Fluid Mechanics for Power Generation P M V Subbarao Associate Professor Mechanical Engineering Department IIT Delhi An Essential Science for All Thermal Processes !!!!!

As early as 400,000 BC, fire was kindled in the caves of Peking man.

The Aelopile : Generation of Mechanical Motion In 130BC. Hero, a Greek mathematician and scientist is credited with inventing the first practical application of steam power, the aelopile. Simply a cauldron with a lid, the aelopile had two pipes that channeled steam into a hollow sphere. The sphere, which pivoted on the steam pipes, had two nozzles situated on opposite sides of its axis. Thus, the cauldron was fired, the water in it boiled, the steam was channeled into the sphere, and as the steam escaped through the nozzles, the sphere would spin. It was a thought the device and a novelty.

Truths of Modern Life Using the steam/Gas to make the Electric Power ! Rotating the shaft(Rotor) is the ultimate goal of any power plant !!! How do you get mechanical power from Live-steam or Gas? “How to get super energized (Live) steam/Gas ? “ How do u generate life in live-steam ? A science of Fluid Power is basis for all current and future power generation technologies. This Science of Fluid Power is called Fluid Mechanics.

Philosophy of Fluid Power Present and future power generation technologies are based on: Conversion of any natural power into fluid power. Transfer fluid power to shaft power. Conversion of shaft power into Electric power. Basic laws of Fluid power based power generation. Impulse principle Reaction principle Impulse-reaction principle Aerofoil theory. Every Power Engineer should study FLUID MECHANICS.

Further Applications of Fluid Mechanics Transportation of Fuel. Internal supply of fuel and air through the fuel handling equipment. Internal circulation of flue gas and steam through steam generator & Condenser. Operation of all journal bearings. Operation of all the pumps, fans & compressors. Operation of Many control systems.

Mechanical Engineering Department Fluid Mechanics P M V SUBBARAO Associate Professor Mechanical Engineering Department IIT Delhi A Science, which devalued the importance of time !!!!

Time : A Pseudo Scientific Firm Concept A powerful pseudo concept. Became an utmost important in engineering and science after Newton. Changes with respect to time, in a body is the core of Engineering. But Past and Present are more known than the future. Past and future are not two distinct entities like Delhi and Mumbai. ………….. ………… Present day Engineering and Science is strongly centered around Time base. Fluid Mechanics reduces the weight of time in Engineering.

Energy and Power The scalar product of force and displacement is Work. Capability to execute a work is energy. Rate of doing work or rate of change in energy is Power. Finally Generation of Power is a temporal act.

Newton’s Second Law for Flow Device

Newton’s Second Law for Flow Device Newton’s Force: All quantities are invariant in time. Vary in spacial direction only…. Still it is possible to accomplish Power Generation…. More Advanced systems are more invariant with time….

Stage of A Turbine

Sequence of Energy Transactions Steam Thermal Power Blade kinetic Power Steam kinetic Power Nozzle Losses Stage Losses Moving Blade Losses Isentropic efficiency of Nozzle Blade Friction Factor

Fluid Dynamics of Coal Preparation & Supply BY P M V Subbarao Associate Professor Mechanical Engineering Department I I T Delhi Aerodynamics a means of Transportation ……

Major Components of Coal Fired Steam Generator

Schematic of typical coal pulverized system A Inlet Duct; B Bowl Orifice; C Grinding Mill; D Transfer Duct to Exhauster; E Fan Exit Duct.

Velocity through various regions of the mill during steady operation

Cyclone-type classifier. Axial and radial gas velocity components

Centrifugal Classifiers The same principles that govern the design of gas-solid separators, e.g. cyclones, apply to the design of classifiers. Solid separator types have been used preferentially as classifiers in mill circuits: centrifugal cyclone-type and gas path deflection, or louver-type classifiers. The distributions of the radial and axial gas velocity in an experimental cyclone precipitator are shown in Figures. The flow pattern is further characterized by theoretical distributions of the tangential velocity and pressure, the paths of elements of fluid per unit time, and by the streamlines in the exit tube of the cyclone.

Particle Size Distribution--Pulverized-Coal Classifiers The pulverized-coal classifier has the task of making a clean cut in the pulverized-coal size distribution: returning the oversize particles to the mill for further grinding but allowing the "ready to burn" pulverized coal to be transported to the burner. The mill's performance, its safety and also the efficiency of combustion depend on a sufficiently selective operation of the mill classifier.

