energies Article Analysis of Propellant Weight under Re-Entry Conditions for a Reusable Launch Vehicle Using Retropropulsion Yongchan Kim, Hyoung-Jin Lee and Tae-Seong Roh * Department of Aerospace Engineering, Inha University, Incheon 21999, Korea; [email protected] (Y.K.); [email protected] (H.-J.L.) * Correspondence: [email protected] Abstract: In this study, a minimum amount of required propellant was calculated by analyzing the sequence with various re-entry conditions. This study aims to obtain data related to variation in trajectory and required propellant weight according to various re-entry scenarios. The drag coefficient at various altitudes, velocities, and thrust was calculated through numerical simulations to raise the reliability of the results. The calculation results were compared to the optimal values extracted from the genetic algorithm. It was observed that the duration of the entry-burn phase is dominant to the total required propellant weight. As a general tendency, high entry-burn starting altitude, high ending Mach number, and low landing-burn starting thrust make the required propellant weight low. However, if the entry-burn ending condition is set to the Mach number, it is necessary to select an appropriate re-entry condition. Additionally, from comparisons with the optimized results, it was confirmed that accurate calculation of the drag coefficient is important to succeed a soft landing of RLV. Keywords: reusable launch vehicle; retropropulsion; re-entry; trajectory Citation: Kim, Y.; Lee, H.-J.; Roh, T.-S. Analysis of Propellant Weight under Re-Entry Conditions for a Reusable Launch Vehicle Using 1. Introduction Retropropulsion. Energies 2021, 14, With increasing interest in space development and exploration, the satellite market, as 3210. https://doi.org/10.3390/ well as the demand for space launch vehicles essential for satellite launch, has also been en14113210 growing. The increase in the demand for launch vehicles has led to a request to reduce the launch cost. Among the various methods proposed for reducing the launch cost, the most Academic Editor: Jeong Yeol Choi considerable cost reduction can be achieved using the vehicle reuse technology, which recovers and reuses vehicles. Currently, the Falcon 9 launch vehicle, developed by SpaceX Received: 21 April 2021 in the United States, is the only successful commercialization and in operation. The Falcon Accepted: 28 May 2021 Published: 31 May 2021 9 heavy launch vehicle aims to reduce the launch cost by up to 50 million USD [1]. To apply the reuse technology, it is necessary to grasp the operation concept of a Publisher’s Note: MDPI stays neutral reusable launch vehicle (RLV). An RLV using retropropulsion technology was launched with regard to jurisdictional claims in with an extra propellant for retropropulsion. Because this leads to a weight loss of the published maps and institutional affil- payload or reduction in the satellite target orbit, it is vital to minimize the amount of pro- iations. pellant required for retropropulsion by establishing an optimal re-entry operation concept and method. In advanced countries, trajectory optimization and re-entry technology for RLVs are being actively researched. Trajectory optimization is mainly targeted at space vehicles in space shuttles. Various techniques in terms of control were proposed, and performance analyses have been per- Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. formed according to changes in the optimization method [2–9]. In terms of the re-entry This article is an open access article technology, the flow characteristics during re-entry have also been widely studied. These distributed under the terms and studies were mainly related to Mars re-entry, and relatively recent studies have been con- conditions of the Creative Commons ducted on Falcon 9. Berry et al. [9] and McDaniel et al. [10] observed the deceleration Attribution (CC BY) license (https:// effect upon entering Mars according to various variables such as nozzle position, angle, creativecommons.org/licenses/by/ and injection pressure. They analyzed the nozzle conditions capable of deceleration by 4.0/). retropropulsion. Based on previous studies, Edquist et al. [11,12] proposed a supersonic Energies 2021, 14, 3210. https://doi.org/10.3390/en14113210 https://www.mdpi.com/journal/energies Energies 2021, 14, x FOR PEER REVIEW 2 of 25 injection pressure. They analyzed the nozzle conditions capable of deceleration by retro- Energies 2021, 14, 3210 propulsion. Based on previous studies, Edquist et al. [11,12] proposed a supersonic2 of retro- 25 propulsion technology for landing on Mars with a heavier payload and analyzed the act- ing force through transient computational simulations by applying the actual