Question

Water is the working fluid in an ideal Rankine cycle.Saturated vapor enters the turbine at 16 MPa, and thecondenser pressure is 8 kPa. The mass flow rate of steam enteringthe turbine is 120 kg/s. Determine

(a) the net power developed, in kW.

(b) the rate of heat transfer to the steam passing through theboiler, in kW.

(c) the thermal efficiency.

(d) the mass flow rate of condenser cooling water, in kg/s, ifthe cooling water undergoes a temperature increse of 18 degrees Cwith negligible pressure change in passing through thecondenser.

Please fill the table :

States	p (kPa)	volume	T(K)	h	s	q(kW)	w(kW)
state 1-2
state 2-3
state 3-4
state 4-1

Answer 1

Concepts and reason

Mass flow rate:

It is the mass of the substance which is passing per unit time. It is denoted as and its SI unit is .

Heat transfer:

It is a branch of thermal engineering which deals with the generation, conversion, and transfer of thermal energy in the form of heat across the boundary of a system. The movement of thermal energy is due to the difference in the temperature between system and surroundings.

Ideal Rankine Cycle:

It is a thermodynamic cycle in which heat addition and rejection takes place in constant pressure process and isentropic expansion and compression takes place. Ideal cycle does not include the irreversibility in the processes. Cycle uses working fluid in both liquid and vapor phases.

Thermal efficiency:

Thermal efficiency of a Rankine cycle is the ratio of net work output from the system to the heat supplied to the boiler.

Fundamentals

The schematic diagram of an Ideal Rankine cycle is shown as in Figure.

Show the diagram of the Ideal Rankine cycle as in Figure.

Here, work output from the turbine is , work input to the pump is , heat output from the condenser is ,heat input to boiler is .

Turbine (Isentropic expansion process 1-2):

The superheated steam from the boiler is at higher temperature and pressure. Work is produced by the expansion of the steam in the turbine. Steam at low pressure is transferred to the condesor. Neglect the heat transfer with the surroundings.

The mass and energy balance in the turbine is given as follows:

Here, work output from the turbine is , mass flow rate is , enthalpy at state 1 is , and enthalpy at state 2 is .

Condenser (Constant pressure heat rejection process 2-3):

In this process the steam enters the condenser from the turbine is condensed to liquid state at constant pressure in the condenser.

The mass energy balance in the condenser is given as follows:

Here, heat output from the condenser is , enthalpy at state 3 is , and enthalpy at state 2 is .

Pump (Isentropic compression process 3-4):

In the Isentropic compression process, the working fluid (water) is pumped into boiler at high pressure from the condenser at low pressure. In this process, no heat is transferred to the surroundings.

The mass and energy balance in the pump is given as follows:

Here, work input to the pump is and enthalpy at state 4is .

Boiler (Constant pressure heat addition process 4-1):

The high pressure saturated liquid water enters the boiler and is converted into steam by addition of heat, conversion takes place at constant pressure.

The mass and energy balance in the boiler is given as follows:

$Qu=m(h-h,) $

Here, heat input to boiler is .

The formula to calculate the thermal efficiency of the cycle is given as follows:

Here, thermal efficiency of the cycle is and net work output from the cycle is .

The net work output from the cycle is calculated as follows:

From the tables of “Saturated steam”, select the properties of water at pressure of and dryness fraction of saturated vapor of $x=1 $.

Specific enthalpy at state 1,

Specific volume at state 1,

Entropy at state 1,

Temperature at state 1,

Since, the process 1-2 is an isentropic, thenthe entropy at state 1 is equal to entropy at state 2.

From the tables of “Saturated pressure table of water”, selectthe properties of water at pressure of .

Specific enthalpy of fluid,

Enthalpy of vaporization,

Specific entropy of fluid,

Entropy of vaporization,

Specific volume of fluid,

Specific volume of vapor,

Calculate the dryness fraction at state 2 .

Substitute for , for , and for .

Calculatespecific volume at state 2:

Substitute for , for , and for .

Calculate specific enthalpy at state 2.

Substitutefor , for , and for .

From the tables of “Saturated water”, select the properties of water at pressure of and dryness fraction of saturated liquid of .

Specific enthalpy at state 3,

Specific volume at state 3,

Calculate enthalpy at state 4.

Substitute for , for , for , and for .

Calculate the rate of heat output from the condenser .

Substitute for , for , and for .

Show the properties of all states as in Table .

(a)

Write the mass and energy balance in the turbine.

Substitute for , for , and for .

The mass and energy balance in the pump is given as follows,

Substitute for , for , and for .

Calculate the net power developed .

Substitute for , and for .

(b)

Calculate the rate of heat transfer to the steam passing through the boiler.

$Qu=m(h-h,) $

Substitute for , for , and for .

(c)

Calculate the thermal efficiency.

Substitute for and for .

(d)

Write the relation to calculate the mass flow rate of condenser cooling water.

Here, specific heat capacity of water is , and increase in temperature is .

Substitute for , for , for , for , and for .

List out the calculated values as shown in Table .

[Part d.2]

Ans: Part a

The net power developed is.

Part b

The rate of heat transfer to the steam passing through the boiler is.

Part c

The thermal efficiency is .

Part d.1

The mass flow rate of condenser cooling water is .