On the Oscillatory Instability of Closed-Loop Thermosyphons

1985 ◽  
Vol 107 (4) ◽  
pp. 826-832 ◽  
Author(s):  
K. Chen
Keyword(s):  
Turbulent Flows ◽  
Closed Loop ◽  
Numerical Solutions ◽  
Angular Frequency ◽  
Oscillatory Instability ◽  
Neutral Stability ◽  
Horizontal Segment ◽  
Aspect Ratios ◽  
The Stability ◽  
Laminar And Turbulent Flows

The stability of natural convection flows in single-phase closed-loop thermosyphons is investigated. The thermosyphons considered in the present analysis are fluid-filled tubes bent into rectangular shapes. The fluid is heated over the lower horizontal segment and cooled over the upper horizontal segment. Analytical and numerical solutions are presented for a range of loop aspect ratios and radii for both laminar and turbulent flows. It is found that the steady-state results for thermosyphons with different aspect ratios and radii can be expressed in terms of a single dimensionless parameter. When this parameter is less than a critical value, the flow is always stable. Above this critical point, oscillatory instability exists for a narrow range of a friction parameter. The calculated neutral stability conditions show that the flow is least stable when the aspect ratio of the loop approaches unity. The frequency of the convection-induced oscillation is slightly higher than the angular frequency of a fluid particle traveling along the loop.

Electrohydrodynamic stability: Taylor–Melcher theory for a liquid bridge suspended in a dielectric gas

2002 ◽  
Vol 452 ◽  
pp. 163-187 ◽  
Author(s):  
C. L. BURCHAM ◽  
D. A. SAVILLE
Keyword(s):  
Surface Tension ◽  
Dielectric Constant ◽  
Electric Fields ◽  
Liquid Bridge ◽  
Numerical Solutions ◽  
Specific Conductivity ◽  
Axisymmetric Deformation ◽  
Aspect Ratios ◽  
The Stability ◽  
Theory And Experiment

A liquid bridge is a column of liquid, pinned at each end. Here we analyse the stability of a bridge pinned between planar electrodes held at different potentials and surrounded by a non-conducting, dielectric gas. In the absence of electric fields, surface tension destabilizes bridges with aspect ratios (length/diameter) greater than π. Here we describe how electrical forces counteract surface tension, using a linearized model. When the liquid is treated as an Ohmic conductor, the specific conductivity level is irrelevant and only the dielectric properties of the bridge and the surrounding gas are involved. Fourier series and a biharmonic, biorthogonal set of Papkovich–Fadle functions are used to formulate an eigenvalue problem. Numerical solutions disclose that the most unstable axisymmetric deformation is antisymmetric with respect to the bridge’s midplane. It is shown that whilst a bridge whose length exceeds its circumference may be unstable, a sufficiently strong axial field provides stability if the dielectric constant of the bridge exceeds that of the surrounding fluid. Conversely, a field destabilizes a bridge whose dielectric constant is lower than that of its surroundings, even when its aspect ratio is less than π. Bridge behaviour is sensitive to the presence of conduction along the surface and much higher fields are required for stability when surface transport is present. The theoretical results are compared with experimental work (Burcham & Saville 2000) that demonstrated how a field stabilizes an otherwise unstable configuration. According to the experiments, the bridge undergoes two asymmetric transitions (cylinder-to-amphora and pinch-off) as the field is reduced. Agreement between theory and experiment for the field strength at the pinch-off transition is excellent, but less so for the change from cylinder to amphora. Using surface conductivity as an adjustable parameter brings theory and experiment into agreement.

On Oscillatory Instability of Convective Flows at Low Prandtl Number

1997 ◽  
Vol 119 (4) ◽  
pp. 823-830 ◽  
Author(s):  
A. Yu. Gelfgat ◽  
P. Z. Bar-Yoseph ◽  
A. L. Yarin
Keyword(s):  
Aspect Ratio ◽  
Prandtl Number ◽  
Lower Boundary ◽  
Oscillatory Instability ◽  
Weakly Nonlinear ◽  
Convective Flows ◽  
Stability Diagrams ◽  
Aspect Ratios ◽  
The Stability ◽  
Upper Boundary

Numerical investigation of the oscillatory instability of convective flows in laterally heated rectangular cavities is presented. Cavities with no-slip isothermal vertical boundaries, no-slip adiabatic lower boundary, and stress-free adiabatic upper boundary are considered. Dependence of the critical Grashof number and the critical frequency of oscillations on the aspect ratio (A = length/height) of the cavity are investigated. The stability diagrams were obtained for the whole interval of the aspect ratio 1 ≤ A ≤ 10. The study was carried out for two values of the Prandtl number, Pr = 0 and 0.015. It was shown that the oscillatory instability sets in as a result of the Hopf bifurcation. It was found that at two different values of the Prandtl number considered the instability is caused by different infinitely small dominant perturbations, which means that the convective heat transfer strongly affects stability of the flow even for cases having small Prandtl number. No asymptotic behavior for large aspect ratios was found up to A = 10. Slightly supercritical oscillatory flows were approximated asymptotically by means of the weakly nonlinear analysis of the calculated bifurcation.

