A. Select a Problem
Open a new browser window - we will call it the Problems window to distinguish it from the current (tutorial) window. To select the particular problem we are about to solve, open the Problems>Chapter-9 page, by first clicking the Problems link on the task bar (see Fig. A.1) and then on Chapter-9. Browse the chapter until you find the following problem statement (note that the problem number may change as additional problems are inserted in the future) shown in Fig. A.2 below.

It is a standard problem from the simple Rankine cycle used by steam power plants. Click the schematic and you will see an animation linking the schematic to a T-s diagram on the bottom-half of the window. You can drag the divider (the red arrow in Fig. A.3) to resize the animation window and close it using the button at the corner.

B. Simplify the Problem
TEST offers scores of daemons, thermodynamic calculators for problem solving. Knowing what daemon to launch to solve a particular problem requires a thorough knowledge of how thermodynamic systems are simplified during an analysis. If you are familiar with thermodynamic simplification, you can use the TEST-map to locate and launch the daemon very quickly. Others (everyone should do this at least once) should follow the systematic approach, a slightly time consuming but rewarding exercise. These approaches are explained in more details in the navigation tutorial.

TEST-Map: Launch a third browser window - we will call it the daemon window - alongside the problems and tutorial windows. Launch TEST and click on the Map link on the task bar.

This brings up the TEST-Map as shown in Fig. B.2. The desired destination is Daemons>Systems> Open> SteadyState> Specific> PowerCycles (see the red arrows in Fig. B.2). Click on the Power Cycles link on the Map to jump to the open power cycle daemon page (shown in Fig. B.5). The logic that leads you that page is described briefly in the following section and in details in the Navigation tutorial.

Systematic Approach: Launch a third browser window - we will call it the daemon window - alongside the problems and tutorial windows. Start the daemon hunt by clicking the daemons link on the task bar. It takes you to the Home.Daemons page.

The Home.Daemons page (and every subsequent page we are going to visit) offers a simplification table that contains multiple choices for further simplification of the problem. You select the Systems option unless you are interested in evaluating properties only. This brings up the Home.Daemons.Systems page (see Fig. B.4), which offers its own simplification table. By answering the question posed at the table header (Is the system closed or open, for instance), you proceed to the next level of simplification.

If you scroll down the Systems page, you will find an animation describing a very general system. Further down, you will find the complete set of balance equations (mass, energy, entropy, exergy, and momentum).

As more specificity is added (for the problem at hand we select open system since the cycle is composed of open devices connected back to back to form a loop, and then steady state since the global state of the system does not change with time), the animation as well as the balance equations simplify to accommodate the assumptions made. Finally, as we select the specific branch and then power cycles, we arrive at the same page (see Fig. B.5) as the one we would had we pursued the TEST-Map.

Simplification of systems and page layout are discussed in details in the Navigation tutorial.

Material Model: The final simplification table (see Fig. B.5) offers a number of material models to represent the working fluid. Note that a power cycle can be executed by a gas (modeled by PG or IG model) as in gas turbine, by a phase-change fluid (PC model) as in a steam power plant, or by two completely different fluids (PC/PC or IG/PC model) executing two cycles one top of another as in a combined cycle. You can find an in-depth discussion of material models in the Tutorial>Daemons>States>Manual page.

Selecting the material model launches the daemon - in our case, we select the PC model (the red arrow in Fig. B.5) which handles steam, refrigerants, and all other fluids that may undergo a change of phase. It may take a minute or so for the daemon to load for the first time. The access speed, however, will increase remarkably the next time you access the same daemon (this is because modern browsers cache recently accessed pages).

C. Evaluate the Principal States
The layout of the daemon will be covered in more details in the Daemons section of the tutorial. A brief review is given below.

Layout: The daemon is enclosed within the rectangular box under its hierarchical address. The first line, called the title panel, displays the pathname as well as the version number - v7.5ce3 in Fig. B.6 - of the daemon. In the next line, called the global control panel, you select a unit system (mixed, SI, or English) for the entire problem, mixed unit being the default choice. Try selecting SI system and watch how the units adjust. Now select the SI and then the Mixed system again. The Super buttons next to the unit buttons are for global calculations and can be ignored at this point.

Below the global control panel is the tab panel, allowing you to switch among state panel, device panel, cycle panel, and the I/O (input/output) panel. Try these panels out by clicking each tab and watch the display area below the tabs change accordingly. Finally, click on the state tab to select the state panel.

The state panel has its own control panel with two buttons (Calculate and Initialize), three choices (state choice, plot choice, and working fluid selector), and a text box (phase composition). Nineteen properties constitute the extended flow state in this daemon - of those, one (red symbol) is an invariant material property, nine (blue symbols) are thermodynamic properties comprising the core thermodynamic state, six (green symbols) are extrinsic properties (they depend on observer's velocity and location), and three (black symbols) are system properties (they depend on system geometry). As you move the pointer over any property, you will find a short explanation on the message panel located right below the state schematic.

Without going into too much details, let us evaluate the principal states - state 1 through 6, as shown in the schematic of the cycle (Fig. A.2).

