Thermal Performance Characteristics of an 80-Ton Variable-Thrust Liquid Engine for Reusable Launch Rockets

: In this paper, an 80-ton thrust liquid rocket engine (hereinafter referred to as an LRE) with a gas generator cycle, a 5:1 thrust throttling ratio, and an integrated ﬂow regulator/gas generator (hereinafter referred to as an IFRGG) is analyzed. This LRE can be used during the ﬁrst stage of launching, second-stage and upper-stage space missions, and moon/mars low-orbit hovering and soft landing, and it can also be used with various near-space multipurpose ﬂight vehicles. The thermal performance model of the variable-thrust LRE is established, the inﬂuence of the main LRE design parameters on the performance optimization is analyzed, and an optimal selection of the design parameters under certain constraints is completed. A performance evaluation was successfully conducted, and we determined the main structural parameters at the sea-level design point; additionally, we evaluated the LRE performance, matched the system parameters under a 100–20% variable-thrust operation, and conducted an analysis on the LRE operating characteristics under a wide range of variable-thrust operations. The LOX/kerosene propellants were selected, and the vacuum-speciﬁc impulse of the LRE decreased from 303.2 s to 289.2 s; this followed an approximate linear law, with a decrease of about 4.62% when the thrust was varied in the wide range of 100–20%. The variable-thrust LRE still had a better vacuum performance under a very deep throttling condition. The reason why the speciﬁc impulse was low under the deep throttling condition is that it was greatly affected by the different atmospheric pressure that was caused by the varying ﬂight height and the insufﬁcient atomization and combustion of the propellant; however, because of its wide range of variable-thrust working abilities, it is suitable for various special ﬂight missions.


