Theory of Steam Production P M V Subbarao

Theory of Steam Production P M V Subbarao Professor Mechanical Engineering Department The Impact of Heat Addition at High Temperature……. .

A Deeper Study of Steam Production

The Microscopic View • When a liquid evaporates to a gas in a closed container, the molecules cannot escape. • Some of the gas molecules will eventually strike the condensed phase and condense back into it. • When the rate of condensation of the gas becomes equal to the rate of evaporation of the liquid or solid, the net amount of gas, liquid and/or solid no longer changes. • The gas in the container is in equilibrium with the liquid or solid.

Starting from Liquid State Let's consider the results of heating liquid from 20°C For Ammonia Pressure must be greater than 857. 5 k. Pa For water Pressure must be greater than 2. 339 k. Pa 20 C

State 1 Liquid Ammonia @ 1 MPa Liquid Water @ 100 k. Pa 20 C • It is in a compressed liquid region or • Sub-cooled liquid region. • Start heating….

Constant Pressure Heating Process • Process from 1 -----: • The temperature and specific volume will increase from the compressed liquid, or subcooled liquid (state 1). • Proceed to reach the saturated liquid state 2 Saturated Liquid Ammonia @ 1 MPa &24. 9 C Saturated Liquid Water @ 100 k. Pa & 99. 62 C

Further Heating from Saturated Liquid Vapour @ Constant Pressure • Process form 2 ---: • At state 2 the liquid has reached the temperature at which it begins to boil, called the saturation temperature, and is said to exist as a saturated liquid. • Properties at the saturated liquid state are noted by the subscript f and v 2 = vf. • During the phase change both the temperature and pressure remain constant. • Water boils at 99. 62°C when the pressure is 100 k. Pa. • Ammonia boils at 24. 99°C when the pressure is 1000 k. Pa.

State 3 : Saturated Vapour • • Process 2 -3: At state 3 a saturated vapor exists and vaporization is complete. The subscript g will always denote a saturated vapor state. Note : v 4 = vg.

Saturated Water Vs Saturated Steam Temperature Pressure 0 C 100 120 150 200 250 300 MPa 0. 1013 0. 1985 0. 4759 1. 554 3. 973 8. 581 Specific Volume, m 3/kg Saturated Liquid Saturated Vapour 0. 001044 0. 00106 0. 00109 0. 001156 0. 001251 0. 001404 1. 673 0. 8919 0. 3928 0. 1274 0. 05013 0. 02167

Saturated Liquid Ammonia Vs Saturated Vapour Ammnia Temperature 0 C 100 120 132. 3 Pressure MPa 6. 254 9. 107 11. 33 Specific Volume, m 3/kg Saturated Liquid Saturated Vapour 0. 002188 0. 002589 0. 004255 0. 01784 0. 01003 0. 004255

State 4 : Superheated Vapour • Process 3 -4: • If the constant pressure heating is continued, the temperature will begin to increase above the saturation temperature. • State 4 is called a superheated state because T 4 is greater than the saturation temperature for the pressure. Superheated Ammonia @ 1 MPa &300 C Superheated Water @ 100 k. Pa & 300 C

Constant Pressure Process

The Theory of Producing Steam • Water and steam can be easily used as heat carriers in heating systems. • Water boils and evaporates at 100°C under atmospheric pressure. • By higher pressure, water evaporates at higher temperature e. g. a pressure of 10 bar equals an evaporation temperature of ~179. 90 C. • At a constant pressure of 10 MPa the saturation temperature is 311. 10 C.

