A proposed modification to Lundgren's physical space velocity forcing method for isotropic turbulence

Carroll, Phares L.; Blanquart, Guillaume

doi:10.1063/1.4826315

Cited by 98 publications

(104 citation statements)

References 13 publications

(7 reference statements)

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“…The Lundgren force is a method for achieving a controllable injection of energy in a turbulent flow without unnecessary real-life complications. It has been shown 1,27,28 that the Lundgren force is consistent with Kolmogorov's inertial range energy spectrum scaling so it does not "contaminate" the statistical structure of normal-fluid turbulence. This force is introduced in the Navier-Stokes equation for the following reason: the structure of pure normalfluid turbulence is identical to that of turbulence in a simple-fluid, which is a topic of numerous investigations and many of its aspects are very well understood.…”

Section: Navier-stokes Fluid Dynamicsmentioning

confidence: 86%

“…Thus, since the other (non-coupling related) forces in the Navier-Stokes equation conserve energy, any normal-fluid energy dynamics in the computations are due entirely to its coupling with the vortices, and the energy transfer between the two subsystems because of their coupling can be explicitly demonstrated. Moreover, since the Lundgren force does not alter spectral scalings, 1,27,28 any normal-fluid turbulence deviation from standard simple-fluid turbulence physics can be safely attributed to the effects of the mutual-friction and lift force couplings.…”

Section: Navier-stokes Fluid Dynamicsmentioning

confidence: 99%

“…This steady state is established in a separate, pure normal-fluid computation, where an initially random normal-fluid velocity field with Gaussian statistics 39 is allowed to evolve under Navier-Stokes dynamics whilst the Lundgren force injects kinetic energy at a specified, constant rate. 27,28 The level of energy injection is determined by the value of the targeted steady state Taylor Reynolds number. The latter, in turn, is dictated by combined computational complexity considerations, since, in a superfluid computation, the demanding resolution of fully developed normal-fluid turbulence is only partially responsible for the computational load, and one needs to correctly anticipate the size of the superfluid vortex problem too, in order to design manageable computations.…”

Section: Setting Up a Finite Temperature Superfluid Turbulencementioning

confidence: 99%

“…As a result, by performing a harmless redefinition of the pressure p/(ρ n + ρ s ) → p, one can scale the normal-fluid equation with three nondimensional numbers. The last term of the equation (also known as Lundgren force) [26][27][28] is a force that mimics the injection of energy in a normal-fluid turbulent flow. In real-life situations, there are many ways to stir up a fluid, for example, by having it interact with a solid or a gravitational/electromagnetic field.…”

Section: Navier-stokes Fluid Dynamicsmentioning

confidence: 99%

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Energy spectra of finite temperature superfluid helium-4 turbulence

Kivotides

2014

Physics of Fluids

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This version is available at https://strathprints.strath.ac.uk/55195/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. A mesoscopic model of finite temperature superfluid helium-4 based on coupled Langevin-Navier-Stokes dynamics is proposed. Drawing upon scaling arguments and available numerical results, a numerical method for designing well resolved, mesoscopic calculations of finite temperature superfluid turbulence is developed. The application of model and numerical method to the problem of fully developed turbulence decay in helium II, indicates that the spectral structure of normal-fluid and superfluid turbulence is significantly more complex than that of turbulence in simplefluids. Analysis based on a forced flow of helium-4 at 1.3 K, where viscous dissipation in the normal-fluid is compensated by the Lundgren force, indicate three scaling regimes in the normal-fluid, that include the inertial, low wavenumber, Kolmogorov k −5/3 regime, a sub-turbulence, low Reynolds number, fluctuating k −2.2 regime, and an intermediate, viscous k −6 range that connects the two. The k −2.2 regime is due to normal-fluid forcing by superfluid vortices at high wavenumbers. There are also three scaling regimes in the superfluid, that include a k −3 range that corresponds to the growth of superfluid vortex instabilities due to mutual-friction action, and an adjacent, low wavenumber, k −5/3 regime that emerges during the termination of this growth, as superfluid vortices agglomerate between intense normal-fluid vorticity regions, and weakly polarized bundles are formed. There is also evidence of a high wavenumber k −1 range that corresponds to the probing of individual-vortex velocity fields. The Kelvin waves cascade (the main dynamical effect in zero temperature superfluids) appears to be damped at the intervortex space scale. C 2014 AIP Publishing LLC.

