Turbulent Thermal Diffusion Over a Locally-Heated Two-Dimensional Hill

2010 ◽  
Author(s):  
T. Houra ◽  
Y. Nagano ◽  
M. Tagawa
Keyword(s):  
Thermal Diffusion ◽  
Passive Scalar ◽  
Heated Wall ◽  
Windward Side ◽  
Two Dimensional ◽  
Hill Model ◽  
Mean Temperature ◽  
The Mean ◽  
The Hill ◽  
Heated Case

We measure flow and thermal fields over a locally heated two-dimensional hill. The heated sections on the wall are divided into upstream and downstream portions of the hill model. These sections are heated independently, yielding various thermal boundary conditions in contrast to the uniformly heated case. In the separated region formed behind the hill, it is found that the mean temperature profiles in the uniformly heated case are well decomposed into the separately heated cases. This is because the velocity fluctuation produced by the shear layer formed behind the hill is large, so the superposition of a passive scalar in the thermal field can be successfully realized. The rapid increase in the mean temperature near the uniformly heated wall should be due to the heat transfer near the leeward slope of the hill. On the other hand, the mean temperature distributions away from the wall are strongly affected by the turbulent thermal diffusion on the windward side of the hill.

scholarly journals Diffusion of a Passive Scalar in a Two-dimensional Channel Flow

1973 ◽  
Vol 26 (3) ◽  
pp. 327 ◽  
Author(s):  
MJ Manton
Keyword(s):  
Channel Flow ◽  
Asymptotic Representation ◽  
Open Channel ◽  
Passive Scalar ◽  
Channel Flows ◽  
Two Dimensional ◽  
Open Channel Flows ◽  
The Mean

The asymptotic representation of the distribution of a passive scalar within a two-dimensional channel flow is derived. The distribution is shown to be Gaussian with a skewness and longitudinal variance determined primarily by the mean shear. The distributions corresponding to both laminar and turbulent open channel flows are discussed.

scholarly journals Transport and instability in driven two-dimensional magnetohydrodynamic flows

2016 ◽  
Vol 799 ◽  
pp. 541-578 ◽  
Author(s):  
Sam Durston ◽  
Andrew D. Gilbert
Keyword(s):  
Magnetic Field ◽  
Time Scale ◽  
Large Scale ◽  
Body Force ◽  
Passive Scalar ◽  
Fast Time ◽  
Two Dimensional ◽  
Mean Flow ◽  
The Mean ◽  
Background Shear

This paper concerns the generation of large-scale flows in forced two-dimensional systems. A Kolmogorov flow with a sinusoidal profile in one direction (driven by a body force) is known to become unstable to a large-scale flow in the perpendicular direction at a critical Reynolds number. This can occur in the presence of a ${\it\beta}$-effect and has important implications for flows observed in geophysical and astrophysical systems. It has recently been termed ‘zonostrophic instability’ and studied in a variety of settings, both numerically and analytically. The goal of the present paper is to determine the effect of magnetic field on such instabilities using the quasi-linear approximation, in which the full fluid system is decoupled into a mean flow and waves of one scale. The waves are driven externally by a given random body force and move on a fast time scale, while their stress on the mean flow causes this to evolve on a slow time scale. Spatial scale separation between waves and mean flow is also assumed, to allow analytical progress. The paper first discusses purely hydrodynamic transport of vorticity including zonostrophic instability, the effect of uniform background shear and calculation of equilibrium profiles in which the effective viscosity varies spatially, through the mean flow. After brief consideration of passive scalar transport or equivalently kinematic magnetic field evolution, the paper then proceeds to study the full magnetohydrodynamic system and to determine effective diffusivities and other transport coefficients using a mixture of analytical and numerical methods. This leads to results on the effect of magnetic field, background shear and ${\it\beta}$-effect on zonostrophic instability and magnetically driven instabilities.

Thermal Diffusion in Mixtures of Alcohols and Aromatic Hydrocarbons

1971 ◽  
Vol 26 (1) ◽  
pp. 48-51 ◽  
Author(s):  
P. S. Belton ◽  
H. J. V. Tyrrell
Keyword(s):  
Temperature Gradient ◽  
Thermal Diffusion ◽  
Aromatic Hydrocarbons ◽  
Thermal Gradient ◽  
Average Degree ◽  
Quantitative Interpretation ◽  
Mean Temperature ◽  
The Mean ◽  
Degree Of Association

Abstract The thermal diffusion factors observed for these systems vary considerably with concentration, and frequently show a change in sign at some concentration. New data on ethanol-toluene mixtures show that the sign and magnitude of the separation of the components in a thermal gradient are also strongly dependent on the mean temperature of the system. These observations, together with earlier ones on similar systems, can be given a semi-quantitative interpretation in terms of a shift in the average degree of association of the alcohol along the temperature gradient.

