cob09721 - design of experiments in statistical analysis of an evaporative condenser

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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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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EXPERIMENTAL SETUP AND VIRTUAL MODEL OF EVAPORATIVE CONDENSER


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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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DESIGN OF EXPERIMENTS (DOE) MODEL OF THE PROCESS FLOW

Parameters

(controlled)

Variable

(Uncontrolled)

Inputs OutputsSystem

Response


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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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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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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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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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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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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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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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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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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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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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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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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

cob09721 - design of experiments in statistical analysis of an evaporative condenser

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