Dimensional analysis and experimental study of gas penetration depth model for submerged side-blown equipment

• Experiments are performed under different gas flow rates and temperatures.
• Penetration equation related to three dimensionless numbers is developed.
• Different dimensionless penetration models are discussed.
• Fr  ′ and Reρg0.5ρl-0.5 are most related to dimensionless penetration within Fr′ less than 30.

A dimensionless penetration depth equation related to modified Froude number, Reynolds number and density ratio of gas–liquid was established by dimensional analysis and Buckingham pi theorem. Based on the experimental data of side-blown penetration, extracted by MATLAB digital image processing algorithm in this scaled water model experiment, a dimensionless expression which serves as a convenient way to determine the penetration depth under different operation conditions was developed by the Least Square Estimation (LES) method. Meanwhile, detailed comparison of different empirical equations from this study and other related researches has also been sufficiently investigated. At last, the influence of each dimensionless number on the penetration depth was discussed by partial correlation analysis.