Cycle optimization of the staged combustion rocket engines

Abstract

Purpose

The purpose of this paper is to introduce new and modified “staged combustion” cycles in the form of engineering algorithm as a possible propulsion contender for future aerospace vehicle to achieve the highest possible “total impulse” to “mass” of propulsion system.

Design/methodology/approach

In this regard, the mathematical cycle model is formed to calculate the engine’s parameters. In addition, flow conditions (pressure, temperature, flow rate, etc). in the chamber, nozzle and turbopump are assessed based on the results of turbo machinery power balance and initial data such as thrust, propellant mixture ratio and specifications. The developed code has been written in the modern, object-oriented C++ programming language.

Findings

The results of the developed code are compared with the Russian RD180 engine which demonstrates the superiority and capability of new “thermodynamic diagrams”.

Research limitations/implications

This algorithm is under constraint to control the critical variation of combustion pressure, turbine rpm, pump cavitation and turbine temperature. It is imperative to emphasize that this paper is limited to “oxidizer-rich staged combustion” engines with “single pre-burner”.

Originality/value

This study sheds light on using fuel booster turbopump and the second-stage fuel pump to moderate the effect of cavitation on pumps which reduces tank pressure and, as a consequence, decreases the propulsion system weight.

Nomenclature

Symbols

Ī_sp

= average specific impulse, s

I_T

= total impulse, s

M̅

= rocket mass ratio

M_o

= start launch vehicle mass, kg

M_F

= final launch vehicle mass, kg

M_P

= propellant mass (burning mass), kg

M_E

= engine mas, kg

M_TP

= turbopump mass, kg

t

= engine burning time, s

P_cc

= combustion chamber pressure, Pa

P_out.ox.p

= oxidizer pump discharge pressure, Pa

ΔP_fu.ch.cc

= pressure drop in chamber fuel line, Pa

ΔP_ox.ch.gg

= pressure drop in oxidizer line, Pa

ΔP_t

= pressure difference of turbine, Pa

P_out.fu.p.I

= 1st fuel pump discharge pressure, Pa

P_out.fu.p.II

= 2nd fuel pump discharge pressure, Pa

P_gg

= preburner pressure, Pa

P_in

= pump inlet pressure, Pa

P_s

= propellant vapor pressure, Pa

H_P

= developed head of pumps, m

ω

= turbopump rotational speed, rpm

Q

= pump volumetric flow rate, m³/s

Δh_sb

= critical net positive suction head, m

C_cav.max

= pump suction specific speed coefficient

η_pn

= pump efficiency

n_s

= pump specific speed, m/s

N¯_T

= specific power of turbine, J/kg

N¯_o

= specific power of oxidizer pump, J/kg

N¯_f

= specific power of fuel pump, J/kg

π_T

= turbine pressure ratio

η_T

= turbine efficiency

k

= ratio of specific heat

RT

= working capability of gasses, J/kg

Definitions, acronyms and abbreviations

Fu

= fuel

LRPS

= liquid rocket propulsion system

Ox

= oxidizer

SBORSC

= single-burner, oxidizer-rich staged combustion

Introduction

The engine with “staged combustion cycle” has the supreme energetics performance of all launch vehicle engine, especially when considered as a first stage for “liquid rocket propulsion systems (LRPS)” that deliver payload into low earth orbit. As the higher cost of launching satellites to space usually leads engineer to select “staged combustion” cycle and also optimizing engine’s parameters to increase the ratio of “total impulse” to “gross mass” of propulsion system.

One of the well-known Russian engines in this category is RD-180, equipped with oxidizer (ox)-rich pre-burner, which releases more energy than fuel (fu)-rich pre-burner at the same temperature. Therefore, high energetic production of Lox-rich pre-burner allows a lower turbine pressure ratio and ultimately higher chamber pressure.

This research introduces new thermodynamics diagrams of single-burner, “oxidizer-rich staged combustion”. Applying the new generation of diagrams to RD-180 engine leads us to new concept of RD-180 propulsion system by higher level of mass and energetic properties and lower level of combustion chamber pressure. For proposing the various diagrams on the basis of the considered cycle, the various ideas which published in the papers, reports and patents have been studied (Arkhangelski et al., 2007; Balotin, 2010; Boukhmatov et al., 2010; Klepikov et al., 1997; Lebedenski et al., 2002).