Mill Pressure Drop The pressure loss coefficients for the pulverized-coal system elements are not well established. The load performance is very sensitive to small variations in pressure loss coefficient. Correlation of pressure loss coefficient with Reynolds number through the mill section of an exhauster-type mill.

Fundamentals of Fluid Mechanics

Introduction Fluid mechanics is the science of fluids either at rest (fluid statics) or in motion (fluid dynamics) and their effects on boundaries such as solid surfaces or interfaces with other fluids. Definition of a fluid: a substance that deforms continuously when subjected to a shear stress. Consider a fluid between two parallel plates, which is subjected to a shear stress due to the impulsive motion of the upper plate No slip condition: no relative motion between fluid and boundary, i.e., fluid in contact with lower plate is stationary, whereas fluid in contact with upper plate moves at speed U. Fluid deforms, i.e., undergoes strain θ due to shear stress t

Properties of Fluids for Fluid Mechanics P M V Subbarao Associate Professor Mechanical Engineering Department IIT Delhi Basic Steps to Design………….

Continuum Hypothesis In this course, the assumption is made that the fluid behaves as a continuum, i.e., the number of molecules within the smallest region of interest (a point) are sufficient that all fluid properties are point functions (single valued at a point). For example: Consider definition of density ρ of a fluid δV* = limiting volume below which molecular variations may be important and above which macroscopic variations may be important.

Static Fluid For a static fluid Shear Stress should be zero. For A generalized Three dimensional fluid Element, Many forms of shear stress is possible.

One dimensional Fluid Element +Y u=U u=0 +X +

Fluid Statics tyx txy tyz tzy tzx txz Pressure : For a static fluid, the only stress is the normal stress since by definition a fluid subjected to a shear stress must deform and undergo motion. Y tyx tyz txy tzy txz tzx X Z What is the significance of Diagonal Elements? Vectorial significance : Normal stresses. Physical Significance : ? For the general case, the stress on a fluid element or at a point is a tensor

Stress Tensor X Y Z tyy tzz tyz tyx tzx tzy txx txy txz

First Law of Pascal Proof ?

Simple Non-trivial Shape of A Fluid Element

Fluid Statics for Power Generation P M V Subbarao Associate Professor Mechanical Engineering Department IIT Delhi Steps for Design of Flow Devices………….

Pressure Variation with Elevation For a static fluid, pressure varies only with elevation within the fluid. This can be shown by consideration of equilibrium of forces on a fluid element Basic Differential Equation: Newton's law (momentum principle) applied to a static fluid ΣF = ma = 0 for a static fluid i.e., ΣFx = ΣFy = ΣFz = 0 1st order Taylor series estimate for pressure variation over dz

For a static fluid, the pressure only varies with elevation z and is constant in horizontal xy planes. The basic equation for pressure variation with elevation can be integrated depending on whether ρ = constant i.e., the fluid is incompressible (liquid or low-speed gas) or ρ = ρ(z), or compressible (high-speed gas) since g is constant.

Pressure Variation for a Uniform-Density Fluid

Draft Required to Establish Air Flow Flue as out Air in

Natural Draft Zref pA = pref +Dp Hchimney Tgas Tatm B A

Zref,,pref pA = pref +Dp Hchimney Tgas Tatm B A

Pressure variations in Troposphere: Linear increase towards earth surface Tref & pref are known at Zref. a : Adiabatic Lapse rate : 6.5 K/km

Reference condition: At Zref : T=Tref & p = pref

Pressure at A: Pressure variation inside chimney differs from atmospheric pressure. The variation of chimney pressure depends on temperature variation along Chimney. Temperature variation along chimney depends on rate of cooling of hot gas Due to natural convection. Using principles of Heat transfer, one can calculate, Tgas(Z). If this is also linear: T = Tref,gas + agas(Zref-Z). Lapse rate of gas, agas is obtained from heat transfer analysis.

Natural Draft Natural Draft across the furnace, Dpnat = pA – pB The difference in pressure will drive the exhaust. Natural draft establishes the furnace breathing by Continuous exhalation of flue gas Continuous inhalation of fresh air. The amount of flow is limited by the strength of the draft.

