Turbomachinery Design Considerations EGR 4347 Analysis and Design of Propulsion Systems

Euler Pump Equation

Compressor Axial Schematic

Compressor Centrifugal Schematic

Compressor Typical Velocity Diagram

Compressor Repeating Row Nomenclature

Airfoil Pressure and Velocity

Important Parameters Compressor Efficiency, c Stage Efficiency, s Polytropic Efficiency, ec Stage Pressure Ratio, s Overall Pressure Ratio, c

Degree of Reaction Desirable value around 0.5

Diffusion Factor Quantifies the correlation between total pressure loss and deceleration (diffusion) on the upper (suction) surface of blade (rotor and stator)  is the solidity – the ratio of airfoil chord to spacing

Diffusion Factor Data

Hub, Mean, and Tip Velocity Diagrams

Stall and Surge

Parameters Affecting Turbine Blade Design Vibration Environment Number of Blades Tip Shroud Airfoil Shape Inlet Temperature Trailing-Edge Thickness Blade Cooling Allowable Stress Levels (AN2) (N = Speed, RPM) Material Service Life Requirements

Turbine Prelim Design Focuses on Defining a ‘Flowpath’ that Meets Customer Requirements Customer Req’ts/Desires Performance Mission Cost & Risk FN, SFC Req’ts Aero Technology Life Req’ts Mech. & Cooling Technologies Performance Cycle Design Material Selections Combustor Design Component Temp to other areas Turbine Aero Design Turbine Mech Design AN2 wrh a,b Wc Clearance Manufacturing No No Yes Meet Requirements Preliminary Design = “Frozen” Turbine Flowpath

Turbine Mechanical Detailed Design Detailed Design Accomplishes Two Functions: Verify Assumptions/Choices Made in Preliminary Design Provide Detailed Geometry Required to Achieve Preliminary Design Goals Detail Mechanical Design Disciplines: Materials Selection - satisfy life/performance goals Secondary Flow Analysis - define/control nonflowpath air (e.g. cooling) Heat Transfer - component temperature definition Stress Analysis - component stresses Vibration Analysis - design to avoid natural frequencies Life Analysis - define component life for all failure modes

Turbine Nomenclature

50% Reaction Turbine

0% Reaction or Impulse Turbine

Hub, Mean and Tip Velocity Diagrams

Velocity Triangles “ABSOLUTE” FLOW ANGLES “RELATIVE” BLADE ANGLES Relating a’s and b’s

TURBINE ANALYSIS – Velocity Triangles

TURBINE ANALYSIS Euler Turbine Equation: v2 V2 u2 inlet, i v3 u3 exit, e V3 convention: v3 = -ve also, ri = re= r

TURBINE ANALYSIS Turbine Efficiency: Stage Loading Coefficient, y: Adiabatic (Isentropic) Polytropic Stage Loading Coefficient, y: Typical values: 1.3 - 2.2

TURBINE ANALYSIS Flow Coefficient, F: Typical values 0.5 - 1.1 Degree of Reaction, °R: °Rt = 0 Impulse turbine Reaction turbine

TURBINE ANALYSIS Pressure Loss Coefficient, ft: Velocity Ratio, VR: Typical values: 0.5 - 0.6 Tip Leakage Cooling Loss Profile Loss Endwall Loss

Turbine Mechanical Design AN2: Rotor Exit Annulus Area x [Max Physical Speed]2 Units: in2 x RPM2 x 1010, typical values: 0.5<AN2<10 x1010 Typical Limits: Cooled Blade < 5 x 1010 Advanced Technology < 6.5 x 1010 Uncooled Solid Blade < 10 x 1010 LPT < 7 x 1010 Use max physical speed; not design point or TO speed Blade Airfoil Stress is Primarily Driven by AN2 Blade Pull Load Driven by AN2

Turbine Mechanical Design – Hub and Tip Speed Limits rhw2: Hub radius x 2p/60 x Max Physical RPM Units: ft/s Typical Values: HPT - 1000 ft/s < rhw2 < 1500 ft/s LPT - 500 ft/s < rhw2 < 1000 ft/s Use max physical RPM; not design point or TO speed Disk Stress is Driven Primarily by rhw2 Disk and Blade Attachment Stresses are a function of rhw2 and AN2

Structures - Rotational Stress (Centrifugal Stress) - Bending Stress due to the lift of “airfoils” - Buffet/Vibrational Stress - Flutter due to resonant response - Torsion from shaft torque - Thermal Stress due to temperature gradients - FOD - Erosion, Corrosion, and Creep

Structures

Structures

Structures - Stress Calculations - Rotational Stress (Centrifugal Stress) -- Same as for compressor, sc, sblade - Disk Thermal Stress, st -- assume T = T(r) = T0 + DT(r/rH) -- a - coef of linear thermal expansion -- E - Modulus of Elasticity rH T T0 T+DT r rH Disk r q radial stress tangential stress