Introduction
In recent years, reusable launch rockets, which can substantially reduce launch costs, have attracted extensive attention from the international space community.In 2015, the Falcon 9 Reusable launch rocket, which was developed by SpaceX, successfully completed the first stage of launching for the first time (as shown in Figure 1) [1,2], which caused a sensation in the international aerospace community and once again focused the world's attention on variable-thrust LRE technology.Various research institutes favor the Merlin series of a wide range of variable-thrust LOX/kerosene propellant engines.Variable-thrust LREs, with their wide range of variable-thrust capabilities, provide important technical support for the effective reusable and LRE reuse of carrier rockets.Variable-thrust LRE technology is not a new field of technology.However, with the successful reuse of the first stage of the Falcon 9 retrievable carrier rocket on the Earth's surface and the successful space exploration missions of Chang'e-3, Chang'e-4, Chang'e-5, and Tianwen-1 in China, another research on variable-thrust rocket engines has begun.Variable-thrust LREs are an important part of advanced power systems for various space missions [3][4][5] and have the following advantages: improve the rendezvous and docking accuracy; enhance the maneuverability; allow for soft landings on the ground; allow for landing-zone control; and improve the performance of rocket-based combined-cycle engines.The Soviet Union/Russia and the United States have long histories of variable-thrust LRE development, as well as rich accumulations of related technologies [6][7][8][9][10].
In fact, deep-throttling variable-thrust LRE technology has good application prospects in liquid rocket propulsion technology [11][12][13][14] and shows great superiority in space transportation [3,5], space-flight maneuvers [15,16], vertical takeoff, landing launch vehicles, lunar soft landings, and RBCC ejector rockets.As a high-density energy release device, a variable-thrust LRE is different from the fixed-thrust version, which still requires solutions to many technical issues in system design and thrust control.
The LRE with the pintle Injector is preferred in many variable-thrust LREs [17,18].Although there are many methods to control LREs via variable thrust, most of them are not applied in rocket engineering.So far, controlling the injection area and controlling the propellant mass flow rate in the supply line is still the main method of adjusting the LRE thrust [19,20], and this mainly includes strategies such as the monotone method, double adjustable traffic location system, adjustable area of cavitation, venturi tube combined with a fixed section injection device, and the throttle valve regulating the dual-supply turbine pump flow.
The MIRA-10K series engines of the Apollo lunar module [21] used a mechanical connection scheme that involved dual-channel variable-cross-section-area injectors and variable-cross-section-area venturi tube flow control valves.When thrust throttling is needed, the piston in the throttling valve and the connected pintle are moved by the electric action mechanism so that the flow area of the throttle valve is changed and the movement of the pintle changes the injection area of the oxidizer and fuel and thus achieves a 10:1 ratio of wide-range thrust throttling.A substage of the Falcon 9 rocket was powered by nine Merlin-1D variable-thrust liquid oxygen/kerosene engines, which used the same pintle.The first author and his team carried out some research work on pintle displacement closed-loop control and obtained many important results that were published [22] before this paper.
The Apollo lunar module descent LRE used for soft lunar landings in the 1960s is the earliest best-known variable-thrust LRE.The first moon landing was finally achieved with a thrust ratio of 10:1 and a thrust range of 46.75-467.5 kN [23].
Typical examples of variable-thrust rocket engines in China are the CE-3, CE-4, CE-5, and YF-36 engines used in space exploration missions on the moon and mars [24].Variable-thrust LRE technology is not a new field of technology.However, with the successful reuse of the first stage of the Falcon 9 retrievable carrier rocket on the Earth's surface and the successful space exploration missions of Chang'e-3, Chang'e-4, Chang'e-5, and Tianwen-1 in China, another research on variable-thrust rocket engines has begun.Variable-thrust LREs are an important part of advanced power systems for various space missions [3][4][5] and have the following advantages: improve the rendezvous and docking accuracy; enhance the maneuverability; allow for soft landings on the ground; allow for landing-zone control; and improve the performance of rocket-based combined-cycle engines.The Soviet Union/Russia and the United States have long histories of variablethrust LRE development, as well as rich accumulations of related technologies [6][7][8][9][10].
In fact, deep-throttling variable-thrust LRE technology has good application prospects in liquid rocket propulsion technology [11][12][13][14] and shows great superiority in space transportation [3,5], space-flight maneuvers [15,16], vertical takeoff, landing launch vehicles, lunar soft landings, and RBCC ejector rockets.As a high-density energy release device, a variable-thrust LRE is different from the fixed-thrust version, which still requires solutions to many technical issues in system design and thrust control.
The LRE with the pintle Injector is preferred in many variable-thrust LREs [17,18].Although there are many methods to control LREs via variable thrust, most of them are not applied in rocket engineering.So far, controlling the injection area and controlling the propellant mass flow rate in the supply line is still the main method of adjusting the LRE thrust [19,20], and this mainly includes strategies such as the monotone method, double adjustable traffic location system, adjustable area of cavitation, venturi tube combined with a fixed section injection device, and the throttle valve regulating the dual-supply turbine pump flow.
The MIRA-10K series engines of the Apollo lunar module [21] used a mechanical connection scheme that involved dual-channel variable-cross-section-area injectors and variable-cross-section-area venturi tube flow control valves.When thrust throttling is needed, the piston in the throttling valve and the connected pintle are moved by the electric action mechanism so that the flow area of the throttle valve is changed and the movement of the pintle changes the injection area of the oxidizer and fuel and thus achieves a 10:1 ratio of wide-range thrust throttling.A substage of the Falcon 9 rocket was powered by nine Merlin-1D variable-thrust liquid oxygen/kerosene engines, which used the same pintle.The first author and his team carried out some research work on pintle displacement closed-loop control and obtained many important results that were published [22] before this paper.
The Apollo lunar module descent LRE used for soft lunar landings in the 1960s is the earliest best-known variable-thrust LRE.The first moon landing was finally achieved with a thrust ratio of 10:1 and a thrust range of 46.75-467.5 kN [23].
Typical examples of variable-thrust rocket engines in China are the CE-3, CE-4, CE-5, and YF-36 engines used in space exploration missions on the moon and mars [24].In December 2013, the YF-36 7500N pintle variable-thrust LRE developed by the Academy of Aerospace Propulsion Technology was used for the first time, and the CE-3 probe successfully landed on the lunar surface.The YF-36 variable-thrust LRE adopted a flowpositioning double-adjusted open-loop regulation system and variable-area-cavitation Venn tube flow regulator.The stepping motor moves the adjusting cone up and down, changes the throat area of the cavitation tube, and adjusts a wide range of the LRE flow.The actual variable-thrust ratio of the LRE is 6.87:1, and the thrust deviation is less than ±3%.The soft landing of the Tianyun-1 landing rover on the surface of mars in May 2021 was successfully achieved with the YF-36 series of variable-thrust engines.The YF-36 LRE is a low-thrust extruded LRE.In the field of wide-thrust and pump-fed engines, China's new-generation YF-100 series with 120-ton LOX/kerosene propellants and a highpressure supplementary-combustion-cycle LRE can achieve adjustments within 65-100% of the rated thrust [25][26][27][28][29][30][31][32].
Researchers have also conducted work on variable-thrust LREs in China's private aerospace field.The "Thunder 5" pintle electric-pump LOX/kerosene propellants LRE, which was independently developed by Jiangsu Shenlan Aerospace, has a vacuum thrust of 50 kN, which can achieve a 50-110% variable-thrust adjustment [33].In January 2020, researchers completed a wide range of variable-thrust long-range tests on the whole LRE, as well as a jump recoverable test.The maximum thrust of the "Thunder 100" LRE under development was 1000 kN, which is comparable to the thrust of the YF-100 series engines in service, and the thrust adjustment ability ranged from 110% to 50%.The 200 kN grade LOX/kerosene propellant rocket LRE "Xuanyuan-1" is the first one of its kind in the domestic commercial space field [34].Xuanyuan-1 can have multiple startups and widerange thrust adjustment, which can meet the demand of liquid rocket first-stage reuse.The first full-system test was completed in May 2021.
In 2018, Wen took a motor-pump supercharged variable-thrust LRE as the research object and designed and controlled the variable-thrust control system [35].In 2020, Cui Peng et al. conducted a scheme study on a liquid LOX/methane expansion-cycle variablethrust LRE system, and they evaluated the methane expansion power capacity and the feasibility of the variable-thrust adjustment scheme [36].At the same time, a new scheme for an electrothermal cooperative variable-thrust LRE was proposed, which combines the motor-pump booster and expansion-cycle LRE in parallel, and the motor and turbine drive the same pump on a common axis [37][38][39].In 2020, Huang [40] studied the system characteristics of a variable-thrust rocket LRE under deep throttling conditions.Li and Yue [41] carried out a numerical simulation of the spray combustion process of a pintle LRE, which provided a reference for the design of the key components of a variable-thrust LRE.In 2018, Jin et al. [42] unveiled an aero-LOX/kerosene pintle variable-thrust LRE based on a mechanically positioned dual modulation system with a thrust ratio of 15:1.
According to the analysis above, the reusable launch rockets put forward a 5:1 widerange variable-thrust demand for the liquid rocket engine.With such a wide range of variable demand, it is very difficult to regulate the injections and flow.
When undergoing a wide range of variable thrusts, the high-efficiency atomization, high-frequency unstable combustion, and acoustic stability of the variable structure injector in the regulating range need to be overcome.Adopting an IFRGG mode is a feasible scheme to realize flow regulating and bipropellant injecting synchronously.But this also brings many difficulties in the design methods.In the process of adjusting the thrust, in order to ensure that the mixing ratio and combustion temperature of the generator are basically unchanged as much as possible, one must use the same pintle displacement to synchronously adjust the oxidizer and fuel propellants.This requires the flow area of the internal and external injectors to be changed synchronously and continuously, the two propellants to always be mixed and atomized efficiently, and the adjustment accuracy to be very high due to the very short moving distance.
Therefore, this paper mainly focuses on exploring the component parameter matching method in the process of 5:1 wide-range thrust throttling.By adopting a special IFRGG structure, it can not only achieve a 5:1 wide range thrust throttling, but it can also maintain the optimal performance of the LRE.The authors of this paper have long been engaged in the research, development, and testing of advanced variable-thrust forces in near space.In this study, we attempted to study the system scheme of a variable-thrust LRE and analyze the performance under variable-thrust conditions, with the aims of applying variable-thrust LREs in various new space vehicles in the space age and providing a useful reference for scholars and scientists.

