Turbomachinery Design Considerations EGR 4347 Analysis and Design

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 Tip Shroud Number of Blades Airfoil Shape Inlet Temperature Blade Cooling Material Trailing-Edge Thickness Allowable Stress Levels (AN 2) (N = Speed, RPM) Service Life Requirements

Turbine Prelim Design Focuses on Defining a ‘Flowpath’ that Meets Customer Requirements Customer Req’ts/Desires Performance Mission FN, SFC Req’ts Aero Technology Cost & Risk Life Req’ts Mech. & Cooling Technologies Performance Cycle Design Turbine Aero Design Combustor Design AN 2 wrh a, b Wc Clearance Material Selections Turbine Mech Design Manufacturing No No Meet Requirements Yes Preliminary Design = “Frozen” Turbine Flowpath Component Temp to other areas

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: u 2 V 2 v 2 inlet, i V 3 u 3 exit, e v 3 convention: v 3 = -ve also, ri = re= r

TURBINE ANALYSIS • Turbine Efficiency: – 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: Tip Leakage Cooling Loss Profile Loss Endwall Loss • Velocity Ratio, VR: Typical values: 0. 5 - 0. 6

Turbine Mechanical Design • AN 2: Rotor Exit Annulus Area x [Max Physical Speed]2 – Units: in 2 x RPM 2 x 1010, typical values: 0. 5<AN 2<10 x 1010 – 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 AN 2 – Blade Pull Load Driven by AN 2

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

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, c, blade - Disk Thermal Stress, st -- assume T = T(r) = T 0 + DT(r/r. H) -- a - coef of linear thermal expansion -- E - Modulus of Elasticity r q r H radial stress tangential stress Disk T+DT T T 0 0 r r. H