Passive scalar statistics in high-Péclet-number grid turbulence

1998 ◽  
Vol 358 ◽  
pp. 135-175 ◽  
Author(s):  
L. MYDLARSKI ◽  
Z. WARHAFT
Keyword(s):  
Reynolds Number ◽  
Velocity Field ◽  
Peclet Number ◽  
Passive Scalar ◽  
Structure Functions ◽  
Order Structure ◽  
Grid Turbulence ◽  
Temperature Derivative ◽  
Péclet Number ◽  
Transverse Temperature

The statistics of a turbulent passive scalar (temperature) and their Reynolds number dependence are studied in decaying grid turbulence for the Taylor-microscale Reynolds number, Rλ, varying from 30 to 731 (21[les ]Peλ[les ]512). A principal objective is, using a single (and simple) flow, to bridge the gap between the existing passive grid-generated low-Péclet-number laboratory experiments and those done at high Péclet number in the atmosphere and oceans. The turbulence is generated by means of an active grid and the passive temperature fluctuations are generated by a mean transverse temperature gradient, formed at the entrance to the wind tunnel plenum chamber by an array of differentially heated elements. A well-defined inertial–convective scaling range for the scalar with a slope, nθ, close to the Obukhov–Corrsin value of 5/3, is observed for all Reynolds numbers. This is in sharp contrast with the velocity field, in which a 5/3 slope is only approached at high Rλ. The Obukhov–Corrsin constant, Cθ, is estimated to be 0.45–0.55. Unlike the velocity spectrum, a bump occurs in the spectrum of the scalar at the dissipation scales, with increasing prominence as the Reynolds number is increased. A scaling range for the heat flux cospectrum was also observed, but with a slope around 2, less than the 7/3 expected from scaling theory. Transverse structure functions of temperature exist at the third and fifth orders, and, as for even-order structure functions, the width of their inertial subranges dilates with Reynolds number in a systematic way. As previously shown for shear flows, the existence of these odd-order structure functions is a violation of local isotropy for the scalar differences, as is the existence of non-zero values of the transverse temperature derivative skewness (of order unity) and hyperskewness (of order 100). The ratio of the temperature derivative standard deviation along and normal to the gradient is 1.2±0.1, and is independent of Reynolds number. The refined similarity hypothesis for the passive scalar was found to hold for all Rλ, which was not the case for the velocity field. The intermittency exponent for the scalar, μθ, was found to be 0.25±0.05 with a possible weak Rλ dependence, unlike the velocity field, where μ was a strong function of Reynolds number. New, higher-Reynolds-number results for the velocity field, which smoothly follow the trends of Mydlarski & Warhaft (1996), are also presented.

Numerical Analysis of Heat Transfer Enhancement in a Micro-Channel Due to Mechanical Stirrers

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
M. Sreejith ◽  
S. Chetan ◽  
S. N. Khaderi
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Heat Transfer Enhancement ◽  
Peclet Number ◽  
Periodic Case ◽  
Two Dimensional ◽  
Transfer Enhancement ◽  
Fluidic Channel ◽  
Enhancement Of Heat Transfer ◽  
Péclet Number

Abstract Using two-dimensional numerical simulations of the momentum, mass, and energy conservation equations, we investigate the enhancement of heat transfer in a rectangular micro-fluidic channel. The fluid inside the channel is assumed to be stationary initially and actuated by the motion imparted by mechanical stirrers, which are attached to the bottom of the channel. Based on the direction of the oscillation of the stirrers, the boundary conditions can be classified as either no-slip (when the oscillation is perpendicular to the length of the channel) or periodic (when the oscillation is along the length of the channel). The heat transfer enhancement due to the motion of the stirrers (with respect to the stationary stirrer situation) is analyzed in terms of the Reynolds number (ranging from 0.7 to 1000) and the Peclet number (ranging from 10 to 100). We find that the heat transfer first increases and then decreases with an increase in the Reynolds number for any given Peclet number. The heat transferred is maximum at a Reynolds number of 20 for the no-slip case and at a Reynolds number of 40 for the periodic case. For a given Peclet and Reynolds number, the heat flux for the periodic case is always larger than the no-slip case. We explain the reason for these trends using time-averaged flow velocity profiles induced by the oscillation of the mechanical stirrers.

