Quasi-equilibrium Region Research Articles

Turbulent wall plumes with detrainment

This article presents a theoretical modelling framework for the previously unconsidered case of turbulent wall plumes that detrain continually with height in stably stratified environments. Built upon the classic turbulent plume model, our approach incorporates turbulent detrainment with a variable coefficient of detrainment. Based on a linear constitutive relationship between the ratio of the detrainment to entrainment coefficients and the ambient buoyancy gradient, it is found that for linear ambient stratifications, a dynamic quasi-equilibrium region, characterised by a near invariant local plume Richardson number, is achieved, downstream of which this equilibrium rapidly breaks down. With increasing ambient buoyancy gradient, while the plume becomes increasingly slender with weaker vertical motions, the level at which the plume breaks down to form a horizontal intrusion first decreases and then increases. Moreover, distinct from classic purely entraining plumes, a detraining wall plume can swell within the pre-equilibrium adjustment stage provided the local Richardson number is sufficiently low $({Ri\ll 6})$ , behaviour which is in accordance with observations made in filling-box experiments.

Modeling transverse momentum exchange in partially vegetated flow

In this study, theoretical and experimental methods are applied to investigate streamwise velocity profiles and transverse momentum exchange in the quasi-equilibrium region in partially vegetated channels. A new eddy viscosity model is proposed to model the transverse momentum exchange in consideration of bottom turbulence, stem-scale turbulence, and turbulence induced by coherent structures. Results show that turbulence induced by coherent structures is the dominant contributor to the momentum exchange. The proposed eddy viscosity model can be well applied for different setups by varying only one proportionality constant (ξ), which is inversely proportional to the canopy drag (CDa). The lateral distribution of eddy viscosity is also well predicted and shows a peak just outside the canopy. By assuming the canopy as a rough wall and setting the zero-plane displacement within the canopy to the distance of penetration width, we find that the lateral profiles of the mean streamwise velocity in the outer shear layer follow logarithmic curves. A quantitative relationship between roughness length and canopy drag (CDa) is, thus, determined similar to that in turbulent rough-wall boundary layers.

Flow characteristics in partially vegetated channel with homogeneous and heterogeneous layouts.

This study presents the experimental results of the flow characteristics, such as the flow adjustment, velocity profiles, mixing layer, and the momentum exchange, in the partially vegetated channel with homogeneous and heterogeneous layouts. Three cases are considered, including two homogeneous canopies with uniform sparse and dense vegetation patches respectively, and a heterogeneous canopy consisting of alternating patches of both densities. Results show that heterogeneous canopy requires a longer adjustment distance to reach the quasi-equilibrium region, compared with the homogenous canopy of the same density. In heterogeneous canopy flow, the mixing layer width and the momentum thickness fluctuates with the alternation of vegetation density. The increased values for these two parameters compared to those values for the homogeneous canopies indicate that the greater resistance and momentum loss occur for the heterogeneous layout. A wavy region of the enhanced in-plane turbulence kinetic energy (TKE) is observed in the heterogeneous canopy, suggesting a comparatively more chaotic flow condition, whereas the contours of in-plane TKE are smooth in homogeneous canopies. The presence of the coherent structures in heterogeneous canopy is identified by spectral analysis and the quasi-periodic fluctuations of velocities. The Reynolds stress associated with the coherent structures is found to be the dominator of the contribution to the total Reynolds stress. The comparison between the homogenous canopies of different density is also conducted. These results will be of practical importance for the design of vegetation layouts in water ecological restoration projects and for river management.

Mathematical modeling of the influence of non-catalytic dissociation / recombination of water molecules in the desalination channel on electric convection

The article formulates a two-dimensional mathematical model of non-stationary transport of 1: 1 electrolyte in a potentiodynamic mode, taking into account electroconvection and non-catalytic dissociation / recombination reaction of water molecules in electromembrane systems, which are considered as the desalting channel of an electrodialysis device. The model is described by a system of coupled Navier-Stokes and Nernst-Planck-Poisson equations taking into account the electric force and physically justified boundary conditions. The article establishes the basic laws of mass transport, taking into account the dissociation / recombination of water molecules. It was shown for the first time that a double electric layer of hydrogen and hydroxyl ions arises in the recombination region. It is shown that between the region of recombination and quasi-equilibrium regions of space charge there are regions of electroneutrality and equilibrium with an almost linear distribution of concentrations. It was found that even under prelimiting, but close enough to the limiting current, modes, non-catalytic dissociation of water molecules in the quasi-equilibrium region of space charge occurs so intensely that the concentration of hydrogen and hydroxyl ions becomes comparable to the concentration of potassium and chlorine ions. At overlimiting current densities, due to the appearance of an extended space charge region and intense dissociation of water molecules in this region, as well as an increase in the electric double layer in the recombination region, the space charge and the dissociation / recombination reaction of water molecules significantly affect each other. In turn, this has a decisive effect on electroconvection and, accordingly, on the transport of salt ions.

