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Tutorial>Approach to Find the Right Daemon |
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This approach should be the last resort. |
a. The Time-Tested Approach:
Overwhelmed by the fact that the same set of governing equations assume so
many forms as to make a chameleon jealous, students often resort to the time
tested engineering approach of finding a solved example that resembles the
problem at hand.
There are three different repositories of solved examples in TEST. (i) The Daemons section of this Tutorial contains detailed hands-on instructions for selected examples. (ii) The visual examples found in the Slide Show, on the other hand, are screen shots of the daemons as a solution proceeds. (iii) The Archive contains solved examples, complete with TEST-Codes, organized into fifteen chapters in the tradition of existing text books. However, once you master the systematic approach that follows, you may never need to go back to a solved example. |
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Truth tables or the TEST-Map? |
b. The Systematic Approach: In this thermodynamically sound approach, you start at the Home.Daemons Page (not to be confused with the Tutorial.daemons page) and allow the Truth Tables to guide you to the appropriate daemon step by step. In the beginning it may appear to be a time consuming task, but soon you will be ready to use the TEST-Map to simplify the problem instantly. To use the TEST-Map effectively, you must know how TEST classifies thermodynamic systems (and, hence, daemons). |
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c. Daemon Classification:
In most thermodynamics textbooks, the first chapter is devoted to rudimentary
general concepts such as unit conversion. Problems from such topics are handled
by the daemons on the Daemons.Basics
page.
Evaluation of selected thermodynamic properties are typically done in the second chapter and later in chapter twelve or thirteen of most contemporary textbooks. TEST treats all materials (including mixtures and moist air) in a consistent manner with the state daemons found on the Daemons.States page. When we evaluate a state, say, at a turbine inlet, we evaluate the state at the inlet port at a given instant. It is assumed that the state does not vary across the cross-section. Such states are called a surface state in TEST. Similarly, when we say that a gas in a piston-cylinder device is at a particular state, it is assumed that the system is uniform so that a single state describes the entire system. This is called a volume state . The rest of all thermodynamic problems involve a system and are handled starting with the Daemons.Systems page. Because of the range of systems encountered in thermodynamics, further classification of the system daemons is necessary. |
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| Fig. 2 Daemon are
classified in a tree structure. Users can jump to a page using the
TEST-Map link on the Task Bar. |
| You answer a maximum of six questions to classify a system and get to the right daemon. Open or Closed? |
d. Answer Six Questions to Classify
a System: In thermodynamics, a clearly defined
boundary is all it takes to define a system
and separate it from its surroundings
. Given the breath of this definition, TEST uses both physical and
practical arguments to produce narrow classifications (see Fig. 2) where a
group is identified with a particular form of the balance equations. We begin
the process by asking if the system is open or closed.
d1. Open vs. Closed Daemons: A system that allows mass transfer across its boundary (tubes and pipes carrying flow in and/or out of the system) is called an open system. A closed system, on the other hand, does not allow any mass transfer. |
Question #1: |
"Is there any mass flow across the boundary of the system?" Yes: Open system; No: Closed system. |
Steady or Unsteady? |
d2. Steady vs. Unsteady Daemons: A system, open or closed, is steady when its state-picture - a snapshot taken with an imaginary state-camera recording all the state variables (pressure, temperature, velocity etc.) at each location of the system at a given instant - does not change with time. While the state of the fluid flowing through a steam turbine continuously changes from the inlet to the exit, the picture of the turbine, with hot zones near the inlet and relatively cooler zones near the exit, exhibits no change with time if it is operating at steady state . The total mass, energy or entropy of the system, obtained by summing up the corresponding property over the entire system, therefore, can not change with time. That is dm/dt, dE/dt, and dS/dt=0. The governing differential balance equations, thus, simplify to algebraic equations. |
Question #2: |
"Is the state of the system changing with time?" Yes : Unsteady system ; No: Steady system . |
Closed and steady problems are rare except for overall cycles.
Open and steady problems Unsteady problems generally involve a Process. |
Steady systems
can both be open or closed. Except for trivial examples (for instance, a
piece of rock at a stationary state) , closed
steady systems can be found in closed-loop
cycles, heat engines and refrigerators if the entire cycle is enclosed
within the system boundary. For such an overall cycle, you can go through
the examples found in the three areas discussed in section-a.
Open steady systems, on the other
hand, are abundant. Further classification, discussed in section d4,
is necessary before you can locate the right open, steady daemon. d3. UnSteady Systems: In most thermodynamic problems involving unsteady systems, we are generally interested in what happens over a finite period of time rather than an instant. During the period of interest, the system - open or closed - goes from a begin-state (b-state) to a finish-state (f-state) executing what is called a process. The governing equations are integrated between the two limits (b-state to f-state) producing the process equations which are, again, algebraic in nature. |
Question #3: |
"Is there a clear begin-state (b-state) and a clear finish-state (f-state) in this unsteady problem?" Yes : Process ; No: Instantaneous . |
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Open and Closed Processes. |
Instantaneous
problems are rare in undergraduate thermodynamics and are not addressed by
TEST currently.
