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Herrada M.,University of Seville | Shtern V.,Shtern Research and Consulting
Physics of Fluids | Year: 2014

A sealed cylindrical container is filled with air and water. The container rotation and the axial gradient of temperature induce the steady axisymmetric meridional circulation of both fluids due to the thermal buoyancy and surface-tension (Marangoni) effects. If the temperature gradient is small, the water circulation is one-cellular while the air circulation can be one- or two-cellular depending on water fraction Wf. The numerical simulations are performed for the cylinder length-to-radius ratio l = 1 and l = 4. The l = 4 results and the analytical solution for l → ∞ agree in the cylinder's middle part. As the temperature gradient increases, the water circulation becomes one-, two-, or three-cellular depending on Wf. The results are of fundamental interest and can be applied for bioreactors. © 2014 AIP Publishing LLC.


Shtern V.N.,Shtern Research and Consulting | Torregrosa M.M.,University of Seville | Herrada M.A.,University of Seville
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2011

This numerical study of an axisymmetric motion of a viscous incompressible fluid in an elongated cylindrical container explains how a swirling inflow develops the global meridional circulation and two U-shaped throughflows (TFs). For moderate values of the Reynolds (Re) number, there is a single U-shaped TF: The fluid moves from the peripheral annular inlet near the sidewall to the dead end, turns around, goes back near the axis, and leaves the container through the central exhaust. As Re increases, vortex breakdown occurs near the dead end. If the exhaust orifice is wide, the ambient fluid is sucked into the container near its axis, reaches the dead-end vicinity, merges with the U-shaped TF, and goes back inside an annular region. Thus, a double counterflow develops, where the fluid moves to the dead end near both the sidewall and the axis and goes back in between. The physical mechanism of the double counterflow is a swirl decay combined with the focused flow convergence near the dead end. This double counterflow is beneficial for combustion applications. © 2011 American Physical Society.


Shtern V.N.,Shtern Research and Consulting | Del Mar Torregrosa M.,University of Seville | Herrada M.A.,University of Seville
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2011

This numerical study of the axisymmetric motion of a viscous incompressible fluid in an elongated cylindrical container explains how colliding counterflows develop. Two swirling flows enter the container through peripheral inlets and leave it through central exhausts symmetrically from both ends. Different flow rates, characterized by the Reynolds number Re, are studied for a fixed swirl number. For small Re, the throughflow (TF) is limited to the inlet-exhaust vicinities and a few circulation cells occupy the rest of the interior. As Re grows, (i) the circulation cells disappear while the TF reaches the container's midsection and becomes U shaped, moving near the sidewall inward and going back near the container axis; elongated circulation regions develop separating the TF branches; (ii) the flow convergence to the axis focuses near the container's midsection, resulting in the vortex breakdown development; (iii) the swirl-induced low pressure causes suction of the ambient fluid through the central parts of the exhausts; (iv) the suction flow reaches the container's midsection, turns around, mixes with the driving TF, forms an annular outflow, and leaves through the exhaust periphery. The two factors, (a) swirl decay due to friction at the sidewall and (b) the focused flow convergence to the axis, constitute the physical mechanism of the colliding counterflows. Such flow pattern is favorable for a vortex solid-fuel combustor. © 2011 American Physical Society.


Herrada M.A.,University of Seville | Shtern V.N.,Shtern Research and Consulting | Lopez-Herrera J.M.,University of Seville
Physics of Fluids | Year: 2013

The numerical study of the steady axisymmetric air-water flow in a vertical sealed cylinder, driven by the rotating top disk, describes topological transformations as the rotation intensifies. The air meridional flow (AMF) and swirl induce meridional motions of opposite directions in water. For slow (fast) rotation, the effect of AMF (swirl) dominates. For very fast rotation, large-scale regions of clockwise meridional circulation in air and water are separated by a thin layer of anticlockwise circulation adjacent to the interface in water. This pattern develops for other fluids as well. Physical reasoning behind the flow evolution is provided. © 2013 AIP Publishing LLC.