State-1: Since the mass flow rate is not known, we will use 1 kg/s as a basis. To enter pressure, click on the checkbox of the p1 widget (see Fig. C.1), type in 10 in the text box with a yellow background, select MPa from the unit selector, and press the Enter key. After the daemon reads the entry, the background of the text box turns green. If you hover the pointer over the p1 widget, you will see the value of p1 displayed on the message panel. Enter mdot1 as 1 kg/s in a similar manner. Although Vel1 and z1 are already initialized to zero values, the state calculation is still not complete. This is because two independent thermodynamic properties are necessary to evaluate the core thermodynamic state.

The second property can be deduced from the fact that steam is saturated vapor at state-1. The quality being 100% for saturated vapor, x1=1 (or y1, the volume fraction of vapor, =1). Click on the checkbox of x1 but do not enter the property as yet. Now try to click on any other thermodynamic property - T1, h1, s1, etc. The daemon will prevent you from turning on a third property since two properties (p1 and x1 in this case) are sufficient to evaluate the core thermodynamic state. Enter x1=1 and press Enter, and the state is completely evaluated, except for the exergy variables phi1 and psi1. These properties depend on the dead state and will be discussed later.

How do you check the properties? One simple way is to see the state on a thermodynamic diagram. Select T-s from the diagram menu and see the saturated state displayed on a floating T-s diagram (Fig. C.2). You can resize the diagram, scribble on it, or click on the Data Used button to copy the TEST data into a more elaborate plotting application (such as Microsoft Excel). Thermodynamic diagrams, however, can only verify a state qualitatively. If you would like a thorough verification, there is nothing like an actual look-up table, and it is available in TEST.

Open a new browser window (beside the ones displaying this tutorial and the daemon). Use the map to open the Daemons>Basics>Tables page. There, you will find the icon for the superheated steam table (see Fig. C.3). Browse down the superheated table until you find the 10 MPa table. Compare the thermodynamic properties u, v, h, and s calculated by the TEST daemon with the entry in the table (underlined).

States 2 through 6: Select state-2 from the state menu. Enter p2 as 0.01 MPa, s2 as '=s1' and mdot2 as '=mdot1' (for each state mdot will be equated to mdot1). Press the Enter key to complete the evaluation of the isentropic state at the turbine exit. For state-3, the actual exit state, p3 is '=p2'. The second thermodynamic property h3 can be deduced as '=h1-0.85*(h1-h2)' from the definition of the isentropic efficiency. For state-4, the condenser exit, use '=p2' for p4 and x4=0 (saturated liquid). For the isentropic state after the pump, use '=p1' for p5 and '=s4' for s5. Again, using the isentropic efficiency, express h6 as '=h4+(h5-h4)/0.85' while p6 is '=p1'.

When a state is calculated it is automatically saved in the memory stack. To retrieve a particular state, say, state-3, simply select it from the state menu. But how can we save the calculated states for later use? After all, in some complex problem it is not uncommon to calculate 30 or 40 states.

TEST-codes: To save a partially completed or a fully completed solution for later use, click on the Super-Calculate button on the global control panel. In a few seconds the I/O panel is displayed with what looks like a block of codes. This is known as TEST-codes, which can be used to reproduce a solution at a later time without having to re-enter every input property. As shown in the figure below, TEST-codes are easy to read and they follow the simple syntax of Java or C++ programming language. The codes simply list the input properties (value and unit) for every state computed. Just by looking at the TEST-codes it is easy to figure out how the TEST-solution (in this case calculation of the six states) was carried out.

To save the codes, simply copy (select, Ctrl-C, switch to your favorite application, Ctrl-V, and save the document) and paste the code into a different application and save. Reproduction of the visual solution will be discussed in a latter section.

D. Analyze Devices
With all the six states calculated, switch to the Device Panel to analyze the devices - device A as the turbine (1-3), device B as the condenser (3-4), device C as the pump (4-6), and device D (6-1) as the boiler.

Layout: The device panel has its own control panel - Initialize and Calculate buttons, a device selector, and two radio buttons to make the device mixing or non-mixing. Click on each radio button and you will see the device schematic adjust to the selection made - the non-mixing mode representing a heat exchanger. The device allows up to two inlet (i1-State and i2-State) and two exit (e1-State and e2-State) states. The variables that can be entered are Qdot (heat transfer rate), Wdot_ext (the external power), T_B (the boundary temperature), and Sdot_gen (the rate of entropy generation). The mass, energy, and entropy equations are displayed next to the device schematic. When an inlet or exit state is left at State-Null, that means that the port is blocked. Thus a single-flow device can be modeled by selecting one of the inlet states and one of the exit states, while leaving the other ports at State-Null.

Turbine (device-A): Select state-1 as the i1-state (or i2-state) and state-3 as the e1-state (or e2-state). Enter Qdot=0 (adiabatic) and leave T_B at its default value. Press the Enter key or the Calculate button to produce Wdot_ext (see Fig. D.1). The transport terms of the energy and entropy equations, Jdot_net and Sdot_net, are also displayed. Note that it does not matter whether the mixing or non-mixing radio-button is selected (although the mixing button should be selected by default).

