WOLFRAM SYSTEM MODELER

TurbopropEngine

Turboprop engine: unparameterized

Diagram

Wolfram Language

In[1]:=
SystemModel["Aircraft.Physical.FixedWing.Parts.Propulsions.Engines.TurbopropEngines.TurbopropEngine"]
Out[1]:=

Information

This turboprop engine model extends the EngineBase model and models the thrust, drag and mass properties (if weight estimation method is used) of a turboprop engine.

Parameters

The required parameters for the turboprop engine model are listed in the Propulsion tab, as shown in Figure 1.


Figure 1: Required input parameters for turboprop engine model.

Should the value of any of the estimated properties listed in the Estimated Properties parameter tab be known (such as engine mass, nacelle length or diameter), the equations can be bypassed by entering the known value directly to the respective parameter input field. Similarly, if the surface roughness height of the nacelles is known, its value can be entered inside the Aerodynamic Coefficients tab. Otherwise its value is propagated from the global surface roughness height declared in AircraftBase.

The remaining parameters listed in the Propagated Properties tab are propagated from the AircraftBase as the propulsion system is compiled in TurbopropPropulsion, and thus they can and should be left unchanged.

Thrust Available

The thrust available (Tavail) for turboprop engines is solved through dividing the power available (Pavail) by the total velocity (vtot), and the factors for representing the propeller (ηprop) and power transmission efficiencies (ηmech) are also added, thus

.

For solving the power available, a relation presented by Anderson [1] is used

,

where P0 is the engine power at sea level, ρalt is air density at flight altitude and ρ0 is air density at sea level.

Fuel Consumption

The parameter for brake-specific fuel consumption (BSFC) is propagated to the energySystem component, where fuel consumption calculations are performed.

Drag Due to Nacelle

For solving the parasite drag coefficient (CD,0,nac) of different components in the aircraft, including the engine nacelles, the component buildup method presented by Raymer [2] is used, defined as

,

where the nacelle form factor (FFnac) and the nacelle wetted area (Swet,nac) are functions of the estimated (or entered, if known) values of nacelle diameter and length. The nacelle dimensions are estimated through empirical relationships as a function of the engine static thrust. However, the performance of a turboprop engine is described by its power at sea level rather than the static thrust. To derive a static thrust value for turboprop engine, a relation presented by Sforza [3] is used

,

where dprop is the propeller diameter. Thus, the more powerful the engine and the larger the propeller, the larger the parasite drag coefficient.

The skin friction coefficient (Cf,nac) is a function of the nacelle surface roughness height, Mach number and the Reynolds number for the flow over the nacelle, and thus the air compressibility effects are included in the drag calculations. The complete derivation of the CD,0,nac can be found in section 3.3.1 in Reference [4].

The magnitude of the drag force itself (Dnac) is the parasite drag coefficient times the dynamic pressure (q) times the main wing reference area (Sref,w)

.

In this model, only the parasite drag of the nacelle is considered, and thus the drag force generated by the nacelle is invariable with the angle of attack. Consequently, the lift generated by the nacelle due to angle of attack is also omitted.

Mass Properties

If the weight estimation method is used and no mass properties are entered by the user, the engine mass is solved by using the empirical relationship based on the calculated Tstatic value, as presented by Isikveren [5].

The engine moments of inertia are estimated as if the engine were a solid cylinder with its estimated length and diameter. Hence, the center of mass of the engine is also estimated to be at the geometric center of this cylinder.

The full derivations of the estimated engine mass and moments of inertia are also shown in Reference [4] in sections 3.4.4 and 3.6.1, respectively. 

References

[1]  Anderson, J. D. (2012). Aircraft Performance and Design. Mcgraw-Hill Higher.

[2]  Raymer, D. P. (1992). Aircraft Design: A Conceptual Approach, 2nd Ed. American Institute of Aeronautics and Astronautics.

[3]  Sforza, P. M. (2017). Theory of Aerospace Propulsion, 2nd Ed. Elsevier.

[4]  Erä-Esko, N. (2022). "Development and Use of System Modeler 6DOF Flight Mechanics Model in Aircraft Conceptual Design."
      Available atmodelica://Aircraft/Resources/Documents/EraeEskoThesis.pdf.

[5]  Isikveren, A. T. (2002). "Quasi-analytical Modelling and Optimisation Techniques for Transport Aircraft Design," Thesis, Institutionen för
      flygteknik, Department of Aeronautics.

