Summary EES Manual

General commands F1: help file The Options menu provides commands for setting the guess values and bounds of variables, the unit system, default information, and program preferences. A command is also provided for displaying information on built-in and user-supplied functions. The Calculate menu contains the commands to check, format and solve the equation set. The Tables menu contains commands to set up and alter the contents of the Parametric and Lookup Tables and to do linear regression on the data in these tables. The Parametric Table, similar to a spreadsheet, allows the equation set to be solved repeatedly while varying the values of one or more variables. The Lookup table holds user-supplied data which can be interpolated and used in the solution of the equation set. The Plot menu provides commands to modify an existing plot or prepare a new plot of data in the Parametric, Lookup, or Array tables. Curve-fitting capability is also provided. Options menu Unit system

Unit conversion capabilities with the CONVERT function

Note the use of the Convert function in this example to convert the units of the specific kinetic energy [m^2/s^2] to the units used for specific enthalpy [kJ/kg] The Convert function has the following format: Convert(From, To) where From and To are character strings identifying the unit type such as Btu/hr-ft2-R or mph.

Comments Array variables X[5,3] A Lookup file = 2-dimensional matrix

String Variables $ at the end Raising to a power ^ or **

Underscore character is used to indicate a subscript lb_m will appear as lbm Multiple equations may be entered on one line if they are separated by a semi-colon ; The order in which the equations are entered does not matter. The position of knowns and unknowns in the equation does not matter. Thermodynamic property functions:

General: variable=thermodynamic property function(substance name, Independent variables e.g. T, P, H, U, S, V, and X, corresponding to temperature, pressure, specific enthalpy, specific internal energy, specific entropy, specific volume, and quality) Or via Options Function Information

For example: Specific volume v1=volume(R134a,T=T1,P=P1)

Before solving the equation: Set guess values and (possibly) the lower and upper bounds for the variables Options Variable Information

Equation Window:

Checking the syntax using the Check/Format command in the Calculate menu

Solving the equation:

Calculate Menu Solve

Number of iterations and residual:

Options Menu Stop Criteria

If the maximum residual is larger than the value set for the stopping criteria, the equations were not correctly solved, possibly because the bounds on one or more variables constrained the solution.

Parametric studies: to see how one variable varies with another.

Table Menu New Parametric Table

Add the variables in the table (Add), also the one that will be used for the sensitivity analysis

The first column is the one which will vary (type in or enter automatically by the clicking on the arrow of the first column)

In the equation window the variable should be added with some code to prevent fixing the variable to a certain defined value

$ifnot Parameter Table P2 = 300

$ endif Solve

Calculate Menu Solve Table

Plot the Table

Plot Menu New Plot Window o Choose x and y axis

Plots of the thermodynamic properties can be generated using the Property Plot command Example: Type: T-s diagram R245fa Reference: DFT (IIR, if you work with REFprop for mixtures; REFprop must be imported via package) Optimization Min/Max: to find the minimum or maximum of an undetermined variable in an equation set for which there is one or more (limited to 10) degrees of freedom.

Methods: The recursive Quadratic Approximations method is usually faster, but the Golden Section method is more reliable. Multi-dimensional optimization may be done using either Direct Search or a Variable Metric algorithm. The Variable Metric method, which uses numerical

derivatives, usually performs much better than the Direct Search method, but it may be confounded if the optimum is constrained to be on a bound. Careful selection of the bounds and the guess value(s) of the independent variables will improve the likelihood of finding an optimum. Min/Max Table provides the same capability as the Min/Max command, except that the calculations will be repeated for each row in the Parametric Table. Update Guesses replaces the guess value of each variable in the Equations window with the value determined in the last calculation. This command is accessible after calculations have been successfully completed.

Built-in functions

Mathematical functions From page 91 in Manual if (A, B, X, Y, Z)

allows conditional assignment statements.

If AB, the function will return the value of Z. lookup(Filename, Row, Column)

Returns the value in the Lookup Table or Lookup file at the specified row and column.

