# Challenges of Ablatively Cooled Hybrid Rockets for Satellites or Upper Stages

## Abstract

**:**

## 1. Introduction

## 2. Hybrid Rocket Combustion Chamber Sizing

_{max}:

_{max}but even the R

_{min}necessary for a good volume loading. This is the typical problem of boosters that is repeatedly discussed in the hybrid literature. However, in this paper, an often overlooked opposite situation is highlighted, which is typical of the application under consideration, i.e., satellites and upper stages. If the thrust is low and the burning time is very long, the value of a can result to be too low and incompatible with any of the classical polymeric fuels that have been successfully used for hybrid propulsion. On a few occasions, some fuels have been used with even lower regression rates (such as blocks of graphite) but without the same combustion performance.

_{max}for maximum packaging) the length of the grain is proportional only to the burning time, not to the thrust of the motor. This result seems counter-intuitive, as in general it is expected that a larger motor is also longer. Moreover, for the same total impulse, an increase in the burning time should shorten the motor, not the opposite. Nevertheless, in the common literature, the regression rate level is considered as constant, while in this analysis the regression rate is tailored to achieve but not overcome R

_{max}. As already pointed out, this is not always possible at the two extremes of the range of allowable regression rate levels.

_{max,}two motors with different propellant masses (i.e., total impulse and thrust) will have the same length as the smaller motor needs to burn with a lower regression rate level (e.g., changing the fuel or the injection pattern) in order to keep the web thickness proportional to the smaller initial port diameter.

## 3. Satellites and Spacecrafts

#### 3.1. Current Status Quo

^{TM}motor series, it is possible to note that, even with a certain level of data dispersion due to the different design requirements, the burning time of the solid motors tend to increase with the scale of the motor, from a dozen of seconds at few hundred newtons up to asymptotically reach a value around 100 s at dozens of kN. This implies that an increase in total impulse is necessarily related with an increase in motor thrust. On the contrary, the typical radiative in-space small liquid engine has virtually an unlimited firing time (on the order of hours), so it can provide a large total impulse at very low thrust. Liquid engines operate for a long burning time for several reasons: keep the engine and fluidic size/mass/cost/emitted heat at a minimum, limit the spacecraft acceleration, operate at low pressures with a benefit on the pressurization budget and chamber thermal loads without compromising the engine size.

#### 3.2. Hybrid Analysis

- The satellite/spacecraft is limited by a maximum allowable acceleration;
- No significant acceleration limits are considered;
- The satellite/spacecraft requires a minimum acceleration level for a specific maneuver.

#### 3.3. Heat Soak-Back and Fuel Issue for Satellites

## 4. Upper Stages

#### 4.1. Current Status Quo

#### 4.2. Hybrid Analysis

_{2}O

_{2}) and two fuels, a high regressing one (such as paraffin wax) and a low regressing one (such as HDPE, [High Density PolyEthylene]). The specific impulse was fixed to 340 s for the LOX combinations and to 300 s for the H

_{2}O

_{2}ones. The regression rate coefficients for LOX-paraffin have been defined as a = 0.117 and n = 0.62 [31] (with G

_{ox}in kg/m

^{2}s and $\dot{r}$ in mm/s); for H

_{2}O

_{2}–paraffin a = 0.15 and n = 0.5 [37]. The regression rate of the HDPE cases was fixed as five times lower than the paraffin one [31]. The paraffin fuel density was set to 930 kg/m

^{3}while the HDPE density to 950 kg/m

^{3}. The mixture ratio for the LOX combinations was set equal to 2.7, while 7.5 was chosen for the H

_{2}O

_{2}combinations. The initial oxidizer flux was fixed to 500 kg/m

^{2}·s. The internal diameter D

_{0}was calculated from the oxidizer mass flow and initial mass flux while the external diameter was calculated with the following equation:

_{f}can be determined. The results are shown in the following Table 3, Table 4, Table 5 and Table 6.

_{2}O

_{2}is lower than that with LOX, so the diameter ratio is higher with the latter. The length to diameter ratio of the grain is much lower for H

_{2}O

_{2}thanks to its higher optimal mixture ratio and, consequently much lower fuel mass. For very long burning times (relative to the thrust level), the paraffin motors turn out to have too high diameter ratios and sometimes too low L/D

_{f}(the latter particularly for H

_{2}O

_{2}). On the contrary, reducing the regression rate with the HDPE fuel makes the diameter ratio more manageable but significantly increases the L/D

_{f}to values that are generally not acceptable.

_{f}tabulated values refer to the grain, not to the whole stage. As the majority of the propellant is the oxidizer, it is easy to understand that, if the oxidizer is placed in a tank with the same diameter of the grain, the total length to diameter ratio will be more compatible with a booster than an upper stage. The only way to achieve a very low hybrid stage length to diameter ratio with a serial configuration is to use a cluster of combustion chambers or a multiport grain, but both solutions come with several drawbacks and have a significant impact on the inert mass of the stage, which is a fundamental parameter for an upper stage. Therefore, it is necessary to place the oxidizer in a different way. Three possible solutions have been presented by Karabeyoglu [9] as shown in Figure 5.

