A local nonlinear solution as an approximation to low-frequency spanwise jitter in thermoconvective flows

2002 ◽  
Vol 469 ◽  
pp. 343-367
Author(s):  
P. GRASSIA ◽  
D. RICHARDSON
Keyword(s):  
Boundary Layer ◽  
Rayleigh Number ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Low Frequency ◽  
Temperature Fields ◽  
Microgravity Environment ◽  
Anomalous Scaling ◽  
Dimensional Complexity ◽  
Large Rayleigh Number

A shallow fluid-filled cavity with a longitudinal applied temperature gradient is subjected to spanwise accelerations (g-jitter) representing the space-based microgravity environment. A simplified slot model is introduced to describe the buoyancy-driven flow and advected temperature fields produced in the cavity. Numerical solutions indicate that boundary layer behaviour can manifest itself in the limit of strong g-jitter (large Rayleigh number Ra). However, boundary layer thicknesses do not obey the conventional Ra−1/4 scaling that typically arises in free thermal convection problems. This anomalous scaling results from the three-dimensional complexity of the flow and advected temperature fields, which are not themselves produced by a single fixed applied temperature change. Three different regimes are identified at large Rayleigh number characterized by the shapes of the advected temperature profiles. These regimes are selected according to the values of the Biot number Bi and an aspect ratio parameter. Simple models are presented of the boundary layer behaviour which reproduce, in each regime, the numerically predicted scalings for boundary layer thickness and advected temperature. These models give a succinct overall picture of the slot behaviour in the buoyancy-dominated limit.

Boundary layer at a swept stagnation line of semi-infinite extent

1970 ◽  
Vol 41 (4) ◽  
pp. 737-750 ◽  
Author(s):  
Paul A. Libby ◽  
Karl K. Chen
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Cross Flow ◽  
Differential Analysis ◽  
Eigenvalues And Eigenfunctions ◽  
Stagnation Line ◽  
Infinite Extent ◽  
Dimensional Boundary ◽  
Upstream Flow

A three-dimensional boundary layer developing along a semi-infinite swept stagnation line from a starting edge and evolving into that associated with such a line of infinite extent is calculated. A series solution useful for assessing the counteracting effects of cross-flow and mass transfer near the starting edge and for providing initial data for a subsequent streamwise, numerical solution is developed. The asymptotic behaviour far from the starting edge is examined and shown to involve only eigenfunction contributions associated with the far upstream flow. However, it is not presently possible to determine the relevant eigenvalues and eigenfunctions. Numerical solutions based on a difference-differential analysis yield the entire development of the boundary layer and indicate the streamwise length required for the case of the boundary layer at an infinite stagnation line to be obtained.

Three-Dimensional Laminar Natural Convection in a Vertical Air Slot With Hexagonal Honeycomb Core

1990 ◽  
Vol 112 (1) ◽  
pp. 130-136 ◽  
Author(s):  
Y. Asako ◽  
H. Nakamura ◽  
M. Faghri
Keyword(s):  
Natural Convection ◽  
Numerical Solutions ◽  
Transfer Problem ◽  
Three Dimensional ◽  
Convection Heat Transfer ◽  
Side Wall ◽  
Temperature Fields ◽  
Honeycomb Core ◽  
Wall Boundary Conditions ◽  
Laminar Natural Convection

Numerical solutions are obtained for a three-dimensional natural convection heat transfer problem in a vertical air slot with a thin hexagonal honeycomb core. The air slot is assumed to be of such dimensions that the velocity and temperature fields repeat themselves in successive enclosures. The numerical methodology is based on an algebraic coordinate transformation technique, which maps the complex cross section onto a rectangle, coupled with a calculation procedure for fully elliptic three-dimensional flows. The calculations are performed for the Rayleigh number in the range of 103 to 105, for a Prandtl number of 0.7, and for five values of the aspect ratio of the honeycomb enclosure. The average Nusselt number results for the case of a thin honeycomb core are compared with the previously obtained results for a thick honeycomb core with conduction and adiabatic side wall boundary conditions.

