Width Of Boundary Layer Research Articles

Performance evaluation of a novel adaptive variable structure state estimator

An improved nonlinear adaptive state estimator called Adaptive Smooth Variable Structure Filter ASVSF has been proposed and its algorithm described. ASVSF extends the functionality and performance of a previously reported robust smooth variable structure filter (SVSF) with optimal boundary layer (SVSF-OBL). Improvement in performance includes the provision for accommodating unknown and time varying process noise covariance, which generally characterizes modelling uncertainty. The novelty of this proposed ASVSF estimator, which inherits the features of the SVSF, is that it adaptively provides an estimate of the unknown time varying process noise covariance (and hence called adaptive SVSF or ASVSF) which is required for determining the optimal boundary layer width of SVSF-OBL thus obviating the need of the prior knowledge of the process noise covariance. This makes the proposed estimator performance to be insensitive to (and therefore robust with respect to) unknown time varying process noise covariance while retaining the optimality of SVSF-OBL. The performance of the proposed ASVSF estimator is evaluated using Monte Carlo simulation and is compared with previously reported state estimators using a case of maneuvering civilian aircraft where a simplified and grossly approximate process model is used in the estimator/filter for tracking and thereby generating a time varying and unknown process noise covariance situation. Three different measures of Root Mean Square (RMS) error over the trajectory have been used for comparison which demonstrates the strengths of the proposed ASVSF estimator.

MHD nanofluid flow over an absorbent plate in the company of chemical response and zero nanoparticle flux

The aspire of this article is to examine the combined influences of suction/injection and external magnetic field on forced convection motion of nanoliquid past an absorbent plate in attendance with the first order compound response. To manage the flow, zero nanoparticle flux at the border has been assumed to urge the elements left from the plate surface. This condition make the model applicable to various engineering sectors for passive control of nanoelements part. The present analysis is based on two-phase model of nanoliquid. Using suitable alterations the foremost pdes (partial differential equations) have been abridged to odes (ordinary differential equations) and the numerical solutions for the nonlinear equations are obtained. Our outcomes for some particular cases are evaluated with the accessible outcomes in unwrap literature and found a fine conformity. The consequences of this study have significant impact on flow, heat and mass transport characteristics. Owing to enhanced magnetic parameter, though the speed and concentration of the liquid are found to amplify, hotness diminishes. By diminishing the width of boundary layer, the rising injection parameter causes the fluid velocity to augment while hotness diminishes. Rate of mass transport diminishes for higher values of Brownian motion parameter and Lewis number. The consequences of this study expose many motivating characters which deserve additional study of the problem.

Thermodynamic models for a concentration and electric field dependent susceptibility in liquid electrolytes

The dielectric susceptibility χ is an elementary quantity of the electrochemical double layer and the associated Poisson equation. While most often χ is treated as a material constant, its dependency on the salt concentration in liquid electrolytes is demonstrated by various bulk electrolyte experiments. Moreover, it is theoretically well accepted that the susceptibility declines for large electric fields. An analysis based on non-equilibrium thermodynamics reveals that, compared to the case of a constant χ, non-obvious generalizations of the model equations are required if the susceptibility is a function of species concentrations and the electric field. Particular attention needs to be paid to the consistent coupling of the Poisson equation, the momentum balance and the chemical potentials functions. In a numerical study, we systematically analyze the effects of a concentration and field dependent susceptibility on the double layer of a planar electrode|electrolyte interface. We observe that the field dependence can cause strong reduction of the boundary layer width. Concentration dependent susceptibility can prevent complete removal of the solvent from the interface and combination of field and concentration dependency can further change the qualitative behavior of the boundary layer model such that profiles of the ion concentrations are non-monotonous. Both dependencies of χ have the tendency to reduce the capacitance maxima height.

Autonomous underwater glider observations in southern Lake Ontario and Niagara River plume.

The nearshore areas of the Laurentian Great Lakes provide valuable ecosystem services including habitat for a variety of species and water for surrounding communities. Recent declines in nearshore water quality have increased the need for understanding the connectivity between nearshore and offshore areas; however, observing water quality variability across the dynamic nearshore to offshore transition zone poses logistical challenges for traditional observing systems. Here we evaluate cross-shore and along-shore water quality gradients using observations from two three-week deployments of a Slocum autonomous glider in southern Lake Ontario. The glider was deployed between the Niagara River mouth and Rochester, NY during early and late summer 2018, and each deployment resulted in over 3000 vertical profiles of the water column, and several transects between 2 km and 20 km from shore. In early summer, the cross-shore chlorophyll gradient was characterized by highest values just below the surface, at the frontal zone between weakly stratified conditions closer to shore and unstratified conditions offshore. In late summer, stratified conditions extended across the entire survey area. The depth of the thermocline was deeper and chlorophyll values were lower within 10 km of shore than offshore, where the highest chlorophyll values were observed in a distinct layer below the thermocline. In both early and late summer, the frontal boundary indicated by the cross-shore chlorophyll gradient was located below the surface and well offshore of what is typically considered the nearshore zone but was within the width of the coastal boundary layer. The high-resolution glider observations provide a detailed view of patterns of variability across a dynamic coastal zone and pinpoint the cross-shore frontal boundary that may be important for biologists to differentiate biological communities.

Computational examination of Jeffrey nanofluid through a stretchable surface employing Tiwari and Das model

Abstract In this research, we analyze the magnetohydrodynamics heat act of a viscous incompressible Jeffrey nanoliquid, which passed in the neighborhood of a linearly extending foil. As a process, we employ alumina ( Al 2 O 3 ) \left({{\rm{Al}}}_{2}{{\rm{O}}}_{3}) as nanoparticles, assuming that the base fluid is ethylene glycol. In this involvement, we consider the heating by Joule effect and viscous dissipation. We select the passable transformations, motion, and temperature formulas converting into non-linear differential equation arrangement. We solved the system by using a Keller-box method. Then, we provide a graphical description of outcomes according to the selected control parameters. Higher values of dissipation parameter cause a surge in temperature field as well as strengthen width of the heat boundary layer. The velocity, drag coefficient, and heat transfer (HT) rate for the base fluid are comparatively greater than that of the Al 2 O 3 {{\rm{Al}}}_{2}{{\rm{O}}}_{3} –ethylene glycol nanofluid, although the temperature is embellished by the inclusion of nanoparticles. Moreover, we report depreciation in surface drag as well as HT by the virtue of amplification in the Deborah number. The proclaimed outcomes are advantageous to boost the incandescent light bulb’s, cooling and heating processes, filament emitting light, energy generation, multiple heating devices, etc.

Darcy–Forchheimer electromagnetic flow of entropy optimized microrotating Casson–Carreau nanomaterials

AbstractIt is apparent that non‐Newtonian nanofluids (especially, Casson and Carreau) find their ubiquitous utilization in diverse industrial processes. The magnetohydrodynamics concept is significantly implemented in the engineering design process. Darcy–Forchheimer's effect characterized by inertia and boundary effects ameliorates the rate of heat transportation outstandingly in association with the flow of nanofluids. Entropy optimization analysis is accentuated as its minimization is the best measure to enhance the efficiency of thermal systems. In view of this, the present article is intended to investigate electromagnetic flow and thermal characteristics of Casson and Carreau nanofluids over the exponential stretched surface. Microrotation facets are entailed. Arrhenius pre‐exponential factor law and Robin's condition are implemented. The nondimensional governing equations are solved by the spectral quasi‐linearization method. The major outcomes of this study are that axial and transverse flow velocities and heat transfer rate get controlled due to strengthening Casson and microinertia density parameters. More thermal stratification augments the rate of heat transportation efficaciously. Amplification of the Weissenberg parameter intensifies the axial and transverse flow velocities and the associated boundary layer widths. Axial and transverse surface viscous drag enervate due to the rise in porosity, inertia, and magnetic parameters. The entropy generation rate is regulated by the varied Reynolds number.