shape of Falconretropropulsion 9 to the vehicle. technology Brandt for landing [13] observ on Marsed the with nozzle a heavier flow payload and pressure and analyzed distribution the generatedacting force during through retropropulsion, transient computational assuming simulations the falling by of applying the space the actuallaunch shape vehicle. Horvathof Falcon et 9 al. to [14] the vehicle.observed Brandt the heat [13 ]distribution observed the of nozzlethe flow flow around and pressure a launch distribu- vehicle by photographingtion generated duringinfrared retropropulsion, rays. Ecker et al. assuming [15] numerically the falling analyzed of the space the thermal launch vehicle.load upon theHorvath re-entry et al.of [a14 vehicle.] observed the heat distribution of the flow around a launch vehicle by photographingHowever, infraredto develop rays. a Eckerspace etlaunch al. [15 ]vehicle numerically that applies analyzed the the reuse thermal technology, load upon it is necessarythe re-entry to ofobtain a vehicle. accurate data regarding the results obtained from various re-entry scenariosHowever, and estimate to develop the aamount space launch of propellant vehicle required. that applies In thethisreuse regard, technology, for ease of it inter- is necessary to obtain accurate data regarding the results obtained from various re-entry pretation, most previous studies have assumed that the drag coefficient acting on the ve- scenarios and estimate the amount of propellant required. In this regard, for ease of hicle upon re-entry is an approximately constant value. However, when the vehicle re- interpretation, most previous studies have assumed that the drag coefficient acting on the enters,vehicle the upon drag re-entry and force is an acting approximately on the vehi constantcle vary value.depending However, on the when altitude the vehicleand veloc- ityre-enters, as well theas whether drag and the force retropropulsion acting on the is vehicle on or off vary [15]. depending This can onsignificantly the altitude affect and the velocityvelocity asincrement well as whether and altitude the retropropulsion change. Theref is onore, or offhigher [15]. reliability This can significantly can be secured affect by accuratelythe velocity calculating increment and altitudeapplying change. the genera Therefore,ted force, higher including reliability drag, can beto the secured aircraft accordingby accurately to the calculating flight conditions and applying when the falling. generated force, including drag, to the aircraft accordingIn this to study, the flight the re-entry conditions operation when falling. concept was established as fundamental research on theIn re-entry this study, vehicle the re-entry reuse technology. operation concept The minimum was established required as fundamental propellant weight research was calculatedon the re-entry by analyzing vehicle reuse the sequence technology. for Theeach minimum re-entry condition. required propellant By applying weight the wasspecifi- cationscalculated to the by analyzingtest vehicle the on sequence which the for eachflight re-entry test was condition. performed, By applying controllable the specifi- variables werecations selected to the among test vehicle various on whichre-entry the conditions. flight test wasFrom performed, the sequence controllable analysis, variables the re-entry conditionswere selected under among which various landing re-entry with conditions. the minimum From propellant the sequence weight analysis, was theachieved re-entry were derived.conditions The under drag which force landingwas accurately with the derived minimum according propellant to weightthe altitude was achieved and Mach were num- derived. The drag force was accurately derived according to the altitude and Mach number ber and applied through computational simulations. The calculated trajectory results and and applied through computational simulations. The calculated trajectory results and propellant weight were compared to the optimized values extracted from the optimiza- propellant weight were compared to the optimized values extracted from the optimization tionprocess process using using the genetic the genetic algorithm. algorithm. 2.2. Sequence Sequence for for Computing MinimumMinimum Propellant Propellant Weight Weight 2.1.2.1. Operational Operational Concept ofof RLVRLV ForFor the the development ofof anan RLV,RLV, it it is is necessary necessary to to establish establish an an operational operational concept concept andand a a re-entry re-entry sequence. The re-entryre-entry sequencesequence for for Falcon Falcon 9, 9, the the only only commercial commercial RLV RLV currentlycurrently in operation,operation, comprises comprises boostback-burn, boostback-burn, entry-burn,