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Turbomachinery Lecture 1

- Pumps, Turbines- Subcomponents- Units, Constants, Parameters- Thermodynamics

www.engr.uconn.edu/barbertj~- ME3280 / ME6160

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Turbomachinery• Turbomachine: A device in which energy is transferred to or from a

continuously flowing fluid through a casing by the dynamic action of a rotor.

• Rotor or impellor: Changes stagnation enthalpy of fluid moving through it by either doing positive or negative work.

• Works on fluid to produce either power or flow• Turbomachine categories:

– Those which absorb power to increase fluid pressure or head [compressor, pump].

• Fan: pressure rise up to 1 lbf/in2

• Blower: pressure between 1 - 40 lbf/in2

• Compressor: pressure rise above 40 lbf/in2

– Those which produce power by expanding fluid to lower pressure or head [turbine].

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Turbomachinery

• Turbomachine classification– Impulse: pressure change takes place in one or more

nozzles– Reaction: takes place in all nozzles

• Path of through flow– Mainly or wholly parallel to axis of rotation: axial flow

machine– Mainly or wholly in a plane perpendicular to axis of

rotation: radial flow machine

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Brayton Thermodynamic Cycle for Single Spool Turbojet Engine

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Meridional Projection of Axial & Centrifugal Compressor Stages

Essentially constant radius Substantial change in radius

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Turbomachinery - Pumps

• Positive Displacement: moving boundary forces fluid along by volume changes.– Reciprocating, rotary: piston, screw, ...

• Dynamic: momentum change by means of moving blades or vanes (No closed volume).– Axial, centrifugal, mixed– Fluid increases momentum while moving through open passages

and then converts high velocity to pressure rise in diffuser section• In radial machines doughnut-shaped diffuser is called a scroll

• Through a casing...........Not wind mills, water wheels or propellers

• Flow conditioning..........Stators, scrolls

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Screw

Centrifugal Axial

Turbomachinery - Pumps

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Turbomachinery - Turbines• Extracts energy from a fluid with high head

[pump run backwards].• Reaction turbine: fluid fills blade passages

and pressure drop occurs within the impeller.– Low-head, high-flow devices– V across rotor increases, p decreases– Stators merely alter direction of flow

• Impulse turbine: converts high head to high velocity using a nozzle; then strikes blades as they pass by. – The impeller passages are not fluid filled, and

the jet flow past the blades is essentially at constant pressure.

– Discharge velocity relative inlet velocity across rotor

– no net change in p across rotor– stators shaped to increase V, decrease p

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Gas Generator

• Purpose: Supply High-Temperature and High-Pressure Gas– compressor, combustor, turbine

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Turbojet

• Purpose: Provide High-Velocity Thrust– inlet, compressor, combustor, turbine, nozzle

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Turbofan• Purpose: Produce Lower-Velocity Thrust

Through the Addition of a Fan– inlet, fan, compressor, combustor, turbine, nozzle

Stations0=1= Upstream2 =compressor inlet2.5=low-to-high comp3 =combustor inlet4 =turbine inlet4.5=high-to-low turb.5 =nozzle inlet8 =exit

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Turboprop

• Purpose: Produce Low-Velocity Thrust Through Addition of a Propeller

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Turboshaft• Purpose: Produce Shaft Power for Rotating

Component [Not for Thrust] - helicopter

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Low BPR

BPR= mass flow through bypass/mass flow through core

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High BPR

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Gas Turbine Components• Main Flow-Path

Components of a Gas Turbine Engine:– inlet– compressor– combustor– turbine– nozzle

• Secondary Flow-Path Components:– disk cavities– cooling flow bleed ducts– bearing compartments

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Inlet• Inlet Reduces the Entering Air Velocity to a Level Suitable for the

Compressor• Often Considered Part of Nacelle• Critical Factors:

– Mach Number– Mass Flow– Attached Flow

• Subsonic Inlet– Divergent area usedto reduce velocity

• Supersonic Inlet– Shocks often used toachieve reduced velocityand compression

Nacelle

Engine Inlet

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Fan/Compressor• Axial-Flow Fan• Axial-Flow Compressor

– Low-Pressure – High-Pressure

• Centrifugal Compressor– Mixed Axial/Radial Flow Fan

Low-Pressure Compressor

High-Pressure Compressor

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Combustor• Designed to Burn a Mixture of Fuel

and Air and Deliver to Turbine– Uniform Exit Temperature– Complete Combustion– Exit Temperature Must Not

Exceed Critical Limit Set By Turbine Metal + Cooling Design

Combustor

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Turbine• Extracts Kinetic Energy form

