Document
Propulsion System Models for Rotorcraft Conceptual Design
Wayne Johnson Aeromechanics Office National Aeronautics and Space Administration Ames Research Center, Moffett Field, California wayne.johnson@nasa.gov ABSTRACT The conceptual design code NDARC (NASA Design and Analysis of Rotorcraft) was initially implemented to model conventional rotorcraft propulsion systems, consisting of turboshaft engines burning jet fuel, connected to one or more rotors through a mechanical transmission. The NDARC propulsion system representation has been extended to cover additional propulsion concepts, including electric motors and generators, rotor reaction drive, turbojet and turbofan engines, fuel cells and solar cells, batteries, and fuel (energy) used without weight change. The paper describes these propulsion system components, the architecture of their implementation in NDARC, and the form of the models for performance and weight. Requirements are defined for improved performance and weight models of the new propulsion system components. With these new propulsion models, NDARC can be used to develop environmentally-friendly rotorcraft designs.
analysis computer program for rapidly sizing and . .
INTRODUCTION conducting performance analysis of new rotorcraft The objectives of rotorcraft design work in a government concepts. NDARC has a modular code base, facilitating its laboratory are to support research and to support rotorcraft extension to new concepts and the implementation of new acquisition. Research activities require a robust design computational procedures. The theoretical basis and capability to aid in technology impact assessments and to architecture is described in Ref. 2; design results from the provide system level context for research. At the applied development are presented in Ref. 3.
research level, it is necessary to show how technology will The NDARC code performs design and analysis tasks impact future systems, and to justify the levels of (figure 1). The design task sizes the rotorcraft to satisfy a investment required to mature that technology to an set of design conditions and missions. The analysis tasks engineering development stage. Conceptual design can include off-design mission performance analysis, provides one avenue to accomplishing these objectives.
flight performance calculation for point operating NASA research activities requiring rotorcraft design work conditions, and generation of subsystem or component include concept exploration, concept decision, concept performance maps. The aircraft size is characterized by refinement, and technology development. During these parameters such as design gross weight, weight empty, activities, performing quantitative evaluation and rotor radius, and engine power available. From the design independent synthesis of a wide array of aircraft designs is flight conditions and missions, the task can determine the necessary.
total engine power or the rotor radius, as well as the design The design code NDARC (NASA Design and Analysis of gross weight, maximum takeoff weight, drive system Rotorcraft) was developed to fulfill these requirements torque limit, and fuel tank capacity.
(Ref. 1). NDARC is a conceptual/preliminary design and NDARC was initially implemented to model conventional . rotorcraft propulsion systems, consisting of turboshaft Presented at the Fifth Decennial AHS Aeromechanics engines burning jet fuel, connected to one or more rotors Specialists’ Conference, San Francisco, CA, January 22- through a mechanical transmission.
24, 2014. This is a work of the U.S. Government and is not subject to copyright protection.
The NDARC propulsion system representation has been AIRCRAFT DESCRIPTION extended to cover additional propulsion concepts. A major Decomposition of the aircraft system into components is objective is to be able to develop environmentally-friendly critical to achieving the ability to rapidly model a wide rotorcraft designs. The new propulsion elements include array of rotorcraft concepts. Thus the aircraft consists of a electric motors and generators, rotor reaction drive, set of components, including fuselage, rotors, wings, tails, turbojet and turbofan engines, fuel cells and solar cells, and propulsion. For each component, attributes such as batteries, and fuel (energy) used without weight change.
performance, drag, and weight can be calculated. The This paper describes these propulsion system elements, aircraft attributes are obtained from the sum of the and the architecture of their implementation in NDARC.
component attributes. Description and analysis of Requirements are defined for improved performance and conventional rotorcraft configurations are facilitated, weight models of the new propulsion system components.
while retaining the capability to model novel and advanced concepts. Specific rotorcraft configurations considered are single main-rotor and tail-rotor helicopter; tandem helicopter; coaxial helicopter; and tiltrotors. Novel and advanced concepts typically are modeled by starting with one of these conventional configurations. For example, compound rotorcraft can be constructed by adding wings and propellers.
The aircraft is formed from components that include a fuselage and landing gear, usually rotors, perhaps wings and tails, and the following components related to the propulsion representation.
Original NDARC Propulsion Representation NDARC was initially implemented to model conventional rotorcraft propulsion systems, consisting of turboshaft engines burning jet fuel, connected to one or more rotors through a mechanical transmission. The original aircraft model had the following propulsion elements (figure 2): – Propulsion Groups: A propulsion group represents the Figure 1. Outline of NDARC tasks.
drive system, which connects a set of rotors and engine groups. The components (rotors) define the power required, and the engine groups define the power available. There are one or more drive states, with a set of gear ratios for each state. The power required equals the sum of component power, transmission losses, and accessory losses. There are drive system torque limits, and rotor and engine shaft ratings.
– Engine Groups: Each engine group has one or more engines of the same type. For each engine type an engine model is defined. The engine performance information includes mass flow, fuel flow, jet thrust, and momentum drag at the required power.
– Fuel Tank: There is one fuel tank component for the Figure 2. NDARC original propulsion representation.
aircraft. The fuel quantity stored and burned is measured in weight. A fuel tank component can include a number of auxiliary tanks.
– Forces: The force component is a simple model to generate a force on the aircraft (representing a lift, propulsion, or control subsystem), including a weight and fuel flow description.
– Rotors: In addition to main rotors, tail rotors, propellers, proprotors, and ducted fans can be modeled. A rotor can be tilting, ducted, antitorque, and/or reaction drive. The rotor power required is evaluated using the energy method, as a sum of induced, profile, and parasite power.
Extended NDARC Propulsion Representation The NDARC propulsion system model has been extended in the present work to cover additional propulsion system concepts, including electric motors and generators, rotor reaction drive, turbojet and turbofan engines, fuel cells and solar cells, batteries, and fuel (energy) used without weight change (figure 3). The components of the propulsion system can be classified as producing or absorbing shaft torque (engine groups), producing force (jet groups), or producing energy (charge groups): – Engine Groups: An engine group transfers power by shaft torque, so is associated with a propulsion group. An engine model describes a particular engine, used in one or more engine groups. Models include turboshaft engines (perhaps convertible, for turbojet operation or reaction drive), reciprocating engines, compressors (perhaps for reaction drive), electric motors (perhaps with fuel cells), electric generators, and generator-motors.
– Jet Groups: A jet group produces a force on the aircraft.
A jet model describes a particular jet, used in one or more jet groups. Models include turbojet and turbofan engines (perhaps convertible, for reaction drive), reaction drive, and a simple force model. A reaction drive supplies a blade force that provides the rotor power required.
– Charge Groups: A charge group generates energy for the aircraft. A charge model describes a particular charger, used in one or more charge groups. Models include fuel cells and solar cells.
– Fuel Tank System: There are one or more fuel tank systems for the aircraft. The fuel quantity stored and burned is measured in weight or energy. Each component that uses fuel (engine, jet, and charge groups) is associated with a fuel tank system of the appropriate type. There can be one or more sizes of auxiliary fuel tanks. Tanks that use Figure 3. NDARC extended propulsion representation.
weight include jet fuel, gasoline, and hydrogen. Tanks that use energy include batteries, capacitors, and flywheels.