Analysis of Main Specifications of Variable-Thrust LRE
There are many technical indexes of variable-thrust LREs, including the following: the propellant type, cycle mode, supply mode, sea-level thrust, sea-level specific impulse, vacuum thrust, vacuum-specific impulse, variable-thrust ratio range, thrust-to-weight ratio, swing angle, total number of timers for ignition, total working time, etc.In this paper, we primarily assessed the system scheme and performance of the variable-thrust LRE; thus, we mainly focused on the thrust, specific impulse, variable-thrust ratio range, and other technical indicators.
With the successful application of China's new generation of high-thrust LOX/kerosene engines in the launch missions of the CZ-5, CZ-6, and CZ-7 vehicles, new green nontoxic propellants such as liquid LOX/kerosene, LOX/hydrogen, and LOX/methane are replacing traditional toxic propellants.Considering that the Falcon 9 vehicle, which uses the LOX/kerosene-propellant Merlin-1D LRE, successfully performed retrievable launch services, in this paper, we selected the LOX/kerosene propellants for the variable-thrust LRE to increase the comparability.
The thrust of the Merlin-1D LRE continues to increase, and it currently stands at about 86 tons per LRE.A single thrust of the conventional YF-20 series propellant engines, which are the main power sources of China's CZ-2, CZ-3, and CZ-4 carriers, is about 75 tons.The thrust of the YF-100 series, which consists of a new generation of high-thrust LOX/kerosene high-pressure supplementary combustion-cycle engines for the CZ-5, CZ-6, and CZ-7 carriers, is about 120 tons.Moreover, the thrust of YF-102, the open-cycle LOX/kerosene LRE, is 85 tons.After comprehensive consideration, and to increase the comparability, we selected 80 tons of sea-level thrust for the LRE as the research benchmark.
The thrust ratio is defined as the ratio of the maximum thrust to the minimum one of the LRE.The wider the variable-thrust ratio, the stronger the variable-thrust capability, and the wider its applicability.Currently, the maximum variable-thrust ratio LRE in China is the YF-36 descent LRE, which was used for the hovering and landing of the Chang'e-3, Chang'e-4, and Chang'e-5 lunar probes and the Tiangwen 1 mars probe.The thrust adjustment range is 7500-1500 N, and the variable-thrust ratio is 5:1.However, the YF-36 LRE has an extrusion supply system, which has a low chamber pressure and small thrust, and the system is relatively simple.The typical representative of the new generation of widethrust pump-pressure engines in China is the YF-100 series 120-ton engines, which have a high-pressure reburning-cycle scheme and a certain working ability to pull the deflection condition.However, the YF-100 system is complex and the development cost is high.The Merlin-1D first-stage LRE has a throttling capacity from 60 to 70 percent of the central LRE; however, this is based on the Falcon 9's 3.6 m arrow diameter, which can accommodate nine engines.In fact, the Merlin-1D LRE's nozzle is still partially exposed.However, the arrow diameter of China's main carrier rocket is 3.35 m; thus, it is impossible to arrange many engines, which requires a greater thrust ratio of the central LRE.In addition, to reduce the development difficulty and costs, the main parts of the first and second engines should be as consistent as possible.The engines with different requirements can only be realized by changing the nozzle area ratio.In fact, the Merlin-1D vacuum version of the LRE has a throttling capacity of 30%.In addition, as the moon, mars, and other planets have lower gravitational accelerations than Earth, the minimum thrust of the LRE during the descent phase is required to be reduced to less than 20% of the rated value for the vehicle to land on these planets more stably.In addition, according to the current development trend, LREs are increasingly being used for various multipurpose flight vehicles in near space, and the thrust demand varies during the flight process, which also places a wide range of variable-thrust demands on the LRE.In this study, as it was scientific, we considered thrust changes in the range of 100-20% (i.e., a thrust ratio of 5:1) in order to provide a useful reference for scholars and scientists.
The specific impulse is defined as the ratio of the LRE thrust to the mass flow rate of the propellant (i.e., the thrust generated per unit mass flow rate of the propellant).The specific impulse is an economic index of the LRE, and it represents the efficiency of the LRE's utilization of the energy contained in the propellant.A higher specific impulse indicates a better LRE economy and more thrust per unit of propellant, which means that less propellant is consumed for the same payload weight.With the same propellant tank volume and amount of propellant refueling, the vehicle can launch more, larger, and heavier loads, with a higher delivery efficiency and lower launch costs.Corresponding to the sea-level thrust and vacuum thrust, the specific impulse can be divided into the sealevel-specific impulse and vacuum-specific impulse.The sea-level-specific impulse is lower than the vacuum-specific impulse.The specific impulse depends on the characteristics of the propellant, the LRE combustion chamber pressure, and the nozzle area ratio.The goal of the LRE design is to obtain as high of a specific impulse as possible, which is also the focus of this paper.The area ratio of a Merlin-1D first-stage LRE is 16, the chamber pressure is 9.7 MPa, and the vacuum specific impulse is 310 s.The area ratio of the Merlin-1D vacuum version is 165, and the vacuum specific impulse reaches 348 s.The Merlin-1D is not only an example of a high-performance LRE, but it is also the ultimate in terms of design.