The initial input data of this algorithm has been determining by designers such as mixture ratio and thrust level. This algorithm picks the engine optimum operating regime according to desirable working condition of turbopump.

Until recently, two software tools have been developed which are called “SCORES II” and “REDTOP2”. SCORES II determines the nominal engine performance with the use of “mixture ratio, chamber pressure, throat area, and expansion ratio” (Shyy et al., 1999; Way et al., 1999; Bradford, 2002) and “REDTOP2” provides for an initial design of an LRPS (Bradford et al., 2002). Unlike REDTOP2, the present work’s calculations are based on several operating points; for each operating point and by considering the combustion chamber pressure and information from characteristic pump curves, the working regime of the feed system and other engine parameters such as gas-generator mass flow rate and pressure are then calculated.

In Kwon-Su et al.’s (2004) research, a method for optimization of a gas generators is introduced which is based on maximizing the turbine power only. In Berkhardt et al.’s (2002) research, the performance of a closed-cycle propulsion system of one of the stages of a launch vehicle is analyzed for two different propellants.

Other methods have been introduced to optimize the main elements of LRPSs (Shyy et al., 1999; Papila et al., 2000; Rai and Madavan, 2000; Matlock et al., 2001); however, system optimization is not considered. The “FORDY” software is developed by Kazlov (1987, 1999) to achieve the highest possible “final velocity” to assess the parameters such as engine mixture ratio, pumps inlet pressures and engine mass. Unlike the Kazlov method, the developed algorithm is used to determine the engine parameters such as the turbopumps’ angular speed, pumps’ discharge pressures and pre-burner pressure.

Thermodynamic diagrams description

Figure 1 shows the schematic of the staged combustion cycle without the booster turbopump, such as Russian RD-253 engine.

Figure 2 shows the schematic of the staged combustion cycle with oxidizer and fuel booster turbopumps. One of the characteristics of this cycle is implementation of booster turbopumps to increase the inlet pump pressure that cause to decrease tanks weight (Sutton, 2001). Also, this methodology provides an increscent in turbopump rpm to reduce the mass of turbopump, especially for cryogenic propellant. In this cycle with oxidizer-rich pre-burner, only a portion of fuel flow with high pressure is directed to pre-burner. So use of the second fuel pump with low flow and high developed head reduced the required pumps power which leads to a higher level of combustion pressure.

Figure 3 shows the basic schematic of “RD-180” cycle. Ox booster turbine of RD-180 is feed by oxidizer-rich gas.

In this paper, the RD-180 and new thermodynamic cycles with oxidizer-rich pre-burner are studied.

The first suggested cycle is shown in Figure 4. “Boukhmatov’s idea” has been used in this diagram (Boukhmatov et al., 2005). According to this idea, the flow of “fuel booster turbine” is supplied by the total flow of the “first stage of fuel pump”; however, the “fuel flow” of the thrust chamber and pre-burner are supplied from the “second stage of fuel pump”.

The second suggested cycle is shown in Figure 5. In this cycle, the flow of “fuel booster turbine” is supplied by the total flow of the “first stage of fuel pump”; however, the fuel flow of the pre-burner is supplied from the “second stage of fuel pump”, and the fuel flow of the chamber is supplied from the “first stage of fuel pump”.

The third suggested cycle is shown in Figure 6. In this diagram, the flow of “fuel booster turbine” is supplied from the “first stage of fuel pump” and the outlet flow of fuel booster turbine is directed to the “second stage of fuel pump” and is finally directed to the pre-burner.

Figure 7 is the best known schematic of pre-burner cycles, which is “Dual-Burner” cycle. It is excellent decision for LH2-LOX; however, it is not suitable for kerosene-LOX propellant components.

Optimization criterion in rocket engine design

The most important characteristic of an aerospace vehicle is final flight velocity V_F.i (m/s), the ideal amount of which is obtained by Konstantin Eduardovich Tsiolkovsky (Koodriatsev, 1993): (1)$$V_{F.i}={\overline{I}}_{sp}.g_0.Ln\overline{M}$$

Where “${\overline{I}}_{sp}={\displaystyle \underset{0}{\overset{t}{\int }}{I}_{sp}d\tau /\tau }$ ” is the average specific impulse (s) at the active flight path, M¯=M₀/M_F is the ratio of initial mass of the launch vehicle M₀ (kg) to the final launch vehicle mass M_F (kg), t is the engine burning time (s) and g₀ is acceleration of gravity. The index i shows the considered stage of launch vehicle. For example, this research studied the first-stage final velocity (V_{F 1}).

