systems is being emphasized as the necessary step towards possible future missions of large satellites. Traditionally, xenon has always been the propellant of choice for EP applications due to the optimal compromise between performance and ease of handling it can provide. Although xenon has several technical advantages, its high price suffers of a remarkable fluctuation, posing serious budget concerns. To reduce the propellant cost in high power electric propulsion applications, a more economical alternative to xenon needs to be identified, while retaining thruster performance levels. For a proper propellant selection, system level considerations will be a crucial aspect. Funded by the European Space Agency under the ARTES 5.1 programme element, an experimental campaign was performed at Sitael to test a 5 kW class Hall-effect thruster, operated with a 75% Kr-25% Xe blend, that allowed to characterise thruster

performances as well as the erosion evolution of the channel walls. The results of the test campaign were processed and exploited to validate a reduced order performance and erosion model. The effect of the selected alternative propellant on thruster lifetime and performance were extrapolated as well, along with the consequences at system level of its implementation. This paper presents the modellization and model validation work and provides a trade-off analysis to identify the order of magnitude of potential improvement at system level through the use of different krypton-xenon mixtures.

1. THRUSTER UNDER ANALYSIS

1.1. The HT5k

The SITAEL HT5k is a high power Hall-effect thruster designed to operate in the 2 to 7 kW power range and especially intended for GEO and interplanetary applications. The thruster has a very flexible magnetic circuit composed of two main coils and two auxiliary coils in order to modify the intensity and the topology of the magnetic field. The HT5k can be operated in a wide range of operating conditions that spans from the High Thrust Mode, suitable for orbit insertion, raising or repositioning to the High Specific Impulse Mode, typically used for station-keeping applications.

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The HT5k, installed on the thrust stand is shown in Figure 1. The HT5k is coupled with the HC20 cathode, a LaB6 high-current hollow cathode developed by SITAEL in the past few years [1].

Figure 1. SITAEL HT5k on the thrust stand.

1.2. Alternative propellant

Although xenon has several advantages as a propellant, namely low ionization energy, high atomic mass and easy storage and flow metering, its relatively high price and scarcity hinders the use of xenon in high-power thrusters. Searching for alternative propellants may potentially have two main benefits: the independence from the natural resource market and the reduction in EP development and qualification costs. In particular krypton represents a promising alternative due to its very low cost, its handling properties and the small performance reduction that its use as a propellant implies. Therefore, in the framework of the present project, SITAEL’s HT5k was tested with the selected alternative propellant, i.e. krypton, along with pure xenon and three different mixtures in an initial compatibility test (ICT) to identify the performance envelope and main functional parameters of the thruster. Then, a specific propellant mixture of 75%Kr/25%Xe was selected for further investigations. A first 33 hours test with xenon was performed to have a reference operating condition. Then, the thruster, operating with the chosen alternative propellant mixture, was tested in a limited endurance test of 500 hours at 4.5 kW in SITAEL’s vacuum chamber. During the test, the thruster was periodically switched off, every 30-50

hours, to perform erosion and thrust measurements. For details regarding the experimental campaign see [2][3].

2. SIMULATIONS AND COMPARISON

The model described in [4] was used to study the influence on thruster operation and lifetime of different propellants, comparing the predictions with experimental data gathered for the thruster. We simulated the HT5k operation with pure xenon at the same operative point of the first 33 hour phase, taking into account the real ceramic profile before starting the test. Then, we simulated the thruster operating point with 75%Kr-25%Xe at which the whole 500 hours endurance test was performed [3], taking into account the actual ceramic profile after the first 33 hours phase. The actual magnetic field inside the thruster, simulated through FEMM software, was used to define the magnetic coordinates. The results are reported in Figure 2 and Figure 3. Once the plasma properties in the channel and near plume were computed, we also calculated the performance of the thruster predicted by the model and we compared them with experimental data. As reported in Table 1 and Table 2 the model exhibited a very high accuracy in the prediction of the thruster performance, even though only one free parameter was used.

