#### Title

Effect Of Bottom Topography On Surface Shear And/or Buoyancy Driven Laminar Flow Inside Enclosed Domains: A Two-Dimensional Time-Dependent Numerical Investigation

#### Date of Award

1986

#### Availability

Article

#### Degree Name

Doctor of Philosophy (Ph.D.)

#### Department

Mechanical Engineering

#### Abstract

A finite difference code which uses a vertical stretching transformation and the stream function vorticity formulation has been developed to investigate the effect of bottom topography on the surface shear and/or buoyancy driven laminar flow inside enclosures.Transient and steady state solutions have been obtained for lid driven cavities of slopes of 0, 1/4, 1/2 and 3/4 for Reynolds numbers of 100, 1000 and 2000. The 0 slope (square cavity) case was used for the verification of the code. It is found that a sloping bottom causes the disappearance of a lower downstream corner secondary eddy for a Reynolds number of 100. The size of the lower upstream corner secondary eddy increases as the slope is increased. This increase is sharper for a Reynolds number of 2000. Two counterrotating secondary eddies can be seen for a 31 x 31 grid at the lower acute angled corner for Re = 2000. The inception of the lower upstream secondary eddy takes place earlier in time as the slope is increased.Laminar natural convection inside asymmetric cavities with differentially heated vertical side walls and sloping bottom side has also been investigated using the above mentioned code. The slopes considered are 1/4, 1/2 and 3/4 for Rayleigh numbers of 10('3), 10('4), 10('5) and 10('6). The flow is similar to that in a square cavity for Rayleigh numbers uptil 10('4) with a unicellular pattern. At a higher Rayleigh number of 10('6) the secondary core rolls present for square cavities are absent in cavities with 1/2 and 3/4 slope. The Nusselt (Nu) numbers decrease as the slope is increased. A correlation for average Nusselt numbers with slope (S) and Rayleigh (Ra) number has been developed.The location of the maximum Nusselt number on the hot wall is also significantly influenced by a change in slope. Transient oscillations in flow and heat transfer are damped as the slope is increased for a given Rayleigh number.As the final part of this study a lid driven square cavity with buoyancy and shear driven flow has been studied. Reynolds numbers of 1000, 5000 and 10,000 have been considered for water for bulk Richardson (Ri(,b)) numbers of 5.7, 0.228, 0.057 respectively. It is found that the flow moves in the direction of the lid initially, inspite of the stable thermal stratification. The number of secondary cells increases with an increase in Ri(,b) and the flow shows an oscillatory behavior before reaching steady state. A critical Ri(,b) exists below which the mixing in the cavity is nearly complete. (Abstract shortened with permission of author.)

#### Keywords

Engineering, Mechanical

#### Recommended Citation

Chattree, Mayank, "Effect Of Bottom Topography On Surface Shear And/or Buoyancy Driven Laminar Flow Inside Enclosed Domains: A Two-Dimensional Time-Dependent Numerical Investigation" (1986). *Dissertations from ProQuest*. 1622.

http://scholarlyrepository.miami.edu/dissertations/1622

## Link to Full Text

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