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Tutorial (TOC) > Daemons > Closed Processes >Manual |
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a. Closed Process: In Navigation section, we have discussed the questions that need to be
answered to classify a system. When there is no mass transfer across
the boundary, the system is closed. Now suppose the snapshot of the system taken with the
state camera (discussed in States.Manual
page) evolves from an initial or begin- image ( b-state) to a final or
finish-image ( f-state ) as the system exchanges heat and work (called the process
variables) with its surroundings. Such a transition from a b-state to a f-state by a closed system
is called a closed process .
For instance, when a hot block of copper cools down to ambient temperature, or a gas in a piston-cylinder device expands to twice its original volume, easily identifiable b-state and f-state serve as anchors for the process. In these instances the system is uniform, that is, a single unique state can describe the system at any given time during the process. The daemons that handle such closed processed can be found in the following branch: Daemons. Systems. Closed. Process. Generic. Uniform. In a non-uniform closed systems (a block of copper coming to thermal equilibrium when dropped in a tank of cold water, or gases in two different chambers mixing to form a uniform mixture), two or more states may be required to describe the b- and f-states of the composite system. Daemons that handle such problems appear under the branches Daemons. Systems. Closed. Process. Generic.NonUniformMixing and Daemons...NonUniformNonMixing. Closed processes can also be found under the Specific branch, in Closed Cycles , HVAC and Combustion chapters. They will be discussed in the appropriate chapters linked from the Daemons menu. However, in all problems involving closed processes - from a single process involving mixing of two gases to a sequence of processes executed by a diesel cycle- a complete understanding of the process daemon involving an uniform system is essential. |
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b. Anchor States: The b-state and the f-state, which are system states, are the anchors of a uniform
process, process executed by an uniform system. For a non-uniform system
composite states made of multiple system states are necessary to represent
the anchor states. The non-uniform (mixing and non-mixing) daemons allows
up to two states, bA- and bB-state, for the composite begin-state and up
to two states, fA-
and fB-state, for the composite finish-state. The anchor states must be evaluated as best
as possible on the state panel before working on Process Panel.
A text field on the control panel displays the process type (p=constant, Vol=constant, etc.) once the anchor states are loaded. |
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| Fig. 1 Image of Process Panel of a uniform process
daemon. For PG and IG models, the process variables include the polytropic coefficient n, which can be entered if known. |
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c. Process Variables: There are several types of variables that appear in a process: (a) heat transfer Q; Work transfer divided into (b) boundary work W_B and (c) other kinds of work W_O (which mostly consists of W_sh and W_el); (d) boundary temperature T_B (in most situations it is the ambient temperature); and (e) S_gen , the entropy generated during the process. For gas models, a polytropic coefficient n is also included in the process panel. Unlike the state properties, the process variables (except for boundary temperature) depend on the path the system takes in migrating from the b- to f -state. The daemon attempts to evaluate the boundary work (and polytropic coefficient, where applicable) based on simple assumptions. For instance, if pressure remains unchanged between the b- and f- states, a constant pressure assumption is made. You can always override W_B calculated by the daemon, if necessary. Whenever applicable, the polytropic coefficient is also automatically computed, which you can override just like W_B.
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| Fig. 2
Hierarchical page address to launch a generic,
uniform-system, closed-process daemon. |
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d. Uniform Process Daemons: Uniform process daemons like single-flow open steady daemons
have four tabbed panels: (i) State Panel (ii) Process Panel,
(iii) Exergy Panel, and (iv) I/O Panel. The state and i/o
panels are identical to those in any system state daemon. The state panel
is used to calculate the anchor states which are used by the process and
exergy panels. The process variables, Q, W_B, W_O, T_B, Sdot_gen, and n (where applicable) have checkboxes, meaning you can set these variables. Delta_E and Delta_S 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 process 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 similar to the one used with open steady daemons. (a) Evaluate the anchor states as best as possible. (b) Switch to Process Panel select a process name (Process-A, for instance), and select from the calculated states the b- and f-states. (c) Enter the known process variables (for instance Q=0 in an adiabatic process, S_gen=0 in an internally reversible process). (d) Press the Enter key (or the Calculate button). If the anchor states are fully known, the
desired process variables are calculated and displayed. On the other hand,
if a state property - m, e, or s at the begin or finish state - is calculated
through the solution of mass, energy and entropy equations, the calculated
value is posted in the appropriate state. For instance, if s2 is calculated
in a particular analysis, you will find it posted in State-2. The background
color for s2 in State-2 is changed to gray to remind you that the property
has been calculated in another 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, which does several things. It updates
all states and relevant processes, generates a detailed output and TEST-codes
on I/O Panel, which is brought in front of all other panels. As an example, consider an analysis of an
isentropic compression process involving an ideal gas. Suppose the begin-state
is completely specified and only the volume is known at the finish-state.