Shtern V.N.,Shtern Research and Consulting | del Mar Torregrosa M.,University of Seville | Herrada M.A.,University of Seville
Physics of Fluids | Year: 2012

This numerical study of the steady axisymmetric motion of a viscous incompressible fluid in a sealed cylindrical container with one end wall rotating reveals that swirl decay, induced by friction at the sidewall, plays an important role in the development of vortex breakdown (VB). When the flow is slow, it is multi-cellular. As the flow strength increases (i) meridional circulation becomes global, (ii) flow convergence toward the axis focuses near the still end wall, (iii) a few local minima of pressure appear, (iv) a few flow reversals occur near the axis, and (v) circulation regions merge and an elongated double counterflow develops. Stages (i)-(v) are common for a number of vortex devices. If the swirl decay is diminished by additional rotation of the sidewall, VB disappears. © 2012 American Institute of Physics.


Herrada M.,Polytechnic University of Valencia | Shtern V.,Shtern Research and Consulting
Physics of Fluids | Year: 2015

This numerical study reveals that the thermal convection, induced by the axial gradient of temperature in a rotating pipe, suffers from the shear-layer instability if the Prandtl number, Pr, is small. As Pr increases, this instability is suppressed by the stable density stratification in the field of centrifugal force. In an annular pipe, the thermal instability develops for large Pr if a temperature of walls is prescribed. For a narrow annulus, these features agree with the known results for a planar flow driven by gravity and a horizontal gradient of temperature. It is shown here that the thermal instability does not develop if the walls are adiabatic. The centrifugal and Marangoni convection of a liquid, partially filling the pipe, also suffers from the shear-layer instability for small Pr and has no thermal instability. These features agree with the experiments for the planar flow performed by Kirdyashkin. The obtained results are of fundamental interest and can be relevant for the development of centrifugal heat exchangers. © 2015 AIP Publishing LLC.


Shtern V.,Shtern Research and Consulting
Theoretical and Computational Fluid Dynamics | Year: 2014

It is shown that an infinite set of eddies can develop near the interface–wall intersection in a two-fluid flow. A striking feature is that the eddy occurrence depends on from what side of the interface the flow is driven. In air–water flows where the viscosity ratio is 0.018, the eddies develop if a driving source is located on (i) the air side for (Formula presented.)(Formula presented.), (ii) any side for (Formula presented.)(Formula presented.), and (iii) the water side for (Formula presented.)(Formula presented.), where (Formula presented.)(Formula presented.) is the upper interface–wall angle. © 2014, Springer-Verlag Berlin Heidelberg.


Herrada M.A.,Polytechnic University of Valencia | Shtern V.N.,Shtern Research and Consulting | Lopez-Herrera J.M.,Polytechnic University of Valencia
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2013

The off-axis emergence of vortex breakdown (VB) is revealed. The steady axisymmetric flow in a vertical sealed cylinder, which is partially filled with water and the rest is filled with air, is driven by the rotating bottom disk. The numerical simulations show that VB can emerge away from the rotation axis, interface, and walls. As the rotation intensifies, VB first develops in the water region. If the water height is less (larger) than nearly one half of the cylinder radius, VB emerges off (on) the axis. As the rotation further increases, the off-axis VB ring touches the interface and then a thin countercirculation layer develops in the air flow above the water VB domain. This two-fluid VB ring shrinks (it even disappears in a very shallow whirlpool) as the interface approaches the bottom disk. © 2013 American Physical Society.


Shtern V.,Shtern Research and Consulting
Journal of Fluid Mechanics | Year: 2012

The paper describes an asymptotic flow of a viscous fluid in an infinite annular cylindrical cavity as the distance from the flow source tends to infinity. If the driving flow near the source is axisymmetric then the asymptotic pattern is cellular; otherwise it is typically not. Boundary conditions are derived to match the asymptotic axisymmetric flow with that near the source. For a narrow cavity, the asymptotic solutions for the axisymmetric and three-dimensional flows are obtained analytically. For any gap, the flow is described by a numerical solution of an eigenvalue problem. The least decaying mode corresponds to azimuthal wavenumber m = 1. © 2012 Cambridge University Press.


Shtern V.N.,Shtern Research and Consulting
Physics of Fluids | Year: 2013

It is shown that the viscous fluid motion in the depth of a narrow cavity is a counterflow moving and periodically varying along the cavity length. The obtained exact solutions of the Stokes equations describe unsteady three-dimensional flows, developing as the distance from the cavity surface increases. The found asymptotic motion is common for a variety of boundary conditions and cavity shapes. Creeping flows between parallel and inclined planes, coaxial cylinders, and concentric cones are particularly addressed. For these flows, the analytical asymptotes and numerical results merge as the gap width decreases. © 2013 AIP Publishing LLC.

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