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Application of Frequency Response Technique to the Analysis of Turbulent Diffusion Phenomenon JAMES R. HAYS, Graduate Student, Chemical Engineering KARL B. SCHNELLE, Associate Professor of Chemical Engineering PETER A. KRENKEL, Associate Professor of Sanitary and Water Resources Engineering Vanderbilt University Nashville, Tennessee SUMMARY This paper presents a review of the pulse testing method for dynamic analysis of systems. Experimental pulse data is reduced to frequency domain information by numerically computing the Fourier transform. A digital computer is necessary for the data reduction. The procedure by which the frequency domain information is found is presented in the paper, and a brief description of the FORTRAN data reduction program for the IBM 7072 computer is given. Simultaneous mass transport of dissolved or suspended material can be de described by the following equation: dc dt = D, c)2C Jc dx Two solutions of this equation are presented in this paper. One solution, due to Levenspiel (1), is given for a mass of material rapidly injected at the origin of the test system boundary. The second solution, by Clements (2), is applicable when both the input and output concentrations are measured in the pipe. Under such conditions the pulse testing method may be used for data reduction. Leven spiel's solution is in the time domain while Clements' of necessity presents a frequency domain equation. A mathematical modeling procedure is described which uses the integral of the squared error as a measure of deviation. This parameter is minimized by a nonlinear least squares procedure due to Marquardt (3). This technique simultaneously presents the statistical best values of the model parameters and the standard error of estimate, a measure of how well the model describes the system. Application of both the pulse testing techniques and the modeling procedure was made to the problem of axial mixing in a 35ft long, onein. diameter, Pyrex glass pipe. Sodium chloride pulses were injected and the input and output recorded through electrical conductivity bridges. The results of the investigation are presented in this paper. The study showed that athigher Reynolds Number the standard error of estimate is of the same order of magnitude as the experimental error. Thus, the model is a near perfect fit in the higher Reynolds Number region^ It was found that over the range of Reynolds Number 3 x 103 through 3 x 105 the data could be correlated by the following expression:  777
Object Description
Purdue Identification Number  ETRIWC196461 
Title  Application of frequency response technique to the analysis of turbulent diffusion phenomenon 
Author 
Hayes, James R. Schnelle, Karl B. Krenkel, Peter A. 
Date of Original  1964 
Conference Title  Proceedings of the nineteenth Industrial Waste Conference 
Conference Front Matter (copy and paste)  http://earchives.lib.purdue.edu/u?/engext,11114 
Extent of Original  p. 777795 
Series 
Engineering extension series no. 117 Engineering bulletin v. 49, no. 1(a)2 
Collection Title  Engineering Technical Reports Collection, Purdue University 
Repository  Purdue University Libraries 
Rights Statement  Digital object copyright Purdue University. All rights reserved. 
Language  eng 
Type (DCMI)  text 
Format  JP2 
Date Digitized  20090519 
Capture Device  Fujitsu fi5650C 
Capture Details  ScandAll 21 
Resolution  300 ppi 
Color Depth  8 bit 
Description
Title  page 777 
Collection Title  Engineering Technical Reports Collection, Purdue University 
Repository  Purdue University Libraries 
Rights Statement  Digital object copyright Purdue University. All rights reserved. 
Language  eng 
Type (DCMI)  text 
Format  JP2 
Capture Device  Fujitsu fi5650C 
Capture Details  ScandAll 21 
Transcript  Application of Frequency Response Technique to the Analysis of Turbulent Diffusion Phenomenon JAMES R. HAYS, Graduate Student, Chemical Engineering KARL B. SCHNELLE, Associate Professor of Chemical Engineering PETER A. KRENKEL, Associate Professor of Sanitary and Water Resources Engineering Vanderbilt University Nashville, Tennessee SUMMARY This paper presents a review of the pulse testing method for dynamic analysis of systems. Experimental pulse data is reduced to frequency domain information by numerically computing the Fourier transform. A digital computer is necessary for the data reduction. The procedure by which the frequency domain information is found is presented in the paper, and a brief description of the FORTRAN data reduction program for the IBM 7072 computer is given. Simultaneous mass transport of dissolved or suspended material can be de described by the following equation: dc dt = D, c)2C Jc dx Two solutions of this equation are presented in this paper. One solution, due to Levenspiel (1), is given for a mass of material rapidly injected at the origin of the test system boundary. The second solution, by Clements (2), is applicable when both the input and output concentrations are measured in the pipe. Under such conditions the pulse testing method may be used for data reduction. Leven spiel's solution is in the time domain while Clements' of necessity presents a frequency domain equation. A mathematical modeling procedure is described which uses the integral of the squared error as a measure of deviation. This parameter is minimized by a nonlinear least squares procedure due to Marquardt (3). This technique simultaneously presents the statistical best values of the model parameters and the standard error of estimate, a measure of how well the model describes the system. Application of both the pulse testing techniques and the modeling procedure was made to the problem of axial mixing in a 35ft long, onein. diameter, Pyrex glass pipe. Sodium chloride pulses were injected and the input and output recorded through electrical conductivity bridges. The results of the investigation are presented in this paper. The study showed that athigher Reynolds Number the standard error of estimate is of the same order of magnitude as the experimental error. Thus, the model is a near perfect fit in the higher Reynolds Number region^ It was found that over the range of Reynolds Number 3 x 103 through 3 x 105 the data could be correlated by the following expression:  777 
Resolution  300 ppi 
Color Depth  8 bit 
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