System Scheme of Variable-Thrust LRE
Variable-thrust LREs use a LOX/kerosene green nontoxic propellant, combine the gas-generator-cycle mode with the pump-pressure supply system scheme, and cool the thrust chamber body and nozzle by using the active fuel-cooling method.The LRE is mainly composed of a thrust chamber, turbo pump, IFRGG, throttle plate, and control valve.A special precooling device is required to establish the LOXpipeline, and a discharge device is required to establish the kerosene passage.We present the system scheme of the variable-thrust LRE in Figure 2.
Before the LRE begins to work, preparation work is first carried out, including liquidchamber-nitrogen replacement blowing, precooling discharge, prepressurization, prefilling, etc.After the pump pressurization, the oxidant and fuel are divided in two ways: (1) the oxidant enters the head of the thrust chamber after passing through the orifice plate of the oxidant main passage and oxidant main valve, and (2) the oxidant enters the IFRGG through the orifice plate of the oxidant secondary passage and oxidant secondary valve.In the first case, the fuel enters the nozzle section of the thrust chamber after passing through the orifice plate of the fuel main passage and fuel main valve, and it enters the head of the thrust chamber after passing through the cooling nozzle and body.In the second case, the fuel enters the IFRGG through the fuel auxiliary orifices and fuel auxiliary valves.The oxidizer and fuel that enter the head of the thrust chamber are atomized and burned to generate high-temperature gas, which is ejected at a high speed through the nozzle to generate thrust.The oxidizer and fuel that enter the IFRGG are synchronously regulated by the flow, and they are atomized and burned to generate gas that meets the requirements of the turbine.After the gas is powered by the turbine, the LRE also generates a certain thrust.The turbine output power drives the oxidizer pump and fuel pump to pressurize.After starting, the LRE works according to the control sequence.When the rocket needs the LRE to provide a variable thrust, the variable-condition-control command is sent to the power system, which synchronously realizes the regulation of the oxidant and fuel flow of the auxiliary system through the IFRGG to realize the wide range of variable-thrust works of the LRE.
ble-condition-control command is sent to the power system, which synchronously re izes the regulation of the oxidant and fuel flow of the auxiliary system through t IFRGG to realize the wide range of variable-thrust works of the LRE.In Figure 3, we present a detailed structure of an IFRGG that not only realizes t synchronous regulation of the oxidant and fuel but also realizes the combustion of t propellants.The oxidant and fuel flow into the regulator body from the center and o side of the regulator, respectively, and the propellant that enters from the outside ent the chamber of the regulator along the axial direction of the circumferential seam outsi the head of the pintle injector.Another propellant that enters from the center is radia sprayed into the chamber from the channel of the head of the pintle injector.The relati position is changed by moving the sleeve or head of the pintle injector to change t minimum flow area of the two propellants, which realizes the flow regulation and th changes the thrust.In Figure 3, we present a detailed structure of an IFRGG that not only realizes the synchronous regulation of the oxidant and fuel but also realizes the combustion of the propellants.The oxidant and fuel flow into the regulator body from the center and outside of the regulator, respectively, and the propellant that enters from the outside enters the chamber of the regulator along the axial direction of the circumferential seam outside the head of the pintle injector.Another propellant that enters from the center is radially sprayed into the chamber from the channel of the head of the pintle injector.The relative position is changed by moving the sleeve or head of the pintle injector to change the minimum flow area of the two propellants, which realizes the flow regulation and then changes the thrust.

Performance Analysis Model
In this section, we analyze the performance calculation model of the variable-thrust LRE.The thrust of the LRE is related to the flight altitude.In the design stage, in order to determine a design basis, the thrust at sea level (i.e., the thrust at zero altitude) is usually selected as the design thrust of the LRE.The sea-level thrust is defined as Equation ( 1), where Ae is the nozzle outlet area, Pe is the exhaust pressure at the nozzle outlet, and Pa is the atmospheric pressure at sea level.It should be noted that Equation ( 1) is applicable to any flight altitude.The vacuum thrust is defined as the thrust when the vacuum pressure is zero.For the same engine, the difference between the vacuum thrust and sea level thrust is Ae*Pa and is shown in Equation ( 2): V m e e e g e a F q V A P F A We present the characteristic LRE velocity in Equation ( 3): Equation ( 4) expresses the expansion ratio of the nozzle area, and Equations ( 5) and ( 6) express the ground thrust and vacuum thrust, respectively: Then, we can obtain the ground-specific impulse of the LRE at the sea-level design point from Equation (7): Based on this, we can calculate the flow rate of the design point and obtain the design parameters of the LRE throat area, as shown in Equations ( 8) and ( 9), respectively:

Performance Analysis of Variable-Thrust LRE 4.1. Performance Analysis Model
In this section, we analyze the performance calculation model of the variable-thrust LRE.The thrust of the LRE is related to the flight altitude.In the design stage, in order to determine a design basis, the thrust at sea level (i.e., the thrust at zero altitude) is usually selected as the design thrust of the LRE.The sea-level thrust is defined as Equation (1), where A e is the nozzle outlet area, P e is the exhaust pressure at the nozzle outlet, and P a is the atmospheric pressure at sea level.It should be noted that Equation ( 1) is applicable to any flight altitude.The vacuum thrust is defined as the thrust when the vacuum pressure is zero.For the same engine, the difference between the vacuum thrust and sea level thrust is A e *P a and is shown in Equation (2): We present the characteristic LRE velocity in Equation (3): Equation ( 4) expresses the expansion ratio of the nozzle area, and Equations ( 5) and ( 6) express the ground thrust and vacuum thrust, respectively: F g = q m I g (5) Then, we can obtain the ground-specific impulse of the LRE at the sea-level design point from Equation ( 7): Based on this, we can calculate the flow rate of the design point and obtain the design parameters of the LRE throat area, as shown in Equations ( 8) and ( 9), respectively: After evaluating the performance of the design point and determining the main design parameters, we can conduct the performance calculation under the variable-thrust nondesign condition.Equations ( 10)-( 12) represent the total LRE flow rate, LRE chamber pressure, and ground specific impulse under variable-thrust conditions, respectively: Equations ( 13)-( 15) represent the power balance of the turbopump when the performance is being evaluated: N t = L t q mt η t (14) where Lt is the diabatic work of the turbine and is defined as Equation ( 16), and Equation (15) gives the definition of turbine adiabatic specific work.Under a determined turbine pressure ratio and the gas adiabatic exponent, the turbine adiabatic specific work is mainly affected by the gas constant R gg and the total temperature T gg , and the turbine adiabatic specific work is almost linearly proportional to R gg *T gg : Equations ( 17) and ( 18) represent the combustion efficiencies of the IFRGG and thruster, respectively: Equations ( 19)-( 21) represent the efficiencies of the nozzle, pump, and turbine, respectively: The flow-resistance coefficients of the oxidant and fuel flow of the regulator are determined through the process of pressure matching, in which we obtained the chamber pressure (P gg ) of the IFRGG by the power balance of the turbo-pump:

Study on Selection of Main Design Parameters
The O/F mixing ratio is an important design parameter of the thrust chamber, and it directly determines the chamber's temperature, thrust, and thermal protection design.The thrust chamber O/F mixing ratio of the typical gas generator cycle LOX/kerosene engines in the Soviet Union/Russia and the United States is mostly concentrated around 2.2~2.5 [43][44][45], which indicates that the combustion structure, thermal protection, and thrust chamber performance are better under this O/F mixing ratio.Based on this, we selected a chamber O/F mixing ratio of 2.5 to conduct the relevant theoretical analysis in this paper.
The thrust chamber pressure and nozzle area ratio are also important design parameters.Theoretically, the higher the design value of the combustion chamber pressure, the larger the maximum value of the nozzle area ratio that can be reached, and certainly the higher the specific impulse performance of the LRE that can be achieved.However, the high chamber pressure poses a greater challenge to the material properties, development, and verification.Thus, the nozzle area ratio cannot be indefinitely increased.When the area ratio is small, the vacuum specific impulse and specific impulse on the ground increase with the increase in the area ratio; however, the specific impulse will decrease rapidly with the further increase in the area ratio due to flow separation.We demonstrate the influence of the pressure and nozzle area ratio on the thrust of the LRE in Figure 4.The higher the chamber pressure, the higher the vacuum specific impulse, and this is because the increase in the chamber pressure increases the combustion efficiency, total combustion temperature, and characteristic velocity.However, in general, the chamber pressure had little effect on the combustion efficiency, total combustion temperature, and characteristic velocity, and thus it had little effect on the vacuum-specific impulse.All these data were calculated with CEA open-source software.The specific impulse on the ground initially increased and then decreased with the increase in the nozzle expansion ratio, which was because the specific impulse on the ground was substantially affected by the exhaust and atmospheric pressures.As shown in Figure 4d, with the increase in the nozzle area ratio, the exhaust pressure rapidly decreased; however, when the nozzle area ratio was relatively small, the exhaust pressure was still high, and it was greater than the atmospheric pressure at sea level, which means that the nozzle was in a state of underexpansion.With the increase in the area ratio, the exhaust gas further expanded, and the speed could be further improved; thus, the specific impulse further increased.However, with the continuous increase in the area ratio, the exhaust pressure continuously decreased until it was lower than the ambient atmospheric pressure, the nozzle was in an overexpansion state, and the shock wave was pushed into the nozzle.At this time, the quality of the exhaust flow field was affected, and the specific impulse of the LRE was reduced.Due to the limitations of technology, materials, and processing, the chambe sure of the early engines was generally low.With the development of technolo chamber pressure gradually increased.The chamber pressure of the F-1A LRE r 8.98 MPa, and that of a Merlin-1D LRE reached 9.7 MPa.Considering that the m performance of China is lower than that of the United States, we chose a thrust ch pressure of 9.0 MPa for the theoretical analysis in this paper.
The selection of the nozzle area ratio was not only constrained by the perfor but also by the rocket's outer diameter, number of engines, processing difficul processing cost.
In general, the larger the nozzle area ratio, the lower the outlet pressure in t uum environment, and the higher the vacuum-specific impulse.However, the LRE paper was mainly used for the reusable first-stage rocket, and the performance atmosphere should also be considered.Therefore, the nozzle area ratio should no large, because if it is too large, the exhaust pressure of the nozzle will be less th ambient atmospheric pressure, and a shock wave will be formed inside the nozzle will result in a loss in the engine thrust and specific impulse performance.Seco reusable first-stage rockets, it is often necessary to install many engines, such as 7 If the area is too large, it will be impossible to install these many engines.Third, the selection of special 3D printing technology, the current 3D printing equipm under development and cannot produce larger size nozzles.
The research in this paper is theoretical, and so we did not consider the con of the structural layout and processing difficulty in engineering practice, and w ducted the research according to the constraints that allow the thrust chamber exh Due to the limitations of technology, materials, and processing, the chamber pressure of the early engines was generally low.With the development of technology, the chamber pressure gradually increased.The chamber pressure of the F-1A LRE reached 8.98 MPa, and that of a Merlin-1D LRE reached 9.7 MPa.Considering that the material performance of China is lower than that of the United States, we chose a thrust chamber pressure of 9.0 MPa for the theoretical analysis in this paper.
The selection of the nozzle area ratio was not only constrained by the performance, but also by the rocket's outer diameter, number of engines, processing difficulty, and processing cost.
In general, the larger the nozzle area ratio, the lower the outlet pressure in the vacuum environment, and the higher the vacuum-specific impulse.However, the LRE in this paper was mainly used for the reusable first-stage rocket, and the performance in the atmosphere should also be considered.Therefore, the nozzle area ratio should not be too large, because if it is too large, the exhaust pressure of the nozzle will be less than the ambient atmospheric pressure, and a shock wave will be formed inside the nozzle, which will result in a loss in the engine thrust and specific impulse performance.Second, for reusable first-stage rockets, it is often necessary to install many engines, such as 7 and 9.If the area is too large, it will be impossible to install these many engines.Third, due to the selection of special 3D printing technology, the current 3D printing equipment is under development and cannot produce larger size nozzles.
The research in this paper is theoretical, and so we did not consider the constraints of the structural layout and processing difficulty in engineering practice, and we conducted the research according to the constraints that allow the thrust chamber exhaust to be smoothly discharged under sea-level design conditions to achieve the optimal performance.Based on the above analysis, a suboptimal nozzle area ratio of 15.0 was selected, which is a compromise value considering both the acceptable specific impulse performance and the lower cost of manufacturing under current conditions.

