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, entry-burn, free-fall free-fall flight, flight, and landing- and land- burn phases. In the boostback-burn phase, a falling direction of the vehicle is altered to ing-burn phases. In the boostback-burn phase, a falling direction of the vehicle is altered head toward the recovery point. In the entry-burn phase, retropropulsion is performed to head toward the recovery point. In the entry-burn phase, retropropulsion is performed with a maximum thrust to obtain the maximum deceleration effect at high altitudes. In withthe free-falla maximum flight thrust phase to after obtain the entry-burnthe maximum phase, deceleration natural deceleration effect at high by altitudes. drag occurs. In the free-fallFinally, flight the landing-burn phase after phasethe entry-burn is aimed atphase, soft landing. natural Thedeceleration operational by conceptdrag occurs. of RLV Finally, is thetypically landing-burn divided phase into ground is aimed and at oceansoft landin landings.g. The The operational boostback-burn concep phaset of RLV is omittedis typically dividedin ocean into landing ground because and theocean first landings. stage is recovered The boostback-burn on the ocean bargephase nearis omitted the expected in ocean landingfall point. because the first stage is recovered on the ocean barge near the expected fall point. FigureFigure 11 shows shows the the basic basic operational operational concept. concept. In this In study, this detailed study, re-entrydetailed sequences re-entry se- quenceswere established were established by referring by toreferring the ocean to landingthe ocean of landing the Falcon of 9the vehicle. Falcon 9 vehicle.

Figure 1. Basic re-entry sequence.

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A Korean engine test vehicle, which has a thrust of 75 tonf, was selected as the launch vehicle for the analysis. The initial altitude and velocity of the basic sequence 1 were based on the flight results of the test vehicle. However, while the exact maximum altitude and range were disclosed, the flight velocity remained unknown. Thus, the velocity at the maximum altitude was estimated through a 3 Degree of Freedom (DOF) motion analysis. The maximum altitude was calculated as 209 km and the velocity at the maximum altitude was 1042.7 m/s. The retropropulsion is the only factor that the energy consumption occurs in the re-entry sequence. The retropropulsion is operated twice generally: Entry-burn and Landing-burn. The energy(propellant) consumption is determined by thrust and duration of each retropropulsion phase, and the duration is controlled by the starting and ending condition of each phase. Various parameters can be regarded as the starting and ending conditions, but the parameters related to vehicle operation directly are altitude and velocity. As a result, in this study, the required propellant weight was calculated with the starting altitude and ending Mach number of the entry-burn phase and the landing-burn starting thrust as the re-entry condition variables. The RLV can land without the entry-burn phase through a natural deceleration with drag force theoretically, but it is impractical in that it may cause harmful damage to the vehicle by aerodynamic heating. For that reason, it makes sense to achieve adequate deceleration through entry burning. The variable values about re-entry condition were selected by referring to the re-entry data of the Falcon 9 vehicle released online, which is based on the entry-burn starting altitude of 60 km and the entry-burn ending Mach number of 3.0. The landing-burn starting thrust was set to 1–10 tonf. Table1 shows the values for each variable. The starting altitude of the landing- burn phase for sequence 4 in Figure1 was set to an altitude of 3 km by referring to various Falcon 9 re-entry sequences published online [16–18].

Table 1. Parameters for controlling the re-entry condition.

Parameters Values Entry-burn starting altitude [km] 40, 60, 80 Entry-burn ending Mach number 2.0, 3.0, 4.0 Landing-burn starting thrust [tonf] 1.0–10.0

Table2 presents the basic input values, including the specifications of the test vehi- cle [19,20] and the physical properties of kerosene combustion gas. The combustion gas properties derived through the NASA CEA program were set to remain constant by fixing the combustion gas temperature regardless of the thrust.

Table 2. Specification and gas properties.

Parameters Values Max. Diameter [m] 2.6 Length [m] 25.8 Nozzle exit diameter [m] 1.048 Specification of Launch Vehicle Nozzle expansion ratio 12.0 Nozzle exit Mach number 3.35 Dry weight [t] 5.3 Specific heat [J/kg-K] 4838.0 Molecular weight [kg/kmol] 376.20 Gas Properties of Combustion Gas Dynamic viscosity [Pa-s] 1.0706 × 10−4 Thermal conductivity [W/m-K] 1.1441

2.2. Procedure of Re-Entry Sequence The trajectory calculation only considered the falling motion of the vehicle. Because the effect of the angle of attack was relatively insignificant, it was assumed to be zero in the Energies 2021, 14, 3210 4 of 25

related previous studies [15]. The equations of motion can be expressed as Equations (1)–(4), which represent the velocity, flight path angle, altitude, and propellant mass, respectively. The flight path angle is the angle between the horizontal and velocity vectors, which describes whether the vehicle is climbing or descending. The U.S. Standard Atmosphere data were applied to the density and temperature changes with altitude [21].

dV Te cos α − D = − g sin γ (1) dt md + mp

dγ Te sin α + L g cos γ V cos γ =
− + (2) dt md + mp V V r dh = V sin γ (3) dt

dmp Te = − (4) dt ue

2.2.1. Entire Calculation Process In this study, the bisection method was used to find a minimum propellant weight. The bisection method is a successive approximation method that finds the root of continuous function through repeatedly bisecting the interval. The method solves the equation f (x) = 0 numerically, where f (x) is a function defined over the interval [a, b] and where f (a) and f (b) have opposite signs. At each iteration, the method divides the interval by midpoint c = (a + b)/2 and solve the equation to obtain a solution f (c). If f (a) and f (c) have opposite signs, the method sets c as the new value for b, and if f (b) and f (c) have opposite signs, then the method sets c as the new a. If convergence is satisfied, the iteration stops and the method return the output value c. For using the bisection method, the function and interval should be set. The entire calculation process composed of the entry-burn and free-flight phase module and the landing-burn modules was used as the function. The lower and upper bound of the propellant weight was applied to the interval of the function. The return value of the calculation process is set to +1 or −1 according to the success or failure of landing. The criterion of convergence is that an error between the propellant weight that is set to each interval (a, b) is lower than tolerance value. Figure2 shows the entire calculation process with the bisection method.

2.2.2. Entry-Burn and Free-Fall Flight Modules The entry-burn module aims to obtain the residual propellant amount after passing through the entry-burn and free-fall flight phases with the re-entry condition from a given initial propellant amount. Figure3 shows the calculation process of the entry-burn and free-fall flight modules. Tables3 and4 present the fixed input values and variables of the entry-burn module, respectively. The free fall starts from the initial velocity and altitude, as presented in Table4 , where the initial flight path angle is set to zero to assume a state horizontal to the ground. Based on the atmospheric density and temperature according to the altitude, the drag acting on the vehicle is calculated. The entry-burn phase starts when altitude reaches the value listed in Table4. In the entry-burn phase, the engine thrust maintains a maximum thrust of 75 tonf to achieve maximum deceleration. In the free-fall flight phase after the entry-burn phase, natural deceleration is performed by drag. Therefore, both thrust and drag are considered within the entry-burn phase when calculating the acceleration of the vehicle. However, only drag is acted except at the entry-burn phase so that the natural deceleration is performed by drag. The drag is calculated based on the atmospheric density and the vehicle’s velocity, and the drag coefficient is calculated by conducting computational simulations. The changes in velocity, flight path angle, altitude, and propellant mass are Energies 2021, 14, x FOR PEER REVIEW 5 of 25

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updated through the calculated acceleration. The calculation process is repeated until a Energies 2021, 14, x FOR PEER REVIEW 5 of 25 landing-burn starting altitude of 3 km is satisfied. If the landing-burn starting altitude is satisfied, the calculation ends, and the output value is obtained.

Figure 2. Calculation process of the minimum required propellant weight.

2.2.2. Entry-Burn and Free-Fall Flight Modules The entry-burn module aims to obtain the residual propellant amount after passing through the entry-burn and free-fall flight phases with the re-entry condition from a given initial propellant amount. Figure 3 shows the calculation process of the entry-burn and Figure 2. Calculation process of the minimum required propellant weight. Figurefree-fall 2. Calculationflight modules. process of the minimum required propellant weight. 2.2.2. Entry-Burn and Free-Fall Flight Modules The entry-burn module aims to obtain the residual propellant amount after passing through the entry-burn and free-fall flight phases with the re-entry condition from a given initial propellant amount. Figure 3 shows the calculation process of the entry-burn and free-fall flight modules.

FigureFigure 3.3.Calculation Calculation process process of of the the entry-burn entry-burn and and free-fall free-fall flight flight modules. modules.

Figure 3. Calculation process of the entry-burn and free-fall flight modules.

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Table 3. Input data for the entry-burn and free-flight modules.

Parameter Value Initial velocity [m/s] 1042.7 Initial altitude [km] 209.0 Initial flight path angle [deg] 0.0 Dry weight [t] 5.3 Entry-burn thrust [tonf] 75.0 Landing-burn starting altitude [km] 3.0

Table 4. Input and output parameters of the entry-burn and free-flight modules.

Entry-burn starting altitude Input Entry-burn ending Mach number Total propellant weight Entry-burn residual propellent weight Output Landing-burn starting velocity Landing-burn starting flight path angle

2.2.3. Landing-Burn Module The calculation process for the landing-burn module is illustrated in Figure4. This module aims to allow the vehicle to land softly, which ensures that the altitude and velocity simultaneously meet the value of zero. The landing-burn module executes the calculation by applying the output value of the entry-burn module as an input value. The thrust in the landing-burn phase varies through the quadratic function according to the analysis result obtained for the Falcon 9 vehicle [22]. However, in this study, an appropriate thrust throttling rate that satisfies the minimum propellant weight is calculated by assuming that the thrust takes the form of a linear equation considering the calculation cost. The analysis process of the landing-burn module presented in Figure4 can be described as follows. The acceleration is calculated using the initial thrust and drag at the initial altitude and velocity. The changes in the velocity, altitude, and propellant weight are sequentially updated, and an iterative calculation is performed until either the velocity or altitude meets zero. Let us assume that the velocity is zero, whereas the altitude exceeds zero. In this case, the acceleration should be lowered so that the velocity decreases slowly, which can be satisfied by reducing the thrust throttling rate. In contrast, when the altitude is zero but the velocity is higher, the thrust throttling rate should be increased to reduce the velocity more rapidly, which is possible only when the residual propellant is present, because it simultaneously increases the propellant’s consumption. Therefore, if the altitude is zero and the velocity is higher, but there is no remaining propellant, it is judged as a landing failure. Finally, if the velocity and altitude meet the value of zero simultaneously, it is judged as a landing success, in which the remaining propellant weight and thrust throttling rate are obtained. Table5 shows the input and output variables of the landing-burn module.