Linear stability of the dissipative, two-fluid, cylindrical Couette problem. Part 1. The stably-stratified hydrodynamic problem

1971 ◽  
Vol 45 (1) ◽  
pp. 91-110 ◽  
Author(s):  
G. P. Schneyer ◽  
S. A. Berger
Keyword(s):  
Eigenvalue Problems ◽  
Numerical Solutions ◽  
Outer Cylinder ◽  
Neutral Stability ◽  
Two Fluids ◽  
Multiple Eigenvalues ◽  
Fluid Properties ◽  
The Stability ◽  
Nuclear Rocket ◽  
Two Fluid

The stability of a two-fluid vortex is studied as a step towards understanding the separation and containment problems in a gaseous-core nuclear rocket. In particular, the linear hydrodynamic stability of two incompressible, immiscible, viscous fluids occupying separate annular regions of a cylindrical Couette apparatus is considered. Neglecting surface tension and gravity, a conservative assumption, the governing equations for arbitrary jumps in fluid properties are derived and numerical solutions to the resultant eigenvalue problems obtained. Results are presented for the effect on neutral stability of density and viscosity jumps, varying gap widths, and differing fluid-fluid interfacial positions. The solutions are limited, however, to the case of stably stratified fluids and a stationary outer cylinder.Two separate modes (multiple eigenvalues) have been discovered for all cases in which two fluids, differing in any property, are present. A rationale is presented for this phenomenon as well as for most of the other observed results.While most results are believed to be manifestations of the Taylor cylindrical Couette instability phenomenon, evidence is presented for the existence of additional ‘hidden’ eigenvalues attributable to the classical Kelvin–Helmholtz and/or the recently reported Yih viscosity-stratification instability phenomena.

scholarly journals Instability of a binary liquid film flowing down a slippery inclined heated plate

2021 ◽  
Author(s):  
Eglal Ellaban
Keyword(s):  
Liquid Film ◽  
Numerical Solutions ◽  
Soret Effect ◽  
Critical Conditions ◽  
Heated Plate ◽  
Neutral Stability ◽  
Inclined Plate ◽  
Binary Liquid ◽  
Chebyshev Spectral Collocation ◽  
The Stability

In this thesis we studied the stability of a binary liquid film flowing down a heated porous inclined plate. It is assumed that the heating induces concentration differences in the liquid mixture (Soret effect), which together with the differences in temperature affects the surface tension. A mathematical model is constructed by coupling the Navier- tokes equations governing the flow with equations for the concentration and temperature. The effect of substrate permeability is incorporated by applying a specific slip condition at the bottom of the liquid layer. We carry out a linear stability analysis in order to obtain the critical conditions for the onset of instability. We used a Chebyshev spectral collocation method to obtain numerical solutions to the resulting Orr-Sommerfeld type equations. We also obtained an asymptotic solution which yielded an expression for the state of neutral stability of long perturbations as a function of the parameters controlling the problem. We present our findings by illustrating and interpreting our results for the critical Reynolds number for instability.

scholarly journals Heat Transfer Enhancement in a Novel Annular Tube with Outer Straight and Inner Twisted Oval Tubes

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1213
Author(s):  
Chao Luo ◽  
KeWei Song ◽  
Toshio Tagawa ◽  
TengFei Liu
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Factor ◽  
Turbulent Flows ◽  
Geometrical Parameters ◽  
Straight Tube ◽  
Aspect Ratios ◽  
Oval Tube ◽  
Annular Tube ◽  
Laminar And Turbulent Flows

The thermal-hydraulic performance in a novel annular tube formed by outer straight and inner twisted oval tubes is numerically investigated. An annular tube formed by two straight oval tubes is also studied for comparison. Inner twisted oval tubes with different aspect ratios and twist ratios are studied. The heat transfer is well improved by the symmetrical secondary flow in the annulus. The Nusselt number generally increases when the inner oval tube becomes flatter and the twists stronger in the studied range of geometrical parameters. The largest Nusselt number Nu of the inner twisted tube increases by 116% while the friction factor f increases by only 46% compared with that of the inner straight tube, and the largest value of the thermal performance factor (JF) can be up to 1.9. Correlations of the Nusselt number and friction factor are proposed for laminar and turbulent flows, and the deviations of the correlations are within ±5% and ±4% for Nu and f, respectively.

scholarly journals Instability of a binary liquid film flowing down a slippery inclined heated plate

2021 ◽  
Author(s):  
Eglal Ellaban
Keyword(s):  
Liquid Film ◽  
Numerical Solutions ◽  
Soret Effect ◽  
Critical Conditions ◽  
Heated Plate ◽  
Neutral Stability ◽  
Inclined Plate ◽  
Binary Liquid ◽  
Chebyshev Spectral Collocation ◽  
The Stability

