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 (T_avail) for turboprop engines is solved through dividing the power available (P_avail) by the total velocity (v_tot), and the factors for representing the propeller (η_prop) and power transmission efficiencies (η_mech) 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, ρ_alt 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 (C_D,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 (FF_nac) and the nacelle wetted area (S_wet,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 d_prop 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 (C_f,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 C_D,0,nac can be found in section 3.3.1 in Reference [4].

The magnitude of the drag force itself (D_nac) is the parasite drag coefficient times the dynamic pressure (q) times the main wing reference area (S_ref,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 T_static 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 at: modelica://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.