The engine, jet, and charge groups introduce an overall classification of the propulsion system components, each with a general performance characterization, from which NDARC propulsion group is a mechanical drive train, the architecture of the code follows. A model consists of a which connects designated rotors and engine groups.
parameterized, surrogate representation of the component Referred performance parameters are used for propulsion performance and weight, applicable to a wide range of system components that operate with air. Referred operating conditions and component size. It is the models parameters account for the characteristic velocity, density, where simplifications and approximations are found, and and pressure associated with the working fluid. The future improvements developed.
operating condition and atmosphere give the standard conditions (temperature T and pressure p ) for a std std SIZING TASK specified pressure altitude; the sea-level standard The sizing task determines the dimensions, power, and conditions (temperature T and pressure p ); and the 0 0 weight of a rotorcraft that can perform a specified set of operating temperature T and pressure p . Here the design conditions and missions. Sizing is an iterative temperatures are in deg R or deg K. The engine procedure to find a consistent description of the system.
characteristics depend on the temperature ratio = T / T Optimization is handled external to NDARC. The aircraft and pressure ratio = p / p . The flight Mach number M size is characterized by parameters such as design gross is obtained from the aircraft speed. The inlet ram air weight or weight empty, rotor radius, and engine power temperature ratio and pressure ratio are obtained from M available. From the design flight conditions and missions, and the inlet ram recovery efficiency : d 2 2 3.5 the task can determine the total engine power or the rotor = (1 + 0.2 M ) and = (1 + 0.2 M ) , using the M M d radius (or both power and radius can be fixed), as well as ratio of specific heats = 1.4 .
the design gross weight, maximum takeoff weight, drive The reference performance is at sea-level-standard static system torque limit, and fuel tank capacity. Refs. 1–2 conditions (subscript 0 ), and maximum continuous power describe the sizing options of NDARC in detail. Here the or thrust (subscript C ). Referred or corrected engine extended propulsion models introduce additional sizing parameters are used in the model: power P /( ) , mass options.
˙ flow m /( / ) , specific power ( P / ˙ m ) / , fuel flow For each propulsion group, the engine power or the rotor ˙ w /( ) , thrust F / , and turbine speed N / .
radius can be sized. The engine power is the maximum of Engine performance depends on the engine rating. Each the power required for all designated sizing flight engine rating has specific operating limitations, most conditions and sizing missions. Hence the engine power is importantly an operating time limit intended to avoid changed by the ratio of the propulsion group power damage to the engine. The power available from a required to power available. Alternatively, the rotor radius turboshaft engine depends on the engine rating. Engine can be adjusted so power required equals power available; power is generally specified in terms of SLS static max or both engine power and rotor radius can be input rather continuous power (MCP). Takeoff typically uses than sized.
maximum rated power (MRP). The thrust available from a For each jet group, the design thrust can be sized. The turbojet or turbofan engine depends on the engine rating, design thrust is the maximum of the thrust required for all including maximum continuous thrust (MCT).
designated sizing flight conditions and sizing missions.
Geometry and control are defined for engine groups, jet Hence the design thrust is changed by the ratio of the jet groups, and charge groups. The component amplitude and group thrust required to thrust available.
mode are control variables. The amplitude can be power For each charge group, the design power can be sized. The (engine group), thrust (jet group), or power (charge design power is the maximum of the power required for all group). The mode can be mass flow (for convertible designated sizing flight conditions and sizing missions.
engines), or power flow (for generator-motor). The group Hence the design power is changed by the ratio of the orientation is specified by selecting a nominal direction.
charge group power required to power available.
The yaw and incidence angles can be connected to the aircraft controls.
PROPULSION SYSTEM The group produces a force acting in the direction of the The aircraft propulsion system can be constructed from a component; and a drag acting in the wind direction. An number of components: propulsion groups, engine groups, aerodynamic model is defined for engine groups, jet jet groups, charge groups, and fuel tank systems. The groups, and charge groups. The group includes a nacelle, which contributes to the aircraft drag. The reference area The unit of fuel energy is Mega-Joules (MJ). For for the nacelle drag coefficient is the nacelle wetted area. reference, 1 BTU = 1055.056 Joule.
Rotor Reaction Drive Fuel Tank Systems that Store and Burn Weight A rotor reaction drive can be modeled using either an For fuel use measured by weight, the fuel properties are engine group or a jet group. density (weight per volume, lb/gal or kg/liter) and fuel specific energy e (MJ/kg). Table 1 gives the properties fuel The total rotor power required P consists of induced, rotor of a number of aviation fuels, based on military and profile, interference, and parasite terms. In most helicopter industry specifications. Fuels considered include jet fuel, designs the power is delivered to the rotor by a mechanical gasoline, diesel, and hydrogen. From the fuel weight drive, through the rotor shaft torque. Such designs require W , the energy is E = e W (MJ) and the volume fuel fuel fuel fuel a transmission and a means for balancing the main rotor is (gallons or liters). A motive device V = W / fuel fuel fuel torque. The shaft power is , which contributes P = P shaft rotor ˙ has a fuel flow w (lb/hour or kg/hour), and its specific P to the propulsion group power required, , and reqPG ˙ ˙ fuel consumption is sfc = w / P or sfc = w / T .
produces a torque on the aircraft.
The fuel tank capacity W (maximum usable fuel fuel-cap An alternative is to supply the power by a jet reaction weight) is input or determined from designated sizing drive of the rotor, using cold or hot air ejected out of the missions. The corresponding volumetric fuel tank capacity blade tips or trailing edges. Helicopters have also been is V = W / . The fuel system weight fuel-cap fuel-cap fuel designed with ram jets on the blade tips, or with jet flaps consists of the tank weight (including support) and the on the blade trailing edges that use compressed air plumbing weight.
generated in the fuselage. Since there is no torque reaction between the helicopter and rotor (except for the small Fuel Tank Systems that Store and Burn Energy bearing friction), no transmission or anti-torque device is For fuel use and storage measured by energy, there is no required, resulting in a considerable weight saving. With a weight change as energy is used. The energy storage jet reaction drive, the propulsion system is potentially (tank) is characterized by specific energy e (MJ/kg) lighter and simpler, although the aerodynamic and thermal tank and energy density (MJ/liter). Table 2 gives the efficiency are lower. The helicopter must still have a tank properties of a number of energy storage systems. The mechanism for yaw control.
tank weight and volume are obtained from the energy With reaction drive the shaft power is zero ( P = 0 ), shaft capacity E (MJ). The fuel weight W is zero. A fuel-cap fuel and the reaction power P = P contributes to the ˙ react rotor motive device has an energy flow E , and its specific fuel engine group or jet group power required. The reaction ˙ consumption is sfc = E / P (inverse of efficiency).
drive produces a force F on the rotor blade at effective react Storage systems considered include batteries, capacitors, radial station r , so P = r F . Momentum react react react react and flywheels. A battery (or capacitor) stores charge (A- balance gives the total force. The average force in the hr), so the capacity is expressed as energy for a nominal nonrotating frame is the drag of the inlet momentum voltage. Variation of the voltage with operation affects the ˙ ( m V ), which is accounted for in the engine group or react efficiency of the relation between useful power and the jet group model. The mean in the rotating frame gives the rate of change of the energy stored. Efficiency of ˙ total jet force required F = m ( V r ) . The react react react react charge/discharge is accounted for in the model of the engine group or jet group performance includes the blade device supplying or using the energy. Each fuel tank duct and nozzle, perhaps even with tip burning. If the system that stores and burns energy has a battery model reaction drive is turned off, then the rotor must be trimmed for computation of the efficiency.
such that P = 0 .
rotor The fuel tank capacity E (maximum usable fuel fuel-cap FUEL TANK energy) is input or determined from designated sizing The fuel quantity stored and burned can be measured in missions. The fuel tank weight is W = E / e (lb tank fuel-cap tank weight or energy. Each component (engine group, jet or kg) and the fuel tank volume is V = E / fuel-cap fuel-cap fuel group, charge group) that uses or generates fuel is (gallons or liters).
associated with a fuel tank system of the appropriate type.