Passive scalar dispersion and mixing in a turbulent jet

1995 ◽  
Vol 292 ◽  
pp. 1-38 ◽  
Author(s):  
Chenning Tong ◽  
Z. Warhaft
Keyword(s):  
Reynolds Number ◽  
Cross Correlation ◽  
Thermal Field ◽  
Temperature Fluctuations ◽  
Passive Scalar ◽  
Turbulent Jet ◽  
Grid Turbulence ◽  
Far Field ◽  
The Cross ◽  
Heated Jet

The dispersion and mixing of passive scalar (temperature) fluctuations is studied in a turbulent jet. The temperature fluctuations were produced by heated fine wire rings placed axisymmetrically in the flow. Typically the ring diameters were of the same order as the jet, Dj, and they were placed in the self-similar region. However, other initial conditions were studied, including a very small diameter ring used to approximate a point source. Using a single ring to study dispersion (which is analogous to placing a line source in a planar flow such as grid turbulence), it was found that the intense local thermal field close to the ring disperses and fills the whole jet in approximately 1.5 eddy turnover times. Thereafter the thermal field evolves in the same way as for the traditional heated jet experiments. Two heated rings were used to study the mixing of two independently introduced scalar fields. Here an inference method (invoking the principle of superposition) was used to determine the evolution of the cross-correlation coefficient, ρ, and the segregation parameter, α, as well as the coherence and co-spectrum. While initially strongly dependent on ring locations and spacing, ρ and α reached asymptotic values of 1 and 0.04, respectively, also in about 1.5 eddy turnover times. These results are contrasted with mixing and dispersion in grid turbulence where the evolution is slower. Measurements in the far field of the jet (where ρ = 1) of the square of the scalar derivative conditioned on the scalar fluctuation itself, as well as other conditional statistics, showed strong dependence on the measurement location, as well as the direction in which the derivative was determined. The cross-correlation between the square of the scalar derivative and the signal showed a clear Reynolds-number trend, decreasing as the jet Reynolds number was varied from 2800 to 18 000. The far-field measurements, using the heated rings, were corroborated by new heated jet experiments.

scholarly journals Flow Rate Prediction for a Semi-permeable Membrane at Low Reynolds Number in a Circular Pipe

2021 ◽  
Author(s):  
Suguru Miyauchi ◽  
Shuji Yamada ◽  
Shintaro Takeuchi ◽  
Asahi Tazaki ◽  
Takeo Kajishima
Keyword(s):  
Reynolds Number ◽  
Osmotic Pressure ◽  
Membrane Permeability ◽  
Flow Rate ◽  
Peclet Number ◽  
Concentration Polarization ◽  
Circular Pipe ◽  
Permeate Flux ◽  
Permeable Membrane ◽  
Péclet Number

AbstractA concise and accurate prediction method is required for membrane permeability in chemical engineering and biological fields. As a preliminary study on this topic, we propose the concentration polarization model (CPM) of the permeate flux and flow rate under dominant effects of viscosity and solute diffusion. In this model, concentration polarization is incorporated for the solution flow through a semi-permeable membrane (i.e., permeable for solvent but not for solute) in a circular pipe. The effect of the concentration polarization on the flow field in a circular pipe under a viscous-dominant condition (i.e., at a low Reynolds number) is discussed by comparing the CPM with the numerical simulation results and infinitesimal Péclet number model (IPM) for the membrane permeability, strength of the osmotic pressure, and Péclet number. The CPM and IPM are confirmed to be a reasonable extension of the model for a pure fluid, which was proposed previously. The application range of the IPM is narrow because the advection of the solute concentration is not considered, whereas the CPM demonstrates superior applicability in a wide range of parameters, including the permeability coefficient, strength of the osmotic pressure, and Péclet number. This suggests the necessity for considering concentration polarization. Although the mathematical expression of the CPM is more complex than that of the IPM, the CPM exhibits a potential to accurately predict the permeability parameters for a condition in which a large permeate flux and osmotic pressure occur.

scholarly journals Shallow water wave turbulence

2019 ◽  
Vol 874 ◽  
pp. 1169-1196 ◽  
Author(s):  
Pierre Augier ◽  
Ashwin Vishnu Mohanan ◽  
Erik Lindborg
Keyword(s):  
Reynolds Number ◽  
Structure Function ◽  
Shallow Water ◽  
Water Wave ◽  
Structure Functions ◽  
Wave Turbulence ◽  
Order Structure ◽  
Third Order ◽  
Shallow Water Wave ◽  
The Mean