Table 5. Input and output parameters of the landing-burn modules.

Entry-burn residual propellent weight Landing-burn starting velocity Input Landing-burn starting flight path angle Landing-burn starting thrust Landing-burn residual propellant weight Output Landing-burn thrust throttling rate Landing-burn ending thrust Energies 2021, 14, x FOR PEER REVIEW 7 of 25

velocity is higher, but there is no remaining propellant, it is judged as a landing failure. Finally, if the velocity and altitude meet the value of zero simultaneously, it is judged as a Energies 2021, 14, 3210 7 of 25 landing success, in which the remaining propellant weight and thrust throttling rate are obtained. Table 5 shows the input and output variables of the landing-burn module.

FigureFigure 4. 4.Calculation Calculation process process of the of landing-burnthe landing-burn module. module. 3. Calculation of Drag Coefficient through CFD Table 5. Input and output parameters of the landing-burn modules. In most previous studies, the drag coefficient of the vehicle was considered constant. However, in the re-entry sequence, the altitudeEntry-burn and velocity residual continuously propellent change weight and retropropulsion is performed for deceleration. BecauseLanding-burn the vehicle is starting operated velocity at supersonic Input velocity in the entry-burn and free-fall flight phases,Landing-burn a strong starting shockwave flight ispath generated angle in front of the nozzle exit. At this moment, if a flowLanding-burn is injected starting from the thrust nozzle for retropropulsion, a very complex flowfield is formedLanding-burn owing to residual the interaction propellant between weight the shock wave andOutput nozzle flow, which induces a changeLanding-burn in the force actingthrust onthrottling the surface rate and the drag coefficient. Therefore, to apply an accurate drag value, it is necessary to consider Landing-burn ending thrust the drag coefficient with the altitude, velocity, and presence or absence of the thrust. In this study, numerical simulations were performed to calculate the drag coefficient under various3. Calculation conditions, of includingDrag Coefficient the entry-burn, through free-fall CFD flight, and landing-burn phases. The geometryIn most of the previous test launch studies, vehicle the was drag applied, coeffi andcient detailed of the specifications vehicle was wereconsidered referred constant. toHowever, from previous in the studies re-entry [19 ,sequence,20]. the altitude and velocity continuously change and ret- ropropulsion is performed for deceleration. Because the vehicle is operated at supersonic 3.1. Numerical Techniques and Validation velocity in the entry-burn and free-fall flight phases, a strong shockwave is generated in The numerical simulations were performed using a commercial program (Star-CCM+ front of the nozzle exit. At this moment, if a flow is injected from the nozzle for retropro- 14.02). A two-dimensional axisymmetric steady-state RANS equation with a density-based coupledpulsion, solver a very was complex applied. flowfield Turbulence is formed modeling owing was to performed the interaction using the between Spalart– the shock Allmaraswave and model, nozzle which flow, can which simulate induces high-velocity a change external in the flows. force The acting advection on the upstream surface and the splittingdrag coefficient. method (AUSM+) Therefore, was to applied apply an for accurate the inviscid drag convective value, it termis necessary and 2nd-order to consider the drag coefficient with the altitude, velocity, and presence or absence of the thrust. In this

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study, numerical simulations were performed to calculate the drag coefficient under var- ious conditions, including the entry-burn, free-fall flight, and landing-burn phases. The geometry of the test launch vehicle was applied, and detailed specifications were referred to from previous studies [19,20].

3.1. Numerical Techniques and Validation The numerical simulations were performed using a commercial program (Star-CCM+ 14.02). A two-dimensional axisymmetric steady-state RANS equation with a density- based coupled solver was applied. Turbulence modeling was performed using the Spalart–Allmaras model, which can simulate high-velocity external flows. The advection upstream splitting method (AUSM+) was applied for the inviscid convective term and 2nd-order central discretization was applied for the diffusion term. In addition, spatial discretization maintained the 3rd-order accuracy by applying the Monotonic Upwind Scheme for Conservation Laws (MUSCL), and the gas was considered an ideal gas. Suth- erland’s law was used to compute the dynamic viscosity, and the specific heat at constant pressure was calculated from the polynomial function of temperature. The combustion Energies 2021, 14, 3210 8 of 25 gas of kerosene and oxygen fuel was applied as a gas component with air. For an accurate analysis of the turbulent flow and boundary layer, the wall condition was set to an iso- thermal no-slip condition, and the Y+ value at the wall was set to close to 1. It was con- centralfirmed discretizationthat the continuity was appliedresidual for decreased the diffusion to less term. than 10 In-3 addition, , and thus, spatial stably discretization converged. maintainedFigure 5 presents the 3rd-order the mesh accuracy domain by and applying boundary the types. Monotonic Upwind Scheme for Conser- vationTo Laws validate (MUSCL), the numerical and the gas technique was considered used in anthis ideal study, gas. the Sutherland’s numerical lawresults was were used tocompared compute with the dynamic those obtained viscosity, previously and the specific[23], with heat the at aim constant of analyzing pressure the was effect calculated of ret- fromropropulsion the polynomial on Mars function entry. Most of temperature. retropropulsion The combustion technologies gas for of RLV kerosene are sought and oxygento en- fuelter planets was applied such as as Mars a gas and component Earth. In withadditi air.on, Foras many an accurate research analysis results have of the been turbulent pub- flowlished, and it is boundary thought to layer, be suitable the wall for condition validation. was set to an isothermal no-slip condition, and theThe Y+ geometry value at [23] the of wall reference was setsimulation to close is to a1. 2.6% It was scale confirmed model of the that Apollo the continuity capsule. residualThe model’s decreased base diameter to less than is 101.6 10−3 ,mm and and thus, the stably nozzle converged. exit diameter Figure is 512.7 presents mm; the the meshfreestream domain and and retropropulsion boundary types. conditions are listed in Table 6.

FigureFigure 5.5. MeshMesh andand boundary condition and mesh configurations. configurations.

TableTo 6. validateBoundary the condition numerical of reference technique [23]. used in this study, the numerical results were compared with those obtained previously [23], with the aim of analyzing the effect of Parameters Values retropropulsion on Mars entry. Most retropropulsion technologies for RLV are sought to Mach number 3.48 enter planetsFreestream such as Mars and Earth.Static In pressure addition, [Pa] as many researchresults 4170 have been published, it is thought to be suitableStatic for temperature validation. [K] 8.24 The geometry [23] of reference simulationMach number is a 2.6% scale model of the 3.48 Apollo capsule. The model’s baseJet diameter is 101.6Static mm pressure and the [Pa] nozzle exit diameter 4170 is 12.7 mm; the freestream and retropropulsion conditionsStatic temperature are listed [K] in Table6. 8.24

TableThe 6. Boundary Mach number condition contour of reference and Mach [23]. number distribution on the centerline are pre- sented in Figure 6, and the result can be considered to be consistent with that obtained for Parameters Values the reference study [23] when the mesh size around the nozzle is 0.5 mm. Therefore, the numerical technique and mesh presentedMach above number were used to analyze the 3.48 drag in the re- Static pressure [Pa] 4170 entry sequence.Freestream Static temperature [K] 8.24 Mach number 3.48 Jet Static pressure [Pa] 4170 Static temperature [K] 8.24

The Mach number contour and Mach number distribution on the centerline are presented in Figure6, and the result can be considered to be consistent with that obtained for the reference study [23] when the mesh size around the nozzle is 0.5 mm. Therefore, the numerical technique and mesh presented above were used to analyze the drag in the re-entry sequence.

3.2. Drag Analysis Results 3.2.1. Entry-Burn Phase The entry-burn phase proceeded at a high altitude and supersonic velocity, and the vehicle in this phase generated maximum thrust to achieve maximum deceleration. Therefore, the freestream condition was set to an altitude of 50–70 km and a Mach number of 4–7 to observe the tendency of the change in thrust and drag coefficient. The thrust of the vehicle was fixed at 75 tonf, which is the maximum vacuum thrust of the test launch vehicle. Energies 2021, 14, 3210 9 of 25 Energies 2021, 14, x FOR PEER REVIEW 9 of 25

FigureFigure 6. 6. ValidationValidation results. results. (a ()a )Geomery Geomery and and mesh; mesh; (b ()b Mach) Mach number number contour; contour; (c) (Machc) Mach number number distribuationdistribuation on on axis. axis.

3.2. DragFigure Analysis7 shows Results the force coefficients at different altitudes and Mach numbers in the entry-burn phase. Cd, CT, and CAF are the drag, thrust, and total axial force coefficients, 3.2.1.respectively, Entry-Burn as defined Phase by Equations (5)–(7). As the acting directions of the nozzle thrust andThe the externalentry-burn drag phase force proceeded coincide when at a high the retropropulsionaltitude and supersonic is on, the velocity, total axial and force the vehicleacting onin this the vehiclephase generated is expressed maximum as the sum thru ofst theto achieve drag and maximum thrust. deceleration. There- fore, the freestream condition was set to an altitude of 50–70 km and a Mach number of 4–7 D to observe the tendency of the change inC thrust= and drag coefficient. The thrust of the vehicle(5) d 1 2 was fixed at 75 tonf, which is the maximum vac2 ρ∞uumu∞S thrust of the test launch vehicle. Figure 7 shows the force coefficients at different altitudes and Mach numbers in the Te entry-burn phase. 𝐶, 𝐶, and 𝐶 areC the= drag, thrust, and total axial force coefficients,(6) T 1 2 respectively, as defined by Equations (5)–(7).2 ρAs∞u the∞S acting directions of the nozzle thrust and the external drag force coincide when the retropropulsion is on, the total axial force D + Te Energies 2021, 14, x FOR PEER REVIEWacting on the vehicle is expressedC as= the sum of the= C drag+ C and thrust. (7)10 of 25 AF 1 2 d T ρ∞u∞S 2 𝐷 𝐶 = 1 (5) 𝜌 𝑢 𝑆 2

𝑇 𝐶 = 1 (6) 𝜌 𝑢 𝑆 2

𝐷+𝑇 𝐶 = = 𝐶 +𝐶 1 (7) 𝜌 𝑢 𝑆 2 As the Mach number increases at the same altitude and the altitude decreases at the same Mach number, the dynamic pressure increases, and thus, the thrust and drag coef- ficient decrease. In addition, the magnitude of the thrust is at least 100 times the drag force, and the drag is negligible when the thrust is generated under high altitude and high-velocity conditions, such as the entry-burn phase. Thus, only thrust was considered in the acceleration calculation in the entry-burn phase, ignoring drag. Figure 7.7. ThrustThrust and and drag drag coefficient coefficient in in the the entry-burn entry-burn phase. phase.

