Use of turbulent kinetic energy in free mixing studies

Harsha, P. T.; Lee, S. C.

doi:10.2514/3.5826

Cited by 45 publications

(25 citation statements)

References 5 publications

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“…~ 0.242 and c ~ 1.445 come from the locally homogeneous shear problemf, and these represent the ratio of the time scale of return to isotropy to that of dissipation and the ratio of the rate of strain time scale to that of return to isotropy, respectively; they are taken as constants throughout the shape assump tion. The ratio of the Reynolds shear stress to the kinetic energy is 2(1 -3c ~ 0.35, which is amazingly close to that obtained from observations on shear flows (Brad shaw, Ferriss & Atwell 1967;Lee & Harsha 1970). One of the important conse quences of this simple form of the shape assumption (2.5) is that the vertical distribution is an equilibrium one; that is, as much energy is extracted from the mean flow as is dissipated through viscosity.…”

Section: (I) the Mean Flowsupporting

confidence: 85%

On the interactions between large-scale structure and fine-grained turbulence in a free shear flow I. The development of temporal interactions in the mean

Alper

Liu

1976

Proc. R. Soc. Lond. A

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In this problem a mean turbulent shear layer originally exists, homogeneous in the streamwise direction, formed perhaps by previous instabilities, but in equilibrium with the fine-grained turbulence. At a given time, a large eddy of a fixed horizontal wavenumber is initiated. We study the subsequent time development of the non-equilibrium interactions between the three components of flow as they adjust towards ultimate simultaneous equilibrium, using the integrated energy-balance conservation equations to derive the amplitude equations. This necessarily involves the usual averaging procedure and a conditional or phase-averaging procedure by which the large structure motion is educed from the total fluctuations. In general, the mean flow growth is due to the energy transfer to both fluctuating components, the large eddy gains energy from the mean motion and exchanges energy with the fine-grained turbulence, while the fine-grained turbulence gains energy from the mean flow and exchanges with the large eddy and converts its energy to heat through viscous dissipation of the smallest scales. The closure problem is obtained via the shape assumptions which enter into the interaction integrals. The situation in which the fine-grained turbulent kinetic energy production and viscous dissipation are in local balance is considered, the displacement from equilibrium being due only to the energy transfer from the large eddy. The large eddy shape is taken to be two-dimensional, instability-wavelike, with its vorticity axis perpendicular to the direction of the mean outer stream. Prior to averaging, detailed but approximate calculations of the wave-induced turbulent Reynolds stresses are obtained; the product of these stresses with the appropriate large-eddy rates of strain give the energy transfer mechanism between the two disparate scales of fluctuations. Coupled, nonlinear amplitude or energy density equations for the three components of motion are obtained, the coefficients of which are the interaction integrals guided by the shape assumptions. It is found that for the special case of parallel flow, the energy of the large eddy first undergoes a hydrodynamic-instability type of amplification but eventually decays due to the energy transfer to the fine-grained turbulence, while the turbulent kinetic energy is displaced from an original level of equilibrium to a new one because of the ability of the large eddy to negotiate an indirect energy transfer from the mean flow. For the growing shear layer, approximate considerations show that if the mechanism of energy transfer from the large to the small scale is eventually weakened by the shear layer growth compared to the large-eddy production mechanism so that the amplification and decay process repeats, ‘bursts’ of the remnant of the same large eddy will occur repeatedly until an ultimate equilibrium is reached among the three interacting components of motion. However, for the large eddy whose wavenumber corresponds to that of the initially most amplified case, the ‘bursting’ phenomenon is much less pronounced and equilibrium is very nearly reached at the end of the very first ‘burst’.

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Section: (I) the Mean Flowsupporting

confidence: 85%

On the interactions between large-scale structure and fine-grained turbulence in a free shear flow I. The development of temporal interactions in the mean

Alper

Liu

1976

Proc. R. Soc. Lond. A

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“…In the studies mentioned above, a 1 took on a value of 0.3 if τ/ρ calculated using measured (q 2 /2) in Equation ( 1) was required to give the best correlation with measurements. This value of a 1 has been tested by Bradshaw et al [9,10], Lee and Harsha [5], Harsha and Lee [6] and Harsha [7]. Consistently good agreement was obtained for a wide range of isothermal free turbulent shear flows that include two-dimensional (2-D) as well as axisymmetric wakes and jets, coaxial jets and jets in moving streams.…”

