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 Introduction Marking Scheme Midterm – 40% Project – 20% (added to final exam ‐ elective) Final Exam – 60% 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 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. 4 Introduction to Turbomachinery Some Applications of Turbomachinery 5 Introduction to Turbomachinery Classification of Turbomachines ‐ Energy Extracting –Energy Absorbing ‐ Flow Direction: Axial, radial, mixed ‐ Fluid type: Compressible, incompressible ‐ Impulse, reaction (For hydro turbines) 6 Introduction to Turbomachinery Energy Extracting Devices Gas Turbine: Energy production is accomplished by extracting energy from a compressible gas such as air, helium, or CO2. 7 Introduction to Turbomachinery 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 Introduction to Turbomachinery Energy Extracting Devices Wind Turbine: Converts kinetic energy of air into mechanical energy. 9 Introduction to Turbomachinery Energy Extracting Devices Hydro Turbine: Hydoturbines are used to convert the potential energy of water into mechanical energy. 10 Introduction to Turbomachinery Energy Absorbing Devices Pumps: Absorbs energy to increase the pressure of a liquid. 11 Introduction to Turbomachinery Energy Absorbing Devices Fans: Low pressure increase of high flow rate gases. 12 Introduction to Turbomachinery Energy Absorbing Devices Blowers: Medium pressure increase of medium flow rate gases. 13 Introduction to Turbomachinery Energy Absorbing Devices Compressors: High pressure increase of low flow rate gases 14 Introduction to Turbomachinery Positive displacement vs dynamic turbomachines Courtesy of slidesharecdn.com 15 Introduction to Turbomachinery Fluid Type Compressible: (Fans, blowers, compressors, gas turbines) Incompressible: (hydro turbines) 16 Introduction to Turbomachinery 1. Coordinate System 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 Introduction to Turbomachinery 1. Coordinate System The 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 View Axial View Stream surface View 18 Introduction to Turbomachinery 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 Introduction to Turbomachinery 2. 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 20 Introduction to Turbomachinery 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 Introduction to Turbomachinery 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 Introduction to Turbomachinery 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 ,, 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 23 Introduction to Turbomachinery 24 Introduction to Turbomachinery 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 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 25 conditions are equal to each other (This is applied to compressible isentropic processes) 2017 Midterm Q: Using the first law of thermodynamics, show the Bernoulli equation yields to Hin = Hout for hydraulic turbomachines 26 27 Introduction to Turbomachinery 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: (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 : 28 (v) Introduction to Turbomachinery 2. Fundemental Laws used in Turbomachinery Deriving Speed of sound 29 Introduction to Turbomachinery 2. Fundemental Laws used in Turbomachinery Deriving Speed of sound 30 Introduction to Turbomachinery 2. Fundemental Laws used in Turbomachinery Deriving Speed of sound 31 Introduction to Turbomachinery 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 Introduction to Turbomachinery 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 Introduction to Turbomachinery 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 Introduction to Turbomachinery 2. Fundemental Laws used in Turbomachinery 2.8.1 Steam and Gas Turbines Temperature (K) Enthalpy –entropy relation for turbines and compressors 35 Introduction to Turbomachinery 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 (h2s) 2.8.2. Hydraulic turbines 1. Turbine hydraulic efficiency 36 Introduction to Turbomachinery 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 Introduction to Turbomachinery 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 Introduction to Turbomachinery 2. Fundemental Laws used in Turbomachinery 2.8.5. Small Stage (Polytropic Efficiency) for an ideal gas For energy extracting devices 39.