3.2.2. Free-Fall Flight The altitude in the free-fall flight phase is lower than that in the entry-burn phase.

Because the dynamic pressure increases as the altitude decreases, the drag force also in- creases and natural deceleration can be performed. In addition, as the starting and ending conditions differ according to the initial input, obtaining data for a broader range of freestream conditions is necessary. Therefore, the freestream conditions were set to an altitude of 10–50 km and a Mach number of 2–6, and the total axial force was equal to the drag because there is no thrust. Figure 8 presents the flowfield of the free-fall flight phase, where (a) and (b) indicate the Mach number and Cp contour at an altitude of 40 km and Mach number of 3.0, respec- tively. Cp indicates a dimensionless pressure coefficient by dividing the pressure by the dynamic pressure and has the same tendency as the drag coefficient. Figure 8a shows that at the constant altitude, the pressure coefficient around the nozzle decreases as the Mach number increases. However, as shown in Figure 8b, at the same Mach number, the pres- sure coefficient field is similarly formed regardless of the altitude. Figure 9a shows the axial force coefficient as a function of the altitude and Mach number, which is the same to the drag coefficient in free-fall flight phase. As the Mach number increases at the same altitude, the total axial force coefficient decreases by 0.1–0.3. In addition, as the altitude increases at the same Mach number, the total axial force coef- ficient increases by a maximum value of 0.1, as presented previously [24]. Hence, the total axial force coefficient in the free-fall flight phase was calculated using Equation (8), which was derived by curve fitting, as shown in Figure 9b.

𝐶 = 0.9383 + 3.711 ∗ 10 ∗ ℎ − 0.1346 ∗ 𝑀 + 2.845 ∗ 10 ∗ℎ − 2.522 ∗ 10 ∗ 𝑀 ∗ ℎ + 0.01143 ∗ 𝑀 (8)

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As the Mach number increases at the same altitude and the altitude decreases at the same Mach number, the dynamic pressure increases, and thus, the thrust and drag coefficient decrease. In addition, the magnitude of the thrust is at least 100 times the drag force, and the drag is negligible when the thrust is generated under high altitude and high-velocity conditions, such as the entry-burn phase. Thus, only thrust was considered in the acceleration calculation in the entry-burn phase, ignoring drag.

3.2.2. Free-Fall Flight The altitude in the free-fall flight phase is lower than that in the entry-burn phase. Because the dynamic pressure increases as the altitude decreases, the drag force also increases and natural deceleration can be performed. In addition, as the starting and ending conditions differ according to the initial input, obtaining data for a broader range of freestream conditions is necessary. Therefore, the freestream conditions were set to an altitude of 10–50 km and a Mach number of 2–6, and the total axial force was equal to the drag because there is no thrust. Figure8 presents the flowfield of the free-fall flight phase, where (a) and (b) indicate the Mach number and Cp contour at an altitude of 40 km and Mach number of 3.0, respectively. Cp indicates a dimensionless pressure coefficient by dividing the pressure by the dynamic pressure and has the same tendency as the drag coefficient. Figure8a shows Energies 2021, 14, x FOR PEER REVIEWthat at the constant altitude, the pressure coefficient around the nozzle decreases as the 11 of 25 Mach number increases. However, as shown in Figure8b, at the same Mach number, the pressure coefficient field is similarly formed regardless of the altitude.

FigureFigure 8. 8.Mach Mach number number and and pressure pressure coefficient coefficient contour co inntour the free-fall in the flight free-fall phase. flight (a) Flowfields phase. ( ata) Flowfields altitudeat altitude of 40 of km; 40 (bkm;) Flowfields (b) Flowfields at Mach at number Mach ofnumber 3.0. of 3.0.

Figure 9. Results with Mach number and altitude for free-fall flight phase. (a) CAF values obtained by CFD; (b) CAF prediction curve.

3.2.3. Landing-Burn Phase The velocity of the vehicle exceeds the supersonic velocity in the entry-burn and free- fall flight phases but decelerates to subsonic velocity when it enters the landing-burn phase. Both thrust and drag must be considered simultaneously because the drag force is significant owing to the low altitude and high density in the landing-burn phase. The freestream conditions were set to an altitude of 1–4 km and a Mach number of 0.3–0.9. A landing-burn starting altitude of up to 4 km was considered to improve the reliability by referring to the launch data of the Falcon 9 vehicle [16], although it was set to 3 km in this study. Four thrust values between 1 and 20 tonf were selected, based on 10 tonf which is

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Energies 2021, 14, 3210 11 of 25

Figure9a shows the axial force coefficient as a function of the altitude and Mach number, which is the same to the drag coefficient in free-fall flight phase. As the Mach number increases at the same altitude, the total axial force coefficient decreases by 0.1–0.3. In addition, as the altitude increases at the same Mach number, the total axial force coeffi- cient increases by a maximum value of 0.1, as presented previously [24]. Hence, the total axial force coefficient in the free-fall flight phase was calculated using Equation (8), which was derived by curve fitting, as shown in Figure9b.

Figure−7 8. Mach number and pressure coefficient−11 2 contour in the− 7free-fall flight phase. (a) Flowfields2 CAF = 0.9383 + 3.711 ∗ 10 ∗ h − 0.1346 ∗ M + 2.845 ∗ 10 ∗ h − 2.522 ∗ 10 ∗ M ∗ h + 0.01143 ∗ M (8) at altitude of 40 km; (b) Flowfields at Mach number of 3.0.

Figure 9. Results with Mach number and alti altitudetude for free-fall flightflight phase. (a) CAF values obtained obtainedby CFD; (byb) CAFCFD; prediction(b) CAF prediction curve. curve. 3.2.3. Landing-Burn Phase 3.2.3. Landing-Burn Phase The velocity of the vehicle exceeds the supersonic velocity in the entry-burn and The velocity of the vehicle exceeds the supersonic velocity in the entry-burn and free- free-fall flight phases but decelerates to subsonic velocity when it enters the landing-burn fall flight phases but decelerates to subsonic velocity when it enters the landing-burn phase. Both thrust and drag must be considered simultaneously because the drag force phase. Both thrust and drag must be considered simultaneously because the drag force is is significant owing to the low altitude and high density in the landing-burn phase. The significant owing to the low altitude and high density in the landing-burn phase. The freestream conditions were set to an altitude of 1–4 km and a Mach number of 0.3–0.9. A freestream conditions were set to an altitude of 1–4 km and a Mach number of 0.3–0.9. A landing-burn starting altitude of up to 4 km was considered to improve the reliability by landing-burn starting altitude of up to 4 km was considered to improve the reliability by referring to the launch data of the Falcon 9 vehicle [16], although it was set to 3 km in this referringstudy. Four to the thrust launch values data between of the Falcon 1 and 209 vehicle tonf were [16], selected, although based it was on set 10 to tonf 3 km which in this is study.approximately Four thrust 1/6th values the thrustbetween in the1 and entry-burn 20 tonf were phase selected, as referred based to on from 10 Falcontonf which 9. The is drag in each condition was derived according to the Mach number. Figure 10a shows the drag coefficient according to the Mach number for each altitude, where the thrust is 5 and 10 tonf, respectively. The drag coefficient was calculated by dividing the drag force by dynamic pressure and reference area, and the drag force is obtained by integrating the pressure over the outer surface of the vehicle. At the same Mach number, the drag coefficient is constant regardless of the altitude but decreases as the Mach number increases. However, as the thrust increases, the drag coefficient variation changes, even if the Mach number is equal. Figure 10b shows the result of the drag coefficient according to the Mach number for different thrusts at an altitude of 2 km. As the thrust increases, the drag coefficient is higher at Mach numbers of 0.3 and 0.45. However, at Mach numbers of 0.75 and 0.9, the drag coefficient increases as the thrust decreases. Figure 11 shows the pressure, Mach number, and temperature fields for thrust values of 1 and 20 tonf at Mach numbers of 0.3 and 0.9, respectively. Energies 2021, 14, x FOR PEER REVIEW 12 of 25

approximately 1/6th the thrust in the entry-burn phase as referred to from Falcon 9. The drag in each condition was derived according to the Mach number. Figure 10a shows the drag coefficient according to the Mach number for each alti- tude, where the thrust is 5 and 10 tonf, respectively. The drag coefficient was calculated by dividing the drag force by dynamic pressure and reference area, and the drag force is obtained by integrating the pressure over the outer surface of the vehicle. At the same Mach number, the drag coefficient is constant regardless of the altitude but decreases as the Mach number increases. However, as the thrust increases, the drag coefficient varia- tion changes, even if the Mach number is equal. Figure 10b shows the result of the drag coefficient according to the Mach number for different thrusts at an altitude of 2 km. As the thrust increases, the drag coefficient is higher at Mach numbers of 0.3 and 0.45. How- ever, at Mach numbers of 0.75 and 0.9, the drag coefficient increases as the thrust de- Energies 2021, 14, 3210 12 of 25 creases. Figure 11 shows the pressure, Mach number, and temperature fields for thrust values of 1 and 20 tonf at Mach numbers of 0.3 and 0.9, respectively.

Energies 2021, 14, x FOR PEER REVIEWFigure 10. Drag coefficient in the landing-burn phase. (a)C with different altitude and13 Mach of 25 Figure 10. Drag coefficient in the landing-burn phase. (a) Cd withd different altitude and Mach b number; (b)C) Cd withwith different different thrust at altitude of 2 km.