Experimental Study of Turbulent Transport in Non-Isothermal Oscillating Grids Turbulence Using Particle Image Velocimetry

2003 ◽  
Author(s):  
Alexander Eidelman ◽  
Tov Elperin ◽  
Nathan Kleeorin ◽  
Alexander Krein ◽  
Igor Rogachevskii ◽  
...  
Keyword(s):  
Particle Image Velocimetry ◽  
Spatial Distribution ◽  
Temperature Gradient ◽  
Thermal Diffusion ◽  
Particle Image ◽  
Turbulent Transport ◽  
Mean Temperature ◽  
Image Velocimetry ◽  
Oscillating Grids ◽  
The Mean

An oscillating grids turbulence generator was constructed for studies of a new effect associated with turbulent transport of inertial particles — turbulent thermal diffusion. This phenomenon was predicted theoretically in Phys. Rev. Lett. 76, 224 (1996) and has been detected experimentally in oscillating grids turbulence with an imposed mean temperature gradient in air flow. This effect implies an additional mean flux of particles in the direction opposite to the mean temperature gradient and results in formation of large-scale inhomogeneities in the spatial distribution of particles. We used Particle Image Velocimetry to determine the turbulent velocity field and an Image Processing Technique to determine the spatial distribution of particles. Velocity distributions were measured in the flow generated with one and two grids in the Oscillating Grids Turbulence Generators at RWTH (Aachen) and BGU (Beer-Sheva). Analysis of the intensity of laser light Mie scattering by particles showed that they are accumulated in the vicinity of the minimum of the mean temperature of the surrounding fluid. The latter finding confirms the existence of the effect of turbulent thermal diffusion predicted theoretically.

Passive Scalar Turbulent Channel Flow at Pr=25: DNS-LES Approach

2007 ◽  
Author(s):  
Iztok Tiselj ◽  
Luka Sˇtrubelj
Keyword(s):  
Heat Transfer ◽  
Velocity Field ◽  
Buffer Layer ◽  
Channel Flow ◽  
Turbulent Channel Flow ◽  
Passive Scalar ◽  
Temperature Profiles ◽  
Temperature Scales ◽  
Mean Temperature ◽  
The Mean

DNS-LES numerical simulations of a passive scalar field in the turbulent channel flow were performed at friction Reynolds number Re_Tau = 180 and Prandtl number Pr = 25. Direct numerical simulation is used for description of the velocity field. Temperature field is described with LES-like approach with the smallest resolved temperature scales equal to the smallest scales of the velocity field. The consistency of the applied physical modelling and pseudo-spectral scheme is tested with the grid refinement study (grid refine ∼3 times in each direction) and with comparison of the results with the existing DNS simulations of Schwertfirm and Manhart (2006) at the same conditions. The comparison shows that the proposed approach produces very accurate mean temperature profiles, heat transfer coefficients and other low-order moments of the turbulent thermal field. It is shown that the mean temperature profiles near the wall can be accurately predicted even when the temperature scales between the Batchelor and Kolmogorov scale are not resolved. The key to the success of the proposed approach lies in the fact that the large-scale structures govern the turbulent heat transfer at high Prandtl numbers, while the role of the sub-Kolmogorov temperature scales in the diffusive sublayer and the thermal buffer layer (y+<5) is practically negligible. The contribution of the sub-Kolmogorov thermal scales becomes relevant above the thermal buffer layer (y+>5), where the unresolved temperature scales affect spectra and RMS temperature fluctuations, but not the log-law shape of the mean temperature profile and the mean heat transfer coefficient.

The Thermal Boundary Layer Far Downstream of a Spanwise Line Source of Heat

1980 ◽  
Vol 102 (4) ◽  
pp. 755-760 ◽  
Author(s):  
J. Andreopoulos ◽  
P. Bradshaw
Keyword(s):  
Temperature Fluctuation ◽  
Outer Part ◽  
Heated Wall ◽  
Two Dimensional ◽  
Turbulent Prandtl Number ◽  
Dimensional Boundary ◽  
Wall Flow ◽  
The Mean ◽  
Thermal Layer ◽  
Point Source Of Heat

Measurements are presented of velocity and temperature fluctuation statistics in two-dimensional boundary layers over nominally adiabatic, smooth, and rough surfaces far downstream of spanwise line sources of heat. All quantities are found to scale satisfactorily on uτ, δ and ΔTmax. The generation term in the transport equation for the mean-square temperature fluctuation reaches a maximum at a distance of about 0.7δ above the surface and the turbulent Prandtl number is about 1.0 in the outer layer falling to zero near the surface. The outer part of the thermal layer behaves like a uniformly heated wall flow and the results are relevant to the central region of the plume from a point source of heat or pollutants, which will be approximately two-dimensional at large distances from the source.

