Drag of a heated sphere at low Reynolds numbers in the absence of buoyancy

2019 ◽  
Vol 869 ◽  
pp. 264-291 ◽  
Author(s):  
Swetava Ganguli ◽  
Sanjiva K. Lele
Keyword(s):  
Reynolds Numbers ◽  
Boussinesq Approximation ◽  
Base Flow ◽  
Subsequent Paper ◽  
Heating Regime ◽  
Low Reynolds Numbers ◽  
Low Mach Number ◽  
Low Reynolds ◽  
Drag Law ◽  
O 10

Fully resolved simulations are used to quantify the effects of heat transfer in the absence of buoyancy on the drag of a spatially fixed heated spherical particle at low Reynolds numbers ($Re$) in the range $10^{-3}\leqslant Re\leqslant 10$ in a variable-property fluid. The case where buoyancy is present is analysed in a subsequent paper. This analysis is carried out without making any assumptions on the amount of heat addition from the sphere and thus encompasses both the heating regime where the Boussinesq approximation holds and the regime where it breaks down. The particle is assumed to have a low Biot number, which means that the particle is uniformly at the same temperature and has no internal temperature gradients. Large deviations in the value of the drag coefficient as the temperature of the sphere increases are observed. When $Re<O(10^{-2})$, these deviations are explained using a low-Mach-number perturbation analysis as irrotational corrections to a Stokes–Oseen base flow. Correlations for the drag and Nusselt number of a heated sphere are proposed for the range of Reynolds numbers $10^{-3}\leqslant Re\leqslant 10$ which fit the computationally obtained values with less than 1 % and 3 % errors, respectively. These correlations can be used in simulations of gas–solid flows where the accuracy of the drag law affects the prediction of the overall flow behaviour. Finally, an analogy to incompressible flow over a modified sphere is demonstrated.

An Electrokinetic Micro Mixer for Lab-on-Chip Applications: Modeling, Validation, and Optimization

2011 ◽  
Author(s):  
Hendryk Bockelmann ◽  
Vincent Heuveline ◽  
Peter Ehrhard ◽  
Dominik P. J. Barz
Keyword(s):  
Electrical Potential ◽  
Reynolds Numbers ◽  
Base Flow ◽  
Secondary Flows ◽  
Electrical Field ◽  
Lab On Chip ◽  
Low Reynolds Numbers ◽  
Micro Particle Image Velocimetry ◽  
Low Reynolds ◽  
Micro Mixer

Mixing of liquids in micro mixers at low Reynolds numbers is a challenging task since the flow regime is laminar and it is difficult to engage instabilities of the flow. In many microfluidic systems, mixing can be improved by means of electrokinetic effects. A favorable micro mixer design consists of a Y-junction, where the different liquid streams merge, and a subsequent meandering microchannel. A pressure gradient pumps the liquids to be mixed through the microchannel. An oscillating electrical field is superimposed onto the pressure-driven base flow which generates an additional electrokinetic (electro osmotic) flow. These oscillating secondary flows in conjunction with the meandering geometry are responsible for stretching and folding of the contact area of the liquids to be mixed which enhances the mass transfer rates considerably. In this contribution, we present a mathematical model which allows for the numerical simulation of flow, electrical potential, and species concentration. The model is validated by experiments relying on Micro Particle Image Velocimetry (μPIV). Consequently, this model can be used to numerically optimize the electrical field in order to achieve fast and high mixing even at low Reynolds numbers.

Biologically Generated Mixing in the Ocean

2019 ◽  
Vol 11 (1) ◽  
pp. 215-226 ◽  
Author(s):  
Eric Kunze
Keyword(s):  
Deep Ocean ◽  
Reynolds Numbers ◽  
Ocean Tide ◽  
Strong Wind ◽  
Ocean Mixing ◽  
Low Reynolds Numbers ◽  
Dissipation Rates ◽  
Low Reynolds ◽  
O 10 ◽  
Marine Biosphere

This article assesses the contribution to ocean mixing by the marine biosphere at both high and low Reynolds numbers Re= uℓ/ ν. While back-of-the-envelope estimates have suggested that swimming marine organisms might generate as much high-Reynolds-number turbulence as deep-ocean tide- and wind-generated internal waves, and that turbulent dissipation rates of O(10−5W kg−1) (Re ∼ 105) could be produced by aggregations of organisms ranging from O(0.01 m) krill to O(10 m) cetaceans, comparable to strong wind and buoyancy forcing near the surface, microstructure measurements do not find consistently elevated dissipation associated with diel vertically migrating krill. Elevated dissipation rates are associated with schools of O(0.1– 1 m) fish but with low mixing coefficients ( γ ∼ 0.002–0.02, as compared with γ ∼ 0.2 for geophysical turbulence). Likewise, viscously induced drift at low Reynolds numbers produces little mixing of temperature, solutes, dissolved nutrients, and gases when realistic swimmers and molecular scalar diffusion are taken into account. The conclusion is that, while the marine biosphere can generate turbulence, it contributes little ocean mixing compared with breaking internal gravity waves.

