The goal of cycle analysis is to estimate operation parameters of the propellant feed system which meets required design parameters, such as:
 Thrust chamber pressure
 Propellant components mass flow rate
 Propellant components mixture ratio
Table of contents
Cycle Analysis
When configured properly, the program obtains the following operation parameters of the propellant feed system:
 Operational parameters of combustion devices (gas generators or preburners): pressure, mass flow rate and mixture ratio
 Operational parameters of each of turbopump components: mass flow rate, inlet pressure, discharge pressure, shaft power
 Overall performance of the rocket engine (usually estimated only for gas generator and tapoff cycles)
The diagram below presents the typical cycle analysis flowchart (click the image to enlarge it):
Input data
The following input data has to be available before starting the preparation of design parameters for cycle analysis:
 Design parameters required for performance analysis and thrust chamber sizing
 Physical properties of propellant components
 Engine cycle type
 Propellant feed system flow schematic
 Parameters of elements in propellant feed system
 Parameters of propellant components at engine inlet
Prerequisites: performance analysis and thrust chamber sizing
Cycle analysis module utilizes the results of performance analysis and thrust chamber sizing, therefore the user has to provide all design parameters required for performance analysis and thrust chamber sizing.
Because the cycle analysis depends on results of performance analysis and thrust chamber sizing, it can be performed only if the mentioned two modules were succesfully executed.
Physical properties of propellant components
Similar to thermal analysis, cycle analysis can only be used with propellant components which were properly defined either in standard data library file
<RPA installation directory>/resources/properties.inp
or in user data library
<user.application.data>/resources/usr_properties.inp
.
The proper component definition includes such parameters as density, viscosity, thermal conductivity, and heat of evaporation. These parameters may be defined either for normal conditions or for the range of conditions (pressure, temperature).
Standard data library delivered in RPA distribution package includes following components with defined physical properties:
Component  Ranges 

LH2  p=(0.1...60) MPa, T=(20...600) K 
LOX  p=(0.1...60) MPa, T=(63...973) K 
C2H5OH(L)  p=(0.1...30) MPa, T=(253...593) K 
CH4(L)  p=(0.1...60) MPa, T=(100...600) K 
C3H8(L)  p=(0.1...49) MPa, T=(140...590) K 
CH6N2(L)  p=0.1 MPa, T=(223...323) K 
C2H8N2(L),UDMH  p=0.1 MPa, T=(203...333) K 
N2H4(L)  p=0.1 MPa, T=(289...387) K 
N2O4(L)  p=0.1 MPa, T=(263...343) K 
RP1  p=0.1 MPa, T=(289...422) K 
T1  p=0.1 MPa, T=(273...298) K 
Physical properties of component at conditions within defined ranges are calculated using one of interpolation methods. Component properties at conditions below or above defined ranges are taken at nearest point in the available range.
User may specify properties for further components, defining them in user data library file. To make it easier, RPA provides embedded thermodynamic database editor.
Type of engine cycle and its toplevel parameters
RPA Standard v.2 supports following cycle types:
 gas generator cycle (GG)
 staged combustion cycle (SC)
 fullflow staged combustion cycle (FFSC)
All cycles allow variations of the flow diagram including the number of combustion devices (gas generator or preburner), the number of turbopumps, arrangement of turbines (serial or parallel), availability of booster pumps, availability of kick pumps, availability of tapoff branches.
Toplevel parameters include:
 Type of combustion devices:
 oxidizerrich
 fuelrich
 Number of independent turbopumps
 Number of gas generators/preburners
GG cycle typically utilizes a fuelrich combustion device (gas generator), because combustion products generated in such device usually have better energetics and lower chemical activity which allows higher temperature, which in turn provides yet more drive power.
SG cycle may utilize both fuelrich and oxidizerrich combustion devices (preburners). The selection depends on concrete type of propellant: engines operating on liquid hydrogen are designed with fuelrich preburner, whereas engines operating on hydrocarbon fuels are usually designed with oxidizerrich preburner.
Because of its design, FFSC cycle utilizes both types at once.
Propellant feed system flow diagram
Propellant feed system flow diagram has to be defined.
For example, the following flow diagram represents the SC cycle with oxidizerrich prebirner (click the image to enlarge it):
Flow schematic 

Parameters of elements in propellant feed system
The current version of the program is capable of obtaining the operational parameters of the whole feed system, but parameters of many of its subcomponents have to be specified by the user.
User has to provides following parameters:
 Efficiency of pumps and turbines
 Pressure drop in valves, injectors, cooling jackets
The following table provides information on how to define required parameters:
Subcomponent  Parameter  Typical Values  Comments 

Combustion device  Pressure 

For GG cycle the gas generator pressure is an input parameter. For SC and FFSC cycles the preburner pressure is obtained by RPA as a result of analysis. 
Pressure drop coefficient  0.9...0.95  The value defines the pressure drop between injector of the combustion device and turbine inlet.  
Temperature 