Instability in a viscous flow driven by streamwise vortices

2001 ◽  
Vol 432 ◽  
pp. 127-166 ◽  
Author(s):  
K. W. BRINCKMAN ◽  
J. D. A. WALKER
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Wall Layer ◽  
External Flow ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Wall Flow ◽  
Turbulent Wall ◽  
Near Wall

Unsteady separation processes at large finite, Reynolds number, Re, are considered, as well as the possible relation to existing descriptions of boundary-layer separation in the limit Re → ∞. The model problem is a fundamental vortex-driven three-dimensional flow, believed to be relevant to bursting near the wall in a turbulent boundary layer. Bursting is known to be associated with streamwise vortex motion, but the vortex/wall interactions that drive the near-wall flow toward breakdown have not yet been fully identified. Here, a simulation of symmetric counter-rotating vortices is used to assess the influence of sustained pumping action on the development of a viscous wall layer. The calculated solutions describe a three-dimensional flow at finite Re that is independent of the streamwise coordinate and consists of a crossflow plane motion, with a developing streamwise flow. The unsteady problem is constructed to mimic a typical cycle in turbulent wall layers and numerical solutions are obtained over a range of Re. Recirculating eddies develop rapidly in the near-wall flow, but these eddies are eventually bisected by alleyways which open up from the external flow region to the wall. At sufficiently high Re, an oscillation was found to develop in the streamwise vorticity field near the alleyways with a concurrent evolution of a local spiky behaviour in the wall shear. Above a critical value of Re, the oscillation grows rapidly in amplitude and eventually penetrates the external flow field, suggesting the onset of an unstable wall-layer breakdown. Local zones of severely retarded streamwise velocity are computed which are reminiscent of the low-speed streaks commonly observed in turbulent boundary layers. A number of other features also bear a resemblance to observed coherent structure in the turbulent wall layer.

Three-Dimensional Laminar Natural Convection in an Inclined Air Slot With Hexagonal Honeycomb Core

1991 ◽  
Vol 113 (4) ◽  
pp. 906-911 ◽  
Author(s):  
Y. Asako ◽  
H. Nakamura ◽  
Z. Chen ◽  
M. Faghri
Keyword(s):  
Natural Convection ◽  
Numerical Solutions ◽  
Transfer Problem ◽  
Three Dimensional ◽  
Convection Heat Transfer ◽  
Temperature Fields ◽  
Honeycomb Core ◽  
Inclination Angles ◽  
Side Walls ◽  
Rayleigh Numbers

Numerical solutions are obtained for a three-dimensional natural convection heat transfer problem in an inclined air slot with a hexagonal honeycomb core. The air slot is assumed to be long and wide such that the velocity and temperature fields repeat themselves in successive enclosures. The numerical methodology is based on an algebraic coordinate transformation technique, which maps the complex cross section onto a rectangle, coupled with a calculation procedure for fully elliptic three-dimensional flows. The calculations are performed for Rayleigh numbers in the range of 103 to 105, inclination angles in the range of −90 to 80 deg, Prandtl number of 0.7, and for five values of the aspect ratio. Three types of thermal boundary condition for the honeycomb side walls are considered. The average Nusselt number results are compared with those for a rectangular two-dimensional enclosure.

Boundary layer over spinning blunt body of revolution at incidence including Magnus forces

1978 ◽  
Vol 363 (1714) ◽  
pp. 357-380 ◽  
Keyword(s):  
Boundary Layer ◽  
Skin Friction ◽  
Blunt Body ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Longitudinal Direction ◽  
Meridional Flow ◽  
Meridional Plane ◽  
Magnus Force ◽  
Displacement Thickness