Selection of Design Parameters of IFRGG
On the one hand, the function of the IFRGG is to synchronously regulate the oxidant and fuel flow of the auxiliary system.On the other hand, its other function is to generate high-temperature gas to drive the turbine to perform work.The parameter R gg *T gg represents the ability of 1 kg of hot gas to fully drive the turbine to perform work.The higher the O/F mixing ratio of the IFRGG, the higher the combustion temperature, the more sufficient the combustion, the smaller the molecular weight (which increases the R gg *T gg value, where R gg is the gas constant and T is the gas temperature), and the stronger the work ability of the gas.We present the influence results of different IFRGG chamber pressures and O/F mixing ratios on the R gg *T gg value in Figure 5.
performance and the lower cost of manufacturing under current con

Selection of Design Parameters of IFRGG
On the one hand, the function of the IFRGG is to synchronously and fuel flow of the auxiliary system.On the other hand, its other fu high-temperature gas to drive the turbine to perform work.The pa resents the ability of 1 kg of hot gas to fully drive the turbine to perfo the O/F mixing ratio of the IFRGG, the higher the combustion tem sufficient the combustion, the smaller the molecular weight (which value, where Rgg is the gas constant and T is the gas temperature), work ability of the gas.We present the influence results of differ pressures and O/F mixing ratios on the Rgg*Tgg value in Figure 5.The pressure on the chamber had little effect on the Rgg*Tgg va crease in the O/F mixing ratio substantially improved the Rgg*Tgg v cause in the rich combustion state, with the increase in the O/F m combustion temperature of the IFRGG increased and the combu proved.With more combustion, the concentration of the combusti smaller molecules) was larger, the concentration of the combustio smaller, and thus the average molecular weight of the product was l action of the high total combustion temperature and low average m creased the Rgg*Tgg value and strengthened the work ability of the details in Figure 6).The pressure on the chamber of the IFRGG had average molecular weight.The increase in the chamber pressure en rate in the positive chemical reaction; as a result, the concentration the concentration of CH4 and the average molecular weight increase eral, the effect of the pressure on the concentration and average mo products was small.The pressure on the chamber had little effect on the R gg *T gg value; however, the increase in the O/F mixing ratio substantially improved the R gg *T gg value, which was because in the rich combustion state, with the increase in the O/F mixing ratio, the total combustion temperature of the IFRGG increased and the combustion efficiency improved.With more combustion, the concentration of the combustion product H 2 (with smaller molecules) was larger, the concentration of the combustion product CH 4 was smaller, and thus the average molecular weight of the product was lower.The combined action of the high total combustion temperature and low average molecular weight increased the R gg *T gg value and strengthened the work ability of the gas (we present the details in Figure 6).The pressure on the chamber of the IFRGG had a slight effect on the average molecular weight.The increase in the chamber pressure enhanced the reaction rate in the positive chemical reaction; as a result, the concentration of H 2 decreased, and the concentration of CH 4 and the average molecular weight increased.However, in general, the effect of the pressure on the concentration and average molecular weight of the products was small.matching.However, an IFRGG chamber pressure that is too high will create dif regarding the structural strength of the design.Considering that the flow and te ture of the IFRGG are substantially lower than those of the thrust chamber, w perform the matching calculation assuming that the chamber pressure of the IFR slightly higher than that of the thrust chamber.In this paper, we selected an chamber pressure of 11 MPa for the research and analysis.

Performance Design Results and Analysis
According to the system scheme of the variable-thrust LRE with the gas-ge cycle determined in Section 3, as well as the performance evaluation method an tion of the main parameters analyzed and determined in Sections 4.1 and 4.2, tively, we performed a study on the system parameter matching and overall perfo evaluation of the variable-thrust LRE.We present the results in Table 1 and Figur  The O/F mixing ratio of the IFRGG should not be too high.An O/F mixing ratio that is too high will make the gas temperature too high.Under the effect of an uneven gas temperature, it may cause the risk of structural damage, such as the local ablation of the turbine inlet pipe, turbine disc, or blade.In addition, due to the rich combustion organization of the LOX/kerosene in the IFRGG, the problem of carbon deposition is more prominent, which also limits the selection of the O/F mixing ratio.This problem is due to the insufficient combustion during rich combustion with a low O/F mixing ratio of LOX/kerosene and with a large number of solid carbon particles in the hot gas, which may block small channels such as the turbine inlet nozzle and reduce the power performance of the turbine.However, a small amount of carbon coating on the wall can protect the wall and channel structure under high-heat loads.According to the results, there is a strong correlation between the carbon particle deposition rate and O/F mixing ratio, but only a weak correlation with the combustion pressure.The O/F mixing ratio threshold of LOX/kerosene is about 0.42.Below this value, the amount of soot is small.When the O/F mixing ratio is about 0.6, the carbon particle fraction in the gas reaches the maximum.After comprehensive consideration, we chose an IFRGG O/F mixing ratio of 0.35.
Because the IFRGG and flow regulator adopt the integrated design idea, the decreases in the chamber pressure and regulator/injector pressure need to be repeatedly matched; thus, the chamber pressure of the IFRGG is the result of system parameter matching.However, an IFRGG chamber pressure that is too high will create difficulties regarding the structural strength of the design.Considering that the flow and temperature of the IFRGG are substantially lower than those of the thrust chamber, we could perform the matching calculation assuming that the chamber pressure of the IFRGG was slightly higher than that of the thrust chamber.In this paper, we selected an IFRGG chamber pressure of 11 MPa for the research and analysis.