Parameters (25)

weightEst

Value:

Type: Boolean

Description: true, if weight estimation method is used for masses, center of mass location and inertia tensor

bWing

Value:

Type: Length (m)

Description: Main wing span

SrefWing

Value:

Type: Area (m²)

Description: Main wing reference area

CADshapes

Value:

Type: Boolean

Description: true, if external CAD files are used for animation

negThrust

Value:

Type: Real

Description: Maximum negative thrust (0 to 1 of thrust available)

rho0

Value:

Type: Density (kg/m³)

Description: Air density at sea-level

Psealevel

Value:

Type: Power (W)

Description: Engine power at sea level

BSFC

Value:

Type: BrakeSpecificFuelConsumption (kg⋅W⁻¹⋅s⁻¹)

Description: Brake-specific fuel consumption in cruise

dProp

Value:

Type: Length (m)

Description: Propeller diameter

etaProp

Value:

Type: Real

Description: Propeller efficiency

etaEng

Value:

Type: Real

Description: Power transmission efficiency

kSkinNac

Value:

Type: Length (m)

Description: Nacelle surface roughness height

mNac

Value: 0.345 * 0.47 * mEngDry

Type: Mass (kg)

Description: Nacelle mass

mProp

Value: 6.13 * (Tstatic * N2kg) / 1000

Type: Mass (kg)

Description: Propeller mass

mEngDry

Value: 0.0117 * 1.2 * Tstatic ^ 1.0572

Type: Mass (kg)

Description: Engine dry mass

mEngInstalled

Value: mEngDry + mNac + mProp

Type: Mass (kg)

Description: Installed engine mass

xEngCM

Value: lNac / 2

Type: Length (m)

Description: Engine center of mass x-coordinate w.r.t. engine rear end

IxxEng

Value: mEngInstalled * (dNac / 2) ^ 2 / 2

Type: MomentOfInertia (kg⋅m²)

Description: Engine roll moment of inertia

IyyEng

Value: mEngInstalled * (dNac / 2) ^ 2 / 4 + mEngInstalled * lNac ^ 2 / 12

Type: MomentOfInertia (kg⋅m²)

Description: Engine pitch moment of inertia

IzzEng

Value: mEngInstalled * (dNac / 2) ^ 2 / 4 + mEngInstalled * lNac ^ 2 / 12

Type: MomentOfInertia (kg⋅m²)

Description: Engine yaw moment of inertia

dNac

Value: 4 * (0.0625 + 1 / (4 * sqrt(2)) * max(1.730 * log(max(Tstatic / 1000, 1)) - Modelica.Constants.pi, 0) ^ 0.5)

Type: Length (m)

Description: Nacelle diameter

lNac

Value: 5 * (Tstatic / 1000) ^ 0.9839 / (6 * Modelica.Constants.pi * (1.730 * log(max(Tstatic / 1000, 1)) - Modelica.Constants.pi))

Type: Length (m)

Description: Nacelle length

SwetNac

Value: 2 * Modelica.Constants.pi ^ 2 * 0.2028 * dNac * ((0.20571 * lNac ^ 2 + 0.04661 * dNac ^ 2) ^ 0.5 + (0.1853 * lNac ^ 2 + 0.07557 * dNac ^ 2) ^ 0.5 - (0.005077 * lNac ^ 2 + 0.01611 * dNac ^ 2) ^ 0.5 - (0.01651 * lNac ^ 2 + 0.03666 * dNac ^ 2) ^ 0.5)

Type: Area (m²)

Description: Nacelle wetted area

FFnac

Value: 1.17 * (1 + 0.35 * (dNac / max(lNac, 0.01)))

Type: Real

Description: Nacelle form factor

Tstatic

Value: (Modelica.Constants.pi / 2 * rho0 * dProp ^ 2 * Psealevel ^ 2) ^ (1 / 3)

Type: Force (N)

Description: Static thrust of one engine at sea level

Inputs (1)

flightData

Type: FlightData

Description: Global flight data variables

Connectors (3)

deltaThrotCmd

Type: RealInput

Description: Throttle position command

engineRP

Type: Frame_b

Description: Connector to engine reference point

yConsumption

Type: RealOutput

Description: Consumed electric energy or fuel in an engine

Components (15)

flightData

Type: FlightData

Description: Global flight data variables

energySystem

Type: FuelSystemBrakeSpecific

Description: Model to calculate the consumed electric energy or fuel in an engine

thrustEngine

Type: WorldForce

Description: Engine net thrust

engShape

Type: FixedShape

Description: Engine visualization

thrustAvailable

Type: RealExpression

Description: Thrust available of one engine

engineThrustDmd

Type: Product

Description: Thrust demand for one engine

engineDynamics

Type: CriticalDamping

Description: Simplified model of the engine dynamics

throttleOnGround

Type: Limiter

Description: Limits the throttle from maximum negative thrust to 1 once on the ground

dragNacelle3D

Type: RealExpression[3]

Description: Drag due to one nacelle

dragNacelle

Type: WorldForce

Description: Drag of nacelle

translEng

Type: FixedTranslation

Description: Translation from engine rear end to the point where thrust and drag are acting on (currently no translation)

bodyEng

Type: Body

Description: Mass and inertia of engine

switch

Type: Switch

Description: Switch between two Real signals

throttleInAir

Type: Limiter

Description: Limits the throttle from 0 to 1 once airborne

onGround

Type: BooleanExpression

Description: Boolean expression for indicating aircraft being on ground

Extended by (1)

RollsRoyceAE2100

Aircraft.Physical.FixedWing.Parts.Propulsions.Engines.TurbopropEngines

Turboprop engine: Rolls-Royce AE 2100