The dynamics of irrotational shallow water wave turbulence forced at large scales and dissipated at small scales is investigated. First, we derive the shallow water analogue of the ‘four-fifths law’ of Kolmogorov turbulence for a third-order structure function involving velocity and displacement increments. Using this relation and assuming that the flow is dominated by shocks, we develop a simple model predicting that the shock amplitude scales as $(\unicode[STIX]{x1D716}d)^{1/3}$, where $\unicode[STIX]{x1D716}$ is the mean dissipation rate and $d$ the mean distance between the shocks, and that the $p$th-order displacement and velocity structure functions scale as $(\unicode[STIX]{x1D716}d)^{p/3}r/d$, where $r$ is the separation. Then we carry out a series of forced simulations with resolutions up to $7680^{2}$, varying the Froude number, $F_{f}=(\unicode[STIX]{x1D716}L_{f})^{1/3}/c$, where $L_{f}$ is the forcing length scale and $c$ is the wave speed. In all simulations a stationary state is reached in which there is a constant spectral energy flux and equipartition between kinetic and potential energy in the constant flux range. The third-order structure function relation is satisfied with a high degree of accuracy. Mean energy is found to scale approximately as $E\sim \sqrt{\unicode[STIX]{x1D716}L_{f}c}$, and is also dependent on resolution, indicating that shallow water wave turbulence does not fit into the paradigm of a Richardson–Kolmogorov cascade. In all simulations shocks develop, displayed as long thin bands of negative divergence in flow visualisations. The mean distance between the shocks is found to scale as $d\sim F_{f}^{1/2}L_{f}$. Structure functions of second and higher order are found to scale in good agreement with the model. We conclude that in the weak limit, $F_{f}\rightarrow 0$, shocks will become denser and weaker and finally disappear for a finite Reynolds number. On the other hand, for a given $F_{f}$, no matter how small, shocks will prevail if the Reynolds number is sufficiently large.

The effective diffusivity of ordered and freely evolving bubbly suspensions

2018 ◽  
Vol 840 ◽  
pp. 215-237 ◽  
Author(s):  
Aurore Loisy ◽  
Aurore Naso ◽  
Peter D. M. Spelt
Keyword(s):  
Numerical Simulations ◽  
Peclet Number ◽  
Random Media ◽  
Chemical Species ◽  
Effective Diffusivity ◽  
Passive Scalar ◽  
Solid Particles ◽  
Péclet Number ◽  
Mechanical Dispersion ◽  
Fixed Beds

We investigate the dispersion of a passive scalar such as the concentration of a chemical species, or temperature, in homogeneous bubbly suspensions, by determining an effective diffusivity tensor. Defining the longitudinal and transverse components of this tensor with respect to the direction of averaged bubble rise velocity in a zero mixture velocity frame of reference, we focus on the convective contribution thereof, this being expected to be dominant in commonly encountered bubbly flows. We first extend the theory of Kochet al.(J. Fluid Mech., vol. 200, 1989, pp. 173–188) (which is for dispersion in fixed beds of solid particles under Stokes flow) to account for weak inertial effects in the case of ordered suspensions. In the limits of low and of high Péclet number, including the inertial effect of the flow does not affect the scaling of the effective diffusivity with respect to the Péclet number. These results are confirmed by direct numerical simulations performed in different flow regimes, for spherical or very deformed bubbles and from vanishingly small to moderate values of the Reynolds number. Scalar transport in arrays of freely rising bubbles is considered by us subsequently, using numerical simulations. In this case, the dispersion is found to be convectively enhanced at low Péclet number, like in ordered arrays. At high Péclet number, the Taylor dispersion scaling obtained for ordered configurations is replaced by one characterizing a purely mechanical dispersion, as in random media, even if the level of disorder is very low.

On higher order passive scalar structure functions in grid turbulence

2004 ◽  
Vol 16 (11) ◽  
pp. 4012-4019 ◽  
Author(s):  
Armann Gylfason ◽  
Zellman Warhaft
Keyword(s):  
Passive Scalar ◽  
Structure Functions ◽  
Higher Order ◽  
Grid Turbulence ◽  
Scalar Structure

Investigation of internal intermittency by way of higher-order spectral moments

2021 ◽  
Vol 932 ◽  
Author(s):  
S. Lortie ◽  
L. Mydlarski
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Scalar Fields ◽  
Passive Scalar ◽  
Higher Order ◽  
Inertial Subrange ◽  
Grid Turbulence ◽  
Spectral Moments ◽  
Number Range ◽  
High Reynolds

