Assistant Professor · 2018. 3. 6. · Since there are stationary and rotating blades in...

Turbomachinery

Hasan OzcanAssistant Professor

Mechanical Engineering DepartmentFaculty of Engineering Karabuk University

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Introduction

Hasan Ozcan, Ph.D, (Assistant Professor)

B.Sc :Erciyes University, 2009M.Sc :Karabuk University, 2011Doctorate :University of Ontario Institute of

Technology, 2015

Research Fields: Thermal system design, renewable energy, hydrogen production, Energy Storage

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IntroductionMarking SchemeMidterm – 40%Project – 20% (added to final exam ‐ elective)Final Exam – 60%

SourcesBasic Concepts in Turbomachinery ( Ingram, 2009)Turbomachinery Performance Analysis (Levis, 1996 )Fluid Mechanics and thermodynamics of Turbomachinery (Dixon and Hall, 2010)

Course ContentWeek 1: Introduction and Basic PrinciplesWeek 2: Relative and Absolute MotionWeek 3: Turbomachine OperationWeek 4: Basic Concepts for Fluid MotionWeek 5: Dimensionless Parameters in TurbomacineryWeek 6: Efficiency and Reaction for TurbomachineryWeek 7‐9: Axial flow MachinesWeek 9‐12: Hydraulic Turbines Week 11‐13: Analysis of Pumps Week 14: Project presentations

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Introduction to Turbomachinery

What is a turbomachine?

‐ Turbomachine is a device exchanging energy with a fluid by either absorbing

from or extracting energy to the fluid.

‐ The energy extracting devices are called Turbine, while energy absorbing devices

can be called pump, blower, fan, and compressor.

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Some Applications of Turbomachinery

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Classification of Turbomachines

‐ Energy Extracting – Energy Absorbing

‐ Flow Direction: Axial, radial, mixed

‐ Fluid type: Compressible, incompressible

‐ Impulse, reaction (For hydro turbines)

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Energy Extracting Devices

Gas Turbine: Energy production is accomplished by extracting energy from a

compressible gas such as air, helium, or CO2.

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Steam Turbine: Energy production is accomplished by extracting energy from

superheated high pressure steam. Many other liquid woring fluids are also in use.

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Wind Turbine: Converts kinetic energy of air into mechanical energy.

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Hydro Turbine: Hydoturbines are used to convert the potential energy of water

into mechanical energy.

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Energy Absorbing Devices

Pumps: Absorbs energy to increase the pressure of a liquid.

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Fans: Low pressure increase of high flow rate gases.

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Blowers: Medium pressure increase of medium flow rate gases.

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Compressors: High pressure increase of low flow rate gases

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Positive displacement vs dynamic turbomachines

Courtesy of slidesharecdn.com

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Introduction to TurbomachineryFluid Type

Compressible: (Fans, blowers, compressors, gas turbines)

Incompressible: (hydro turbines)

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Introduction to Turbomachinery1. Coordinate SystemSince there are stationary and rotating blades in turbomachines, they tend to form a cylindrical form,

represented in three directions;

1. Axial

2. Radial

3. Tangential (Circumferential ‐ rθ)

Axial View

Side View

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Introduction to Turbomachinery1. Coordinate SystemThe Velocity at the meridional direction is:

Where x and r stand for axial and radial.

NOTE: In purely axial flow machines Cr = 0, and in purely radial flow machines Cx=0

Axial ViewAxial View Stream surface View

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Introduction to Turbomachinery1. Coordinate SystemTotal flow velocity is calculated based on below view as

Stream surface View

The swirl (tangential) angle is (i)

Relative Velocities

Relative Velocity (ii)

Relative Flow Angle (iii)

Combining i, ii, and iii ;

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Introduction to Turbomachinery2. Fundemental Laws used in Turbomachinery

2.1. Continuity Equation (Conservation of mass principle)

2.2. Conservation of Energy (1st law of thermodynamics)

Stagnation enthalpy;

if gz = 0;

For work producing machines

For work consuming machines

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2.3. Conservation of Momentum (Newtons Second Law of Motion)

• For a steady flow process;

• Here, pA is the pressure contribution, where it is cancelled when there is rotational symmetry. Using

this basic rule one can determine the angular momentum as

• The Euler work equation is:

where

The Euler Pump equation

The Euler Turbine equation

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Writing the Euler Eqution in the energy equation for

an adiabatic turbine or pump system (Q=0)

NOTE: Frictional losses are not included in the Euler Equation.

