By Hrishikesh Gadre Email: [email protected] Session II Department of Mechanical Engineering Louisiana...
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Transcript of By Hrishikesh Gadre Email: [email protected] Session II Department of Mechanical Engineering Louisiana...
ByHrishikesh Gadre
Email: [email protected]
Session II
Department of Mechanical Engineering
Louisiana State University
Engineering Equation Solver Tutorials
Spring 2004
File Menu
Open, New, Save, Print: need no mention
Merge: merges equations in a saved file with the current
contents of the Equations window at the cursor position.
Load Textbook: reads a Textbook index file (.txb) and uses
the information in that file to create a Textbook menu at the
far right of the menu bar.
Load library: is used to load library files (.lib) and also to
load external functions and procedures.
Options Menu
Variable Info: will provide a window containing the
information about the variables currently appearing in
Equations window. Information includes guess value, lower
and upper limits, display format, and units.
This information can not only be viewed but also changed.
Function Info (Options Menu)
This command will bring up the window as shown. It provides
different types of built-in functions like math functions,
thermodynamic functions etc.
The button ‘Function Info’ provides specific information
about the function selected. ‘Fluid Info’ gives information
related to source and range of applicability of property
correlations.
An example of the function selected with default variables
will be shown in the example rectangle at the bottom. We
can edit and paste this information.
The ‘External Routines’ button refers to external routines
which can be linked to EES.
Unit Conversion Info (Options Menu)
This command provides information to support the use of
the ‘Convert’ function (already discussed in session 1).
The left window shows the different dimensions and right
window lists the units for that dimension.
The conversion is given at the bottom.
Options Menu continued…
Constants: lists the different constants with description and
units.
Unit System: already discussed in Session 1.
Tolerances: will let you set stop criteria and parameters for
Integration.
Calculate Menu
Check/Format: will check the entered equations for any
syntax errors, if no errors are found, it’ll return number of
equations and variables.
Solve: will try to solve the equations entered. It will also
check the syntax of equations before actually solving them.
Solve Table: will initiate calculations using Parametric
table. The table, first run and the last run is to be selected.
Calculate Menu continued…
Min/Max: used to find the minimum or maximum of an
undetermined variable in an equation set.
Check Units: will check the dimensional and unit
consistency of all equations in the Equations window.
Update Guesses: replaces the guess value of each variable
in the Equations window with the value determined in the
last calculation (only accessible after calculations have
been successfully completed).
Reset Guesses: replaces the guess value of each variable
with the default guess value.
A simple example
‘Update Guesses’ improves the computational efficiency of an
EES calculation. We will have a look at a simple example to
illustrate this. Consider this set of equations.
By default, the guess value of each variable is set to 1.
With this guess value, EES may give error for this problem.
So, to solve this problem, we will proceed as follows:
Add a variable, Delta, such that
QB = AH*Sigma*(TH^4 - T^4)+Delta
Then, set Parametric Table containing variables T and Delta.
Use the Alter Values command to set a range of values of T and
Solve Table to calculate the corresponding values of Delta.
Plot Delta against T.
The value of T for which Delta is zero gives the solution.
Find out that value from the plot (T=905). Then put that
value as an equation in Equations window and Solve again.
Then use ‘Update Guesses’ and set Delta=0 and remove the
equation T=905 and again Solve the set of equations.
EES will now quickly converge to the correct solution.
This illustrates the use of ‘Update Guesses’.
Here, by selecting ‘Reset Guesses’, EES will again make
the Guess values of all variables equal to 1.
Tables Menu
New Parametric Table, Alter values: already discussed in
Session 1.
Insert/Delete Runs: allows the number of runs in an
existing Parametric Table to be changed by inserting or
deleting one or more rows in a specified Parametric table at
a specified position.
Insert/Delete Vars: allows variables in an existing
Parametric Table to be added or removed.
Tables Menu continued…
New Lookup Table: A Lookup table is a two-dimensional set
of data with a specified number of rows and columns.
This command creates a such new table in which numerical or
string data may be entered. This data can then be accessed by
different commands like Differentiate, Interpolate.
Open Lookup: will allow access to previously stored Lookup
file and will read its contents into Lookup Table Window.
Save Lookup: will write the data of Lookup Table into a
Lookup file on disk which can be read later.
Plots Menu
New Plot window: It has three options to generate plot from
two or more variables defined in tables or arrays. The options
are: X-Y plot, Bar plot and X-Y-Z plot .
X-Y Plot: Already discussed in Session I.
Bar plot: operates in exactly same manner as X-Y Plot.
X-Y-Z Plot: will generate a contour plot, i. e. it will plot lines
of constant z in X-Y space.
The options are Isometric Lines or Color Bands.
Plots Menu continued…
Overlay Plot: allows a new plot curve to be drawn over existing
plots. Works identical to New Plot Command.
Modify Plot: this dialog can also be accessed by double-clicking
or right-clicking the plot window to be modified.
This command allows manipulation of existing plots by giving
options to change parameters like line type, color, symbol, size
and frequency of symbol etc.
Property plot: creates a new plot with thermodynamic property
for selected substance and specified axes. We can also add
isotherms or isobars on this plot.
Curve Fitting and Linear Regression
The ‘Curve Fit’ command will find the best fit of a smooth curve
through a previously plotted set of data points using least squares.
The dialog box as shown appears. Choose the plot to be fitted from
the list and also select the type of equation. A sample of the
equation will appear below.
Curve Fitting
We can also enter any equation of the form y= f(x) in the
window below with coefficients as a0, a1 etc…
Clicking ‘Fit’ will determine
these coefficients and the
final equations will be
displayed in the window. The
button ‘Fit’ will be replaced
by ‘Plot’. That will plot the
curve fit equation in the same
plot window.
Linear Regression
The difference between Curve Fitting and Linear Regression is
that Curve Fitting provides a fit with only single independent
variable while in Linear Regression, one can have as many as 6
independent variables.
The dialog box as shown appears.
One has to select the type and
name of table from the drop
down list and then select a
dependent variable and one or
more independent variables.
Linear Regression continued…
The dependent variable will be represented as a linear
polynomial function of the independent variables depending on
the order of the polynomial.
The terms involving product of the independent variables can
be included by checking the ‘Include cross-terms’ check box.
Some of the terms from the equation can be excluded by
selecting that term and then clicking ‘Exclude’ button.
Clicking the ‘Fit’ button determines the unknown coefficients
and will display the final equation in the window. This can be
copied to the clip-board.
Recap
What we have learnt today
How different Menu commands in EES work
How to insert property functions
Curve fitting and Linear Regression