From the pressure field shown in Figure 11, the pressure variation induced by the noz- zle flow mainly occurs near the outer surface of the nozzle. At a Mach number of 0.3, the pressure around the nozzle is higher at a thrust value of 20 tonf. However, at a Mach number of 0.9, the pressure is larger when at a thrust value of 1 tonf. As shown in Figure 11b, when the Mach number is 0.9, the pressure and Mach number drastically change based on the point where the nozzle flow and freestream flow meet, similar to the supersonic flow. In addition, as the nozzle thrust increases to 20 tonf, the distribution of the high-temperature nozzle flow expands to the rear end of the vehicle. Accordingly, the influence of the high- temperature flow in the vicinity of the nozzle is relatively small, which makes the temper- ature and pressure around the nozzle lower. However, when the Mach number is 0.3, as shown in Figure 11a, the change induced in the flowfield by the nozzle flow is relatively small, which expands the nozzle flow and increases the temperature around the nozzle as the nozzle thrust increases from 1 tonf to 20 tonf. Therefore, when the Mach number is small, the drag force increases owing to the high temperature and pressure around the nozzle as the nozzle thrust increases. As a result of the analysis, it was confirmed that the flight Mach number and nozzle thrust had a dominant effect on the drag coefficient in the landing-burn phase, which is a subsonic velocity region, and the effect of altitude was insignificant. Therefore, the drag coefficient for the Mach number and thrust can be derived through curve fitting as shown in Figure 12 and Equation (9), which was used to calculate the landing-burn phase. FigureFigure 11.11. FlowfieldFlowfield atat differentdifferent MachMach numbersnumbers and and thrust thrust values. values. ( a()a) Flowfields Flowfields at at Mach Mach number number of 𝐶 = 0.459 − 0.9947 ∗ 𝑀 + 1.78810 ∗ 𝑇 + 0.7253 ∗ 𝑀 − 2.514 ∗ 10 ∗𝑀∗𝑇−7.033∗10 ∗𝑇 (9) 0.3;of 0.3; (b) ( Flowfieldsb) Flowfields at Machat Mach number number of 0.9.of 0.9.

From the pressure field shown in Figure 11, the pressure variation induced by the nozzle flow mainly occurs near the outer surface of the nozzle. At a Mach number of 0.3, the pressure around the nozzle is higher at a thrust value of 20 tonf. However, at a Mach number of 0.9, the pressure is larger when at a thrust value of 1 tonf. As shown in Figure 11b, when the Mach number is 0.9, the pressure and Mach number drastically change based on the point where the nozzle flow and freestream flow meet, similar to the supersonic flow. In addition, as the nozzle thrust increases to 20 tonf, the distribution of the high-temperature nozzle flow expands to the rear end of the vehicle. Accordingly, the influence of the high-temperature flow in the vicinity of the nozzle is relatively small, which makes the temperature and pressure around the nozzle lower. However, when the Mach number is 0.3, as shown in Figure 11a, the change induced in the flowfield by the nozzle flow is relatively small, which expands the nozzle flow and increases the temperature around the nozzle as the nozzle thrust increases from 1 tonf to 20 tonf. Therefore, when

Figure 12. Cd prediction using different Mach numbers and thrust values.

4. Result and Discussion The re-entry sequence was analyzed under various re-entry conditions, and the re- quired amount of propellant was calculated. In addition, the amount of propellant with different values of landing-burn starting thrust was analyzed and the landing-burn start- ing thrust for the minimum propellant weight was derived.

4.1. Code Validation Using Flight Data of Falcon 9 The analysis program was validated by comparing the previous analysis results [22] with the actual re-entry data of the Falcon 9 FT vehicle [16]. The specifications and initial conditions of the vehicles used in the previous studies are listed in Table 7. The initial condition was assumed to be the start time of the entry-burn phase.

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the Mach number is small, the drag force increases owing to the high temperature and pressure around the nozzle as the nozzle thrust increases. As a result of the analysis, it was confirmed that the flight Mach number and nozzle thrust had a dominant effect on the drag coefficient in the landing-burn phase, which is a subsonic velocity region, and the effect of altitude was insignificant. Therefore, the drag coefficient for the Mach number and thrust can be derived through curve fitting as shown in Figure 12 and Equation (9), which was used to calculate the landing-burn phase. Figure 11. Flowfield at different Mach numbers and thrust values. (a) Flowfields at Mach number C = 0.459 − 0.9947 ∗ M + 1.78810−6 ∗ T + 0.7253 ∗ M2 − 2.514 ∗ 10−6 ∗ M ∗ T − 7.033 ∗ 10−13 ∗ T2 (9) d of 0.3; (b) Flowfields at Mach number of 0.9.

Figure 12. Cd prediction using different Mach numbers and thrust values.values. 4. Result and Discussion 4. Result and Discussion The re-entry sequence was analyzed under various re-entry conditions, and the requiredThe re-entry amount sequence of propellant was wasanalyzed calculated. under various In addition, re-entry the conditions, amount of and propellant the re- withquired different amount values of propellant of landing-burn was calculated. starting In thrust addition, was analyzedthe amount and of the propellant landing-burn with differentstarting thrust values for of thelanding-burn minimum propellantstarting thrust weight was was analyzed derived. and the landing-burn start- ing thrust for the minimum propellant weight was derived. 4.1. Code Validation Using Flight Data of Falcon 9 4.1. CodeThe Validation analysis program Using Flight was Data validated of Falcon by comparing9 the previous analysis results [22] withThe the actualanalysis re-entry program data was of thevalidated Falcon by 9 FTcomparing vehicle [ 16the]. previous The specifications analysis results and initial [22] withconditions the actual of the re-entry vehicles data used of the in theFalcon previous 9 FT vehicle studies [16]. are The listed specifications in Table7. The and initial initial conditionscondition was of the assumed vehicles to beused the in start the time previous of the studies entry-burn are listed phase. in Table 7. The initial condition was assumed to be the start time of the entry-burn phase. Table 7. Specification and initial condition of Falcon 9 [22]. Parameter Value Entry-burn starting altitude [km] 70.0 Entry-burn starting velocity [m/s] 2294.0 Dry weight [t] 22.2 Total propellant weight [t] 36.0 Entry-burn thrust [tonf] 279.6 Landing-burn starting altitude [km] 3.3

The iteration process for determining the minimum required propellant weight was omitted, and the remaining propellant weight obtained after landing was compared for the same total propellant weight. To calculate the drag coefficient of the vehicle, computational simulations were performed under two altitude and velocity conditions based on the actual re-entry data [16]. Because the geometry of the Falcon 9 vehicle is not axisymmetric and has nine engines, a 3D analysis with 1/4 symmetric geometry was performed. The Energies 2021, 14, x FOR PEER REVIEW 14 of 25

Table 7. Specification and initial condition of Falcon 9 [22].

Parameter Value Entry-burn starting altitude [km] 70.0 Entry-burn starting velocity [m/s] 2294.0 Dry weight [t] 22.2 Total propellant weight [t] 36.0 Entry-burn thrust [tonf] 279.6 Energies 2021, 14, x FOR PEER REVIEW 14 of 25 Landing-burn starting altitude [km] 3.3 The iteration process for determining the minimum required propellant weight was Tableomitted, 7. Specification and the and remaining initial condition propellant of Falcon weig 9 [22].ht obtained after landing was compared for

the same total Parameterpropellant weight. To calculate the dragValue coefficient of the vehicle, compu- tationalEntry-burn simulations starting were altitude performed [km] under two altitude 70.0 and velocity conditions based on the actualEntry-burn re-entry starting data velocity [16]. [m/s] Because the geometry of the 2294.0 Falcon 9 vehicle is not axisym- metric and hasDry nine weight engines, [t] a 3D analysis with 1/4 symmetric 22.2 geometry was performed. The numericalTotal propellant approach weight described [t] in Section 3.1 was applied, 36.0 and two freestream condi- Entry-burn thrust [tonf] 279.6 tionsLanding-burn were selected starting from altitude the [km] actual vehicle data [16]. 3.3 The computational grid and freestream conditions are presented in Figure 13 and Table 8, respectively. The flowfield The iteration process for determining the minimum required propellant weight was under Cases 1 and 2’s conditions is shown in Figure 14, and the calculated drag coeffi- omitted, and the remaining propellant weight obtained after landing was compared for thecients same under total propellant each condition weight. Toare calculate 1.56 and the 1.65, drag respectively.coefficient of the In vehicle, a previous compu- study [15], the drag coefficient was calculated as 1.56–1.61, which is similar to the drag coefficient ana- Energies 2021, 14, 3210 tational simulations were performed under two altitude and velocity 14conditions of 25 based on thelyzed actual in re-entrythis study. data [16].In previous Because the studies geom etry[16, of22], the it Falcon was assumed9 vehicle is that not axisym-the drag coefficient metricremained and has constant. nine engines, Therefore, a 3D analysis the average with 1/4 valu symmetrice of the geometry drag coefficie was performed.nt calculated through numericalThethe numericalcomputational approach approach described simulations described in Section 3.1 in werewas Sectio applied, setn 3.1 to and was a twoconstant applied, freestream andvalue conditions two for freestream the code condi- validation. weretions selected were fromselected the actual from vehicle the dataactual [16 ].vehicl The computationale data [16]. grid The and computational freestream grid and conditionsfreestream are conditions presented in Figureare presented 13 and Table in8 ,Figure respectively. 13 and The Table flowfield 8, underrespectively. Cases 1 The flowfield Table 8. Boundary conditions for validation [16]. andunder 2’s conditionsCases 1 and is shown 2’s conditions in Figure 14, andis shown the calculated in Figure drag 14, coefficients and the under calculated each drag coeffi- condition are 1.56 and 1.65, respectively. In a previous study [15], the drag coefficient wascients calculated under aseach 1.56–1.61, condition whichAltitude are is similar 1.56 [km] toandthe 1.65, drag coefficientrespectively.M∞ analyzed In a in previous this study.P∞ [Pa] study [15], the T∞ [K] drag coefficient was calculated as 1.56–1.61, which is similar to the drag coefficient ana- In previousCase studies 1 [16,22], it was assumed 31.2 that the drag coefficient 4.70 remained constant. 20 021 227.7 Therefore,lyzed in thethis average study. value In previous of the drag studies coefficient [16, calculated22], it was through assumed the computational that the drag coefficient Case 2 20.3 2.79 105 510 216.8 simulationsremained wereconstant. set to aTherefore, constant value the foraverage the code valu validation.e of the drag coefficient calculated through the computational simulations were set to a constant value for the code validation.

