Create a Rankine cycle Simulator to calculate Net-work output & Back work ratio and T-S & h-S plot.
AIM:
Create a Rankine cycle Simulator to calculate the Net-work output & Back work ratio and T-S & h-S plot.
THEORY:
The Rankine cycle is a model used to predict the performance of steam turbine systems. It was also used to study the performance of reciprocating steam engines. The Rankine cycle is an idealized thermodynamic cycle of a heat engine that converts heat into mechanical work while undergoing a phase change. It is an idealized cycle in which friction losses in each of the four components are neglected. The heat is supplied externally to a closed loop, which usually uses water as the working fluid. It is named after William John Macquorn Rankine, a Scottish polymath and Glasgow University professor.
The Rankine cycle closely describes the process by which steam-operated heat engines commonly found in thermal power generation plants generate power.
Power depends on the temperature difference between a heat source and a cold source. The higher the difference, the more mechanical power can be efficiently extracted out of heat energy, as per Carnot's theorem.
The heat sources used in these power plants are usually nuclear fission or the combustion of fossil fuels such as coal, natural gas, and oil, or concentrated solar power. The higher the temperature, the better.
The cold source (the colder the better) used in these power plants are usually cooling towers and a large water body (river or sea). The efficiency of the Rankine cycle is limited on the cold side by the lower practical temperature of the working fluid.
The four processes in the Rankine cycle:
There are four processes in the Rankine cycle. The states are identified by numbers (in brown) in the T–s diagram.
Process 1–2: The working fluid is pumped from low to high pressure. As the fluid is a liquid at this stage, the pump requires little input energy.
In other words Process, 1-2 is [Isentropic compression]
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. The input energy required can be easily calculated graphically, using an enthalpy–entropy chart (h–s chart, or Mollier diagram), or numerically, using steam tables.
In other words Process, 2-3 is [Constant pressure heat addition in boiler]
Process 3–4: The dry saturated vapor expands through a turbine, generating power. This decreases the temperature and pressure of the vapour, and some condensation may occur. The output in this process can be easily calculated using the chart or tables noted above.
In other words Process, 3-4 is [Isentropic expansion]
Process 4–1: The wet vapor then enters a condenser, where it is condensed at a constant pressure to become a saturated liquid.
In other words Process, 4-1 is [Constant pressure heat rejection in condenser]
In an ideal Rankine cycle, the pump and turbine would be isentropic, i.e., the pump and turbine would generate no entropy and hence maximize the net-work output. Processes 1–2 and 3–4 would be represented by vertical lines on the T–s diagram and more closely resemble that of the Carnot cycle. The Rankine cycle shown here prevents the state of the working fluid from ending up in the superheated vapor region after the expansion in the turbine, which reduces the energy removed by the condensers.
The actual vapor power cycle differs from the ideal Rankine cycle because of irreversibilities in the inherent components caused by fluid friction and heat loss to the surroundings; fluid friction causes pressure drops in the boiler, the condenser, and the piping between the components, and as a result the steam leaves the boiler at a lower pressure; heat loss reduces the net-work output, thus heat addition to the steam in the boiler is required to maintain the same level of net-work output.
GOVERNING EQUATIONS:
Variables:
Equations:
In general, the efficiency of a simple Rankine cycle can be written as;
Each of the next four equations is derived from the energy and mass balance for a control volume.
defines the thermodynamic efficiency of the cycle as the ratio of net power output to heat input. As the work required by the pump is often around 1% of the turbine work output, it can be simplified.
When dealing with the efficiencies of the turbines and pumps, an adjustment to the work terms must be made:
Additional Equations;
Net-Work;
`W_net=W_turbine- W_pump`
Back Work Ratio (BWR);
`BWR=W_turbine- W_pump`
Specific Steam Conductivity;
`S.S.C=3600/W_turbine`
OBJECTIVES OF THE PROJECT:
- Create a Rankine Cycle Simulator using OCTAVE/MATLAB.
- Calculate the state points of the Rankine Cycle (any type of your choice) based on user inputs.
- Then, plot the corresponding T-s and h-s plots for the given set of inputs. Title and axes labels are a must, while legends could be used if necessary.
- Calculate the following: Net-work output, Back work ratio.
GIVEN:
Required Inputs:
Turbine Inlet temperature = 400° C
Turbine Inlet Pressure = 30 bars
Turbine Outlet Pressure = 0.05 bars = Condenser Inlet Pressure
The link for the standard Xsteam library to get the steam table data for water is given below. It must be used to calculate the points in between the state variables:
https://drive.google.com/open?id=1RK_fvrOj38CIaQvmLT1S3daqHnxKCGU-
BODY OF THE CONTENT:
Start the program writing by creating new script;
Always use the comments in the program for the validation of specific inputs and thus the commands have been used through the program;
Inputs;
Started with the instruction for the comments and the inputs for the base condition and some state variables and also provided the engine kinematics parameters as shown below.
Calculating the state point variables for 4 states.
For state -1:
For state -2:
For state -3:
For state -4:
Use the equation to set the variables to determine Work, Efficiency, and other related parameters for the Rankine cycle.
Write the loop and code to get the state plot and saturation plot for T-S & h-S;
Plot T-S:
Use the saturation state points to get the curve on the plot.
Use Entropy and Temperature state point to plot the idle connection of the Rankine cycle.
In the end, write the text that you want to show on the plot along with labels & titles.
Plot h-S:
Use the saturation state points to get the curve on the plot.
Use Entropy and Enthalpy state point to plot the idle connection of the Rankine cycle.
In the end, write the text that you want to show on the plot along with labels & titles.
Now graph plotting and create 2 figure for actual and theoretical cycle
Now write down the comments and the letters that you wish to show along with answers for the command window;
After this save the program and run it.
RESULT:
All the answers are recorded in the command window and at the workplace;
For the input;
Plots;
Plot T-S;
Plot h-S:
ERROR or ISSUES:
The below error poped as I did use the color notation at the right place;
It can be resolved by using ‘color’, ’k’, or just place ‘k’ at the beginning after state point.
For the below error, I missed writing a saturating point plot along with the loop. I also corrected the position point.
REFERENCCES: