Heat Exchangers, Mixing Chambers, Pipe Flow Analysis - Analyze Single and Multiple Flow Systems with or without Mixing - Manual for the Web-Based Device Analysis Software

Tutorial (TOC) > Daemons > Open Steady > Manual

a. Open Steady Systems These are the most prevalent open systems.

In the Navigation section, we have discussed the six questions that lead you to the right daemon. If there is mass transfer across the boundary, the system is open. In a steady problem the snapshot of the system taken with the state camera (discussed in the States page) remains unchanged with time even though the system may exchange heat , work and mass with its surroundings.

For instance, when steam expands in a steady turbine, the global state of the system - a composite of all the different states (or colors in our camera analogy) at different locations - does not change with time. Steam, as it passes through the turbine, cools down dramatically from the inlet to the exit. However, at a given location, the state (or color) remains frozen in time. The mass, stored energy, entropy, and stored exergy in such a system remain constant, thereby, simplifying the balance equations.

The open steady daemons for a single flow system appear under the branch Daemons. Systems. Open. SteadyState. Generic.SingleFlow while the multi-flow daemons are sub-divided into two branches: Daemons...MultiFlowMixed and Daemons...MultiFlowUnMixed .

Open and steady systems can also be found under the Daemons. Systems. Open. SteadyState. Specific branch in the Open Cycles, HVAC, Combustion and GasDynamics chapters. They will be discussed in the corresponding chapters. However, all open steady daemons, generic or specific, are rooted on the daemon currently under discussion.

b. Anchor States To characterize the mass transfer across the control surface of an open, steady single-flow device, all that is required is to identify two unique flow states, the i- and e-state, at the inlet and exit ports. In more complicated multi-flow devices, such as heat exchangers, mixing chambers, separators, etc., there can be more than one inlet or exit. Multi-flow daemons allow up to two inlets, represented by i1 and i2 states, and up to two exits, represented by e1 and e2 states. If a system has more than two inlets or exits, it can be broken into several devices with each component having at the most four ports.

Figure 1 shows an image of the device panel captured from a single-flow daemon. The choices for i-state and e-state contains all the states calculated in State Panel. As the appropriate anchor states are selected, the inlet and exit states in the system schematic are dynamically adjusted. State-Null is the default state of a port which means that it is blocked (no flow).

Fig. 1 Image of Device Panel for a single-flow open steady daemon. You load the i- and e-states,
enter the device variables and solve the balance equations by pressing the Enter key or the
Calculate button.

c. The Device Variables: There are three kinds of variables that appear in the Device Panel . (a) The rate of heat and work transfer represented by symbols Qdot and Wdot_ext; (b) The rate of entropy generation Sdot_gen , and boundary temperature T_B (initialized with a default value of 25 deg-C); and (c) Jdot_net , and Sdot_net , the net rate of energy and entropy transport by the mass flow. These variables have no checkboxes, indicating that they are meant for output only. With the help of these variables each term of the energy and entropy equations, displayed on Device Panel, can be completely evaluated. Note that the calculator in I/O Panel recognizes only the state properties and device variables such as Qdot, Sdot_gen, etc., cannot be used in legal expressions.

Fig. 2 Hierarchical path leading to the generic, open-steady, single-flow daemon.

d. Single-Flow Daemon: Single-flow open steady daemons have four tabbed panels: (i) State Panel (ii) Device Panel, (iii) Exergy Panel, and (iv) I/O Panel. The state and i/o panels are identical to those in any flow state daemon. The state panel is used to calculate the anchor states which are used by the device and exergy panels.

An image of a device panel is shown in Fig.1, which is same for all material models. The global control panel, obviously, is shared by all tabs. On the local control panel, the i-State and the e-State selectors contain only those states which have been already calculated in the state panel. A device is identified by a letter, A through Z, (just like a State is identified by a number), Device-A being the default device.

The device variables, Qdot, Wdot_ext, T_B, and Sdot_gen, have checkboxes, meaning you can set these variables. Jdot_net and Sdot_net are meant for output only and, therefore, do not have checkboxes. These variables are explained through a system schematic and customized balance equations embedded on the device panel as shown in Fig. 1. The boundary temperature, which enters the entropy balance equation only, is assigned a default value of 25 deg-C.

e. Solution Procedure The solution procedure is quite simple. (a) Evaluate the anchor states, the i- and e-state as best as possible. (b) On the device panel, choose a device name (Device-A, for instance), and select from the list of calculated states the appropriate anchor states. (c) Enter the known device variables (for instance Qdot=0 for an adiabatic device, Sdot_ gen=0 for an internally reversible device). (d) Press the Enter key (or the Calculate button).