Table 8. Boundary conditions for validation [16].

Altitude [km] M∞ P∞ [Pa] T∞ [K] Case 1 31.2 4.70 20 021 227.7 Case 2 20.3 2.79 105 510 216.8

FigureFigure 13. Mesh13. Mesh of validation of validation case. case.

Table 8. Boundary conditions for validation [16].

Altitude [km] M∞ P∞ [Pa] T∞ [K] Case 1 31.2 4.70 20 021 227.7 Case 2 20.3 2.79 105 510 216.8 Figure 13. Mesh of validation case.

Figure 14. Mach number contour of validation cases.

Figure 14. Mach number contour of validation cases. Figure 14. Mach number contour of validation cases. A comparison of the results with those obtained previously [22] is presented in Figure 15. The thrust variation in the landing-burn phase took the form of a linear equation instead of a second-order one. This caused a slight difference in the altitude and accelera- tion; however, most of the results were consistent with those obtained previously. After landing, the remaining propellant amount was found to be approximately 8 tons; thus, it was thought that the program could thoroughly simulate the existing vehicle analysis data. Energies 2021, 14, x FOR PEER REVIEW 15 of 25 Energies 2021, 14, x FOR PEER REVIEW 15 of 25

A comparison of the results with those obtained previously [22] is presented in Fig- ure 15.A comparisonThe thrust variation of the results in the landing-buwith thosern obta phaseined took previously the form [22] of a is linear presented equation in Fig- insteadure 15. ofThe a second-order thrust variation one. Thisin the caused landing-bu a slightrn difference phase took in the the altitude form andof a acceleration; linear equation however,instead of most a second-order of the results one. were This consistent caused awith slight those difference obtained in previously. the altitude After and acceleration;landing, thehowever, remaining most propellant of the results amount were was consistent found to bewith approximately those obtained 8 tons; previously. thus, it was After thought landing, Energies 2021, 14, 3210 thatthe remaining the program propellant could thoroughly amount wassimula foundte the to existing be approximately vehicle analysis 8 tons; data. thus, 15it was of 25 thought that the program could thoroughly simulate the existing vehicle analysis data.

Figure 15. Validation of trajectory data obtained from a previous study [22]. (a) Velocity; (b) Altitude; (c) Acceleartion rate; (d) Thrust; (e) Drag; (f) Total mass. FigureFigure 15. 15.Validation Validation of trajectoryof trajectory data data obtained obta fromined a from previous a previous study [22 study]. (a) Velocity; [22]. (a) ( bVelocity;) Altitude; (b) (Altitude;c) AcceleartionThe (actualc) Acceleartion rate; re-entry (d) Thrust; rate;data (e ()usedd Drag;) Thrust; for (f) Totalthe (e )validati Drag; mass. (fon) Total were mass. the Falcon 9 FT vehicle’s flight data Theobtained actual for re-entry the NROL-76 data used mission for the validationin May 2017. were The the altitude Falcon 9and FT vehicle’svelocity data flight were dataextracted obtainedThe actualfrom for the re-entry the launch NROL-76 datawebcast mission used provided for in the May validatiby 2017. SpaceX Theon altitude were[16]. The the and entry-burnFalcon velocity 9 FT data starting vehicle’s were con- flight extractedditionsdata obtained included from the for an launch the altitude NROL-76 webcast of 63.5 provided mission km and byin velocity SpaceXMay 2017. [of16 1406]. The The m/s; entry-burnaltitude the vehicle and starting velocity specifications condi- data were tionsareextracted listed included infrom Table an the altitude 7. launch Because of 63.5webcast the km data and provided from velocity the by ofactual SpaceX 1406 vehicle m/s; [16]. the provides The vehicle entry-burn specificationsonly the starting velocity con- areandditions listed altitude, included in Table the7 . comparisonan Because altitude the ofdatawas 63.5 fromperformed km the and actual velocity only vehicle for of the provides 1406 corresponding m/s; only the the vehicle velocity value, specifications and as pre- altitude,sentedare listed in the Figurein comparison Table 16. 7. The Because was entry-burn performed the data starting only from for point thethe correspondingactual to the vehicle landing value, provides trajectory as presented only is generally the in velocity Figureconsistentand altitude, 16. Theand entry-burnthethe comparisonlanding starting time wasis point similar. performed to the Ho landingwever, only trajectorythere for the is a corresponding isslight generally difference consistent value, between as pre- andthesented free-fall the landingin Figure flight time and16. is The similar.landing-burn entry-burn However, phases, starting there which is apoint slight is inducedto difference the landing by betweenassuming trajectory the that free-fall theis generally drag flight and landing-burn phases, which is induced by assuming that the drag coefficient is coefficientconsistent isand constant the landing and the time thrust is insimilar. the landing-burn However, phasethere hasis a aslight linear difference variation. Evenbetween constantif the drag and coefficient the thrust is in applied the landing-burn as an average phase value has afor linear the variation.entire operating Even if time, the drag it is not coefficientthe free-fall is applied flight and as an landing-burn average value forphases, the entire which operating is induced time, by it is assuming not a significant that the drag acoefficient significant is problemconstant for and obtaining the thrust the in overallthe landing-burn trajectory becausephase has the a draglinear coefficient variation. is Even problemnot required for obtaining in the entry-burn the overall phase trajectory and is because almost the constant drag coefficient in the free-fall is not requiredflight phase. inif the the entry-burndrag coefficient phase is and applied is almost as an constant average in thevalue free-fall for the flight entire phase. operating However, time, to it is not However, to obtain more accurate results about propellant weight, it is crucial to consider obtaina significant more accurate problem results for aboutobtaining propellant the overall weight, ittrajectory is crucial tobecause consider the the drag drag coefficient coef- is the drag coefficient variation, especially in the landing-burn phase, which takes up about ficientnot required variation, in especiallythe entry-burn in the landing-burn phase and is phase, almost which constant takes upin aboutthe free-fall 20% of totalflight phase. 20% of total propellant consumption, as shown in Figure 15f. Through the validation of the propellantHowever, consumption,to obtain more as accurate shown in results Figure 15aboutf. Through propellant the validation weight, it of is the crucial analysis to consider analysis program, the calculation process of the re-entry sequence was found to be valid. program,the drag thecoefficient calculation variation, process ofespecially the re-entry in the sequence landing-burn was found phase, to be valid.which takes up about 20% of total propellant consumption, as shown in Figure 15f. Through the validation of the analysis program, the calculation process of the re-entry sequence was found to be valid.

Figure 16.16.Validation Validation with with the the actual actual re-entry re-entry data. data. (a) ( Velocity;a) Velocity; (b) Altitude.(b) Altitude. 4.2. Analysis Results under Different Re-Entry Conditions 4.2.1. Entry-Burn Starting Altitude

FigureAs 16. shown Validation in Table with1, the the entry-burn actual re-entry starting data. altitude (a) Velocity; was set ( tob) 40,Altitude. 60, and 80 km, and the entry-burn ending Mach number was fixed at 3.0 as a representative value. Figure 17 shows the result obtained by varying the landing-burn start thrust from 1 to 10 tonf at an

Energies 2021, 14, x FOR PEER REVIEW 16 of 25

4.2. Analysis Results under Different Re-Entry Conditions 4.2.1. Entry-Burn Starting Altitude Energies 2021, 14, 3210 16 of 25 As shown in Table 1, the entry-burn starting altitude was set to 40, 60, and 80 km, and the entry-burn ending Mach number was fixed at 3.0 as a representative value. Figure 17 shows the result obtained by varying the landing-burn start thrust from 1 to 10 tonf at an entry-burnentry-burn start start altitude altitude of of 60 60 km km and and an an end end Ma Machch number number of of 3.0. 3.0. As As shown shown in in Figure Figure 17a,c, 17a,c, aa small small change change occurs occurs in in the the velocity velocity and and altitude altitude in the in thelanding-burn landing-burn phase; phase; however, however, the overallthe overall tendency tendency with different with different landing-burn landing-burn start thrust start thrustvalues valuesremains remains the same. the There- same. fore,Therefore, the results the results obtained obtained for different for different entry-bu entry-burnrn starting starting altitudes altitudes are presented are presented for only for oneonly starting one starting thrust thrust (10 tonf). (10 tonf).

Energies 2021, 14, x FOR PEER REVIEW 17 of 25

FigureFigure 17. 17. TrajectoryTrajectory data data with with different different landing-burn landing-burn st startingarting thrust thrust values values (altitude (altitude of of entry-burn entry-burn start:start: 60 60 km). km). (a (a) )Thrust; Thrust; (b (b)) Velocity; Velocity; ( (cc)) Altitude. Altitude. As shown in Figure 18d, as the entry-burn starting altitude increases, the maximum drag in theFigureFigure free-fall 1818 presents presentsflight phase the the trajectoryalso increases. analysis analysis When results results the for forentry-burn each entry-burn starting startingaltitude altitudeis high, whenwhenthe duration the the landing-burn landing-burn and distance starting starting of thethrust thrust free-fall is is 10 10 tonf tonf. flight. The The phase changes changes increase, in in velocity, velocity, increasing altitude, altitude, the acceleration, acceleration, maximum andandspeed axial axial within force force theare are free-fallshown shown in in flight Figure Figure phase. 18a–d.18a–d. Thus, The The daas dash-dotted sh-dottedthe entry-burn line line and and start dotted dotted altitude line line increases,represent represent the the endendvelocity of of the the at entry-burn entry-burn the same phasealtitude phase and and increases, the the start start resultingof of the the landing-burn landing-burn in an increase phase, phase, in respectively.drag. respectively. In the case of the acceleration rate shown in Figure 18c, the positive value indicates deceleration and the negative value indicates acceleration. As shown in Figure 18a, the velocity and altitude decrease in the entry-burn phase because the deceleration in Figure 18c increases rapidly by the thrust of the retropropulsion in the entry-burn phase. After entering the free-fall flight phase, the velocity increases. However, as shown in Figure 18d, the drag increases rapidly owing to the increased dynamic pressure by decreasing alti- tude. This leads to an increase in positive acceleration, so that the velocity decreases again. When entering the landing-burn phase, the deceleration changes due to the thrust varia- tion; thus, the velocity and altitude change, and finally, the vehicle lands. As shown in Figure 18a, as the entry-burn starting altitude decreases, the initial free-fall distance and duration before the entry-burn starts increase, and accordingly, the entry-burn starting velocity increases and the start time of the entry-burn phase is delayed. However, as the entry-burn starting altitude decreases, the vehicle reaches the end altitude of the free-fall flight phase faster, resulting in shorter total duration for landing. Additionally in Figure 18a, when the entry-burn starting altitude is 60 or 80 km, the velocity increases again after the end of the entry-burn phase. However, at the entry-burn starting altitude of 40 km, the velocity does not increase in the free-fall flight phase because of the large drag force acting on the vehicle at low altitudes. As shown in Figure 18d, when the entry-burn start- ing altitude is 60 or 80 km, the drag increases after a certain period from the end of the entry-burn phase, whereas at the altitude of 40 km, the drag is already increased in the entry-burn phase. As a result, in the case of an entry-burn starting altitude of 40 km, as shown in Figure 18c, because the acceleration at the end of the entry-burn is already a positive value that acts in the direction of decreasing speed, the velocity continuously de- creases in the free-fall flight phase. The drag acted earlier at the low entry-burn starting altitude, but the value of drag is greater when the entry-burn starting altitude is higher.

