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Density and compressibility effects in turbulent subsonic jets part 1: mean velocity field

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Abstract

The behavior of compressible jets originated from initially turbulent pipe flows issuing in still air has been investigated at three different subsonic Mach numbers, 0.3, 0.6 and 0.9. Helium, nitrogen and krypton gases were used to generate the jet flows and investigate the additional effects of density on the flow structure. Particle image velocimetry, high-frequency response pressure transducers and thermocouples were used to obtain velocity, Mach number and total temperature measurements inside the flow field. The jets were formed at the exit of an adiabatic compressible frictional turbulent pipe flow, which was developing toward its corresponding sonic conditions inside the pipe, and continued to expand within the first four diameters distance after it exited the pipe. Theoretical considerations based on flow self-similarity were used to obtain the decay of Mach number along the centerline of the jets for the first time. It was found that this decay depends on two contributions, one from the velocity field which is inversely proportional to the distance from the exit and one from the thermal field which is proportional to this distance. As a result, a small non-linearity in the variation of the inverse Mach number with downstream distance was found. The decay of the Mach number at the centerline of the axisymmetric jets increases by increasing the initial Mach number at the exit of the flow for all jets. The decay of mean velocity at the centerline of the jets is also higher at higher exit Mach numbers. However, the velocity non-dimensionalized by the exit velocity seems to decrease faster at low exit Mach numbers, suggesting a reduced mixing with increasing exit flow Mach numbers. Helium jets were found to have the largest spreading rate among the three different gas jets used in the present investigation, while krypton jets had the lowest spreading rate. The spreading rate of each gas decreases with increasing its kinetic energy relatively to its internal energy.

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Abbreviations

D :

jet exit diameter

D e :

equivalent jet exit diameter

M :

Mach number U/α

M E :

energy based Mach number M E = (1/2U 2/c p T)1/2 = (1/2γ(γ−1))1/2 M

M CL :

centerline Mach number

M J :

jet exit Mach number

p :

static pressure

p 0 :

total pressure

T :

static temperature

St:

Stokes number \( {\text{St}} = {\frac{{{{\rho_{\text{p}} d_{\text{p}}^{2} } \mathord{\left/ {\vphantom {{\rho_{\text{p}} d_{\text{p}}^{2} } {18\mu }}} \right. \kern-\nulldelimiterspace} {18\mu }}}}{{D/U_{\text{J}} }}} \)

T 0 :

total temperature

γ = c p/c v :

ratio of specific heats

λU = U a/U J :

velocity ratio

λρ = ρa/ρJ :

density ratio

λγ = γa/γJ :

ratio of specific heats ratio

ρa :

ambient air density

ρJ :

jet exit flow density

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Acknowledgments

The authors would like to thank Drs. Savvas Xanthos and Minwei Gong for helping with the experimental set-up. The financial support provided by NASA Glenn Research Center through Grant #: NAG3-2163 is greatly appreciated.

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Authors and Affiliations

  1. Experimental Aerodynamics and Fluid Mechanics Laboratory, Department of Mechanical Engineering, The City College of CUNY, New York, NY, 10031, USA

    Zhexuan Wang & Yiannis Andreopoulos

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  1. Zhexuan Wang
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  2. Yiannis Andreopoulos
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Correspondence to Yiannis Andreopoulos.

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Wang, Z., Andreopoulos, Y. Density and compressibility effects in turbulent subsonic jets part 1: mean velocity field. Exp Fluids 48, 327–343 (2010). https://doi.org/10.1007/s00348-009-0738-y

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