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Flow structures of gaseous jets injected into water for underwater propulsion

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Abstract

Gaseous jets injected into water are typically found in underwater propulsion, and the flow is essentially unsteady and turbulent. Additionally, the high water-to-gas density ratio can result in complicated flow structures; hence measuring the flow structures numerically and experimentally remains a challenge. To investigate the performance of the underwater propulsion, this paper uses detailed Navier-Stokes flow computations to elucidate the gas-water interactions under the framework of the volume of fluid (VOF) model. Furthermore, these computations take the fluid compressibility, viscosity, and energy transfer into consideration. This paper compares the numerical results and experimental data, showing that phenomena including expansion, bulge, necking/breaking, and back-attack are highlighted in the jet process. The resulting analysis indicates that the pressure difference on the rear and front surfaces of the propulsion system can generate an additional thrust. The strong and oscillatory thrust of the underwater propulsion system is caused by the intermittent pulses of the back pressure and the nozzle exit pressure. As a result, the total thrust in underwater propulsion is not only determined by the nozzle geometry but also by the flow structures and associated pressure distributions.

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Abbreviations

A e :

Area of nozzle exit

A s :

Area of cross-section of propulsion system

A t :

Area of nozzle throat

d s :

Diameter of cross-section of propulsion system

d t :

Diameter of nozzle throat

D :

Diameter of nozzle exit

E g :

Energy of gas

E w :

Energy of water

F :

Thrust

h g :

Enthalpy of gas

h w :

Enthalpy of water

k eff :

Effective thermal conductivity, k eff = k + k t

k g :

Thermal conductivity of gas

k t :

Turbulent thermal conductivity

k w :

Thermal conductivity of water

ṁ:

Mass flow rate

Ma :

Mach number

p :

Pressure

p*:

Normalized pressure

p 0 :

Stagnant pressure

p 1 :

Atmosphere pressure

p a :

Ambient pressure

p B :

Back pressure

p e :

Pressure at nozzle exit

p ref :

Reference pressure

P r,g :

Prandtl number of gas

P r,w :

Prandtl number of water

Re :

Reynolds number

T :

Temperature

U*:

Normalized Axial-velocity

U :

Reference velocity

v e :

Normal velocity at nozzle exit

α g :

Volume fraction of gas

α w :

Volume fraction of water

γ :

Ratio of specific heats of gas

µg :

Dynamic viscosity of gas

µ m :

Dynamic viscosity of mixture

µw :

Dynamic viscosity of water

ρ g :

Density of gas

ρ l :

Density of liquid

ρ m :

Density of mixture

ρ ref :

Reference density

ρ w :

Density of water

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Author information

Authors and Affiliations

  1. School of Aerospace Engineering, Beijing Institute of Technology, 100081, Beijing, China

    Jia-Ning Tang & Ning-Fei Wang

  2. Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, 48109, USA

    Jia-Ning Tang & Wei Shyy

  3. Department of Mechanical Engineering, Hong Kong University of Science and Technology, Kowloon, Hong Kong, China

    Wei Shyy

Authors
  1. Jia-Ning Tang
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  2. Ning-Fei Wang
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  3. Wei Shyy
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Correspondence to Wei Shyy.

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Tang, JN., Wang, NF. & Shyy, W. Flow structures of gaseous jets injected into water for underwater propulsion. Acta Mech Sin 27, 461–472 (2011). https://doi.org/10.1007/s10409-011-0474-4

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