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STEAM NOZZLES

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A presentation on Steam Nozzles.

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STEAM NOZZLES

  1. 1. LECTURE NOTES – POWER PLANT ENGINEERING STEAM NOZZLES VANITA THAKKAR ASSOCIATE PROFESSOR MECHANICAL ENGINEERING DEPARTMENT, BABARIA INSTITUTE OF TECHNOLOGY, VARNAMA, VADODARA
  2. 2. VANITA THAKKAR - BIT 2 INTRODUCTION  A Power Plant / Power Station is an industrial facility for generation of Electric Power.  It is a set-up consisting of systems and sub-systems, equipments and auxiliaries required for the generation of Electricity, which involves conversion of energy forms like chemical energy, heat energy or gravitational potential energy into Electrical Energy.
  3. 3. 3 VANITA THAKKAR - BIT ENERGY CONVERSION PROCESS The energy content in a primary source of energy, like  Chemical Energy of a Fossil Fuel,  Potential Energy of water stored at a height,  Renewable / Non-conventional sources, like Solar Thermal Energy, Wind energy, Geothermal Energy, Tidal Energy, Wave Energy, etc. is converted stage-wise to Mechanical Energy (Rotational Energy) to obtain Electricity by creating relative motion between a magnetic field and a conductor.
  4. 4. VANITA THAKKAR - BIT 4 THERMAL POWER PLANTS  In Thermal Power Plants, mechanical power is produced by a Heat Engine that transforms Thermal Energy, often from Combustion of a Fuel, into Rotational Energy.  Most Thermal Power Stations produce steam, and these are sometimes called Steam Power Plants / Stations.  Not all thermal energy can be transformed into mechanical power, according to the Second Law of Thermodynamics. Therefore, there is always heat lost to the environment.  If this loss is employed as useful heat, for industrial processes or distinct heating, the power plant is referred to as a Cogeneration Power plant or CHP (combined heat-and- power) plant.
  5. 5. VANITA THAKKAR - BIT 5 RANKINE CYCLE  A Thermal Power Plant is a power plant in which the prime mover is steam driven.  Water is heated, turns into steam in Boiler and spins a Steam Turbine which either drives an Electrical Generator or does some other work, like Ship Propulsion.  After it passes through the turbine, the steam is condensed in a Condenser and recycled to where it was heated.  This is known as a Rankine cycle – as shown in the figure.
  6. 6. VANITA THAKKAR - BIT 6 MORE ABOUT RANKINE CYCLE  The Rankine cycle is a thermodynamic cycle which converts heat into work.  The heat is supplied externally to a closed loop, which usually uses water as the working fluid.  This cycle generates about 80% of all electric power used throughout the world, including virtually all solar thermal, biomass, coal and nuclear power plants.  It is named after William John Macquorn Rankine, a Scottish polymath.
  7. 7. VANITA THAKKAR - BIT 7 WILLIAM RANKINE  The Rankine Cycle is named after William Rankine. Trained as a civil engineer, William Rankine was appointed to the chair of civil engineering and mechanics at Glasgow in 1855. He developed methods to solve the force distribution in frame structures.  He worked on heat, and attempted to derive Sadi Carnot's law from his own hypothesis. His work was extended by Maxwell.  Rankine also wrote on fatigue in the metal of railway axles, on Earth pressures in soil mechanics and the stability of walls. He was elected a Fellow of the Royal Society in 1853.  Among his most important works are Manual of Applied Mechanics (1858), Manual of the Steam Engine and Other Prime Movers (1859) and On the Thermodynamic Theory of Waves of Finite Longitudinal Disturbance.
  8. 8. VANITA THAKKAR - BIT 8 PROCESSES IN RANKINE CYCLE  There are Four processes in the Rankine cycle, each changing the state of the working fluid.  Process 1-2: Working fluid is PUMPED from low to high pressure, as the fluid is a liquid at this stage the pump requires little input energy.  Process 2-3: The high pressure liquid enters a BOILER where it is heated at constant pressure by an external heat source to become a dry saturated vapour (or wet vapour).  Process 3-4: The dry saturated vapour expands through a TURBINE, generating power. Due to decrease in temperature and pressure of the vapour, and some condensation may occur.  Process 4-1: The wet vapour then enters a CONDENSER where it is condensed at a constant pressure and temperature to become a saturated liquid. The pressure and temperature of the condenser is fixed by the temperature of the cooling coils as the fluid is undergoing a phase- change.
  9. 9. VANITA THAKKAR - BIT 9 RANKINE CYCLE : PRACTICAL CARNOT CYCLE  The Rankine cycle is sometimes referred to as a Practical Carnot cycle as, when an efficient turbine is used, the TS diagram will begin to resemble the Carnot cycle.  The main difference is that a pump is used to pressurize liquid instead of gas. This requires about 1/100th (1%) as much energy than that in compressing a gas in a compressor (as in the Carnot cycle).
