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Experimental study on flow kinematics and impact pressure in liquid sloshing

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Abstract

This paper experimentally studied flow kinematics and impact pressure of a partially filled liquid sloshing flow produced by the periodic motion of a rectangular tank. The study focused on quantifying the flow velocities and impact pressures induced by the flow. Filled with water at a 30 % filling ratio, the tank oscillated at a resonant frequency and generated the violent sloshing flow. The flow propagated like breaking waves that plunged on both side walls and formed up-rushing jets that impacted on the top wall. Velocities of the multiphase flow were measured using the bubble image velocimetry technique. A total of 15 pressure sensors were mounted on the top wall and a side wall to measure the impact pressures. The local kinetic energy obtained by the measured local velocities was used to correlate with the corresponding pressures and determine the impact coefficient. In the sloshing flow, the flow direction was dominantly horizontal in the same direction of the tank motion before the wave crest broke and impinged on a side wall. At this stage, the maximum flow velocities reached 1.6C with C being the wave phase speed. After the wave impingement, the uprising jet moved in the vertical direction with a maximum velocity reached 3.6C before it impacted on the top wall. It was observed that the impact coefficients differed by almost one order of magnitude between the side wall impact and the top wall impact, mainly due to the large difference between the local velocities. A nearly constant impact coefficient was found for both side wall and top wall impacts if the impact pressures were directly correlated with the flow kinetic energy calculated using C instead of the local velocities.

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Acknowledgments

The authors wish to thank the graduate research team and Professor Ho Hwan Chun in the Department of Naval Architecture and Ocean Engineering, Pusan National University, for their assistance during the experiments.

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Authors and Affiliations

  1. Zachry Department of Civil Engineering, Texas A&M University, College Station, TX, USA

    Youn Kyung Song, Kuang-An Chang & Yonguk Ryu

  2. River Experiment Center, Korea Institute of Construction Technology, Andong, Korea

    Yonguk Ryu

  3. Department of Naval Architecture and Ocean Engineering, Pusan National University, Pusan, Korea

    Sun Hong Kwon

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  1. Youn Kyung Song
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Correspondence to Kuang-An Chang.

Appendix: Discussion on reliability of the pressure measurements

Appendix: Discussion on reliability of the pressure measurements

While their effect should be consider, a decreased ullage pressure above the free surface of the sloshing liquid inside a tank seems to have an insignificant effects on the response patterns of impact pressures unless it reached a very low pressure that is close to the vapor pressures (Bass et al. 1985; Rafiee et al. 2011). Particularly, the impact pressure varies dramatically when the ullage pressure is lower than 0.01 bar. In the present investigation, the experimental setup aims no specific prototype and the ullage pressure inside the closed tank was kept at the atmospheric pressure.

For the rapidly evolving sloshing flow, a sampling rate of 20 kHz or higher has typically been recommended for pressure measurements in order to capture certain peak pressures and rise times accurately during sloshing impacts. For instance, Yung et al. (2009) conducted scaled sloshing model experiments to simulate the local behavior of a LNG liquid sloshing in a squared tank under a simple, longitudinal harmonic excitation. Based on the local impact pressure measurements using 75 densely distributed pressure sensors, they suggested that LNG tank experiments scaled at a geometric ratio of 30–50 requires a minimum sampling frequency of 20 kHz. They found a 5 % reduction in peak pressure when the sampling rate was decreased from 40 to 20 kHz. Similarly, Wang et al. (2011) employed a 19.2 kHz sampling rate in laboratory sloshing tests to investigate liquid impacts on a tank structure. Lugni et al. (2010b) employed a 16 kHz sampling rate to investigate the evolution of dynamic pressures during the flip-though moment of wave impingement on a rigid wall. In the present study, the sampling rate of 20 kHz was employed while peak pressures of the order of O(10 kPa) were observed. Accordingly, the measured peak pressures may increase slightly if a higher sampling rate of 40 kHz were used, but the discrepancy should fall in the 5 % range as concluded in Yung et al. (2009).

Other parameters affecting the dynamic behavior of liquid sloshing include filling ratio, frequencies of tank motion, ullage pressure, density of the liquid, temperatures of liquid and gas entrapped during impacts. Various studies have been conducted to examine the effects of those parameters, and some reviews were provided in the “Introduction” section. It is generally accepted that the dynamic responses of the sloshing flow are most dominantly affected by the liquid filling ratio and motion of the containing structure (e.g., the degrees of freedom and oscillation frequencies). The present work mainly focused on the quantitative evaluations of the kinematics and corresponding dynamic impacts of the multiphase liquid sloshing, and their impact correlations under a fixed experimental condition (i.e., a selected filling ratio and motion of the tank).

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Song, Y.K., Chang, KA., Ryu, Y. et al. Experimental study on flow kinematics and impact pressure in liquid sloshing. Exp Fluids 54, 1592 (2013). https://doi.org/10.1007/s00348-013-1592-5

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