Flow Destabilization Research Articles

Formation mechanism and evolution of flow patterns for thermal convection in an inner cylinder-heated annular pool

In this paper, a set of numerical simulations were carried out to analyze the evolution and formation mechanism of various flow patterns for thermal convection in inner cylinder-heated annular pools at different depths. The results show that the basic flow bifurcates into the second type of hydrothermal waves, standing waves, petal-like structures, and spoke patterns after the flow destabilization. The formation mechanisms of these four flow patterns are all due to the lag in phase between temperature and velocity fluctuations. The reduction in surface azimuthal temperature fluctuation causes the second type of hydrothermal waves to bifurcate into standing waves. The bifurcation from standing waves to petal-like structures is due to the amplitude of azimuthal velocity fluctuation on the free surface being one order of magnitude smaller than that of radial velocity fluctuation. The bifurcation from petal-like structures to spoke patterns is because basic flow varies as the depth rises. Unlike the second type of hydrothermal waves, for standing waves, petal-like structures, and spoke patterns, the temperature fluctuation on different horizontal planes is different. Besides, for standing waves, the periodical variation process of the flow field depends on the azimuthal position.

Flow across a circular cylinder in an inclined channel stabilized by buoyancy

In this study, flow across a circular cylinder confined in an inclined channel is considered, with account taken of mixed convection. Cases with opposing or aiding buoyancy that is not in alignment with the incoming flow are considered, and it is found that the flow around and in the wake of the cylinder is affected. The effects of inclination and buoyancy on the flow and heat transfer patterns are investigated, with a focus on the stabilization and destabilization of flow by these two factors. Simulation results are analyzed with regard to the flow field, lift and drag forces, heat transfer, the deviation of separation and through-flow in the channel, and the temperatures on the channel walls. The flow is more strongly destabilized by an opposing buoyancy, but can be fully stabilized by an aiding buoyancy in an inclined channel. The drag on the cylinder is minimized around a critical Richardson number Ricr. The inclination of the channel has significant effects on the local heat transfer on the cylinder and on the characteristics of the through-flow. The pattern of the wake flow, i.e., whether it is steady or unsteady, affects the heating of the channel walls.

Influence of dispersed phase flow-rate pulsations on the liquid–liquid parallel flow in a T-junction microchannel

Active flow control in microfluidic devices to broaden the range of desired conditions is a significant practical concern. In this study, we experimentally investigate liquid–liquid parallel flow under the dispersed phase flow-rate pulsations in a T-junction microchannel. Sinusoidal flow rate disturbances with variations in amplitude and period were applied to dispersed phases of different viscosities. The study involves flow visualization and velocity field measurements using the micro-PIV technique for both free and excited flow conditions. The analysis of flow pattern maps, velocity fields, velocity gradients, and phase-averaged velocity profiles in a T-junction region and far downstream provided insights into the evolution of disturbances, which is different in low- and high-viscosity liquids. In the less viscous liquid, transverse waves amplify longitudinal ones due to relaxation of the liquid–liquid interface, while in the high-viscosity dispersed phase, longitudinal waves are damped significantly, with the transverse wave amplitude remaining almost constant. As a result, we revealed two distinct mechanisms of disturbance wave propagation and the loss of parallel flow stability, which are both dependent on the Ohnesorge number of the dispersed phase. Destabilization of the parallel flow led to the formation of plugs with a narrow length distribution. Single-mode, double-mode, triple-mode, and multi-mode plug formation regimes were identified. The results of the study can potentially be used to extend the range of segmented flow regimes and generate plugs of a desired length.

Linear stability of viscoplastic flows down an incline

The stability analysis of viscoplastic flows down an inclined plane is done by comparing results obtained through theoretical and numerical studies of “regularized” models. The theoretical analysis is performed for Regularized Bingham and Casson-like fluids via the long-wave approximation method. In particular, the Bingham and the Casson flow have different stability characteristics, for Bingham-type materials an increase in yield stress leads to flow destabilization, while Casson-type materials show the opposite behaviour. The numerical study is performed by using the Papanastasiou and the “exact” Bingham model via a spectral method. The comparison between theoretical and numerical results shows excellent agreement. Our findings highlight that “regularized” and “exact” flow and can have stability characteristics, although they are “practically indistinguishable”. We validate our approach with the Regularized Bingham-like model, which is in rather satisfactory agreement with the experimental data.

