Parameter Selection with the Secant Method


Assignment :

Complete HW 11 and Prepare for the second exam

Last time you adjusted an area in the input deck choke1.inp to obtain a requested mass flow of 5 kg/s . Most people had to run TRACE a significant (order of 10) number of times to obtain the requested precision. Today I'll show you a systematic way to approach this task. Start by reading my general discussion of the Secant Method  to obtain a solution to a nonlinear equation in the form "f(x)=0". For this application the function "f" is the difference between the desired mass flow (5 kg/s) and the flow rate produced by the combination of TRACE and its input choke1.inp . The independent variable "x" is the area to be adjusted. When f(x) is a know closed form function you can implement the Secant method as a relatively simple program. However, our function (TRACE) is a little complex for this approach. The quickest way out is to build a table (or spread sheet) with the key terms in the Secant method's formula. Enter relevant results from the output or graphics files (.out via text editor or .xtv via APTplot) into the table by hand, compute the area change for the next run, and enter the new area into your input file, repeating this process until the result is obtained to the desired accuracy.




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