Gas Turbine Engine Performance Analysis. S. Jan

Transcription

1 Gas Turbine Engine Performance Analysis S. Jan Jul

2 Chapter 1 Basic Definitions Potential & Kinetic Energy PE = mgz/g c KE = mv 2 /2g c Total Energy Operational Envelopes & Standard Atmosphere Correction factors; δ, Ө and σ Air Breathing engines Aircraft Performance Parameters Thrust, Lift, Drag, Thrust Specific Fuel Consumption Thermal efficiency Figures 1-17s

3 Chapter 1 Basic Definitions Aircraft Performance Parameters Specific thrust versus fuel consumption Aircraft Performance Lift and Drag Stall, Takeoff and landing speed Aircraft Design Figure 1-38

4 Chapter 2 Thermodynamics Review System and Control Volume System is a collection of matters of fixed identity within a prescribed boundary Control volume is a specified space bounded by control surfaces System and surrounding Control surfaces are interacting with surrounding Extensive and intensive properties Intensive property is independent Extensive property is derivation from the intensive properties.

5 Chapter 2 Thermodynamics Review State is the condition of a system Process describes how does a system change from one state to the other. Adiabatic, Isothermal, Isentropic, Isobaric process. Isolated system Entropy determines the direction of a process and measures the degree of disorder at microscopic level.

6 Chapter 2 Thermodynamics Review Compressible system Homogeneous and invariant in chemical composition no motion, force field, capillary effects, distortion of solid phase. Equations of State Thermal equation of state, f (P,v,T) = 0 Energy equation of state, u = f(t, v) = f(p, v) = f(p, T) Enthalpy, C v, C p and sound speed First and second laws of Thermodynamics

7 Chapter 2 Thermodynamics Review Rate of Change of extensive properties within a system dr/dt = dr/dt+r out -R in Steady Flow dr/dt = 0 One Dimensional flow Uniform flow across control surfaces Conservation of mass ρva = constant

8 Chapter 2 Thermodynamics Review Steady Flow energy Equation Eq Example 2-1 Steady Flow Entropy S out S in Momentum Equation Eq Example 2-2 Summary of laws p.p. 95

9 Chapter 2 Thermodynamics Review Perfect Gas P = ρrt U = f (T) Specific heat, universal constant, Gibbs equation and sound speed Isentropic Process Eq.s , Mollier diagram (pp 101) Fig Mixtures of perfect gases (pp102) Eqs Partial pressure P i = N i R u T/V Gas Table Fuel-Air Ratio

10 Chapter 3 Compressible Flow Three independent properties; temperature, pressure and mach number; define a flow fluid system. Energy equation Total enthalpy & Total temperature Stagnation temperature/aerodynamic heating Stagnation total pressure Eq 3-7 (reversible) Total temperature and pressure measurements

11 Chapter 3 Compressible Flow For an adiabatic and no shaft work constant T flow P2/P1 1 Relationship between T/T t, P/P t and mach number Eqs 3-9 and 3-10 Mass Flow Parameters Eqs 3-12 and 3-13 Isentropic area ration Eq 3-14

12 Velocity-area variation Chapter 3 Compressible Flow A steady one-dimension incompressible flow with uniform stream properties AV = constant For compressible flow ρva = constant Two dimensional small amplitude wave propagation Pp 130 Adiabatic steady flow ellipse a 2 /a t2 + V 2 /V max2 = 1 Fig 3-16

13 Chapter 3 Compressible Flow Incompressible Flow pp135 Subsonic Compressible Flow pp135 Insignificant density change at speed below M 0.4 At speed M 0.4, the density change Δρ/ρ = M 12 /2 Transonic Flow Supersonic Flow Hypersonic Flow

14 Chapter 3 Compressible Flow Normal Shock Wave pp 138 & fig Eqs 3-18 to 3-29 fig 3-19 Normal Shock Wave Propagation Speed pp Oblique Shock Wave pp & fig 3-25 Eqs 3-31 to 3-32 Steady One-Dimensional Gas Dynamics pp

15 Simple Flow Chapter 3 Compressible Flow Single independent variable controls the change in the flow properties. Constant area Frictionless Constant total temperature No gas ingestion into the flow Nozzle flow Simple heating flow Simple frictional flow Table 3-5

16 Chapter 4 Aircraft Gas Turbine Engine Thrust Equation Aircraft Propulsion System The engine The nacelle Uninstalled engine thrust Eq. 4-1 Installed engine thrust Eq 4-2 Nacelle drag Pressure drag Additive drag Pp 222 Propulsive efficiency