2.1. Erosion simulations

Once the model is integrated, taking into account the real eroded profile of the thruster, and all the plasma properties profiles are known in the channel and near plume, the data can be used as an input to compute the erosion rate on both the inner and outer ceramic walls. The calculation of the erosion rate is performed using the semi-empirical model described in [5] that also takes into account the effects of different propellants. With the ion current per unit surface to the wall (𝐽𝑖𝑤) given by the model solution, the erosion rate in the direction orthogonal to the wall can be simply computed as 𝜀 = 𝑌𝐽𝑖𝑤 (1)

Then, for short time intervals Δ𝑡, we assume that the change of the channel area has a negligible impact on the plasma properties and we evaluate the actual erosion as the product between the erosion rate and

Δ𝑡.

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Figure 2. HT5k Xe operating point: �̇� = 𝟏𝟓

𝒎𝒈

𝒔, 𝑽𝒅 = 𝟑𝟎𝟎𝑽, 𝑰 = 𝟏𝟒. 𝟕𝟓 𝑨. Simulated plasma properties in the channel and

near plume.

Table 1. Comparison between predicted and experimental performance parameters of the 33 hours test of the HT5k

operating with pure Xe.

Thrust [mN] Anodic 𝑰𝒔𝒑 [s-1] Anodic efficiency

Predicted 267 1814 0.54

Experimental 263 1787 0.52

Figure 3. HT5k 75%Kr-25%Xe operating point: �̇� = 𝟏𝟎

𝒎𝒈

𝒔, 𝑽𝒅 = 𝟑𝟓𝟎𝑽, 𝑰 = 𝟏𝟐. 𝟔 𝑨. Simulated plasma properties in the

channel and near plume.

Table 2. Comparison between predicted and experimental performance parameters of the 500 hours endurance test of

the HT5k operating with 75%Kr-25%Xe. Ceramic profile at the beginning of the test.

Thrust [mN] Anodic 𝑰𝒔𝒑 [s-1] Anodic efficiency

Predicted 213 2136 0.50

Experimental 210 2138 0.50

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In the results presented here we propagated the erosion rate, starting from measured profiles, with a time step of about 50 hours. The results of the model are compared with the data gathered during the 500 hours mixture endurance test. The model predictions are in substantial agreement with the experimental results even though a slightly higher erosion rate is recorded near the channel exit while a lower one is found inside the channel, see Figure 4.

Figure 4. Comparison between measured (solid line) and

computed (dashed line) eroded profiles. (24, 98, 222, 400 and 500 hours endurance test).

Furthermore, as shown in Table 3 the performance predicted by the model are in remarkable agreement even after many hours of endurance firing with the mixture, showing the robustness of the numerical description also with severely eroded channel profiles.

2.2. Alternative propellants effect on total impulse

To generalize the influence on the thruster lifetime of the use of alternative propellants we used a zero order model. The thruster erosion can be obtained as a function of the propellant proprieties, thruster operating parameters and geometry through a set of scaling relations describing the erosion processes inside the channel. The erosion rate at the exit plane of the thruster (𝜀𝑒𝑥) can be expressed as 𝜀𝑒𝑥 = 𝑌𝐽𝑖𝑤𝑒𝑥 , (2) where 𝐽𝑖𝑤𝑒𝑥 is ion current per unit surface to the wall at the exit of the channel. Following [5], at the energy levels of interest for Hall-effect thrusters the sputtering yield can be approximately expressed as

𝑌 ∝𝐸𝑖

𝐸𝑡ℎ∝

𝑢𝑖(𝑒𝑥)2 𝑚𝑖

𝐸𝑡ℎ , (3)

where 𝐸𝑡ℎ is the energy threshold, i.e. the value below which no significant erosion is observed, 𝑢𝑖(𝑒𝑥) is the ion velocity at the channel exit and 𝑚𝑖 is

the propellant mass. Furthermore, we have that

𝐽𝑖𝑤𝑒𝑥 ∝ 𝑢𝐵𝑛𝑒𝑥 , (4) where 𝑢𝐵 and 𝑛𝑒𝑥 represents the Bohm velocity and plasma density at the exit of the channel respectively.

Table 3. Comparison between predicted and experimental performance parameters during the 500 hour endurance test,

with the 75%Kr/25%Xe.

