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Research Papers: Fundamental Issues and Canonical Flows

Scaling Laws for the Peak Overpressure of a Cannon Blast

[+] Author and Article Information
Robert A. Carson

U.S. Army/Armament Research, Development,
and Engineering Center (ARDEC)/Benet
Laboratories, Watervliet Arsenal,
Watervliet, NY 12189

Onkar Sahni

Mechanical, Aerospace and
Nuclear Engineering Department,
Rensselaer Polytechnic Institute,
Troy, NY 12180

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received February 23, 2016; final manuscript received September 2, 2016; published online November 3, 2016. Assoc. Editor: Oleg Schilling.

J. Fluids Eng 139(2), 021204 (Nov 03, 2016) (12 pages) Paper No: FE-16-1119; doi: 10.1115/1.4034639 History: Received February 23, 2016; Revised September 02, 2016

For large cannons, blast overpressure can have a detrimental effect on the crew in the near field (i.e., within a distance of 50 tube diameters or calibers from the muzzle center) as well as on the support personnel and equipment in the far field (i.e., at a distance greater than 50 calibers). Therefore, an efficient method to determine the peak overpressure due to a cannon blast is highly desired. In this study, we investigate scaling laws for the peak overpressure, due to the primary blast of a large cannon, with the aim that they can be applied as an efficient method to evaluate the peak overpressure in the far field. We explore two types of scaling laws; each type is based on a power-law model involving a prefactor and an exponent as model parameters. The two types of the power-law models differ in the way they incorporate the polar angle dependence. The first type was proposed by Fansler and Schmidt (1983, “The Prediction of Gun Muzzle Blast Properties Utilizing Scaling,” U.S. Army Ballistic Research Laboratory, Aberdeen Proving Ground, MD, Report No. ARBRL-TR-02504). They developed a muzzle-center based scaling law (MCSL) in which the polar angle dependence was incorporated through a reference length scale to define a nondimensional or scaled radial distance from the muzzle center and the model parameters were independent of the polar angle. They calibrated the parameters by employing least-squares fit to a wide range of experimental data. In this study, we recalibrated or updated the parameters for the current cannon by using the numerical simulation data for the cannon blast in the near field. Additionally, we developed a second type of scaling law in which the radial distance is defined from the blast center (in contrast to the muzzle center) and scaled using the inner tube diameter. In this model, the angular dependence is incorporated directly into the model parameters. For this model too, we calibrated the parameters by using the numerical simulation data. We observe that both the modified version of the muzzle-center based scaling law as well as the blast-center based scaling law (BCSL) show a significantly closer fit to the numerical and experimental data and achieve a similar level of accuracy. This indicates that the current form or structure of the two types of power-law based scaling models is able to fit well with the near-field data; however, the current methodology requires a calibration process for a given cannon of interest. In the future, with far field data, we plan to evaluate predictions in the far field.

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References

Figures

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Fig. 1

Schematic of the normalized overpressure along normalized distance over two rays in the rearward muzzle region for a cannon blast, where relative strength of the peak overpressure is shown at four instances of time

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Fig. 2

Projectile and solid propellant block at its initial position inside the cannon tube

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Fig. 3

Computational domain—a quarter cylinder (shading is used to distinguish different surfaces)

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Fig. 4

Mesh near the projectile (left) and tube exit (right); solid black color is used in the mesh for solid regions

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Fig. 5

Blast overpressure locations from the experiments (with the cannon at 0 deg elevation)

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Fig. 6

Normalized peak overpressure from the experiments and numerical simulation

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Fig. 7

Schematic of different length scales for the muzzle-center based power-law

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Fig. 8

Schematic of the length scale for the blast-center based power-law

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Fig. 9

Density contours showing the Mach disk location

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Fig. 10

Five rays over which data from the numerical simulation are used to perform calibration of the MCSL-mod

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Fig. 11

Normalized primary blast peak overpressure along a scaled radial distance from the muzzle center, r¯mc, without a polar angle dependence over five rays at four time instances from 9.5 ms to 11 ms

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Fig. 12

Normalized primary blast peak overpressure along a scaled radial distance from the muzzle center, r̃mc, with a polar angle dependence over five rays at four time instances from 9.5 ms to 11 ms

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Fig. 13

Density contours at 11 ms with the blast center at the centerline position

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Fig. 14

Density contours at 11 ms with the blast center at the off-centerline position

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Fig. 15

Density contours at 11 ms (left plot) and at 11.75 ms (right plot) with the blast center at an off-centerline position

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Fig. 16

Density contours along with velocity vectors at 11 ms with the blast center at an off-centerline position (two vectors are traced back to the blast center)

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Fig. 17

Five rays over which data from the numerical simulation are used to perform calibration of the BCSL

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Fig. 18

Normalized primary blast peak overpressure along a scaled radial distance (from the blast center) without a polar angle dependence over five rays at six time instances from 8.5 ms to 11 ms

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Fig. 19

Eight additional positions in the numerical simulation at a radial distance of 5 calibers

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Fig. 20

Comparison of the primary blast peak overpressure between the MCSL-org, numerical simulation, and experiment

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Fig. 21

Comparison of the primary blast peak overpressure between the MCSL-mod, numerical simulation, and experiment

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Fig. 22

Comparison of the primary blast peak overpressure between the BCSL, numerical simulation, and experiment

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Fig. 23

Comparison of the primary blast peak overpressure between the MCSL-mod, BCSL, numerical simulation, and experiment (left plot is without any shift and a constant shift is applied to each dataset in the right plot)

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