17 Chapter 4 Aircraft Gas Turbine Engine Thrust Equation The ratio of the useful power output to the total power output of the propulsion system. Gas Turbine Engine Inlet Compressor Combustor Turbine Exhaust nozzle Thrust augmentation Brayton cycle

18 Chapter 5 Parametric Cycle Analysis Parametric cycle analysis design point Analyze engine performance at different flight conditions and value of design choice, e.g. compression ratio and design limit parameter. Engine performance analysis off-design Determines the performance of a specific engine at all flight conditions and throttle settings. Notation Total temperature, pressure, ratio of total pressure, ratio of total temperature Total/static pressure, temperature Design input Flight conditions Design limits Component performance Design choices

19 Chapter 5 Parametric Cycle Analysis Steps of engine parametric cycle analysis (pp 245) Engine Thrust Velocity ratio Exit Mach number Temperature ratio Fuel air ratio Turbine power output Specific thrust Specific fuel consumption Thermal and propulsive efficiencies

20 Chapter 5 Parametric Cycle Analysis Assumptions Isentropic compression and expansion in the inlet, compressor, fan, turbine and nozzle. τ d = τ n = 1 π d = π n = 1 τ c = π c (γ-1)/γ τ t = π t (γ-1)/γ Constant pressure combustion. Fuel mass flow rate is much smaller than the air mass flow rate Air behaves as an ideal gas and has constant specific heat. Exhaust nozzle exit pressure is the same as P 0

21 Chapter 5 Parametric Cycle Analysis Ideal Turbofan Cycle Analysis Improve engine efficiency by reducing the air exhaust velocity. Pp Ideal Turbofan with optimum bypass ratio (pp ) Increase compressor pressure ratio until 20 increasing spciefic thrust and specific fuel consumption. For compression ratio above 20, no increase in specific thrust and better fuel consumption are observed. Ideal turbofan with optimum fan pressure ratio (pp ) Effect of bypass ratio on specific thrust and fuel consumption (pp309, fig 3-30)

22 Chapter 5 Parametric Cycle Analysis Comparison of optimum ideal turbofan (pp310) Figures 5-34 a&b The higher the bypass ratio and the lower fan pressure ratio will have better fuel consumption. The lower fan pressure ratio and the higher bypass ratio decrease the specific thrust.

23 Chapter 6 Component Performance Gas properties variation Enthalpy, h, Specific heat c p and specific heat ratio of JP-4 and air combustion products (fig 6-1a,b,c) Inlet and diffuser pressure recovery Isentropic efficiency ɳ d = (τ γ πd (γ-1)/γ 1)/( τ γ -1) τ γ is the free stream temperature ratio Supersonic flight inlet shock wave pressure loss Ram pressure recovery Compressor and Turbine efficiencies Compressor isentropic efficiency ɳ c, eq 6-9 Compressor stage efficiency ɳ s,eq 6-10 overall compressor efficiency, eq 6-11,12,13 Polytropic efficiency e c, eq 6-15 Polytropic efficiency approaches isentropic efficiency with a large number of compressor stages, eq 6-16

24 Chapter 6 Component Performance Turbine efficiency Pp Burner efficiency and pressure loss Exhaust nozzle loss Component performance with variable c p

25 Chapter 7 Parametric Cycle analysis of Real Engines Cycle analysis includes components losses from variable specific heat and combustion gas. Turbofan Separate exhaust stream Generally used in subsonic (commercial) aircraft Pp Assumptions Eqs summary pp Exit pressure is greater than atmospheric pressure Pp 398 Eqs 7-53 to 7-55 Optimum by-pass ratio pp405

26 Chapter 8 Engine Performance Analysis Parametric cycle analysis selects compression ratio, burner exit temperature and flight condition etc. to determine the turbine temperature ratio. Engine performance analysis uses selected compression ratio, corresponding turbine temperature ratio to calculate the engine s performance based on the throttle setting and flight conditions. (table 8-1) Engine built variation Compression ratio, turbine temperature, air flow leakage, combustor performance. Pumping characteristics Performance model Engine data

27 Chapter 8 Engine Performance Analysis Nomenclature High pressure compressor & turbine Low pressure compressor & turbine High pressure & low pressure spool Turbofan engine Pp

28 Chapter 9 Turbomachinery Axial flow, radial flow and mixed flow turbomachinery. Euler s pump equation, eqs 9-1,2 Euler s turbine equation, eqs 9-1,4,5 Axial Flow Compressor Analysis Blade and stator Through flow field Row of blades is modeled as a thin disk Flow field is uniform in the Ө direction Meridional projection Secondary field Cascade field A stage is made of a rotor and a stator Repeating array of airfoils