  10. 10. VANITA THAKKAR - BIT 10 Thus, BASIC COMPONENTS OF THERMAL POWER PLANT  BOILER  STEAM TURBINE : The Prime Mover  CONDENSER  FEED PUMP Supported by various sub-systems / accessories / equipments required for their proper, efficient working and to ensure their proper working in co-ordination with each other.
  11. 11. VANITA THAKKAR - BIT 11 SCHEMATIC OF A STEAM POWER PLANT
  12. 12. VANITA THAKKAR - BIT 12 STEAM TURBINES  A steam turbine is a mechanical device – a PRIME MOVER - that extracts thermal energy from high pressure, high temperature steam, and converts it into rotary motion.  PRIME MOVER : A machine that transforms energy from thermal or pressure form to mechanical form; typically  ENGINE : A mechanical device used to produce rotation to move vehicle or otherwise provide the force needed to generate kinetic energy OR  TURBINE : Any of various rotary machines that use the kinetic energy of a continuous stream of fluid - a liquid or a gas - to turn a shaft.
  13. 13. VANITA THAKKAR - BIT 13 HISTORICAL BACKGROUND OF STEAM TURBINES  The AEOLIPILE is considered to be the first recorded steam engine or reaction steam turbine. The name – derived from the Greek words "aeolos" and "pila" – translates to "the ball of Aeolus“ (Aeolus : Greek god of the wind).  It is a rocket style jet engine described in the first century BC by Vitruvius in his treatise De architectura. Later, in the first century AD, Hero of Alexandria also described the instrument, and many sources mistakenly give him the credit for its invention.  It used steam power directed through two jet nozzles so as to cause a sphere to spin rapidly on its axis.  It was a stand-alone device, and was presumably intended as a temple 'wonder', like many of the other devices described in Hero’s Pneumatica.
  14. 14. VANITA THAKKAR - BIT 14 HISTORICAL BACKGROUND OF STEAM TURBINES (contd.)  More than a thousand years later, the first impact steam turbine with practical applications was invented in 1551 by Taqi al-Din in Ottoman, Egypt, who described it as a prime mover for rotating a SPIT (a cooking aid – a long solid rod used to hold food while it is being cooked over a fire in a fireplace or over a campfire, or roasted in an oven ).  Similar smoke jacks were later described by John Wilkins in 1648 and Samuel Pepys in 1660.  Another steam turbine device was created by Italian Giovanni Branca in 1629. Spitted fowl are rotated by a hand-crank and basted with a long-handled spoon in this illustration from the Romance of Alexander, Bruges, 1338-44 (Bodleian Library).
  15. 15. VANITA THAKKAR - BIT 15 HISTORICAL BACKGROUND OF STEAM TURBINES (contd.)  The modern steam turbine was invented in 1884 by the Englishman Sir Charles Parson, whose first model was connected to a dynamo that generated 7.5 kW of electricity.  The invention of Parson's steam turbine made cheap and plentiful electricity possible and revolutionized marine transport and naval warfare.  His patent was licensed and the turbine scaled-up shortly after by an American, George Westinghouse. A number of other variations of turbines have been developed.  The de Laval turbine (invented by Gustaf de Laval – Swedish Engineer) accelerated the steam to full speed before running it against a turbine blade (IMPULSE TURBINE). This was good, as the turbine is simpler, less expensive and does not need to be pressure-proof. It can operate with any pressure of steam. It is, however, considerably less efficient. The Parson's turbine also turned out to be relatively easy to scale- up. His invention adopted for all major world power stations. The size of his generators had increased from his first 7.5 kW set up to units of 50,000 kW capacity. Within Parson's lifetime the generating capacity of a unit was scaled-up by about 10,000 times.
  16. 16. VANITA THAKKAR - BIT 16 ENERGY CONVERSION IN STEAM TURBINE Energy Conversion in Steam Turbine takes place in TWO STEPS :  High Pressure, High Temperature Steam expands in Nozzles and comes out at a high velocity.  High velocity steam jets from Nozzles impinge on the blades mounted on a wheel – Rotor – get deflected by an angle and suffer a loss of momentum which is absorbed by the Rotor in producing Torque. Thus, STEAM TURBINE = Assemblage of Nozzles and Blades (mounted on Rotor).
  17. 17. VANITA THAKKAR - BIT 17 NOZZLES  A NOZZLE is a device, a DUCT of smoothly varying c/s area, that increases the velocity of a fluid at the expense of pressure.  The chief use of nozzle is to produce a jet of steam (or gas) of high velocity to produce thrust for the propulsion of rocket motors and jet engines and to drive steam or gas turbines.  A DIFFUSER is a device that increases the pressure of a fluid by slowing it down.  Diffusers are used in compressors, combustion chambers etc.