Section: Introductionmentioning

confidence: 62%

“…At this point, it should be pointed out that the analytically derived equations are valid for all Re, while Equation (1) and a 1 might only be valid for the Re range of the atmospheric data used to deduced Equation (1). Even then, the approach has been adopted by Laster [4], Lee and Harsha [5], Harsha and Lee [6][7][8] in their simulations of free mixing layers and free shear flows. In addition, Harsha and Lee [7,8] determined a 1 by correlating measurements of τ/ρ with (q 2 /2) for a variety of free turbulent mixing flows.…”

Section: Introductionmentioning

confidence: 99%

An Analytically Derived Shear Stress and Kinetic Energy Equation for One-Equation Modelling of Complex Turbulent Flows

2021

Symmetry

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The Reynolds stress equations for two-dimensional and axisymmetric turbulent shear flows are simplified by invoking local equilibrium and boundary layer approximations in the near-wall region. These equations are made determinate by appropriately modelling the pressure–velocity correlation and dissipation rate terms and solved analytically to give a relation between the turbulent shear stress τρ and the kinetic energy of turbulence (k =q22). This is derived without external body force present. The result is identical to that proposed by Nevzgljadov in A Phenomenological Theory of Turbulence, who formulated it through phenomenological arguments based on atmospheric boundary layer measurements. The analytical approach is extended to treat turbulent flows with external body forces. A general relation τρ = a11 - AFRiFq22 is obtained for these flows, where FRiF is a function of the gradient Richardson number RiF, and a1 is found to depend on turbulence models and their assumed constants. One set of constants yields a1= 0.378, while another gives a1= 0.328. With no body force, F ≡ 1 and the relation reduces to the Nevzgljadov equation with a1 determined to be either 0.378 or 0.328, depending on model constants set assumed. The present study suggests that 0.328 is in line with Nevzgljadov's proposal. Thus, the present approach provides a theoretical base to evaluate the turbulent shear stress for flows with external body forces. The result is used to reduce the k–e model to a one-equation model that solves the k-equation, the shear stress and kinetic energy equation, and an e evaluated by assuming isotropic eddy viscosity behavior.

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“…As reported in the literature [31] , [32] , [33] , the Turbulence Kinetic Energy (

is utilized to describe the flow mixing level. Since this study aims to assess the level of COVID 19 spread which is highly dependent on the level of the flow mixing, the Turbulence Kinetic Energy (

has been adopted as a determinate parameter for this paper.…”

Section: Methodsmentioning

confidence: 99%

“…Since this study aims to assess the level of COVID 19 spread which is highly dependent on the level of the flow mixing, the Turbulence Kinetic Energy (

has been adopted as a determinate parameter for this paper. The Turbulence Kinetic Energy (

is plotted in ANSYS CFX using Equations (1-4) [31] , [32] , [33] .

…”

Section: Methodsmentioning

confidence: 99%

Airflow dynamics in an emergency department: A CFD simulation study to analyse COVID-19 dispersion

Alrebi

Obeidat

Abdallah

et al. 2022

Alexandria Engineering Journal

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Emergency departments (EDs) in hospitals are hotspots for highly transmissible infectious diseases and pose the most significant risk of viral infection spreading. With the recent COVID-19 outbreak, it became clear that emergency department design must evolve in order to be adequately prepared to handle the epidemic. The purpose of this research is to examine the design of the emergency department at a University Hospital using a computational fluid dynamics (CFD) simulation based on the ANSYS CFX package. Turbulence Kinetic Energy and Velocity profiles were analyzed to determine which areas of the ED were most susceptible to virus spread. The analysis revealed that three critical areas of the emergency department, namely overnight patient beds, operating rooms, and resuscitation rooms, had significantly higher air velocity, dispersion, and mixing levels than the rest of the department's spaces. According to the scenario examined, the possibility of air transmission from these locations to neighboring areas becomes apparent, increasing the likelihood of transmitting the virus from these locations and infecting people in the adjacent areas, including patients or health care providers. Using the results of these simulations, a solution in the form of instructions for the arrangement of inlets and outlets, the separation of spaces, and the interior design of the spaces and hallways can be presented to the hospital administration. All of which can be implemented in the current design of the emergency department.

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Use of turbulent kinetic energy in free mixing studies

Cited by 45 publications

References 5 publications

On the interactions between large-scale structure and fine-grained turbulence in a free shear flow I. The development of temporal interactions in the mean

On the interactions between large-scale structure and fine-grained turbulence in a free shear flow I. The development of temporal interactions in the mean

An Analytically Derived Shear Stress and Kinetic Energy Equation for One-Equation Modelling of Complex Turbulent Flows

Airflow dynamics in an emergency department: A CFD simulation study to analyse COVID-19 dispersion

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