Mechanism Of Flow Instability Research Articles

Instability investigation of creeping viscoelastic flows between the rotating cylinders

In this paper, instability in the creeping viscoelastic flow between the rotating cylinders is investigated numerically. Due to the low speed of flow field, the second order fluid (SOF) model is used as the constitutive equation and the governing equations are solved by a second order finite difference method based on the artificial compressibility algorithm in a staggered mesh. The effects of normal stress differences on the flow stability are investigated for a wide range of gap ratios. Unlike the previous studies, the origin and mechanism of flow instability resulted from normal stress differences are investigated in detail. Numerical results indicate that the hoop stress and radial-normal stress components are appeared in viscoelastic flows between the rotating cylinders and they have an important role on the flow stability.

Characterization of hot processing parameters of powder metallurgy TiAl-based alloy based on the activation energy map and processing map

Abstract The hot deformation behavior of powder metallurgy Ti–47Al–2Nb–2Cr alloy was studied by using the activation energy map and processing map in this work. The isothermal compression tests were performed over a range of temperatures 950–1200 °C and strain rates 0.001–0.1 s − 1 on a Gleeble-1500D hot working simulator. The hot working flow behavior and softening of flow stress were discussed. The variation of calculated Q value with hot processing parameters has been presented, it was found that the Q value increases with increasing temperature and strain rate on the whole. Based on the constructed processing maps, the optimal hot processing window of this alloy corresponds to the temperature range of 1025–1075 °C and the low strain rate of 0.001–0.004 s − 1 , with a peak efficiency of 55% at 1050 °C/0.001 s − 1 . Meanwhile, the instability maps were developed with the help of the comparison between Murty and Prasad instability criteria. The instability domain that should be kept away is located at high strain and strain rate higher than 0.01 s − 1 for the whole deformation temperature. Both of the optimal process conditions and the predominant flow instability mechanism of PM TiAl-based alloy were validated by microstructure observation involving DRX refined microstructure and cracking, respectively.

Steam-water flow in geothermal wells

A mathematical model was developed for calculation of steam-water flow in a geothermal well for the feeding interval. The model assumes a variable mass flow rate over the channel length. The basis for this model are the flow continuity equation, momentum and energy conservation equations, taken with account for variable mass flow. The model was implemented as a computer code suitable for calculation of flow parameters upstream (downward the top level of the feeding zone). Then this model was applied for wells in the Mutnovskii geothermal field, this revealed a geyser-type mechanism of flow instabilities with the pressure oscillation period about ten minutes. The remedy for these oscillations was offered.

Numerical investigation of the mechanism of two-phase flow instability in parallel narrow channels

In this paper, the mechanism of two-phase flow instability in parallel narrow channels is studied theoretically, and the characteristic of the flow instability is discussed in detail. Due to the significant confining effect of the narrow channel on the vapor–liquid interface, the two-phase flow resistance in the narrow channel is probably different from that in conventional channel. Therefore, the vapor confined number (Nconf), defined by the size of narrow channel and bubble detachment diameter, is considered in the “Chisholm B model” to investigate the two-phase flow pressure drop. The flow instability boundaries are plotted in parameter plane with phase-change-number (Npch) and subcooling-number (Nsub) under different working conditions. It is found that the predicted result agrees well with the experimental result. According to the predicted result, the oscillation behaviors near the flow instability boundary indicate that the Supercritical Hopf bifurcation appears in high sub-cooled region and the Subcritical Hopf bifurcation appears in low sub-cooled region. Also, a detailed analysis about the effects of key parameters on the characteristic of two-phase flow instability and the flow instability boundary is proposed, including the effects of inlet subcooling, heating power, void distribution parameter and drift velocity.