Performance Design Results and Analysis
According to the system scheme of the variable-thrust LRE with the gas-generator cycle determined in Section 3, as well as the performance evaluation method and selection of the main parameters analyzed and determined in Sections 4.1 and 4.2, respectively, we performed a study on the system parameter matching and overall performance evaluation of the variable-thrust LRE.We present the results in Table 1 and Figure 7. impulse is that with the decline in the working conditions, the injection pressure of the thrust chamber and IFRGG substantially decreases, as does the propellant atomization mixing efficiency.Moreover, the chamber pressure combustion efficiency and propulsion efficiency substantially decrease, which results in the decrease in the specific impulse under low working conditions.Also, the insufficient atomization and combustion of the propellant are also important reasons.However, the 20% very low working condition is not only used in vacuum environments but also in near space, the atmosphere, and the low-altitude reusing and landing stages.As the flight altitude decreases to zero, the specific impulse on the ground decreases to 1848.8 m/s (188.5 s), which is 31.18%lower than the ground specific impulse of 2686.4 m/s (274.0 s) at the design point, which indicates that a 20% extremely deep throttling working condition is not suitable for long-term operations, but only for some special flight missions under short-term requirements.With a different flight altitude, the specific impulse under the 20% working condition is between the vacuum-specific impulse of 2835.7 m/s (289.2 s) and sea-level-specific impulse of 1848.8 m/s (188.5 s), and it is closely related to the specific flight altitude.As shown in Figure 7b, when the LRE was operating under variable working conditions, the proportion of the auxiliary system flow in the total LRE flow decreased from 3.239% under the 100% working condition to 1.636% under the 20% working condition, which was because with the decrease in the LRE working conditions, the chamber pressure and flow of the thrust chamber show an approximate linear decline; however, the flow resistances of the pipelines, valves, and various throttling elements decrease with The data in Table 1 and the curve in Figure 7 show a jump of 60% in the operating conditions.This is because when the variable-thrust works in such a wide range of 100-20%, the traditional centrifugal injector with a fixed area cannot be used in the thrust chamber to reduce the pressurization burden of the auxiliary system, and the variable-structure injectors, such as the pintle injector or dual-channel injector, need to be used.This causes the injection pressure drop in the thrust chamber to show a sudden jump when crossing or switching the working conditions so that all the parameters of the system show the corresponding sudden jump phenomenon.
The thruster chamber is the core component of the LRE that directly generates the main thrust.The engine design must be based on the thruster state.The chamber pressure, combustion temperature, mass flow rate, and thereby thrust are not allowed to jump in the LRE design.However, in order to achieve a thrust change of 5:1 or an even wider range, the injector pressure drop will have a change of 25:1, which is unbearable for the propellant supply system.Therefore, the dual-channel variable-structure injector is adopted in this paper, and the variable-structure adjustment is carried out at 60% working conditions.The chamber pressure, total temperature, flow rate, and thrust of the thruster are almost unchanged, but the pressure drop of the injection will have a big jump, which will result in a jump in the pipeline pressure, pump pressure, and generator pressure.
According to Table 1, the thrust of the variable-thrust LRE at the design point at sea level was 784.5 kN (80 t), the specific impulse on the ground was 2686.4 m/s (274.0 s), the vacuum thrust was 868.3 kN, the vacuum specific impulse was 2973.2 m/s (303.2 s), the total O/F mixing ratio of the LRE was 2.334, and the proportion of the secondary system flow to the total LRE flow was 3.239%.According to the results, the specific impulse of the variable-thrust LRE at the design point was high, and the cost proportion of the mass flow rate of the secondary system to the LRE main system was low, which means the secondary system was designed well and was a low-energy-consumption system.As the working condition of the variable-thrust LRE decreased from 100% to 20%, the vacuum specific impulse increased from 2973.7 m/s (303.2 s), following an approximate linear trend, to 2835.7 m/s (289.2 s).A decrease in the vacuum-specific impulse at a 20% throttling condition compared with the design point was just about 4.62%, which is small, which indicated that the variable-thrust LRE still had a better vacuum performance under 20% extremely deep throttling conditions.The reason for the decrease in the specific impulse is that with the decline in the working conditions, the injection pressure of the thrust chamber and IFRGG substantially decreases, as does the propellant atomization mixing efficiency.Moreover, the chamber pressure combustion efficiency and propulsion efficiency substantially decrease, which results in the decrease in the specific impulse under low working conditions.Also, the insufficient atomization and combustion of the propellant are also important reasons.However, the 20% very low working condition is not only used in vacuum environments but also in near space, the atmosphere, and the low-altitude reusing and landing stages.As the flight altitude decreases to zero, the specific impulse on the ground decreases to 1848.8 m/s (188.5 s), which is 31.18%lower than the ground specific impulse of 2686.4 m/s (274.0 s) at the design point, which indicates that a 20% extremely deep throttling working condition is not suitable for long-term operations, but only for some special flight missions under short-term requirements.With a different flight altitude, the specific impulse under the 20% working condition is between the vacuum-specific impulse of 2835.7 m/s (289.2 s) and sea-level-specific impulse of 1848.8 m/s (188.5 s), and it is closely related to the specific flight altitude.
As shown in Figure 7b, when the LRE was operating under variable working conditions, the proportion of the auxiliary system flow in the total LRE flow decreased from 3.239% under the 100% working condition to 1.636% under the 20% working condition, which was because with the decrease in the LRE working conditions, the chamber pressure and flow of the thrust chamber show an approximate linear decline; however, the flow resistances of the pipelines, valves, and various throttling elements decrease with the square of the flow, and thus the decline is faster and the proportion of the total flow also decreases faster.
We used the total O/F mixing ratio of the LRE to evaluate the total propellant consumption and relative size of the tank volume.As shown in Figure 7b, the O/F mixing ratio of the thrust chamber at the design point was 2.5, but the total O/F mixing ratio of the LRE at the design point was 2.334, which was because the subsystem consumed 3.239% of the propellant; however, the subsystem IFRGG used rich combustion, and its O/F mixing ratio was 0.35.Therefore, the total O/F mixing ratio of the LRE was 2.334.As the working condition of the variable-thrust LRE decreased to 20%, the proportion of the subsystem flow to the total LRE flow gradually decreased to 1.636%; thus, the total LRE O/F mixing ratio showed a gradual increasing trend and finally increased to 2.414.
We further demonstrated the variation law of the key parameters of some of the key components of the variable-thrust LRE under variable working conditions in Figure 8, in which the head and power of the oxidizer pump and fuel pump under variable-thrust operation can be seen.In addition to the sudden jump phenomenon under switching conditions, with the decrease in the variable-thrust LRE working conditions, the pump head showed an approximate linear downward trend.The pump power showed an approximate downward quadratic curve trend.With the decrease in the thrust, the IFRGG chamber pressure/turbine inlet pressure substantially decreased.In addition, the concentration of H 2 in the gas mixture increased; thus, the molecular weight showed a downward trend.Although the Rgg value showed an upward trend, with the decrease in the thrust and IFRGG chamber pressures, the combustion efficiency and gas temperature of the IFRGG substantially decreased, which caused the RT value to eventually show a downward trend, and the power capacity of the turbine decreased.The IFRGG/turbine flow rate and turbine power also showed an approximate quadratic curve downward trend.The IFRGG is both a combustion component and an integrated synchronous flow-regulating element.The flow resistance coefficient of the IFRGG is defined as the ratio of the flow resistance to the square of the flow, and this parameter reflects the throttling flow characteristics of the regulator/injector and is an important design parameter.As shown in Figure 8d, as the working condition of the variable-thrust LRE decreased from 100% to 20%, the flow resistance coefficients of the oxidant and fuel showed a rapidly increasing trend of the power exponent, which indicated that the integrated regulator had throttled to a great extent.The flow resistance coefficients of the oxidant circuit and fuel circuit were substantially different, which was caused by the substantial difference in the flow rates of these two propellants with an O/F mixing ratio of 0.35.The coefficient also provided a reference basis to determine the flow area and the design of the complex geometric surface of the integrated regulator.
Presently, no 80-ton LRE with a 5:1 throttling ratio that can actually work in the world exists.Using the specific structure of the IFRGG in this paper, this is the first time that the lower thrust limit is reduced to 20% of the rated value, which is indeed a great innovation.
throttling flow characteristics of the regulator/injector and is an important design parameter.As shown in Figure 8d, as the working condition of the variable-thrust LRE decreased from 100% to 20%, the flow resistance coefficients of the oxidant and fuel showed a rapidly increasing trend of the power exponent, which indicated that the integrated regulator had throttled to a great extent.The flow resistance coefficients of the oxidant circuit and fuel circuit were substantially different, which was caused by the substantial difference in the flow rates of these two propellants with an O/F mixing ratio of 0.35.The coefficient also provided a reference basis to determine the flow area and the design of the complex geometric surface of the integrated regulator.