The temperature in combustion device is limited by corrosion and heatresistance as well as hightemperature strength of used construction materials.  
Turbine  Pressure ratio  10...20  Required for GG cycle only. Obtained by RPA for SC and FFSC cycles. 
Efficiency  0.5...0.8  
Arrangement  Serial or parallel flow  Required for second turbine in configurations with one combustion device  
Main pump  Efficiency  0.6...0.8  For singleshaft turbopumps typical values are: 0.70.8 for oxidizer pump 0.550.7 for fuel pump. 
Booster pump  Efficiency  0.5...0.7  Optional parameter if booster pump is available 
Discharge pressure  (1.5...2)p_{inlet}  Optional parameter if booster pump is available  
Booster pump drive  Type 

Optional parameter if booster pump is available 
Turbine pressure ratio 

Optional parameter if booster pump with dedicated turbine is available  
Turbine efficiency  0.5...0.7  Optional parameter if booster pump with dedicated turbine is available  
Valve  Pressure drop  (0.1...0.2)p_{c}  Main feed branch 
(0.1...0.15)p_{c}  Combustion device feed branch  
Cooling jacket  Pressure drop  (0.25...0.35)p_{c}  
Injector  Pressure drop 
(0.4...0.8)(p_{c})^{0.5} or (0.3...1.5) MPa 

Kick pump  Efficiency  0.3...0.5  If no kick pump is defined, the pump of the main branch has to produces such a discharge pressure that it fits to inlet of gas generator/preburner. Usually no kick pump is required for gas generator cycle, whereas an absence of kick pump in staged combustion cycle leads to significant pressure raise. 
Secondary feed branch  Inlet relative crosssection area  0.1...0.3  Defines the inlet crosssection area of the branch relative to the inlet crosssection area the main branch. 
Parameters of propellant components at engine inlet
Inlet parameters of component such as pressure and velocity have to be selected:
Parameter  Typical Values  Comments 

Inlet pressure of component  (0.3...0.8) MPa  Inlet pressure of component is defined by conditions in the component tank. 
Inlet velocity of component 

Inlet velocity of component is mainly defined by mass flow rate and crosssection area of the inlet. In order to reduce the hydraulic losses, inlet velocity is usually selected from the specified range. 
Propellant feed system decomposition
The modelling of the engine cycle with RPA requires the decomposition of the the feed system into 3 subsystems:
 Fuel feed subsystem
 Oxidizer feed subsystem
 Power subsystem
Component (fuel or oxidizer) feed subsystem begins at component inlet of the fuel and ends at injectors of combustion chamber and/or combustion device (GG or preburner). It includes booster, main and kick pumps, valves, cooling jackets, injectors, and subbranches.
Power subsystem begins at combustion device (GG or preburner) and ends either at injector of thrust chamber (in SC and FFSC cycles) or at exhaust nozzle (in GG cycle). It includes combustion device, gas ducts, turbine, injector (in SC and FFSC cycles) and nozzle (in GG cycle).
Example
To demonstrate the selection and definition of input data, an example problem has been prepared using the flow diagram specified above.
Input data:
Subsystem  Parameter  Value 

Engine  Nominal thrust  200 kN at sea level 
Number of thrust chambers  1  
Thrust chamber  Pressure  20 MPa 
Propellant components 