Decoding the Dynamics of Climate Change Impact: Temporal Patterns of Surface Warming and Melting on the Nivlisen Ice Shelf, Dronning Maud Land, East Antarctica

This study analyzes the dynamics of surface melting in Antarctica, which are crucial for understanding glacier and ice sheet behavior and monitoring polar climate change. Specifically, we focus on the Nivlisen ice shelf in East Antarctica, examining melt ponds, supra glacial lakes (SGLs), seasonal surface melt extent, and surface ice flow velocity. Spatial and temporal analysis is based on Landsat and Sentinel-1 data from the austral summers of 2000 to 2023. Between 2000 and 2014, melt ponds and SGLs on the ice shelf covered roughly 1 km2. However, from 2015 to 2023, surface melting increased consistently, leading to more extensive melt ponds and SGLs. Significant SGL depths were observed in 2016, 2017, 2019, and 2020, with 2008, 2016, and 2020 showing the highest volumes and progressive SGL area growth. We also examined the relationship between seasonal surface melt extent and ice flow velocity. Validation efforts involved ground truth data from a melt pond in central Dronning Maud Land (cDML) during the 2022–2023 austral summer, along with model-based results. The observed increase in melt pond depth and volume may significantly impact ice shelf stability, potentially accelerating ice flow and ice shelf destabilization. Continuous monitoring is essential for accurately assessing climate change’s ongoing impact on Antarctic ice shelves.

Analysis of factors affecting destabilization of a viscous liquid flow in channels

An analysis of the influence of inertia forces and ponderomotive forces on the destabilization of the flow of viscous fluids in the hydrodynamic initial section is given. Cases of flow of viscous, anomalously viscous and electrically conductive liquids are considered; the degree of influence of mass forces on the destabilization of the flow is estimated. As applied to the flow in the hydrodynamic initial section, the degree of influence of inertia forces from convective acceleration and forces with a magnetic nature can be different. Inertia forces stimulate the accelerated movement of the fluid, and in the case of forces with a magnetic nature, ponderomotive forces contribute to deceleration, which is confirmed by the results of studies of the velocity field. Recommendations are given for calculating the length of the hydrodynamic initial section in the presence of mass forces with different nature.

Instability of liquid film with odd viscosity and slip effect under the action of external electric field

The influence of odd viscosity on the instability of a liquid film flowing along a porous inclined plane under a normal electric field is investigated. It is assumed that the flow at the porous inclined plane satisfies the Beavers–Joseph slip boundary condition. By utilizing the long-wave approximation and employing the method of systematic asymptotic expansion, a nonlinear evolution equation for the film thickness under the influence of the electric field is derived. The stability analysis of this evolution equation reveals that the odd viscosity of the film has a stabilizing effect, while the electric field has a destabilizing effect. Additionally, the permeability of the porous inclined plane enhances the instability of the liquid film flow. Numerical simulations are conducted using a fast Fourier transform algorithm to solve the nonlinear evolution equations. The numerical results demonstrate that, within the stable region and with all parameters fixed, the wave amplitude decreases as the evolution time increases, indicating a gradual stabilization of the liquid film flow. Conversely, in the unstable region, the opposite behavior is observed. As the evolution time increases, the fluctuation amplitude grows larger, resulting in a gradual destabilization of the liquid film flow. Furthermore, when the evolution time is kept constant and the odd viscosity coefficient is nonzero, the film exhibits greater stability. The amplitude of the wave increases with the electrical parameter E. In the unstable region, an increase in the permeability β of the porous medium leads to a tendency for the film flow to stabilize.

General relationships of dimensionless parameters for thermocapillary-buoyancy flow in side-heated annular pools

It is well-known that thermocapillary-buoyancy flow instability can be affected by several dimensionless control parameters. The general relationships among them are helpful for actively controlling flow instability but were not clear. This work reported some experiments in the annular pool with a radius ratio of 0.25, and proposed the general relationships among these dimensionless control parameters, especially for the critical Marangoni number of the flow destabilization and the dimensionless oscillatory frequency of pulsating pattern. Combined with previous studies, these general relationships are achieved within no more than 15% relative deviations, whose applicability is for the thermocapillary-buoyancy flow of medium Prandtl number fluids in side-heated annular pools. Based on the experimental findings, we can confirm that the flow destabilization can be suppressed by buoyancy. The steady multicellular flow appears before flow destabilization. When the flow is destabilized, the pulsating pattern first appears, and then a superimposition of the pulsating pattern and the flower-like wave.