On Global Linear Instability Mechanisms of Flow Around Airfoils at Low Reynolds Number and High Angle of Attack

The existence of modal and non-modal linear three-dimensional global instabilities of spanwise-homogeneous low-Reynolds number laminar incompressible flow around two-dimensional airfoils is documented. Work has commenced to examine the relative significance of such instabilities as a function of airfoil thickness and camber at conditions close to stall: the symmetric NACA0009 and NACA0015 airfoils as well as the cambered NACA4415 are used for these analyses at angles of attack 15 ≤ AoA ≤ 20. At all conditions examined, the combination of the Re and AoA parameters is chosen such that steady two-dimensional flow over the airfoil is obtained. Four independent codes, one based on finite-volume, one on finite-element and two on spectral-element spatial discretization have been used to cross-validate the base flow and instability analysis results presented, all delivering consistent pre- dictions. In line with previous findings on the NACA0015 airfoil, two classes of three-dimensional stationary and traveling global eigenmodes are recovered. Contrary to what was previously reported, the traveling wake-mode instability dominates that pertain- ing to the stationary three-dimensional flow eigenmode. Furthermore, neither traveling nor stationary unstable three-dimensional modes have been found in the NACA0015 airfoil, prior to the two-dimensional wake mode undergoing a Hopf bifurcation. Conse- quently, amplified three-dimensional structures akin to the stall cells reported in earlier work have not been observed in the present analyses. Finally, relatively strong transient energy growth is shown here for the first time for flows around airfoils, as known from earlier analyses of flow around bluff bodies. In the context of non-modal instability too, strongest energy amplification is found to be associated with the two-dimensional flow and converts, via the Orr mechanism, optimal initial conditions to wake-mode perturbations.

Hot deformation behavior and processing maps of fine-grained SiCp/AZ91 composite

Hot deformation behavior of fine-grained SiCp/AZ91 composite was investigated at the temperature of 543–693K and strain rate of 0.001–1s−1. Processing maps based on dynamic material model (DMM) were developed at the strain of 0.1–0.5. Both the optimum process conditions and the dominant flow instability mechanism of fine-grained SiCp/AZ91 composite were given and analyzed. To describe the hot deformation behavior of fine-grained SiCp/AZ91 composite more exactly, the stress calculated by three typical constructive equations was compared with the measured value. The results show that the power law is deduced to be the most suitable constructive relationship for fine-grained SiCp/AZ91 composite, which is unlike previous reports. The calculated Q value increases with increasing temperature and strain rate. At 0.001s−1, the deformation mechanism of the composite is deduced to be grain boundary diffusion controlled dislocation climb; while, the deformation mechanism is deduced to be dislocation climb at 0.1–1s−1.

NUMERICAL SIMULATION OF FLOW INSTABILITY AND HEAT TRANSFER

This paper numerically investigates the physical mechanism of flow instability and heat transfer of natural convection in a cavity with thin fin(s). The left and the right walls of the cavity are differentially heated. The cavity is given an initial temperature, and the thin fin(s) is fixed on the hot wall in order to control the heat transfer. The finite volume method with the SIMPLE scheme is used to simulate the flow. Distributions of the temperature, the pressure, the velocity and the total pressure are achieved. Then, the energy gradient method is employed to study the physical mechanism of flow instability and the effect of the thin fin(s) on heat transfer. Based on the energy gradient method, the energy gradient function K represents the characteristic of flow instability. It is observed from the simulation results that the positions where instabilities take place in the temperature contours accord well with those of higher K value, which demonstrates that the energy gradient method reveals the physical mechanism of flow instability. Furthermore, the effect of the fin length, the fin position, the fin number, and Ra on heat transfer is also investigated. It is found that the effect of the fin length on heat transfer is negligible when Ra is relatively high. When there is only one fin, the most efficient heat transfer rate is achieved as the fin is fixed at the middle height of the cavity. The fin blocks heat transfer with a relatively small Ra, but the fin enhances heat transfer with a relatively large Ra. The fin(s) enhances heat transfer gradually with the increase of Ra under the influence of the thin fin(s). Finally, it is observed that both Kmax and Ra can reveal the physical mechanism of natural convection from different approaches.