Pressure Measurement

Pressure Measurement Pressure is an important variable in fluid mechanics and many instruments have been devised for its measurement. Many devices are based on hydrostatics such as barometers and manometers, i.e., determine pressure through measurement of a column (or columns) of a liquid using the pressure variation with elevation equation for an incompressible fluid.

PRESSURE Barometric pressure is actual atmospheric pressure Force exerted on a unit area : Measured in kPa Atmospheric pressure at sea level is 1 atm, 76.0 mm Hg, 101 kPa In outer space the pressure is essentially zero. The pressure in a vacuum is called absolute zero. All pressures referenced with respect to this zero pressure are termed absolute pressures. Barometric pressure is actual atmospheric pressure

Many pressure-measuring devices measure not absolute pressure but only difference in pressure. This type of pressure reading is called gage pressure. Whenever atmospheric pressure is used as a reference, the possibility exists that the pressure thus measured can be either positive or negative. Negative gage pressure are also termed as vacuum pressures.

Manometers Enlarged Leg Inverted U Tube U Tube Two Fluid Inclined Tube

Absolute, Gauge & Vacuum Pressures System Pressure Gauge Pressure Absolute Pressure Atmospheric Pressure Absolute zero pressure

Absolute, Gauge & Vacuum Pressures Atmospheric Pressure Vacuum Pressure System Pressure Absolute Pressure Absolute zero pressure

An important Property of A Fluid

Shear stress(t): Tangential force on per unit area of contact between solid & fluid

Elasticity (Compressibility) Increasing/decreasing pressure corresponds to contraction/expansion of a fluid. The amount of deformation is called elasticity.

Surface Tension Two non-mixing fluids (e.g., a liquid and a gas) will form an interface. The molecules below the interface act on each other with forces equal in all directions, whereas the molecules near the surface act on each other with increased forces due to the absence of neighbors. That is, the interface acts like a stretched membrane, e.g.

Vapour Pressure When the pressure of a liquid falls below the vapor pressure it evaporates, i.e., changes to a gas. If the pressure drop is due to temperature effects alone, the process is called boiling. If the pressure drop is due to fluid velocity, the process is called cavitation. Cavitation is common in regions of high velocity, i.e., low p such as on turbine blades and marine propellers.

Properties of Fluids for Fluid Mechanics P M V Subbarao Associate Professor Mechanical Engineering Department IIT Delhi Basic Steps to Design………….

Continuum Hypothesis In this course, the assumption is made that the fluid behaves as a continuum, i.e., the number of molecules within the smallest region of interest (a point) are sufficient that all fluid properties are point functions (single valued at a point). For example: Consider definition of density ρ of a fluid δV* = limiting volume below which molecular variations may be important and above which macroscopic variations may be important.

Static Fluid For a static fluid Shear Stress should be zero. For A generalized Three dimensional fluid Element, Many forms of shear stress is possible.

One dimensional Fluid Element +Y u=U u=0 +X +

Fluid Statics tyx txy tyz tzy tzx txz Pressure : For a static fluid, the only stress is the normal stress since by definition a fluid subjected to a shear stress must deform and undergo motion. Y tyx tyz txy tzy txz tzx X Z What is the significance of Diagonal Elements? Vectorial significance : Normal stresses. Physical Significance : ? For the general case, the stress on a fluid element or at a point is a tensor

Stress Tensor X Y Z tyy tzz tyz tyx tzx tzy txx txy txz

First Law of Pascal Proof ?

Simple Non-trivial Shape of A Fluid Element

Fluid Statics for Power Generation P M V Subbarao Associate Professor Mechanical Engineering Department IIT Delhi Steps for Design of Flow Devices………….

Pressure Variation with Elevation For a static fluid, pressure varies only with elevation within the fluid. This can be shown by consideration of equilibrium of forces on a fluid element Basic Differential Equation: Newton's law (momentum principle) applied to a static fluid ΣF = ma = 0 for a static fluid i.e., ΣFx = ΣFy = ΣFz = 0 1st order Taylor series estimate for pressure variation over dz

For a static fluid, the pressure only varies with elevation z and is constant in horizontal xy planes. The basic equation for pressure variation with elevation can be integrated depending on whether ρ = constant i.e., the fluid is incompressible (liquid or low-speed gas) or ρ = ρ(z), or compressible (high-speed gas) since g is constant.

