1Introduction-to-EES-3-23-12

1、1Introduction to EESGreg Nellis and Sandy KleinProfessors of Mechanical EngineeringUniversity of Wisconsin, Madison2Engineering Equation Solver (EES)lEES solves non-linear sets of equations equations are entered in the Equations Window EES uses equations vs assignments assignment: all variables to t

2、he right of the equal sign must have been previously determined equation: a relationship between unknown variables sets of equations are solved using an iterative solution technique starting from the Guess values3Example of a Set of EquationslFor example, consider the set of 3 nonlinear equations in

3、 3 unknownslNot directly solvable by most programming languages Either successive substitution or algebra would be required with sufficient algebra: which has two solutions:2343xyyzzx2100 xx122.702 and 3.702xx 4Entering & Solving EquationslEquations are entered in the Equations window 1 equation

4、 per line unless separated with ; use & sign to break line EES is NOT case sensitive Variable names must start with a letterlEquations CAN be entered in any orderlEES will check that there are enough equations & unknowns5Variable Information WindowlWhy did EES identify one solution and not t

5、he other?lEES solves systems of equations iteratively starting from a set of initial guesses Solution progresses until tolerances reach a specified levellVariable Information Window guess values & limits for each variable display format for each variable6Variable Information WindowlChanging the

6、guesses and limits controls the iteration process7CommentslYour equations can be annotated to make the problem more understandable use comments “”, or comments do not affect the solution comments are useful for temporarily removing (commenting out) sections of code8PreferenceslPreferences control ma

7、ny of the settings in EES Display and EquationsChange fontSet tabs$TabStops directive9Formatted Equations WindowlThe formatted equations window provides the equations in a more readable format greek variable names become greek symbols comments do not appear in formatted equations “” comments do appe

8、ar in formatted equations _ gives subscript, _dot gives a dot, others10Formatted Equations Window11Copying Equations from the Formatted Equations WindowlThe formatted equations in the Formatted Equations Window can be copied in various formats12Key VariableslImportant variables can be designated as

9、key variables and placed in a separate Key Variables Solution Window Can be specified in the Solutions or Variable Information Window13ExerciseSolve the equation: for a = 1, b = 2, and c = 0.5.Include comments for each line of code and display x as a key variable in the solution window a/xbcx2114EES

10、 ExamplelExample: plot the pressure loss through a 45 degree bend (in kPa) as a function of flow rate from 200 to 2000 liter/min diameter, D = 2 cm density, r = 1000 kg/m3 dimensionless resistance coefficient, K = 0.3lStart by calculating DP at one value of V_dot 22uPKr15UnitslMost engineering probl

11、ems involve variables that correspond to physical quantities with unitslEES can: help you convert between units allows you to assign a unit to each variable checks to see if the units assigned to the variables are consistent with the set of equations that you are usinglEES will NOT adjust your units

12、 so that they are consistent 16Setting Units of ConstantslThe units of numerical constants can be specified using square bracketslUnit Conversion Info from the Options menu:Units assigned to variables17ConstantslCompute cross-sectional area:lThere are many built-in constants in EES Constants from th

13、e Options menu22 in cm4cDAnote the # sign18Setting Units of VariableslEES automatically checks unit consistency of equations Can be disabled Can be accomplished anytime using Check Units from the Calculate menulThe units of variables can be set in the Solutions Window or the Variable Information Win

14、dow are not set by default can let EES try to set units (Preferences) cannot be set using square brackets:19Converting between UnitsThe function Convert( unit1 , unit2 ) returns the conversion factor to go from unit1 to unit2returns the factor 12 inch/ftThe function Converttemp( unit1 , unit2 ,tempe

15、rature) returns the temperature converted from unit1 to unit2returns 283 K (which is 10C)20Converting between UnitslCompute velocity: uVAc (in litermin cm2 liter/min-cm2)note the hyphen21Compute Pressure DroplCompute pressure drop:2232 (in kg-cm /min -s )2uPKr22Suggested Method for UnitslSuggested m