Hot Deformation Behavior of As-cast AISI M2 High-speed Steel Containing Mischmetal

The hot deformation behavior of as-cast AISI M2 high-speed steel containing mischmetal (RE) has been investigated on a Gleeble-3500 simulator in the temperature range of 1000–1150 °C and strain rate range of 0. 01 – 10 s−1 at true strain of 1.0. The mechanical behavior has been characterized using stress-strain curve analysis, kinetic analysis, processing maps, etc. Metallographic investigation was performed to evaluate the mechanism of flow instability. The results show that the deformation activation energy decreases with increasing deformation temperature; the efficiency of power dissipation increases with decreasing strain rate and increasing temperature; flow instability is observed at low-to-medium temperature and higher strain rate region when the strain is smaller, but extends to lower strain rate and high temperature regions with the increment of strain, in which it is manifested as flow localization near the grain boundary. Hot deformation equations and processing maps are obtained. The optimal processing window is suggested and the deformation mechanism is dynamic recrystallization (DRX).

Natural convective heat transfer of water near its density maximum in an eccentric horizontal annulus

In order to understand the effect of eccentricity on natural convective heat transfer of water near its density maximum in a horizontal annulus, a series of two-dimensional numerical simulations from steady-state convection to oscillatory convection were performed by using finite volume method. The radius ratio of the annulus was 1.5, and density inversion parameter and eccentricity ranged from 0 to 1. Results showed that horizontal eccentricity leads to an asymmetric flow pattern, which combines the characteristic of flow in a large-gap on one side with that in a narrow-gap on another side of the annulus. For vertical eccentricity, the flow pattern has the characteristics of coupling flow in the large-gap at the bottom with that in the narrow-gap at the top of the annulus at an upward vertical eccentricity. Furthermore, when oscillatory convection appears, mechanisms of flow instability for different density inversion parameters are the same as these in horizontal concentric annulus. The variation of average Nusselt number with the Rayleigh number and the density inversion parameter is also exhibited. Based on simulation results, the heat transfer correlation for the horizontal annulus has been proposed according to the multiple linear regression technique.

Prediction of Aeroacoustic Resonance in Cavities of Hole-Pattern Stator Seals

Abstract This article discusses the mechanism for prediction of aeroacoustic resonance in cavities of hole-pattern stator seals. A Reynolds-averaged Navier–Stokes (RANS) solver developed in-house was used to simulate grazing channel flow past a cavity located in a channel. The numerical results generated with the RANS solver showed good agreement with those obtained using a commercial large eddy simulation code. In addition, the numerical results agreed well with the experimental data. Rossiter’s formula, a popular semi-empirical model used to predict frequencies of holetone acoustic instabilities caused by grazing fluid flow past open cavities, was modified using the RANS solver results to allow for its application to channel flows. This was done by modifying the empirical constant, the ratio of vortex velocity, and the freestream velocity. The RANS solver accurately captured the salient features of the flow/acoustic interaction and predicted well the dominant acoustic frequencies measured in an experimental investigation. The flow solver also provided detailed physical insight into the cavity flow instability mechanism.

Hot deformation behavior of an 8% Cr cold roller steel

An 8% Cr cold roller steel was compressed in the temperature range 900–1200 °C and strain rate range 0.01–10 s−1. The mechanical behavior has been characterized using stress–strain curve analysis, kinetic analysis, processing maps, etc. Metallographic investigation was performed to evaluate the microstructure evolution and the mechanism of flow instability. It was found that the work hardening rate and flow stress decreased with increasing deformation temperature and decreasing strain rate in 8% Cr steel; the efficiency of power dissipation decreased with increasing Z value; flow instability was observed at higher Z-value conditions and manifested as flow localization near the grain boundary. The hot deformation equation and the dependences of critical stress for dynamic recrystallization and dynamic recrystallization grain size on Z value were obtained. The suggested processing window is in the temperature range 1050–1200 °C and strain rate range 0.1–1 s−1 in the hot processing of 8% Cr steel.