Table 1. Fuel properties (Refs. 4–6).
fuel specification density specific energy energy density lb/gal kg/L MJ/kg BTU/lb lb/hp-hr MJ/L gasoline MIL-STD-3013A 6.0* 0.719 43.50 18700* 0.136 31.3 diesel nominal 7.0 0.839 43.03 18500 0.138 36.1 range 6.84–7.05 0.820–0.845 43.0 18487 0.138 35.8 JetA/A-1 MIL-STD-3013A 6.7* 0.803 42.80 18400* 0.138 34.4 range 6.84/6.71 0.820/0.804 42.8 18401 0.138 34.8 JP-4 nominal 6.5 0.779 42.80 18400 0.138 33.3 MIL-DTL-5624U 6.23–6.69 0.751*–0.802* 42.8* 18401 0.138 32.2 JP-5 MIL-STD-3013A 6.6* 0.791 42.57 18300* 0.139 33.7 alternate design 6.8* 0.815 42.91 18450* 0.138 35.0 MIL-DTL-5624U 6.58–7.05 0.788*–0.845* 42.6* 18315 0.139 34.8 JP-8 MIL-STD-3013A 6.5* 0.779 42.80 18400* 0.138 33.3 alternate design 6.8* 0.815 43.19 18570* 0.137 35.2 MIL-DTL-83133H 6.45–7.01 0.775*–0.840* 42.8* 18401 0.138 34.6 hydrogen (700 bar) 0.328 0.03930 120. 51591 0.0493 4.72 hydrogen (liquid) 0.592 0.07099 120. 51591 0.0493 8.52 *specification value Table 2. Energy storage properties.
tank specific energy tank energy density efficiency power MJ/kg kW-hr/kg MJ/L kW-hr/m kW/kg lead-acid battery 0.11–0.14 0.03–0.04 0.22–0.27 60–75 70–90% 0.18 nickel-cadmium battery 0.14–0.20 0.04–0.06 0.18–0.54 50–150 70–90% 0.15 lithium-ion state-of-art 0.54–0.90 0.15–0.25 0.90–1.30 250–360 ~99% 1.80 +5 years 1.26 0.35 1.80 500 +10 years 2.34 0.65 2.25 625 ultracapacitor 0.01–0.11 0.004-0.03 0.02–0.16 6–45 1.00 flywheel steel 0.11 0.03 ~90% graphite 0.90 0.25 Figure 4. Propulsion group power flow.
group, P = P . An engine group power can be reqEG reqPG PROPULSION GROUP fixed at an input amplitude, or at a fraction of engine The propulsion group is a set of components and engine power available, or at a fraction of engine rated power.
groups connected by a drive train. The components The power required for the remaining (perhaps all) engine (rotors) define the power required. The engine groups groups is distributed proportional to the engine rated define the power available. Figure 4 illustrates the power power.
flow. Power available is evaluated starting from engine The drive train rating is defined as a power limit, P .
DS limit installed power, subtracting installation losses and The rating is properly a torque limit, implementing a mechanical limit (engine installed power), Q = P / , but is conventionally expressed as a DS limit DS limit accounting for inoperative engines, a power factor for power limit. The drive train rating is a limit on the entire margins, and the engine shaft rating (engine group power), propulsion group. To account for differences in the summing over all engine groups and implementing a drive distribution of power through the drive train, limits are train torque limit (propulsion group power available), also used for the torque of each rotor shaft and of each subtracting transmission losses and accessory power, and engine group.
implementing a rotor shaft rating (power available to the rotor). Power required is evaluated starting from ENGINE GROUP component (rotor) power required, summing over all The engine group consists of one or more engines of a components and adding transmission losses and accessory specific type. An engine group transfers power by shaft power (propulsion group power required), distributing torque, so is associated with a propulsion group. For each power to engine groups, accounting for inoperative engine engine type an engine model is defined. The engine model (engine installed power required), and adding installation describes a particular engine, used in one or more engine losses (engine uninstalled power). See Refs. 1–2 for more groups. The models include turboshaft engines (perhaps details.
convertible, for turbojet operation or reaction drive), The drive train defines gear ratios for all the components reciprocating engines, compressors, electric motors that it connects. The gear ratio is the ratio of the (perhaps with fuel cells), electric generators, and component rotational speed to that of the primary rotor.
generator-motors.
There is one primary rotor per propulsion group (for The engine size is described by the power , which is which the reference tip speed is specified); other P eng the sea-level static power available per engine at a components are dependent (for which a gear ratio is specified takeoff rating. The number of engines is specified). There can be more than one drive train state, in N eng specified for each engine group.
order to model a multiple-speed or variable-speed transmission. Each drive train state corresponds to a set of The propulsion group power available is obtained from the gear ratios.
sum over the engine groups: . The P = P avPG avEG propulsion group power required P consists of the The flight state specifies the tip speed of the primary rotor reqPG component power, transmission losses, and accessory and the drive train state, for each propulsion group. The power. The component power P includes compressor drive train state defines the gear ratio for dependent rotors comp power, generator power, and generator-motor power when and the engine groups. From the rotor radius the rotational it is producing energy.
speed of the primary rotor is obtained; from the gear ratios, the rotational speed of dependent rotors and the The installed power required P and power available req engine groups are obtained; and from the rotor radius, the P P are measured at the engine output shaft. In av req tip speed of the dependent rotor is obtained.
addition to shaft power, the engine exhaust produces a net jet thrust F , from mass flow that goes through the engine The component power required P is evaluated for a N comp core. The fuel flow and mass flow are the total required to specified flight condition, as the sum of the power produce the shaft power and jet thrust. The forces required by all the components of the propulsion group.
produced by mass flow that does not go through the The total power required for the propulsion group is engine core (such as IR suppressor or cooling air) are obtained by adding the transmission losses and accessory treated as momentum drag .
power: P = P + P + P . D aux reqPG comp xmsn acc In general, the engine performance is described by the The power required for the propulsion group must be uninstalled power available , at each engine rating and distributed to the engine groups. With only one engine P a ˙ the specification engine speed N ; the mass flow m and as functions of q = P /( P ) , = T / T , M , and spec q 0 C 0 ˙ fuel flow w required to produce uninstalled power n = N / .
required P at engine turbine speed N ; and the gross jet q The performance of the engine group is: thrust F at P . The difference between net and gross jet g q ˙ m = ( N N ) ˙ m thrust is the momentum drag: reqEG eng inop req ˙ w = ( N N ) ˙ w K reqEG eng inop req ffd ˙ ˙ F = F m V = m ( V V ) n g req req j F = ( N N ) F N EG eng inop N where V is the engine jet exhaust velocity. The specific j power is SP = P / ˙ m , the specific thrust is ST = F / ˙ m , D = ( N N ) D G aux EG eng inop aux ˙ and the specific fuel consumption is here sfc = w / P .
The fuel flow has been multiplied by a factor K ffd accounting for deterioration of the engine efficiency.
Turboshaft Engine Turboshaft engine performance is obtained from the Installation Referred Parameter Turboshaft Engine Model (RPTEM).
The difference between installed and uninstalled power is the inlet and exhaust losses P . The installed gross jet loss Power Available thrust is F = K F , where K accounts for exhaust G fgr g frg Given the flight condition and engine rating, the power ˙ effects. The net jet thrust is F = F m V . The N G req available P is calculated from the specific power a momentum drag of the auxiliary air flow is a function of ˙ SP = P / ˙ m and mass flow m : a a a a ˙ ˙ the mass flow m = f m : aux aux req SP a = SP g ( , M , n ) ˙ D = (1 ) ˙ m V = (1 ) f m V 0 sp aux aux aux aux aux req ˙ m where is the ram recovery efficiency.
a aux ˙ = m g ( , M , n ) 0 m / Convertible Engine: Turbojet/Turbofan P a = P g ( , M , n ) 0 p The engine mode B is the mass flow fraction diverted for a convertible engine: B = 0 for all mass flow to the power as functions of temperature ratio = T / T , Mach number turbine (turboshaft operation), and B = 1 for all mass flow M , and referred engine turbine speed n = N / .
to the jet exhaust or a fan (turbojet/turbofan operation). A Installation losses are subtracted ( ), and the P = P P separate engine model defines the performance for av a loss mechanical limit is applied.
turbojet/turbofan operation (not all parameters of which are used; in particular, there is only one value for the size The power available of the engine group is obtained by P ). The engine group power P is a measure of the eng reqEG multiplying the single engine power by the number of jet thrust, and this engine does not contribute to the engines operational (total number of engines less propulsion group shaft power available. The inoperable engines), including a specified power fraction turbojet/turbofan thrust is the engine group net jet thrust, f : P = f ( N N ) P (typically to implement a P avEG P eng inop av ˙ F = F m V .