Condenser (device-B) : Select Device-B from the device menu, set the i1 and e1 states as state-3 and state-4 respectively, enter Wdot_ext as 0 and Calculate. Qdot is calculated as -1726 kW.

Pump (device-C) : Select Device-C from the device menu, set the i1 and e1 states as state-4 and state-6 respectively, enter Qdot as 0 and Calculate. Wdot_ext is calculated as -11.87 kW.

Boiler (device-D) : Select Device-D from the device menu, set the i1 and e1 states as state-6 and state-1 respectively, enter Wdot_ext as 0 and Calculate. Qdot is calculated as 2521 kW.

TEST-codes : Just as we generated TEST-codes after state evaluation, you can do the same at this point. The TEST-codes within the Analysis block (see Fig. D.2) explains how each device has been analyzed.

E. Analyze Cycle Once all the devices comprising the cycle are analyzed, the cycle variables - thermal efficiency, net power output, etc., - are automatically calculated in the cycle panel.

Cycle Panel: Simply switch to the Cycle Panel to display the calculated cycle variables. Keeping in mind that the net output calculated, Wdot_net=794.8 kW, is based on a mass flow rate of 1 kg/s, we evaluate the actual mass flow rate as 150,000/794.8=188.7 kg/s.

This calculation can be done on the I/O panel as shown in Fig. E.1. In addition to scientific calculations, the I/O panel recognizes all the calculated state variables, making it very easy to determine auxiliary quantities through expressions such as '=rho2/rho1', '=mdot1*psi1', etc.

I/O Panel as Calculator: Having found the mass flow rate through the cycle, we now change mdot1 to 188.7 kg/s. For that switch to the State Panel, select state-1, select mdot1, and enter mdot1 as 188.7 kg/s. Press the Enter key to register the change. To propagate the change throughout, click the Super-Calculate button. The Cycle Panel (see Fig. E.2) contains all the answers sought in this problem - efficiency 31.5%, Qdot_in 475.7 MW, and Qdot_out as 325.7 MW.

Saving and Reproducing the Solution : As already mentioned, the TEST solution can be saved through TEST-codes, generated in the I/O panel at any stage of the solution when the Super-Calculate button is pressed.

The TEST-codes (Fig. E.4) comprise of two blocks - one for states and one for device or process analysis. They borrow syntax from the C++ (or Java) programming language and essentially list all the input to the problem. Although simple to read, TEST-codes should be generated automatically (using the Super-Calculate button) rather than writing manually. Hundreds of such TEST-codes are available in the Problems module. The purpose of these codes is to save a TEST solution, describe the solution process, and reproduce the solution.

In addition to TEST-codes, the I/O panel displays a detailed output when the Super-Calculate button is used. Print it out (by copying and pasting the output on a word processor first) for a detailed record of your solution.

Copy the TEST-codes from the I/O panel and save it in a file using a simple word processor (notebook in Windows, for instance).

Reproducing a TEST solution can save quite a bit of time if one is interested in a parametric study or to solve a similar problem.

To do so, close the browser with the daemon and open a new browser window. In the new window, launch the power cycle daemon (its path indicated in the comment lines, beginning with the character '#').

Copy the TEST-codes in its entirety (do not forget the closing curly brace) into the I/O panel. Click the Load button. As the codes are parsed, a floating window appears with compilation messages (see Fig. E.5). Now click the Super-Calculate button - the pop-up window is closed and the entire solution (each state and device) is reproduced. Go back to the cycle panel or state panel to make sure that the original solution is posted without any distortion. For very complex problems, it may be necessary to use the Super-Iterate button if some of the state calculations are unfinished after a Super-Calculate operation.

F. What-if Studies Once a TEST-solution is obtained, it is quite easy to change any parameter and recalculate the entire solution.

Changing Unit System: The unit system used in the entire system can be changed after the solution. To do so, simply select the English radio-button in the global control panel and Super-Calculate. The entire output (except for the TEST-codes) are now in the English system. This makes it easier for a user to stick to his or her favorite unit system, reducing the possibilities of errors.

Effect of Turbine Inlet Temperature: Suppose we are interested in how the thermal efficiency and net output will be affected if steam at the turbine inlet is superheated to 400°C, everything else adjusted accordingly. For this what-if study, go back to state-1 and instead of specifying x1 (uncheck the x1 checkbox to initialize the variable), enter T1 as 400 deg-C. Press the Enter button to record the change. Now Super-Calculate. In a few seconds the entire solution is updated to produce new answers - efficiency is now 32.8% and the net output is 179.0 MW. We could continue this study with different temperatures to generate more data points to be able to draw (using a different application) a plot of thermal efficiency against the turbine inlet temperature to complete the study.

Effect of Turbine Efficiency: Suppose we are interested in how the turbine efficiency affects the cycle efficiency. For that we go back to the original solution. To change the turbine efficiency, revisit state-3, and change h3 (note that when you click on the h3 checkbox, the equation is not deleted but set in the edit mode) to '=h2'. Press the Enter key to register the change and Super-Calculate. The new answer can be found in the cycle panel - thermal efficiency is now 37.2%.

Since all the input variables are changeable, you can pursue any what-if study you can imagine.