Endurance firing time [h]

Performance Thrust [mN] Anodic 𝑰𝒔𝒑 [s-1] Anodic efficiency

24 Predicted 210 2136 0.52

Experimental 210 2138 0.50

98 Predicted 213 2173 0.51

Experimental 215 2195 0.53

222 Predicted 212 2164 0.51

Experimental 209 2126 0.50

400 Predicted 211 2150 0.50

Experimental 209 2130 0.50

500 Predicted 210 2136 0.50

Experimental 208 2124 0.49

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In particular, 𝑛𝑒𝑥, 𝑢𝐵 and 𝑢𝑖(𝑒𝑥) are related to 𝑛𝑖𝑛 and

𝑉𝑑 as follows:

𝑛𝑒𝑥 ∝ 𝑛𝑖𝑛

√𝑉𝑑 , (5)

𝑢𝑖(𝑒𝑥) ∝ √𝑉𝑑

𝑚𝑖 , (6)

𝑢𝐵 ∝ √𝑇𝑒

𝑚𝑖∝

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√𝑚𝑖 , (7)

where 𝑛𝑖𝑛 represents the gas density at the injection

plane of the thruster. The density 𝑛𝑖𝑛 can be written as

𝑛𝑖𝑛 ∝ �̇�

𝐴√𝑚𝑖 , (8)

where �̇� and 𝐴 represent the thruster mass flow rate and channel area respectively. Therefore, the erosion rate results

𝜀𝑒𝑥 ∝�̇�√𝑉𝑑

𝐸𝑡ℎ𝐴𝑚𝑖 . (9)

Finally, the total impulse can be written as

𝐼𝑇𝑂𝑇 = 𝑇∆𝑡𝑡𝑜𝑡 ∝ 𝑇𝑏

𝜀𝑒𝑥∝ 𝑏𝐴𝐸𝑡ℎ√𝑚𝑖 , (10)

where ∆𝑡𝑡𝑜𝑡 represent the thruster lifetime and b is the ceramic wall thickness. This simple model shows that in first approximation the thruster total impulse does not explicitly depend on the thruster operating regime, but is only a function of the thruster geometry and propellant proprieties. In particular, the effect of the propellant on the thruster total impulse is given by the constant term 𝐸𝑡ℎ. With the results presented above the effect of the alternative propellant can be evaluated,

𝐼𝑇𝑂𝑇

𝑚𝑖𝑥

𝐼𝑇𝑂𝑇𝑋𝑒 =

𝐸𝑡ℎ𝑚𝑖𝑥

𝐸𝑡ℎ𝑋𝑒 √

𝑚𝑖𝑚𝑖𝑥

𝑚𝑖𝑋𝑒 , (11)

where the subscript Xe is relative to pure xenon, whereas the subscript mix indicates the 75%Kr-25%Xe mixture.

The ratio 𝐸𝑡ℎ𝑚𝑖𝑥 𝐸𝑡ℎ

𝑋𝑒 ⁄ can be evaluated from

experimental data,

𝐸𝑡ℎ

𝑚𝑖𝑥

𝐸𝑡ℎ𝑋𝑒 ∝

𝜀𝑒𝑥𝑋𝑒

𝜀𝑒𝑥𝑚𝑖𝑥

𝑚𝑖𝑋𝑒

𝑚𝑖𝑚𝑖𝑥

�̇�𝑖𝑚𝑖𝑥

�̇�𝑖𝑋𝑒 √

𝑉𝑑𝑚𝑖𝑥

𝑉𝑑𝑋𝑒 . (12)

In particular, we used the experimental data gathered after 33 hours of operation with both pure Xe and 75%Kr-25%Xe [3]. The average erosion rate of the outer wall was the highest and therefore it was used in order to estimate the thruster total impulse with the mixture. Notice that an equivalent atomic mass of the mixture was defined as a weighted average of the atomic mass of pure propellants. The results, reported in Table 4, show that the effect of krypton is to reduce the total impulse of the thruster by a factor of about ~1.82.

Table 4. Xenon and mixture total impulse comparison.

𝑬𝒕𝒉𝒎𝒊𝒙 𝑬𝒕𝒉

𝑿𝒆 ⁄ 0.64

𝑰𝑻𝑶𝑻𝑿𝒆 𝑰𝑻𝑶𝑻

𝒎𝒊𝒙⁄ 1.82

These results are in agreement with those presented for the SPT 100 in [6], in which a higher erosion rate for krypton is reported, which

corresponds to a factor 𝐼𝑇𝑂𝑇𝑋𝑒 /𝐼𝑇𝑂𝑇

𝐾𝑟 ~1.5.

3. SYSTEM TRADE OFF ANALYSIS

A trade-off analysis was carried out to evaluate potential benefits of the selected propellant including performance, system and financial aspects. The study was composed by three different phases: i) selection of one or more mission scenarios to compare the propellant performance; ii) preliminary assessment of the performance; iii) validation of the previous results by means of low-thrust numerical simulations.

3.1. Preliminary System Architecture

The preliminary system architecture of the Electric Propulsion Subsystem (EPS) considered in this study is composed by: i) a set of Thruster Units (TUs) composed by one thruster, one Flow Control Unit (FCU) and one cathode; ii) a set of Power Processing Units (PPUs) capable of powering and commanding one or more TUs; iii) a set of Filter Units (FUs) to reduce high frequency current noise absorbed by the thruster; iv) a Tank Assembly (TA) composed by one or more tanks for xenon, one or more tanks for krypton and a low pressure plenum tank for the mixing of the two propellants at any required ratio.

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Table 5. Most relevant characteristics and operational constraints for the three telecommunication platforms identified.

Small Medium Large

Launch Mass Up to 3000 kg Up to 4500 kg Up to 6000 kg

On-board Power @ BOL < 11 kW < 15 kW < 20 kW

EPS Available Power @EOL

EOR < 9 kW < 13 kW < 18 kW

SK < 3 kW < 3 kW < 3 kW

EOR Duration < 180 days < 140 days < 100 days

S/C Lifetime ≥ 15 years ≥ 15 years ≥ 15 years

Thruster Supply Voltage 250 – 450 V 250 – 450 V 250 – 450 V

3.2. Investigated Scenarios

The Next Generation Telecom Platforms with a dedicated EPS power higher than 3 kW were selected in this study as potential application of EPS based on alternative propellants. Starting from the baseline requirements and information provided by satellite operator and from the state-of-the-art launcher performance, three different classes of telecommunication platforms (Small, Medium and Large) and different operational scenarios have been identified to assess the performance enabled by each propellant blend. Two different tasks for the platforms have been preliminary analyzed to compare the propellant performance: an Electric Orbit Raising (EOR) to a Geostationary Earth Orbit (GEO) and a 15-years Station Keeping (SK) manoeuvre. Table 5 summarizes the characteristics of each platform in terms of platform launch wet mass, power available for the EPS during the EOR and SK phases, as well as their operational requirements that are the EOR transfer time and S/C lifetime. The duration of the EOR phase represents one of the main constraints and therefore one of the most important performance parameters, due to the high costs associated with the significant delay between the launch and the

actual start of commercial service of the platform, especially for the Large platform. A small set of candidate launch orbits has been identified for each of the launchers presented in Table 6. These were studied in order to assess the total impulse, velocity increment, time required to reach the target GEO orbit and the corresponding amount of propellant, as well as other parameters, such as the propellant mass, volume and cost associated to the different blends analyzed. The selected launchers, as well as the delivered mass for each strategy are presented in Table 6 [7][8][9][10]. It is worth noting that this list is not meant to be an exhaustive overview of the available launch vehicle options, but just some reference cases of common use among the platform classes selected.

3.3. Preliminary Mission Analysis

This preliminary analysis is aimed at comparing the performance in terms of transfer time and propellant mass consumption enabled by each proposed blend. The first step of the study is devoted to preliminary estimate the velocity increment required to perform the EOR manoeuvre with the three investigated platforms taking into account the following simplifying assumptions:

Table 6. Delivered mass for selected launch vehicles and orbits.

Proton Falcon Ariane 5 Soyuz

Strategy GTO1 GTO2 GTO3 SSTO GTO1 GTO2 GTO3 SSTO GTO GTO

Delivered mass [kg]

4450 5250 6150 5250 4682 4503 3875 2828 7000 3250

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- At the beginning of the EOR phase, the platform is released by the launcher on the exact target orbit and no orbit correction maneuver is required.

- No external perturbation forces (atmospheric drag, Earth’s oblateness, J2 effect, solar radiation pressure, etc.) are considered during the low thrust transfers. The magnitude of the acceleration exerted by the thruster on the platform is significantly higher than the one due to perturbation forces.

- No orbit phasing is considered to adjust the platform initial position with respect to a specific target longitude on the GEO orbit.

- The time required for the commissioning in orbit is neglected with respect to the time needed for orbital maneuvers. Moreover, the time required for the early orbit phase is not expected to change significantly with respect to traditional telecommunication missions.

- The thruster is assumed to be operating during the whole transfer phase. The duration of eclipse phases during the EOR is typically negligible with respect to the whole transfer.

Given these assumptions, the equations used in the following for the modeling of the EOR phase are the Pollard approximation for the eccentricity (Δe) change [11] and the Edelbaum approximation [12] for the assessment of the velocity increment required for the semi-major axis (Δa) and inclination change (Δi) between non-coplanar circular orbits. These laws do not apply directly to the case of a combined and simultaneous change of all the three parameters (a, e, i) and, for this reason, the ∆V required for the transfer from elliptical parking orbits considered to the GEO orbit is computed as the Euclidean norm of the two velocity increment (ΔV) values. The change of the orbit eccentricity can then be assessed by means of the Pollard equation [11]:

Δ𝑉Δ𝑒 = 2

3√

𝜇

𝑎|arcsin 𝑒1 −arcsin 𝑒2|, (13)

where a is the orbit semi-major axis, µ is the Earth gravitational parameter, and e1 and e2 the initial and the target values of the orbit eccentricity. This maneuver is accomplished with in-plane acceleration perpendicular to the major axis of the ellipse. Furthermore, the Edelbaum approximation providing the ∆V required for the combined semi-major axis and inclination change is [12]:

Δ𝑉Δ𝑎,Δ𝑖 = √𝑉02 − 2𝑉𝑉0𝑐𝑜𝑠 (

𝜋

2Δ𝑖) + 𝑉2, (14)

where V0 and V represent, respectively, the orbital velocity on the initial and final orbit and ∆i is the desired inclination change angle. Computed ΔV values required to move the platform from the launcher delivery orbit to the GEO target orbit are presented in Table 7. The values presented in Table 7 together with platform scenario characteristics (Table 5) and the thruster’s performance measured during the test campaign [2] have been utilized to assess the amount of propellant required to reach the target orbit, the number of thrusters required to perform the maneuver and the time needed to get to orbit using the different propellant mixtures. Since the power available during the EOR phase (Pav) is sufficient to sustain one or more TU(s) operating at the same discharge power (Pthr), the maneuver time to accomplish the task has been evaluated considering more than one TU firing at the same time (Eq. 15).

∆𝑡𝑡𝑜𝑡 =𝑚𝑝

�̇�𝑡𝑜𝑡

𝑃𝑎𝑣

𝑃𝑡ℎ𝑟⁄ , (15)

This latter quantity has been simply obtained dividing the overall available power by the power required by one TU, resulting from case to case in fractional numbers. Even if a fractional number does not represent a reasonable solution, these values have been accepted to obtain results reflecting completely the characteristics of the described scenarios where the platform uses all the thruster available power to perform the EOR.

Table 7. Velocity increments required for taking the platform from the parking orbit to the target GEO.

Proton Falcon Ariane 5 Soyuz

GTO1 GTO2 GTO3 SSTO GTO1 GTO2 GTO3 SSTO GTO GTO

ΔVΔe 0.858 1.547 1.673 1.281 2.211 2.211 2.211 2.106 2.198 2.198

ΔVΔa.Δi 0.927 1.306 2.312 1.143 1.302 1.084 0.970 1.574 1.128 1.122

ΔVTOT 1.263 2.025 2.854 1.717 2.565 2.462 2.414 2.629 2.470 2.467

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In order to compare the propellant performance, a reference launcher has been selected for the EOR phase for each platform. Starting from the ∆V values reported in Table 7, the reference values have been selected taking into account the transfer time required to accomplish the EOR task, the mass/cost advantage of using a specific launcher and the typical ∆V for the EOR and SK maneuvers found in literature. For the case of the large platform, it is verified that a full-electric EOR does not comply with the time requirement (< 100 days), so an orbit topping strategy has been assumed in this analysis. This strategy implies that an initial rise is done by means of a chemical thruster, and only the final transfer is attained by the electric thruster, to the equivalent value of ∆V=1.1 km/s [13]. The representative launchers for each platform, and the relative ∆V selected for the EOR mission are presented in Table 8. Table 8. Typical ∆V values for each platform scenario for

the EOR phase.

