Turbomachinery Hasan Ozcan Assistant Professor Mechanical Engineering Department Faculty of Engineering Karabuk University
Introduction Hasan Ozcan, Ph.D, (Assistant Professor) B.Sc :Erciyes University, 2009 M.Sc :Karabuk University, 2011 Doctorate :University of Ontario Institute of Technology, 2015 Research Fields: Thermal system design, renewable energy, hydrogen production, Energy Storage 2
Marking Scheme Midterm 40% Project 20% (added to final exam elective) Final Exam 60% Introduction Sources Basic Concepts in Turbomachinery ( Ingram, 2009) Turbomachinery Performance Analysis (Levis, 1996 ) Fluid Mechanics and thermodynamics of Turbomachinery (Dixon and Hall, 2010) Course Content Week 1: Introduction and Basic Principles Week 2: Relative and Absolute Motion Week 3: Turbomachine Operation Week 4: Basic Concepts for Fluid Motion Week 5: Dimensionless Parameters in Turbomacinery Week 6: Efficiency and Reaction for Turbomachinery Week 7 9: Axial flow Machines Week 9 12: Hydraulic Turbines Week 11 13: Analysis of Pumps Week 14: Project presentations 3
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. 4
Some Applications of Turbomachinery 5
Classification of Turbomachines Energy Extracting Energy Absorbing Flow Direction: Axial, radial, mixed Fluid type: Compressible, incompressible Impulse, reaction (For hydro turbines) 6
Energy Extracting Devices Gas Turbine: Energy production is accomplished by extracting energy from a compressible gas such as air, helium, or CO 2. 7
Energy Extracting Devices Steam Turbine: Energy production is accomplished by extracting energy from superheated high pressure steam. Many other liquid woring fluids are also in use. 8
Energy Extracting Devices Wind Turbine: Converts kinetic energy of air into mechanical energy. 9
Energy Extracting Devices Hydro Turbine: Hydoturbines are used to convert the potential energy of water into mechanical energy. 10
Energy Absorbing Devices Pumps: Absorbs energy to increase the pressure of a liquid. 11
Energy Absorbing Devices Fans: Low pressure increase of high flow rate gases. 12
Energy Absorbing Devices Blowers: Medium pressure increase of medium flow rate gases. 13
Energy Absorbing Devices Compressors: High pressure increase of low flow rate gases 14
Positive displacement vs dynamic turbomachines Courtesy of slidesharecdn.com 15
Fluid Type Compressible: (Fans, blowers, compressors, gas turbines) Incompressible: (hydro turbines) 16
1. Coordinate System Introduction to Turbomachinery Since 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 17
1. Coordinate System Introduction to Turbomachinery The Velocity at the meridional direction is: Where x and r stand for axial and radial. NOTE: In purely axial flow machines C r = 0, and in purely radial flow machines C x =0 Axial View Axial View Stream surface View 18
1. Coordinate System Total flow velocity is calculated based on below view as The swirl (tangential) angle is (i) Relative Velocities Relative Velocity (ii) Relative Flow Angle (iii) Stream surface View Combining i, ii, and iii ; 19
2. Fundemental Laws used in Turbomachinery 2.1. Continuity Equation (Conservation of mass principle) 2.2. Conservation of Energy (1 st law of thermodynamics) Stagnation enthalpy; if gz = 0; For work producing machines For work consuming machines 20
2. Fundemental Laws used in Turbomachinery 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 21
2. Fundemental Laws used in Turbomachinery 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: 22
2. 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, reversible and adiabatic (hence isentropic)., that we can evaluate the isentropic process when the process is Here we can re write the above definition as dq dw=dh=du+pdv and and using the first law of thermodynamics: 23
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2. Fundamental Laws used in Turbomachinery 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 p o 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) 25
2017 Midterm Q: Using the first law of thermodynamics, show the Bernoulli equation yields to Hin = Hout for hydraulic turbomachines 26
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2. Fundemental Laws used in Turbomachinery 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: Knowing that: (i) and, one gets 1 (ii) Replacing (ii) into (i) one obtains relation between static and stagnation temperatures: Applying the isentropic process enthalpy ( / ) to the ideal gas law ( ): / and one gets: (iv) (iii) Integrating one obtains the relation between static and stagnation pressures : 28 (v)
2. Fundemental Laws used in Turbomachinery Deriving Speed of sound 29
2. Fundemental Laws used in Turbomachinery Deriving Speed of sound 30
2. Fundemental Laws used in Turbomachinery Deriving Speed of sound 31
2. Fundemental Laws used in Turbomachinery 2.7. Compressible flow relations 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 32
2. Fundamental Laws used in Turbomachinery 2.7. Compressible flow relations Temperature (K) Relation of static relative stagnation Temperature gas properties relation temperatures on a T s diagram 33
2. Fundemental Laws used in Turbomachinery 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: : 34
2. Fundemental Laws used in Turbomachinery 2.8.1 Steam and Gas Turbines Temperature (K) Enthalpy entropy relation for turbines and compressors 35
2. Fundemental Laws used in Turbomachinery 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 (h 2s ) 2.8.2. Hydraulic turbines 1. Turbine hydraulic efficiency 36
2. Fundemental Laws used in Turbomachinery 2.8.3. Pumps and compressors 1. Isentropic (hydraulic for pumps) efficiency 2. Overall efficiency 3. Total to total efficiency 4. For incompressible flow : 37
2. Fundemental Laws used in Turbomachinery 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. 38
2. Fundemental Laws used in Turbomachinery 2.8.5. Small Stage (Polytropic Efficiency) for an ideal gas For energy extracting devices 39