_{2}O

_{2}is preferable when the orbital mission duration becomes relevant. Metal additives [40] can increase the specific impulse and fuel density but they generally also operate at lower optimal mixture ratios.

#### 4.3. Heat Soak-Back, Fuel Issue, and Orbit Insertion for Upper Stages

## 5. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

a, n | regression rate law coefficients |

D_{0} | initial port diameter |

D_{f} | final port diameter |

D_{t} | nozzle throat diameter |

$\dot{er}$ | nozzle throat erosion rate |

G_{0} | initial port oxidizer mass flux |

G_{ox} | port oxidizer mass flux |

G_{max} | maximum (initial) port oxidizer mass flux |

I_{tot} | total impulse |

L | fuel length |

${\dot{m}}_{ox}$ | oxidizer mass flow |

p_{c} | chamber pressure |

$\dot{r}$ | fuel regression rate |

R | diameter ratio |

R_{min} | minimum diameter ratio |

R_{max} | maximum diameter ratio |

t_{b} | burning time |

T | thrust |

V_{fuel} | fuel grain volume |

ΔV | spacecraft velocity increment |

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**Figure 1.**Examples of hybrid rocket design limits for satellites: (

**a**) Propellant mass vs. thrust; (

**b**) Velocity increment vs. thrust for different maximum allowable accelerations. Reprinted with permission from ref. [30]. Copyright 2020 American Institute of Aeronautics and Astronautics.

**Figure 2.**Examples of liquid propelled space tugs: (

**a**) NPO Lavochkin Fregat (Soyuz/Zenit); (

**b**) GKNPTs Khrunichev Briz-M (Proton). Note the extremely compact length to diameter ratio and the propellant tank arrangement. Copyright: publicly available pictures on the internet.

**Figure 3.**Examples of upper stages for small launch vehicles: (

**a**) Liquid propelled SpaceX Falcon 1; (

**b**) ORPHEE Hybrid Upper Stage proposal. Note the relatively high length to diameter ratio of the serial hybrid and the compact packaging of the common bulkhead liquid propellant design. (

**a**) Reprinted with permission from ref. [36]. Copyright 2008 International Astronautical Federation. (

**b**) Reprinted with permission from ref. [6]. Copyright 2010 American Institute of Aeronautics and Astronautics.

**Figure 4.**Examples of solid rocket upper stages: (

**a**) Avio Zefiro 9 (Vega); (

**b**) Northrop Grumman Star 48 (Minotaur IV). Note the very compact length to diameter ratio. (

**a**) Reprinted with permission from https://www.avio.com/ (accessed on 9 July 2021). Copyright 2021 Avio. (

**b**) Reprinted with permission from ref. [34]. Copyright 2016 Northrop Grumman.

**Figure 5.**Examples of hybrid upper stage arrangements: (

**a**) Serial; (

**b**) Toroidal; (

**c**) Multiple tanks. Reprinted with permission from ref. [9]. Copyright 2011 American Institute of Aeronautics and Astronautics.

**Figure 6.**Sampling of Scorpius

^{®}[USA] Composite Tanks (1.7 MPa MEOP (250 psi)): Volume vs. Tank mass factor. Reprinted with permission from ref. [39]. Copyright 2010 American Institute of Aeronautics and Astronautics.

