Steam enters the first-stage turbine shown in Fig. P4.50 at 40 bar and 500℃ with a volumetric flow rate of 90 m3/min. Steam exits the turbine at 20 bar and 400℃. The steam is then reheated at constant pressure to 500℃ before entering the second-stage turbine. Steam leaves the second stage as saturated vapor at 0.6 bar. For operation at steady state, and ignoring stray heat transfer and kinetic and potential energy effects, determine the
(a) mass flow rate of the steam, in kg/h.
(b) total power produced by the two stages of the turbine, in kW.
(c) rate of heat transfer
Concepts and reason
Volume flow rate:
The volume flow rate of a fluid is defined as the volume of a fluid that passes through a given cross-sectional area per unit of time.
Units: The S.I. unit of volume of flow rate in m3/s.
Mass flow rate:
The mass flow rate of a fluid is defined as the mass of a fluid that passes through a given cross sectional area. It is also defined as the rate of movement of liquid mass through a unit area. This mass flow rate depends on the density of the fluid, velocity of the flowing fluid and also the area of cross section.
Units: The S.I. unit of mass of flow rate is kg/s.
Compounding of steam turbines:
In Compounding of steam turbines the energy from steam is extracted in a number of stages to reduce the wastage of steam and also to protect the turbine structure from centrifugal forces caused by the high speeds of the rotor.
Fundamentals
Mass flow rate:
The volume rate of a fluid is denoted by Q which is defined as,
Here, the volume of the fluid is and the time for which the fluid flows is t.
But, the volume of a body is the product of cross-sectional area A and thickness d.
Hence,
The term is the thickness of the fluid per unit time which is nothing but the speed of the fluid. So, we can replace the term with the velocity of the fluid V.
The mass flow rate of a fluid is denoted by which is defined as,
Here, the mass of the fluid is m, and the time for which a particular mass of fluid flows is t.
But, the mass of a body is the product of volume v and density P.
Hence,
The term is known as the volume rate Q of a fluid.
But,
Hence,
But the density of a fluid is equal to the reciprocal of the specific volume. Then,
Hence,
Work output from a two stage turbine:
Consider a steam turbine in which the steam is expanded in two stages. The T-s diagram of the turbine is shown below:
Here, the steam expansion in the first stage of the turbine from state (1) to state(2) and then it is heated in the reheater from state (2) to state (2’) and again the steam is expanded from state (2’) to state (3).
The work output of the two stage turbine is given by,
The rate of heat transfer to the steam flowing through the reheater is given by,
Draw the T-s diagram of the cycle as shown below.
Here, process 1-2 is isentropic process in first stage turbine,
Process 2-3 is constant pressure heat addition in reheater,
Process 3-4 is isentropic process in second stage turbine.
Calculate the mass flow rate of steam by using the equation,
…… (1)
Here, the volumetric flow rate at state 1 is (AV)1 and the specific volume of steam at state 1 is v1.
Obtain specific volume at pressureand temperature from superheated water tables,
Now substitute in equation (1)
Calculate the work output from the two stages of the turbine by using the equation,
…… (2)
Here, the enthalpy of steam at respective points is h.
Obtain enthalpies at states 1, 2, 3 and 4 from “superheated water tables” as shown below:
At pressureand temperature,
Atand,
Atand,
At state 4 the steam is saturated vapor, obtain specific enthalpy of saturated vapor atfrom saturated water tables
Substitute the above values in equation (2).
Calculate the rate of heat transfer to the steam flowing through the reheater by using the equation:
Steam enters the first-stage turbine shown in Fig. P4.50 at 40 bar and 500℃
How do i solve C??? Please details Steam enters a two stage steady state turbine at 8 MPa and 500 C. It expands in the first stage to a state of 2 MPa and 350°C. Steam is then reheated at constant pressure to a temperature of 500°C before it enters the second stage, where it exits at 30 kPa and a quality of 98%. The net power output of the turbine is 3 MW Assume the surroundings to be at...
5. Steam at 140 bar and 600 °C enters a turbine at a mass flow rate of 0.5 kg/s. This steam exits the turbine as a saturated vapor at 300 °C. During operation, the turbine loses 200 kW of heat to the surroundings. Assume that the turbine operates at steady state and that the change of kinetic energy and gravitational energy can be ignored. (a) Sketch the system and boundary (4 points); (b) Label all mass flows and energy transfer...
Steam enters a turbine operating at steady state at 30 bar, 400 °C with a mass flow rate of 126 kg/min and exits as saturated vapor at 0.2 bar, producing power at a rate of 1.5 MW. Kinetic and potential energy effects can be ignored. Determine the followings. (a) (5 points) The rate of heat transfer, in kW. (b) (15 points) The rate of entropy production, in kW/K, for an enlarged control volume that includes the turbine and enough of...
3. 50 points) Steam enters a turbine operating at a steady state at 12 MPa and 700 C. The mass flow rate of the steam is 200 kg'min. The steam exits the turbine as a saturated vapor at 3 bar. The turbine produces 3.0 MW of power. Ignore potential and kinetic energy effects. Assuming heat transfer from the turbine to the surroundings occurs at 20 C, determine: (a) (20 pts) The rate of heat transfer, in kW (b) (20 pts)...
Water vapor enters a turbine operating at steady state at 600°C, 40 bar, with a velocity of 200 m/s, and expands adiabatically to the exit, where it is saturated vapor at 0.8 bar, with a velocity of 150 m/s and a volumetric flow rate of 15 m3/s. Determine the power developed by the turbine, in kW.
Steam enters a turbine operating at steady state at 700oF and 450 lbf/in2 and leaves as a saturated vapor at 0.8 lbf/in2. The turbine develops 12,000 hp, and heat transfer from the turbine to the surroundings occurs at a rate of 2 x 106 Btu/h. Neglect kinetic and potential energy changes from inlet to exit. Determine the exit temperature, in oF, and the volumetric flow rate of the steam at the inlet, in ft3/s.
2. In an ideal reheat Rankine cycle, steam enters the first-stage turbine at 20 MPa, 550° C. The steam exits the first-stage turbine at 4 MPa and is reheated to 500 9 C at constant pressure. What is the heat input in kJ/kg required for reheating? Answer: 498 kJ/kg
thermo question 2. (20 points) Steam enters a turbine operating at steady state at 2 MPa, 360°C with a velocity of 100 m/s. Saturated vapor exits at 0.1 MPa and a velocity of 50 m/s. The elevation of the inlet is 3 m higher than at the exit. The mass flow rate of the steam is 15 kg's, and the power developed is 7 MW. Let g -9.81 m/s Determine (a) the area at the inlet, in m, and (b)...
761 Steam enters a turbine operating at steady state at 4 MPa, 500 C with a mass flow rate of 50 kg/s Saturated vapor exits at 10 kPa and the corresponding power developed is 42 MW The effects of motion and gravity negligible. are (a) For a control volume enclosing the turbine, determine the rale of heat Iransfer, in MW, from the turbine to its surrmundings Asuming 50°C. determine the rate of exergy destruction, in MW (b) If the turbine...
1. (20 points) Consider a cogeneration system operating at steady state. Superheated steam enters the first turbine stage at 6 MPa, 540 °C. Between the first and second stages, 45% of the steam is extracted at 500 kPa and diverted to a process heating load of 5 x 108 kl/h. Condensate exits the process heat exchanger at 450 kPa with specific enthalpy of 589.13 kl/kg and is mixed with liquid exiting the lower pressure pump at 450 kPa. The entire...