MHD flow properties due to a porous rotating disk in a mixed convective fluid flow with buoyancy and radiation

The importance and differs applications of Magnetohydrodynamics, MHD and mixed convective flow through a porous medium has led to investigation of buoyancy force and thermal radiation on the flow. The modeled ordinary differential equations were transformed by means of similarity transformation into partial differential equations. The resulting equations were solved using Nachtsheim–Swigert iteration technique. The obtained results were conformed to existing ones, and displayed on tables and through graphs. In conclusion the investigated parameters have significant effects on the flow. Close to the boundary positive values of y is found to give rise to the familiar inflection point profile leading to the destabilization of the laminar flow. Strong injection also leads to the similar destabilization effect. Also, hall parameter m has an interesting effect on the radial and axial velocity profiles. For large values of m(>2.0), the resistive effects of the magnetic field are diminished and hence the radial and axial velocity profiles decrease with the increase of m, among others.

Stability of a Regularized Casson Flow down an Incline: Comparison with the Bingham Case

In this paper, we study the two-dimensional linear stability of a regularized Casson fluid (i.e., a fluid whose constitutive equation is a regularization of the Casson obtained through the introduction of a smoothing parameter) flowing down an incline. The stability analysis has been performed theoretically by using the long-wave approximation method. The critical Reynolds number at which the instability arises depends on the material parameters, on the tilt angle as well as on the prescribed inlet discharge. In particular, the results show that the regularized Casson flow has stability characteristics different from the regularized Bingham. Indeed, for the regularized Casson flow an increase in the yield stress of the fluid induces a stabilizing effect, while for the Bingham case an increase in the yield stress entails flow destabilization.

Stokes layers in oscillatory flows of viscoelastic fluids

<h2>Abstract</h2> Oscillatory fluid flows play an important role in industrial problems such as pumping, drilling, and oil recovery, and in physiological processes such as mucous flow in respiration and blood pumping. A key concept in oscillatory flows is the Stokes layer, i.e. the region of fluid adjacent to a wall that is in motion as a result of the wall oscillatory motion along its own plane. In this talk we will discuss oscillatory flows of viscoelastic fluids from the perspective of Stokes viscoelastic layers. We will first revisit Stokes' second problem for a viscoelastic fluid modelled by a single-mode Maxwell constitutive equation, and the generation of viscoelastic shear waves. Next, we will turn the attention to wall-bounded zero-mean oscillatory flows, for which we will identify the governing dimensionless variables and discuss the presence of resonances in the one-dimensional base flow. Finally, we will present experimental evidence of the destabilization of the one-dimensional base flow for a wormlike micellar solution in a cylindrical pipe as the oscillatory forcing increases, and sketch a perturbative analysis based on the Giesekus constitutive equation that links the first instability of the base flow to the divergence of normal radial stresses. If there is enough time, we will also present recent experimental results of oscillatory pipe flow of shear-thinning non-elastic solutions.

Energy transfer mechanism during ethanol evaporation with external tangential temperature gradient under low pressure environment

For the purpose of revealing the energy-transfer process during ethanol evaporation under low pressure environment, experimental measurement and numerical simulation are adopted for ethanol evaporation at different liquid depths and external radial temperature differences in annular pools. The results show that two thermocapillary vortexes appear below the liquid–vapor interface. Most of the latent heat of vaporization is from the liquid phase, but little from the gas phase. With the increase of liquid layer depth, the steady axisymmetric flow will transform into three-dimensional time-dependent convection. The mechanism of flow instability should be attributed to the variation lag of velocity behind the variation of flow resistance. The critical vapor pressure of flow destabilization depends on radial temperature difference and liquid layer depth. Furthermore, the magnitude of temperature discontinuity across the liquid–vapor interface is the largest near the hot inner cylinder. With the increase of the liquid layer depth, the temperature discontinuity decreases.

Impact of Channels Aspect Ratio on the Heat Transfer in Finned Heat Sinks with Tip Clearance.

A 3D numerical study is used to analyze the flow topology and performance, in terms of heat transfer efficiency and required pumping power, of heat sink devices with different channel aspect-ratio in the presence of tip-clearance. Seven different channel aspect ratios , from 0.25 to 1.75, were analyzed. The flow Reynolds numbers , based on the average velocity evaluated in the device channels region, were in the range of 200 to 1000. Two different behaviors of the global Nusselt were obtained depending on the flow Reynolds number: for , the heat transfer increased with the channels aspect ratio, e.g., for , the global Nusselt number increased by 14% for configuration when compared to configuration . For , the maximum Nusselt is obtained for the squared-channel configuration, and, for some configurations, flow destabilization to a unsteady regime appeared. For , Nusselt number reduced when compared with the squared-channel device, 11% and 2% for configurations with and 1.75, respectively. Dimensionless pressure drop decreased with the aspect ratio for all cases. In the context of micro-devices, where the Reynolds number is small, these results indicate that the use of channels with high aspect-ratios is more beneficial, both in terms of thermal and dynamic efficiency.