N G req power margin).
Convertible Engine: Reaction Drive Performance at Power Required The engine mode B is the mass flow fraction diverted for The power required of a single engine is obtained from the a convertible engine: B = 0 for all mass flow to the power engine group power: P = P /( N N ) ; and req reqEG eng inop turbine (turboshaft operation), and B = 1 for all mass flow installation losses are added, P = P + P . The engine q req loss to the rotor (reaction jet operation). A separate engine performance is calculated for a specified power required model defines the engine performance for reaction jet P and flight condition: q operation (not all parameters of which are used; in ˙ m req particular, there is only one value for the size P ). The eng ˙ = m g ( q , , M , n ) 0 C m engine group power is obtained from the rotor power / ˙ ( P = P ), and this engine does not contribute to the w req reqEG react ˙ = w g ( q , , M , n ) 0 C w propulsion group shaft power available. The gross jet thrust is zero, so the net thrust is the momentum drag, F g ˙ = F g ( q , , M , n ) F = m V .
g 0 C f N req ˙ m N / N req spec ˙ ˙ = m g m Reciprocating Engine 0 C m 0 C / Reciprocating engine performance is described in Ref. 7.
˙ w req The work per cycle is W = Pn / R , where R is the ˙ ˙ = w g w q c 0 C w 0 C rotational speed (rev/sec), n is the revolutions per cycle c F g (2 for a 4-stroke engine, 1 for a 2-stroke engine), and = F g 0 g 0 C f R / n is the cycles per second. The engine displacement is c V (volume). The mean effective pressure is defined as d where q = P /( P ) .
q 0 C W Pn / R Qn 2 c c mep = = = V V V Compressor d d d A compressor converts input shaft power to a jet velocity from the power ; so is the specific P = NQ = 2 RQ mep and thrust. The shaft power contributes to the propulsion torque. The engine output is the brake horsepower (BHP), group power required. The compressor does not use fuel.
which equals indicated power (IHP) less friction power (FHP): Given the flight condition and engine rating, the power available P is calculated from the specific power a BHP = IHP–FHP = IHP – (MHP+PHP+CHP+AHP–THP) ˙ SP = P / ˙ m and mass flow m : a a a a The friction power is composed of losses due to SP a = SP g ( , M , n ) mechanical friction (MHP), pumping (PHP, the work of 0 sp the piston during inlet and exhaust strokes), compressor or ˙ m a ˙ supercharger (CHP), auxiliary or accessories (AHP, such = m g ( , M , n ) 0 m / as oil pump, water pump, cooling fan, generator), and P a exhaust turbine (THP, treated as negative friction). The = P g ( , M , n ) 0 p mechanical efficiency is = BHP/IHP. The sum of airflow ˙ ˙ ˙ and fuel flow is the charge flow: w = w + w . The fuel- c f a as functions of = T / T , M , and referred compressor ˙ air ratio is F = w / ˙ w . The mass flow is f a speed n = N / . The power available of the engine ˙ ˙ m = e m = e V ( R / n ) ; so mep ( P / ˙ m ) . The v ideal v d c group is P = f ( N N ) P , including a avEG P eng inop av indicated power is the product of the fuel flow, fuel specified power fraction f .
P specific energy ( e = JQ , from the heat of combustion fuel c The power required of a single compressor is Q and Joule's constant J relating work and heat), and c P = P /( N N ) . Accounting for installation thermal efficiency: ˙ . These equations have req reqEG eng inop P = e w I fuel th losses gives the uninstalled power required constant factors when conventional units are used.
P = P + P . The compressor performance at P is: q req loss q The maximum brake mean effective pressure is typically ˙ 2 2 m req 125–250 lb/in (850–1700 kN/m ). Typical brake specific ˙ = m g ( q , , M , n ) 0 C m ˙ fuel consumption is bsfc = w / P = 0.38 to 0.45 lb/hp-hr. / ˙ Typically the volumetric efficiency e = m / ˙ m = 0.8 to ST v ideal req = ST g ( q , , M , n ) 0 C st 0.9.
F The power available P is calculated from the specific g a = F g ( q , , M , n ) g 0 C f ˙ power SP = P / ˙ m and mass flow m : a a a a SP mep as functions of q = P /( P ) , = T / T , M , and a q 0 C 0 = SP g 0 sp n = N / . The specific thrust gives the gross thrust, N / N F = ( ST ) ˙ m . The performance of the engine group is: ˙ m spec g a ˙ ˙ = m g m 0 m 0 / ˙ m = ( N N ) ˙ m reqEG eng inop req Installation losses are subtracted from P , and the F = ( N N ) F a N EG eng inop N mechanical limit is applied. The engine performance at P q D = ( N N ) D aux EG eng inop aux is: P = ( N N ) P K comp eng inop q ffd The component power is the product of the uninstalled and a factor K accounting for deterioration of the ffd power required and the number of operational engines, engine efficiency.
and a factor K accounting for deterioration of the ffd Generator-Motor engine efficiency.
The engine mode B is the direction of power flow for a Compressor for Reaction Drive generator-motor: B positive for motor operation, and B If the compressor supplies the jet force for rotor reaction negative for generator operation. Separate motor models drive, then the engine group power required is obtained are used for the two modes (not all parameters of which from the rotor power: P = P . The gross jet thrust are used; in particular, there is only one value for the size reqEG react is zero, so the net thrust is the momentum drag, P ).
eng ˙ F = m V .
N req Motor and Fuel Cell A motor with a fuel cell burns a fuel (typically hydrogen) Electric Motor or Generator to produce electrical energy, which is converted to shaft A motor converts electrical energy (fuel) to shaft power. A power. The device can also be modeled as separate motor generator converts input shaft power to electrical energy.
and fuel cell components, with a battery (fuel tank) to The uninstalled shaft power contributes to the propulsion transfer the electrical energy.
group power required.
The engine performance is calculated for P and a q The power available is related to the size P . Given the eng specified flight condition: flight condition, the uninstalled power available is P a calculated. The installed power available is P = P ˙ ˙ ˙ m = m g ( q , n ) = K w av a i req 0 C m mf req (where is the efficiency). Then the mechanical limit is i ˙ ˙ w = w g ( q , n ) = sfc P req 0 C w q applied. The power available of the engine group is P = f ( N N ) P , including a specified power as a function of q = P / P and n = N / N . The net avEG P eng inop av q eng spec ˙ fraction f . thrust is the inlet momentum drag, F = m V . The P N req performance of the engine group is From the engine group power required P , the power reqEG ˙ m = ( N N ) ˙ m required of a single engine is P = P /( N N ) .
reqEG eng inop req req reqEG eng inop The uninstalled power required is P = P / .
˙ w = ( N N ) ˙ w K q req i reqEG eng inop req ffd Motor F = ( N N ) F N EG eng inop N The motor power required determines the energy flow D = ( N N ) D aux EG eng inop aux from the fuel tank. The energy flow is calculated for P q ˙ ˙ The fuel flow has been multiplied by a factor K and a specified flight condition: E = E g ( q , n ) as a ffd req 0 C e accounting for deterioration of the engine efficiency.
function of q = P / P and engine speed n = N / N .
q eng spec The performance of the engine group is ˙ ˙ JET GROUP E = ( N N ) E K . The energy flow has reqEG eng inop req ffd been multiplied by a factor K accounting for A jet group produces a force on the aircraft, possibly used ffd deterioration of the engine efficiency. for lift, propulsion, or control. A jet model describes a particular jet, used in one or more jet groups. The models Generator include turbojet and turbofan engines (perhaps The generator energy flow to the fuel tank defines the convertible, for reaction drive), reaction drive, and a power required. The energy flow is calculated for P and simple force. A reaction drive supplies a blade force that q ˙ ˙ a specified flight condition: E = E g ( q , n ) as a provides the rotor power required.
req 0 C e function of q = P / P and engine speed n = N / N .
q eng spec The jet size is described by the thrust T , which is the jet The performance of the engine group is sea-level static thrust available per jet at a specified ˙ ˙ E = ( N N ) E takeoff rating. The number of jets N is specified for reqEG eng inop req jet each jet group.