  18. 18. VANITA THAKKAR - BIT 18 TYPES OF NOZZLES TWO types of nozzles :  Convergent : The cross section of the nozzle tapers to a smaller section to allow for changes which occur due to changes in velocity, specific volume, dryness fraction – as the fluid expands. It has lower Expansion Ratio and hence lower outlet velocities.  THE SMALLEST SECTION OF THE NOZZLE IS CALLED THROAT.  Convergent – Divergent (c-d nozzle) : The nozzle which converges to throat and diverges afterwards. It has higher Expansion Ratio – as addition of divergent portion produces steam at higher velocities. CONVERGENT NOZZLE CONVERGENT-DIVERGENT NOZZLE
  19. 19. VANITA THAKKAR - BIT 19 FLOW THRO’ NOZZLES : VELOCITY AND HEAT DROP ASSUMPTIONS :  Steady state  Adiabatic boundaries (Fluid Velocity is very high, so there is no time available for heat exchange with surroundings.)  Equilibrium states at inlet and outlet  Mass average velocities adequate for calculations  No shaft work  Change in potential energy is negligible. 1 2 Consider fluid flow through a nozzle, initially at : pressure = p1; Enthalpy = h1, inlet velocity = V1 Outlet conditions are respectively p2, h2 and V2 (denoted by subscript 2). According to Steady Flow Energy Equation (SFEE) : (h1 + V1 2/2) = (h2 + V2 2/2) => (h1 - h2 ) = (V2 2/2 - V1 2/2 )
  20. 20. VANITA THAKKAR - BIT 20 FLOW THRO’ NOZZLES : VELOCITY AND HEAT DROP (contd.) => V2 = √{V1 2 + 2 (h1 – h2)} Since, V1 << V2, V2 = √{2 (h1 – h2)} OR V2 = √{2 ∆h} Since, enthalpy is usually expressed in kJ/kg, and velocity in m/s, V2 = √1000{2 ∆h} => V2 = [44.72√∆h] m/s ….. (1) When the expanding fluid is a vapour, ∆h is called Rankine Heat Drop, which can be found from Mollier Chart or Steam Tables for steam. For Gases : pvγ = Constant ∆h = Cp.∆T
  21. 21. VANITA THAKKAR - BIT 21 CROSS SECTION AREA AT OUTLET FOR GIVEN INLET AREA From Continuity Equation : (A1V1/v1) = (A2V2/v2) = m = (AV/v) (in general); Where, A = Area (m2); v = specific volume (m3/kg); m = mass flow rate (kg/s) Area per unit mass flow, (A/m) = (v/V) i.e., (A/m) = (v/ 44.72√∆h) [From (1)] Thus, it can be seen that : for calculating variations in area of the nozzle, it is essential to know how expansion takes place, i.e. how specific volume and enthalpy vary in the duct.
  22. 22. VANITA THAKKAR - BIT 22 2. GENERAL RELATIONSHIP BETWEEN AREA, VELOCITY AND PRESSURE (Effect of Area on Flow Properties in Isentropic Flow)  To Study : the effect of Area variation on the velocity and pressure.  Here, we determine the effect of change in area, A, on the velocity V, and the pressure p. From Steady Flow Energy Equation (SFEE) between two planes at an infinitesimal distance apart : dQ = dh + d(V2/2) +dW For adiabatic flow in a Nozzle / Diffuser : dQ = 0 and dW = 0 Hence, dh + d(V2/2) = 0 ……………. (1) From Second Law of Thermodynamics, for reversible flow between planes at infinitesimal distance : dQ = T.ds From First Law of Thermodynamics : (dQ)rev = du + p.dv Thus, Tds = du + p.dv = [dh – d(pv)] + p.dv = dh – v.dp For an isentropic process, dQ = T.ds = 0, hence, dh = v.dp ………….. (2) From (1) and (2) : v.dp + d(V2/2) = 0 i.e., dp/ρ + d(V2/2) = 0 ……………… (3) [as v = 1/ρ]
  23. 23. VANITA THAKKAR - BIT 23 GENERAL RELATIONSHIP BETWEEN AREA, VELOCITY AND PRESSURE (Effect of Area on Flow Properties in Isentropic Flow) – contd. Dividing by ρ/V2, ………….. (4) Logarithmic Differentiation of Continuity Equation, (AV/v) = constant : [ln A+ lnV – lnv = contant]; Differentiating : (dA/A) + (dV/V) – (dv/v) = 0 i.e. …………. (5) From (4) and (5) : OR
  24. 24. VANITA THAKKAR - BIT 24 GENERAL RELATIONSHIP BETWEEN AREA, VELOCITY AND PRESSURE (Effect of Area on Flow Properties in Isentropic Flow) – contd. For Isentropic Process : [a2 = dp/dρ] Hence : ……….. (5) Thus, we see that For Ma<1 an area change causes a pressure change of the same sign, i.e. positive dA means positive dp for Ma<1. For Ma>1, an area change causes a pressure change of opposite sign, i.e. positive dA means negative dp for Ma>1.