Figure 18. ResultsResults obtained obtained by by entry-burn entry-burn starting starting altitude altitude variation. variation. (a)Velocity; (a)Velocity; (b) Altitude; (b) Altitude; (c) (Accelerationc) Acceleration rate; rate; (d) ( dThrust) Thrust and and Drag. Drag.

InFigure the case 19 shows of the the acceleration required total rate propellant shown in Figure weight, 18 durationc, the positive of the valueentry-burn indicates and decelerationlanding-burn and phases, the negative and thevalue amount indicates of propellant acceleration. consumed As shown according in Figure to the 18 a,landing- the ve- burn starting thrust at each entry-burn starting altitude. The Mach number at the end of the entry-burn is fixed at 3.0. The results indicate two main features. First, as shown in Figure 19a, as the entry-burn starting altitude increases (Figure 19a), the total propellant weight decreases regardless of the landing-burn start thrust. Second, as shown in Figure 19b, the durations of both the entry-burn and landing-burn phases decrease as the entry- burn start altitude increases. However, because the propellant consumption in the land- ing-burn phase is constant regardless of the entry-burn starting altitude shown in Figure 19c, the required total propellant weight is dominantly influenced by the propellant con- sumption of the entry-burn phase. As the entry-burn starting altitude increases, the re- quired propellant weight decreases owing to the reduction in duration at the entry-burn phase. Second, as shown in Figure 19a, at a constant entry-burn starting altitude, the total propellant weight decreases with the landing-burn starting thrust.

Energies 2021, 14, 3210 17 of 25

locity and altitude decrease in the entry-burn phase because the deceleration in Figure 18c increases rapidly by the thrust of the retropropulsion in the entry-burn phase. After en- tering the free-fall flight phase, the velocity increases. However, as shown in Figure 18d, the drag increases rapidly owing to the increased dynamic pressure by decreasing altitude. This leads to an increase in positive acceleration, so that the velocity decreases again. When entering the landing-burn phase, the deceleration changes due to the thrust variation; thus, the velocity and altitude change, and finally, the vehicle lands. As shown in Figure 18a, as the entry-burn starting altitude decreases, the initial free-fall distance and duration before the entry-burn starts increase, and accordingly, the entry-burn starting velocity increases and the start time of the entry-burn phase is delayed. However, as the entry-burn starting altitude decreases, the vehicle reaches the end altitude of the free-fall flight phase faster, resulting in shorter total duration for landing. Additionally in Figure 18a, when the entry-burn starting altitude is 60 or 80 km, the velocity increases again after the end of the entry-burn phase. However, at the entry-burn starting altitude of 40 km, the velocity does not increase in the free-fall flight phase because of the large drag force acting on the vehicle at low altitudes. As shown in Figure 18d, when the entry-burn starting altitude is 60 or 80 km, the drag increases after a certain period from the end of the entry-burn phase, whereas at the altitude of 40 km, the drag is already increased in the entry-burn phase. As a result, in the case of an entry-burn starting altitude of 40 km, as shown in Figure 18c, because the acceleration at the end of the entry-burn is already a positive value that acts in the direction of decreasing speed, the velocity continuously decreases in the free-fall flight phase. The drag acted earlier at the low entry-burn starting altitude, but the value of drag is greater when the entry-burn starting altitude is higher. As shown in Figure 18d, as the entry-burn starting altitude increases, the maximum drag in the free-fall flight phase also increases. When the entry-burn starting altitude is high, the duration and distance of the free-fall flight phase increase, increasing the maximum speed within the free-fall flight phase. Thus, as the entry-burn start altitude increases, the velocity at the same altitude increases, resulting in an increase in drag. Figure 19 shows the required total propellant weight, duration of the entry-burn and landing-burn phases, and the amount of propellant consumed according to the landing- burn starting thrust at each entry-burn starting altitude. The Mach number at the end of the entry-burn is fixed at 3.0. The results indicate two main features. First, as shown in Figure 19a, as the entry-burn starting altitude increases (Figure 19a), the total propellant weight decreases regardless of the landing-burn start thrust. Second, as shown in Figure 19b, the durations of both the entry-burn and landing-burn phases decrease as the entry-burn start altitude increases. However, because the propellant consumption in the landing-burn phase is constant regardless of the entry-burn starting altitude shown in Figure 19c, the required total propellant weight is dominantly influenced by the propellant consumption of the entry-burn phase. As the entry-burn starting altitude increases, the required propellant weight decreases owing to the reduction in duration at the entry-burn phase. Second, as shown in Figure 19a, at a constant entry-burn starting altitude, the total propellant weight decreases with the landing-burn starting thrust.

4.2.2. Entry-Burn Ending Mach Number In this section, the trajectory and required propellant weight according to each re-entry condition are analyzed by changing both the entry-burn ending Mach number and the entry-burn starting altitude. Figure 20 shows the velocity, altitude, acceleration, thrust, and drag values according to the entry-burn start altitude for different entry-burn ending Mach numbers. The dash-dotted line and dotted line indicate the entry-burn end and the landing-burn start, respectively. In addition, because the results are similar regardless of the landing-burn starting thrust, only the result corresponding to the starting thrust of 10 tonf is presented. EnergiesEnergies 20212021, 14, 14, x, 3210FOR PEER REVIEW 18 of18 25 of 25

FigureFigure 19. 19. RequiredRequired propellant propellant weight weight according according to to the the landing-burn landing-burn starting starting thrust. thrust. (a ()a Total) Total propellantpropellant weight; (bb)) Duration;Duration; ( c()c) Propellant Propellant consumption. consumption.

4.2.2. AsEntry-Burn shown in FigureEnding 20 Mach, as the Number entry-burn ending Mach number increases, the duration of the entry-burn phase and time taken to land decrease, regardless of the entry-burn startingIn this altitude. section, For the the sametrajectory entry-burn and required starting altitude,propellant as the weight entry-burn according ending to Macheach re- entrynumber condition increases, are theanalyzed decreasing by changing rate of altitude both the in entry-burn the free-fall ending flight phaseMach increases.number and theThe entry-burn altitude and starting velocity altitude. at the endFigure of the20 sh entry-burnows the velocity, phase are altitude, high; thus, acceleration, the free-fall thrust, andflight drag phase values rapidly according descends. to the However, entry-burn at an start entry-burn altitude starting for different altitude entry-burn of 40 km, ending the Machdecreasing numbers. rate ofThe altitude dash-dotted is similar line regardless and dotted of the line entry-burn indicate endingthe entry-burn Mach number. end and At the landing-burnthe end of the start, entry-burn respectively. phase, theIn addition, altitude is because too low, the which results generates are similar significant regardless drag. of theThis landing-burn has a dominant starting effect thrust, on descent. only the result corresponding to the starting thrust of 10 tonf isAt presented. a constant entry-burn ending Mach number, increasing the entry-burn starting altitudeAs shown decreases in Figure the entry-burn 20, as the starting entry-burn velocity, ending which Mach induces number the entry-burn increases, ending the dura- tionMach of numberthe entry-burn to quickly phase satisfy and the time entry-burn taken to duration.land decrease, However, regardless when theof the entry-burn entry-burn starting altitude is 40 km, the drag increases within the entry-burn phase regardless of starting altitude. For the same entry-burn starting altitude, as the entry-burn ending Mach the entry-burn ending Mach number. Thus, the acceleration at the end of the entry-burn number increases, the decreasing rate of altitude in the free-fall flight phase increases. The decreases the velocity as a positive value. After the entry-burn phase, the velocity does not altitudeincrease and in the velocity free-fall at flight the end phase of andthe entry-bu decreasesrn continuously. phase are high; thus, the free-fall flight phaseIn rapidly the landing-burn descends. However, phase, the at thrust an entry- is setburn to increasestarting linearly.altitude of The 40 landing-burnkm, the decreas- ingstarting rate of Mach altitude number is similar increases regardless with the of entry-burn the entry-burn starting ending altitude Mach and endingnumber. Mach At the endnumber, of the and entry-burn a faster deceleration phase, the isaltitude required is too for landinglow, which over generates the same distance. significant Therefore, drag. This hasas thea dominant entry-burn effect starting on descent. altitude and end Mach number are higher, both the thrust throttlingAt a constant rate in the entry-burn landing-burn ending phase Mach and landing-burn number, increasing ending thrust the entry-burn increase. starting altitudeFigure decreases 21 shows the the entry-burn required propellant starting ve weightlocity, and which the timeinduces duration the entry-burn for the landing- ending Machburn phasenumber according to quickly to the satisfy landing-burn the entry-bu startingrn duration. thrust for eachHowever, entry-burn when ending the entry-burn Mach startingnumber altitude and starting is 40 altitude.km, the drag As the increases entry-burn within ending the Mach entry-burn number phase increases, regardless the total of the entry-burnpropellant weightending decreases Mach number. regardless Thus, of thethe entry-burnacceleration starting at the altitude.end of the entry-burn de- creases the velocity as a positive value. After the entry-burn phase, the velocity does not increase in the free-fall flight phase and decreases continuously. In the landing-burn phase, the thrust is set to increase linearly. The landing-burn starting Mach number increases with the entry-burn starting altitude and ending Mach

Energies 2021, 14, x FOR PEER REVIEW 19 of 25

number, and a faster deceleration is required for landing over the same distance. There- Energies 2021fore,, 14, 3210 as the entry-burn starting altitude and end Mach number are higher, both the thrust 19 of 25 throttling rate in the landing-burn phase and landing-burn ending thrust increase.