P = ( N N ) P K comp eng inop q ffd The uninstalled thrust required is T , and the thrust q The component power is the product of the uninstalled available T . The jet model calculates T as a function of a a power required and the number of operational engines, flight condition and engine rating; or calculates mass flow ST and fuel flow at T . The specific thrust is ST = T / ˙ m , and a q = ST g ( , M ) 0 st ˙ the specific fuel consumption is here sfc = w / T . The forces produced by mass flow that does not go through the ˙ m a ˙ = m g ( , M ) 0 m core or fan are treated as momentum drag D .
aux / T a = T g ( , M ) 0 t Turbojet or Turbofan The thrust of a turbojet is as functions of temperature ratio = T / T and Mach ˙ T = m ((1 + f ) V V ) + ( p p ) A number M . Installation losses are subtracted e e atm e ( T = T T ), and the mechanical limit is applied. The av a loss ˙ ˙ where m is the mass flow; f = w / ˙ m is the fuel-air ratio; thrust available of the jet group is obtained by multiplying and V , p , A are the velocity, pressure, and area at the e e e the single jet thrust by the number of jets operational (total exit. The pressure term is zero or small, and the fuel-air number of jets less inoperable jets), including a specified ratio is small, so the net thrust is approximately thrust fraction f : T = f ( N N ) T (typically T avJG T jet inop av ˙ ˙ T = m ( V V ) , from the gross thrust T = mV and the e G e to implement a thrust margin).
˙ inlet-momentum or ram drag mV .
Performance at Thrust Required The thrust of a turbofan is The thrust required of a single jet is ˙ ˙ T = m ((1 + f ) V V ) + m ( V V ) e fan e fan T = T /( N N ) . Installation losses are added req reqJG jet inop ˙ ˙ = m ((1 + f ) V + V ) m (1 + ) V e e fan to get the uninstalled thrust required ( T = T + T ).
q req loss ˙ with bypass ratio = m / ˙ m .
The jet performance is calculated for a specified thrust fan required T and flight condition: q The difference between net and gross thrust is the ˙ ˙ m momentum drag: T = T m ( ST ) , where req N G mom ˙ = m g ( t , , M ) 0 C m ( ST ) = (1 + ) V for a turbojet or turbofan, or mom / ( ST ) = r for a reaction drive.
˙ mom react w req ˙ = w g ( t , , M ) 0 C w Turbojet or turbofan performance is obtained from the Referred Parameter Jet Engine Model (RPJEM), based on as functions of t = T /( T ) (or referred gross thrust), q 0 C Refs. 8 and 9. The referred thrust, specific thrust = T / T , and M . The performance of the jet group is: ˙ ST = T / ˙ m , and specific fuel consumption sfc = w / T are ˙ m = ( N N ) ˙ m functions of the flight Mach number M and compressor reqJG jet inop req speed n = N /( N ) : ˙ w = ( N N ) ˙ w K reqJG jet inop req ffd T D = ( N N ) D = G ( M , n ) aux JG jet inop aux t The fuel flow has been multiplied by a factor K T / ˙ m ffd = G ( M , n ) st accounting for deterioration of the jet efficiency.
˙ w / T 1 Convertible Engine: Reaction Drive = G ( M , n ) sfc b The jet mode B is the mass flow fraction diverted for a The independent variable can be the compressor speed, or convertible engine: B = 0 for all mass flow to the exhaust the turbine inlet temperature, or the fuel flow. The (turbojet operation), and B = 1 for all mass flow to the combustion efficiency depends on the atmosphere rotor (reaction jet operation). A separate jet model defines b (altitude and temperature), hence the specific fuel the engine performance for reaction jet operation (not all consumption is not a function of just M and n . parameters of which are used; in particular, there is only one value for the size T ). The jet thrust required is jet Thrust Available T = F = P / r . The mass flow and fuel reqJG react rotor react Given the flight condition and engine rating, the thrust flow follow. The jet group net thrust is the inlet available T is calculated from the specific thrust ˙ momentum drag, F = m V .
a N req and mass flow ˙ : ST = T / ˙ m m a a a a ˙ ˙ E = E K /( N N ) req reqCG ffd chrg inop Reaction Drive The energy flow has been multiplied by a factor K ffd The jet group performance for reaction drive includes the accounting for deterioration of the charger efficiency. The blade duct and nozzle, perhaps even with tip burning. The ˙ ˙ uninstalled energy flow required is E = E / , where q req i rotor power required P gives the required force on the rotor is the installation efficiency. The cell energy flow i rotor blade ˙ at F = P / r = m ( V r ) react rotor react react react react ˙ required E is obtained from the uninstalled energy q cell effective radial station r . The net jet group thrust react ˙ flow. Then P = ( N N ) E is the total cell ˙ req total chrg inop q cell required is T = F = T m r . T is the reqJG react G reqJG react G power required.
gross thrust. From P , the jet performance (mass flow reqJG and fuel flow) is calculated. The jet group net thrust is the Fuel Cell ˙ inlet momentum drag, F = m V .
N req A fuel cell burns a fuel (typically hydrogen) and generates electrical energy. The cell energy flow is calculated for Simple Force ˙ ˙ ˙ E and a specified flight condition: E = E g ( q ) , q q cell 0 e For the simple force model, the design maximum thrust is ˙ where q = E / P . The fuel cell performance is obtained q 0 (per jet). The thrust available is thus . The T T = T max a max ˙ from E , or q cell force generation can use fuel as weight or as energy.
˙ ˙ m = m g ( q ) req 0 C m If the component burns fuel weight, the fuel flow is ˙ ˙ w = w g ( q ) calculated from an input thrust-specific fuel consumption: req 0 C w ˙ ˙ w = T (sfc) = w q , where q = T / T . Then req q 0 C q max ˙ The net thrust is the inlet momentum drag, F = m V .
N req ˙ w = ( N N ) ˙ w K .
reqJG jet inop req ffd The performance of the charge group is If the component uses fuel energy, the energy flow is ˙ m = ( N N ) ˙ m reqCG chrg inop req calculated from an input thrust-specific fuel consumption: ˙ w = ( N N ) ˙ w ˙ ˙ reqCG chrg inop req E = T (sfc) = E q , where q = T / T . Then req q 0 C q max ˙ ˙ E = ( N N ) E K .
reqJG jet inop req ffd F = ( N N ) F N CG chrg inop N The simple force weight is calculated from specific D = ( N N ) D aux CG chrg inop aux weight S plus a fixed increment: W = ST + W .
max The momentum drag of the auxiliary air flow is a function ˙ ˙ of the mass flow m = f m : aux aux req CHARGE GROUP ˙ A charge group generates energy for the aircraft. A D = (1 ) ˙ m V = (1 ) f m V aux aux aux aux aux req charger model describes a particular charger, used in one where is the ram recovery efficiency.
aux or more charge groups. The models include fuel cells and solar cells.
Solar Cell The charger size is described by the power , which is P chrg The power available from solar radiation is approximately the sea-level static power available per charger at a 1.36 kW/m , reduced by atmospheric effects (absorption, specified takeoff rating. The number of chargers is N chrg reflection, scattering) to about 1.00 kW/m . The average specified for each charge group.
solar radiation in the continental United States is 3.5–7.0 (kW/m )(hour/day), hence approximately 15 to 25% of the Given the flight condition and the charger rating, the cell ˙ available power. Typical efficiencies of solar cells are 10– power available is E = P . The total cell power a cell 0 35%, with some sensitivity to temperature. The solar cell available is obtained by multiplying the single charger is characterized by power density (W/m ) and weight power by the number of chargers operational (total density (kg/m ).
number of chargers less inoperable chargers): ˙ ˙ The cell energy flow is calculated for E and a specified P = f ( N N ) E q av total P chrg inop a cell ˙ ˙ ˙ flight condition: E = E g ( q ) , where q = E / P .
q cell 0 e q 0 including a specified power fraction f .