The mass, energy and entropy equations for a uniform process (State-1 to
State-2) produce m2=m1, e2=e1 and s2=s1 respectively. Using the given
Vol2, '=m1' for mdot2, '=e1' for j2, and '=s1' for s2, State-2 can
be completely evaluated. In Process Panel load the anchor states, State-1
and State-2, as the b- and f- state respectively. Enter W_O (other types
of work) as zero and Calculate to obtain the boundary work. Q and S_gen are
also calculated to be zero as expected. Another way to obtain the same answer
is to enter Vol2 and partially evaluate State-2. Then in the process panel,
enter Q=0, S_gen=0, W_O=0, and Super-Calculate. The balance equations
are used to deduce and post m2, j2, and s2 into
State-2. After the state is completely evaluated the boundary work is found
in the process panel. A number of detailed
examples are discussed on the companion Example page.
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| Fig. 3 Image of Exergy Panel showing various exergy terms evaluated for a polytropic compression problem. |
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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 a process
executed by a closed uniform system while exchanging heat with up to two
TER's (thermal energy reservoir), one of which is the atmosphere. Q_0 and
Q_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 Q_1, but not Q_0; this is because Q (from Process Panel)
must be equal to Q_0 plus Q_1. The default state of the exergy panel assumes
that TER-1 does not exist (Q_1=0 so that Q=Q_0). To overwrite this, simply
enter Q_1 and T_1, and the daemon will adjust Q_0 from Q_0=Q-Q_1. For a system
that exchanges heat only with the atmosphere, simply click Calculate to evaluate
all the exergy variables for the process selected in Process Panel, provided
the process 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 for a polytropic compression process, the Second Law or exergetic efficiency can be evaluated from W_rev/W_u = Delta_Phi/W_u =0.219/0.24=91.5%. Note that the calculator in I/O Panel recognizes only the state properties, so exergy related variables such as W_u cannot be used in legal expressions. |
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g. Parametric Studies: Once a closed process has been set up, it is quite simple
to evaluate the effect of changing one or more variables on the problem. Simply
change the variable(s) of interest - be it a state property or process variable
- Calculate and Super-Calculate. All variables in each panel are updated.
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. h. TEST Codes
As in the case of state daemons (see
state daemon manual), Super-Calculate operation produces TEST-codes on I/O
Panel. An analysis block is added after the states block that lists the known
process variables. The procedure to regenerate a solution from TEST-codes
remains the same as discussed in the state manual and in a separate page
on TEST-codes. |
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| Fig. 4
Hierarchical page address to launch a generic,
non-uniform-system, fully-mixing, closed-process daemon. |
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i. Mixing Process Daemons: Mixing process daemons
can be found in the branch Daemons.Systems.Closed. Process. Generic.
NonUniform-Mixing. A mixing non-uniform daemon allows two uniform
systems to go through a mixing process resulting in a single uniform system
at the end of the process. The begin-state, therefore, is represented by
a composite state made of two system states, bA- and bB-state. Accordingly,
two begin states and a single finish-state are supplied on the control panel
of the process panel (see Fig. 5). To simplify
the panel further, the work transfer terms (W_B and W_O) are consolidated
into a single term W (in most mixing problems W=0). The system schematic
and governing balance equations reflect the composite nature of the begin-state
and the meaning of the terms Delta_E and Delta_S. The solution procedure remains the same as that developed for uniform processes. Evaluate the begin and finish states as best as possible, enter the known process variables, and Super-Calculate. There are slight variations between daemons that handle two identical or dissimilar fluids. For two identical gases, for instance, the same working fluid is used for all three anchor states - bA, bB and f states. On the other hand, if two different gases are to be mixed, each state must have different composition. This is accomplished through the use of binary mixture model (see state daemon manual) in which each anchor state is treated as a mixture of two gases A and B. Using different values of the mass fraction x (or mole fraction y) - 1, 0, and m1/(m1+m2) - composition of the anchor states can be varied (pure gas A , pure gas B, or a mixture of the two) as desired. Note that mixing between two different fluids are allowed as long as each of them and the resulting mixture can be represented by the same material model (for instance, IG/IG and not PC/IG). |
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| Fig. 5 Image of Process Panel for a mixing
process daemon. Observe the similarities and differences among the corresponding balance equations by comparing this figure with Fig. 1 for uniform-system, closed process. |
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| Fig. 6
Hierarchical page address to launch a generic,
non-uniform-system, semi-mixing, closed-process daemon. |
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j. Semi-Mixing Process Daemons: These daemons are a slight
variation of the mixing daemons discussed in the previous section. Mixing
between the two subsystems are prematurely terminated before a single f-state
is achieved. These daemons can be found in the branch Daemons.Systems.Closed.
