Presentation on theme: "By Hrishikesh Gadre Session II Department of Mechanical Engineering Louisiana State University Engineering Equation Solver Tutorials."— Presentation transcript:
By Hrishikesh Gadre Email: email@example.com Session II Department of Mechanical Engineering Louisiana State University Engineering Equation Solver Tutorials Spring 2004
Session 2 Outline Menu commands in EES Inserting property functions Curve fitting Linear Regression
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