Effects of boundary-layer bleed parameters on supersonic intake buzz

Extensive wind tunnel tests were conducted to study effects of the location, entrance slant angle, entrance width, and type (slot or porous) of boundary layer bleed on the buzz phenomenon in a supersonic air intake. The intake was a mixed-compression axisymmetric intake for the design Mach number of 2.0 that was studied at zero degrees angle of attack at three free stream Mach numbers of 1.8, 2.0, and 2.2 through shadowgraph visualization system and pressure recordings. For every free stream Mach number and bleed geometry, eight different back pressures were examined. Results showed that the bleed can significantly postpone the buzz onset and increase the stability range of the intake. The bleed location was the most effective parameter among the examined parameters of the bleed system. According to the results, the bleed restricts the domain of shock oscillations to downstream of the bleed entrance and consequently, it increases the frequency of buzz as compared with the no-bleed case. In addition, the slot bleed is more effective in stabilizing the intake flow field than the porous bleed.

Boundary layers in turbulent vertical convection at high Prandtl number

Many environmental flows arise due to natural convection at a vertical surface, from flows in buildings to dissolving ice faces at marine-terminating glaciers. We use three-dimensional direct numerical simulations of a vertical channel with differentially heated walls to investigate such convective, turbulent boundary layers. Through the implementation of a multiple-resolution technique, we are able to perform simulations at a wide range of Prandtl numbers ${Pr}$ . This allows us to distinguish the parameter dependences of the horizontal heat flux and the boundary layer widths in terms of the Rayleigh number $\mbox {{Ra}}$ and Prandtl number ${Pr}$ . For the considered parameter range $1\leq {Pr} \leq 100$ , $10^{6} \leq \mbox {{Ra}} \leq 10^{9}$ , we find the flow to be consistent with a ‘buoyancy-controlled’ regime where the heat flux is independent of the wall separation. For given ${Pr}$ , the heat flux is found to scale linearly with the friction velocity $V_\ast$ . Finally, we discuss the implications of our results for the parameterisation of heat and salt fluxes at vertical ice–ocean interfaces.

Investigation on flow field structure and aerodynamic load in vacuum tube transportation system

Vacuum Tube Transportation (VTT) system utilizes the low-pressure environment to achieve aerodynamic drag reduction and reduce the energy consumption of high-speed trains. Within this system, even for trains operating at subsonic speed, the flow acceleration around the streamlined train may leads to local supersonic flow. The appearance of the supersonic flow will dramatically alter the flow field structure and aerodynamic load of the high-speed train. Therefore, this study investigates two types of representative flow fields under different blockage ratio through the improved delayed detached eddy simulation (IDDES) method. The initialization, propagation, reflection and intersection process of shock waves in transonic case are captured and analyzed. It is shown that, the boundary layer thickness and width of vortex group in wake has experienced a slight increase with the increase of vacuum level. Compared with the subsonic case, the occurrence of choked flow and shock wave in transonic flow field lead to a decrease of wake region's vortex group width. As a result, the total drag coefficient of the train is increased by approximately one order of magnitude, and the dominant St number of tail car's drag coefficient has shifted from 0.16 to 0.11.

On the statics and dynamics of granular-microstructured rods with higher order effects

Granular-microstructured rods show strong dependence of grain-scale interactions in their mechanical behavior, and therefore, their proper description requires theories beyond the classical theory of continuum mechanics. Recently, the authors have derived a micromorphic continuum theory of degree n based upon the granular micromechanics approach (GMA). Here, the GMA is further specialized for a one-dimensional material with granular microstructure that can be described as a micromorphic medium of degree 1. To this end, the constitutive relationships, governing equations of motion and variationally consistent boundary conditions are derived. Furthermore, the static and dynamic length scales are linked to the second-gradient stiffness and micro-scale mass density distribution, respectively. The behavior of a one-dimensional granular structure for different boundary conditions is studied in both static and dynamic problems. The effects of material constants and the size effects on the response of the material are also investigated through parametric studies. In the static problem, the size-dependency of the system is observed in the width of the emergent boundary layers for certain imposed boundary conditions. In the dynamic problem, microstructural effects are always present and are manifested as deviations in the natural frequencies of the system from their classical counterparts.