P COMPONENT MODELS The energy flow to the fuel tank gives the charge group ˙ power required: P = E . The energy flow The engine group, jet group, and charge group provide a reqCG reqCG required of a single charger is general framework for the propulsion system components.
For each group, an engine, jet, or charger model is used to evaluate performance and weight. A model can be used by either engine rating or engine power required. These more than one group. The performance of each component curve-fits, typically based on real engines, are scaled to is described by a number of quantities ( ) that depend on the required size and adjusted to the appropriate g power or thrust, atmosphere, speed, and other parameters. technology level to represent a notional engine. Engine A component model has a specific functional form for size is represented by mass flow. Engine technology is each quantity, typically piecewise linear or polynomial represented by specific power available and specific fuel functions of the independent parameters. The objective is consumption at maximum continuous power (MCP), sea to find a parameterized, surrogate representation of the level standard day (SLS), static (zero airspeed) conditions.
component performance and weight, applicable to a wide Engine installation effects (inlet and exhaust losses) are range of operating conditions and component size. also modeled.
The engine group models implemented are the Referred The power available P is calculated for the flight a Parameter Turboshaft Engine Model (RPTEM), condition and engine rating. The specific power and ˙ compressor model, and motor/generator model. The jet referred mass flow (at N , relative to SP and m for spec 0 0 group model implemented is the Referred Parameter Jet this rating) are approximated by functions of the ambient Engine Model (RPJEM), in addition to the simple force temperature ratio and inlet ram air ratios: model. The charge group models implemented are fuel X spa SP ( N ) = SP K
[ ]
cell and solar cell models. There is also a battery model, a spec 0 spa M M associated with fuel tank systems that store and burn X K mfa mfa ˙ ˙ m ( N ) = m ( / ) e
a spec 0 M M [ ]
energy.
where the static lapse rate ( K , K ) and ram air spa mfa REFERRED PARAMETER TURBOSHAFT ENGINE exponents ( X , X ) are piecewise linear functions of spa mfa MODEL . The power available is then ˙ . The P = SP m a a a Aircraft gas turbine engine performance capabilities are uninstalled power available at N is calculated, installation formally specified by computer programs known as engine losses are subtracted, and the mechanical limit is applied.
decks, which are created by engine manufacturers in an The engine performance (mass flow, fuel flow, and gross industry-standard format. Engine decks are typically based jet thrust) is calculated for the power required P , flight q on thermodynamic cycle analysis using real engine condition, and engine rating. Uninstalled power at component performance maps. The most important specification turbine speed P ( N ) is obtained from q spec performance maps for turboshaft engines are compressor, P ( N ) . The referred quantities (relative to SLS static q gas generator turbine, and power turbine. These MCP quantities) are approximated by cubic functions of component performance maps are critical to obtaining q = P ( N ) /( P ) : q spec 0 C realistic off-design engine performance. Design and analysis codes calculate aircraft performance for a very ˙ ˙ w = w ( )( K + K q req 0 C ffq 0 ffq 1 wide range of operating conditions. Thus engine X 2 3 ffq + K q + K q )
[ ]
ffq 2 ffq 3 M performance must be realistic even far from the engine design point. A simple thermodynamic cycle analysis that ˙ ˙ m = m ( / )( K + K q req 0 C mfq 0 mfq 1 assumes design point component efficiencies everywhere X 2 3 mfq + K q + K q )
[ ]
mfq 2 mfq 3 M is not realistic for such an application. Rather than F = F ( K + K q developing models for component performance, the g g 0 C fgq 0 fgq 1 approach taken is to use a model for the total engine X 2 3 fgq + K q + K q )
[ ]
fgq 2 fgq 3 M performance. The engine is not being designed.
˙ at N , with w = sfc P . The mass flow and fuel spec 0 C 0 C 0 C The Referred Parameter Turboshaft Engine Model flow are primarily functions of the gas power, and are (RPTEM) is based on curve-fits of performance data for assumed to be independent of turbine speed. Then the existing or projected engines over a range of operating installed net jet thrust F and momentum drag D are N aux conditions. The curve-fits are typically obtained by calculated.
exercising an engine deck. The use of referred parameters tends to collapse the data, and provides a basis for scaling The parameters of the engine model can be defined for a the engine. The operating condition is described by specific engine, but scaling the parameters as part of the pressure altitude, ambient air temperature, flight Mach aircraft sizing task is also neceaary, in order to define an number, power turbine speed, exhaust nozzle area, and engine for a specified power. In addition, advanced ˙ F = ST m = F ( K + K q technology must be represented in the model. Scaling and G req req g 0 C mfq 0 mfq 1 advanced technology are handled in terms of specific X + X 2 3 stq mfq
+ K q + K q ) [ ]
mfq 2 mfq 3 M power and specific fuel consumption (at SLS static conditions, MCP, and N ).
Then the installed net jet thrust F and momentum drag spec N D are calculated. The influence of compressor aux The engine weight can be calculated as a function of rotational speed is not considered.
power, or scaled with engine mass flow. As a function of power, the weight of one engine is The compressor weight can be calculated as a function of X power: eng W = K + K P + K P one eng 0eng 1eng 2eng X comp W = K + K P + K P one eng 0comp 1comp 2comp where P is the installed takeoff power per engine.
where P is the installed power (SLS static, specified Alternatively, the specific weight SW = P / W can be rating) per compressor.
˙ scaled with the mass flow m .
0 C MOTOR MODEL COMPRESSOR MODEL A motor converts electrical energy (fuel) to shaft power. A A compressor converts input shaft power to a jet velocity generator converts input shaft power to electrical energy.
and thrust. The shaft power contributes to the propulsion The model follows Refs. 10 to 12.
group power required. The compressor does not use fuel.
The power available is P = P . The motor power The operating condition is described by pressure altitude, a eng ˙ required determines the energy flow: E = P / , where ambient air temperature, flight Mach number, and either req q the efficiency = includes the battery compressor rating or power required. The parametric batt motor discharging losses. The generator energy flow to the fuel model is scaled to the required size and adjusted to the ˙ tank is related to the power required: E = P , where appropriate technology level to represent a notional req q the efficiency includes the battery charging = compressor. Compressor size is represented by mass flow. batt motor losses.
Technology is represented by specific power available at maximum continuous power (MCP), sea level standard For a motor and fuel cell, the performance is calculated for day (SLS), static (zero airspeed) conditions.
a specified power required: The specific power and referred mass flow (relative to SP ˙ ˙ ˙ m = m ( q / ) = K w req 0 C mf req ˙ and m for this rating) are approximated by functions of ˙ ˙ w = w ( q / ) = sfc ( P / ) req 0 C 0C q the ambient temperature ratio , here just: The efficiency = includes both motor and fuel X spa cell motor SP = SP
[ ]
a 0 M M cell losses. The fuel cell efficiency as a function of power X is mfa ˙ ˙ m = m ( / )
a 0 M M [ ]
P 1 P 1 eng = 1 + 1 + c ˙ The power available is then P = SP m . The influence of a a a P P cell eng ref compressor rotational speed is not considered.
The ratio of mass flow and fuel flow ( K ) follows from mf The compressor performance (mass flow and gross jet the chemistry of the reaction.
thrust) is calculated for a specified power required P , q flight condition, and rating. The referred quantities Motor loss sources include copper (internal resistance, (relative to SLS static MCP quantities) are approximated proportional to current-squared hence torque-squared), by functions of q = P /( P ) : iron core (eddy current and hysteresis, proportional to q 0 C rotational speed), and mechanical (friction, proportional to ˙ ˙ m = m ( / )( K + K q req 0 C mfq 0 mfq 1 speed, and windage, proportional to speed-cubed). The X 2 3 mfq power loss is described as a polynomial in the motor
+ K q + K q ) [ ]
mfq 2 mfq 3 M torque and rotational speed: X stq ST = ST
[ ]
req 0 C M 3 3 i j P = P C t n
loss eng ij
The gross jet thrust is then j = 0 i = 0 X fft where q = P / P , n = N / N , t = q / n . Controller ˙ ˙
w = w ( )( K + K t + K t ) [ ]
q eng spec req 0 C fft 0 fft 1 fft 2 M losses, including power conversion and conditioning, are K X mft mft ˙ ˙ m = m ( / ) t
[ ]
req 0 C M represented by an efficiency . Then cont The mass flow given T /( T ) can be found analytically P q q 0 C q = = motor cont cont for K = 0, 1, or .
mft P + P q + P / P q loss loss eng The parameters of the jet model can be defined for a is the motor or generator efficiency. Constant efficiency specific turbojet or turbofan, but scaling the parameters as ( P = P ) implies just C = 1/ 1 . The copper, iron, loss q 11 part of the aircraft sizing task is also necesary. In addition, and windage losses imply advanced technology must be represented in the model.
