What are the fundamentals of Fluid Machinery?
Introduction
What is fluid machinery?
 A fluid machinery (turbomachinery) is a mechanical device that converts the energy stored by a fluid into mechanical energy or vice versa
 The energy stored by a working fluid may be in the form of potential, kinetic, and intermolecular energy
 The mechanical energy is usually transmitted by a rotating shaft.
 Hydraulic Machines: Machines use mainly water, for most of the practical applications
 In this article, the basic working principle of fluid machinery and energy transfer is discussed
 The application of fluid machinery is show below :
What is the difference between fluid machinery and turbomachinery?
 Fluid machinery is the device used to transfer energy from fluid to mechanical devices or vice versa. There is an interaction between fluid and machine for power generation or industrial applications. Turbomachinery is part of fluid machinery focussing on mechanical machines.
 Turbomachinery is defined as a device that transfers fluid energy between a rotor (a moving wheel with blades) and a fluid. It involves rotating parts called as rotors. The rotor can be an impeller for pumps and a turbine for power generation.
Classification Turbomachinery
• Turbomachines are classified into two types of power generation or power absorption
 Example of Turbomachinery for power absorption
Parts of the Axial Turbine Stage
 The major components of the axial flow turbine are given as below:
 The stator comprises a series of stationary blades that acts as guide vane for incoming flows
 The rotor comprises a series of moving blades and provides work/power to the shaft
 Application of Axial Flow Turbine: thermal power plant and gas turbine of (aircraft engine)
 Major parts of axial stage turbine: The following figure shows part of the turbine and blades for a singlestage axial turbine
 Parts of Axial stage turbine
Classification Based on Direction of Energy Conversion
The fluid machines may be classified under different categories as follows:
Power Producing Device
 The device in which the energy stored in a fluid is converted in the form of mechanical energy of a rotating member is called as a turbine
 The energy stored in the fluid may in kinetic, potential, or intermolecular energy
Power Absorbing Device
 The machines which transfer mechanical energy from moving parts to a fluid by increasing its pressure or velocity are known as power absorbing fluid machine such as fans, compressors, pumps, or blowers
Power Absorbing Turbomachinery
Compressor Types
 Positive displacement can have different types
Axial Fans or blowers
 Different types of fans/blowers is shown below
 Types of blowers that are popular in many industries and domestic applications like cleaning and cooling purposes
Water Pump
 The water pump consists of a pump casing, an electric motor to run the impeller
 Water is sucked at the inlet at low pressure and it exhausted with high velocity at the outlet
 Parts of the Water pump are shown below
Classification on the Principle of Operation and Fluid type
Positive Displacement Machines
 whose functioning depends essentially on the change of volume of a certain amount of fluid within the machine
 The positive displacement means that there is a physical displacement of the boundary of the closed system containing a certain mass of fluid. This principle has been used in practice with the reciprocating motion of a piston within, a cylinder during the continuous flow of fluid across the system
 Therefore, the word reciprocating engine is also used for positive displacement machines which produce mechanical energy using a reciprocating piston is called a reciprocating pump or reciprocating compressor
Rotodynamic Machines
 The machine whose functioning depends basically on the principle of fluid dynamics is called a Rotodynamic machines
 They are different from positive displacement machines by relative motion between the moving part of the machine and fluid
 The rotating part of the machine usually comprises a number of vanes or blades, called as rotors or impellers. The nonmoving (fixed part) is termed a stator
 Depending upon the major direction of the fluid flow path in the rotor, the machine can be called a radial flow or axial flow machine
 Relative motion: Radial flow or Axial flow machine:
 As per thermodynamic laws, the work is done by the fluid on the rotor of turbines, but the rotor does the work on the fluid of the pump or compressor using external prime movers
 In the rotor of the radial flow machine, the main direction of fluid flow is radial but in the axial flow machine, the fluid path is axial
 For radial flow turbines, all fluid flows toward the center of the rotor. In contrast, for pumps and compressors, the fluid flows away from the center of the machine. Therefore, radial flow turbines can be referred to as radially inward flow machines
 Radial flow pumps, the fluid flows are for radially outward flow machines.