Novel transonic nozzle for Ranque-Hilsch vortex tube

The process of the vortex flow formation in the Ranque-Hilsch vortex tube is studied. Starting from deficiencies of the existing vortex tubes, a novel type for the transonic nozzle is suggested and designed. The proposed nozzle is different from the existing classical ones by the presence of additional supersonic section placed after the blades. This section creates controlled conditions for acceleration of the vortex flow to supersonic speed. Analysis of the gas flow in the transonic nozzle using 3D RANS simulations showed that slightly improper selection of nozzle dimensions may lead to destabilization of the vortex flow and deterioration of the vortex tube performance. Simplified semi-one-dimensional model of swirling gas flow was derived and utilized for correction of the nozzle dimensions in order to stabilize the flow. Detailed validation of this model against full 3D RANS simulations demonstrated its applicability for preliminary engineering computations. It was demonstrated that application of the novel transonic nozzle extends the region in the energy separation chamber occupied by the supersonic vortex. This results in increase of both temperature separation effect and vortex tube energy efficiency. Main advantages and disadvantages of the novel transonic nozzle are summarized in the concluding section.

Flow transition in periodically fully developed wavy channels

In the present study, numerical investigations have been performed to study the flow transition mechanism in wavy channels using finite volume-based open source field operation and manipulation. Two different wavy channel configurations are chosen, which represent two different flow destabilization mechanisms, viz., Kelvin–Helmholtz and centrifugal instabilities. Sinusoidal walls with out-of-phase and in-phase channel configurations have been considered in the present study. Steady to chaotic flow transition in two different channel configurations are investigated by varying Reynolds number. A detailed flow regime map is presented for the two different wavy channel configurations. Unsteady flow features have been illustrated with the help of instantaneous streamlines, velocity contours, vorticity contours, and iso-Q surfaces. For the out-of-phase configuration, the flow changes from two-dimensional steady to two-dimensional unsteady in the Re range of 175–185, and then three-dimensional unsteady flow is observed for the Re varying from 250 to 260. On the contrary, for the in-phase configuration, the transition happens directly from steady two-dimensional flow (Re &amp;lt; 101) to unsteady three-dimensional (Re &amp;gt; 102) in a very narrow range of Re. Transitions in the two different wavy channels have been examined in detail using Hilbert–Huang transformation, phase-space reconstruction, Poincaré section, recurrence plot, and dynamic mode decomposition. Frequency, growth rate, and vortex structures of the dominant modes are illustrated corresponding to each value of Re for the considered channel configurations.

Effect of surface curvature on destabilization and unsteadiness of low-Re flow across two tandem elliptic cylinders

This work performed a direct simulation investigation on two-dimensional flow across two tandem elliptic cylinders at Re = 100. The cylinders are placed with a center-to-center distance D/ d = 2-10 where d is the diameter, and the minor-to-major axis ratio, denoted as aspect ratio AR, varies as AR = 0.25-1.00. The objective of this study is to quantitatively identify the effect of surface curvature of the cylinders, as represented by AR, and the separating distance on the destabilization and unsteadiness of flow. Numerical results reveal that the local surface curvature at the ends of major axis of the cylinder has substantial influence on the separation and detachment of boundary layer flow on the leeward side of the upstream cylinder, determines the characteristics of gap flow, perturbs the flow around the downstream cylinder, and finally produces various patterns of wake flow. As AR increases, the gap flow tends to be stabilized for small separating distance and even quasi-steady flow for the AR = 0.75 and 1.00 cylinders at D/ d = 2; the wake flow after the downstream cylinder also gets less unstable and only sheds in the far-wake region. The non-uniformity of time-averaged pressure coefficient around the downstream cylinder is reduced but the fluctuating amplitude increases, while the flow around the upstream cylinder is quite close to that of the single cylinder case.

Flow destabilization and nonlinear solutions in low aspect ratio, corrugated duct flows

Flows through narrow, rectangular ducts, with width to height aspect ratio below the established linear stability threshold of 3.2 and modified with grooves on top and bottom walls, are investigated. The primary objective of the current work lies in reintroduction of the linear destabilization mechanism, which is not present for the case of low aspect ratio rectangular ducts, via geometrical modifications of boundaries. The flow is assumed periodic in the streamwise- and bounded by sidewalls in the spanwise-direction. Applied geometrical modifications consist of two wavelengths of sinusoidal grooves running parallel to the flow direction. The current analysis starts with a brief characterization of flows through rectangular ducts and recalls some canonical results on hydrodynamic stability in such flows. In the second part, we illustrate that grooved geometries may lead to the onset of unstable modes in the form of waves traveling downstream, in the case of narrow ducts, already at relatively low values of the Reynolds number. The work is concluded with a concise characterization of flow states resulting from amplification of unstable modes into the nonlinear regime.