2 3 P = K Q + K N + K N + K Scaling and advanced technology are handled in terms of loss c i w 0 specific thrust and specific fuel consumption.
but more terms are required in order to represent a peak in efficiency as a function of torque and speed.
The jet weight can be calculated as a function of thrust: X jet The motor weight can be calculated as a function of W = K + K T + K T one jet 0 jet 1jet 2 jet power: where T is the installed takeoff thrust (SLS static, X motor W = K + K P + K P specified rating) per jet.
one eng 0motor 1motor 2motor where P = P .
eng FUEL CELL MODEL A fuel cell burns a fuel (typically hydrogen) and generates REFERRED PARAMETER JET ENGINE MODEL electrical energy, which is stored in a fuel tank system or The Referred Parameter Jet Engine Model (RPJEM) is used directly by a motor. The energy flow defines the defined following the pattern of the RPTEM turboshaft power required. The power available is related to the size engine model. It based on curve-fits of performance data . The model follows Ref. 12.
P chrg for existing or projected jets over a range of operating conditions. The parametric model is scaled to the required Given the flight condition and the charger rating, the cell ˙ size and adjusted to the appropriate technology level to power available is E = P . The uninstalled power a cell 0 ˙ represent a notional jet. Jet size is represented by mass required E is defined by the charge group energy flow.
q ˙ ˙ flow. Jet technology is represented by specific thrust The cell power required is E = E / , where the q cell q available and specific fuel consumption.
efficiency = includes the battery charging batt chrg losses.
The thrust available T is calculated for the flight a condition and jet rating. The gross specific thrust and The fuel cell performance is calculated from the cell ˙ referred mass flow (relative to ST and m for this rating) power required: 0 0 are approximated by functions of the ambient temperature ˙ ˙ ˙ m = m ( q / ) = K w req 0 C mf req ratio , here just: ˙ ˙ ˙ w = w ( q / ) = sfc E req 0 C 0C q cell X sta ST = ST
[ ]
a 0 M M ˙ where , ˙ , ˙ ˙ . The q = E / P w = sfc P m = K w q 0 0 C 0 C chrg 0 C mf 0 C X mfa ˙ ˙ specific fuel consumption is given by the fuel specific m = m ( / )
a 0 M M [ ]
energy and the fuel cell thermal efficiency: .
sfc = e / fuel th Then The ratio of mass flow and fuel flow follows from the chemistry of the reaction. For hydrogen and air ˙ ˙ T = ST m m ( ST ) a a a a mom X + X sta mfa m A A A ˙ = T m ( ST ) K = = 68.59
[ ]
0 M M a mom mf x m H O H H is the thrust available.
The molar masses of hydrogen and air are 2.016 and m = H 28.97 g/mole; 0.2095 is the molar fraction of The jet performance is calculated for a specified thrust m = x = A O oxygen in air. The supply ratio is from required T , flight condition, and jet rating. The referred / = 1/ 2 A H q stoichiometry, and typically in practice.
quantities (relative to SLS static MCT quantities) are / 1.25 A H approximated by functions of referred gross thrust The fuel cell efficiency as a function of power is estimated ˙ t = ( T + m ( ST ) ) /( T ) : q mom 0 C considering an equivalent circuit, defined by internal resistance R and current I . The voltage is V = V IR . P 1 P 1 chrg 0 o 2 = 1 + P ( R / V ) + P / P = 1 + 1 + c o 0 The efficiency is = P /( P + P ) , from the power loss P P chrg loss chrg chrg ref P = I R + P . For small loss, I P / V . In terms of loss 0 o 1 So = (1/ + c ) at . The efficiency P = P , let P chrg ref chrg chrg decreases with P because of the internal resistance, but is 1 1 zero at P = 0 because of the internal current term.
R / V = 1 o P chrg ref Alternatively, the efficiency can be a fixed value.
P = cP 0 chrg BATTERY MODEL Then A battery is a fuel tank system for which the fuel quantity P stored and burned is measured in energy. The unit of fuel 1 P 1 2 chrg = 1 + P ( R / V ) + P / P = 1 + 1 + c o 0 energy is Mega-Joules (MJ). The operating state affects P P chrg chrg ref the efficiency of the relation between useful power and the 1 So = (1/ + c ) at . The efficiency P = P chrg ref chrg rate of change of the energy stored. Efficiency of charge decreases with P because of the internal resistance, but is and discharge is accounted for in the model of the device zero at P = 0 because of the internal current term.
supplying or using the energy (motor, generator, or fuel Alternatively, the efficiency can be a fixed value.
cell). The battery model can be used for capacitors and flywheels as well.
The fuel cell weight can be calculated as a function of power: The battery capacity is E (maximum usable fuel fuel-cap X energy). The battery is characterized by specific energy cell W = K + K T + K T one chrg 0cell 1cell 2cell e (MJ/kg) and energy density (MJ/liter), so the tank tank where .
P = P chrg tank weight and volume are obtained from the capacity.
The current amount of energy stored is E . The state-of- fuel SOLAR CELL MODEL charge is s = E / E . The useable state-of-charge is fuel fuel-cap A solar cell generates electrical energy, which is stored in typically 20–30% of capacity, and can be accounted for a fuel tank system. The energy flow defines the power either as a factor on specific energy and energy density, or required. The power available is related to the size .
P as a factor on capacity.
chrg The solar cell is characterized by power density e solar The model follows Ref. 12. A battery stores charge (A-hr), 2 2 (W/m ) and weight density (kg/m ). From the size solar so the capacity is expressed as energy for a nominal , the area is ; and then the weight P A = P / e chrg solar chrg solar voltage. The rated capacity is described as C (A-hr) at is W = W = A .
one chrg solar solar solar current I = xC (A), hence for a discharge time of 1/ x Given the flight condition and the charger rating, the cell hours. A typical specification is for 20-hour discharge.
˙ power available is E = P . The uninstalled power The capacity depends on the discharge current. The a cell 0 ˙ k k 1 required E is defined by the charge group energy flow.
Peukert model assumes I T = I C = constant , where T is q ˙ ˙ The cell power required is E = E / , where the the discharge time for current I . The Peukert coefficient q cell q efficiency = includes the battery charging k = 1.2 to 1.3 for lead-acid batteries, and k = 1.01 to 1.05 batt chrg losses.
for lithium-ion batteries (weak dependence). Thus the k 1 capacity (A-hr). The charge capacity C = C ( I / I ) ref ref The solar cell efficiency as a function of power is does not change, but for a larger current the battery estimated considering an equivalent circuit, defined by reaches a specified discharge voltage sooner (due to internal resistance R and current I . The voltage is internal resistance), hence effectively has a reduced V = V IR . The efficiency is = P /( P + P ) , from o chrg loss 2 capacity as long as that current is maintained. This effect the power loss P = I R + P . For small loss, I P / V .
loss 0 o is assumed to be accounted for in the discharge efficiency In terms of , let P chrg value.
1 1 R / V = 1 The power density (kW/kg) generally varies o batt P chrg ref inversely with specific energy (MJ/kg or kW-hr/kg). The P = cP 0 chrg battery power limit ( ) is compared to the P = W batt batt batt charge or discharge energy rate. No other limits are Then considered.