 Examples of radial flow machines: Francis turbines, centrifugal pumps, compressors
 Examples of axial flow machines: are Kaplan turbines and axial flow compressors.
 However, in some machines the flow can be partly radial and partly axial such a machine is called a mixedflow machine
Based on the Type of Fluid Used
 Depending on availability, fluid machines use either liquid (water) or gas as the working fluid
 A machine such as hydraulic pump transfers the mechanical energy of the rotor to the energy of the liquid. Gas turbines use hightemperature and pressure dry steam (H_{2}O) in gas phase. A compressor or a fan or a blower uses air as working fluid.
 A compressor is a machine where main purpose is to increase the static pressure of a gas. Therefore, the mechanical energy stored by the fluid is mainly in the form of pressure energy. On the other hand, fans and blowers utilize the mechanical energy of the rotor to increase mostly the kinetic energy of the fluid. In these machines, the change in static pressure is relatively small compared to pumps.
 Water or Hydraulic Turbines: For all practical cases, water is used as working fluid in turbines which is known as water turbines or hydraulic turbines.
 Steam or Gas Turbine: turbines using gases as a working fluid in practical fields are usually known to as steam turbines, gas turbines, and air turbines depending upon whether they use steam, gas (the mixture of air and products of burnt fuel in the air), or air.
Representation of A Singlestage Axial Turbine
A single stage Turbine
 A simple turbine consist of one stator and rotor arranged on one single shaft
 Due to fluid force, the torque is generated to rotate the shaft connected with electrical power generator
Cascade view of the axial turbine
 The view of the turbine is taken by the plane passing through the axis of the turbine
Meridional view of axial flow turbine
 The view of the turbine is taken by the radial plane
Multistage Axial Turbine

A series of stages form a multistage turbine

The energy (work) transfer in a single stage is limited by the blade speed

If more energy transfer per unit mass is required, then the number of stages is added one after other
Multistage steam turbine for thermal power plant
 Schematic of multistage steam turbine
 Turbine powerhouse
 Multistage Steam turbine without casing
Parts of the Radial Turbine
 Application of radial turbine: Gas turbine, turbocharger, and process industry
 Components of radial turbine
Representation of Flow through the Pump
Sectional View of Pump
 The pump is easy to understand with two sectional views of the pumps
 The impeller is an essential part of the pump which rotates to create the desired pressure of water
Cascade view of Pump
 The cascade view of the pump is shown below with a 3D view
 Cascade view of a centrifugal pump
Aerofoil Theory
What is an aerofoil?
 Aerofoil is a curved structure designed to give the most desirable ratio of lift to drag in flight
 It is used as the basic form of the wings, fins, windmills,s and planes of most aircraft are defined as an airfoil.
 The major role of an airfoil is to produce the maximum lift. Lift is used to produce torque for power generation. There is drag force which is undesirable.
Forces acting on Aerofoil
 Both lift and drag are perpendicular to each other
 Lift is the component of fluid force such that the force is perpendicular to the direction of motion, and drag is the component parallel to the direction of motion but opposite fluid flows.
Fundamental Laws used in Turbomachinery
Second Law of Thermodynamics
 The second law of thermodynamics is devised based on a physical understanding with universal experience related to heat and energy interconversion.
 Heat always moves from hotter objects (source – high energy level ) of to colder objects (sinklow energy level) unless external energy is supplied to reverse the direction of heat or energy flow. Another example is that water flows under gravity.
 The Clasius Inequality
 For a reversible cyclic process
 Entropy changes of a state for an isentropic process when the process is reversible and adiabatic
 We can re‐write the above definition using the first law of thermodynamics
Bernoulli’s Equation
 Writing an energy balance for a flow without heat transfer or power generation
 Applying Bernoulli’s equation for infinitesimal (differential) control volume: dh + cdc + gdz = 0
where enthalpy is dh = vdp=dp/ρ When the process is isentropic: Tds =dhvdp
Euler’s motion equation:
 Integrating this equation into stream direction, the Bernoulli equation is obtained
 When the flow is incompressible, density does not change, thus the equation becomes
Where P_{o} is the stagnation pressure
 For hydraulic turbomachines, head is defined as
H= Z + p/(ρg)
 If the pressure and density change are small than the stagnation pressures at inlet and outlet conditions are equal to each other. This is applied to compressible isentropic processes.