Super-twisting sliding mode control with defined boundary layer for chattering reduction of permanent magnet linear synchronous motor

The super-twisting algorithm (STA, a class of second-order sliding mode control (SOSMC)) is widely used in permanent magnet linear synchronous motor (PMLSM) systems for its least amount of information and simplest calculations among the SOSMC algorithms. Due to the discretization and sign function of the STA, the chattering problem may be induced. In this paper, we propose an STA method with a defined boundary layer (called δSTA) to further reduce chattering in high-precision positioning system. With the δSTA method, when the sliding variable crosses the zero point, the speed is adjusted via two different saturation functions, instead of discontinuous sign functions of the STA. The proposed control law was proven to be stable, ensuring the establishment of a second-order sliding mode. Both the simulation and experimental results showed that the proposed control scheme, with a defined boundary layer width, can improve the steady-state positioning accuracy and significantly reduce system chattering.

Effects of the Plasmapause on the Radial Propagation of Fast Magnetosonic Waves: An Analytical Approach

AbstractIn this study, analytical approximation is used to solve the wave equations near the plasmapause boundary layer in order to examine the validity of ray tracing approach for fast magnetosonic (MS) wave propagations, and then analytical solutions for electromagnetic fields of MS waves through the plasmapause boundary layer are provided for the first time. Both theoretical calculations from the analytical expressions and observations of Van Allen Probes have indicated that electric fields of MS waves decrease rapidly but magnetic fields increase rapidly when propagating across the plasmapause boundary layer from the outside. Considering effects of the plasmapause width and wave frequency, parameter analysis has shown that when the width of the plasmapause boundary layer is narrow in comparison with the wavelength of MS waves, a significant part of waves will be reflected. In these circumstances, the WKB approximation and then ray tracing method might become invalid, and analytical approach provided in this paper could be utilized to solve the wave equation.

Inversion-Free Hysteresis Compensation via Adaptive Conditional Servomechanism With Application to Nanopositioning Control

In this article, an adaptive conditional servocompensator is proposed to achieve precise tracking control of systems with hysteresis without requiring explicit inversion of the hysteresis. Motivated by a range of applications, such as the piezoelectric-actuated nanopositioning, the system considered in this work consists of a chain of integrators preceded by a hysteresis nonlinearity modeled by a modified Prandtl-Ishlinskii (MPI) operator with uncertainty. To facilitate the proposed control design, the MPI operator is rearranged into a form comprised of three parts: a linear term, a nominal hysteretic term represented by a classical Prandtl-Ishlinskii (PI) operator, and a hysteretic perturbation. The bound on the hysteretic perturbation is further derived based on the parameter uncertainty of the MPI operator. The controller consists of two major elements. The first is a continuously implemented sliding mode controller (SMC), which exploits the bound on hysteretic perturbation and drives the system states to a bounded set in finite time. To properly “cancel” the nominal hysteresis effect without inversion, a technique involving a low-pass filter is introduced. The second element of the proposed controller is an adaptive conditional servocompensator that aims to eliminate periodic components in the tracking error. We show that, with persistent excitation, the closed-loop variables are ultimately bounded and the tracking error approaches a neighborhood of zero, where the neighborhood can be made arbitrarily small via the choice of the SMC boundary-layer width parameter and the servocompensator order. The proposed approach is implemented experimentally on a commercial nanopositioner under different types of periodic references, and it shows superior tracking performance over the traditional proportional-integral control, as well as several hysteresis inversion-based approaches reported in the literature.