Pressure Variation for a Uniform-Density Fluid

Reading Material Fluid Mechanics – Frank M White, McGraw Hill International Editions. Introduction to Fluid Mechanics – Fox & McDOnald, John Wiley & Sons, Inc. Fluid Mechanics – V L Streeter, E Benjamin Wylie & K W Bedfore, WCB McGraw Hill. Fluid Mechanics – P K Kundu & I M Cohen, Elsevier Inc.

Pressure Variation for Compressible Fluids Basic equation for pressure variation with elevation Pressure variation equation can be integrated for γ(p,z) known. For example, here we solve for the pressure in the atmosphere assuming ρ(p,T) given from ideal gas law, T(z) known, and g ≠ g(z).

Draft Required to Establish Air Flow Flue gas out Air in

Natural Draft Zref,,pref pA = pref +Dp Hchimney Tgas Tatm B A

Zref,,pref pA = pref +Dp Hchimney Tgas Tatm B A

Pressure variations in Troposphere: Linear increase towards earth surface Tref & pref are known at Zref. a : Adiabatic Lapse rate : 6.5 K/km

Reference condition: At Zref : T=Tref & p = pref

Pressure at A: Pressure variation inside chimney differs from atmospheric pressure. The variation of chimney pressure depends on temperature variation along Chimney. Temperature variation along chimney depends on rate of cooling of hot gas Due to natural convection. Using principles of Heat transfer, one can calculate, Tgas(Z). If this is also linear: T = Tref,gas + agas(Zref-Z). Lapse rate of gas, agas is obtained from heat transfer analysis.

Natural Draft Natural Draft across the furnace, Dpnat = pA – pB The difference in pressure will drive the exhaust. Natural draft establishes the furnace breathing by Continuous exhalation of flue gas Continuous inhalation of fresh air. The amount of flow is limited by the strength of the draft.

Another Application of Fluid Statics Pressure Measurement Another Application of Fluid Statics

Pressure Measurement Pressure is an important variable in fluid mechanics and many instruments have been devised for its measurement. Many devices are based on hydrostatics such as barometers and manometers, i.e., determine pressure through measurement of a column (or columns) of a liquid using the pressure variation with elevation equation for an incompressible fluid.

PRESSURE Barometric pressure is actual atmospheric pressure Force exerted on a unit area : Measured in kPa Atmospheric pressure at sea level is 1 atm, 76.0 mm Hg, 101 kPa In outer space the pressure is essentially zero. The pressure in a vacuum is called absolute zero. All pressures referenced with respect to this zero pressure are termed absolute pressures. Barometric pressure is actual atmospheric pressure

Many pressure-measuring devices measure not absolute pressure but only difference in pressure. This type of pressure reading is called gage pressure. Whenever atmospheric pressure is used as a reference, the possibility exists that the pressure thus measured can be either positive or negative. Negative gage pressure are also termed as vacuum pressures.

Manometers U Tube Enlarged Leg Inverted U Tube Two Fluid Inclined Tube

U-tube or differential manometer Right Limb fluid statics : Left Limb fluid statics : Point 3 and 2 are at the same elevation and same fluid

Gauge Pressure:

Absolute, Gauge & Vacuum Pressures System Pressure Gauge Pressure Absolute Pressure Atmospheric Pressure Absolute zero pressure

Absolute, Gauge & Vacuum Pressures Atmospheric Pressure Vacuum Pressure System Pressure Absolute Pressure Absolute zero pressure

Stress Tensor for A Static Fluid X Y Z tyy tzz txx

An important Property of A Fluid under Motion

Shear stress(t): Tangential force on per unit area of contact between solid & fluid

Elasticity (Compressibility) Increasing/decreasing pressure corresponds to contraction/expansion of a fluid. The amount of deformation is called elasticity.

Surface Tension Two non-mixing fluids (e.g., a liquid and a gas) will form an interface. The molecules below the interface act on each other with forces equal in all directions, whereas the molecules near the surface act on each other with increased forces due to the absence of neighbors. That is, the interface acts like a stretched membrane, e.g.

