Cob09721 - Design of Experiments in Statistical Analysis of an Evaporative Condenser
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Transcript of Cob09721 - Design of Experiments in Statistical Analysis of an Evaporative Condenser
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7/31/2019 Cob09721 - Design of Experiments in Statistical Analysis of an Evaporative Condenser
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APPLICATION OF DESIGN OF EXPERIMENTS INANALYSIS OF AN EVAPORATIVE CONDENSE
Rodrigo Ghiorzzi Donni, Paulo Smith Schneider and Ivoni Carlos Acunha Jr
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APPLICATION OF DESIGN OF EXPERIMENTS IN THE ANALYSISOF AN EVAPORATIVE CONDENSER
Apply the methodology of design of experiments in an experimental model of an evaporative condenbuilt in small scale, keeping geometric similarity to real size equipments, distinguishing the parametethat actually influence the phenomena;
Artificial Neural Network (ANN) is used to simulate a condenser behavior on a more controlled baseallowing for the statistical assessment by Design of Experiments (DoE).
OBJECTIVES
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APPLICATION OF DESIGN OF EXPERIMENTS IN THE ANALYSISOF AN EVAPORATIVE CONDENSER
Heat exchange efficiency can be increased by the aid of phase change processes;
Simultaneous heat and mass transfer in an evaporative heat exchanger, the process becomecomplex in comparison to the conventional system;
It is difficult to determine objectively what parameters are important to be controlled or monitored;
In the experimental model, controlled parameters are only the volumetric flow of air and mass of swater . All experimental tests are conducted in steady state.
INTRODUCTION
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APPLICATION OF DESIGN OF EXPERIMENTS IN THE ANALYSISOF AN EVAPORATIVE CONDENSER
EXPERIMENTAL SETUP AND VIRTUAL MODEL OF EVAPORATIVE CONDENSER
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APPLICATION OF DESIGN OF EXPERIMENTS IN THE ANALYSISOF AN EVAPORATIVE CONDENSER
Experiment as a procedure in which intentional changes are made in the parameters of a systprocess in order to evaluate the possible changes experienced by the response variable and estheir causes;
Statistical design of experiments refers to the process of planning the experiment allowing approdata are collected and analyzed by statistical methods resulting in valid and objective conclusions;
Experimental design becomes indicated because it allows all the considered parameters to vary alall possible combinations of parameters and levels are possible;
Reduces the experimental effort and allows for obtaining reliable conclusions;
The DoE methodology allow us to implement a model of regression to fit the experimentaconsidering the effects of interactions of the parameters.
DESIGN OF EXPERIMENTS (DOE) PRINCIPLES
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APPLICATION OF DESIGN OF EXPERIMENTS IN THE ANALYSISOF AN EVAPORATIVE CONDENSER
DESIGN OF EXPERIMENTS (DOE) MODEL OF THE PROCESS FLOW
Parameters
(controlled)
Variable
(Uncontrolled)
Inputs OutputsSystem
Response
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APPLICATION OF DESIGN OF EXPERIMENTS IN THE ANALYSISOF AN EVAPORATIVE CONDENSER
Artificial Neural Networks (ANN) are computational structures similar to those present in the braiapplied to simulate the learning functions similar to the human nervous system;
An ANN is capable of learning from inputs, and from this point, produces different outputs from thosein their training;
The process of training an ANN to simulate functions based on input and output data begins by adjthe weights and subsequent comparison between the value found and the actual value;
The weights are adjusted iteratively until the difference found between the simulated and actual resis within an acceptable error value or until it reaches a maximum value of iterations.
ARTIFICIAL NEURAL NETWORK (ANN) PRINCIPLES
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APPLICATION OF DESIGN OF EXPERIMENTS IN THE ANALYSISOF AN EVAPORATIVE CONDENSER
ARTIFICIAL NEURAL NETWORK (ANN) MODEL OF THE NEURON PROCESS
W1
W2
Wn
f
Bias
bActivation
Function
OutputData
SumFunction
Weighs
X1
InputData
X2
Xn
.
.
.
.
.
.
u
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APPLICATION OF DESIGN OF EXPERIMENTS IN THE ANALYSISOF AN EVAPORATIVE CONDENSER
ParametersLevels
Low High
ExperiemtnalSetup
Not
controlled
Dry bulb temperature at the entry of the condenser Tdb,e 19.7C 23.5C
Wet bulb temperature at the entry of the condenser Twb,e 15.5C 19.3C
Condensation temperature (of R22) Tr22,cds 28.0C 31.0C
Sprayed water temperature Tag,asp 22.0C 25.5C
Controlled
Mass flow rate of water(*) mag 0.075kg/s 0.115kg/
Mass flow rate of air in the condenser(*) mar 0.105kg/s 0.185kg/
MAIN VARIABLES AND LEVELS USED IN ANN MODEL TO PREDICT OVERALL HEA
TRANSFER COEFFICIENT IN THE EVAPORATIVE CONDENSER
(*) Volumetric flows measured and evaluated at air and water temperatures to get the mass flows.