Comparative study of sensorless control of Permanent magnet synchronous motor realised by sliding‐mode observer

In this study, the permanent-magnet synchronous motor sensorless control systems realised by sliding-mode observers in stationary αβ and estimated γδ coordinates are systematically studied and compared. First, based on the sufficient condition of sliding-mode stability, a more reasonable selection method of boundary layer width and sliding-mode gain is derived, effectively reducing the system chattering. Furthermore, in extracting estimated extended electromotive force, the advantages and disadvantages of the backforward method in the αβ-axis and the influence of filter cut-off frequency on estimation error in the γδ-axis are analysed. Finally, the estimation error, speed range, stability, and the effect of speed error of these two sensorless control systems are analysed and compared. The results indicate that these two systems have equivalent position error above a certain speed, and the γδ-axis estimation system has a larger position error in low-speed range, but still operating well. Moreover, the γδ-axis estimation algorithm has better stability and wider-speed range. Owing to the fast track of phase-locked loop, the effect of speed error on estimation accuracy of the γδ-axis system can be neglected. Simulation and experiment verified the theoretical analysis and comparison.

Direct numerical simulation of the wake adjustment and hydrodynamic characteristics of a circular cylinder symmetrically attached with fin-shaped strips

This work has numerically studied the effects of the coverage ratio and angular position of a pair of fin-shaped strips on the hydrodynamic forces and wake structures of a circular cylinder at both low and medium Reynolds numbers (Re = 60–500) using direct numerical simulation (DNS). The coverage ratio varies from 0.11 to 0.22, corresponding to the coverage angle (β) of a strip from 20° to 40°. The angular position (θ), measured from the forward stagnation point to the front edge of strips, ranges from 30° to 120° with increment of 30°. The numerical results indicate that the hydrodynamic coefficients are sensitive to the coverage and placement angles of the strips. The fluid forces are reduced with the introduction of a couple of 20°-fin-shaped strips, while they are amplified by placing 30°-fin-shaped strips or 40°-fin-shaped strips in the front surface of cylinder. The amplification/suppression is associated with the development of boundary layer and the wake structure, embodied in the length of recirculation bubble, the wake width, the tripping and reattachment of boundary layer as well as the separation point. By placing a pair of 40°-fin-shaped strips at θ = 60°, the time-mean drag and the lift fluctuation at Re = 180 are increased by 38.7% and 97.7%, respectively. For the cylinder equipped with 30°-fin-shaped strips at θ = 30°, the three-dimensional mode A and mode B wake structures are observed at medium Re = 200–500.

Harmonic and subharmonic waves on the surface of a vibrated liquid drop.

Liquid drops and vibrations are ubiquitous in both everyday life and technology, and their combination can often result in fascinating physical phenomena opening up intriguing opportunities for practical applications in biology, medicine, chemistry, and photonics. Here we study, theoretically and experimentally, the response of pancake-shaped liquid drops supported by a solid plate that vertically vibrates at a single, low acoustic range frequency. When the vibration amplitudes are small, the primary response of the drop is harmonic at the frequency of the vibration. However, as the amplitude increases, the half-frequency subharmonic Faraday waves are excited parametrically on the drop surface. We develop a simple hydrodynamic model of a one-dimensional liquid drop to analytically determine the amplitudes of the harmonic and the first superharmonic components of the linear response of the drop. In the nonlinear regime, our numerical analysis reveals an intriguing cascade of instabilities leading to the onset of subharmonic Faraday waves, their modulation instability, and chaotic regimes with broadband power spectra. We show that the nonlinear response is highly sensitive to the ratio of the drop size and Faraday wavelength. The primary bifurcation of the harmonic waves is shown to be dominated by a period-doubling bifurcation, when the drop height is comparable with the width of the viscous boundary layer. Experimental results conducted using low-viscosity ethanol and high-viscocity canola oil drops vibrated at 70Hz are in qualitative agreement with the predictions of our modeling.