Energies 2021, 14, x FOR PEER REVIEW 20 of 25 FigureFigure 20. Simulation 20. Simulation results withresults ending with Mach ending number Mach of number entry-burn of entry-burn phase. (a) Entry-burn phase. (a starting) Entry-burn altitude of 80 km; (b) Entry-burnstarting altitude starting altitudeof 80 km; of 60 (b km;) Entry-burn (c) Entry-burn starting starting altitude altitude of of 60 40 km; km. (c) Entry-burn starting altitude of 40 km.

Figure 21 shows the required propellant weight and the time duration for the land- ing-burn phase according to the landing-burn starting thrust for each entry-burn ending Mach number and starting altitude. As the entry-burn ending Mach number increases, the total propellant weight decreases regardless of the entry-burn starting altitude.

FigureFigure 21. Propellant 21. Propellant weightwith weightwith different different landing-burn land startinging-burn thrust starting values. thrust (a) Entry-burn values. ending(a) Entry-burn Mach number of 2.0; (b) Entry-burnending Mach ending number Mach numberof 2.0; ( ofb) 3.0; Entry-burn (c) Entry-burn ending ending Mach Mach number number of of 3.0; 4.0. (c) Entry-burn ending Mach number of 4.0.

In addition, as the entry-burn starting altitude increases at the same entry-burn end- ing Mach number, the propellant weight tends to decrease, which results from a reduction in the time duration for the landing-burn phase. However, when the entry-burn ending Mach number has values of 3.0 and 4.0, the difference between different ending Mach num- bers for the same initial thrust decreases as the entry-burn starting altitude increases. At an entry-burn starting altitude of 80 km and the entry-burn ending Mach number is 3.0, the total propellant weight is minimal, which is related to the entry-burn duration. Figure 22 shows the sequence analysis results for each entry-burn ending Mach num- ber at the entry-burn starting altitudes of 60 and 80 km. The figure includes average values for the landing-burn starting thrust at the entry-burn starting altitude of 60 km and a ratio of the value of 80 km to that of 60 km. The ratio value of 1.0 means that the results at 60 km and 80 km are equal, and if the value is above 1.0, the result of 80 km is smaller than that of 60 km. As the entry-burn ending Mach number increases, the entry-burn duration decreases regardless of the entry-bury starting altitude. It leads to a reduction of the pro- pellant consumption at the entry-burn phase, resulting in a decrease in the amount of propellant. In addition, when the entry-burn ending Mach number is 2.0 and 3.0, the en- try-burn duration and propellant consumption at the entry-burn starting altitude of 60 km is larger than those at the entry-burn starting altitude of 80 km. However, when the entry-burn ending Mach number is 4.0, the result values increase as the entry-burn start- ing altitude increases, which is confirmed by the fact that the ratio is above 1 when the entry-burn ending Mach number is 4.0. This opposite trend appears because the entry- burn termination condition is set for the Mach number.

Figure 22. Summary of results with Entry-burn starting altitude of 60 and 80 km. (a) Total propellant weight; (b) Entry-burn duration; (c) Entry-burn propellant consumption.

The air temperature decreases as the altitude changes from an altitude of 50 km. At an entry-burn starting altitude of 80 km, the atmospheric temperature in the entry-burn phase continuously increases as RLV falls because the entry-burn ending altitude is more than 50 km regardless of the entry-burn ending Mach number. However, when the entry- burn starting altitude is 60 km and the entry-burn ending Mach number is less than 4.0, the

Energies 2021, 14, x FOR PEER REVIEW 20 of 25

Figure 21. Propellant weightwith different landing-burn starting thrust values. (a) Entry-burn Energies 2021, 14, 3210 ending Mach number of 2.0; (b) Entry-burn ending Mach number of 3.0; (c) Entry-burn ending20 of 25 Mach number of 4.0.

In addition, as the entry-burn starting altitude increases at the same entry-burn end- ing MachIn addition, number, as the the propellant entry-burn weight starting tends altitude to decrease, increases which at the results same entry-burn from a reduction ending inMach the number,time duration the propellant for the landing-burn weight tends ph toase. decrease, However, which when results the fromentry-burn a reduction ending in Machthe time number duration has forvalues the of landing-burn 3.0 and 4.0, phase.the difference However, between when different the entry-burn ending ending Mach num- Mach bersnumber for the has same values initial of 3.0 thrust and decreases 4.0, the difference as the entry-burn between starting different altitude ending increases. Mach numbers At an entry-burnfor the same starting initial altitude thrust decreasesof 80 km and as the the entry-burn entry-burn starting ending altitudeMach number increases. is 3.0, At the an entry-burn starting altitude of 80 km and the entry-burn ending Mach number is 3.0, the total propellant weight is minimal, which is related to the entry-burn duration. total propellant weight is minimal, which is related to the entry-burn duration. Figure 22 shows the sequence analysis results for each entry-burn ending Mach num- Figure 22 shows the sequence analysis results for each entry-burn ending Mach ber at the entry-burn starting altitudes of 60 and 80 km. The figure includes average values number at the entry-burn starting altitudes of 60 and 80 km. The figure includes average for the landing-burn starting thrust at the entry-burn starting altitude of 60 km and a ratio values for the landing-burn starting thrust at the entry-burn starting altitude of 60 km and of the value of 80 km to that of 60 km. The ratio value of 1.0 means that the results at 60 a ratio of the value of 80 km to that of 60 km. The ratio value of 1.0 means that the results km and 80 km are equal, and if the value is above 1.0, the result of 80 km is smaller than at 60 km and 80 km are equal, and if the value is above 1.0, the result of 80 km is smaller that of 60 km. As the entry-burn ending Mach number increases, the entry-burn duration than that of 60 km. As the entry-burn ending Mach number increases, the entry-burn decreases regardless of the entry-bury starting altitude. It leads to a reduction of the pro- duration decreases regardless of the entry-bury starting altitude. It leads to a reduction of pellant consumption at the entry-burn phase, resulting in a decrease in the amount of the propellant consumption at the entry-burn phase, resulting in a decrease in the amount propellant. In addition, when the entry-burn ending Mach number is 2.0 and 3.0, the en- of propellant. In addition, when the entry-burn ending Mach number is 2.0 and 3.0, the try-burnentry-burn duration duration and and propellant propellant consumptio consumptionn at the at theentry-burn entry-burn starting starting altitude altitude of 60 of km60 kmis larger is larger than than those those at the at theentry-burn entry-burn starting starting altitude altitude of 80 of km. 80 km.However, However, when when the entry-burnthe entry-burn ending ending Mach Mach number number is 4.0, is the 4.0, re thesult result values values increase increase as the asentry-burn the entry-burn start- ingstarting altitude altitude increases, increases, which which is confirmed is confirmed by bythe the fact fact that that the the ratio ratio is is above above 1 1 when when the the entry-burnentry-burn ending MachMach numbernumber is is 4.0. 4.0. This This opposite opposite trend trend appears appears because because the entry-burnthe entry- burntermination termination condition condition is set is for set the for Mach the Mach number. number.

FigureFigure 22. 22. SummarySummary of of results results with Entry-burn startingstarting altitudealtitude ofof 6060 and and 80 80 km. km. ( a(a)) Total Total propellant propellantweight; (b )weight; Entry-burn (b) Entry-burn duration; ( cduration;) Entry-burn (c) Entry-burn propellant propellant consumption. consumption.

TheThe air air temperature temperature decreases decreases as as the the altitude altitude changes changes from from an an altitude altitude of 50 km. At At anan entry-burn entry-burn starting starting altitude altitude of of 80 80 km, km, th thee atmospheric temperature in in the entry-burn phasephase continuously continuously increases increases as as RLV RLV falls because the the entry-burn entry-burn ending ending altitude altitude is is more more thanthan 50 50 km km regardless regardless of of the the entry-burn entry-burn ending ending Mach Mach number. number. However, However, when when the the entry- entry- burnburn starting starting altitude altitude is is 60 60 km km and and the the entry-bu entry-burnrn ending ending Mach Mach number number is less is lessthan than 4.0, the 4.0, the ending altitude is less than 50 km. The atmospheric temperature increases and then decreases again during the entry-burn phase as RLV enters stratospheric region. A de- crease in the air temperature leads to a decrease in the speed of sound; thus, the velocity must decrease much more to reach the entry-burn ending Mach number. Accordingly, when the entry-burn end Mach number is 2.0 and 3.0, and the entry-burn start altitude is 60 km, a large deceleration is required, which increases the entry-burn duration. How- ever, when the entry-burn ending Mach number is 4.0, both the entry-burn starting and ending altitudes are 50 km or more. In addition, at a higher entry-burn start altitude of 80 km, the atmospheric temperature is lower and requires a more significant deceleration. Therefore, the duration of the entry-burn phase increases, and eventually, the consump- tion of the propellant in the entry-burn phase increases, increasing the total amount of propellant required. However, the required propellant weight decreases generally as the entry-burn starting altitude or the entry-burn ending Mach number increases, except in some instances of the Energies 2021, 14, 3210 21 of 25

ending Mach number of 4.0 at the starting altitude of 80 km for the entry-burn phase. As the entry-burn starting altitude and ending Mach number are higher, the duration of the entry-burn phase decreases. Consequently, it is confirmed that the duration of the entry- burn phase has a dominant effect on the total amount of propellant required. In addition, for the same entry-burn starting altitude and entry-burn ending Mach number, as the landing-burn start thrust decreases, the landing-burn duration decreases due to high thrust throttling rate, resulting in a decrease in the required total propellant weight. However, because there is a limitation on the thrust throttling rate, the landing-burn starting thrust should be adjusted within controllable range.