Thermophysical property functions From page 104 in Manual

EES Functions, Procedures and Modules

A function is a subprogram that accepts one or more inputs and returns a single result.

A procedure can return one or more results.

A module is similar to a procedure in that it can return one or more results. However, it differs from a procedure in that it employs equalities rather than assignment statements.

Functions At the top of the Equations Window

An assignment statement sets the variable identified on the left of the statement to the

numerical value on the right.

FUNCTION function name(argument1, argument2,)

X:=X+1 is a valid assignment statement but it obviously cannot be an equality

END

If then else, repeat until and goto statements may be used Example

The specific availability of a flowing stream, often called , is

= (h - ho) - To (s - so) + V2/2 + g z Once the temperature and pressure of the dead state are selected, ho and so are constants. A user function for the availability of steam, with To=530 R and Po=1 atm, could be implemented by placing the following statements at the top of the Equations window. A reference to psi(T1, P1, V1, Z1) from an equation would return the specific availability of steam in Btu/lbm for the chosen dead state. FUNCTION psi(T, P, V, Z)

To := 530 R dead state temperature ho := 38.05 Btu/lbm specific enthalpy at dead state conditions so := 0.0745 Btu/lbm-R specific entropy at dead state conditions h := enthalpy(STEAM, T=T, P=P) s := entropy(STEAM, T=T, P=P) g = 32.17 ft/s^2 gravitational acceleration psi := (h-ho)- To * (s so) + (V^2 / 2 + g * Z) * Convert(ft^2/s^2, Btu/lbm)

END

Procedures EES procedures are very much like EES functions, except that they allow multiple outputs. At the top of the Equations Window

The format of a Procedure is:

PROCEDURE procedure name(input1, input2, : output1, output2,) ... ... X :=... Y :=...

END To use the procedure, place a CALL statement anywhere within your equations. The CALL

statement appears as ... CALL test(1,2,3 : X,Y)

... If then else, repeat until and goto statements may be used

Single-Line If Then Else Statements Only in functions and procedures (not in modules and in the main body text).

Recognized operators are =, , =, and (for not equal).

The AND and OR logical operators can also be used in the conditional test.

The single-line format has the following form:

If (Conditional Test ) Then Statement 1 Else Statement 2

Example: Function MIN3(x,y,z) { returns smallest of the three values}

If (xz) Then m:=z MIN3:=m

End Y = MIN3(5,4,6) { Y will be set to 4 when this statement executes}

Multiple-Line If Then Else Statements The format is as follows:

If (Conditional Test) Then Statement Statement ...

Else Statement Statement ...

EndIf Example: Function IFTest(X, Y)

If (X

GoTo Statements EES will normally process the assignment statements in a function or procedure in the order

they appear starting with the first statement. However, the flow control can be altered using GoTo statements.

The format of a GoTo statement is simply GoTo # where # is a statement label number which must be an integer number between 1 and 30000.

Statement labels precede an assignment statement separated with a colon (:). Example: Function FACTORIAL(N)

F:=1 i:=1

10: i:=i+1 F:=F*i If (i

Library Files EES allows files containing one or more functions, procedures or modules (subprograms) to

be saved as Library files. A Library file has a .LIB filename extension.

Advanced Features

String Variables Examples:

A$=carbon dioxide B$=A$ h=enthalpy(R$,T=T,P=P) String variables may be used with the Parametric table.

The DUPLICATE Command The DUPLICATE command provides a shorthand way of entering equations into EES. The

equations which are to be duplicated are enclosed between the DUPLICATE and END command words.

DUPLICATE is useful only when used with array variables. For example, the following statements: N=5 X[1]=1 DUPLICATE j=2,N

X[j]=X[j1]+j END are equivalent to: X[1]=1 X[2]=X[1]+2 X[3]=X[2]+3 X[4]=X[3]+4 X[5]=X[4]+5