Examples of open processes include charging and discharging. For such problems, all that is left to launch the daemon is to select a model for the working fluid, which is discussed in section-e. Examples of closed processes are abundant, and, like open-steady systems, require further classification. |
Generic vs. |
d4. Generic vs. Specific Daemons:
Because most thermodynamic problems
belong to either closed-process
or open-steady
categories, this artificial division is created to distinguish a general
purpose problem from special purpose topics listed below.
Specific topics on closed processes include: (i) Air-standard cycles such as the Otto Cycle, Diesel Cycle, Ericson Cycle etc., which execute a sequence of processes (strokes) on a closed mass of gas (Problems.Chapter08 ); (ii) HVAC (Problems. Chapter13); (ii) Combustion (Problems. Chapter14). Specific topics on Open-Steady Systems include: (i) Power cycles such as the Rankine Cycle, Brayton Cycle etc., where a series of open-steady devices are connected end-to-end ( Problems.Chapter08 and Problems.Chapter09); (ii) Refrigeration cycles (Problems.Chapter10); (iii) HVAC (Problems. Chapter13); (iv) Combustion (Problems. Chapter14); (v) Gas dynamics (Problems. Chapter15). |
Question #4: |
"Does the problem involve a special topic listed above?" Yes: Specific ; No: Generic . |
Closed-System:
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Generic problems involving
closed processes and
open-steady systems are generally covered
in the first half of thermo texts (chapters 1 through 7) while specific system
problems are covered in the later half (chapters 8 through 16).
d5. Closed Generic Processes - Uniform vs. NonUniform: A working substance is called uniform if the state (and, hence, composition) of the working substance do not change with location within the system at a given instant. Note that a uniform system must be made up of a pure substance (same chemical composition at all locations). |
Question #5: |
"Do scoops of material, taken from any two locations, exhibit identical states at all time during the process?" Yes : Uniform ; No: Non-uniform . |
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NonUniformMixed
Open-System: |
For
uniform, generic, closed systems undergoing
a process all that is left is to select a material model (section-e).
NonUniform
systems have at least two identifiable uniform sub-systems. If the
sub-systems are allowed to mix (for instance, a valve connecting two different
gases in two tanks is opened), the system is called
non-uniform-mixed. On the other hand, if
the subsystems do not mix (a hot block of copper dropped into a bucket of
water), the system is called Non-uniform-unmixed
. Once you classify a problem down to this level, you are ready to select
the material model and launch the daemons. d6. Open, Steady, Generic Systems - SingleFlow vs. MultiFlow: If an open system, also called an open device , has a single inlet and a single exit, it is called a single-flow device. Most open-steady problems fall into this category. |
Question #6: |
"Is there one inlet (i-state) and one exit (e-state) in the device?" Yes: Single-flow ; No: Multi-flow . |
| Open-System:
MultiflowMixed or
The last step: |
All that is left for the open, steady,
generic, single-flow
problem is to select a material model (secgtion-e) to launch the desired
daemon.
In Multi-flow systems, there must be multiple openings or ports at the system boundary resulting in more than one flow in and out of the system. If the flows remain separated as in a heat exchanger, such a system is called the multi-flow-unmixed device. On the other hand, if the flows are allowed to mix or separate, as in a mixing chamber or separation chamber, the system is called a multi-flow-mixed device. Once you classify a problem down to this level, you are ready to choose a model for the working fluids. e. Classification of Working Substance: Having classified the system, all that remains to be done is to classify the working substance, the last step before launching a daemon. TEST divides all working substances into four categories. (i) Solids and liquids are in a single group because they are both characterized by constant specific heat and density. (ii) Gases are sub-divided into three categories: Perfect gas is the simplest model with constant specific heats; Ideal gas , which has a variable specific heat, is more accurate, especially if there is substantial temperature change in a problem; Real gas is a generalized model based on the compressibility chart used mostly for gases under extreme pressure or very low temperature. It should be kept in mind that the generality of the real gas model is achieved at the expense of accuracy. (iii) Gas Mixture are sub-divided into mixtures of perfect, ideal or real gases. Moist Air , a mixture of dry air and water vapor, is also treated as a gas mixture. Dry air, a fixed mixture of oxygen and nitrogen, is usually treated as a pure gas rather than a gas mixture. Finally the (iv) Phase Change Model, which is based on saturated and super-heated tables is the most accurate of all models. Supercooled liquid is modeled as saturated liquid at the same temperature except for H2O*, which uses compressed liquid table for better accuracy. The "*" suffix is also used when a different reference value for enthalpy is used (Air vs. Air*, R-134 vs. R-134* etc.). The absolute value of enthalpy is different for Air and Air*, but the difference in enthalpy between two given states, which really counts, is identical for the two fluids. The refrigerants with a "%" suffix (R-401% for instance) are mixtures of pure fluids with a variable saturation pressure at a given temperature. |
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Fig. 3 Image of the TEST.Daemons.States page showing material classification. |
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Now that we have covered the Approach that leads us to the right daemon for a given problem, let us work with a few daemons in the Daemons section. |
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