Compressible flow relations
 For a perfect gas, the Mach # can be written as,
 For a perfect gas, the Mach # can be written as, . Here a is the speed of sound, R, T and γ are universal gas constant, temperature in (K), and specific heat ratio, respectively
 For the Mach number greater than 0.3, the flow is considered as compressible, therefore fluid density is not constant
 With the stagnation enthalpy definition, for a compressible fluid:
 Relation between static and stagnation temperatures
 Relation between static and stagnation pressures
 Stagnation temperature – pressure relation between two arbitrary points
 Capacity (non‐dimensional flow rate)
 Relative stagnation properties and Mach
Thermodynamic Graphs
 Relation of static‐relative‐stagnation temperatures on a T‐s diagram
 Temperature – gas properties relation
Efficiency definitions used in Turbomachinery
Overall efficiency
 Isentropic – hydraulic efficiency:
Mechanical efficiency
Steam and Gas Turbines
The adiabatic total‐to‐total efficiency:
 When inlet‐exit velocity changes are small
Expansion and compression Process
 Enthalpy – entropy relation for turbines and compressors
Total‐to‐static efficiency
 The definition of The following efficiency is used when the kinetic energy is not utilized and entirely wasted. Here, the exit condition corresponds to ideal‐ static exit conditions are utilized (h2s)
 Hydraulic turbines
Polytrophic Efficiency
 Polytrophic efficiency is defined to show the differential pressure effect on the overall efficiency, resulting in an efficiency value higher than the isentropic efficiency
Working principle of Rotodynamic Machine
 In this section, the basic principle of rotodynamic machines and the performance of different types of fluid machines are discussed
 The major part of a rotodynamic machine is the rotor which consists of several vanes or blades
 The relative motion exists between the rotor blades/vanes and the fluid. The fluid enters over a blade with a certain velocity component and hence of momentum in the direction tangential to the rotor. While fluid flows over the rotor blades, its tangential velocity, and momentum change compared to incoming fluids.
 The rate of change of tangential momentum changes corresponds to a tangential force on the rotor
 In a turbine, the tangential momentum of the fluid is drawn to cause rotational effect. Therefore, work is done by the working fluid to the moving rotor. However, in the case of pumps or compressors, there is an increase in the tangential momentum of the fluid by supplying external energy source. Therefore work is absorbed by the working fluid from the moving rotor.
Basic Equation of Energy Transfer in Rotodynamic Machines
 The basic equations of mass, momentum and energy of fluid dynamics is applied to a fluid element flowing a rotor using the Newton’s Laws of Motion. These equations is same for all rotodynamic machines
 Here we shall discuss the momentum theorem applied to a fluid element while flowing through moving or fixed blades or vanes.
 The following represents diagrammatically a rotor of a generalized fluid machine, with 0 – 0 the axis of rotation and the angular velocity.
 The fluid enters initially the rotor at the first point 1, then it passes through the rotor and discharged at the end point 2. The points 1 and 2 are at radii and from the center of the rotor, and the directions of fluid velocities at 1 and 2 may be at any arbitrary angles.
Assumptions considered for the analysis of energy transfer
 Steadystate flow
 The mass flow rate is constant across any section. There is no storage or depletion of fluid in the rotor
 The heat and work interactions between the rotor and its surroundings take place at a constant rate
 Uniform velocity over any area normal to the flow direction. This means that the velocity vector at any point is representative of the total flow over a finite area. There is no leakage and the entire fluid undergoes the same conditions
Details of Velocity Triangles
 The velocity (V) at any point can be resolved into three mutually perpendicular components (V_{a}, V_{f}, V_{w})
 is the axial component of velocity as it is directed parallel to the axis of rotation
 is the radial component which is directed radially through the axis to the rotation
 is the tangential component which is directed at right angles to the radial direction and the tangent to the rotor at that part
 Changes in the axial velocity components at the inlet and outlet of the rotor result in a change in the axial momentum and give rise to an axial force, which is taken by a thrust bearing of the stationary rotor casing. The rate of change in radial velocity results in the change of rotor momentum in the radial direction.