If the anchor states are fully known, the desired device variables are calculated and displayed. On the other hand, if a state property - mdot, j, or s at the inlet or exit state - is calculated through the solution of mass, energy and entropy equations, the resulting property is posted in the appropriate state. For instance, if s2 is calculated in a particular analysis, you will find it posted in State-2. A gray background for s2 in State-2 reminds you that the property has been calculated in the device panel. State-2 now can be updated by using a local Calculate or pressing the Enter key. This process of updating states after the balance equations are solved can be automated through the use of Super-Calculate button. After all the states and relevant devices are updated, a detailed output and TEST-codes are generated on I/O Panel, which is brought in front of all other panels.

As an example, consider an analysis of a steady, reversible (adiabatic and frictionless) nozzle. Suppose the inlet state is completely specified and only the pressure is known at the exit. In evaluating State-2 (the e-state), Vel2 must be made an unknown. The mass, energy and entropy equations produce mdot2=mdot1, j2=j1 and s2=s1 respectively. Using '=mdot1' for mdot2, '=j1' for j2, and '=s1' for s2, State-2 can be completely evaluated. The device panel, in this case, simply confirms the assumption as Qdot and Sdot_gen are calculated as zero once the anchor states, State-1 and State-2, are loaded as the i- and e- states. Another way to obtain the same answer is to enter p2 and partially evaluate State-2. In the device panel, enter Qdot=0, Sdot_gen=0 and Super-Calculate. The balance equations are used to deduce and post mdot2=mdot1, j2=j1, and s2=s1 into State-2, which is completely evaluated. A number of detailed examples are discussed on the companion Example page.

Fig. 3 Image of Device Panel for a multi-flow mixing system.

f. Exergy Panel Once a steady open device has been analyzed, an availability or exergy analysis can be carried out in Exergy Panel, provided a designated dead-State, State-0, is evaluated first. Atmospheric temperature and pressure are all that is necessary to calculate the dead state. Remember, the working substance at the dead state must be the working substance in the system, which may not be air. The variables displayed in the exergy panel are essentially different terms of the exergy balance equation for an open steady device exchanging heat with up to two TER's (thermal energy reservoir), one of which is the outside atmosphere. Qdot_0 and Qdot_1 are heat transfer to the system from TER-0, the atmospheric reservoir at temperature T_0, and TER-1, another reservoir at temperature T_1. Note that you can set Qdot_1, but not Qdot_0; this is because Qdot (from Device Panel) must be equal to Qdot_0 plus Qdot_1. The default state of the exergy panel assumes that TER-1 does not exist (Qdot_1=0 so that Qdot=Qdot_0). To overwrite this, simply enter Qdot_1 and T_1, and the daemon will calculate Qdot_0=Qdot-Qdot_1. For a system that exchanges heat only with the atmosphere, simply click Calculate to evaluate all the exergy variables for the device selected in Device Panel, provided the device has been already analyzed.

Most variables on the exergy panel are for output purpose only as indicated by the absence of checkbox in the variable widgets. With all the terms of the exergy balance equation evaluated, a device-specific exergetic efficiency can be easily calculated. For instance, from the exergy terms displayed in Fig. 2, the Second Law or exergetic efficiency can be evaluated from Wdot_u/Psidot_net = 81/89.8. Note that the calculator in I/O Panel recognizes only the state properties and exergy related variables such as Wdot_u cannot be used in legal expressions.

g. Parametric Study Once a problem is solved, a parametric or what-if study is quite simple. Simply change any number of variables (you have to press the Enter key to register a change) and press Super-Calculate. A fixed number of iterations are performed between the state and device panels and the results, along with TEST-codes, are displayed on I/O Panel. To facilitate a parametric study, use of absolute values for state properties should be avoided as much as possible in favor or algebraic expressions. In an isentropic device entering s2 as '=s1' allows State-2 to be appropriately updated when State-1 is changed; using absolute value for s2 would not allow such propagation of information. A parametric study does not have to be limited to physical variables only. The working substance can be changed as a parameter. Even conversion of units from one system to another for the entire problem must be carried out by pressing Super-Calculate.