  25. 25. VANITA THAKKAR - BIT 25 GENERAL RELATIONSHIP BETWEEN AREA, VELOCITY AND PRESSURE (Effect of Area on Flow Properties in Isentropic Flow) – contd. From (4) and (5) : ….(6) Thus, we see that For Ma<1, an area change causes a velocity change of opposite sign, i.e. positive dA means negative dV for Ma<1. For Ma>1, an area change causes a velocity change of same sign, i.e. i.e. positive dA means positive dV for Ma>1
  26. 26. VANITA THAKKAR - BIT 26 GENERAL RELATIONSHIP BETWEEN AREA, VELOCITY AND PRESSURE (Effect of Area on Flow Properties in Isentropic Flow) – contd.  If a nozzle is used to obtain a supersonic stream staring from low speeds at the inlet, then the Mach number should increase from Ma=0 near the inlet to Ma>1 at the exit.  It is clear that the nozzle must converge in the subsonic portion and diverge in the supersonic portion.  Such a nozzle is called a convergent- divergent nozzle (De Laval Nozzle).  It is also clear that the Mach number must be unity at the throat, where the area is neither increasing nor decreasing. This is consistent with Equation (6), which shows that dV can be non-zero at the throat only if Ma=1. It also follows that the sonic velocity can be achieved only at the throat of a nozzle or a diffuser.
  27. 27. VANITA THAKKAR - BIT 27 More about Flow through c-d nozzle Ma may not necessarily be unity at the throat. According to Eq. (6), such situations are possible when Ma≠1 at the throat and if dV=0.  The flow in a convergent-divergent duct may be subsonic everywhere with Ma increasing in the convergent portion and decreasing in the divergent portion with Ma≠1 at the throat (see upper Fig.). The first part of the duct is acting as a nozzle, whereas the second part is acting as a diffuser.  Alternatively, in a convergent-divergent duct in which the flow is supersonic everywhere with Ma decreasing in the convergent part and increasing in the divergent part and again at the throat Ma≠1 (see lower Fig.). Here, First part : Diffuser; Second Part : Nozzle.
  28. 28. VANITA THAKKAR - BIT 28 4. CONDITION FOR MAXIMUM FLOW THROUGH A NOZZLE Consider fluid flow through a nozzle, initially at : pressure = p1; Enthalpy = h1, inlet velocity = V1 Outlet conditions are respectively p2, h2 and V2 (denoted by subscript 2). According to Steady Flow Energy Equation (SFEE) : (h1 + V1 2/2) = (h2 + V2 2/2) => (h1 - h2 ) = (V2 2/2 - V1 2/2 ) => V2 = √{V1 2 + 2 (h1 – h2)} Since, V1 << V2, V2 = √{2 (h1 – h2)} OR V2 = √{2 ∆h} From Second Law of Thermodynamics, for reversible flow between planes at infinitesimal distance : dQ = T.ds From First Law of Thermodynamics: (dQ)rev = du + p.dv Thus, Tds = du + p.dv = [dh – d(pv)] + p.dv = dh – v.dp For an isentropic process, dQ = T.ds = 0, hence, dh = v.dp ………….. (1)
  29. 29. VANITA THAKKAR - BIT 29 CONDITION FOR MAXIMUM FLOW THROUGH A NOZZLE (contd.) => Assuming that the pressure and volume of steam during expansion obey the law pvn = constant, where n is the isentropic index, ( ) 1 1 1 2 2 2 1 1 n n n n n n p v p p n − −   −   = −   −    
  30. 30. VANITA THAKKAR - BIT 30 CONDITION FOR MAXIMUM FLOW THROUGH A NOZZLE (contd.) i.e., ∆h Now, mass flow rate : => Therefore, the mass flow rate at the exit of the nozzle : ….. (2) OR …....(2) (As V = √{2 ∆h}) ( ) 1 1 2 2 1 1 1 1 n n n n p v p v p n −  − −  −  
  31. 31. VANITA THAKKAR - BIT 31 CONDITION FOR MAXIMUM FLOW THROUGH A NOZZLE (contd.) The exit pressure, p2 determines the for a given inlet condition. There will be only one value of pressure ratio called critical pressure ratio which gives maximum discharge (mass flow rate). The mass flow rate is maximum when, i.e. For maximum , ……(3) i.e., the discharge through the nozzle will be the maximum at the critical pressure ratio (p*/p1), shown above.
