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Homogeneous turbulence in a random-jet-stirred tank

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Abstract

We report an investigation into random-jet-stirred homogeneous turbulence generated in a vertical octagonal prism-shaped tank where there are jet arrays on four of the eight vertical faces. We show that the turbulence is homogeneous at all scales in the central region of the tank that span multiple integral scales in all directions. The jet forcing from four sides in the horizontal direction guarantees isotropy in horizontal planes but leads to more energy in the horizontal fluctuations compared with the vertical fluctuations. This anisotropy between the horizontal and vertical fluctuations decreases at smaller scales, so that the inertial and dissipation range statistics show isotropic behavior. Using four jet arrays allows us to achieve higher turbulence intensity and Reynolds number with a shorter jet merging distance compared to previous facilities with two-facing arrays. By changing the array-to-array distance, the parameters of the algorithm that drives random-jet stirring, and attachments to the exits of each jet, we show that we are able to vary the turbulence scales and Reynolds number. We provide scaling relations for the turbulent fluctuation velocity, integral scale, and dissipation rate, and we show how these scales of motion are primarily determined by the properties of individual jets and the diffusion of their momentum with distance from the nozzles. Finally, we examine the signatures of individual jets in the turbulent velocity spectra and report the conditions under which individual jet flows, not fully mixed with the background turbulence, produce a spectral peak and the corresponding frequency associated with the jet forcing timescale.

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Abbreviations

\((u,v,w) = (u_1,u_2,u_3)\) :

Instantaneous velocities aligned with x, y, z coordinates

\(\varvec{e}_j\) :

Directional unit vector

\(\ell _{\rm DI}\) :

Demarcation scale between inertial and dissipation ranges, estimated from the lower bound of the inertial subrange

\(\ell _{\rm EI}\) :

Demarcation scale between energy-containing and inertial ranges, estimated from the upper bound of the inertial subrange

\(\tau_{F}\) :

Forcing timescale

\(\eta ,u_\eta ,\tau _\eta\) :

Kolmogorov microscales in length, velocity, and time

\(\Gamma\) :

Gamma function

\(\lambda\) :

Taylor microscale

\(\langle \cdot \rangle\) :

Ensemble average

\(\langle \epsilon \rangle\) :

Mean turbulent kinetic energy dissipation rate

\(\mu _{\text{on}}, \mu _{\text{off}}\) :

Mean on/off time in sunbathing algorithm

\(\nu\) :

Kinematic viscosity

\(\overline{\cdot }\) :

Spatial average over homogeneous region

\(\phi\) :

Source fraction in sunbathing algorithm

\(\rho _{ij}\) :

Two-point autocorrelation

\(\sigma _{\text{on}}, \sigma _{\text{off}}\) :

Standard deviation of on/off time in sunbathing algorithm

\(\text {Ku}\) :

Kurtosis

\(\text {Sk}\) :

Skewness

\(B\) :

Jet centerline velocity-decay constant

\(D_J\) :

Jet diameter

\(D_{ij}^2\) :

Second-order structure function

\(\mathrm{d}r\) :

Spatial resolution

\(f\) :

Frequency

\(f_{\text {exp}}\) :

Exponential fit to the autocorrelation function

\(f_{\text {model}}\) :

Model function fit to the autocorrelation function

\(h(r)\) :

Osculating parabola fit to the autocorrelation function

\(J\) :

Inter-jet spacing

\(k\) :

Turbulent kinetic energy

\(K_{q}\) :

Modified Bessel function of the second kind

\(L_A\) :

Array-to-array distance

\(L_{g}\) :

Grid spacing

\(L_{ij}\) :

Integral length scale

\(L_{\rm JM}\) :

Jet merging distance

\(M_1\) :

Mean flow-to-turbulence ratio

\(M_2\) :

Kinetic energy of mean flow-to-turbulent kinetic energy ratio

\(P_{uu}\) :

Power spectral density of \(u^\prime\)

\(r\) :

Spatial lag

\({\rm Re}_\lambda\) :

Taylor scale Reynolds number

\({\rm Re}_J\) :

Jet Reynolds number

\({\rm Re}_L\) :

Turbulence Reynolds number

\(S\) :

Jet half-width spreading rate

\(t_{\text{on}}, t_{\text{off}}\) :

Duration of on/off signal

\(t_g\) :

Grid thickness

\(t_{A}\) :

Attachment thickness

\(T_{I,w}\) :

Integral time scale estimated from the autocorrelation function up to the first zero-crossing

\(T_{wz}\) :

Integral time scale in z direction using turbulent scales from \(w^\prime\)

\(u^\prime\) :

Fluctuating velocity

\(u_{\text{rms}}\) :

Root-mean-square velocity

\(U_C\) :

Jet centerline velocity

\(U_J\) :

Jet exit velocity

\(x,y,z\) :

Laboratory coordinate

\(x_0\) :

Virtual origin of jet

\(z_c\) :

Vertical center of PIV field of view

References

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Acknowledgements

We thank Luke Summey for help with tank design and construction, and Evan Variano, Gautier Verhille, and Greg Voth for useful discussions. We would also like to thank the anonymous referees whose comments and suggestions helped to improve the paper considerably.

Funding

We gratefully acknowledge support from the US National Science Foundation (CBET-2211704).

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, University of Wisconsin–Madison, Madison, WI, 53706, USA

    Joo Young Bang & Nimish Pujara

Authors
  1. Joo Young Bang
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  2. Nimish Pujara
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Contributions

All authors contributed to the study conception, design, execution, and writing. Material preparation, data collection, and analysis were led by Joo Young Bang. The first draft of the manuscript was written by Joo Young Bang, and all authors subsequently edited the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Nimish Pujara.

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Cite this article

Bang, J.Y., Pujara, N. Homogeneous turbulence in a random-jet-stirred tank. Exp Fluids 64, 185 (2023). https://doi.org/10.1007/s00348-023-03721-9

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