Wet Vapour • Wet vapour is a mixture of vapour and liquid water at same temperature and pressure. • Saturation pressure is the pressure at which the liquid and vapor phases are in equilibrium at a given temperature. • Saturation temperature is the temperature at which the liquid and vapor phases are in equilibrium at a given pressure. • Saturation Pressure is function of temperature or vice versa. T = F(p) The Wagner-Ambrose equation

Equations for Saturation Conditions of Water Saturation Properties of Water :

Superposition of Many Constant Pressure Processes • If all of the saturated liquid states are connected, the saturated liquid line is established. • If all of the saturated vapor states are connected, the saturated vapor line is established. • These two lines intersect at the critical point and form what is often called the “steam dome. ” The critical point of water is 374. 14 o. C, 22. 09 MPa The critical point of ammonia is 132. 3 o. C, 11. 33 MPa

Density of Saturated Liquid

Density of Saturated Vapour

Peculiar Nature of Wet Vapour • • Pressure and temperature are not independent properties. Either p & V or T& V are independent pair. P & v or T & v can also be considered. A new property is to be defined for steam for ease of design. • This is called Quality or dryness fraction of wet steam.

Quality and Saturated Liquid-Vapor (Wet) Mixture • Now, let’s review the constant pressure heat addition process for water shown in Figure. • The state 3 is a mixture of saturated liquid and saturated vapor. • How do we locate it on the T-v diagram? • To establish the location of state 3 a new parameter called the quality x is defined as

Quality or Dryness Fraction • The quality is zero for the saturated liquid and one for the saturated vapor (0 x 1). • The average specific volume at any state 3 is given in terms of the quality as follows. • Consider a mixture of saturated liquid and saturated vapor. • The liquid has a mass mf and occupies a volume Vf. • The vapor has a mass mg and occupies a volume Vg.

Critical Point • The region to the left of the saturated liquid line and below the critical temperature is called the compressed liquid region. • The region to the right of the saturated vapor line and above the critical temperature is called the supercritical region. • At temperatures and pressures above the critical point, the phase transition from liquid to vapor is no longer discrete.

Heat Addition at sub-critical Pressure

Religious to Secular Attitude of Sustance

Thermodynamic Properties at Super Critical Pressures

Property Diagrams

Pressure Volume Diagram

Vapour • Temperature of the substance is higher than the saturation temperature at a given pressure. • Pressure of the substance is lower than the saturation pressure at a given temperature. • Molecules of substance move in random paths. • Weak inter-molecular forces. • Occupy entire volume of the container : No free surface. • Very low density • Highly compressible.

P – v- T Relation • The specific volume of A vapour: v = f (p, T) • Greatest need for Eo. S of saturated and superheated steam. • R and a are constants. • The is called as Rankine’s Equation of state, 1849.

Pressure Volume Diagram

Van der Waals EOS • One of the oldest but most extensively used of the EOS of non ideal gases • Any EOS model must reproduce graphs such as that of the previous • a, b are the Van der Waals constants for the particular gas; • for water: a = 0. 5658 J-m 3/mole 2; b = 3. 049 x 10 -5 m 3/mole,

JO H A N N E S D. V A N D E R W A A L S The equation of state for gases and liquids Nobel Lecture, December 12, 1910 I intend to discuss in sequence: (1) the broad outlines of my equation of state and how I arrived at it; (2) what my attitude was and still is to that equation; (3) how in the last four years I have sought to account for the discrepancies which remained between the experimental results and this equation; (4) how I have also sought to explain the behaviour of binary and ternary mixtures by means of the equation of state.

Van der Waals EOS • a, b are the Van der Waals constants for the particular gas; • for water: a = 0. 5658 J-m 3/mole 2; b = 3. 049 x 10 -5 m 3/mole,

Van der Waals Coefficients Gas a (Pa m 3) B (m 3/mol) Helium 3. 46 x 10 -3 23. 71 x 10 -6 Neon 2. 12 x 10 -2 17. 10 x 10 -6 Hydrogen 2. 45 x 10 -2 26. 61 x 10 -6 Carbon dioxide 3. 96 x 10 -1 42. 69 x 10 -6 Water vapor 5. 47 x 10 -1 30. 52 x 10 -6

Van der Waals Isotherms

Isotherms of Real Gases

Improved Cubic Equations of State

The constants a, b, c, Ao, Bo varies with substance

The Ideal Gas Equation of State