嘉兴学院毕业论文（设计）外文翻译吴依呈

嘉兴学院本科生毕业论文

temperature measurements. The data acquisition and arrangement is accomplished with software written in C++. The thermocouples and the DA system are routinely referenced to an ice bath, and further calibrated with a Standard Platinum RTD (temperature range.

3.4. Experimental procedure

For each modeled winding geometry, the range of operating conditions, such as total oil flow rate and heat generation rate, is selected to match the situation expected in ON transformer windings. With regard to fixed flow rates and heat generations (heat flux densities), a series of experiments are conducted to measure temperature distributions in oil ducts and winding disks.

With one specific value of power supply, one set of experiments is accomplished within one day for various total flow rates. After preliminary heating process in the daytime, all data acquisitions are conducted in the evening to minimize the influence from power fluctuation. The measurement data are recorded once the system reaches steady state. The operation is considered steady state when all measured temperatures have remained constant (within instrument accuracy) for half an hour. Usually the system reaches steady state over 6 h after setting up total heat generation, and within one hour after changing total flow rate. Fifty consecutive readings from each thermocouple are acquired and averaged as the final result, to eliminate the electrical noise from AC as possible in order to obtain the most reliable result for each measurement. 3.5. Experimental uncertainty

) from

to

To minimize the influence from power fluctuation, all measurements are conducted in the evening, while the voltage output tends to be steady. Usually, the relative error of power supply resulted from the voltage fluctuation is lower than ±0.5%.

Measurement errors are mainly due to gain error of the DA boards, and accuracy of the

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嘉兴学院本科生毕业论文

thermocouples, flow meter and voltage meter. The effect of heat leakage from the walls of test rig is generally weak (less than 0.5% in the study), and therefore neglected. Uncertainties from electrical noise caused by alternative current, and manufacture tolerance values were not taken into account. Because the accuracy of flow meter is with full range, the measured data may have higher relative error at lower total flow rates. The measurement items and their uncertainties are summarized in Table 2.

4. Data analysis and discussion

After the experimental conditions, such as model geometry, internal heat generation and total oil flow rate, are setup, the temperature distribution in the modeled disk is dependent on ambient oil temperature, convection thermal resistance at the disk boundary, and conduction thermal resistance within the disk. In the study, the oil temperatures are obtained directly from the measurements, and the effect of the thermal resistance within conductors and heating foils can be neglected due to their high thermal conductivity. Because the thermal conductivity of insulation paper is generally small, it is an important parameter for temperature distribution in the modeled disk, and must be determined accurately. But its value is not available from the manufacturer, and therefore has to be inferred from the present temperature measurements. After having accurate thermal conductivity value of insulation paper, the convection thermal resistance, i.e., the heat transfer coefficient at disk surface, can be further determined from the experimental results.

In the study, the determination of the thermal conductivity of insulation paper and the development of the empirical correlations for local heat transfer coefficient are considered as a general constrained nonlinear optimization problem, and their results should be obtained with the best-fits between observed and predicted temperatures, at overall measurement points in the system and under various operating conditions and model geometries. In the present study, the root mean-square error (RMSE) of all measurement data is taken as the objective function [40], which can be expressed as

where is the observed temperature at location I for condition L; is the

predicted temperature at location I for condition L; IMAX(L) is the number of measurements corresponding to condition L; and LMAX is the total number of experimental conditions

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嘉兴学院本科生毕业论文

corresponding to various model geometries, heat generation rates and total oil flow rates.

The existing comprehensive thermal simulation model is taken as the implicit system constraint executed to the objective function. The constrained conditions for decision variables can be inferred from the practical physical limitation.

A modified algorithm of complex direct search method of Box is employed as the optimization routine

[41,42]

. The detailed algorithm is available elsewhere

[43]

.

4.1. Thermal conductivity of insulation

Due to comparatively large thermal conductivity of the conductor, the temperature in the conductor zone is substantially uniform while the thermal gradients mainly occur across the insulation. Consequently, in the model A, the temperature difference between point M and T,

is mainly determined with the thermal resistance in insulation, and hence taken as the

observed parameter in (11) to regress for the thermal conductivity of insulation paper, bound constraint for decision variable,

（12）

4.2. Heat transfer correlation

In the winding ducts, the cooling oil mainly flows within the thermally developing region, and may enter into the thermally developed region. In the thermally developing region, the local

is a function of dimensionless distance developed region,

, and after the fluid enters into the thermally , is

. The

becomes distance independent and its value remains constant.

In the winding, the horizontal ducts formed with two disks can be approximated as the parallel plates with both-side heating because of the large aspect ratio. Based on (2)–(5), the functional forms, employed to describe the local Nusselt number correlation for the laminar flow thermally developing and developed region, are, respectively

（thermally developing flow） （13a）

（thermally developed flow） （13b）

in which, coefficient

, exponent

and constant

, are basic decision variables.

In each flow pass as shown in Figs. 2 and 6, the first and last horizontal duct and all vertical ducts encounter one-side heating, at which the Nusselt number within the thermally developed region is given in literature and its value is a constant, but the information for the heat transfer in thermally developing region, i.e. the relationship between

and dimensionless distance x*, is

not available. In this study, the functional forms given in (13a and b) are adopted to describe the

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嘉兴学院本科生毕业论文

heat transfer correlation for theparallel plates with one-side heating, as

（thermally developing flow） （13c）

（thermally developed flow） （13d）

The variables

and

, should be obtained with the best-fits between the

observed and predicted temperatures, at overall measurement points in the system and under various operating conditions and model geometries. The bound constraints for the decision variables are,

（14a） （14b） （14c）

For the constraints with unlimited bound, a reasonable constant is assumed. 4.3. Numerical method and results

An iteration method is used for the determination of the thermal conductivity of insulation paper and the development of the empirical correlations for the local heat transfer coefficients.

The measured temperature values from model A, B and C are employed to derive the six decision coefficients in the Nusselt number correlation, and they are finally obtained and applied to the heat transfer simulation in transformer windings. The measurement range for the horizontal both-side and one-side heating ducts is given in Table 3. It is found that the thermal entry length of the fluid with one-side heated is larger than that with both-side heated at the same flow condition.

In general, the accuracy of the temperature prediction using the two correlations developed in this study is within ±1℃. Fig. 8 shows the comparison between the predicted and observed values at a typical operation condition. It can be concluded that the simulation results based on the developed correlation are in good agreement with the experimental data, and the newly developed correlations will be useful for the design calculation and performance prediction of disk-type transformer windings. 4.4. Other issues

In the model A, the temperature difference between the point S and M,

, is investigated, and its value is within ±0.3℃. It can be concluded

from the results that the conductor temperature gradients in circumferential direction can be neglected because of its highconductivity. It also indicates that the present 2-D axisymmetric simulation model is sufficiently accurate for the prediction of the temperature distribution in

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