 However, for an axisymmetric flow, this does not result in any net radial force on the rotor. In case of a nonuniform flow distribution over the periphery of the rotor in practice, a change in momentum in the radial direction may result in a net radial force which is carried as a journal load
 The tangential component only has an effect on the angular motion of the rotor. In consideration of the entire fluid body within the rotor as a control volume, we can write from the moment of momentum theorem
Euler’s Turbomachine Equations
 The velocity diagram for the pump is given below
Torque Generated on Rotor
 The torque exerted by the rotor on the moving fluid
where m is the mass flow rate of fluid through the rotor. The subscripts 1 and 2 denote values at the inlet and outlet of the rotor respectively. The rate of energy transfer to the fluid is then given by
 Where is the angular velocity of the rotor and which represents the linear velocity of the rotor
 Therefore and are the linear velocities of the rotor at points 2 (outlet ) and 1 (inlet) respectively The Eq, (2) is known as Euler’s equation in relation to fluid machines. The Eq. (2) can be written in terms of head gained ‘H’ by the fluid as
 As per the usual sign convention in the fluid machines, the head delivered by the working fluid to the rotor (impeller) is considered to be positive or viceversa. Therefore the above is written with a change in the sign on the righthand side according to the sign convention as
 These equations are applicable irrespective of changes in fluid density or components of velocity in other directions
 Moreover, the shape of the path taken by the fluid in moving from the inlet to the outlet is of no consequence. The expression involves only the inlet and outlet conditions. A rotor, the moving part of a fluid machine, usually consists of a number of vanes or blades mounted on a circular disc.
 Velocity triangles are important to understand the inlet and outlet of a rotor.
 The inlet and outlet portions of a rotor vane may change as per applications
 velocities at the inlet and outlet in the vector diagrams have two velocity triangles, where the velocity of fluid is relative to the rotor
Angle Made by Absolute Velocities:
 The angles made by the directions of the absolute velocities at the inlet and outlet respectively with the tangential direction,
Angle Made by Relative Velocities:
 the angles made by the relative velocities with the tangential direction. The angles must match with vane or blade angles at the inlet and outlet respectively for a smooth. Note that there is shockless entry and exit of the fluid to avoid undesirable losses.
 Now we shall apply a simple geometrical relation as follows: From the inlet velocity triangle,
or
 similarly from the outlet velocity triangle.
Using the expressions of and we get H (Work head, i.e. energy per unit weight of fluid, transferred between the fluid and the rotor as) as
 The above equation is an important form of Euler’s equation for fluid machines as it has the three components of energy transfer. These components illustrate the nature of the energy transfer
 The first term in the equation is a change in absolute kinetic energy or dynamic head of the working fluid while flowing through the rotor
 The second term of is represents the change in fluid energy because of the movement of the rotating fluid from one radius of rotation to another.
Scope of CFD Modeling
 CFD modeling has been used widely in industries for the design and performance evaluation of turbomachinery
 First, the configuration of the turbine or pump must be selected for CFD simulation.
 Steps for CFD simulation for turbomachinery
 Geometry: create a 3D model based on the blade profile and performance curve for a selected turbomachinery
 Meshing: create the mesh model using the meshing platform
 Simulation: select CFD solvers for turbomachinery using suitable CFD models
 Postprocessing
 ANSYS has separate modules for geometry and meshing of turbomachinery
 CFD modeling of Pump is discussed in the post
Conclusion
 Fluid machinery or Turbomachinery works on the second law of thermodynamics
 They are classified based on power absorption or generation, the direction of fluid flows
 The moving part is a rotor which is a common part in all turbomachinery
 CFD modeling will help for the design and optimization of performance
References
 All essential books of turbomachinery are on the page references
 There are several books focussing on thermodynamics, fluid mechanics and CFD modeling of turbomachinery