Hot deformation behavior of a Nb-containing 316LN stainless steel

A Nb-containing 316LN stainless steel was compressed in the temperature range 900–1200 °C and strain rate range 0.01–10 s −1. The mechanical behavior has been characterized using stress–strain curve analysis, kinetic analysis, processing maps, etc. The microstructural evolution was observed and the mechanism of flow instability was discussed. It was found that the work hardening rate and flow stress decreased with increasing deformation temperature and decreasing strain rate. On the contrary, the efficiency of power dissipation increased with them; Flow instability was manifested as cracking and flow localization; The hot deformation equation and the relationships between deformation condition and dynamic recrystallization grain size and fraction were obtained; For Nb-containing 316LN stainless steel, the favorite nucleation sites for dynamic recrystallization are in sequence of triple point, grain boundary, twin boundary and intragranular deformation band; The suggested processing window is given.

Hot springs mediate spatial exchange of heat and mass in the enclosed sediment domain: A stability perspective

In many natural environments, such as in underwater hot springs and hydrothermal vents, thermal gradients are accompanied with changes in the concentration of chemical compounds transported to the seawater, causing the so-called double-diffusive, mixed convection. To study the physical scenarios in such systems, a vertical channel filled with a porous medium saturated with saline water is considered. The motion in the sediment-filled channel is induced by two buoyancy forces and an external pressure gradient, similar to the situation in a vent with an upward flow direction. The fluid flow has been modeled by an extended Darcy model, and the flow instability mechanisms have been studied numerically. The linear stability analysis is performed considering a wide range of Darcy number (Da = 10 −5 –10 −8). The instability boundary curve showed three distinct dynamic regimes: (i) Rayleigh–Taylor (R–T), (ii) log–log non-linear variation, and (iii) log–log linear variation. The domain of different regimes were sensitive to external pressure gradient as well as permeability. Similar to cross-diffusive natural convection in pure viscous fluids, a linear relationship between logarithmic absolute values of critical thermal Rayleigh number (∣Ra T ∣) and solute Rayleigh number (Ra C ) is found in the third regime. Based on the permeability, for any solute Rayleigh number (Ra C ), there existed a minimum value of Reynolds number (Re), below which R–T type of instability appeared. Above this minimum value, the instability was due to two buoyancy forces, known as buoyant instability. Simulations of secondary flow via energy analysis demonstrated the development of complex dynamics at the critical state in all three regimes characterized by transition of multi to uni-cellular structures and vice verse.

DEPTH-INTEGRATED NUMERICAL MODELING OF TURBULENT TRANSPORT BY LONG WAVES AND CURRENTS

In nature, flows are 3D phenomenon, but, in many geophysical settings, the water depth scale is smaller relative to the horizontal scale, such that horizontal 2D (H2D) motions dominate the flow structure. In those cases, especially in large domains, the H2D numerical model can be a practical and accurate tool - if the 3D physical properties can be included properly into the H2D model. Some of the H2D approaches in widespread use are the Boussinesq-type equations (BE) and shallow water equations (SWE) derived by a perturbation approach or depth averaging. The BE can account for some of the dispersive, turbulent and rotational flow properties frequently observed in nature (Kim et al., 2009). Also it has the ability of coupling currents and waves and can predict nonlinear water wave propagation over an uneven bottom from deep (or intermediate) water to the shallow water area. However, during the derivation of a H2D equation set, BE or SWE, some of the 3D flow properties like the dispersive stresses (Kuipers and Vreugdenhill, 1973) and the effects of the unresolved small scale 3D turbulence are excluded. Subsequently, there must be some limitations for predicting horizontal flow structures which can be generated through these neglected 3D effects. Naturally, any inaccuracy of the hydrodynamic flow model is reflected in the results of a coupled scalar transport model. In order to incorporate 3D turbulence effects into H2D flow models, various approaches have been proposed. Among many others, the stochastic backscatter model (BSM) proposed by Hinterberger et al. (2007) can account for the mechanism of inverse energy transfer from unresolved 3D turbulence to resolved 2D flow motions. Reasonable results were obtained by the proposed methods. Similar to the flow model, for scalar transport it is desired to develop a H2D model that can approximately account for the vertical deviations of concentration and velocity, and the associated mixing. For the accurate prediction of transport, an accurate numerical solver which can minimize numerical dispersion, dissipation and diffusion should be developed. Recently, the finite volume method (FVM) using approximate Riemann solvers has been developed and applied successfully. In this study, a depth-integrated model including subgrid scale mixing effects for turbulent transport by long waves and currents is presented. A fully-nonlinear, depth-integrated set of equations for weakly dispersive and rotational flow are derived by the long wave perturbation approach. The same approach is applied to derive a depth-integrated scalar transport model. The proposed equations are solved by a fourth-order accurate FVM. The depth-integrated flow and transport models are applied to typical problems which have different mixing mechanisms. Several important conclusions are obtained from the simulations: (i) From a mixing layer simulation it is revealed that the dispersive stress implemented with a stochastic BSM plays an important role for energy transfer. (ii) The proposed transport model coupled with the depth-integrated flow model can predict the passive scalar transport based on the turbulent intensity - not by relying on empirical constants. (iii) For near field transport simulations, the inherent limitation of the two-dimensional horizontal model to capture vertical structure is recognized. (iv) If the main mechanism of flow instability originates from relatively large-scale bottom topography features, then the effects of the dispersive stresses are less important.