Model (Stage/Launcher) | Manufacturer | Country |
---|---|---|

RD-843 (AVUM-Vega) | Yuzhmash | Ukraine |

17D64 (Volga-Soyuz) | KB Melnikov | Russia |

S5.98M (Briz-Proton) | KBKhM | Russia |

S5.92 (Fregat-Zenit) | KBKhM | Russia |

Rutherford (Electron) | RocketLab | USA-New Zealand |

Aestus (Ariane 5) | Airbus Defence and Space | Europe |

Kestrel (Falcon 1) | SpaceX | USA |

Orion 38 (Pegasus) | Northrop Grumman | USA |

HM7B (Ariane 5 ECA) | Snecma | France |

RL10 (Centaur) | Aerojet Rocketdyne | USA |

Vinci (Ariane 6) | ArianeGroup | Europe |

Zefiro 9 (Vega) | Avio | Italy |

Castor 30 (Antares) | Northrop Grumman | USA |

Merlin 1D (Falcon 9) | SpaceX | USA |

Model (Stage/Launcher) | Thrust (kN) | Burning Time (s) |
---|---|---|

RD-843 (AVUM-Vega) | 2.45 | 300–600 |

17D64 (Volga-Soyuz) | 2.94 | 600 |

S5.98M (Briz-Proton) | 19.6 | 3000 |

S5.92 (Fregat-Zenit) | 19.85 | 1350 |

Rutherford (Electron) | 26 | 258–373 |

Aestus (Ariane 5) | 27 | 1170 |

Kestrel (Falcon 1) | 31 | 378 |

Orion 38 (Pegasus) | 32 | 67.7 |

HM7B (Ariane 5 ECA) | 67 | 945 |

RL10 (Centaur) | 110 | 400–700–1125 |

Vinci (Ariane 6) | 180 | 900 |

Zefiro 9 (Vega) | 314 | 117 |

Castor 30 (Antares) | 300–500 | 127–156 |

Merlin 1D (Falcon 9) | 934 | 397 |

Reference Model | Grain R = D_{0}/D_{f} | Grain L/D_{f} |
---|---|---|

RD-843 (AVUM-Vega) | 11–15 | 1.3–1.1 |

17D64 (Volga-Soyuz) | 14 | 1.1 |

S5.98M (Briz-Proton) | 19 | 0.9 |

S5.92 (Fregat-Zenit) | 13 | 1.1 |

Rutherford (Electron) | 5.9–7 | 2.1–1.9 |

Aestus (Ariane 5) | 11.5 | 1.3 |

Kestrel (Falcon 1) | 6.8 | 1.9 |

Orion 38 (Pegasus) | 3.2 | 3.4 |

HM7B (Ariane 5 ECA) | 8.5 | 1.6 |

RL10 (Centaur) | 5.2–6.7–8.3 | 2.3–1.9–1.6 |

Vinci (Ariane 6) | 6.7 | 1.9 |

Zefiro 9 (Vega) | 2.5 | 4.1 |

Castor 30 (Antares) | 2.6 | 4 |

Merlin 1D (Falcon 9) | 3.3 | 3.3 |

Reference Model | Grain R = D_{0}/D_{f} | Grain L/D_{f} |
---|---|---|

RD-843 (AVUM-Vega) | 10–14 | 0.6–0.4 |

17D64 (Volga-Soyuz) | 13 | 0.4 |

S5.98M (Briz-Proton) | 18 | 0.3 |

S5.92 (Fregat-Zenit) | 12 | 0.4 |

Rutherford (Electron) | 5–6 | 1.1–0.9 |

Aestus (Ariane 5) | 10.5 | 0.5 |

Kestrel (Falcon 1) | 5.8 | 0.9 |

Orion 38 (Pegasus) | 2.6 | 2 |

HM7B (Ariane 5 ECA) | 7.6 | 0.7 |

RL10 (Centaur) | 4.4–5.8–7.3 | 1.2–0.9–0.7 |

Vinci (Ariane 6) | 5.8 | 0.9 |

Zefiro 9 (Vega) | 2.1 | 2.6 |

Castor 30 (Antares) | 2.1 | 2.5 |

Merlin 1D (Falcon 9) | 2.7 | 2 |

Reference Model | Grain R = D_{0}/D_{f} | Grain L/D_{f} |
---|---|---|

RD-843 (AVUM-Vega) | 5–7 | 11–9 |

17D64 (Volga-Soyuz) | 6.8 | 9.2 |

S5.98M (Briz-Proton) | 9.2 | 7.4 |

S5.92 (Fregat-Zenit) | 6.4 | 9.7 |

Rutherford (Electron) | 3–3.5 | 18–16 |

Aestus (Ariane 5) | 5.6 | 11 |

Kestrel (Falcon 1) | 3.4 | 16 |

Orion 38 (Pegasus) | 1.75 | 27 |

HM7B (Ariane 5 ECA) | 4.2 | 13 |

RL10 (Centaur) | 2.7–3.3–4 | 19–16–14 |

Vinci (Ariane 6) | 3.4 | 16 |

Zefiro 9 (Vega) | 1.5 | 32 |

Castor 30 (Antares) | 1.5 | 31 |

Merlin 1D (Falcon 9) | 1.8 | 27 |

Reference Model | Grain R = D_{0}/D_{f} | Grain L/D_{f} |
---|---|---|

RD-843 (AVUM-Vega) | 4–6 | 6–4 |

17D64 (Volga-Soyuz) | 5.9 | 4.4 |

S5.98M (Briz-Proton) | 8.2 | 3.2 |

S5.92 (Fregat-Zenit) | 5.5 | 4.7 |

Rutherford (Electron) | 2.4–2.8 | 11–9 |

Aestus (Ariane 5) | 4.8 | 5.5 |

Kestrel (Falcon 1) | 2.8 | 9.5 |

Orion 38 (Pegasus) | 1.5 | 18 |

HM7B (Ariane 5 ECA) | 3.5 | 7.5 |

RL10 (Centaur) | 2.2–2.7–3.4 | 12–9.6–7.7 |

Vinci (Ariane 6) | 2.7 | 9.5 |

Zefiro 9 (Vega) | 1.3 | 20 |

Castor 30 (Antares) | 1.3 | 20 |

Merlin 1D (Falcon 9) | 1.5 | 17 |

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Barato, F.
Challenges of Ablatively Cooled Hybrid Rockets for Satellites or Upper Stages. *Aerospace* **2021**, *8*, 190.
https://doi.org/10.3390/aerospace8070190

**AMA Style**

Barato F.
Challenges of Ablatively Cooled Hybrid Rockets for Satellites or Upper Stages. *Aerospace*. 2021; 8(7):190.
https://doi.org/10.3390/aerospace8070190

**Chicago/Turabian Style**

Barato, Francesco.
2021. "Challenges of Ablatively Cooled Hybrid Rockets for Satellites or Upper Stages" *Aerospace* 8, no. 7: 190.
https://doi.org/10.3390/aerospace8070190