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APPLICATION OF DESIGN OF EXPERIMENTS IN THE ANALYSISOF AN EVAPORATIVE CONDENSER
Heat rejected in the evaporative condenser is the response used to obtained overall heat transfecoefficient and determinate the performance of each combination of parameters;
Factorial project with 2 levels and 6 parameters;
Simulation of 64 combinations of all parameters and 1 central point (the mean value between highand low levels).
SIMULATION OF DOE WITH ANN MODEL CONSIDERATIONS
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APPLICATION OF DESIGN OF EXPERIMENTS IN THE ANALYSISOF AN EVAPORATIVE CONDENSER
RESULTS ARTIFICIAL NEURAL NETWORK SIMULATION
Experimental
Overall Heat Transfer Coefficient (U)
R = 98,8%
RQME = 9,3W/mC
ERM = 1,63%
Simulated
Experimental data are used tANN model;
Actual overall heat transfer evaporatiare calculated from data and used in ANN training
After training the ANN, we obtwell fitted with the experime
capable to predict Overall HCoefficient to differents input pa
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APPLICATION OF DESIGN OF EXPERIMENTS IN THE ANALYSISOF AN EVAPORATIVE CONDENSER
RESULTS DESIGN OF EXPERIMENTS (DOE)
Standardized Residuals
Percentual(%)
Observation Order
Stan
dardizedResiduals
Normal probability plot of standardized residual
Standardized residual versus observation ord
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APPLICATION OF DESIGN OF EXPERIMENTS IN THE ANALYSISOF AN EVAPORATIVE CONDENSER
RESULTS PARETO CHART OF STANDARDIZED EFFECTS OVER OVERALL HEAT
TRANSFER COEFFICIENT (U) WITH SIGNIFICANCE OF 5%
Significance of 5%
Parameters
Standardized Effects
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APPLICATION OF DESIGN OF EXPERIMENTS IN THE ANALYSISOF AN EVAPORATIVE CONDENSER
RESULTS GRAPH OF MAIN EFFECTS OF EACH PARAMETER OVER THE MEAN
RESPONSE OF OVERALL HEAT TRANSFER COEFFICIENT (U)
MeanResponse
ofU(W/m2C)
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APPLICATION OF DESIGN OF EXPERIMENTS IN THE ANALYSISOF AN EVAPORATIVE CONDENSER
RESULTS GRAPH OF INTERACTIONS EFFECTS OF EACH PAIR OF PARAMETER
OVER THE MEAN RESPONSE OF OVERALL HEAT TRANSFER COEFFICIENT (U)
MeanResponseofU(W/m2C)
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APPLICATION OF DESIGN OF EXPERIMENTS IN THE ANALYSISOF AN EVAPORATIVE CONDENSER
RESULTS SIMULATED VALUES (WITH DOE MODEL) VERSUS PREDICTED VALU
OF OVERALL HEAT TRANSFER COEFFICIENT (U)
R = 98,8%
RQME = 9,3W/mC
ERM = 1,63%
Observed Values
PredictedValues
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APPLICATION OF DESIGN OF EXPERIMENTS IN THE ANALYSISOF AN EVAPORATIVE CONDENSER
RESULTS OVERALL HEAT TRANSFER COEFFICIENT CALCULATED WITH
EXPERIMENTAL DATA AND CORRELATIONS
200
250
300
350
400
450
500
550
600
650
700
750
800
850
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35
Ucondcalcula
ted(W/m2C)
Experimental Sample
Parker e Treybal (1961)
Mizushina et al. (1967)
Leidenfrost e Korenic (1982)
Niitsu et al. (1967)
Dreyer e Erens (1990)
Acunha Jr. (2010)
This Work
Experimental Data
Overall heat transfer coefficient determinate with classical correla
external heat transfer coefficieninternal heat transfer coefficient
with the correlation of Chato (
They have been developfor determining the heatcoefficient between the
water (around the tubesexternal air flow
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APPLICATION OF DESIGN OF EXPERIMENTS IN THE ANALYSISOF AN EVAPORATIVE CONDENSER
It is possible to verify the efficiency of the use of simulation techniques to obtain an ANN from simulatedexperimental data for application to design of experiments, allowing the testing in practice would be excessivecomplex and expensive;
It is noted that mass flow of water spray is a factor of great influence in the global coefficient of heat transfer. Tcomes to agree with literature, confirming that the PE model adopted is correct;
The condensation temperature of the refrigerant inside the condenser wasn't directly influential in the globalcoefficient of heat transfer, being removed from the model;
The methodology of experimental design enable simulated complex experiments could be performed simply awith good accuracy with a EMR of 3,69% and maximum error of 8,89%;
The effects of nonlinearity were not significant, demonstrating that relationships are essentially linear;
Since there were no replication of the experiments was not possible to estimate the pure error, i.e. the error reonly to uncertainty of measurement. Only the error of fitt ing of the model was possible to determinate.
CONCLUSIONS
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APPLICATION OF DESIGN OF EXPERIMENTS INANALYSIS OF AN EVAPORATIVE CONDENSE
Rodrigo Ghiorzzi Donni, Paulo Smith Schneider and Ivoni Carlos Acunha Jr
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Tdb,eTwb,eTr22,cdsTag,aspMagmar