  32. 32. VANITA THAKKAR - BIT 32 CONDITION FOR MAXIMUM FLOW THROUGH A NOZZLE (contd.) Comparing this with the results of sonic properties – Refer : GENERAL RELATIONSHIP BETWEEN AREA, VELOCITY AND PRESSURE (Effect of Area on Flow Properties in Isentropic Flow) – the critical pressure occurs at the throat for Ma = 1. The critical pressure ratio is defined as the ratio of pressure at the throat to the inlet pressure, for choked flow (MAX. MASS FLOW CONDITION), i.e. when Ma = 1 at throat. n For P2/p1 or p*/ p1 1.4 for diatomic gases 0.528 1.3 for super saturated steam 0.546 1.135 for dry saturated steam 0.58 1.035 + 0.1x wet steam with dryness fraction x (Dr. Zenner’s Equation)
  33. 33. VANITA THAKKAR - BIT 33 MAXIMUM DISCHARGE THROUGH THE NOZZLE ( ) ( ) ( ) ( ) 2 1 1 12 2 1 1max 1 1 1 . 2 1 n n n n n n n n n A n m p v v n + − −                     + +             =   −  ( ) ( ) ( ) 2 1 1 12 2 1 1max 1 1 1 . 2 1 n n n n n A n m p v v n + − −       −     + +       =   −  ( ) ( ) ( ) 2 1 1 11 2 2 max 1 1 1 . 2 1 n n n n n pn m A n v + − −       −     + +       =   − 
  34. 34. VANITA THAKKAR - BIT 34 MAXIMUM DISCHARGE THROUGH THE NOZZLE (contd.) ( ) ( ) ( ) 2 1 1 1 1 1 1 2 1max 1 1 . 2 2 1 1 n n n n n n pn m A n v n   +  −    − −   +  −    −   +         =     − +   ( ) ( ) ( ) ( ) 1 1 1 1 1 2 1max 1 1 . 2 2 1 1 n n n n n pn m A n v n − − +  −    −   +         =     − +   ( ) ( ) 1 1 1 1 2 1max 1 1 . 2 2 1 1 n n n pn m A n v n − + −    −   +       =     − +   ( ) 1 1 1 max 1 . 2 1 2 1 1 2 n npn n m A n v n + −  −    =       − +     1 1 1 max 1 . 2 . ., 1 n np i e m A n v n + −   =    +  
  35. 35. VANITA THAKKAR - BIT 35 CONCLUSIONS REGARDING MAXIMUM DISCHARGE CONDITIONS From the equation it is clear that Maximum mass flow or CHOKED FLOW :  depends only on the initial condition of the steam (p1, v1) and the throat area.  does not depend on the final pressure of the steam, i.e. at the exit of the nozzle. The addition of divergent part of the nozzle after the throat does not affect the discharge of steam passing through the nozzle, but it only accelerates the steam leaving the nozzle. 1 1 1 max 1 . 2 1 n np m A n v n + −    =     +  
  36. 36. VANITA THAKKAR - BIT 36 CONCLUSIONS REGARDING MAXIMUM DISCHARGE CONDITIONS (contd.) Discharge through nozzle increases as the pressure at the throat of nozzle (p2) decreases, when the supply pressure p1 is constant. Keeping the inlet pressure p1 constant, when the nozzle outlet pressure, p2 reaches the critical value given by : the discharge becomes maximum and after that the throat pressure and mass flow rate remain constant irrespective of the pressure at the exit.
  37. 37. VANITA THAKKAR - BIT 37 VELOCITY AT THROAT IS SONIC UNDER MAXIMUM DISCHARGE CONDITIONS Under maximum discharge conditions, when the pressure ratio at the throat of the nozzle has critical pressure value, the velocity at throat – critical velocity = sonic velocity. Refer : GENERAL RELATIONSHIP BETWEEN AREA, VELOCITY AND PRESSURE (Effect of Area on Flow Properties in Isentropic Flow)
  38. 38. VANITA THAKKAR - BIT 38 MAXIMUM VELOCITY OF STEAM (CRITICAL VELOCITY) From Continuity Equation : => From equations (2) and (3), i.e. & Thus, the velocity is also dependent on the initial conditions of the steam. ( )max 1 1 1 2 1 1 n n V p v n n   −  =     − +   ( )max 1 12 1 n V p v n   =   +  ( ) 1 1 max 1 1 2 2 1 1 1 n n n nn V p v n n − −          −      − +        
  39. 39. VANITA THAKKAR - BIT 39 CHOKED FLOW THROUGH A CONVERGENT NOZZLE …. WHEN A NOZZLE OPERATES UNDER MAXIMUM FLOW CONDITIONS, IT IS SAID TO BE CHOKED. Consider a convergent nozzle with constant inlet pressure p1, whose back pressure pb can be varied by a valve. When pb= p1, there is no fluid flow through the nozzle. As pb decreases, mass flow through the nozzle increases, as enthalpy decreases and velocity increases. When pb = p*, i.e. CRITICAL PRESSURE, further reduction in pb cannot affect the mass flow. Also, when pb = p*, velocity at the exit is sonic and mass flow rate through the nozzle is maximum.
  40. 40. VANITA THAKKAR - BIT 40 CHOKED FLOW THROUGH A CONVERGENT NOZZLE (contd.) If pb is reduced below p*, mass flow remains maximum, exit pressure p2 remains at p* and fluid expands violently outside the nozzle down to pb. Thus maximum flow through a convergent nozzle is obtained when the pressure ratio across the nozzle is critical pressure ratio.
