A simple Rankine cycle uses water as the working fluid. The...

A simple Rankine cycle uses water as the working fluid. The boiler operates at $6000 \mathrm{kPa}$ and the condenser at $50 \mathrm{kPa} .$ At the entrance to the turbine, the temperature is $450^{\circ} \mathrm{C} .$ The isentropic efficiency of the turbine is 94 percent, pressure and pump losses are negligible, and the water leaving the condenser is subcooled by $6.3^{\circ} \mathrm{C}$. The boiler is sized for a mass flow rate of $20 \mathrm{kg} / \mathrm{s}$. Determine the rate at which heat is added in the boiler, the power required to operate the pumps, the net power produced by the cycle, and the thermal efficiency.

Key Concepts

Thermal Efficiency

Thermal efficiency is defined as the ratio of the net work output of a cycle to the total heat input provided, usually in the boiler. This metric is used to measure the effectiveness of the energy conversion process in power plants and other thermal systems, indicating how well the cycle converts input heat into useful mechanical or electrical energy.

Rankine Cycle

The Rankine cycle is a thermodynamic cycle used primarily in power generation systems, where a working fluid (usually water) undergoes phase change processes. It includes key components such as a boiler for heat addition, a turbine for work extraction, a condenser for heat rejection, and a pump for pressurizing the working fluid, forming a continuous loop that converts thermal energy into mechanical work.

Isentropic Efficiency

Isentropic efficiency measures how closely a real process (typically in turbines or pumps) approaches the ideal, reversible, adiabatic process known as an isentropic process. It is defined as the ratio of the actual work output (or input) to the ideal work output (or input), and it is crucial for assessing the performance losses due to irreversibilities in the equipment.

Heat Transfer in Boilers

Heat transfer in boilers involves adding energy to the working fluid to raise its temperature and pressure, ultimately converting it from liquid to high-energy steam. This process is fundamental to thermal power cycles as it provides the primary source of energy that will be converted to mechanical work in downstream components like turbines.

Net Work Calculation in Cycles

Net work in thermodynamic cycles is determined by subtracting the work consumed by auxiliary components (such as feedwater pumps) from the work produced by the primary work-producing component (typically a turbine). This calculation is essential for evaluating the effective work output of the cycle and assessing its overall performance.

Transcript

00:01 Cycle uses water as the working fluid.

00:04 The boiler operates at 6 ,000 kilopascals and the condenser at 50 kilopascals.

00:11 At the entrance to the turbine, the temperature is 450 celsius.

00:16 The is centropic efficiency of the turbine is 94%.

00:19 Pressure and pump losses are negligible.

00:23 Water leaving the condenser is subcold by 6 .3 degrees celsius.

00:28 The boiler is sized for a last flow of 20 kilograms per second.

00:32 We are asked to determine several things.

00:35 The rate at which heat is added in the boiler, the power required to operate the pumps, the net power produced by the pumps, and the thermal efficiency.

00:47 Okay, let's begin.

00:48 So we will need the enthapes of all four points of the rank and cycle.

00:54 Sorry, h1.

00:59 Oh, we're going to use low pressure, which was 50 kilopascals.

01:09 And then initial temperature, the initial temperature would be, we're going to use 6 .3 degrees.

01:20 And the saturation, under the saturation temperature, that'll be 81 .3 degrees.

01:37 So this will be 50.

01:44 Okay.

01:53 Let's see here.

02:03 So h1 is going to equal 314 kilojoules per kilogram.

02:17 And for h2, that'll be equal h1.

02:25 And this will be equal to 314 times 0 .0013 meters cubed per kilogram times 6 ,000 minus 50, and h2 will be equal to 320 .13 kilojoules per kilogram.

02:57 For h3, we're going to use the high pressure and 450, and so h3 will equal 3300...

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