Equation (1) shows the influence of Ī_sp and M̄ on final velocity. The higher value of M̄ leads to more oxidizer and fuel propellant storage in LRPS (M_P=M₀−M_F). Therefore, burning time is increased, and the launch vehicle attains a higher value of final velocity (V_F.i).

The propulsion system consists of tanks, engine and pressurization subsystems. Decreasing the mass of propulsion system for a determined burning time, increases M̄ and final velocity. On the other hand, increasing specific impulse of engine increases final velocity. The presented algorithm leads to optimize the main parameters of propulsion system. However, the concentration of the research is on the engine parameters, which plays a serious role for the determination of the main parameters of subsystems of propulsion system.

The portion of the engine mass is considerable in “mass balance”, so reducing the engine mass is an important aspect of decreasing the launch vehicle mass. In designing LRPS, the effect of increasing specific impulse and reducing engine mass on final velocity is very important. For studying the influence of Ī_sp and M̄ on ideal final velocity, assume the final velocity of launch vehicle is constant. Then, differentiating and simplifying equation (1) gives: (2)$$d\overline{M}/\overline{M}=-\left(d{\overline{I}}_{sp}/{\overline{I}}_{sp}\right)Ln\overline{M}$$

For further studying the effect of the engine mass on final velocity of the launch vehicle, we assume that the available amount of the propellant in the launch vehicle structure has not been changed (M_P=M₀−M_F=const.), then using the same simplicity which is used to distinct the effect of Ī_sp and M̄ on the final velocity, we get: (3)$$d{M}_F/M_F=\left(\overline{M}/(\overline{M}-1)\right)Ln\overline{M}\left(d{\overline{I}}_{sp}/{\overline{I}}_{sp}\right)$$

If we assumed the launch vehicle structural mass can be altered with the engine mass, equation (3) is expressed in the following form: (4)$$d{M}_E/M_E=\left(M_F/M_E\right)\left(\overline{M}/(\overline{M}-1)\right)Ln\overline{M}\left(d{\overline{I}}_{sp}/{\overline{I}}_{sp}\right)$$

The effect of increasing 1 per cent specific impulse is equivalent to reduce 10 to 15 per cent of the engine mass to attain the same final velocity according to equation (4) for a determined M̄ and (M_F/M_E). Furthermore, it can be concluded that the final velocity is augmented by rising the engine-specific impulse or by lowering the launch vehicle mass (mainly by the engine mass).

Consequently, to achieve the desired final velocity, the launch vehicle initial mass (M₀) should be reduced, which can be achieved by increasing Ī_sp and decreasing engine mass. Thus, the design optimization possibility could not only be assessed from the value of Ī_sp or mass of engine, but the influence of these series of parameters must be studied on the launch vehicle specification. To compare the launch vehicle with constant initial mass, the “total impulse (I_T)” is introduced which is defined as I_T=Ī_sp M_P. Whenever the engine-specific impulse and the propellant mass increase, the total impulse also increases (consider to M_P=M₀−M_F and initial constant mass, the M_P becomes larger as M_F decreases). Therefore, the I_T is the superior criterion of launch vehicle. To compare the different launch vehicle with the initial mass (M₀), the ratio of the total impulse to the initial mass (I_T/M₀) is selected as superior criterion, which means I_T/M₀ is obtained from dividing the left and right side of I_T=Ī_spM_P to M₀ and with considering: (5)$$M_P/M_0=1-M_F/M_0=1-1/\overline{M}$$

The total impulse is equal to: (6)$$I_T/M_0={\overline{I}}_{sp}\left(1-1/\overline{M}\right)$$

Comparing the equations (1) and (5) indicates that the V_F.i and I_T/M₀ parameters depend on Ī_sp and M̄. Therefore, the comparison of the launch vehicles can be made by using V_F.i and I_T/M₀ parameters. The equation (5) shows that if M̄→∞, the I_T/M₀ starts increasing toward Ī_sp, which means the theoretical limit of (I_T/M₀) is Ī_sp and the approach of I_T/M₀ toward Ī_sp is considered as the superior criterion of launch vehicle. The I_T/M_E is used to evaluate the propulsion systems.

