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

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.

Author(s):  
T. Houra ◽  
Y. Nagano ◽  
M. Tagawa

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.


1994 ◽  
Vol 266 ◽  
pp. 175-207 ◽  
Author(s):  
Howard S. Littell ◽  
John K. Eaton

Measurements of the boundary layer on an effectively infinite rotating disk in a quiescent environment are described for Reynolds numbers up to Reδ2 = 6000. The mean flow properties were found to resemble a ‘typical’ three-dimensional crossflow, while some aspects of the turbulence measurements were significantly different from two-dimensional boundary layers that are turned. Notably, the ratio of the shear stress vector magnitude to the turbulent kinetic energy was found to be at a maximum near the wall, instead of being locally depressed as in a turned two-dimensional boundary layer. Also, the shear stress and the mean strain rate vectors were found to be more closely aligned than would be expected in a flow with this degree of crossflow. Two-point velocity correlation measurements exhibited strong asymmetries which are impossible in a two-dimensional boundary layer. Using conditional sampling, the velocity field surrounding strong Reynolds stress events was partially mapped. These data were studied in the light of the structural model of Robinson (1991), and a hypothesis describing the effect of cross-stream shear on Reynolds stress events is developed.


2001 ◽  
Vol 426 ◽  
pp. 297-326 ◽  
Author(s):  
MAGNE LYGREN ◽  
HELGE I. ANDERSSON

Turbulent flow between a rotating and a stationary disk is studied. Besides its fundamental importance as a three-dimensional prototype flow, such flow fields are frequently encountered in rotor–stator configurations in turbomachinery applications. A direct numerical simulation is therefore performed by integrating the time-dependent Navier–Stokes equations until a statistically steady state is reached and with the aim of providing both long-time statistics and an exposition of coherent structures obtained by conditional sampling. The simulated flow has local Reynolds number r2ω/v = 4 × 105 and local gap ratio s/r = 0.02, where ω is the angular velocity of the rotating disk, r the radial distance from the axis of rotation, v the kinematic viscosity of the fluid, and s the gap width.The three components of the mean velocity vector and the six independent Reynolds stresses are compared with experimental measurements in a rotor–stator flow configuration. In the numerically generated flow field, the structural parameter a1 (i.e. the ratio of the magnitude of the shear stress vector to twice the mean turbulent kinetic energy) is lower near the two disks than in two-dimensional boundary layers. This characteristic feature is typical for three-dimensional boundary layers, and so are the misalignment between the shear stress vector and the mean velocity gradient vector, although the degree of misalignment turns out to be smaller in the present flow than in unsteady three-dimensional boundary layer flow. It is also observed that the wall friction at the rotating disk is substantially higher than at the stationary disk.Coherent structures near the disks are identified by means of the λ2 vortex criterion in order to provide sufficient information to resolve a controversy regarding the roles played by sweeps and ejections in shear stress production. An ensemble average of the detected structures reveals that the coherent structures in the rotor–stator flow are similar to the ones found in two-dimensional flows. It is shown, however, that the three-dimensionality of the mean flow reduces the inter-vortical alignment and the tendency of structures of opposite sense of rotation to overlap. The coherent structures near the disks generate weaker sweeps (i.e. quadrant 4 events) than structures in conventional two-dimensional boundary layers. This reduction in the quadrant 4 contribution from the coherent structures is believed to explain the reduced efficiency of the mean flow in producing Reynolds shear stress.


1990 ◽  
Vol 43 (5S) ◽  
pp. S232-S239 ◽  
Author(s):  
J. D. A. Walker

Recent experimental and theoretical results related to the turbulence production process near a wall are reviewed. It is argued that the principal element of boundary-layer turbulence is the convected hairpin vortex and that bursting of the wall-layer flow is a viscous-inviscid interaction provoked by the adverse pressure gradient due to the vortex. The consequences of this picture for the development of models for the mean near-wall flow are discussed. Recent models for the mean wall-layer velocity profile, in both two- and three-dimensional boundary layers, which are based on the dynamical picture presented here, are reviewed.


1991 ◽  
Vol 113 (2) ◽  
pp. 355-362 ◽  
Author(s):  
S. D. Abrahamson ◽  
J. K. Eaton

An experimental investigation of heat transfer through a three-dimensional boundary layer has been performed. An initially two-dimensional boundary layer was made three dimensional by a transverse pressure gradient caused by a wedge obstruction, which turned the boundary layer within the plane of the main flow. Two cases, with similar streamwise pressure gradients and different lateral gradients, were studied so that the effect of the lateral gradient on heat transfer could be deduced. The velocity flowfield agreed with previous hydrodynamic investigations of this flow. The outer parts of the mean velocity profiles were shown to agree with the Squire-Winter theorem for rapidly turned flows. Heat transfer data were collected using a constant heat flux surface with embedded thermocouples for measuring surface temperatures. Mean fluid temperatures were obtained using a thermocouple probe. The temperature profiles, when plotted in outer scalings, showed logarithmic behavior consistent with two-dimensional flows. An integral analysis of the boundary layer equations was used to obtain a vector formulation for the enthalpy thickness, HH≜∫0∞ρuisdyρ∞ii,o(u∞2+w∞2)1/2,0,∫0∞ρwisdyρ∞is,o(u∞2+w∞2)1/2 (where is is the stagnation enthalpy), which is consistent with the scalar formulation used for two-dimensional flows. Using the vector formulation, the heat transfer data agreed with standard two-dimensional correlations of the Stanton number and enthalpy thickness Reynolds number. It was concluded that although the heat transfer coefficient decreased faster than its two-dimensional counterpart, it was similar to the two-dimensional case. The vector form of the enthalpy thickness captured the rotation of the mean thermal energy flux away from the free-stream direction. Boundary layer three dimensionality increased with the strength of the transverse pressure gradient and the heat transfer coefficients were smaller for the stronger transverse gradient.


1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar

“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.


2020 ◽  
Vol 98 (2) ◽  
pp. 100-109
Author(s):  
Minzilya T. Kosmakova ◽  
◽  
Valery G. Romanovski ◽  
Dana M. Akhmanova ◽  
Zhanar M. Tuleutaeva ◽  
...  

1996 ◽  
Vol 118 (2) ◽  
pp. 347-352 ◽  
Author(s):  
R. G. Dominy ◽  
D. A. Kirkham

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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