Evaporation and heat transfer of aqueous salt solutions during crystallization

Evaporation, heat transfer and surface crystallization of thin layers of aqueous solutions of CaCl2, LiBr and LiCl salts have been studied experimentally. The control of crystallization rate is extremely important for a wide range of modern technologies, associated with both slow cooling rates and extremely rapid droplet and film crystallization (for example, in nanocoatings). Usually, when calculating the crystallization, the heat transfer coefficient and the evaporation rate are assumed quasi-constant, and the effect of evaporation rate of solution on the rate of crystallization is not taken into account. In this paper, it is shown that even without crystallization the heat transfer coefficient may vary several times, when the height of the film rapidly decreases. This study has shown that the character of crystallization curve and crystallization rate strongly depend on the rate of solution evaporation before the onset of phase transition. Abnormally high crystallization rates 30–50 mm/s are achieved at extremely low supersaturations of solutions (the salt solution is in the quasi-equilibrium region), and this is associated with the rapid growth of dendritic forms. With the growth of the surface crystalline film, the evaporation rate of the solution in metastable state increases significantly and has a non-stationary “oscillation” character. The coefficient of heat transfer before the onset of crystallization also changes significantly. The formation of dendrites is possible if crystallization is realized in thin supersaturated layers with high gradients of temperature and concentration. In this case, very high crystallization rates will be provided by dendritic forms.

An IMS–IMS threshold method for semi-quantitative determination of activation barriers: Interconversion of proline cis ↔ trans forms in triply protonated bradykinin

Collisional activation of selected conformations by multidimensional ion mobility spectrometry (IMS–IMS), combined with mass spectrometry (MS), is described as a method to determine semi-quantitative activation energies for interconversion of different structures of the nonapeptide bradykinin (BK, Arg-Pro-Pro-Gly-Phe-Ser-Pro-Phe-Arg). This analysis is based on a calibration involving collision-induced dissociation measurements of ions with known dissociation energies (i.e., “thermometer” ions) such as leucine enkephalin, BK, and amino acid–metal cation systems. The energetic barriers between six conformations of [BK+3H]3+ range from 0.23±0.01 to 0.55±0.03eV. Prior results indicate that the major peaks in the IMS distributions correspond to specific combinations of cis and trans configurations of the three proline residues in the peptide sequence. The analysis allows us to directly assess pathways for specific transitions. The combination of structural assignments, experimentally determined barrier heights, onset of the quasi-equilibrium region, and dissociation threshold are used to derive a semi-quantitative potential energy surface for main features of [BK+3H]3+.

Numerical simulation of microparticles transport in a concentric annulus by Lattice Boltzmann Method

Dispersion and removal of microaerosol particles are investigated numerically in a horizontal concentric annulus by Lattice Boltzmann Method and Lagrangian Runge–Kutta procedure with the assumption of one-way coupling. Drag, buoyancy, gravity, shear lift, Brownian motion and thermophoretic are forces that are included in particle equation of motion. All simulations were performed at Rayleigh number of 104 and particles specific density of 1000. The effect of aspect ratio and particles diameter were determined on particles behavior such as removal and dispersion. Results show that recirculation power increases by decreasing of cylinders gap. Particles move in a thinner quasi-equilibrium region by increasing of their diameter and decreasing of cylinders gap. Brownian motion is dominant removal mechanism in particle with diameter of 1μm.