h. TEST Codes As in the case of state daemons (see state daemon manual), Super-Calculate operation produces TEST-codes in the I/O panel. An analysis block is added after the states block to carry the device information. The procedure to regenerate a solution from TEST-codes remains the same as discussed in the state manual. Beside storing solutions, TEST-codes can also be used for advanced parametric studies in which the material model itself can be used as a parameter. For instance, after a compressor problem is solved by treating air as a perfect gas, you can use the generated TEST-codes in the corresponding ideal gas daemon to evaluate the effect of variable specific heats on the answers.

Fig. 4 Hierarchical path leading to the generic, open-steady, multi-flow, mixing daemon.

i. Multi-Flow Mixing Daemons Most multi-flow daemons have the same state panel as the single-flow daemons, the flow state panel discussed in State Manual, which is used to evaluate the anchor states of the device. The device panel allow up to two inlets, i1 and i2, and two exits e1 and e2, as shown in Fig. 3. For a mixing flow, only one of the exits, e1 or e2, is used and the other left plugged (State-Null). For a separating flow, similarly, only one inlet state is used. For that matter, by using only one inlet and one exit port, a multi-flow daemon can be converted into a single-flow daemon. On the control panel the two radio buttons - Mixing Device and Non-Mixing Device - to select mixing or non-mixing modes. The system schematic and mass equation change according to the mode selected. Obviously, for a mixing or separating device, the mixing button should be selected.

As in a single-flow daemon, you choose a device name, load the appropriate inlet and exit states, enter the device variables, which remain identical to the single-flow device variables, and Calculate. Most of the previous discussions on the single flow device (sections c-h) apply to multi-flow daemons. Although a separate exergy panel is not provided, an exergy analysis can be carried out on I/O Panel using the exergies calculated as part of states. In addition to information about multiple inlets and exits, TEST-codes produced by Super-Calculate contain an additional statement in the Analysis block indicating the mixing or non-mixing nature of the device as appropriate.

Most mixing daemons handle two identical fluids - H2O mixing with H2O, air mixing with air, etc. In such cases, simply evaluate the inlet and exit states as best as possible, load them in the device panel, enter the known device variables, press the Enter key and Super-Calculate. TEST also allows mixing between two dissimilar fluids - O2 and N2, H2O and NH3, etc. - as long as the mixture can be represented by one of the three models: PG/PG, IG/IG and RG/RG. The state panel is slightly modified (with gas A and gas B) for these models as explained in the Mixture Model section of the state manual. Note that mixture of two phase-change fluid (PC/PC) is not allowed. In its place the RG/RG model can be used, which uses Kay's model to determine equivalent critical properties of a mixture.

Fig. 5 Hierarchical path leading to the generic, open-steady, multi-flow, non-mixing daemon.

c. Multi-Flow Non-Mixing Systems: The device panel for a multi-flow non-mixing system is shown in Fig. 4. Compare it with the device panel of a mixing daemon shown in Fig. 3. The status of the mixing/non-mixing radio button can be seen to determine the schematic and mass equation of the device. re can be up to two flows into the system.

The two flows are not allowed to mix in this category of systems. Therefore, two different models for the working fluid can be used for the two fluids. For instance, in a heat exchanger where R-12 and air are the two working fluids, the phase-change (PC) and ideal gas (IG) models can be used to represent the the two fluids. Likewise other combinations of fluids: PC/SL (phase-change and solid/liquid) and IG/SL (ideal gas and solid/liquid) are supplied. A new state variable called Model is added to identify which model is used in a particular state - Model has a value of 1 for the first choice on the left and 2 for the choice on the right. If only a single model is necessary the second model can be ignored.

The solution procedure is almost identical to that of the mixing daemon. After the four states are evaluated, they are loaded as i1, e1 and i2, e2 states. Care should be taken in loading the anchor states to ensure that fluid A and B remain separated. If one of the state property (say, an inlet temperature) is an unknown, the iteration between state and device panel may not result in its determination. In such situation, the property (temperature) can be guessed to yield a known device variables (say, Qdot) and the process repeated until the evaluated variable agrees closely with its known value.

Fig. 6 Image of Device Panel for a multi-flow non-mixing system.