scholarly journals Simplified Shape Factors for a Thermal Diffusion Column

1965 ◽  
Vol 20 (4) ◽  
pp. 521-526 ◽  
Author(s):  
C. J. G. Slieker
Keyword(s):  
Thermal Diffusion ◽  
Transport Coefficients ◽  
Experimental Results ◽  
Separation Processes ◽  
Shape Factors ◽  
Mean Temperature ◽  
Diffusion Column ◽  
The Mean

Starting from COHEN’S theory of square cascades and countercurrent separation processes, column constants for the three types of thermal diffusion columns are calculated. It is assumed that the transport coefficients may be regarded as constants, whereas their values are taken at the mean temperature in the column. By comparison with other theories and experimental results our simplified theory appears to be as good as the more refined ones.

Lateral dispersion from a concentrated line source in turbulent channel flow

2011 ◽  
Vol 678 ◽  
pp. 417-450 ◽  
Author(s):  
J. LEPORE ◽  
L. MYDLARSKI
Keyword(s):  
Channel Flow ◽  
Line Source ◽  
Temperature Fluctuation ◽  
Turbulent Channel Flow ◽  
Passive Scalar ◽  
Thermal Plume ◽  
Transverse Dispersion ◽  
Mean Temperature ◽  
Temperature Excess ◽  
The Mean

The dispersion of a passive scalar (temperature) from a concentrated line source in fully developed, high-aspect-ratio turbulent channel flow is studied herein. The line source is oriented in the direction of the inhomogeneity of the velocity field, resulting in a thermal plume that is statistically three-dimensional. This configuration is selected to investigate the lateral dispersion of a passive scalar in an inhomogeneous turbulent flow (i.e. dispersion in planes parallel to the channel walls). Measurements are recorded at six wall-normal distances (y/h = 0.10, 0.17, 0.33, 0.50, 0.67 and 1.0), six downstream positions (x/h = 4.0, 7.4, 10.8, 15.2, 18.6 and 22.0) and a Reynolds number of Re ≡ 〈U〉y = hh/v = 10200 (Reτ ≡ u∗h/v = 502). The lateral mean temperature excess profiles were found to be well represented by Gaussian distributions. The root-mean-square (r.m.s.) profiles, on the other hand, were symmetric, but non-Gaussian. Consistent with homogeneous flows (and in contrast to the work of Lavertu & Mydlarski (J. Fluid Mech., vol. 528, 2005, p. 135) studying transverse dispersion in the same flow), (i) the downstream growth rate of the centreline mean temperature excess, centreline r.m.s. temperature fluctuation and half-width of the mean and r.m.s. temperature profiles followed a power law evolution in the downstream direction, and (ii) the r.m.s. profiles evolved from single-peaked to double-peaked profiles far downstream. By comparing the measured ratios of the centreline r.m.s. temperature fluctuation to the mean temperature excess to the ratios measured in other flows, it was hypothesized that the mean-flow shear, as well as the turbulence intensity, played an important, cooperative role in increasing the mixedness of the flow. The probability density functions (PDFs) were quasi-Gaussian near the wall as well as for large-enough downstream distances. Closer to both the source and the channel centreline, the PDFs were better approximated by exponential distributions, with a sharp peak corresponding to the free-stream temperature. For intermediate downstream distances, the PDFs of the lateral dispersion were better mixed than analogous PDFs of the transverse dispersion, consistent with the mixedness measurements.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

The Influence of Blade Wakes on the Performance of Interturbine Diffusers

1996 ◽  
Vol 118 (2) ◽  
pp. 347-352 ◽  
Author(s):  
R. G. Dominy ◽  
D. A. Kirkham
Keyword(s):  
Performance Modeling ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Two Dimensional ◽  
Correct Performance ◽  
Analysis Methods ◽  
Flow Factor ◽  
The Mean ◽  
Lp Turbine

Interturbine diffusers provide continuity between HP and LP turbines while diffusing the flow upstream of the LP turbine. Increasing the mean turbine diameter offers the potential advantage of reducing the flow factor in the following stages, leading to increased efficiency. The flows associated with these interturbine diffusers differ from those in simple annular diffusers both as a consequence of their high-curvature S-shaped geometry and of the presence of wakes created by the upstream turbine. It is shown that even the simplest two-dimensional wakes result in significantly modified flows through such ducts. These introduce strong secondary flows demonstrating that fully three-dimensional, viscous analysis methods are essential for correct performance modeling.

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