4.3. Optimization Based on the results in Section 4.2, a simple optimization procedure was performed to find a minimum value of the required propellant weight for soft landing. In this study, Genetic Algorithm (GA) technique was used to optimization. Genetic algorithm (GA) is the stochastic optimization process that mimics biological evolution. It can solve constrained and unconstrained problems based on natural selection processes. In the optimization process, the algorithm randomly selects individual solutions from the current population and uses them as the parent solution to generate the next generation of solutions. Only the superior populations survive and evolves to the next generation, and the optimal solution is sought. The genetic algorithm is robust and not sensitive to initial guess. Since the algorithm do not require a single point as initial condition but explore a broad solution space simultaneously and adaptively, it shows good performance to nonlinear complex global optimization problem. Therefore, in this study, the genetic algorithm is suitable to find optimal values of variables for landing with a minimum propellant weight.

4.3.1. Objective Function and Variables The aim of the optimization process is to find the optimal re-entry condition that can land with a minimum propellant weight. Therefore, an objective function of GA is represented as follows. minmp = f (X) (10) u(X) = 0 & h(X) = 0 (11)

Xlb ≤ Xi ≤ Xub (12)

where X represent the set of variables, and Xlb, Xub are the lower and upper bound of variables respectively. The re-entry conditions given in Table1 were set to variables of GA with the initial propellant weight. However, the entry-burn ending Mach number was excluded from the variables according to the analysis results. From the results in Section 4.2.2, it was confirmed that the minimum propellant weight is always calculated at the maximum value in the setting range of the entry-burn Mach number, unlike the entry-burn starting altitude. The variables and lower-upper bound of each variable are presented in Table9.

Table 9. Variables and constraints.

Variables Lower Bound Upper Bound Initial propellant weight [t] 2.0 3.0 Entry-burn starting altitude [km] 40.0 80.0 Landing-burn initial thrust [tonf] 1.0 10.0

4.3.2. Optimization Results The optimal values of each variable for soft landing are given in Table 10. There is no significant difference between calculation results and optimal values, which means that the current calculation process can provide optimal results within a given range of variables. Energies 2021, 14, x FOR PEER REVIEW 22 of 25

variables according to the analysis results. From the results in Section 4.2.2, it was con- firmed that the minimum propellant weight is always calculated at the maximum value in the setting range of the entry-burn Mach number, unlike the entry-burn starting alti- tude. The variables and lower-upper bound of each variable are presented in Table 9.

Table 9. Variables and constraints.

Variables Lower Bound Upper Bound Initial propellant weight [t] 2.0 3.0 Entry-burn starting altitude [km] 40.0 80.0 Landing-burn initial thrust [tonf] 1.0 10.0

4.3.2. Optimization Results The optimal values of each variable for soft landing are given in Table 10. There is no significant difference between calculation results and optimal values, which means that the current calculation process can provide optimal results within a given range of variables.

Table 10. Optimization results.

Variables Calculation Results Optimal Values Energies 2021, 14,Initial 3210 propellant weight [t] 2.67 2.665 22 of 25 Entry-burn starting altitude [km] 60.0 61.02 Landing-burn initial thrust [tonf] 1.0 1.01 Table 10. Optimization results. In addition, trajectory analysis with the optimal values of variables was conducted Variables Calculation Results Optimal Values according to various cases of the drag coefficient. Three cases of the drag coefficient were Initial propellant weight [t] 2.67 2.665 applied to the analysis: Entry-burngeneral startingconstant altitude value, [km] function obtained 60.0 from CFD results, 61.02 and constant value averagedLanding-burn from the calculation initial thrust [tonf] results with function. 1.0 The first case is 1.01 the gen- eral constant value was set to 1.5, which is an approximate value used for validation. The function obtained from InCFD addition, results, trajectory as the analysis second with case, the optimalindicate values Equations of variables (8) wasand conducted(9). In according to various cases of the drag coefficient. Three cases of the drag coefficient were addition, a time-averagedapplied tovalue the analysis: of the drag general co constantefficient value, over function time calculated obtained from from CFD results,the sec- and ond case is the final constantcase of valuethe analysis. averaged from the calculation results with function. The first case is the The comparisongeneral results constant of the value three was cases set to 1.5,are which presented is an approximate in Figure value 23. The used forresults validation. of The function obtained from CFD results, as the second case, indicate Equations (8) and (9). every case in FigureIn 23 addition, were calculated a time-averaged with value same of the initial drag coefficientpropellant over weight time calculated of 2.665 from ton the which is the optimalsecond value. case The is the variation final case of thethe analysis. drag coefficient of each case is shown in Figure 23a. The drag coefficientThe comparison of Case results 1 and of the 3 keep three casesconstant are presented over time, in Figure but 23Case. The 2 results have of complex variation. Figureevery case 23b,c in Figure present 23 were the calculatedvariation with of the same propellant initial propellant weight weight and of trajec- 2.665 ton which is the optimal value. The variation of the drag coefficient of each case is shown in tory. Despite the launchFigure vehicle 23a. The has drag the coefficient same ofpropellant Case 1 and 3weight keep constant for the over re-entry, time, but the Case total 2 have duration to landingcomplex and residual variation. propellant Figure 23b,c presentweight the after variation landing of the propellantare different weight according and trajectory. to how the drag coefficientDespite the is launchcalculated. vehicle hasFurt thehermore, same propellant as described weight for in the Section re-entry, the4.1, total the duration tra- jectory results showto a landingdifference and residualin the free-fall propellant flight weight and after landing-burn landing are different phases according according to how the drag coefficient is calculated. Furthermore, as described in Section 4.1, the trajectory to the method calculatingresults showthe drag a difference coefficient, in the free-fall which flight indicates and landing-burn that inaccurate phases accordingcalculation to the of the drag coefficientmethod can induce calculating a landing the drag fail coefficient, of RLV. which As a indicates result, thatit is inaccurateimportant calculation that the of optimization of the there-e dragntry coefficient conditions can induceshould a landingbe performed fail of RLV. with As a accurate result, it is calculation important that of the optimization of the re-entry conditions should be performed with accurate calculation of the drag coefficient.the drag coefficient.

Figure 23. Trajectory results according to cases of the drag coefficient (Case 1: General constant value, Case 2: Function from CFD results, Case 3: Constant value averaged from calculation result with function). (a) Drag coefficient; (b) Propellant weight; (c) Range-Altitude.

5. Conclusions As a fundamental study on the re-entry technology, the re-entry sequence of a space launch vehicle was established in this study. The trajectory and required amount of propellant were analyzed under various re-entry conditions, and the results were compared to the values from the optimization process using GA. To increase the reliability of the results, the drag coefficient according to the altitude, velocity, and thrust was calculated through computational simulations. The results of the drag analysis indicated that the drag force in the entry-burn phase was negligible and the ratio of the thrust and drag exceeded 99:1. However, as the drag coefficient varied under the re-entry conditions in the free-fall Energies 2021, 14, 3210 23 of 25

and landing-burn phases, the drag coefficient was derived as a function of altitude and velocity for the configuration of launcher applied in this study. The test launch vehicle (TLV) in Korea was applied to the calculation of the re-entry sequence. From the trajectory analysis, the required propellant weight according to the entry- burn starting altitude and ending Mach number with different landing-burn starting thrust values were obtained. The entry-burn ending Mach number was set to 2.0–4.0, and the entry-burn starting altitude and landing-burn starting thrust were set to 40–80 km and 1–10 tonf, respectively. As a result of the analysis, a higher entry-burn starting altitude and ending Mach number decreases the total duration for landing and propellant consumption in the entry-burn phase, resulting in a reduction in the total propellant weight. The propellant consumption in the landing-burn phase shows a slight change according to the re-entry conditions, which indicates that the propellant consumption of the entry-burn phase is dominant for the total propellant weight. In addition, for the same entry-burn starting altitude and ending Mach number, as the landing-burn starting thrust decreases, the landing-burn duration also decreases, resulting in a decrease in the total propellant weight. For TLV, the minimum propellant weight for soft landing is approximately 2.67 t at the entry-burn starting altitude of 60 km and Mach number of 4.0. However, just as the condition such as the entry-burn ending Mach number of 4.0, the total propellant weight may increase as the entry-burn starting altitude increases from 60 km to 80 km, which is due to the change in the sound speed depending on the altitude. As a result, it is necessary to select an appropriate re-entry condition if the entry-burn ending condition is set to the Mach number. Finally, the optimization process using GA was conducted to compare the calculation results. The re-entry conditions except the entry-burn ending Mach number were set to variables for the optimization. From the comparison, it was confirmed that the calculation results and optimized value are very similar, which indicates that the current calculation process can provide the output results close to the optimal values. In addition, trajectory analysis with the optimal values of variables was conducted according to the method that the drag coefficient is calculated. Two constant values of the drag coefficient were applied to the trajectory analysis and compared to the optimized result, and it was observed that the results including trajectory and propellant weight are different according to how to calculate the drag coefficient. Therefore, it is important that the optimization of the re-entry conditions should be performed with accurate calculation of the drag coefficient.

Author Contributions: Conceptualization, Y.K. and H.-J.L.; data curation, Y.K.; methodology, Y.K. and H.-J.L.; software, Y.K.; supervision, T.-S.R.; validation, Y.K. and H.-J.L.; writing—original draft, Y.K.; writing—review and editing, H.-J.L. and T.-S.R. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are available on request from the corresponding author. Acknowledgments: This research was supported by through the Space Core Technology Develop- ment Program of the National Research Foundation (NRF) funded by the Ministry of Science and ICT (MICT) of the Republic of Korea (Grant No. NRF-2018M1A3A3A02065851). Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature

T∞ Atmospheric temperature P∞ Atmospheric pressure Energies 2021, 14, 3210 24 of 25

M∞ Mach number md Dry weight mp Propellant weight mp,ini Initial propellant weight ue Nozzle exit velocity Cd Drag coefficient CT Thrust coefficient CAF Axial force coefficient ρ Density D Drag T Thrust L Lift g Gravitational acceleration V Velocity γ Flight path angle h Altitude S Cross-sectional area

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