29 Chapter 9 Turbomachinery The Secondary Field Velocity gradient between the boundary layer and free stream. The pressure gradient imposed by the free stream causes the fluid in the boundary layer to flow from high pressure region to low pressure regions. Two Dimensional Flow through Blade Rows Absolute and relative coordinate systems Static thermodynamic properties do not depend on the reference frame. Total properties depend on reference frame, eq 9-6 Euler s equation, 9-7a,b. Work done per unit mass flow can be determined by the rotor speed, the velocity ratio, the rotor cascade flow angles or the absolute rotor flow angles. Velocity diagrams, pp 624 Flow annulus area, eq 9-8 Property changes of an isentropic compressor stage, pp629 fig 9-13 Efficiencies Stage efficiency, eq 9-9,10 Polytropic efficiency, eq 9-11,12 Degree of Reaction The split of enthalpy increase between the stator and the rotor, eqs 913a, b

30 Chapter 9 Turbomachinery Cascade airfoil nomenclature and loss coefficient Fig 9-15 Total pressure loss coefficient, eq 9-15 Diffusion factor Pressure side, suction side pressure and velocity distribution, fig 9-17 Total pressure loss due to boundary separation Diffusion factor, eq 9-16 Stage Loading and flow coefficients Ratio of the stage work to the rotor speed square, eq 9-19,20. Rotor speed is limited by material strength. Flow coefficient, eq Fig

31 Stage pressure ratio Eq Chapter 9 Turbomachinery High pressure, high work loading Pressure losses fig. 13 and 21 Blade Mach number Eq 9-31 Stage temperature rise is mainly function of M b and the ratio M 1 /M b Table 9-3 Repeating stage, repeating row, mean line design A stage exit velocity and flow angle equal inlet A stage is made up rows of repeating airfoils. Flow behavior of the flow is based on the average radius, mean radius. Assumptions Pp

32 Chapter 9 Turbomachinery Flow Path Dimensions Annulus Area, eq 9-8 at mean radius. Fig 9-26, 27 Axial dimensions Chord/height ratio Number of blade Blade profile NACA 65A010 Radial variation Constant amount of work on the fluid pass through a stage is independent of radius. Radial equilibrium Free vortex variation of swirl Axial velocity and total enthalpy do not vary with radius. Flow velocity inversely vary with radius, eq 9-45 Degree of reaction Swirl distribution Free vortex Exponential First power

33 Chapter 9 Turbomachinery Design Process Selection of rotational speed and annulus dimensions Assuming blade speed tip, hub/tip ratio and axial velocity AN 2 check Inlet guide vanes Selection number of stages Compressor Performance Compressor map, fig 9-39, 40 Corrected values, P, T, N and m (flow rate). Pp 673 Compressor starting problem

34 Chapter 9 Turbomachinery Axial-Flow Turbine Analysis Blade shape is dictated by stress Stator blade (vane, nozzle), rotor blade (bucket) Fig 9-48a,b Pressure decreases and tangential velocity increase at the exit of the stator. The rotor decreases the tangential velocity and produces power Velocity diagram, eq 9-49 Angles of the diagram determine the blade shape and are used as design parameters. Velocity magnitudes are not significant except the rato and mach number

35 Chapter 9 Turbomachinery Stage Parameters Adiabatic efficiency Eq 9-76 Exit swirl angle A zero swirl angle minimizes the kinetic energy left in the flow exiting the blade It is difficult to convert the kinetic energy to pressure A higher backward swirl angle means higher output Stage loading and flow coefficients Loading coefficient, eq. 9-19,20 Flow coefficient, eq Stage loading vs. flow coefficient, fig Stage efficiency vs. loading and flow coefficients, fig Flow angle vs. loading and flow coefficients, fig Rotor turning (β 2 +β 3 )vs. ψ/φ, fig. 9-55

36 Stage Parameters Degree of reaction Chapter 9 Turbomachinery Ratio of the static enthalpy drop in the rotor to the drop in total enthalpy across both the rotor and stator. Eq.9-81a,b Impulse turbine, zero reaction 50% reaction Zero swirl

37 Chapter 9 Turbomachinery Turbine Airfoil Nomenclature and Design Metal Angles Turbine stage analysis, PP Flow path dimensions Annulus area, eq. 9-8 Design process Pp Turbine cooling, pp Fig Convection cooling Film cooling Impingement cooling Transpiration cooling Turbine performance Turbine map, fig. 9-86,87

38 Chapter 9 Turbomachinery Turbine Airfoil Nomenclature and Design Metal Angles Turbine stage analysis, PP Flow path dimensions Annulus area, eq. 9-8 Design process Pp Turbine cooling, pp Fig Convection cooling Film cooling Impingement cooling Transpiration cooling Turbine performance Turbine map, fig. 9-86,87