A numerical method based on a generalized formulation of hydrodynamic free surface problems

Szymczak, William G.; Solomon, Jay M.; Berger, Alan E.; Rogers, Joel C. W.

doi:10.2514/6.1991-1541

Cited by 4 publications

(19 citation statements)

References 3 publications

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“…These formulas would agree if the ratio a was a constant independent of the depth. However, it follows from (3-2), (3-7), (3)(4)(5)(6)(7)(8) and (3)(4)(5)(6)(7)(8)(9)(10)(11) that a depends on the depth and can be determined using…”

Section: Table 3-3 Values Of Y For Various Explosive Typesmentioning

confidence: 99%

“…These values are substantially lower than the value q = 0.324 I determined using (3-13) based on the data in Table 3-2. As mentioned earlier, this discrepancy may be due to the assumption of a spherical bubble collapse, which was used to derive (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13). How-I ever, the choice q = 0.286 yields results within the experimentally measured data.…”

Section: -7mentioning

confidence: 99%

“…P =d + PA (3)(4)(5)(6)(7)(8)(9)(10)(11) where d is the initial charge depth, and PA is the air pressure. For sea water PA = Pea = 33, feet of water.…”

mentioning

confidence: 99%

“…24 25 This discrepancy is due to several approxim mations performed to simplify formula (3-13b) in Reference 21. We remark that in addition to the assumption that the bubble gases behave adiabatically throughout the bubble oscillation, the additional assumption that the bubble remains spherical was also used to derive (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13). It is this latter assumption which is most suspect as the phenomena of non-spherical bubble collapse is well documented.…”

mentioning

confidence: 99%

“…16 Under the assumption that the bubble remains spherical, as well as the usual U assumptions that the bubble gases behave adiabatically (2-2) and are surrounded by a constant density incompressible liquid, he used potential theory together with the "method of images" to derive I a formula for surface and boundary corrections. This formula can be expressed as ; Td,b = rTji _ -], (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) where b is the initial distance from the bubble center to the bottom surface, Td,b is the corrected I period, T 0 is the "free field" period, F(x) is defined by the infinite series…”

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confidence: 99%

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Computations and Experiments of Shallow Depth Explosion Plumes

Szymczak¹,

Solomon²

1996

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Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. REPORT DATE AUG 19962. REPORT TYPE 3. DATES COVERED 00-00-1996 to 00-00-1996 FOREWORDThis report was prepared in support of the Water Barrier Ship Self-Defense Concept, managed by C. E. Higdon of the Naval Surface Warfare Center, Dahlgren Division (NSWCDD), Dahlgren, Virginia, Code G42. Under the sponsorship of the Office of Naval Research (ONR), Arlington, Virginia, the Center is developing technology that has the potential to be very effective in defending Navy platforms against high speed low flying antiship missiles (ASMs). The concept uses a wall of water to provide a low cost, universal terminal defense system for ships. The wall of water or water barrier is formed from the shallow detonations of multiple underwater explosives to protect the ship from attacking ASMs. This concept can be employed to slow or stop debris and warhead fragments from missiles killed at very short range to preclude significant damage to the defending ship. Furthermore, the barrier would defeat the fuzing and structure of ASMs that have penetrated the inner self-defense layer.The main thrust of this report is to provide validations of a hydrodynamics computer code for predicting explosion plume behavior. The results of experiments conducted at NSWC Carderock Division, Bethesda, Maryland, in May 1993, at a quarry in Arvonia, Virginia in August 1994, and at the Briar Point facility of the Aberdeen Proving Grounds in June 1994, are used for the validation studies.The research in this paper related to the Water Barrier Ship Self-Defense Concept was supported by D. Siegal (ONR, Code 351). The basic research required for the development of the computational method and some of the theory presented was supported, in part, by R. Lau (ONR, Code 311) and the NSWC Independent Research (IR) fund.In addition to the sponsors of this research, the authors would like to acknowledge the work of J. Connor (NSWC Indian Head (IH) 9540A) for providing plume height measurements and underwater bubble and plume profiles; K. Boulais, J. Choe, and K. Erwin (NSWCDD, B42) for providing the microwave data measurements; and L. Lipton (NSWCIH 450) for providing the density probe data. We also thank S. L. Drinnon (NSWCDD, B44) for assisting in preparing t...

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Section: Table 3-3 Values Of Y For Various Explosive Typesmentioning

confidence: 99%

Section: -7mentioning

confidence: 99%

“…P =d + PA (3)(4)(5)(6)(7)(8)(9)(10)(11) where d is the initial charge depth, and PA is the air pressure. For sea water PA = Pea = 33, feet of water.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Computations and Experiments of Shallow Depth Explosion Plumes

Szymczak¹,

Solomon²

1996

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Computations of bubble formation and pulsations generated by impacting cylindrical water jets

Szymczak

Means

Rogers

2004

Journal of Engineering Mathematics

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Computations of violent surface motions: comparisons with theory and experiment

Rogers

Szymczak

1997

Philosophical Transactions of the Royal Society of London. Seri

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A numerical implementation of a generalized hydrodynamics has been used to compute a number of violent surface motions (characterized by the collision of different portions of the free surface). For some of these motions, singular aspects of the surface evolution may be analysed theoretically. Comparisons of the output of the calculations with theoretical predictions are made for these cases. In a second test of the predictions of the generalized hydrodynamics, the evolution of a plume generated by underwater explosions is compared with a computed plume history. An important diagnostic tool for studying violent surface motions has been analysis of the sum of the kinetic and internal energies of the flow. Accordingly, we include some results of an investigation into mechanisms for energy dissipation, as well as a description of some relations between energy loss and modes of cavity collapse.

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A numerical method based on a generalized formulation of hydrodynamic free surface problems

Cited by 4 publications

References 3 publications

Computations and Experiments of Shallow Depth Explosion Plumes

Computations and Experiments of Shallow Depth Explosion Plumes

Computations of bubble formation and pulsations generated by impacting cylindrical water jets

Computations of violent surface motions: comparisons with theory and experiment

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