Onset Of Hydrodynamic Instability Research Articles

Slowing down convective instabilities in corrugated Couette–Poiseuille flow

Couette–Poiseuille (CP) flow in the presence of longitudinal grooves is studied by means of numerical analysis. The flow is actuated by movement of the flat wall and pressure imposed in the opposite direction. The stationary wall features longitudinal grooves that modify the flow, change hydrodynamic drag on the driving wall and cause onset of hydrodynamic instability in the form of travelling waves with a consequent supercritical bifurcation, already at moderate ranges of the Reynolds number. We show that by manipulating this system it is possible to significantly decrease phase speed of the unstable wave and to effectively decouple time scales of wave propagation and amplification with a potential to significantly reduce the distance required for the onset of nonlinear effects. Current analysis begins with concise characterization of stationary, laminar CP flow and the effects of applying a selected corrugation pattern, followed by determination of conditions leading to the onset of instabilities. In the second part we illustrate selected nonlinear solutions obtained for low, supercritical values of the Reynolds numbers and due to the amplification of unstable travelling waves of possibly low phase velocities. This work is concluded with a short discussion of a linear evolution of a wave packet consisting of a superposition of a number of unstable waves and initiated by a localized pulse. This part illustrates that in addition to the reduction of the phase velocity of a single, unstable mode, imposition of the Couette component also reduces group velocity of a wave packet.

Influence of surface properties on the dynamics of fluid flow

In this paper, we study how the fluid flow near the surface of a monocrystalline body is affected by the surface properties due to atom-surface scattering. We propose a toy model for this system by parameterizing the surface with a periodic function of the tangential position. This allows us to derive the velocity probability density function in the Knudsen layer and determine statistical averages of fluid velocity and stress tensor components in the region of interest. The results of this analysis provide a potentially more fundamental and accurate explanation for empirically observed phenomena such as the no-slip boundary condition, boundary layer formation, and the onset of hydrodynamic instability.

On the Onset of Hydrodynamic Instability with Convective Heat Transfer Through a Rotating Curved Rectangular Duct

On the Onset of Hydrodynamic Instability with Convective Heat Transfer Through a Rotating Curved Rectangular Duct

Cathodic contact glow discharge electrolysis: its origin and non-faradaic chemical effects

Normal electrolysis (NE), at sufficiently high voltages, breaks down and undergoes a transition to a phenomenon called contact glow discharge electrolysis (CGDE) in which a sheath of glow discharge plasma encapsulates one of the electrodes, the anode or the cathode. The chemical effects of CGDE are highly non-faradaic e.g. a mixture of H2 and H2O2 plus O2 each in excess of the Faraday law value is liberated at the glow discharge plasma electrode from an aqueous electrolyte solution. Studies of cathodic CGDE, particularly its origin and chemical effects, in comparison to those of anodic CGDE have received significantly less attention and have not been studied in detail. The present paper is an attempt towards elucidation of the mechanisms of the growth of cathodic CGDE during NE and its non-faradaic chemical effects. The findings of the study have led to the inference that emission of secondary electrons from the metal cathode with sufficient kinetic energies, vaporization of the electrolyte solvent in the vicinity of the cathode surface induced by Joule heating and the onset of hydrodynamic instabilities in local vaporization contribute to the generation of the plasma at the cathode during NE. The findings have further shown that non-faradaic yields of CGDE at the cathode originate from energy transfer processes in two reaction zones: a plasma phase reaction zone around the cathode which accounts for ~75% of the yields, and a liquid phase reaction zone near the plasma-catholyte solution interface accounting for the remaining ~25% of the yields.