An incompressible laminar flow over a spinning blunt-body at incidence is investigated. The approach follows strictly the three-dimensional boundary layer theory, and the lack of initial profiles is readily resolved. The rule of the dependence zone is satisfied with the Krause scheme, and complete numerical solutions are obtained for an ellipsoid of revolution at 6° incidence and two spin rates. Spinning causes asymmetry which, in turn, introduces the Magnus force. The asymmetry is most pronounced in crossflow, but is also noticeable in the skin friction and displacement thickness of the meridional flow. A variety of crossflow profiles are determined as are the streamline patterns in the cross- and meridional-plane which are especially useful in visualizing the flow structure. Detailed distribution of skin friction, displacement thickness, and centrifugal pressure are presented. A negative crossflow displacement thickness is found to be physically meaningful. The Magnus forces due to the crossflow skin friction and the centrifugal pressure are determined; these two forces partly compensate for each other. At lower spin rate, the frictional force is larger, resulting in a positive Magnus force. At high spin rate, the opposite is obtained. At high incidence (30°) the present boundary layer calculations could be carried out in the longitudinal direction, only up to the beginning of an open separation.

Convection by a horizontal thermal gradient

2007 ◽  
Vol 586 ◽  
pp. 41-57 ◽  
Author(s):  
H. J. J. GRAMBERG ◽  
P. D. HOWELL ◽  
J. R. OCKENDON
Keyword(s):  
Boundary Layer ◽  
Rayleigh Number ◽  
Thermal Gradient ◽  
Melting Process ◽  
Uniform Heating ◽  
Boundary Layer Analysis ◽  
Layer Analysis ◽  
Convection Problem ◽  
Large Rayleigh Number ◽  
Batch Melting

This paper considers a paradigm large-Prandtl-number, large-Rayleigh-number forced convection problem suggested by the batch melting process in the glass industry. Although the fluid is heated from above, non-uniform heating in the horizontal direction induces thermal boundary layers in which colder liquid is driven over hotter liquid. This leads to an interesting selection problem in the boundary layer analysis, whose resolution is suggested by a combination of analytical and numerical evidence.

Receptivity to free-stream vorticity of flow past a flat plate with elliptic leading edge

2010 ◽  
Vol 653 ◽  
pp. 245-271 ◽  
Author(s):  
L.-U. SCHRADER ◽  
L. BRANDT ◽  
C. MAVRIPLIS ◽  
D. S. HENNINGSON
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Free Stream ◽  
Three Dimensional ◽  
Low Frequency ◽  
Leading Edge ◽  
Sound Waves ◽  
Streamwise Vorticity ◽  
Low Frequencies ◽  
Free Stream Turbulence

Receptivity of the two-dimensional boundary layer on a flat plate with elliptic leading edge is studied by numerical simulation. Vortical perturbations in the oncoming free stream are considered, impinging on two leading edges with different aspect ratio to identify the effect of bluntness. The relevance of the three vorticity components of natural free-stream turbulence is illuminated by considering axial, vertical and spanwise vorticity separately at different angular frequencies. The boundary layer is most receptive to zero-frequency axial vorticity, triggering a streaky pattern of alternating positive and negative streamwise disturbance velocity. This is in line with earlier numerical studies on non-modal growth of elongated structures in the Blasius boundary layer. We find that the effect of leading-edge bluntness is insignificant for axial free-stream vortices alone. On the other hand, vertical free-stream vorticity is also able to excite non-modal instability in particular at zero and low frequencies. This mechanism relies on the generation of streamwise vorticity through stretching and tilting of the vertical vortex columns at the leading edge and is significantly stronger when the leading edge is blunt. It can thus be concluded that the non-modal boundary-layer response to a free-stream turbulence field with three-dimensional vorticity is enhanced in the presence of a blunt leading edge. At high frequencies of the disturbances the boundary layer becomes receptive to spanwise free-stream vorticity, triggering Tollmien–Schlichting (T-S) modes and receptivity increases with leading-edge bluntness. The receptivity coefficients to free-stream vortices are found to be about 15% of those to sound waves reported in the literature. For the boundary layers and free-stream perturbations considered, the amplitude of the T-S waves remains small compared with the low-frequency streak amplitudes.

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