In this thesis we studied the stability of a binary liquid film flowing down a heated porous inclined plate. It is assumed that the heating induces concentration differences in the liquid mixture (Soret effect), which together with the differences in temperature affects the surface tension. A mathematical model is constructed by coupling the Navier- tokes equations governing the flow with equations for the concentration and temperature. The effect of substrate permeability is incorporated by applying a specific slip condition at the bottom of the liquid layer. We carry out a linear stability analysis in order to obtain the critical conditions for the onset of instability. We used a Chebyshev spectral collocation method to obtain numerical solutions to the resulting Orr-Sommerfeld type equations. We also obtained an asymptotic solution which yielded an expression for the state of neutral stability of long perturbations as a function of the parameters controlling the problem. We present our findings by illustrating and interpreting our results for the critical Reynolds number for instability.

scholarly journals Azimuthal magnetorotational instability with super-rotation

2018 ◽  
Vol 84 (1) ◽  
Author(s):  
G. Rüdiger ◽  
M. Schultz ◽  
M. Gellert ◽  
F. Stefani
Keyword(s):  
Reynolds Number ◽  
Prandtl Number ◽  
Numerical Solutions ◽  
Hartmann Number ◽  
Outer Cylinder ◽  
Magnetic Reynolds Number ◽  
Neutral Stability ◽  
Magnetorotational Instability ◽  
Magnetic Prandtl Number ◽  
The Stability

It is demonstrated that the azimuthal magnetorotational instability (AMRI) also works with radially increasing rotation rates contrary to the standard magnetorotational instability for axial fields which requires negative shear. The stability against non-axisymmetric perturbations of a conducting Taylor–Couette flow with positive shear under the influence of a toroidal magnetic field is considered if the background field between the cylinders is current free. For small magnetic Prandtl number $Pm\rightarrow 0$ the curves of neutral stability converge in the (Hartmann number,Reynolds number) plane approximating the stability curve obtained in the inductionless limit $Pm=0$. The numerical solutions for $Pm=0$ indicate the existence of a lower limit of the shear rate. For large $Pm$ the curves scale with the magnetic Reynolds number of the outer cylinder but the flow is always stable for magnetic Prandtl number unity as is typical for double-diffusive instabilities. We are particularly interested to know the minimum Hartmann number for neutral stability. For models with resting or almost resting inner cylinder and with perfectly conducting cylinder material the minimum Hartmann number occurs for a radius ratio of $r_{\text{in}}=0.9$. The corresponding critical Reynolds numbers are smaller than $10^{4}$.

A simulation apparatus for the experimental study of batch reactor control methods

1986 ◽  
Vol 51 (6) ◽  
pp. 1259-1267
Author(s):  
Josef Horák ◽  
Petr Beránek
Keyword(s):  
Experimental Study ◽  
Closed Loop ◽  
Dynamic Properties ◽  
Batch Reactor ◽  
Exothermic Reaction ◽  
Electric Heating ◽  
Batch Reactors ◽  
Exchange Area ◽  
The Stability ◽  
Methods Of Control

A simulation apparatus for the experimental study of the methods of control of batch reactors is devised. In this apparatus, the production of heat by an exothermic reaction is replaced by electric heating controlled by a computer in a closed loop; the reactor is cooled with an external cooler whose dynamic properties can be varied while keeping the heat exchange area constant. The effect of the cooler geometry on its dynamic properties is investigated and the effect of the cooler inertia on the stability and safety of the on-off temperature control in the unstable pseudostationary state is examined.

A numerical study on combined baffles quick-separation device

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ehsan Dehdarinejad ◽  
Morteza Bayareh ◽  
Mahmud Ashrafizaadeh
Keyword(s):  
Turbulent Flows ◽  
Separation Efficiency ◽  
Numerical Study ◽  
Turbulence Models ◽  
Complete Separation ◽  
Solid Particles ◽  
Flow Rates ◽  
Separation Device ◽  
Coupling Technique ◽  
Laminar And Turbulent Flows

Abstract The transfer of particles in laminar and turbulent flows has many applications in combustion systems, biological, environmental, nanotechnology. In the present study, a Combined Baffles Quick-Separation Device (CBQSD) is simulated numerically using the Eulerian-Lagrangian method and different turbulence models of RNG k-ε, k-ω, and RSM for 1–140 μm particles. A two-way coupling technique is employed to solve the particles’ flow. The effect of inlet flow velocity, the diameter of the splitter plane, and solid particles’ flow rate on the separation efficiency of the device is examined. The results demonstrate that the RSM turbulence model provides more appropriate results compared to RNG k-ε and k-ω models. Four thousand two hundred particles with the size distribution of 1–140 µm enter the device and 3820 particles are trapped and 380 particles leave the device. The efficiency for particles with a diameter greater than 28 µm is 100%. The complete separation of 22–28 μm particles occurs for flow rates of 10–23.5 g/s, respectively. The results reveal that the separation efficiency increases by increasing the inlet velocity, the device diameter, and the diameter of the particles.

Sign in / Sign up

Export Citation Format

Share Document