2.4. Rothalpy

An important property for fluid flow in rotating systems is called rothalpy (I)

and

Writing the velocity (c) , in terms of relative velocities :

, simplifying;

Defining a new RELATIVE stagnation enthalpy;

Redefining the Rothalpy:

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Introduction to Turbomachinery2. Fundamental Laws used in Turbomachinery

2.6. Second Law of Thermodynamics

The Clasius Inequality :

For a reversible cyclic process:

Entropy change of a state is , , that we can evaluate the isentropic process when the process is

reversible and adiabatic (hence isentropic).

Here we can re‐write the above definition as and using the first law of thermodynamics:

dQ‐dW=dh=du+pdv and

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2.5. Bernoulli’s Equation

Writing an energy balance for a flow, where there is no

heat transfer or power production/consumption, one obtains :

Applying for a differential control volume:

(where enthalpy is

When the process is isentropic ), one obtains

Euler’s motion equation:

Integrating this equation into stream

direction, Bernoulli equation is obtained:

When the flow is incompressible, density does not change, thus the equation becomes:

where and po is called as stagnation pressure.

For hydraulic turbomachines head is defined as H= thus the equation takes the form.

NOTE: If the pressure and density change is negligibly small, than the stagnation pressures at inlet and outlet

conditions are equal to each other (This is applied to compressible isentropic processes)

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2017 Midterm Q: Using the first law of thermodynamics, show the Bernoulli equationyields to Hin = Hout for hydraulic turbomachines

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2.7. Compressible flow relations

For a perfect gas, the Mach # can be written as, . Here a is the speed of sound, R, T and are

universal gas constant, temperature in (K), and specific heat ratio , respectively.

Above 0.3 Mach #, the flow is taken as compressible, therefore fluid density is no more constant.

With the stagnation enthalpy definition, for a compressible fluid: (i)

Knowing that:

and , one gets 1 (ii)

Replacing (ii) into (i) one obtains relation between static and stagnation temperatures: (iii)

Applying the isentropic process enthalpy ( / ) to the ideal gas law ( ): / and one

gets: (iv)

Integrating one obtains the relation between static and

stagnation pressures : (v)

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Introduction to Turbomachinery2. Fundemental Laws used in TurbomachineryDeriving Speed of sound

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Deriving Speed of sound

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Deriving Speed of sound


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2. Fundemental Laws used in Turbomachinery


Above combinations yield to many definitions used in turbomachinery for compressible flow. Some are listed

below:

1. Stagnation temperature – pressure relation between two arbitrary points:

2. Capacity (non‐dimensional flow rate) :

3. Relative stagnation properties and Mach #:

HOMEWORK: Derive the non dimensional flow rate (Capacity) equation using equations (iii), (v) from the previous

slide and the continuity equation

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Relation of static‐relative‐stagnation

temperatures on a T‐s diagram

Temperature (K)

Temperature – gas properties relation

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2.8. Efficiency definitions used in Turbomachinery

1. Overall efficiency

2. Isentropic – hydraulic efficiency:

3. Mechanical efficiency:

2.8.1 Steam and Gas Turbines

1. The adiabatic total‐to‐total efficiency is :

When inlet‐exit velocity changes are small: :

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2.8.1 Steam and Gas Turbines

Temperature (K)

Enthalpy – entropy relation for turbines and compressors

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2. Total‐to‐static efficiency:

Note: This efficiency definition is used when the kinetic energy is not utilized and entirely wasted. Here, exit

condition corresponds to ideal‐ static exit conditions are utilized (h2s)

2.8.2. Hydraulic turbines

1. Turbine hydraulic efficiency

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2.8.3. Pumps and compressors

1. Isentropic (hydraulic for pumps) efficiency

2. Overall efficiency

3. Total‐to‐total efficiency

4. For incompressible flow :

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2.8.4. Small Stage (Polytropic Efficiency) for an ideal gas For energy absorbing devices

integrating

For and ideal compression process , so

Therefore, the compressor efficiency is:

NOTE: Polytropic efficiency is defined to show the differential pressure effect on the overall efficiency, resulting in an

efficiency value higher than the isentropic efficiency.

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2.8.5. Small Stage (Polytropic Efficiency) for an ideal gas For energy extracting devices

Assistant Professor · 2018. 3. 6. · Since there are stationary and rotating blades in...

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