  41. 41. VANITA THAKKAR - BIT 41 CHOKED FLOW THROUGH A C-D NOZZLE For a C-D Nozzle with sonic velocity at the throat, the cross-section area of the throat fixes the mass flow through the nozzle for fixed inlet conditions. A correctly designed C-D Nozzle is always choked.
  42. 42. VANITA THAKKAR - BIT 42 EFFECT OF FRICTION AND NOZZLE EFFECIENCY For steam flowing through a nozzle, its final velocity for a given pressure drop is reduced due to :  Friction between nozzle surface and steam.  Internal friction of steam itself.  Shock losses. Most of the frictional losses occur between the throat and exit in c-d nozzle, producing following effects :  Expansion is no more isentropic.  Enthalpy drop is reduced.  Final dryness fraction of steam increases (kinetic energy  heat, due to friction and gets absorbed.)  Specific Volume of steam increases. (steam becomes more dry due to frictional reheating.)
  43. 43. VANITA THAKKAR - BIT 43 EFFECT OF FRICTION AND NOZZLE EFFECIENCY (contd.) Point 1 : nozzle entrance, DRY SATURATED STEAM. Line 1-2 : steam expansion from entrance to throat (friction neglected) Line 2-3 : steam expansion from throat to exit (friction neglected). Friction occurs mainly between throat and exit, hence, considering friction, heat drop is represented by Line 2-3’.
  44. 44. VANITA THAKKAR - BIT 44 EFFECT OF FRICTION AND NOZZLE EFFECIENCY (contd.) The horizontal line from point 3’ cuts the pressure line on which point 3 lies on 2’, which represents the final condition of the steam (nozzle exit). Hence actual process of expansion is given by : Line 1-2-2’. Dryness Fraction of steam is more at 2’ than at 3. Hence, the effect of friction is to improve the quality of steam.
  45. 45. VANITA THAKKAR - BIT 45 EFFECT OF FRICTION AND NOZZLE EFFECIENCY (contd.) Point 4 : nozzle entrance, SUPERHEATED STEAM. Line 4-5 : steam expansion from entrance to throat (friction neglected) Line 5-6 : steam expansion from throat to exit (friction neglected) Friction occurs mainly between throat and exit, hence, considering friction, heat drop is represented by Line 4-6’.
  46. 46. VANITA THAKKAR - BIT 46 EFFECT OF FRICTION AND NOZZLE EFFECIENCY (contd.) The horizontal line from point 6’ cuts the pressure line on which point 6 lies on 5’, which represents the final condition of the steam (nozzle exit). Hence actual process of expansion is given by : Line 4-5- 5’. Dryness Fraction of steam is more at 5’ than at 6. Hence, the effect of friction is to superheat the steam.
  47. 47. VANITA THAKKAR - BIT 47 EFFECT OF FRICTION AND NOZZLE EFFECIENCY (contd.) NOZZLE EFFICIENCY : The ratio of ACTUAL ENTHALPY DROP to ISENTROPIC ENTHALPY DROP between the same pressure. Nozzle efficiency : (FOR DRY, SATURATED STEAM) (FOR SUPERHEATED STEAM) 1 3' zzle 1 3 h h h h Νο − η = − 4 6' zzle 4 6 h h h h Νο − η = −
  48. 48. VANITA THAKKAR - BIT 48 Why friction is considered only between throat and exit in c-d nozzle ? Reasons why friction is assumed between throat and exit only for c-d nozzle : 1.Small inlet velocity in the convergent portion, hence friction losses are also small. 2.No losses due to turbulence in convergent part. 3.Divergent part of the nozzle is longer to avoid flow separation. 4.Velocity is high in divergent portion. 5.Angle of divergence is less than 20o. 6.There are losses in the divergent portion due to turbulence.