Process. Generic. NonUniform. Semi-Mixing. Like the mixing daemons, the begin-state is represented by a composite state made of two system states, bA- and bB-state. However, the finish-state must also be represented by a composite state made of fA and fB states of the sub-systems A and B (whose masses have changed during the process). Accordingly, two begin states and two finish-states are supplied on the control panel of the process panel (see Fig. 8). Notice the changes in the balance equation for the semi-mixing process reflecting the composite finish state. The solution procedure remains the same as that developed for mixing processes. The masses in the finish states must be supplied; otherwise, an iterative solution may be necessary. For instance, if the mass exchanged is supplied, m4 can be expressed in terms of m3 which is unknown. In that case m3 may have to be guessed, producing a process variable, say, Q. The guess is improved in an iterative manner to obtain the given value of the process variable (Q=0 for instance) at which point the final solution is reached. An example of a semi-mixing problem is given in the companion Example page. |
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| Fig. 8
Hierarchical page address to launch a generic,
non-uniform-system, non-mixing, closed-process daemon. |
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j. Non--Mixing Process Daemons: The starting page for these daemons is ..Closed.Process.
Generic. NonUniform-NonMixing. The purpose of these daemons is to analyze
processes involving a non-uniform closed system made of up to two uniform
sub-systems, which maintain their separate identity. Both the begin
and finish states, therefore, are represented by composite states - bA and
bB for the begin-state and fA and fB for the finish state. For instance, suppose
two rigid chambers containing two different gases at different states are
brought in thermal contact. The changes in each sub-system (an individual
chamber) can be predicted by an appropriate non-mixing process daemon as the
two systems exchange heat. Since there is no mixing involved, the working
substances of the two sub-systems can be widely different - a gas and a solid
(IG/SL), a solid submerged in a liquid (SL/SL), etc. Of course, if the two
working substances are identical, a simple state panel with only one material
selector can be used. As an example of this class of daemons, let us consider the SL/SL model. If you learn to use this daemon, you should be able to use all other non-mixing process daemons without any problem. Launch the daemon on a separate window. You will notice that on the state control panel there are two material selectors. Also, a new state variable called Model is appended at the end of all state properties. The purpose of this variable is to keep track of the working substance selected for a particular state. When you select a solid or liquid from the first choice (Model-1: SolidLiquid Model), Model is set to 1. Similarly if a substance is chosen from the second choice, Model is set to 2. Suppose the non-uniform system of interest is made of a block of copper and some liquid water (a block of hot copper may have been dropped in a pool of water and the final temperature is desired). Suppose you select Copper from the left selector and Water(L) from the right one. You will notice that as you choose a substance, the background color of the selector turns yellow (showing the selected material) and Model is set to either 1 or 2 (first or second model). To evaluate a state with copper as the working fluid, select a state number, say, State-1, select Copper from the left selector, enter known properties, and Calculate (or press the Enter key). To evaluate a state with liquid water as the working fluid, select a state number, say, State-2, select Water(L) from the right selector, enter known properties, and Calculate (or press the Enter key). In a similar manner evaluate State-3 and 4 as best as possible. Now before we discuss the process panel, let us go over some other possible combinations of the sub-systems. When the two subsystems have the same working substance (example: two copper blocks at two different temperatures are brought into thermal contact, to find the equilibrium temperature and entropy generation), you can use a pure model (SL Model) or a combination model (SL/SL) in which you use only one material selector for evaluating all states. If the two models happen to be the phase-change (PC) and ideal gas (IG) model respectively, the set of properties displayed by the daemon is a superset of all the PC and IG state properties. For instance, the property quality has no meaning in the IG model, but is still displayed. Because the PG/PG, IG/IG and RG/RG models are also used for mixing daemons, the state properties include the mass fraction x_A and mole fraction y_A of the gas-A. To specify a mixture as a pure gas selected from the left choice (gas-A) simply set x_A or y_A to be one. A zero value, on the other hand, will make the mixture a pure gas-B (selected from the right choice). Process Evaluation If the states are completely known, a process analysis is quite straightforward. Simply load the four anchor states - two b-states and two f-states. Enter the known process variables, and Calculate. Note that, like mixing daemons, work transfer is consolidated into a single term W. Iterative Solution Suppose two blocks of solids are brought in thermal contact and we are to find the final equilibrium temperature. If State-3 and State-4 are the fA and fB states, we have two unknowns, T3 and T4. In some other systems (two gas chambers in thermal contact), it may appear that there are four unknowns - p3, T3, p4 and T4. In such situations, an iterative approach works must be used. In this, you leave Q as an unknown (even though it is supplied), enter T4 as '=T3' in State-4, guess T3, and Super-Calculate Q. Improve the guess successively until Q approaches the given value. What-If Scenario Unless the solution is iterative in nature a parametric study can be performed on any variable of interest by simply changing it, pressing the Enter key, and then using Super-Calculate. To change the pair of working substances, however, changes have to be made in two states one with Model=1 (the first choice) and the other with Model=2 (the second choice). Examples: The companion Applications page provides at least one complete example to lead you step-by-step to the solution. To see what types of problems these daemons are capable of solving, visit Problems>Chapter-5 page. |
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| Fig. 9 Image of Process Panel of a non-mixing
process daemon. Note that the begin and finish states are both composite states (bA + bB, and fA+fB states). The mass equations differ from those for semi-mixing daemons (see Fig. 7). |
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| Copyright 1998-: Subrata Bhattacharjee |