Turbulent mixing and passive scalar transport in shallow flows

A depth-integrated model including subgrid scale mixing effects for turbulent transport by long waves and currents is presented. A fully nonlinear, depth-integrated set of equations for weakly dispersive and rotational flow is derived by the long wave perturbation approach. The same approach is applied to derive a depth-integrated scalar transport model which can accommodate small vertical variation of a weakly unsteady scalar. The proposed equations are solved by a fourth-order accurate finite volume method. The depth-integrated flow and transport models are applied to typical problems which have different mixing mechanisms. From the simulations, several important conclusions are obtained. (i) From simulation of a mixing layer generated by internal transverse shear, it is revealed that the dispersive stress implemented with a stochastic backscatter model (BSM) can play an important role for energy transfer in a shallow mixing layer. (ii) From a comparison of the characteristic width of a scalar plume in shallow and uniform flow, the proposed depth-integrated transport model coupled with the depth-integrated flow model can predict the passive scalar transport physically—that is, based on the turbulent intensity—without relying on a coarse empirical constant. (iii) From the same simulation, the inherent limitation of the two-dimensional horizontal model to capture vertical structure is recognized in near field. (iv) If the main mechanism of flow instability originates from relatively large-scale bottom topography features, then the effects of the dispersive stresses (i.e., BSM) are less important.

Prediction of Aeroacoustic Resonance in Cavities of Hole-Pattern Stator Seals

A Reynolds-averaged Navier–Stokes (RANS) solver developed in-house was used to simulate grazing channel flow past single and multiple cavities. The objective of this investigation was to predict fluid instabilities in hole-pattern stator seals. The numerical results generated with the RANS solver showed good agreement with those obtained using a commercial large eddy simulation code. In addition, the numerical results agreed well with experimental data. Rossiter’s formula, a popular semi-empirical model used to predict frequencies of hole-tone acoustic instabilities caused by grazing fluid flow past open cavities, was modified using the RANS solver results to allow for its application to channel flows. This was done by modifying the empirical constant κ, the ratio of vortex velocity, and the freestream velocity. The dominant frequencies predicted using Rossiter’s formula with the new κ value matched well with the experimental data for hole-pattern stator seals. The RANS solver accurately captured the salient features of the flow/acoustic interaction and predicted well the dominant acoustic frequencies measured in an experimental investigation. The flow solver also provided detailed physical insight into the cavity flow instability mechanism.