The noticeable portion of (M₀) is the propellant mass, so reducing the M_P is important in lowering launch vehicle mass. Thus, the “relative total impulse (I_T/M_PS)” is used as criteria to evaluate the propulsion system which (M_PS) is the initial mass of the propulsion systems. The most important difference in initial mass of launch vehicle and propulsion system is the payload mass. Consider this parameter (I_T/M_PS) as “superior criterion ”, the propulsion system optimized parameters can be selected and calculated.

Static design optimization algorithm

The main assumptions which are used in the static mathematical modeling are given as follows:

• The chemical reaction products are homogeneous and obey the perfect gas law.

• All the species of the working fluid are gaseous. Any condensed phases (liquid or solid) add a negligible amount to the total mass.

• There is no heat transfer across the walls; therefore, the flow is adiabatic.

• There is no appreciable friction and all boundary layer effects are neglected.

• There are no shock waves or discontinuities in the nozzle flow.

• The propellant flow is steady and constant. The expansion of the working fluid is uniform and steady, without vibration. Transient effects (i.e. start up and shut down) are of very short duration and may be neglected.

• All exhaust gases leaving the launch vehicle have an axially directed velocity.

• The gas velocity, pressure, temperature and density are all uniform across any section normal to the nozzle axis.

• Chemical equilibrium is established within the combustion chamber and the gas composition does not change in the nozzle (frozen flow).

• All the equations are expressed in “SI” units.

The main steps of optimizing the introduced cycles are shown in the flowchart (Figure 8). First, by using the related input data, the basis algorithm of energy balance is validated by a staged combustion cycle engine such as RD-180. In the next step, according to the result of “sensitive analysis”, the next series of input data is used to generate the multi-dimensional space of the output data. The “sensitive analysis” shows the rate of change of input data to develop some points with the chance of taking the superior point from the static optimization.

Step 1: Calculation of the chamber and pre-burner flow rate: The chamber and pre-burner oxidizer flow are calculated on the basis of engine fuel and oxidizer mass flow (which is obtained by engine thrust and Ī_sp). The pre-burner fuel mass flow is determined in accordance with the pre-burner mixture ratio which is the function of allowable turbine temperature. The remaining fuel flow is used for the chamber and tank pressurization system.

Step 2: Calculation of the pressure drop in oxidizer and fuel lines: One of the most important ways to achieve the highest head of energy is to minimize pressure loss coefficients in the feedline. To calculate the experimental pressure loss coefficients, the data of the Russian rocket engine “RD-180” were compiled (Berkhardt et al., 2002).

The pressure loss coefficient (ξ) has been calculated for every channel by RD-180 data according to following formula: (7)$$\xi =\frac{DP.\rho }{{\dot{m}}^2}$$

where:

• ṁ

  = mass flow;

• DP

  = pressure loss; and

• ρ

  = density of oxidizer or fuel.

The calculated pressure loss coefficients are constant for static regime of engine. So this value is assumed constant for all cycles.

Step 3: The oxidizer pump and fuel pump (first and second stages) discharge pressure and the developed head are determined as follows: (8)$$P_{out.ox.p}={{\rm P}}_{gg}+\Delta {{\rm P}}_{ox.ch.gg}$$ (9)$$P_{out.fu.p.I}={{\rm P}}_{cc}+\Delta {{\rm P}}_{fu.ch.cc}$$ (10)$$P_{out.fu.p.II}={{\rm P}}_{gg}+\Delta {{\rm P}}_{fu.ch.gg}$$ (11)$$P_{gg}={{\rm P}}_{cc}+\Delta {{\rm P}}_t$$ (12)$$H_p=\Delta P_p/\left(\rho .g\right)$$

Where P_out.ox.p (MPa) is the oxidizer pump discharge pressure, P_cc (MPa) is the combustion chamber pressure, ΔΡ_t (MPa) is inlet and outlet pressure difference of turbine, ΔΡ_ox.gg.ch (MPa) is the pressure drop in the pre-burner oxidizer line, P_out.fu.p.I (MPa) the first-stage fuel pump discharge pressure, ΔΡ_fu.ch.cc (MPa) is the pressure drop in the combustion chamber fuel line, Ρ_gg (MPa) is the pre-burner pressure, P_out.fu.p.II is the second-stage fuel pump discharge pressure, H_p is the developed head of the pumps and ΔΡ_fu.ch.gg is the pressure drop in the pre-burner fuel line.