Expanding Gases and Converts to Shaft Horsepower to Drive the Compressor/Fan– Axial Flow Turbine

• High Flow Rates• Low-Moderate Pressure

Ratios

– Centrifugal Turbine• Lower Flow Rates• Higher Pressure Ratio

High-Pressure Turbine

Low-Pressure Turbine

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Nozzle• Increase the Velocity of the Exhaust Gas Before

Discharge from the Nozzle and Straighten Gas Flow From the Turbine– Convergent Nozzle Used When Nozzle Pr < 2

(Subsonic Flow)– Convergent-Divergent Nozzle Used When Nozzle Pr > 2

• Often incorporate variable geometry to control throat areaNozzle

3 Planar Views of a Turbomachine

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Cross Flow Area Variation in Compressor & Turbine Rotors

Cross Flow Area

Diffuser

Nozzle

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Favorable [Turbine] & Unfavorable [Compressor] Pressure GradientsBernoulli: dp dV

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Thermophysical ProcessAcross an AdiabaticStator

Turbine Compressor

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1, 0dA

MA

1, 0dA

MA

Subsonic Supersonic nozzle

Subsonic diffuserSubsonic

Compressibility Can Be A Major Issue in Nozzle Flows

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Gas-Turbine Design Process

Engine Cycle Analysis

Turbomachinery Meanline (1D) Analysis

Through-Flow or Streamline (2D x,r) Analysis

Multi-Component 3-D Steady and Unsteady-Flow Analysis

Turbomachinery 2-D Airfoil Section Design and Analysis

3-D Turbomachinery Airfoil and Design and Analysis

Multi-Stage Turbomachinery and Secondary Flow Path 3-D Steady-Flow Analysis

Multi-Stage Turbomachinery 3-D Unsteady-Flow Analysis

An

aly

sis

Tim

e a

nd

Co

st

Fidelity / Complexity

From Required Thrust, Determine Work Required by Compressor and Turbine and Heat

Addition from Combustor

From Required Compressor / Turbine Work Determine Number of Stages and Velocity

Triangles of”Mean Radius” Streamline

From Velocity Triangles, Determine Airfoil Shape as a Function of Radius for Required Flow

Turning and Pressure Rise/Drop

Upon Stacking Airfoil Sections from Structural or Aero Considerations, Determine Single Blade-Row Performance (i.e.. Loading and Pt Losses)

and Combustor Heat and NOx Release

From Radial Equilibrium or Axisymmetric Streamline Analysis, Determine Spanwise

Variation in Velocity Triangles

Determine Primary Blade-Row and Secondary Flow Path Pressure and Mass-Flow

Distribution Interaction Effects

Determine Unsteady-Flow Interaction Effects on Performance (e.g.. Wake /

Blade, Shock / Blade, Potential, Thermal, and Structural Interactions

Determine “Steady” and Unsteady Coupling Effects Between the Components

Well Developed

Developed - Fairly Mature

Developed - Improvements

Required

Under Development

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Units and Key Constants

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• Conventional Units

Parameter English Units SI Units

– Distance Feet, Inches Meters, M– Time Seconds Seconds, s– Force Pounds (force), lbf 4.448 Newton, N– Pressure psf, psi Pascal, Pa (1N/1m2)

bar (105Pa)

1 ft H2O2.989 kPa– Mass Pounds (mass), lbm 0.4536 kilogram– Energy Btu Joule, J– Power 1 Hp 0.7457 kWatt

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Equivalent Systems of Units

1 Newton = 1 kg-m/sec2

1 Joule = 1 N-m/sec

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Important Constants for Air

R=287 J/kg-R = 287 m2/s2-K

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Useful Equivalents

Atmospheric pressure1 in Hg = 0.49116 psi2116 psf = 14.7 psi = 1.013 Bar = 101,325 Pascals

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• For Liquid Water :

• U.S. Standard Atmosphere - 1976

3/4.62 ftlbm

2696.14

in

lbfpressure

Retemperatur 67.518

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Standard Atmosphere

Stratosphere >65,000 ft

59 FTemperature

Altitude

3.202 psia

14.696 psiaPressure

36,089 ft

Altitude

36,089 ft

http://www.digitaldutch.com/atmoscalc/index.htm

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Thermodynamics Review

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Thermodynamics Review

• Thermodynamic views– microscopic: collection of particles in random motion.