Conclusions
In this study, we analyzed the functional traction and main technical requirements of a variable-thrust LRE for vertical takeoff and the landing of recoverable launch vehicles and various near-space multipurpose vehicles.We propose a gas-generator-cycle wide-range variable-thrust LRE system scheme based on a design idea of an IFRGG.On this basis, we established the performance design model of the variable-thrust LRE, and we also analyzed the influence of the main design parameters on the performance optimization.We optimally selected the design parameters under certain constraints.Compared with the published performance data on variable-thrust LREs, the design and calculation results in this manuscript had good consistency.According to the determined variable-thrust LRE scheme and its main design parameters, we evaluated the performance and determined the main structural parameters at the sea-level design point.At the same time, we also evaluated the LRE performance and conducted parameter matching among the five components under a wide thrust range of 100-20%, and we completed the LRE working characteristic analysis under a wide range of variable-thrust conditions.We summarize the main points of our study as follows: (1) For the 80-ton variable-thrust LRE with a variable-thrust range of 100-20%, combined with the requirements of the technical indexes and the actual situation of the structure, materials, processing, and basic theoretical research, it was appropriate to select 2.5 for the O/F mixing ratio of the thrust chamber, 9.0 MPa for the chamber pressure, and 15.0 for the nozzle area ratio; (2) Combined with the constraints of the work capacity and structural reliability, the O/F mixing ratio of the propellants in the IFRGG generally did not exceed 0.4, and it was more appropriate to select 0.3-0.35.According to the matching requirements of the system parameters, the pressure on the chamber of the IFRGG should be equal to or slightly higher than that on the thrust chamber; (3) When the variable-thrust LRE works in a wide-range of 100-20%, the vacuumspecific impulse decreases from 303.2 s to 289.2 s and followed an approximate linear trend with a decrease range of about 4.62%, which indicated that the variable-thrust LRE still had a better vacuum performance under very low working conditions;
P c = 8 MPa P c = 9 MPa P c = 10 MPa P c = 11 MPa P a = 101.325kPa

Figure 4 .
Figure 4. Influence of chamber pressure and nozzle area ratio on specific impulse performa Vacuum-specific impulse.(b) Sea-level-specific impulse.(c) Combustion total temperature characteristic velocity.(d) Exhaust pressure.

Figure 4 .
Figure 4. Influence of chamber pressure and nozzle area ratio on specific impulse performance.(a) Vacuum-specific impulse.(b) Sea-level-specific impulse.(c) Combustion total temperature and characteristic velocity.(d) Exhaust pressure.

Figure 5 .
Figure 5. Influence of chamber pressure and O/F mixing ratio on gas perform

Figure 5 .
Figure 5. Influence of chamber pressure and O/F mixing ratio on gas performance.

Figure 6 .
Figure 6.Influence of chamber pressure and O/F mixing ratio on gas property parameters.Combustion temperature and gas.(b) Gas molecular weight.

Figure 6 .
Figure 6.Influence of chamber pressure and O/F mixing ratio on gas property parameters.(a) Combustion temperature and gas.(b) Gas molecular weight.

Figure 7 .
Figure 7. Performance characteristics of variable-thrust LRE.(a) LRE thrust and specific impulse.(b) Secondary system flow percentage and total O/F mixing ratio.

Figure 7 .
Figure 7. Performance characteristics of variable-thrust LRE.(a) LRE thrust and specific impulse.(b) Secondary system flow percentage and total O/F mixing ratio.

Figure 8 .
Figure 8. Working characteristics of components of variable-thrust LRE.(a) Pump-pressure head and power.(b) Gas property parameters and performance.(c) IFRGG/turbine mass flow rate.(d) Flow resistance coefficient of IFRGG.

Table 1 .
Parameter matching and performance design results of variable-thrust LRE.

Table 1 .
Parameter matching and performance design results of variable-thrust LRE.