Vapour Pressure When the pressure of a liquid falls below the vapor pressure it evaporates, i.e., changes to a gas. If the pressure drop is due to temperature effects alone, the process is called boiling. If the pressure drop is due to fluid velocity, the process is called cavitation. Cavitation is common in regions of high velocity, i.e., low p such as on turbine blades and marine propellers.

Fluids in Motion An Unique Option for Many Power Generation Devices.. P M V Subbarao Associate Professor Mechanical Engineering Department IIT Delhi An Unique Option for Many Power Generation Devices..

Velocity and Flow Visualization Primary dependent variable is fluid velocity vector V = V ( r ); where r is the position vector. If V is known then pressure and forces can be determined. Consideration of the velocity field alone is referred to as flow field kinematics in distinction from flow field dynamics (force considerations). Fluid mechanics and especially flow kinematics is a geometric subject and if one has a good understanding of the flow geometry then one knows a great deal about the solution to a fluid mechanics problem.

Flow Past A Turbine Blade Particle p at time t1 Uniform Flow Particle p at time t2

Velocity: Lagrangian and Eulerian Viewpoints There are two approaches to analyzing the velocity field: Lagrangian and Eulerian Lagrangian: keep track of individual fluids particles. Apply Newton’s second law for each individual particle! Say particle p is at position r1(t1) and at position r2(t2) then,

Of course the motion of one particle is insufficient to describe the flow field. So the motion of all particles must be considered simultaneously which would be a very difficult task. Also, spatial gradients are not given directly. Thus, the Lagrangian approach is only used in special circumstances.

Eularian Approach Eulerian: focus attention on a fixed point in space. In general, where, u = u(x,y,z,t), v = v(x,y,z,t), w = w(x,y,z,t)

This approach is by far the most useful since we are usually interested in the flow field in some region and not the history of individual particles. This is similar to description of A Control Volume. We need to apply newton Second law to a Control Volume.

Eularian Velocity Velocity vector can be expressed in any coordinate system; e.g., polar or spherical coordinates. Recall that such coordinates are called orthogonal curvilinear coordinates. The coordinate system is selected such that it is convenient for describing the problem at hand (boundary geometry or streamlines).

Fluid Dynamics of Coal Preparation & Supply BY P M V Subbarao Associate Professor Mechanical Engineering Department I I T Delhi Aerodynamics a means of Transportation ……

Major Components of Coal Fired Steam Generator

Schematic of typical coal pulverized system A Inlet Duct; B Bowl Orifice; C Grinding Mill; D Transfer Duct to Exhauster; E Fan Exit Duct.

Velocity through various regions of the mill during steady operation

Cyclone-type classifier. Axial and radial gas velocity components

Centrifugal Classifiers The same principles that govern the design of gas-solid separators, e.g. cyclones, apply to the design of classifiers. Solid separator types have been used preferentially as classifiers in mill circuits: centrifugal cyclone-type and gas path deflection, or louver-type classifiers. The distributions of the radial and axial gas velocity in an experimental cyclone precipitator are shown in Figures. The flow pattern is further characterized by theoretical distributions of the tangential velocity and pressure, the paths of elements of fluid per unit time, and by the streamlines in the exit tube of the cyclone.

Particle Size Distribution--Pulverized-Coal Classifiers The pulverized-coal classifier has the task of making a clean cut in the pulverized-coal size distribution: returning the oversize particles to the mill for further grinding but allowing the "ready to burn" pulverized coal to be transported to the burner. The mill's performance, its safety and also the efficiency of combustion depend on a sufficiently selective operation of the mill classifier.

Mill Pressure Drop The pressure loss coefficients for the pulverized-coal system elements are not well established. The load performance is very sensitive to small variations in pressure loss coefficient. Correlation of pressure loss coefficient with Reynolds number through the mill section of an exhauster-type mill.

Polar Coordinates

Volume Rate of Flow (flow rate, discharge) Cross-sectional area oriented normal to velocity vector (simple case where V . A).

Volume Rate of Flow in A General Control Volume

Acceleration The acceleration of a fluid particle is the rate of change of its velocity. In the Lagrangian approach the velocity of a fluid particle is a function of time only since we have described its motion in terms of its position vector.

In the Eulerian approach the velocity is a function of both space and time; consequently, x,y,z are f(t) since we must follow the total derivative approach in evaluating du/dt.