16、ethod for working with units Convert problem to base SI units (kg, m, s, N, K, etc.) Do problem entirely in base SI units (these are completely self-consistent, no unit conversions should be required) Convert results to whatever units are appropriatelThe result of using this technique is that the un

17、it consistency of the equations are checked23Base SI Method24Parametric TableslWeve seen how to use EES to get a single solution to a set of equationslA Parametric tables allow you to run EES multiple times automatically enables parametric studies each row of a Parametric Table corresponds to a solu

18、tion at a different set of parameters allows us to look at the effect of one variable (the independent variable) on another variable (the dependent variable)25Parametric Study ExampleSolve command provides DeltaP at a single value of V_dotSolve Table command will provide DeltaP at many values of V_d

19、ot, one for each row of a Parametric Table26Create a Parametric TablelInclude independent variable (V_dot) and dependent variable(s)lTable includes one column for each variable add/delete runs add/delete variables27Parametric TablelOperation of a parametric table Values set in each row are placed in

20、 Equations Window Resulting set of equations are solved Solution is placed in the columnslUse alter values command to set values in each row of the column containing the independent variablelBe careful not to over-constrain your problemlSolve Table dialog guess values stop if error reverse order28Na

21、ming & Saving Parametric TableslParametric Tables can be named & documentedlParametric Tables are automatically saved & loaded with EES filelParametric Tables can be saved as .txt or .csv fileslInformation from tables can be copied to the clipboard copy copy (eformat)CopyCopy (eformat)29

22、PlottinglThe results of a parametric study are most conveniently examined in the form of a plot independent variable as a function of the dependent variablelData in any table in EES can be plotted Parametric Table Array Table Lookup Table Integral TablelSelect New Plot Window30New Plot Setup Dialogl

23、Need to specify source of data independent & dependent variables(2) select independent variable(3) select dependent variable(s)(1) select source of data(4) formatting can be done later31Plot Formatting*lModifying axeslResizing plot use Ctrl keylModifying plots symbols, lines, smoothinglOverlayin

24、g plots (K = 0.4)lAutomatic update (K=0.5)lText items link to point, legendlCross hairs & zoom toolslAdd imagelError bars absolute vs relative asymmetric32PrintinglPrinting a hard copy requires that you select the portions of the EES program that are output Note multiple plots, tables, etc. must

25、 be selected (duplicate plot)33Create Latex/PDF ReportlIt is possible to generate a pdf or LaTeX report using LaTex2E. lThe recommended installation is MiKTeX Follow instructions found in Help Setup the report generator34Create Latex/PDF Report35lAn array is a variable with multiple elements (a vect

26、or or matrix rather than a scalar) numerical solutions - each element is a node thermodynamic problems - each element is a statelYou access the elements with brackets following the array namelArray range notation: lArrays are viewed in the Arrays WindowArrays36lArrays can have two indices in order t

27、o create a matrixTwo-Dimensional Arrays*or, using array range notation:37lThe characteristics of all of the elements of an array can be set by collapsing the array in the Variable Information WindowSetting Array Unitscollapse array38lInformation in an array can be used to generate plotsPlotting Arra

28、ysarrays table can beselected as the source of data39lDuplicate loops provide a convenient method for carrying out similar operations on multiple elements of an arrayleach of the equations in the duplicate loop are rewritten with the variable index iterated from start to stopDuplicate LoopsDuplicate

29、 index = start, stopEquation(s) to be duplicatedEndcorresponds to40lRemember that EES uses equations and not assignments do not put equations in the duplicate loop that you dont want duplicatedlDuplicate loops can be nestedDuplicate Loopscorresponds toa is not over-written41lYou will often want to c

30、hange the size of the arrays used grid sensitivity analysis for numerical modelslEES automatically allocates memory for and remembers the characteristics of all variables that have ever been used in the Equations Window you often temporarily remove variableslYou will sometimes want to purge excess variables to save on memory and computation time select Save As