Step 4: Determination of mass flow rate of pumps: The mass flow of pumps depend on the mass flow rate of the chamber, pre-burner and booster turbines which were initially estimated. Then, in the next iteration loop, it is calculated from the required booster pump power.

Step 5: Determination of turbopump rotational speed (ω (rpm)). The most important parameters, which have important effects on turbopump rotational speed, are turbopump mass, inlet pressure and flow rate of pumps, working propellant type and temperature. Owing to the noticeable losses of thrust chamber cooling line and control valves of main fuel channel, the turbopump rpm is calculated from the fuel pump discharge, and then, its inlet pressure is estimated. Furthermore, owing to the critical condition of the oxidizer pump by cavitation, this pump inlet pressure should be computed from the calculated rpm (Avsianikov, 1983): (13)$$H/{\omega }^2=A+B.(Q/\omega )-C.{(Q/\omega )}^2$$

Where ω, H and Q are the pump rotational speed (rpm), developed head (m) and volumetric flow rate (m³/s), respectively; and A, B and C are the constant coefficients which were determined by Avsianikov’s (1983) method or pump test results.

Step 6: Determination of pump inlet pressure (P_in). Oxidizer vapor pressure is usually higher than fuel, so the oxidizer pump is in the worse condition due to cavitation. Thus, pump inlet pressure must be compatible with its rpm. In this step, P_in is estimated for each pump, and then, the compatible rpm is computed. This estimate is changed so as to obtain a predetermined rpm.

Step 6-1: Determination of “critical net positive suction head (Δh_sb)”: In design, this term is used to indicate the minimum suction head required above the propellant vapor pressure to assure suppression of cavitation, which, for LRPS, is considered 10 to 30 (j/kg).

Step 6-2: Calculation of “available net positive suction head” – this term is given by: (14)$$\Delta h_{cav}=\frac{P_{in}-P_s-\rho .\Delta h_{sb}}{\rho }$$

Where P_in is the inlet pressure, P_s is the propellant vapor pressure and ρ is the propellant density.

Step 6-3: Determination of “maximum pump suction specific speed (C_cav.max)”. If the value of “hub to tip inducer diameter ratio” is limited to 0.2 to 0.5, the value of (C_cav.max) can be easily exploited from Figure 10, which is limited from 3,000 to 4,500.

Step 6-4: Determination of turbopump rpm and its compliance with the rpm calculated in Step 5. Using the known flow rate and P_in, the turbopump rpm is estimated. This part of the calculations is iterated by changing P_in, until the computed rpm in Step 5 is attained (Beliaev et al., 1999): (15)$$\omega =C_{cav.\max }\frac{{\Delta hcav}^{0.75}}{248\mathrm{.}{Q}^{0.5}}$$

Step 7: Now according to selective rpm and knowing the main parameters of the pumps, the turbopump mass can be determined by Russian equation (Gakhoun et al., 1989): (16)$$M_{tp}=\frac{K_{tp}}{\omega }({\rho }_{ox}{Q}_{ox}{H}_{ox}^{3/2}+{\rho }_{fu}{Q}_{fu}{H}_{fu}^{3/2})$$ $$K_{tp}=(\mathrm{0.3\dots 0.35})\times {10}^{-3},(s^3.rad/m^3)$$

The abovementioned equation, which is exploited from the available global engine database, demonstrates that increasing rpm leads to reducing the turbopump mass. If the estimated turbopump mass is found to be unacceptable, the rpm should be reassessed until the mass obtained becomes acceptable.

Consequently, by accomplishing this step, in addition to calculating the turbopump rpm and mass, the rpm and mass of the booster turbopump must also be calculated. This differentiation is that the discharge pressure of main turbopump is calculated, but the determination of the “main turbopump inlet pressure” and also “booster turbopump inlet and outlet pressure” is done on the basis of the inlet matrix of oxidizer and fuel tank pressure, and subsequently, the optimum value is selected. The mass process determination of LRPS is presented in Kazlov (1997).

Furthermore, different cycles must be studied. This variable (cycle code) and the other dependent variables are shown in Table I.

Step 8: Calculation “mass flow rate” of booster turbines. In the calculations of booster pumps, by known flow rate and developed head and the selection of efficient booster pumps, the flow rate and power of “booster-turbines” are calculated.