Nozzle cobditions 


Sizing design parameters 


Engine  Cycle type  Staged combustion 
Toplevel cycle parameters 


Power subsystem  Pressure drop coefficient  0.9 
Temperature in preburner  770 K  
Turbine efficiency  0.79  
Oxidizer feed subsystem (main feed branch)  Inlet pressure  0.8 MPa 
Inlet velocity  5 m/s  
Main pump efficiency  0.74  
Valve pressure drop  3.5 MPa  
Injector pressure drop  2.0 MPa  
Fuel feed subsystem (main feed branch)  Inlet pressure  0.75 MPa 
Inlet velocity  5 m/s  
Main pump efficiency  0.74  
Valve pressure drop  3.0 MPa  
Cooling jacket pressure drop  7.0 MPa  
Injector pressure drop  2.0 MPa  
Fuel feed subsystem (preburner feed branch)  Inlet relative crosssection area  0.30 
Kick pump efficiency  0.70  
Kick pump drive type  main gas turbine  
Valve pressure drop  1.0 MPa  
Injector pressure drop  2.0 MPa 
Download prepared configuration file: Example_1.cfg
Estimated operation parameters of the propellant feed system ^{1}:
Propellant Feed Subsystem\s  Path: Oxidizer Feed Subsystem 0 inlet: m_dot= 44.066 kg/s, p_in= 0.800 MPa, p_out= 0.718 MPa 1 pump: m_dot= 44.066 kg/s, p_in= 0.718 MPa, p_out= 41.775 MPa, N= 2102.192 kW 2 pipe: m_dot= 44.066 kg/s, p_in= 41.775 MPa, p_out= 41.333 MPa 3 valve_c_dp: m_dot= 44.066 kg/s, p_in= 41.333 MPa, p_out= 37.833 MPa 4 valve_c: m_dot= 44.066 kg/s, p_in= 37.833 MPa, p_out= 37.827 MPa 5 injector: m_dot= 44.066 kg/s, p_in= 37.827 MPa, p_out= 35.827 MPa Path: Fuel Feed Subsystem 0 inlet: m_dot= 16.755 kg/s, p_in= 0.750 MPa, p_out= 0.696 MPa 1 pump: m_dot= 16.755 kg/s, p_in= 0.696 MPa, p_out= 32.279 MPa, N= 948.814 kW 2 pipe: m_dot= 15.861 kg/s, p_in= 32.279 MPa, p_out= 32.004 MPa 3 valve_c_dp: m_dot= 15.861 kg/s, p_in= 32.004 MPa, p_out= 29.004 MPa 4 valve_c: m_dot= 15.861 kg/s, p_in= 29.004 MPa, p_out= 29.000 MPa 5 cooling: m_dot= 15.861 kg/s, p_in= 29.000 MPa, p_out= 22.000 MPa 6 injector: m_dot= 15.861 kg/s, p_in= 22.000 MPa, p_out= 20.000 MPa Path: branch_g Connected to discharge port of 'pump' 0 branch_g: m_dot= 0.894 kg/s, p_in= 32.279 MPa, p_out= 32.173 MPa 1 pump: m_dot= 0.894 kg/s, p_in= 32.173 MPa, p_out= 38.827 MPa, N= 11.279 kW 2 pump_out: m_dot= 0.894 kg/s, p_in= 38.827 MPa, p_out= 38.827 MPa 3 valve_g_dp: m_dot= 0.894 kg/s, p_in= 38.827 MPa, p_out= 37.827 MPa 4 valve_g: m_dot= 0.894 kg/s, p_in= 37.827 MPa, p_out= 37.827 MPa 5 pipe: m_dot= 0.894 kg/s, p_in= 37.827 MPa, p_out= 37.827 MPa 6 injector: m_dot= 0.894 kg/s, p_in= 37.827 MPa, p_out= 35.827 MPa Power Subsystem  Path: Staged Combustion Power Subsystem 0 gg: m_dot= 44.960 kg/s, p_in= 35.827 MPa, p_out= 32.244 MPa, T= 770.046 K 1 turbo1: m_dot= 44.960 kg/s, p_in= 32.244 MPa, p_out= 20.482 MPa, T= 770.046 K, pi= 1.574, N= 3062.188 kW 2 turbo1_out: m_dot= 44.960 kg/s, p_in= 20.482 MPa, p_out= 20.382 MPa 3 inj_c: m_dot= 44.960 kg/s, p_in= 20.382 MPa, p_out= 19.982 MPa Engine performance  Chamber performance specific impulse (vac): 335.32 s specific impulse (opt): 319.65 s specific impulse (SL): 303.56 s thrust (vac): 200.00 kN (x1) thrust (opt): 190.65 kN (x1) thrust (SL): 181.06 kN (x1) Engine performance specific impulse (vac): 335.32 s specific impulse (opt): 319.65 s specific impulse (SL): 303.56 s correction factor: 1.00 thrust (vac): 200.00 kN thrust (opt): 190.65 kN thrust (SL): 181.06 kN
Main operation parameters fetched from the printout above:
Subsystem  Parameter  Value 

Oxidizer feed subsystem  Mass flow rate  44.066 kg/s 
Inlet pressure  0.800 MPa  
Pump discharge pressure  41.775 MPa  
Pump shaft power  2102.192 kW  
Fuel feed subsystem (main branch) 
Mass flow rate  16.755 kg/s 
Inlet pressure  0.750 MPa  
Pump discharge pressure  32.279 MPa  
Pump shaft power  948.814 kW  
Fuel feed subsystem (preburner branch) 
Mass flow rate  0.894 kg/s 
Inlet pressure  32.279 MPa  
Pump discharge pressure  38.827 MPa  
Pump shaft power  11.279 kW  
Preburner  Propellant total mass flow rate  44.960 kg/s 
O/F ratio  49.291 (44.066/0.894)  
Pressure  35.827 MPa  
Temperature  770.046 K  
Turbine  Inlet pressure  32.244 MPa 
Pressure ratio  1.574  
Shaft power  3062.188 kW 
^{1)} Provided results were obtained with RPA Standard v.2.x running on Windows 7 (64 bit):