Rayleigh-Bénard convection of a gas-vapor mixture with abnormal dependence of thermal expansion coefficient on temperature

In order to reveal basic characteristics of Rayleigh-Bénard convection (RBC) of a gas mixture, which has abnormal dependence of thermal expansion coefficient on temperature, we presented a direct numerical simulation on RBC of a gas mixture of oxygen and cyclohexane near its maximum density. The influences of the density inversion parameter and the Rayleigh (Ra) number on the critical conditions of the flow onset and destabilization were analyzed. The flow evolution with Ra was exhibited. The results show the critical value of Rayleigh number of the flow onset is approximately proportional to the fourth power of the thickness of the upper stable sublayer. Regardless of density inversion parameter, the flow pattern at the flow appearance always has a multicellular structure. With increasing Ra, the multicellular flow structure would be transformed into various steady flow patterns, including parallel flow and pendant pattern. When the density inversion parameter is small, the unsteady flow cells exhibit a back and forth motion along the border. However, at a large density inversion parameter, the cells swing around the centers of the flow rolls. We also found that the local Nusselt (Nu) number on the bottom depends on the flow pattern. The average Nu increases gradually with increasing Ra under a small density inversion parameter. However, an abrupt rise of the average Nu appeared under a large density inversion parameter.

Determination of groove shape with strong destabilization and low hydraulic drag

Flow through a channel equipped with plane, longitudinal grooves is investigated. We focus on determining changes to the flow dynamics due to applied wall manipulations, especially the possibility of drag-reduction, potential for hydrodynamic destabilization and onset of secondary, nonlinear flow solutions. Considered patterns of geometrical manipulation consist of plane walled grooves of triangular, variations of trapezoidal and up to rectangular shapes and are compared with existing results obtained for channels with sinusoidal corrugations. We show that there exists a strong connection in the response of the flow system to the applied pattern of grooves with the leading Fourier component of the wall pattern. The analysis starts with undisturbed, two-dimensional flows investigated with the focus on hydraulic resistance for wide range of geometric parameters. Secondly, critical conditions for the onset of travelling wave instability are determined and compared with existing results. Thirdly, nonlinear flow solutions, obtained for flows through the geometry with lowest destabilization threshold are analyzed at supercritical conditions. Finally quantification of the diffusive transport intensification due to the kinematics of the nonlinear flow solution is attempted. It is shown that, irrespective of the groove shape, longitudinal wall patterns result in flow destabilization due to traveling wave mode already at very low values of the Reynolds number (<102). At the same time such configurations can be energy efficient since overall drag is marginally increased (or in fact reduced) and at the same time diffusive processes are intensified leading to improved mixing. Implications of this study might help in development of small-scale flow devices operating at low and moderate ranges of Reynolds number with the purpose of intensifying mixing, heat transfer or reaction of chemical or biological compounds.

The Role of Curvature in Modifying Frontal Instabilities. Part II: Application of the Criterion to Curved Density Fronts at Low Richardson Numbers

AbstractWe continue our study of the role of curvature in modifying frontal stability. In Part I, we obtained an instability criterion valid for curved fronts and vortices in gradient wind balance (GWB): Φ′ = L′q′ &lt; 0, where L′ and q′ are the nondimensional absolute angular momentum and Ertel potential vorticity (PV), respectively. In Part II, we investigate this criterion in a parameter space representative of low-Richardson-number fronts and vortices in GWB. An interesting outcome is that, for Richardson numbers near 1, anticyclonic flows increase in q′, while cyclonic flows decrease in q′, tending to stabilize anticyclonic and destabilize cyclonic flow. Although stability is marginal or weak for anticyclonic flow (owing to multiplication by L′), the destabilization of cyclonic flow is pronounced, and may help to explain an observed asymmetry in the distribution of small-scale, coherent vortices in the ocean interior. We are referring to midlatitude submesoscale and polar mesoscale vortices that are generated by friction and/or buoyancy forcing within boundary layers but that are often documented outside these layers. A comparison is made between several documented vortices and predicted stability maps, providing support for the proposed mechanism. A simple expression, which is a root of the stability discriminant Φ′, explains the observed asymmetry in the distribution of vorticity. In conclusion, the generalized criterion is consistent with theory, observations, and recent modeling studies and demonstrates that curvature in low-stratified environments can destabilize cyclonic and stabilize anticyclonic fronts and vortices to symmetric instability. The results may have implications for Earth system models.