  49. 49. VANITA THAKKAR - BIT 49 EFFECT OF FRICTION AND NOZZLE EFFECIENCY (contd.) Exit velocity under isentropic conditions = V3 Let, Actual exit velocity = V2’ By steady flow energy equation (SFEE) : or (ISENTROPIC CONDITIONS) or (ACTUAL CONDITIONS) 2 2 1 2' 1 2' 2 2 V V h h+ = + 2 2 2' 1 1 2' 2 V V h h − − = 22 31 1 3 2 2 VV h h+ = + 2 2 2' 1 Nozzle 2 2 3 1 Nozzle Efficiency, V V V V − η = − 2 2 3 1 1 3 2 V V h h − − =
  50. 50. VANITA THAKKAR - BIT 50 EFFECT OF FRICTION AND NOZZLE EFFECIENCY (contd.) As V1 <<< V2’, V3 Value of Nozzle Efficiency depends on : 1.Nozzle material. 2.Workmanship in manufacture of nozzle. 3.Shape and size of nozzle. 4.Angle of divergence. 5.Nature of fluid flowing and its state. 6.Fluid velocity. 7.Friction 8.Turbulence in nozzle flow passages. 2 2' Nozzle 2 3 Nozzle Efficiency, V V η =
  51. 51. VANITA THAKKAR - BIT 51 FACTORS AFFECTING NOZZLE EFFECIENCY Nozzle Type Velocity Coefficient Roughly cast nozzles 0.93 to 0.94 Machined nozzles 0.95 to 0.96 Smoothly milled nozzles 0.96 to 0.97 VELOCITY COEFFICIENT : Ratio of ACTUAL EXIT VELOCITY to the EXIT VELOCITY WHEN THE FLOW IS ISENTROPIC between the same pressure. Thus, Velocity Coefficient is the square root of Nozzle Efficiency when the inlet velocity is assumed to be negligible. 2 ' Nozzle 3 Velocity Coefficient V V = = η
  52. 52. VANITA THAKKAR - BIT 52 SUPERSATURATED FLOW When steam flows / expands through a nozzle, it would be normally expected that the discharge of steam through the nozzle would be slightly less than the theoretical value. But, experiments on flow of wet steam show that Discharge is slightly greater than that calculated by the formulae. This can be explained as follows :  The converging part of the nozzle is so short and the steam velocity is so high that the molecules of steam have insufficient time to collect and form droplets.  So, normal condensation does not take place.
  53. 53. VANITA THAKKAR - BIT 53 SUPERSATURATED FLOW (contd.)  There is a phase of rapid expansion, which is said to be metastable and it produces supersaturated state.  In supersaturated state, steam is undercooled to a temperature less than that corresponding to its pressure.  So, density of the steam increases and hence the weight of discharge.
  54. 54. VANITA THAKKAR - BIT 54 SUPERSATURATED FLOW – WILSON’S LINE Prof. Wilson showed it experimentally that : “When dry saturated steam is suddenly expanded in absence of dust, it does not condense until its density is about EIGHT TIMES that of the saturated vapour at the same pressure.” The limiting condition of under-cooling at which condensation commences and is assumed to restore conditions of normal thermal equilibrium is called WILSON LINE.
  55. 55. VANITA THAKKAR - BIT 55 SUPERSATURATED FLOW (contd.) Consider the h-s diagram shown in the figure. The process 1-2 is the isentropic expansion. The change of phase should begin to occur at point 2. BUT, Vapour continues to expand in a dry state.
  56. 56. VANITA THAKKAR - BIT 56 SUPERSATURATED FLOW(contd.) Steam remains in an unnatural superheated state until its density is about eight times that of the saturated vapour density at the same pressure (As per Prof. Wilson’s Experiment). When this limit is reached, the steam will suddenly condense.
  57. 57. VANITA THAKKAR - BIT 57 SUPERSATURATED FLOW(contd.) Point 3 is achieved by extension of the curvature of constant pressure line p3 from the superheated region which strikes the vertical expansion line at 3 and through which Wilson line also passes. The point 3 corresponds to a metastable equilibrium state of the vapour. The process 2-3 shows expansion under super-saturation condition which is not in thermal equilibrium. It is also called under cooling.
  58. 58. VANITA THAKKAR - BIT 58 SUPERSATURATED FLOW(contd.) At any pressure between p2 and p3 i.e., within the superheated zone, the temperature of the vapours is lower than the saturation temperature corresponding to that pressure. Since at 3, the limit of supersaturation is reached, the steam now condenses instantaneously to its normal state at the constant pressure and constant enthalpy which is shown by the horizontal line 3-3’ where 3’ is on normal wet area pressure line of the same pressure p3.
  59. 59. VANITA THAKKAR - BIT 59 SUPERSATURATED FLOW(contd.) 3’-4’ is again isentropic expansion in thermal equilibrium. To be noted that 4 and 4’ are on the same pressure line. Effect of supersaturation : •Increase in entropy and specific volume of the steam. •Slight reduction in the enthalpy drop during expansion and corresponding reduction in final velocity.
  60. 60. VANITA THAKKAR - BIT 60 SUPERSATURATED FLOW(contd.) Effect of supersaturation (contd.) : •Final dryness fraction increases. •Density of supersaturated steam is more than that for equilibrium conditions [As no condensation during supersaturated expansion => supersaturation temperature < saturation temperature corresponding to the pressure]. •Thus, Measured discharge (=> mass) is greater than that theoretically calculated.
  61. 61. VANITA THAKKAR - BIT 61 SUPERSATURATED FLOW(contd.) Degree of super heat = p3 = Limiting saturation pressure p3s = Saturation pressure at temperature T3 shown on T-s diagram Degree of undercooling = T3s – T3 T3s is the saturation temperature at p3 T3 = Supersaturated steam temperature at point 3 which is the limit of supersaturation. Supersaturated vapour behaves like supersaturated steam (n = 1.3). 3 3s p p
  62. 62. VANITA THAKKAR - BIT 62 Important Note : Problems on supersaturated flow cannot be solved on Mollier Chart UNLESS Wilson Line is drawn on it.