The discharge or charge efficiency as a function of power – Reaction drive is estimated considering an equivalent circuit, defined by – Convertible turbojet: reaction drive internal resistance R and current I . The voltage is Charge group models: V = V IR . The open circuit voltage V is a function of o o – Fuel cell the state-of-charge s = E / E : V = f ( s ) V , fuel fuel-cap o v 100 – Solar cell where V is the voltage at s = 100%. The efficiency is – Battery = P /( P + P ) , from the power loss P = I R + P .
batt loss loss 0 Each model is a surrogate representation of the component For small loss, I P / V = I / f V . In terms of a o v 100 performance and weight. The Referred Parameter reference power, let Turboshaft Engine Model (RPTEM) has proven to be a 1 1 good representation for the design code NDARC. The R / V = 1 P ref ref other models are new to the design code. The models P = cP described in this paper are sufficient to start designing 0 ref rotorcraft and airplanes, but the needed for further Then development and additional information is expected.
1 P 1 P ref For air-breathing propulsion components, the new models = 1 + P ( R / V ) + P / P = 1 + 1 + c o 0 P P f batt ref have been implemented with simple dependence on ref v atmospheric conditions and flight speed. Based on the 1 So = (1/ + c ) at and 100% charge. The P = P batt ref ref turboshaft engine model, more elaborate models likely efficiency decreases with P because of the internal will be needed in order to adequately cover the full range resistance, but is zero at P = 0 because of the internal of operating conditions. Reaction drive and convertible current term. Alternatively, the efficiency can be a fixed engines may ultimately require further complexities in the value.
model. Surrogate models likely will be developed from The efficiency is = P / P P /( P + P ) for detailed engine performance data, as for RPTEM.
batt out store loss ˙ discharge. For energy rate E , the power available is For electrical propulsion components appropriate to ˙ P = E . For charge, the efficiency is batt aircraft, a database of performance characteristics is = P / P P /( P + P ) . For input power P , the batt store in loss needed in order to identify the parameters required by the ˙ energy rate is E = P .
batt models.
For all components, a database is needed that will support CONCLUDING REMARKS development of parametric models of weights. Also, the The propulsion system representation in the rotorcraft influence of technology on performance and weights must conceptual design code NDARC has been extended. A be characterized.
major objective is to be able to develop environmentally- Separate tools, not part of the aircraft design code, are friendly rotorcraft designs, for example aircraft utilizing needed to design the propulsion components. The electric motors, or electrical energy storage, or hydrogen- Numerical Propulsion System Simulation (NPSS, Ref. 13) burning engines.
is currently used for turboshaft engine design, and NPSS Engine groups, jet groups, and charge groups provide a can design turbojet and turbofan engines. Reaction drives general framework for the propulsion system components for rotorcraft have been extensively investigated, so there in NDARC. For each group, an engine, jet, or charger are resources on which a design tool can be based (Refs.
model is identified. The following models have been 14 and 15). Extending design tools for electrical implemented.
machinery to rotorcraft applications should be possible.
Engine group models: REFERENCES – Referred Parameter Turboshaft Engine Model ( RPTEM ) 1) Johnson, W. “NDARC. NASA Design and Analysis of – Reciprocating engine Rotorcraft.” NASA TP 2009-215402, December 2009.
– Convertible turboshaft: turbojet/turbofan; reaction drive – Compressor, including reaction drive 2) Johnson, W. “NDARC — NASA Design and Analysis – Motor, generator, generator-motor of Rotorcraft. Theoretical Basis and Architecture.” American Helicopter Society Specialists' Conference on Jet group models: Aeromechanics, San Francisco, CA, January 2010.
– Referred Parameter Jet Engine Model ( RPJEM ) 3) Johnson, W. “NDARC — NASA Design and Analysis NOMENCLATURE of Rotorcraft. Validation and Demonstration.” American Helicopter Society Specialists' Conference on Acronyms and Subscripts Aeromechanics, San Francisco, CA, January 2010.
CG charge group 4) Department of Defense Military Specification.
EG engine group “Glossary of Definitions, Ground Rules, and Mission ISA International Standard Atmosphere Profiles to Define Air Vehicle Performance Capability.” JG jet group MIL-STD-3013A, September 2008.
MCP maximum continuous power MCT maximum continuous thrust 5) Department of Defense Detail Specification. “Turbine MRP maximum rated power Fuel, Aviation, Grades JP-4 and JP-5.” MIL-DTL-5624U, OEI one engine inoperative September 1998.
PG propulsion group 6) Department of Defense Detail Specification. “Turbine RPJEM referred parameter jet engine model Fuel, Aviation, Kerosene Type, JP-8 (NATO F-34), RPTEM referred parameter turboshaft engine model NATO F-35, and JP-8+100 (NATO F-37).” MIL-DTL- SLS sea level standard 83133H, October 2011.
Propulsion 7) Taylor, C.F. The Internal-Combustion Engine in Theory P power and Practice. Volume 1: Thermodynamics, Fluid Flow, E energy Performance . Second edition. Cambridge, MA: MIT T thrust Press, 1985.
F force ˙ 8) Sanders, N.D. “Performance Parameters for Jet- m mass flow ˙ Propulsion Engines.” NACA TN 1106, July 1946. w fuel flow ˙ E energy flow 9) Hill, P.G., and Peterson, C.R. Mechanics and W weight Thermodynamics of Propulsion . Reading, MA: Addison- P power required, propulsion group reqPG Wesley Publishing Company, Inc., 1965.
P power required, engine group reqEG 10) McDonald, R.A. “Electric Motor Modeling for T thrust required, jet group reqJG Conceptual Aircraft Design.” AIAA Paper No. 2013-0941, P power required, charge group reqCG January 2013.
P power available, propulsion group avPG T thrust available, jet group avJG 11) Sinsay, J.D.; Alonso, J.J.; Kontinos, D.A.; Melton, P power available, charge group avCG J.E.; and Grabbe, S. “Air Vehicle Design and Technology P power available, engine group avEG Considerations for an Electric VTOL Metro-Regional P component power required comp Public Transportation System.” AIAA Paper No. 2012- B component mode 5404, September 2012.
K efficiency deterioration factor ffd 12) Datta, A., and Johnson, W. “Requirements for a Engine Hydrogen Powered All-Electric Manned Helicopter.” P sea level static takeoff power per engine AIAA Paper No. 2012-5405, September 2012.
eng N number of engines in engine group eng 13) Claus, R.W.; Evans, A.L.; Lytle, J.K.; and Nichols, N number of inoperative engines inop L.D. “Numerical Propulsion System Simulation,” P power available, installed av Computing Systems in Engineering , Vol. 2, No. 4, 1991.
P power available, uninstalled a 14) Nichols, J.B. “The Pressure-Jet Helicopter Propulsion P power required, installed req System.” The Aeronautical Journal , Vol. 76, No. 741 P power required, uninstalled q (September 1972). P installation losses loss SP specific power, P / ˙ m 15) Bachmann, B.A. “Power Available Calculation ˙ sfc specific fuel consumption, w / P Procedure and Operational Aspects of a Tipjet-Propelled F gross jet thrust G Rotor System.” American Helicopter Society 26th Annual net jet thrust F N National Forum, Washington, D.C., June 1970.
D momentum drag aux N turbine speed P total cell power available av total P total cell power required req total Jet installation efficiency T sea level static takeoff thrust per jet jet Fuel Tanks N number of jets in jet group jet N number of inoperative jets W fuel capacity, maximum usable fuel weight inop fuel cap T thrust available, installed E fuel capacity, maximum usable fuel energy av fuel cap T thrust available, uninstalled a Environment and Operation T thrust required, installed req density T thrust required, uninstalled q p pressure installation efficiency T temperature, deg R or deg K ST specific thrust, T / ˙ m pressure ratio p / p ˙ sfc specific fuel consumption, w / T 0 temperature ratio T / T D momentum drag 0 aux V aircraft velocity magnitude turbofan bypass ratio aircraft Mach number M Charger W design gross weight D P sea level static takeoff power per charger W empty weight chrg E N number of engines in charge group W fuel weight chrg fuel N number of inoperative chargers inop