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Section: Navier-stokes Fluid Dynamicsmentioning

confidence: 86%

Section: Navier-stokes Fluid Dynamicsmentioning

confidence: 99%

Section: Setting Up a Finite Temperature Superfluid Turbulencementioning

confidence: 99%

Section: Navier-stokes Fluid Dynamicsmentioning

confidence: 99%

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Energy spectra of finite temperature superfluid helium-4 turbulence

Kivotides

2014

Physics of Fluids

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“…Subscripts 1 and Tab correspond to simulations using unity Lewis numbers and tabulated chemistry, respectively; a superscript of 4 corresponds to l o /l F = 4. l o is an estimate of the integral length scales based on the domain size. 26,27 Re conditions of relevance to practical engines (T u = 298-800 K). Cases A, B, and C * have different values of Ka u but the same flame density ratio.…”

Section: A Physical Configurationmentioning

confidence: 99%

Vorticity isotropy in high Karlovitz number premixed flames

Bobbitt

Blanquart

2016

Physics of Fluids

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The isotropy of the smallest turbulent scales is investigated in premixed turbulent combustion by analyzing the vorticity vector in a series of high Karlovitz number premixed flame direct numerical simulations. It is found that increasing the Karlovitz number and the ratio of the integral length scale to the flame thickness both reduce the level of anisotropy. By analyzing the vorticity transport equation, it is determined that the vortex stretching term is primarily responsible for the development of any anisotropy. The local dynamics of the vortex stretching term and vorticity resemble that of homogeneous isotropic turbulence to a greater extent at higher Karlovitz numbers. This results in small scale isotropy at sufficiently high Karlovitz numbers and supports a fundamental similarity of the behavior of the smallest turbulent scales throughout the flame and in homogeneous isotropic turbulence. At lower Karlovitz numbers, the vortex stretching term and the vorticity alignment in the strain-rate tensor eigenframe are altered by the flame. The integral length scale has minimal impact on these local dynamics but promotes the effects of the flame to be equal in all directions. The resulting isotropy in vorticity does not reflect a fundamental similarity between the smallest turbulent scales in the flame and in homogeneous isotropic turbulence. Published by AIP Publishing. [http://dx

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Effect of turbulence intensity and surface tension on the emulsification process and its stationary state—A numerical study

et al. 2022

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We study turbulent emulsions and the emulsification process in homogeneous isotropic turbulence (HIT) using direct numerical simulations (DNS) in combination with the volume of fluid method (VOF). For generating a turbulent flow field, we employ a linear forcing approach augmented by a proportional‐integral‐derivative (PID) controller, which ensures a constant turbulent kinetic energy for two phase flow scenarios and accelerates the emulsification process. For the simulations, the density ratio of dispersed and carrier phases is chosen to be similar to that of oil and water (0.9), representing a typical application. We vary the turbulence intensity and the surface tension coefficient. Thus, we modulate those parameters that directly affect the Hinze scale, which is expected to be the most stable maximum droplet diameter in emulsions in HIT. The considered configurations can be characterized with Taylor Reynolds numbers in the range of 100–140 and Weber numbers, evaluated with the velocity fluctuations and the integral length scale, of 4–70. Using the 3‐D simulation results, we study the emulsification process as well as the emulsions at a statistically stationary state. For the latter, droplet size distributions are evaluated and compared. We observe a Hinze scale similarity of the size distributions considering a fixed integral length scale, that is, similar Hinze scales obtained at different turbulence intensities or for different fluid properties result in similar distributions.

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A proposed modification to Lundgren's physical space velocity forcing method for isotropic turbulence

Abstract: As an alternative to spectral space velocity field forcing techniques commonly used in simulation studies of isotropic turbulence, Lundgren

Cited by 98 publications

References 13 publications

Energy spectra of finite temperature superfluid helium-4 turbulence

Energy spectra of finite temperature superfluid helium-4 turbulence

Vorticity isotropy in high Karlovitz number premixed flames

Effect of turbulence intensity and surface tension on the emulsification process and its stationary state—A numerical study

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