Step 9: The turbopump rpm has not been determined yet, so pump efficiency is attained from technical recommendations. Obviously, pump efficiency influences the turbopump construction, so regarding the calculation of rpm, in which the rpm and pump flow rate are known, the pump efficiency is given according to Beliaev et al.’s (1999) equations: (17)$$\begin{array}{l}if18.8\le n_s\le 70\\ {\eta }_{pn}=-4.777+3.941n_s^{0.25}-0.710n_s^{0.5}\end{array}$$ (18)$$\begin{array}{l}if37.4\le n_s\le 124\\ {\eta }_{pn}=-1.544+1.233n_s^{0.25}-0.167n_s^{0.5}\end{array}$$ (19)$$n_s=34.87\omega \sqrt{Q}/H^{0.75}$$

Where η_pn is pump efficiency, n_s(m/s) is pump-specific speed and H (m) is pump developed head.

Step 10: The specific power of turbine and pumps are calculated by the following equations (Beliaev et al., 1999): (20)$${\overline{N}}_T=N_T/{\dot{m}}_{gg}=R.T.k/(k-1).({1-1/{\pi }_T}^{(k-1)/1}).{\eta }_t$$ (21)$${\overline{N}}_P=N_P/{\dot{m}}_P=\Delta P/(\rho .{\eta }_P)$$

Where N̄_T, N̄_o and N̄_f are the specific power of turbine, oxidizer and fuel pumps, respectively. Also, π_T, η_T and k are the turbine pressure ratio, efficiency and ratio of specific heats, respectively; and RT is the “working capability” of the developed gases in the pre-burner. Turbine inlet temperature is considered by turbine blade limitation.

Step 11: Determination of turbine key ratio which is the ratio of turbine pressure difference and combustion chamber pressure: (22)$$TKR=\frac{\Delta P_t}{P_{cc}}$$

For any input data, this ratio can be determined, in accordance with meeting the requirements for the energy balance of pumps and turbines.

Step 12: Estimation of the mass and size of propulsion system and considered stage of launch vehicle: Based on the relationships presented in Kazlov (1987, 1999) books, the mass of tanks, booster turbopumps and pressurization system are estimated. This explains the effect of “selecting different pressure for tanks” studied on the mass of tanks, pressurization system, booster turbopumps and, finally, the total propulsion system. In estimating the size of an engine, the chamber is considered as the main compartment. Owing to the historical data with similar cycle, the vehicle length is estimated as a coefficient of chamber length because the diameter, length and number of chambers affect the launch vehicle’s length and diameter.

Step 13: Determination of the main criteria of optimizing (the ratio of the total impulse to the LRPS mass).

To deepen the understanding of the turbine key ratio, the surfaces of “turbine developed power” and “pumps required power” should be plotted vs different pressure and turbine key ratios. The considered surfaces for the Russian engine NK-33 with the cycle plan of Figure 1 are shown in Figure 11. For any chamber pressure (Ρ_cc) (which corresponds to Ī_sp), the balance calculation of turbine and pumps power leads to the development of two turbine key ratios. Obviously, the lower ratio is to supply the minimum pump, and turbine discharge pressure level is selected. Figure 11 shows that a “contour curve” lays at the intersection; the intersection of turbine and pumps power surfaces peak corresponded to the maximum attainable combustion chamber pressure. The efficiency improvement of the main and booster pumps and turbines leads to the increase of the intersection of these surfaces. The maximum pressure of combustion chamber is raised because the intersection of the surfaces is increased.

Considering the algorithm in this study, the RD-180 engine input data were used. The plan cycle and nominal parameters of this engine are shown in Figure 12.

Verification of the developed algorithm

To verify the developed algorithm of the introduced cycles, the results were compared with the RD-180 engine and summarized in Table II, and in which the calculation error does not exceed 3 per cent. Therefore, the developed algorithm has sufficient accuracy to optimize the cycles shown in Figures 1 to 6.

According to calculations, using all effective factor except chamber expansion ratio leads to 200kg mass reduction. Among these factors, the most effective is turbine ratio. When the chamber expansion ratio rises from 375 to 475, the mass of stage decreases approximately 647 kg.

Replacing hydraulic booster turbine with gas turbine has a favorable influence on reducing “pumps required power” because the use of “turbine exhaust gas” instead of “pump discharge liquid” has more capability and effectively.