Platform scenario

Launcher Strategy ∆V

Small Falcon 9 GTO3 2.414 km/s

Medium Proton SSTO 1.717 km/s

Large Ariane 5 Orbit

topping 1.1 km/s

3.4. Mission Performance Estimation

Taking into account the ∆V reported in Table 8, the performance of the following propellant blends have been computed according to the thruster performance measured during the test campaign: pure xenon, pure krypton, 75%Xe-25%Kr, 50%Xe-50%Kr, 25%Xe-75%Kr. The following quantities have been considered:

- Mass of the propellant required to perform the explored tasks (EOR and SK);

- Time required to accomplish the maneuver (EOR);

- Propellant cost and volume (EOR and SK);

- Mass of the tanks needed to store the propellant (EOR and SK).

The propellant mass consumption and the maneuver time have been computed using the previously described method. The propellant cost

ratio we considered for the two propellants was Xecost/Krcost ≈ 12, which reflects the current market trends. The volume required to store the propellant has been estimated considering a storage pressure of 150 bar and a temperature of 300 K with a corresponding density value of 1.8 kg/dm3 for Xe and 0.65 kg/dm3 for Kr, computed according to the Redlich-Kwong equation [14]. Since the lower Kr density results in more voluminous tanks, the tank mass has been added to the propellant mass. Under the assumption of storing Xe and Kr in separated tanks at the storage conditions proposed, the tankage mass fraction (defined as the ratio of the tank mass mt to the propellant mass mp) has been calculated with the following relation [14]:

𝑚𝑡

𝑚𝑝=

3 𝑃 𝛽 𝜌𝑡

2 𝜎𝑦 𝜌𝑝 , (16)

where 𝜌𝑝 is the propellant density at the storage

pressure P, 𝛽 is the safety factor, 𝜌𝑡 is the tank

material density and 𝜎𝑦 is the yield strength.

Assuming a spherical titanium tank (𝜌𝑡= 4850 kg/m3,

𝜎𝑦 = 1.4 x 109 N/m2) with a safety factor of 2 [14],

the tankage fraction for xenon is about 8.7% while for krypton is 24%.

3.5. Results

With the aim of comparing the thruster performance with the proposed propellants, a non-dimensional performance index Z was introduced. This allows obtaining a more intuitive representation of the results trend, identifying at the same time a set of suitable solutions as a function of the mission performance parameters. At fixed conditions or working points (e.g. power, mass flow rate, etc.) for each propellant, the figure of merit Z has been defined as the sum of each performance parameter, opportunely normalized with the maximum value among all propellants, multiplied by a specific weight factor (k):

𝑍 = 𝑘∆𝑡

∆𝑡

∆𝑡𝑚𝑎𝑥

+ 𝑘𝑐𝑜𝑠𝑡

𝑐𝑜𝑠𝑡

𝑐𝑜𝑠𝑡𝑚𝑎𝑥

+ 𝑘𝑉

𝑉

𝑉𝑚𝑎𝑥

+𝑘𝑚𝑝

𝑚𝑝

𝑚𝑝𝑚𝑎𝑥+ 𝑘𝑚𝑡𝑜𝑡

𝑚𝑡𝑜𝑡

𝑚𝑡𝑜𝑡𝑚𝑎𝑥 (17)

The lower the value of Z the more performing the propellant is. As a first analysis, the propellant cost and the transfer time have been assumed as the most relevant performance indexes. Therefore, in Eq. 17 only the first two contributions have been considered.

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3.4.1 Small Platform As expected, due to the higher Isp of the thruster fed in krypton, the propellant mass required to perform both EOR and SK tasks with pure Kr is always lower. This difference is always below 12% (~ 50 kg) but, adding the tank mass, this difference becomes negligible and in some cases even negative. Due to the higher thrust to power ratio typical of Xe with respect to Kr, the time saved using Xe for the EOR is about 30% ( ~ 45 days) whereas the high cost difference between Xe and Kr (Xecost/Krcost ≈ 12) results in cost savings of about 85% (600 to 815 k€). Table 9 reports an example of the thruster performance for each propellant blend measured at the same discharge voltage and propellant mass flow rate (AMFR=8mg/s Vd=300V). Table 9. Experimentally measured thruster performance

for different blends (AMFR=8mg/s Vd=300V).