The analysis of turbulence by way of higher-order spectral moments is uncommon, despite the relatively frequent use of such statistical analyses in other fields of physics and engineering. In this work, higher-order spectral moments are used to investigate the internal intermittency of the turbulent velocity and passive-scalar (temperature) fields. This study first introduces the theory behind higher-order spectral moments as they pertain to the field of turbulence. Then, a short-time Fourier-transform-based method is developed to estimate these higher-order spectral moments and provide a relative, scale-by-scale measure of intermittency. Experimental data are subsequently analysed and consist of measurements of homogeneous, isotropic, high-Reynolds-number, passive and active grid turbulence over the Reynolds-number range $35\leq R_{\lambda } \leq ~731$ . Emphasis is placed on third- and fourth-order spectral moments using the definitions formalised by Antoni (Mech. Syst. Signal Pr., vol. 20 (2), 2006, pp. 282–307), as such statistics are sensitive to transients and provide insight into deviations from Gaussian behaviour in grid turbulence. The higher-order spectral moments are also used to investigate the Reynolds (Péclet) number dependence of the internal intermittency of velocity and passive-scalar fields. The results demonstrate that the evolution of higher-order spectral moments with Reynolds number is strongly dependent on wavenumber. Finally, the relative levels of internal intermittency of the velocity and passive-scalar fields are compared and a higher level of internal intermittency in the inertial subrange of the scalar field is consistently observed, whereas a similar level of internal intermittency is observed for the velocity and passive-scalar fields for the high-Reynolds-number cases as the Kolmogorov length scale is approached.

scholarly journals Heat transfer from a moving fluid sphere with internal heat generation

2014 ◽  
Vol 18 (4) ◽  
pp. 1213-1222
Author(s):  
Silvia Alexandrova ◽  
Maria Karsheva ◽  
Abdellah Saboni ◽  
Christophe Gourdon
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Heat Generation ◽  
Peclet Number ◽  
Average Nusselt Number ◽  
Viscosity Ratio ◽  
Fluid Sphere ◽  
Péclet Number ◽  
Convection Equation

In this work, we solve numerically the unsteady conduction-convection equation including heat generation inside a fluid sphere. The results of a numerical study in which the Nusselt numbers from a spherical fluid volume were computed for different ranges of Reynolds number (0<Re<100), Peclet number (0<Pe<10000) and viscosity ratio (0<k<10), are presented. For a circulating drop with Re?0, steady creeping flow is assumed around and inside the sphere. In this case, the average temperatures computed from our numerical analysis are compared with those from literature and a very good agreement is found. For higher Reynolds number (0<Re<100), the Navier-Stokes equations are solved inside and outside the fluid sphere as well as the unsteady conduction-convection equation including heat generation inside the fluid sphere. It is proved that the viscosity ratio k (k = ?d/?c) influences significantly the heat transfer from the sphere. The average Nusselt number decreases with increasing k for a fixed Peclet number and a given Reynolds number. It is also observed that the average Nusselt number is increasing as Peclet number increases for a fixed Re and a fixed k.

Viscous Marangoni migration of a drop in a Poiseuille flow at low surface Péclet numbers

2014 ◽  
Vol 753 ◽  
pp. 535-552 ◽  
Author(s):  
On Shun Pak ◽  
Jie Feng ◽  
Howard A. Stone
Keyword(s):  
Reynolds Number ◽  
Poiseuille Flow ◽  
Peclet Number ◽  
Slip Velocity ◽  
Reciprocal Theorem ◽  
Background Flow ◽  
Spherical Drop ◽  
Péclet Number ◽  
Insoluble Surfactant ◽  
Analytical Formulas

AbstractThe motion of a spherical drop with a bulk-insoluble surfactant immersed in a background flow in the limits of low surface Péclet number and low Reynolds number is investigated. We develop a reciprocal theorem that applies to any prescribed background flow and provide a specific example of an unbounded Poiseuille flow. Analytical formulas for the migration velocity of the drop are obtained perturbatively in powers of the surface Péclet number. We show that the redistribution of surfactant due to the background flow acts to retard the motion of the drop, with the magnitude of this slip velocity being independent of the drop’s position in the Poiseuille flow. Moreover, a surfactant-induced cross-streamline migration of the drop occurs towards the centre of the Poiseuille flow, with its magnitude depending linearly on the distance of the drop from the centre of the Poiseuille flow.

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