Column 1 (Figure 3) of Table III illustrates the result of the optimization algorithm for propulsion system of Stage 1 of Atlas LV family which has four RD-180 engines (Propulsion system includes propellant, tanks and engines.). In addition, Table III shows the comparison of cycles of Figures 3 to 6 for the considered thrust and burning time. The analysis of results of this table is as follows:

Cycle 6 (Figure 6) leads to increase in the specific impulse and decrease in the start mass of the considered stage of launch vehicle.

The nominal regime and parameters of RD-180 cycle can be modified using a new combination of parameters of tanks, booster pumps and engines. In the modified regime of RD-180 with the same cycle, the pressure of combustion chamber and other elements can be decreased.

Conclusion

In this research, a new optimization algorithm is developed to find the best nominal parameters of rocket engines using staged combustion cycle. In this study, new cycles of the staged combustion engines were presented and their capabilities were compared with available engine cycles. In these cycles, the booster pumps are considered mainly and more detailed look into effects of them on engine. The present study focuses attention on new cycles which some of them is the successful suggestion of this research. As it was said, the results were validated by data of RD-180 engine.

Further work

The coupled dynamics optimization study with this algorithm is recommended. For this purpose, the dynamic regime of motor must be modeled to verify the design of the static regime.

Figure 1

The staged combustion cycle without booster turbopump

[Figure omitted. See PDF]

Figure 2

The staged combustion cycle with ox and fuel booster turbopumps

[Figure omitted. See PDF]

Figure 3

The staged combustion cycle with ox and fuel booster turbopumps (Ox booster turbine is feed by oxidizer-rich gas)

[Figure omitted. See PDF]

Figure 4

The staged combustion cycle with ox and fuel booster turbopumps (according to Boukhmatov’s idea)

[Figure omitted. See PDF]

Figure 5

The staged combustion cycle with ox and fuel booster turbopumps (according to author’s idea)

[Figure omitted. See PDF]

Figure 6

The staged combustion cycle with ox and fuel booster turbopumps (according to author’s idea)

[Figure omitted. See PDF]

Figure 7

Schematic of dual-burner cycle

[Figure omitted. See PDF]

Figure 8

Flowchart of the design optimization algorithm

[Figure omitted. See PDF]

Figure 9

Static calculation in the basis input data

[Figure omitted. See PDF]

Figure 10

C_cav.max “hub to tip inducer diameter ratio”

[Figure omitted. See PDF]

Figure 11

The contour curve to determine the turbine key ratio of staged-combustion cycle

[Figure omitted. See PDF]

Figure 12

The RD-180 engine cycle plan

[Figure omitted. See PDF]

Table I

Input data

Item	Dependent variables
1	Combustion chamber pressure
2	Nozzle exit pressure
3	Mixture ratio
4	Oxidizer pump inlet pressure
5	Fuel pump inlet pressure
6	Engine burning time
7	Turbine expansion ratio
8	Cycle code

Table II

Comparing the results and the experimental data on engine RD-180

Item	Parameters	Deterministic Data	Experimental Data	Error (%)
1	Oxidizer pump discharge pressure (MPa)	59.3	60.6	−2.1
2	Fuel 2nd stage pump discharge pressure (MPa)	79.7	81.0	−1.6
3	Pre-burner pressure (MPa)	52.5	53.7	−2.2
4	Pressure drop in turbine (MPa)	24.3	25.6	−5.1
5	Turbine expansion ratio	1.86	1.91	−2.6
6	Turbopump rotational speed (rpm)	19,909	19,390	+2.7

Table III

Comparison of the optimization results for various cycles

Parameter	Figure 3	Figure 4	Figure 5	Figure 6
PCC, kg.f/cm2	214.30	217.9	206.9	232.3
ISP, s	312.4	313.4	311.9	313.7
πT	1.87	1.87	1.92	1.77
P ox tank	5.20	5.22	5.21	5.19
P fu tank	5.88	5.88	4.88	4.87
πchambr	370.0	390.0	360.0	397.5
ME + MTP, kg	4,919.3	5248.6	5,802.1	5,217.3
Mtan ⁡ks, kg	13,551.8	13,523.9	12,877.8	12,756.9
Mo, kg	206,064.3	205,814.7	206,440.1	204,659.5
Isp/M0, m/(kg.s)	275.9	276.2	275.4	277.8