Propellant Power [W]

Thrust [mN]

Isp [s]

TU

Xe 2310 135 1529 3.9

75%Xe- 25%Kr 2550 140 1586 3.5

50%Xe - 50%Kr

2790 144 1631 3.2

25%Xe - 75%Kr

3030 150 1699 30

Kr 3210 151 1710 2.8

Figure 5 shows the value of the Z parameter with respect to the percentage of Kr in the propellant blend as a function of the weight of each performance parameter (k∆t, kcost). As shown in Figure 5, if some relevance is given to the propellant cost, Kr represents the most suitable choice together with the different blends, whereas if the maneuver time is a stringent requirement (k∆t = 90%, kcost = 10%) the Xe solution should be envisaged. In particular, assuming a weight of 20% for the cost and 80% for the maneuver time, a relative minimum of Z can be identified for the 25% Xe - 75% Kr blend. In the SK phase, considering a total EPS available power of 3 kW, only one HT5k can be fired at any given time, and a ΔV of 1 km/s is considered [15]. Considering almost equal thruster power levels (TU with Xe operating at 2940W, TU with Kr operating at 2870 W), the lower thrust level exerted on the spacecraft using Kr as propellant results in an increase of the firing time of about 30% ( ~90days ) with a corresponding propellant mass saving lower than 10% ( ~20kg ) and cost savings of about 80% ( ~360k€ ).

Figure 5. Figure of merit Z for the small platform

scenario (AMFR = 8mg/s, Vd = 300V). Different colors correspond to different 𝑘𝑐𝑜𝑠𝑡.

3.4.2 Medium Platform Similarly to the small platform scenario, the difference between the mass of propellant required to perform the task with Kr with respect to Xe is always lower than 13% ( ~ 54 kg), but taking into account the tank mass this difference becomes very small and in some cases even negative. Also in this case the time saved using Xe for the EOR is about 26% ( ~ 33 days) whereas the high cost difference between Xe and Kr (Xecost/Krcost ≈ 12) results in cost saving about 87% (688 to 895 k€). Table 10 reports the thruster performance at 350 V and a propellant mass flow rate of 8mg/s.

Table 10. Experimentally measured thruster perfor-mance for different blends (AMFR=8mg/s Vd=350V).

Propellant Power [W]

Thrust [mN]

Isp [s] TU

Xe 2611 148 1676 5.0

75%Xe- 25%Kr 3010 154 1744 4.3

50%Xe - 50%Kr

3325 161 1824 3.9

25%Xe - 75%Kr

3605 164 1858 3.6

Kr 3815 168 1903 3.4

Figure 6 shows the value of the Z parameter with respect to the percentage of Kr in the propellant blend as function of the weight of each performance parameter (k∆t, kcost). Also in this case, due to the high cost difference between Xe and Kr, if the cost is the key mission parameter, krypton and the relative blends represent an appropriate solution. For the SK phase, considering the same operative point of the small platform scenario, the lower thrust level exerted on the spacecraft using Kr as propellant results in an increase of the firing time by

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30% ( ~ 135 days) with a corresponding propellant mass saving lower than 10% (~ 30 kg) and cost saving of about 81% (~ 540 k€).

Figure 6. Figure of merit Z for the medium platform

scenario (AMFR = 8mg/s, Vd = 350V). Different colors

correspond to different 𝑘𝑐𝑜𝑠𝑡.

In conclusion, Xenon represents the most suitable choice for the EOR phase if faster maneuvers are required, whereas Kr (thanks to the generally higher specific impulse), represents an ideal alternative for the SK phase despite the lower thrust exerted on the spacecraft. The time available for SK maneuvers allows indeed tolerating lower acceleration levels.