  63. 63. VANITA THAKKAR - BIT 63 EFFECT OF VARIATION IN BACK PRESSURE Nozzles are designed for maximum discharge for given area. When exit pressure(p2) differs from the value for which the nozzle is designed (p*), the flow conditions in the nozzle change. When pb < p*, : UNDEREXPANDING NOZZLE – Expansion of fluid to design pressure inside nozzle; At outlet fluid expands violently and irreversibly down to pb.
  64. 64. VANITA THAKKAR - BIT 64 EFFECT OF VARIATION IN BACK PRESSURE (contd.) When pb > p*, : OVEREXPANDING NOZZLE. In Convergent Nozzle : Reduction in mass flow rate from the nozzle. In C-D Nozzle : Expansion followed by Recompression.
  65. 65. VANITA THAKKAR - BIT 65 EFFECT OF VARIATION IN BACK PRESSURE (contd.) : CONVERGENT NOZZLE Consider a convergent nozzle connected to a large reservoir of fluid. The reservoir is assumed to be so large that the inlet flow conditions to the nozzle remain constant. The back pressure (pb) is varied by a valve – as shown in the figure. When inlet pressure, p1 = pb : No fluid flow – curve (a). On reducing pb : flow starts.
  66. 66. VANITA THAKKAR - BIT 66 EFFECT OF VARIATION IN BACK PRESSURE (contd.) : CONVERGENT NOZZLE With reduction in pb : mass flow rate and velocity increase; pb > p* – curve (b)  OVEREXPANSION. When pb = p* : maximum mass flow rate / discharge through the nozzle – curve (c) : CHOKED FLOW through the nozzle. Upto this point and excluding this point : OVEREXPANDING CONDITIONS.
  67. 67. VANITA THAKKAR - BIT 67 EFFECT OF VARIATION IN BACK PRESSURE (contd.) : CONVERGENT NOZZLE With further reduction in pb i.e. pb < p* : mass flow rate, velocity and specific volume do not change. The fluid expands violently and irreversibly outside the nozzle to pb : UNDEREXPANSION, during which the pressure oscillates and shock wave is formed.
  68. 68. VANITA THAKKAR - BIT 68 EFFECT OF VARIATION IN BACK PRESSURE (contd.) : C-D NOZZLE Consider a C-D nozzle connected to a large reservoir of fluid. The reservoir is assumed to be so large that the inlet flow conditions to the nozzle remain constant. The back pressure (pb) is varied by a valve – as shown in the figure. When inlet pressure, p1 = pb : No fluid flow – curve (a). On reducing pb : flow starts.
  69. 69. VANITA THAKKAR - BIT 69 EFFECT OF VARIATION IN BACK PRESSURE (contd.) : C-D NOZZLE With reduction in pb : mass flow rate and velocity increase; pb > p* – curve (a). Here : Throat pressure is > p*. Velocity at throat is subsonic. Divergent portion acts as Subsonic Diffuser. Nozzle acts as Venturimeter.
  70. 70. VANITA THAKKAR - BIT 70 EFFECT OF VARIATION IN BACK PRESSURE (contd.) : C-D NOZZLE With further reduction in pb : When throat pressure = p* : maximum mass flow rate / discharge through the nozzle – curve (b) : CHOKED FLOW through the nozzle.
  71. 71. VANITA THAKKAR - BIT 71 EFFECT OF VARIATION IN BACK PRESSURE (contd.) : C-D NOZZLE On Further reduction in pb – Curve (c) : No change in the conditions at throat. Mass flow rate remains constant. Fluid velocity increases in the divergent portion, making velocity supersonic. At some point, due to divergence, supersonic steam is decelerated => shock wave is generated. Shock wave : Abrupt rise in pressure, increase in entropy and velocity reduces from supersonic to subsonic.
  72. 72. VANITA THAKKAR - BIT 72 EFFECT OF VARIATION IN BACK PRESSURE (contd.) : C-D NOZZLE On Further reduction in pb : Shock wave travels down the nozzle. A stage comes when pb = design exit pressure – Curve (d). In this condition, flow is accelerated continuously from sonic velocity at the throat to supersonic velocity at exit.
  73. 73. VANITA THAKKAR - BIT 73 EFFECT OF VARIATION IN BACK PRESSURE (contd.) : C-D NOZZLE Finally, on reduction in pb below designed value : Expansion takes place outside the nozzle, as in convergent nozzle : UNDEREXPANSION – Curve (e) – a series of irreversible compressions through shock-waves, alternated with irreversible expansions, until the pressure = pb.
  74. 74. VANITA THAKKAR - BIT 74 THANKS !!! VANITA THAKKAR ASSISTANT PROFESSOR DEPARTMENT OF MECHANICAL ENGINEERING, FACULTY OF TECHNOLOGY AND ENGINEERING, CHAROTAR UNIVERSITY OF SCIENCE AND ENGINEERING, CHANGA, DIST. : ANAND (GUJARAT)

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