Global Linear Instability of Flow Through a Converging–Diverging Channel

2015 ◽  
Vol 138 (3) ◽  
Author(s):  
Mamta R. Jotkar ◽  
Gayathri Swaminathan ◽  
Kirti Chandra Sahu ◽  
Rama Govindarajan
Keyword(s):  
Reynolds Numbers ◽  
Linear Instability ◽  
Stability Study ◽  
Base Flow ◽  
Low Reynolds Numbers ◽  
Critical Reynolds Numbers ◽  
Diverging Channel ◽  
Order Of Magnitude ◽  
Flow Through ◽  
Low Reynolds

The global linear stability, where we assume no homogeneity in either of the spatial directions, of a two-dimensional laminar base flow through a spatially periodic converging–diverging channel is studied at low Reynolds numbers. A large wall-waviness amplitude is used to achieve instability at critical Reynolds numbers below ten. This is in contrast to earlier studies, which were at lower wall-waviness amplitude and had critical Reynolds numbers an order of magnitude higher. Moreover, our leading mode is a symmetry-breaking standing mode, unlike the traveling modes which are standard at higher Reynolds numbers. Eigenvalues in the spectrum lie on distinct branches, showing varied structure spanning the geometry. Our global stability study suggests that such modes can be tailored to give enhanced mixing in microchannels at low Reynolds numbers.

Investigation on the effect of leading edge tubercles of sweptback wing at low reynolds number

2020 ◽  
Vol 21 (6) ◽  
pp. 621
Author(s):  
Veerapathiran Thangaraj Gopinathan ◽  
John Bruce Ralphin Rose ◽  
Mohanram Surya
Keyword(s):  
Leading Edge ◽  
Reynolds Numbers ◽  
Sweep Angle ◽  
Laminar Separation ◽  
Low Reynolds Numbers ◽  
Flow Energy ◽  
Airplane Wing ◽  
Low Reynolds ◽  
Naca 0015 ◽  
Wing Performance

Aerodynamic efficiency of an airplane wing can be improved either by increasing its lift generation tendency or by reducing the drag. Recently, Bio-inspired designs have been received greater attention for the geometric modifications of airplane wings. One of the bio-inspired designs contains sinusoidal Humpback Whale (HW) tubercles, i.e., protuberances exist at the wing leading edge (LE). The tubercles have excellent flow control characteristics at low Reynolds numbers. The present work describes about the effect of tubercles on swept back wing performance at various Angle of Attack (AoA). NACA 0015 and NACA 4415 airfoils are used for swept back wing design with sweep angle about 30°. The modified wings (HUMP 0015 A, HUMP 0015 B, HUMP 4415 A, HUMP 4415 B) are designed with two amplitude to wavelength ratios (η) of 0.1 & 0.24 for the performance analysis. It is a novel effort to analyze the tubercle vortices along the span that induce additional flow energy especially, behind the tubercles peak and trough region. Subsequently, Co-efficient of Lift (CL), Co-efficient of Drag (CD) and boundary layer pressure gradients also predicted for modified and baseline (smooth LE) models in the pre & post-stall regimes. It was observed that the tubercles increase the performance of swept back wings by the enhanced CL/CD ratio in the pre-stall AoA region. Interestingly, the flow separation region behind the centerline of tubercles and formation of Laminar Separation Bubbles (LSB) were asymmetric because of the sweep.

Low Reynolds number flow around and heat transfer from a heated circular cylinder

2010 ◽  
Vol 1 (1-2) ◽  
pp. 15-20 ◽  
Author(s):  
B. Bolló
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Reynolds Number Flow ◽  
Two Dimensional Flow ◽  
Number Flow ◽  
Low Reynolds ◽  
Increasing Temperature

Abstract The two-dimensional flow around a stationary heated circular cylinder at low Reynolds numbers of 50 < Re < 210 is investigated numerically using the FLUENT commercial software package. The dimensionless vortex shedding frequency (St) reduces with increasing temperature at a given Reynolds number. The effective temperature concept was used and St-Re data were successfully transformed to the St-Reeff curve. Comparisons include root-mean-square values of the lift coefficient and Nusselt number. The results agree well with available data in the literature.

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