3.4.3 Large Platform The large platform scenario is based on a hybrid approach for the EOR phase, for which the initial stage of the maneuver is done by means of a chemical launcher and the final rising is performed by the EPS. Given that this platform has a large amount of power available for the EPS, different TUs could be used for the EOR phase. To simplify the EPS design an additional constraint has been imposed in this study on the maximum number of TUs firing at the same time: no more than 5 TUs. The lower velocity increment associated with the EOR phase, allows to identify a wide range of suitable solutions both for Xe and Kr. In particular, envisaging the utilization of TUs operating with a tension of 450 V and AMFR of 8mg/s (Table 11), about 300 kg of Kr are sufficient to complete the EOR phase, whereas 330 kg of Xe are required to perform the same task. This result implies a difference in propellant cost of about 600 k€. In the SK phase, it is possible to consider Kr a suitable alternative for this task with an average reduction in the mass of the required propellant and therefore propellant cost. Figure 7 shows the figure of merit Z for the different propellants tested. As for the previous scenarios, it is possible to define a combination of the time and cost weights that allows for a selection of a specific propellant blend.

Table 11. Experimentally measured thruster perfor-mance for different blends (AMFR=8mg/s Vd=350V).

Propellant Power [W]

Thrust [mN]

Isp [s] TU

Xe 3505.5 175.2 1984 5.0

75%Xe- 25%Kr 3960 180 2039 4.5

50%Xe - 50%Kr

4230 184 2084 4.3

25%Xe - 75%Kr

4455 189 2141 4.0

Kr 4725 192 2175 3.8

Figure 7. Figure of merit Z for the large platform scenario (AMFR = 8mg/s, Vd = 450V). Different colors correspond

to different 𝑘𝑐𝑜𝑠𝑡.

3.6. Thruster lifetime considerations

The results of the 500 hours HT5k endurance test, performed using the mixture of krypton and xenon [3], and the simulated thruster performance have shown that the firing time needed for both the EOR and SK phase (<5000 hours) is compliant with the expected thruster lifetime for all propellant blends.

4. CONCLUSIONS

The performance validation test and the numerical simulations carried out on the HT5k thruster allowed to assess the erosion rates of the ceramic walls for pure xenon and for a 25%Xe-75%Kr mixture. The progression of the erosion was then investigated and the predictions of the numerical code, in terms of both erosion profiles and thruster performance, were validated against the performed experimental measurements. The analysis of these results highlighted the effects of alternative propellants on the thruster lifetime. In agreement with [6], propellant mixtures with a high percentage of krypton can cause a significant reduction of the thruster total impulse. The analyses presented in this study allowed to identify a set of mission scenarios and platform

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characteristics suitable for telecommunication missions performed with the HT5k EPS. After the assessment of the thruster experimental performance, a set of launcher options has been investigated to identify a representative mission profile for each class of platforms (small, medium, large). Then, the performance at system level of the five propellant options (Xe, Kr, 75%Xe-25%Kr, 50%Xe-50%Kr, 25%Xe-75%Kr) have been assessed for the three platform sizes, both for the EOR and SK tasks. From the transfer time point of view, the obtained results have shown that Xe generally represents the best option for the EOR phase, thanks to the high thrust level provided. On the other hand, since the cost of krypton is significantly lower than the one for xenon (Xecost/Krcost ≈ 12), krypton represents the most suitable alternative for both the EOR phase, when the cost savings are important, and for the SK tasks, where the firing time is not a critical parameter and the available higher specific impulse allows saving a significant amount of propellant. In addition, a preliminary estimation of the tank mass needed in the different scenarios has been performed. It is possible to notice that, due to the lower density of krypton, the mass saving deriving from the krypton higher specific impulse could be cancelled by the tank mass needed to store the propellant. The mission performance enabled by propellant blends (Xe-Kr) have been investigated by means of the figure of merit Z, which comprises a weight for each performance parameter. In this case, the results have shown that different blends and configurations might be envisaged in view of specific mission and customer requirements. In particular, for some combination of the performance parameter, the Z figure presents a minimum for some propellant blends. In general, mission targets such as minimum time and volume would identify xenon as the most appropriate propellant, whereas krypton will typically result in lower propellant mass consumption and propellant cost.

5. ACKNOWLEDGMENTS

Fruitful discussions with Cosmo Casaregola and the Eutelsat team involved in the project are gratefully acknowledged. The work described in this paper has been funded by the European Space Agency in the framework of the ARTES 5.1 contract 4000113792/15/NL/NR “Identification, Evaluation and Testing of Alternative Propellants for Electric Propulsion Systems”.

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