MAE 157 DAQ _ Boiling Lab Report

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157

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Mechanical Engineering

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Jan 9, 2024

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1 Data Acquisition and Boiling Lab Report Lucas Beyer University of California, Los Angeles Mech&AE 157: Basic Mechanical and Aerospace Engineering Laboratory Professor Lavine October 26, 2023

2 Abstract Data acquisition (DAQ) is largely important in the engineering field and there are multiple different methods that allow for the most accurate data to be obtained. By immersing a thermocouple embedded in a copper sphere into a dewar field with liquid nitrogen, the resultant boiling curve can be analyzed using different DAQ methods. The different regions within the boiling curve plot can each be studied, with the critical heat flux, q" max , and heat transfer coefficient, , being of particular significance in this experiment. Using Matlab, different ℎ sampling rates and moving average windows were applied to these values. While the moving average windows provided values that did not stray from the true value, a lower sampling rate began to provide very skewed values. Introduction and Theory The objective of this experiment is to understand how heat flux is influenced by temperature sampling rate and noise reduction methods. This was achieved by observing a room temperature copper sphere being immersed in liquid nitrogen, with the process being analyzed by a data acquisition (DAQ) board. From the DAQ board temperature measurements, a boiling curve can be generated and the critical heat flux and film boiling heat transfer coefficient during boiling can be measured. Using the measured temperature from the DAQ board, the First Law of Thermodynamics in rate form for the sphere can be modeled as: − ρ𝑉? ? ?𝑇 ?? = ?" ? 𝐴 ? Rearranging this equation, we can solve for the surface heat flux of the sphere, q" s , in W/m 2 and further simplify to obtain a final expression in terms of density, sphere diameter, specific heat, and the temperature derivative dT/dt (see Appendix A).

3 ?" ? =− ρ𝑉? 𝑉 𝐴 ? ?𝑇 ?? =− 1 6 ρ?? 𝑉 ?𝑇 ?? The derivative in the surface heat flux expression will be evaluated using the central difference approximation, and a boiling curve can be obtained by plotting the q" s vs. excess temperature, ΔT e , on a log-log scale. Once plotted, the critical heat flux, q" max , can be calculated. ?" ?𝑎𝑥 = ? ?𝑎𝑥 ℎ ?? [σρ 𝑣 2 ?(ρ ? − ρ 𝑣 )] 1/4 All properties in the above expression are evaluated at the saturation temperature, T sat . Another value that can be acquired from the boiling curve is the film boiling heat transfer coefficient, . ℎ ℎ = 0. 15[ (ρ ? −ρ 𝑣 )?? 𝑣 2 (ℎ ?? +0.5? ?𝑣 ∆𝑇 ? ) 𝑣 𝑣 ∆𝑇 ? ] 1/3 The vapor properties used in the expression are evaluated at the mean film temperature, T f , whereas ⍴ l and h fg are evaluated at the saturation temperature, T sat . Once the heat transfer coefficient in the film boiling region has been determined, the heat transfer coefficient for the complete boiling curve can be calculated and used to calculate the Biot number, which will provide insight into the validity of the lumped capacitance method. Experimental Method The primary instrument used in this experiment is an oxygen free copper sphere with a high thermal conductivity. The sphere has a diameter of 1.27 cm and a 30-gage copper- constantan (Type T) thermocouple embedded near its center, and is attached to a thin stainless steel rod which is able to suspend the sphere in the liquid nitrogen filled dewar. 10 runs of the experiment will be conducted, with adequate time between each run for the copper sphere / thermocouple to return to room temperature. The leads from the thermocouple are connected to a

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4 Keithley 2701 DAQ system. The voltage generated is amplified and digitized using a 20-bit low-noise high-performance DAQ system, and then converted to temperature data for further analysis. The boiling curve generated has a dependence on sampling rate, noise reduction, and numerical differentiation methods. The boiling curve will be plotted at different sampling rates and moving average windows to see how each parameter affects the results. Further error analysis will be conducted to qualitatively discern the error in the heat flux. Results and Discussion One of the central components of this experiment is to understand how data acquisition techniques affect experimental results. The general form of the boiling curve can be seen in Figures 1 and 2, with 15 additional curves plotted to show how different moving average filters affect the raw temperature data and 4 additional curves plotted to show how different sampling rates affect the data. Figure 1 was created using the Matlab function "movmean" with a window size from 1 to 15, at a fixed sampling rate of 60 Hz. Figure 2 was created using the Matlab function "downsample" to provide sampling rates of 60, 30, 10, 5, and 1 Hz. Figure 1: Copper Sphere Boiling Curves for Different Moving Average Windows

5 Figure 2: Copper Sphere Boiling Curves for Different Sampling Rates The critical heat flux, q" max , was found for each boiling curve analysis (see Appendices B, C). Different moving average windows provided a mean critical heat flux, " max , of 9.2345E+04. ? Different sampling rates provided a mean critical heat flux, " max , of 8.1485E+04. ? The moving average windows provided a closer to true value, and regardless of window size, the critical heat flux was always within one standard deviation of the mean. As the sampling rates decreased, the critical heat flux also decreased. A sampling rate of 1 Hz provided a value of 4.0068E+04 and greatly skewed the mean away from the true value. The heat transfer coefficient, , was also calculated using the DAQ system values, ℎ and a value of 118.45 W/m 2 ᐧ K was obtained. A curve was fitted to this experimental data and plotted in the film boiling regime, as seen in Figure 3.

6 Figure 3: Heat Transfer Coefficients vs Excess Temperature ΔT e with Curve Fit The experimental data is very noisy with the curve fit properly conveying the expected heat transfer coefficient. Conclusion Data Acquisition is a very important subject in laboratory research and this boiling experiment illustrates how different acquisition methods, mainly sampling rates and moving average windows, can alter raw data to properly convey results. Investigating a boiling curve of a copper sphere allowed for a deep analysis into different thermodynamic properties and how potential error can arise based on data acquisition. For future research, a different system other than the Keithley 2701 could be used to see if more variation arises.

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7 Appendix A - Surface Heat Flux Properties ⍴ = density of copper, kg/m 3 V = sphere volume, m 3 c v = specific heat of copper, J/kg ᐧ K T = temperature, K or ℃ t = time, s q" s = surface heat flux, W/m 2 A s = surface area of sphere, m 2 D = sphere diameter Appendix B - Critical Heat Flux for Different Moving Average Windows Table 1: Critical Heat Flux for Different Moving Average Windows Window Size Critical Heat Flux (q" max ) No Filter 9.6432E+04 1 9.6432E+04 2 9.4703E+04 3 9.3667E+04 4 9.2610E+04 5 9.2208E+04 6 9.2334E+04 7 9.2119E+04 8 9.1718E+04 9 9.1256E+04 10 9.1171E+04

8 11 9.1143E+04 12 9.0845E+04 13 9.0352E+04 14 9.0364E+04 15 9.0266E+04 Appendix C - Critical Heat Flux for Different Moving Average Windows Table 2: Critical Heat Flux for Different Sampling Rates Sampling Rate (Hz) Critical Heat Flux (q" max ) 60 9.6432E+04 30 9.3978E+04 10 9.1632E+04 5 8.5497E+04 1 4.0068E+04