Effect of Surface Wave on Development of Turbulent Boundary Layer Over a Train of Rib Roughness

Abstract In this paper, detailed experimental results are reported to study the effect of the surface wave of different frequencies on unidirectional current over the bed-mounted train of rib roughness. The model roughness used in this study is transverse square ribs that lengthened across the entire width of the recirculating wave channel. The center-to-center rib pitch (P) was constant during the experiments, thus generating a broad range of near-bed flow patterns for each of the three different surface wave frequencies studied here. The relative submergence associated with the roughness height (k) was 8, which fall in the category of large roughness. Velocity measurements were conducted using acoustic Doppler velocimeter (ADV), and a surface wave of different frequencies was generated using the plunger-type wavemaker. The measured velocity data were analyzed to determine the relative importance of mean flow over the train of rib roughness. Mean velocity profiles illustrate the well-known downward shift from the flat surface data of the semi-logarithmic portion of the law of the wall. The width of the turbulent boundary layer increases with the superposition of surface wave compared to that of the current-only flow. The results also show that the mean reattachment length decreases due to the superposition of surface wave on unidirectional current.

Multiple convection‐driven Falkner‐Skan flow of Carreau nanofluid along a permeable wedge: An analytical approach

AbstractThe impression of multiple convective conditions on Falkner‐Skan flow along a permeable static/moving wedge is demonstrated here. The Carreau nanofluid model depending on the power law index is incorporated with the effects of thermophoresis and Brownian motion. A suitable similarity conversion is consumed to bring out the nonlinear ordinary differential equations (ODEs) from the partial differential system. The transformed system is tackled via analytical and numerical procedure by homotopy perturbation method and RK‐5 with shooting technique, respectively. Numerical computations assert that the growth of concentration and temperature boundary layer widths are in an inversely proportional relation to the permeability of the medium, whereas reverse effect is observed for conduction convection and conduction diffusion parameters. Also, with the enhancement of Brownian motion parameter, the rate of heat transport gets reduced for static wedge by 14.25% whereas for moving wedge the reduction is 10.61%. Another significant observation shows that the growth in mass transport with conduction diffusion is 17.65% greater for moving wedge in contrast to static one in accordance with other governing parameters.

Computational Analysis for Mixed Convective Flows of Viscous Fluids With Nanoparticles

Abstract In this article, magnetohydrodynamic (MHD) mixed convection in an exponentially stretchable surface saturated with viscous fluid has been studied. BVPh 2.0 is employed which is mathematica-based algorithm created on the basis of optimal homotopy analysis method (OHAM). Adequate transformations are utilized for the conversion of governing system into nonlinear ordinary differential system. Convergence of BVPh 2.0 results is demonstrated through tabular values of squared residual errors. Graphical analysis is executed for broad range of governing parameters. It has been revealed an increase in buoyancy leads to the growth of boundary layer width. Further results predict the heat infiltration into the fluid increases as Brownian motion and Biot number enlarges. Mathematically this work exhibits the potential of BVPh 2.0 for nonlinear differential systems.

ROBUST DIFFERENCE SCHEME FOR THE CAUCHY PROBLEM FOR A SINGULARLY PERTURBED ORDINARY DIFFERENTIAL EQUATION

Grid approximation of the Cauchy problem on the interval D = {0 ≤ x ≤ d} is first studied for a linear singularly perturbed ordinary differential equation of the first order with a perturbation parameter ε multiplying the derivative in the equation where the parameter ε takes arbitrary values in the half-open interval (0, 1]. In the Cauchy problem under consideration, for small values of the parameter ε, a boundary layer of width O(ε) appears on which the solution varies by a finite value. It is shown that, for such a Cauchy problem, the solution of the standard difference scheme on a uniform grid does not converge ε-uniformly in the maximum norm; convergence occurs only under the condition h ε, where h = d N −1 , N is the number of grid intervals, h is the grid step-size. Taking into account the behavior of the singular component in the solution, a special piecewise-uniform grid is constructed that condenses in a neighborhood of the boundary layer. It is established that the standard difference scheme on such a special grid converges ε-uniformly in the maximum norm at the rate O(N −1 lnN). Such a scheme is called a robust one. For a model Cauchy problem for a singularly perturbed ordinary differential equation, standard difference schemes on a uniform grid (a classical difference scheme) and on a piecewise-uniform grid (a special difference scheme) are constructed and investigated. The results of numerical experiments are given, which are consistent with theoretical results.