Similarly for ay & az, In vector notation this can be written concisely

Basic Control-Volume Approach

Control Volume In fluid mechanics we are usually interested in a region of space, i.e, control volume and not particular systems. Therefore, we need to transform GDE’s from a system to a control volume. This is accomplished through the use of Reynolds Transport Theorem. Actually derived in thermodynamics for CV forms of continuity and 1st and 2nd laws.

Flowing Fluid Through A CV A typical control volume for flow in an funnel-shaped pipe is bounded by the pipe wall and the broken lines. At time t0, all the fluid (control mass) is inside the control volume.

The fluid that was in the control volume at time t0 will be seen at time t0 +dt as:           .

The control volume at time t0 +dt . The control mass at time t0 +dt        . The differences between the fluid (control mass) and the control volume at time t0 +dt        .

the same system occupies regions (II+III) at t0 + dt Consider a system and a control volume (C.V.) as follows: the system occupies region I and C.V. (region II) at time t0. Fluid particles of region – I are trying to enter C.V. (II) at time t0. III I II II the same system occupies regions (II+III) at t0 + dt Fluid particles of I will enter CV-II in a time dt. Few more fluid particles which belong to CV – II at t0 will occupy III at time t0 + dt.

The control volume may move as time passes. III has left CV at time t0+dt II III At time t0+dt I II At time t0 I is trying to enter CV at time t0

Reynolds' Transport Theorem Consider a fluid scalar property b which is the amount of this property per unit mass of fluid. For example, b might be a thermodynamic property, such as the internal energy unit mass, or the electric charge per unit mass of fluid. The laws of physics are expressed as applying to a fixed mass of material. But most of the real devices are control volumes. The total amount of the property b inside the material volume M , designated by B, may be found by integrating the property per unit volume, M ,over the material volume :

Conservation of B total rate of change of any extensive property B of a system(C.M.) occupying a control volume C.V. at time t is equal to the sum of a) the temporal rate of change of B within the C.V. b) the net flux of B through the control surface C.S. that surrounds the C.V. The change of property B of system (C.M.) during Dt is add and subtract

The above mentioned change has occurred over a time dt, therefore Time averaged change in BCM is

For and infinitesimal time duration The rate of change of property B of the system.

Conservation of Mass Let b=1, the B = mass of the system, m. The rate of change of mass in a control mass should be zero.

Conservation of Momentum Let b=V, the B = momentum of the system, mV. The rate of change of momentum for a control mass should be equal to resultant external force.

Conservation of Energy Let b=e, the B = Energy of the system, mV. The rate of change of energy of a control mass should be equal to difference of work and heat transfers.

First Law for A Control Volume Conservation of mass: Conservation of energy:

Complex Flows in Power Generating Equipment Separation, Vortices, and Turbulence

Classification of Flows in Power Generation

Pipe Flows

Turbulent Flow Turbulent flow: fuller profile due to turbulent mixing extremely complex fluid motion that defies closed form analysis. Turbulent flow is the most important area of power generation fluid flows. The most important nondimensional number for describing fluid motion is the Reynolds number

Internal vs. External Flows Internal flows = completely wall bounded; Usually requires viscous analysis, except near entrance. External flows = unbounded; i.e., at some distance from body or wall flow is uniform. External Flow exhibits flow-field regions such that both inviscid and viscous analysis can be used depending on the body shape and Re.

Flow in Conduits An important infrastructure for Industrialization .. P M V Subbarao Associate Professor Mechanical Engineering Department IIT Delhi An important infrastructure for Industrialization .. 185

Entrance and developed flows 186

Dimensional Analysis 187

188

189

Shear-Stress Distribution Across a Pipe Section 190

191

Laminar Flow in Pipes 192

193

Shear-Stress Distribution in Laminar Flow 194

195

196

Criterion for Laminar or Turbulent Flow in a Pipe 197

Turbulent Flow in Pipes 198

199

Moody Chart 200

Flow at Pipe Inlets and Losses From Fittings For real pipe systems in addition to friction head loss these are additional so called minor losses due to 1. entrance and exit effects 2. expansions and contractions 3. bends, elbows, tees, and other fittings 4. valves (open or partially closed) For such complex geometries we must rely on experimental data to obtain a loss coefficient 201

202

Drag & Lift 203

204

205

206

207