Stability of a disperse-mixture flow in a boundary layer

The hydrodynamic stability of a dilute disperse mixture flow in a quasi-equilibrium region of a boundary layer with a significantly nonuniform particle concentration profile is investigated. The mixture is described by a two-fluid model with an incompressible viscous carrier phase. In addition to the Stokes drag, the Saffman lifting force is taken into account in the interphase momentum exchange. On the basis of a numerical solution of the boundary-value problem for a modified Orr-Sommerfeld equation, neutral stability curves are analyzed and the dependence of the critical Reynolds number on the governing parameters is studied. It is shown that taking into account the particle concentration nonuniformity in the main flow and the Saffman lifting force significantly changes the stability limits of the two-phase laminar boundary layer flow. The effect of these factors on the boundary layer stability is considered for the first time.

Propagation of wall pressure perturbations in a large aspect ratio shallow cavity

Wall pressure fluctuations generated by turbulent boundary layers over a shallow cavity are studied experimentally in a low-speed wind tunnel facility. The scope of the present work is to characterize the propagation of the pressure perturbations at the wall by means of pressure cross-correlations and cross-spectra measured through a microphone pair translated along the cavity floor. It is found that the mechanism characterizing the pressure propagation close to the backward facing step and in the middle of the cavity is similar to what is commonly observed in equilibrium boundary layer being the convection velocity smaller than the external mean velocity. On the other hand, in the close vicinity of the forward-step, the hydrodynamic contribution of the pressure fluctuations is accompanied by a relevant acoustic effect characterized by a convection velocity close to the speed of sound. Furthermore, in the regions close to the two steps, the spectral decay of the coherence function, even though of exponential type, is faster than that obtained in the quasi-equilibrium region.

Performance Limitation and Autotuning of Inverse Optimal PID Controller for Lagrangian Systems

Abstract The PID trajectory tracking controller for Lagrangian systems shows performance limitation imposed by inverse dynamics according to desired trajectory. Since the equilibrium point cannot be defined for the control system involving performance limitation, we define newly the quasiequilibrium region as an alternative for equilibrium point. This analysis result of performance limitation can guide us the autotuning method for PID controller. The quasiequilibrium region is used as the target performance of autotuning PID trajectory tracking controller. The autotuning law is derived from the direct adaptive control scheme, based on the extended disturbance input-to-state stability and the characteristics of performance limitation. Finally, experimental results show that the target performance can be achieved by the proposed automatic tuning method.

로봇 시스템에 대한 PID 궤적추종 제어기의 자동 성능동조

The PID trajectory tracking controller for robotic systems shows performance limitation imposed by inverse dynamics according to desired trajectory. Since the equilibrium point can not be defined for the control system involving performance limitation, we define newly the quasi-equilibrium region as an alternative for equilibrium point. This analysis result of performance limitation can guide us the auto-tuning method for PID controller. Also, the quasi-equilibrium region is used as the target performance of auto-tuning PID trajectory tracking controller. The auto-tuning law is derived from the direct adaptive control scheme, based on the extended disturbance input-to-state stability and the characteristics of performance limitation. Finally, experimental results show that the target performance can be achieved by the proposed automatic tuning method.

A hydrogen sensing Pd/InGaP metal-semiconductor (MS) Schottky diode hydrogen sensor

An interesting hydrogen sensing Pd/InGaP metal-semiconductor (MS) Schottky diode has been fabricated and studied. Both the steady state and the transient condition of the hydrogen adsorption process are investigated. Even at room temperature, an extremely low hydrogen concentration of 15 ppm H2/air can be detected. In addition, the wide operating temperature range of 250 K of the studied Pd/InGaP hydrogen sensor is found. From experimental results, it is shown that the variation of Schottky barrier height increases with the increase of the operating temperature and hydrogen concentration. As the operation temperature is elevated, the water formation effect is also studied in the quasi-equilibrium region under the transient condition.

Relaxation behind shock waves in ionizing neon

Experiments in ionizing neon are described in which heavy-particle and electron densities are measured and compared with the current kinetic model. The experimental results allow a determination of the atom-atom collisional excitation cross-section constant, giving a value of (8±2) × 10−20 cm2/eV for the range of conditions examined. The population of two of the excited-state levels of the atom are measured and compared with theoretical predictions. The experimental populations are found to follow the expected behaviour in the quasi-equilibrium region, but are several orders of magnitude higher than predicted in the nonequilibrium zone. These findings suggest that the depopulation of excited states through ionizing collisions occurs more slowly than expected. Absorption linewidths and line shifts are also measured in the quasi-equilibrium region and found to compare well with theory. A small precurson population is also observed and population measurements in this region are compared with other experimental results in argon and krypton.