A theory of MHD instability of an inhomogeneous plasma jet

AbstractA problem of the stability of an inhomogeneous axisymmetric plasma jet in a parallel magnetic field is solved. The jet boundary becomes, under certain conditions, unstable relative to magnetosonic oscillations (Kelvin–Helmholtz instability) in the presence of a shear flow at the jet boundary. Because of its internal inhomogeneity the plasma jet has resonance surfaces, where conversion takes place between various modes of plasma magnetohydrodynamic (MHD) oscillations. Propagating in inhomogeneous plasma, fast magnetosonic waves drive the Alfven and slow magnetosonic (SMS) oscillations, tightly localized across the magnetic shells, on the resonance surfaces. MHD oscillation energy is absorbed in the neighbourhood of these resonance surfaces. The resonance surfaces disappear for the eigenmodes of SMS waves propagating in the jet waveguide. The stability of the plasma MHD flow is determined by competition between the mechanisms of shear flow instability on the boundary and wave energy dissipation because of resonant MHD-mode coupling. The problem is solved analytically, in the Wentzel, Kramers, Brillouin (WKB) approximation, for the plasma jet with a boundary in the form of a tangential discontinuity over the radial coordinate. The Kelvin–Helmholtz instability develops if plasma flow velocity in the jet exceeds the maximum Alfven speed at the boundary. The stability of the plasma jet with a smooth boundary layer is investigated numerically for the basic modes of MHD oscillations, to which the WKB approximation is inapplicable. A new 'unstable mode of MHD oscillations has been discovered which, unlike the Kelvin–Helmholtz instability, exists for any, however weak, plasma flow velocities.

Purely elastic instabilities in three-dimensional cross-slot geometries

Creeping and low Reynolds number flows of an upper-convected Maxwell (UCM) fluid are investigated numerically in a three-dimensional orthogonal cross-slot geometry. We analyze two different flow configurations corresponding to uniaxial extension and biaxial extension, and assess the effects of extensional flow type, Deborah and Reynolds numbers on flow dynamics near the interior stagnation point. Using these two flow arrangements the amount of stretch and compression near the stagnation point can be varied, providing further insights on the viscoelastic flow instability mechanisms in extensionally dominated flows with an interior stagnation point. The uniaxial extensional flow arrangement leads to the onset of a steady flow asymmetry, followed by a second purely elastic flow instability that generates an unsteady flow at higher flow rates. On the other hand, for the biaxial extension flow configuration a symmetric flow is observed up to the critical Deborah number when the time-dependent purely elastic instability sets in, without going through the steady symmetric to steady asymmetric transition.

Flow pattern and transition of rectangular spout–fluid bed

Experimental study on the flow patterns and transitions in a rectangular spout–fluid bed (cross-section of 300 mm × 30 mm and height of 2000 mm) packed with Geldart group D particles was carried out. Six distinct flow patterns, i.e. internal jet, spouting, fluidizing, jet in fluidized bed with bubbling, jet in fluidized bed with slugging and spout–fluidizing were identified. Criteria as well as schematic diagrams and typical flow pattern images obtained by a high-resolution digital CCD camera were presented for classifying these flow patterns. Typical flow pattern maps were plotted for describing the transitions between flow patterns with operating conditions. In addition, two kinds of flow instabilities were observed. Based on the flow pattern images recorded by the digital CCD camera, the mechanism of flow instabilities was preliminarily discussed. It was found that the flow instabilities are caused by stochastic visible large bubbles in the boundary of spout jet and near the fluidizing gas distributor. The growth of surface disturbances might exacerbate these flow instabilities.

Mechanism of flow instability and transition to turbulence

In this paper, a new mechanism of flow instability and turbulence transition is proposed for wall bounded shear flows. It is stated that the total energy gradient in the transverse direction and that in the streamwise direction of the main flow dominate the disturbance amplification or decay. Thus, they determine the critical condition of instability initiation and flow transition under given initial disturbance. A new dimensionless parameter K for characterizing flow instability is proposed which is expressed as the ratio of the energy gradients in the two directions for the flow without energy input or output. It is suggested that flow instability should first occur at the position of K max which may be the most dangerous position. This speculation is confirmed by Nishioka et al.'s experimental data. Comparison with experimental data for plane Poiseuille flow and pipe Poiseuille flow indicates that the proposed idea is really valid. It is found that the turbulence transition takes place at a critical value of K max of about 385 for both plane Poiseuille flow and pipe Poiseuille flow, below which no turbulence will occur regardless the disturbance. More studies show that the theory is also valid for plane Couette flows which holds a critical value of K max of about 370.