Application of Statistical Design of Experiment and Numerical Optimization in Optimizing the Effects of Selected Input Variables on the Period of Oscillation in an Unsteady Flow Through Surge Chamber

[1]

**Ilaboya, I. R.**, University of Benin; Department of Civil Engineering, Faculty of Engineering, PMB 1154, Benin City, Nigeria.

[2]

**Oti, E. O.**, University of Benin; Department of Civil Engineering, Faculty of Engineering, PMB 1154, Benin City, Nigeria.

[3]

**Atikpo E.**, Department of Civil Engineering, Igbinedion University, Okada, Edo State, Nigeria.

[4]

**Enamuotor, B. O.**, Department of Civil Engineering, Delta State University, Abraka, Nigeria.

[5]

**Umukoro, L. O.**, Department of Civil Engineering, Igbinedion University, Okada, Edo State, Nigeria.

The focus of the research paper was to study the performance of plint and partners model surge chamber equipment consisting of a large water reservoir supplying a horizontal stainless steel pipeline (penstock) under a constant head arrangement in modeling the behaviour of fluid under unsteady state condition. The inlet valve to the reservoir was opened and adjusted to give some level of discharge from overflow weir for a predetermined period of time. The flow rate of the water was then computed using the volume against time relationship. A surge was then initiated by a sudden closure of the valve and the dynamics of flow was then studied based on the number of complete oscillation (period) that was observed in the surge chamber. critical studies on the effects of selected input variables such as surge tower diameter, time of flow, velocity of flow, and rate of flow on the operational dynamics of unsteady flow in surge chambers was done using design of experiment (DOE) employing the 2-level factorial design with 3 central point’ and one replication. Analysis of the results obtained was done using statistical package (Design Expert Version 7.0). Generation of the optimal equation for both the coded variables and the actual factors including the optimal solution of the selected input variables was done by numerical optimization and the ranking of the variable effects on the response was done using the Pareto chart. The adequacy of the optimal equation was validated using the fisher’s F probability function, coefficient of determination (r2), and the adjusted R square value. The desirability of the model equation obtained reveals that the equation can be applied to any system operating under the same selected condition. Result of numerical optimization shows that, for a complete oscillation period of 15 seconds, the operational conditions needed are; Time of flow (8.20s), flow velocity (409.94m/s), rate of flow (2.34m3/s), and surge diameter (0.08m)

Surge Chamber, Numerical Optimization, Design of Experiment, 2-Level Factorial Design, Unsteady Flow, and Coefficient of Determination

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