Journal of the Korean Applied Science and Technology (한국응용과학기술학회지)

The Korean Society of Applied Science and Technology (한국응용과학기술학회)
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Model setup and optimization of the terminal rise velocity of microbubbles using polynomial regression analysis

다항식 회귀분석을 이용한 마이크로 버블의 종말상승속도 모델식 구축 및 운전조건 최적화

  • Received : 2018.12.03
  • Accepted : 2018.12.21
  • Published : 2018.12.31
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Abstract

In this study, three parameters (Pressure ($X_1$), Airflow rate ($X_2$), Operation time ($X_3$)) were experimentally designed and the predicted model and optimal conditions were established by using the terminal rise velocity of the microbubbles as the response value. The polynomial regression analysis showed that the optimum value for the terminal rise velocity at the Pressure ($X_1$) of 4.5 bar, Airflow rate ($X_2$) of 3.3 L/min and Operation time ($X_3$) of 2.2 min was 5.14 cm/min ($85.7{\mu}m/sec$). Also, the highest microbubble diameter size distribution in the range of 2 to $5{\mu}m$ and 25 to $50{\mu}m$ was confirmed by using a laser particle counting apparatus.

본 연구는 3개의 운전변수(압력, 공기량, 운전시간)를 실험 설계하고 마이크로 버블의 종말부상속도(Terminal rise velocity)를 반응 값으로 하여 예측식 모델과 최적 조건을 수립하였다. 다항식 회귀분석을 통해 펌프의 압력($X_1$) 4.5bar, 공기량($X_2$) 3.3L/min 그리고 운전시간($X_3$)이 2.2min에서 종말상승속도(Terminal rise velocity)에 대한 최적값인 5.14 cm/min ($85.7{\mu}m/sec$)을 얻었다. 또한, 레이저 입자계수 측정장치를 이용하여 $2{\sim}5{\mu}m$ 및 $25{\sim}50{\mu}m$ 영역에서의 가장 높은 마이크로버블 직경크기 분포를 확인하였다.

Keywords

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Fig. 1. Picture of a microbubble generator experimental apparatus.

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Fig. 3. Comparison between predicted and observed TRV (R2=93.3%, Adjusted R2=92.3%, Predict R2=90.4%)

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Fig. 4. 2D Contour plot of response Y (Terminal rise velocity, cm/min) showing interaction (a) between Pressure (bar)(X1) and Airflow rate (LPM)(X2) at fixed 1.75min of Operation time (min)(X3). (b) between Airflow rate (LPM) and Operation time (min)(X3) at fixed 3.75bar of Pressure (bar) (X1), and (c) between Pressure (bar)(X1) and Operation time (min)(X3) at fixed 3LPM of Airflow rate (LPM)(X2).

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Fig. 5. Microbubbles size measurement using Laser Trac particle counter.

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Fig. 6. Indirect Nanobubble measurement using Laser point.

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Fig. 7. Dissolved oxygen measurement (a) DO meter in water tank (b)DO in injection with Air (b) DO in injection with pure oxygen.

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Fig. 2. (a) Schematic diagram of rise velocity measurement (a) Before micro bubbles generation (b) Stop device after micro bubbles formation (c) Measurement of micro bubbles rising velocity (d) Increase of micro bubbles rising velocity (e) Complete disappear of micro bubbles.

Table 1. The main part and specifications of Microbubble genearater

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Table 2. The main part and specifications of Microbubble genearator

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Table 3. The results of terminal rise velocity by operation conditions (Table 2) of microbubble genearator

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Table 4. Estimated regression coefficients and corresponding t and P values for Eq. (5)

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Table 5. ANOVA results for response parameters

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Table 6. Optimization conditions for response Y(Terminal rise velocity)

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