Propagation of wrinkled turbulent flames in the context of hydrodynamic theory

We study the propagation of premixed flames in two-dimensional homogeneous isotropic turbulence using a Navier–Stokes/front-capturing methodology within the context of hydrodynamic theory. The flame is treated as a thin layer separating burnt and unburnt gases, of vanishingly small thickness, smaller than the smallest fluid scales. The method is thus suitable to investigate the flame propagation in the wrinkled flamelet regime of turbulent combustion. A flow-control system regulates the mean position of the flame and the incident turbulence intensity. In this context we study the individual effects of turbulence intensity, turbulence scale, thermal expansion, hydrodynamic strain and hydrodynamic instability on the propagation characteristics of the flame. Results are obtained assuming positive Markstein length, corresponding to lean hydrocarbon–air or rich hydrogen–air mixtures. For stable planar flames we find a quadratic dependence of turbulent speed on turbulence intensity. Upon onset of hydrodynamic instability, corrugated structures replace the planar conformation and we observe a greater resilience to turbulence, the quadratic scaling being replaced by scaling exponents less than one. Such resilience is also confirmed by the observation of a threshold turbulence intensity below which the propagation speed of corrugated flames is indistinguishable from the laminar speed. Turbulent speed is found to increase and later plateau with increasing thermal expansion, this affecting the average flame displacement but not the mean flame curvature. In addition, turbulence integral scale is also observed to affect the propagation of the flame with the existence of an intermediate scale maximizing the turbulent speed. This maximizing scale is smaller for corrugated flames than it is for planar flames, implying that small eddies that will be unable to significantly perturb a planar front could be rather effective in perturbing a corrugated flame. Turbulent planar flames, and more so corrugated flames, were observed to experience a positive mean hydrodynamic strain, which was explained in terms of the overwhelming mean contribution of the normal component of strain. The positive straining causes a decrease in the mean laminar propagation speed which in turn can decrease the turbulent speed. The effect of the flame on the incident turbulent field was examined in terms of loss of isotropy and vorticity destruction by thermal expansion. The latter can be mitigated by a baroclinic vorticity generation which is enhanced for corrugated flames.

Stability of vortex flow in a modulated channel

Linear stability analysis of a fully developed two-dimensional periodic steady flow in a spatially modulated symmetric channel is investigated numerically. Both walls are sinusoidally modulated. The modulation amplitude is assumed to be small. The base steady flow is calculated using a regular perturbation expansion of the flow field coupled to a variable-step finite-difference scheme. The disturbance flow equations are derived within the framework of Floquet theory and solved using a two-point boundary value method. The implemented procedure is simple, direct, and very efficient. The accuracy of this method is established. The influence of geometric parameters on the threshold for the onset of instability is systematically investigated. It is established that the critical Reynolds number for the onset of hydrodynamic instability decreases as the wall modulation amplitude or wave number increases. Modulated channel flow is characterized by the formation of a recirculation region or vortices beneath the modulation crest as the Reynolds number exceeds a certain critical threshold. The relation between the thresholds for the onset of instability and vortex flow is examined over a wide range of geometric parameters. Vortex flow effects on the conditions for the onset of instability are systematically investigated. The parameter regime of stable vortex flow is established. It is found that the parameter regime of stable vortex flow increases significantly with the wall modulation wave number for small wave numbers. This increase become less pronounced as the wave number is further increased.

Study of hydrodynamic instabilities of a Z-pinch during a high-current explosion of a thin wire

Results are presented from laboratory and numerical experiments on the influence of the core and associated hydrodynamic instabilities on the high-current implosion of a plasma of exploding metal wires. The experimental investigation of the discharge structure was carried out using the multiframe X-ray backlighting technique with high temporal and spatial resolution (<1 ns and 1 µm, respectively); X-pinches were used as small-sized radiation sources. The implosion of a dense Z-pinch was modeled by the free-point method with the use of a two-dimensional radiative MHD code. The onset of instabilities at the corona-core boundary was modeled by the NUTCY Eulerian code. The results show that hydrodynamic processes in the core are primarily responsible for the formation of small bright regions observed in X-rays. After the reflection of a shock wave from the axis, the rapid onset of hydrodynamic instabilities can occur at the corona-core boundary.

Contact glow discharge electrolysis: a study on its origin in the light of the theory of hydrodynamic instabilities in local solvent vaporisation by Joule heating during electrolysis

Normal electrolysis at high voltages switches over spontaneously to contact glow discharge electrolysis. The transition is profoundly facilitated by raising the temperature and/or lowering the surface tension of the electrolyte. Results of a systematic study on the influence of these two factors on the breakdown voltage for normal electrolysis have been critically analysed. It has been concluded that solvent vaporisation near an electrode by Joule heating during electrolysis and the onset of hydrodynamic instabilities in local solvent vaporisation are the prime causes for the breakdown of normal electrolysis.

