Multidimensional turbulence spectra – identifying properties of turbulent structures

et al. 2014

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In coalescence and break-up modeling, vortex number density and size distributions of turbulent vortices are required to calculate the rate of interaction between continuous and dispersed phases. Existing number density models are only valid for the inertial subrange of the energy spectrum and no model of the vortex number density, valid for the entire energy spectrum, is available. The number density of the turbulent vortices were studied and modeled for the entire energy spectrum including the dissipative, inertial, and energy containing subranges. It was observed that the new number density model depends on vortex size, local turbulent kinetic energy, and dissipation rate. Moreover, the new number density model was validated by the number density distributions quantified in a turbulent pipe flow. The turbulent vortices of the pipe were identified and labeled using a vortex-tracking algorithm that was developed recently by the authors.

Section: -D Vortex-tracking Algorithmmentioning

confidence: 99%

Number density of turbulent vortices in the entire energy spectrum

Ghasempour

et al. 2014

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“…Q ‐criterion which is a balance between rotation and strain rates is large in the near wall region and does not show structures in the bulk. To identify the turbulent structures in the bulk of the flow, the Q ‐criterion should be normalized by rotation squared and we use the definition

Q_{n} = (Ω^{2} - S^{2}) / Ω^{2}

.…”

Section: Vortex‐tracking Algorithm Using Morphological Methodsmentioning

confidence: 99%

“…As the vorticity in the wall region is higher than in the bulk, the normalized Q ‐criterion ( Q n ) which also captures vortices in the bulk and allows a constant cut‐off criterion for all regions has been used. Still a high value of Q n will not capture all vortices and a low value may identify several close vortices as one vortex . In our algorithm, we want to capture as many vortices as possible and has chosen a low value of Q n = 0.1.…”

Section: Vortex‐tracking Algorithm Using Morphological Methodsmentioning

confidence: 99%

“…Recently, the analysis of the turbulent energy outside the iso surface of the Q ‐criterion revealed that less than 40% of the TKE is within the structures identified using the Q ‐criterion, and the amount of energy captured is even lower for structures identified using the normalized Q ‐criterion . In fact a large fraction of TKE is located outside of the identified structures.…”

Section: Data Postprocessingmentioning

confidence: 99%

See 1 more Smart Citation

Identification and characterization of three‐dimensional turbulent flow structures

Ghasempour

2015

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Many phenomena in chemical processes for example fast mixing, coalescence and break-up of bubbles and drops are not correctly described using average turbulence properties as the outcome is governed by the interaction with individual vortices. In this study, an efficient vortex-tracking algorithm has been developed to identify thousands of vortices and quantify properties of the individual vortices. The traditional algorithms identifying vortex-cores only capture a fraction of the total turbulent kinetic energy, which is often not sufficient for modeling of coalescence and break-up phenomena. In the present algorithm, turbulent vortex-cores are identified using normalized Q-criterion, and allowed to grow using morphological methods. The growth is constrained by estimating the influence from all neighboring vortices using the Biot-Sawart law. This new algorithm allows 82% of the total turbulent kinetic to be captured, at the same time the individual vortices can be tracked in time.

“…Recent advances in turbulence theory, improve the simplifying assumption that binds breakup only to the inertial subrange. Limited efforts have been made to extend the energy spectrum to cover dissipation, inertial and energy‐containing subranges . Solsvik and Jakobsen have analytically solved the second‐order structure function of Davidson and added a semiempirical model, as suggested by Sawford and Hunt, to formulate a model for the number density of vortices for the entire spectrum.…”

Section: Model Descriptionsmentioning

confidence: 99%

Dual mechanism model for fluid particle breakup in the entire turbulent spectrum

Karimi

2019

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This work provides an in-depth understanding of different breakup mechanisms for fluid particles in turbulent flows. All the disruptive and cohesive stresses are considered for the entire turbulent energy spectrum and their contributions to the breakup are evaluated. A new modeling framework is presented that bridges across turbulent subranges. The model entails different mechanisms for breakup by abandoning the classical limitation of inertial models. The predictions are validated with experiments encompassing both breakup regimes for droplets stabilized by internal viscosity and interfacial tension down to the micrometer length scale, which covers both the inertial and dissipation subranges. The model performance ensures the reliability of the framework, which involves different mechanisms. It retains the breakup rate for inertial models, improves the predictions for the transition region from inertia to dissipation, and bridges seamlessly to Kolmogorov-sized droplets. K E Y W O R D S mathematical modeling, multiphase flow, process, simulation, turbulence 1 | INTRODUCTION The size distribution of fluid particles within a continuous medium is of vital importance for different industrial applications. In multiphase processes, knowledge of size distribution determines the rate of momentum, heat and mass transport. The mathematical framework commonly used to tackle this problem is population balance modeling, which requires closure terms for the breakup and coalescence of the dispersed fluid particles. 1,2 The present work concentrates on the breakup mechanisms of fluid particles in turbulent flows.The pioneering models for breakup were formulated by Rayleigh in the nineteenth century for jet flows, and considered dynamic stresses and surface tension. 3 Taylor, 4,5 on the other hand, has shown the relevance of viscous stresses for droplet distortions when the droplets are very small or when the continuous phase is highly viscous. Balancing the deforming and stabilizing stresses, Hinze has proposed a formulation for the maximum stable droplet diameter (d max ) for dispersion in turbulent flows. 6 The above advancements have paved the way for further developments in the field. Typically, the ratio between counteracting stresses acting on fluid particles represents a dimensionless number that indicates the probable breakup mechanism. For instance, when inertia is the principal cause of breakup, a critical Weber number is quantified, and the break up takes place above this number; examples can be found in Reference 7-9 . The other scenario is the definition of a critical Capillary number (i.e., the ratio of viscous stress over surface stresses) for viscous laminar flows. [10][11][12] Although the dimensionless numbers are a relevant means for interpreting the breakup process, relying on dimensionless numbers to explain the complicated physical phenomenon that occurs during the breakup in turbulent multiphase systems is too simplistic. 13,14 Thus, later breakup models are inclined toward the dynamics of bubble or drople...