TURBOPROP ENGINE App. K AIAA AIRCRAFT ENGINE DESIGN

CORSO DI LAUREA SPECIALISTICA IN Ingegneria Aerospaziale PROPULSIONE AEROSPAZIALE I TURBOPROP ENGINE App. K AIAA AIRCRAFT ENGINE DESIGN www.amazon.com LA DISPENSA E E DISPONIBILE SU http://www.ingindustriale.unisalento.it/didattica/ Prof. Ing. A. Ficarella antonio.ficarella@unile.it 1

high thrust and low fuel consumption Mach < 0.8 2

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component,, efficiencies 6

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the compressor is powered by the HP turbine the LP turbine provides mechanical power to the propeller 9

PARAMETRIC ANALYSIS WORK INTERACTION COEFFICIENT for the propeller η prop is the efficiency of the power transfer from the propeller to the air and P prop is the power transferred to the propeller the total power interaction of the propeller is also equal to the effective thrust of the propeller (F prop ) times the velocity of the vehicle (V 0 ) 10

Similarly, the work interaction coefficient for the core engine is defined with respect to the power transferred to the vehicle (thrust x velocity) or The total work interaction coefficient of the turboprop engine is The effective thrust (F) of the engine can be found 11

The specific thrust of the core is given by 12

The velocity and temperature ratios required 13

freestream recovery maximum allowable turbine inlet total temperature T t4 afterburner 14

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INDEPENDENT VARIABLES compressor pressure ratio c turbine total enthalpy ratio t enthalpy ratio across the low-pressure turbine from the enthalpy ratio across the compressor is related to its pressure ratio the enthalpy ratio across the HP turbine obtained from power balances 16

the temperature ratios across the two cooling air mixing processes the pressure ratio across the HP and LP turbine are related to their respective temperature ratio and polytrophic efficiency the fuel-air ratio 17

the only unknowns for solution is the static pressure ratios P 0 /P 9 UNCHOKED FLOW the exit static pressure P 9 is equal to the ambient pressure P 0 exit Mach n. < 1 exit Mach n. M 9 determined using the compressible flow functions 18

CHOKED FLOW P t9 /P 0 obtained by the product of the ram and component for the core airstream 19

Development of an expression for the propeller work interaction coefficient starts with a power balance on the lowpressure spool 20

THRUST SPECIFIC FUEL CONSUMPTION The specific power of the engine the power specific fuel consumption The equivalent specific thrust of the turboprop engine the thrust specific fuel consumption 21

The propulsive efficiency of the turboprop engine is defined as the ratio of the total power interaction with the vehicle producing propulsive power to the total energy available for producing propulsive power 22

The thermal efficiency of the turboprop engine is defined as the ratio of the total power produced by the engine to the energy contained in the fuel 23

SUMMARY OF PARAMETRIC ANALYSIS 24

EXAMPLE PARAMETRIC ANALYSIS flight Mach n. 0.8, standard altitude 25 kft variation of the remaining two design variables for any c there is a turbine enthalpy ratio t * for which F/m 0 is max and S min optimum turbine enthalpy ratio 25

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OPTIMUM TURBINE ENTHALPY RATIO 27

PERFORMANCE ANALYSIS off-design flight conditions and throttle settings 28

ASSUMPTIONS the flow areas are constant at stations 4, 4.5, 6, 16, 6A, 8 dry (AB off) the flow in choked at the high-pressure turbine entrance nozzle (4), at the low-pressure t. (4.5) and at the exhaust nozzle (8) the exhaust nozzle may un-choke at low throttle settings component efficiency and pressure ratio (burner, mixer, AB, exhaust) bleed air and cooling air fractions are constant power takeoffs are constant the air and combustion gases are modeled as perfect gas in thermodynamic equilibrium simplifying gas model: gases are calorically perfect upstream and downstream of the burner and afterburner 29

REFERENCING MASS FLOW PARAMETER (MFP) REFERENCING at any off-design point, a relationship between the two performances variables and - the constant can be evaluated at the reference point MASS FLOW PARAMETER calorically perfect gas 30

FOR HIGH-PRESSURE TURBINE VARIABLE SPECIFIC HEAT COOLED TURBINE nozzle throat stations just downstream of station 4 and 4.5 denoted by 4 and 4.5 31

power balance of the high-speed spool The total pressure ratio of the compressor is determined from the component efficiency equation 32

An expression for the mass flow rate of air through the turboprop engine at any conditions can be obtained for the case of a CPG when The power produced by the low-pressure turbine at off-design is determined by its total pressure ratio The total temperature ratio of the low-pressure turbine is related by the CPG component efficiency relationship 33

work interaction coefficient for the propeller is obtained by a power balance of the low-pressure spool Determination of the value of C prop thus depends mainly on T t4 (τ λ ) and τ tl since η prop, η g, and η ml, τ m1, τ th, and τ m2 are constant or essentially constant Note that the flow is choked at the entrance to the lowpressure turbine (station 4.5) and is normally unchoked at the engine exit (station 9) 34

The total pressure at station 4.5 is related to the flight condition and throttle setting by the total pressure at station 5 is related to the nozzle operation by 35

the only unknowns for solution is the static pressure ratios P 0 /P 9 UNCHOKED FLOW the exit static pressure P 9 is equal to the ambient pressure P 0 exit Mach n. < 1 exit Mach n. M 9 determined using the compressible flow functions 36

CHOKED FLOW P t9 /P 0 obtained by the product of the ram and component for the core airstream 37

Equating the mass flow rate of air at stations 4.5 and 9 yields the following equation for the total pressure ratio of the lowpressure turbine in terms of the exit Mach number and the total temperature ratio of the low-pressure turbine 38

Determination of the conditions downstream of station 4.5 requires an iterative solution 39

The performance of the propeller can be simply modeled as a function of the flight Mach number The equation for the Mach range of 0.7-0.85, given above, models the drop in η prop experienced in this flight regime due to transonic flow losses in the tip region of the propeller 40

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SUMMARY OF PERFORMANCE ANALYSIS 42

EXAMPLE turboprop engine designed for a Mach n. of 0.8 at a standard altitude of 25 kft compressor pressure ratio of 30 turbine enthalpy ratio of 0.6 ENGINE CONTROL: max compressor pressure ratio of 30, max T t4 of 3200 R, max T t3 of 1600 R variation with changes in flight Mach n. and altitude full throttle operation 0break = 0.933 43

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sharp break at M 0 =0.1 due to the assumed prop 45

S is very low compared with other turbine engine cycles 46