An extended theory to predict the onset of viscous instabilities for miscible displacements in porous media

Many enhanced oil recovery schemes involve the displacement of oil by a miscible fluid. Whether a displacement is stable or unstable has a profound effect on how efficiently a solvent displaces oil within a reservoir. That is, if viscous fingers are present, the displacement efficiency and, hence, the economic return of the recovery scheme is seriously impaired bacause of macroscopic bypassing of the oil. As a consequence, it is of interest to be able to predict the boundary which separates stable displacements from those which are unstable. This paper presents a dimensionless scaling group for predicting the onset of hydrodynamic instability of a miscible displacement in porous media. An existing linear perturbation analysis was extended in order to obtain the scaling group. The new scaling group differs from those obtained in previous studies because it takes into account a variable unperturbed concentration profile, both transverse dimensions of the porous medium, and both the longitudinal and the transverse dispersion coefficient. It has been shown that stability criteria derived in the literature are special cases of the general condition given here. Therefore, the stability criterion obtained in this study should be used for a displacement conducted under arbitrary conditions. The stability criterion is verified by comparing it with miscible displacement experiments carried out in a Hele-Shaw cell. Moreover, a comparison of the theory with some porous medium experiments from the literature also supports the validity of the theory.

Effect Of Length On Unstable Miscible Displacements

Abstract Many secondary recovery schemes involve the displacement of oil by a miscible fluid. The success of such schemes depends. to a large extent, on whether the displacement is stable or not. Thus, it is important to be able to predict the boundary at which a displacement becomes unstable. In this paper, a dimensionless scaling group and its critical value for predicting the onset of instability during a miscible displacement in porous medium is derived. The perturbation equations used in the derivation are obtained by employing a small perturbations analysis and are solved using a variational technique. As a consequence, it is possible, for the first time, to infer explicitly the effect that the length of a porous medium has on the instability of a miscible displacement. It is demonstrated that in short laboratory systems, the length has an important effect and it should be taken into account. However, under field conditions, the analyses which consider the porous medium as being infinitely long can be used. The theory developed is used to predict the onset of instability in miscible Hele-Shaw cell displacements. It is shown that the dimensionless scaling group successfully predicts the instability boundary. Moreover, experimental observations indicate that although a displacement initially can be stable, it may become unstable as the interface travels through the system. This, as well, agrees with the theory. Introduction Immiscible secondary recovery methods, even when successful, may leave significant amounts of oil in the reservoir due to the presence of capillary forces which are responsible for the entrapment of the oil. Thus, miscible secondary recovery processes, in theory, are considered to be very efficient because they eliminate capillary forces. However, in practically all miscible displacement tests, the displacing fluid (solvent) is less viscous than the crude oil and, as a result, the displacement front becomes unstable and viscous fingers of the displacing fluid penetrate into the crude oil. Thus, in practice, early breakthrough of the solvent and poor sweep efficiencies are encountered due to the phenomenon of viscous fingering(1–4). Therefore, the success of miscible secondary schemes depends on whether the displacement is stable or unstable. The need to predict the onset of hydrodynamic instability in miscible displacements had led a number of investigators to undertake a stability analysis(5–14). All of these analyses are based on the small perturbations method. The perturbation equations which are obtained in a perturbation type analysis are nonlinear and the analytical solution of them poses problems. Therefore, it is common to linearize the perturbation equations. The time dependence of the perturbations is obtained by expressing an arbitrary disturbance as a superposition of certain basic modes and examining the stability of the system with respect to each of these modes. Because the equations used in the stability analysis have been linearized, only the onset of instability can be predicted. That is, the behaviour of the system, nce it becomes unstable, cannot be evaluated.

Wind‐driven spin‐up in eddy‐resolving ocean models formulated in isopycnic and isobaric coordinates

Wind‐driven spin‐up of the four‐layer, quasi‐isopycnic, eddy‐resolving primitive equation model of Bleck and Boudra (1981) is compared with that obtained with a (numerically dissimilar) “pure” isopycnic coordinate model and an isobaric (i.e., quasi‐Cartesian) coordinate model. In particular, the onset of hydrodynamic instabilities in the flow forced by a double‐gyre wind stress pattern is studied. The spin‐up processes associated with the isopycnic and quasi‐isopycnic model are found to be similar, whereas the flow pattern produced by the quasi‐Cartesian model deviates in the direction of Holland's (1978) and Holland and Lin's (1975a, b) two‐layer solutions.

Nonequilibrium Theory of Fluid Fluctuations

A generalization of previously existing theories of fluctuations in dilute monotonic gases is obtained which describes nonequilibrium states with spatial gradients. A kinetic description of the fluctuations is first derived, and the reduction to the fluid limit is then carried out. The theory can be used to describe the enhanced fluctuations which are expected to occur near the onset of hydrodynamic instabilities.