Equilibrium refers to maximum state of disorder– macroscopic: gas as a continuum. Equilibrium is

evidenced by no gradients

• 0th Law of Thermo [thermodynamic definition of temperature]: – When any two bodies are in thermal equilibrium with a

third, they are also in thermal equilibrium with each other. – Correspondingly, when two bodies are in thermal

equilibrium with one another they are said to be at the same temperature.

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Thermodynamics Review

• 1st Law of Thermo [Conservation of energy]: Total work is same in all adiabatic processes between any two equilibrium states having same kinetic and potential energy.– Introduces idea of stored or internal energy E– dE = dQ - dW

• dW = Work done by system [+]=dWout= - pdV• Some books have dE=dQ+dW [where dW is work done

ON system]• dQ = Heat added to system [+]=dQin

– Heat and work are mutually convertible. Ratio of conversion is called mechanical equivalent of heat J = joule

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Review of Thermodynamics• Stored energy E components

– Internal energy (U), kinetic energy (mV2/2), potential energy, chemical energy

• Energy definitions– Introduces e = internal energy = e(T, p)– e = e(T) de = Cv(T) dT thermally perfect – e = Cv T calorically perfect

• 2nd law of Thermo – Introduces idea of entropy S– Production of s must be positive– Every natural system, if left undisturbed, will change spontaneously

and approach a state of equilibrium or rest. The property associated with the capability of systems for change is called entropy.

revQdS TdS dE dW

T

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Review of Thermodynamics• Extensive variables – depend on total mass of the system, e.g. M, E, S, V

• Intensive variables – do not depend on total mass of the system, e.g. p, T, s, (1/v)

• Equilibrium (state of maximum disorder) – bodies that are at the same temperature are called in thermal equilibrium.

• Reversible – process from one state to another state during which the whole process is in equilibrium

• Irreversible – all natural or spontaneous processes are irreversible, e.g. effects of viscosity, conduction, etc.

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Thermodynamic Properties

Primitive Derived

2

0 0

0

2k p

T

VE E E E or e e gz

Total or stagnation state

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1st Law of Thermodynamics• For steady flow, defining:

• We can write:

• and

2

2

0

/ 2 specific kinetic energy

specific potential energy

specific internal energy

= + + specific enthalpy

e total2

V

gz

e

ph e pv e

Ve gz

specific energy

2

0e2

Vpv e gz pv

0 0h e pv and h e pv

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Equation of State

• The relation between the thermodynamic properties of a pure substance is referred to as the equation of state for that substance, i.e. F(p, v, T) = 0

• Ideal (Perfect) Gas– Intermolecular forces are neglected– The ratio pV/T in limit as p 0 is known as the universal gas constant (R).

p /T R = 8.3143e3

– At sufficiently low pressures, for all gases

p/T = R

or

• Real gas: intermolecular forces are important p RT

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Real Gas

1150 R

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Real Gas

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1st & 2nd Law of Thermodynamics

• Gibbs Eqn. relates 2nd law properties to 1st law properties:

Tds pdv de

h e pv

dh de pdv vdp

dpTds dh

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Gibbs Equation

• Isentropic form of Gibbs equation:

• and using specific heat at constant pressure:

dp

dh

p

p

RTc dT dP

PdT R dP

T c P

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Thermally & Calorically Perfect Gas

• Also, for a thermally perfect gas:

• Calorically perfect gas - Constant Cp

-1 = p

P vv p

c Rc c R

c c

P

dP

T

dT

1

2

1

2

1

1

P

dP

T

dT

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Isentropic Flow

• For Isentropic Flow:

• Precise gas tables available for design work – Thermally Perfect Gas good for compressors not for turbines because of burned fuel.

1 /

1 /2 2

1 1

T Por T CP

T P

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Gibbs Equation• Rewriting Gibbs Equation:

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Gibbs Equation• Rewriting Gibbs Equation:

02 022 1

01 01

0

022 1

01

02 2 1

01

1ln ln

,

1ln

exp 1

p

p

Apply at stagnation state

T Ps s

c T P

For adiabatic processes T constant

Ps s

c P

P s s

P R

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Mollier Chart for Air

500

1,000

1,500

2,000

2,500

3,000

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16

Entropy - BTU/Lbm/deg R

Tem

pera

ture

Deg

R

P=50Atm

20

10

5

2

1

Isobars are not parallel

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Mollier for Static / Total States

450

650

850

1,050

1,250

1,450

1,650

-0.02 -0.01 0.00 0.01 0.02 0.03 0.04 0.05 0.06

S

T

IdealReal

P in

P out

s

Poin

Poout

V2/2

h02i

h02

h01

2

0 2

Vh h

We will soon see