Width Of Boundary Layer Research Articles

Thermo-mechanical behavior of functionally graded circular sector plates

By reformulating the governing equations of the first-order theory into those describing the interior and edge-zone problems of the plate, closed-form solutions are presented for analysis of functionally graded circular sector plates with vertex angle \({\theta_0 \leq \pi /2}\) whose radial edges are simply supported and subjected to transverse loading and heat conduction through the plate thickness. Various types of clamped, simply supported, and free-edge boundary supports are considered on the circular edge of the plate. The material properties are graded through the plate thickness according to a power-law distribution of the volume fraction of the constituents. The effects of material property, boundary conditions, sector angle \({\theta_0}\), and boundary-layer phenomena on various response quantities in a circular sector plate are studied and discussed. Under a mechanical load, radial stress resultants in an FG circular sector plate with various clamped supports are zero, and consequently, their responses are seen to be identical. Simply supported FG circular sector plates which are immovable in radial direction do not show a neutral plane in bending, while in FG circular sector plates with other types of boundary supports this plane exists and its z-coordinate depends on the material constant. It is observed that the boundary-layer width is approximately equal to the plate thickness both in thermal and mechanical loadings with the boundary-layer effects being the strongest near a free edge.

Response of microscale turbulence and transport to the evolution of resistive magnetohydrodynamic magnetic island

Nonlinear evolution of microscale turbulence interacting with a naturally growing MHD magnetic island is simulated based on a Landau-fluid model. Here, we report on a new short wavelength magnetic-island-induced ion temperature gradient (ITG) instability triggered by a critical threshold of magnetic island width in multiscale turbulence, which is referred to as sw-MITG mode. The sw-MITG mode is characterized by a substantially low stability threshold and a global structure propagating along the ion diamagnetic drift direction. Its generation results from the response of microscale fluctuations to turbulent cross-field heat transport associated with increasing boundary layer width about the island separatrix. An intermittency of heat transport is caused by the sw-MITG mode interacting with dynamical magnetic island and microturbulence.

Theory of wind accretion

A review of wind accretion in high-mass X-ray binaries is presented. We focus attention to different regimes of quasi-spherical accretion onto the neutron star: the supersonic (Bondi) accretion, which takes place when the captured matter cools down rapidly and falls supersonically toward NS magnetospghere, and subsonic (settling) accretion which occurs when plasma remains hot until it meets the magnetospheric boundary. Two regimes of accretion are separated by an X-ray luminosity of about $4\times10^{36}$ erg/s. In the subsonic case, which sets in at low luminosities, a hot quasi-spherical shell must be formed around the magnetosphere, and the actual accretion rate onto NS is determined by ability of the plasma to enter the magnetosphere due to Rayleigh-Taylor instability. We calculate the rate of plasma entry the magnetopshere and the angular momentum transfer in the shell due to turbulent viscosity appearing in the convective differentially rotating shell. We also discuss and calculate the structure of the magnetospheric boundary layer where the angular momentum between the rotating magnetosphere and the base of the differentially rotating quasi-spherical shell takes place. We show how observations of equilibrium X-ray pulsars Vela X-1 and GX 301-2 can be used to estimate dimensionless parameters of the subsonic settling accretion theory, and obtain the width of the magnetospheric boundary layer for these pulsars.

Propagation of Meridional Circulation Anomalies along Western and Eastern Boundaries

Abstract Motivated by the adjustment of the meridional overturning circulation to localized forcing, solutions are presented from a reduced-gravity model for the propagation of waves along western and eastern boundaries. For wave periods exceeding a few months, Kelvin waves play no role. Instead, propagation occurs through short and long Rossby waves at the western and eastern boundaries, respectively: these Rossby waves propagate zonally, as predicted by classical theory, and cyclonically along the basin boundaries to satisfy the no-normal flow boundary condition. The along-boundary propagation speed is cLd/δ, where c is the internal gravity/Kelvin wave speed, Ld is the Rossby deformation radius, and δ is the appropriate frictional boundary layer width. This result holds across a wide range of parameter regimes, with either linear friction or lateral viscosity and a no-slip boundary condition. For parameters typical of contemporary ocean climate models, the propagation speed is coincidentally close to the Kelvin wave speed. In the limit of weak dissipation, the western boundary wave dissipates virtually all of its energy as it propagates toward the equator, independent of the dissipation coefficient. In contrast, virtually no energy is dissipated in the eastern boundary wave. The importance of background mean flows is also discussed.

Roll control using discrete-time robust sliding hyperplanes and fast output sampling

Robustness to unmatched parametric uncertainty is prime requirement of roll control algorithm, especially when it is modelled in discrete time domain and implemented through on-board processor. Sliding mode control is a well established nonlinear control technique, which ensures a robust performance in presence of matched uncertainties and disturbances. In case of the discrete version of sliding mode control, due to finite operational sampling frequency, the system trajectories cannot be forced to slide on the switching manifold. The trajectories remain confined to certain domain around the sliding surface and this is known as Quasi Sliding Mode (QSM) motion. The bound of QSM decides the accuracy and performance of the discrete version of sliding mode. By design, the discrete-time sliding modes are robust to the matched bounded perturbations, however, unmatched perturbations directly affect the boundary layer width and hence the performance of the system. In the present paper, discrete time Lyapunov inequality based sliding hyperplane is designed, which enables robustness to unmatched perturbations arising due to uncertain system matrix A. Further, the requirement of full state-vector for the design of control and sliding surface is met through the multi-rate output feedback (MROF). This control strategy is then demonstrated with application to roll position control of missile with a bandwidth limited actuator.

Magnetic turbulence suppression by a helical mode in a cylindrical geometry

To study processes involved in a helical structure formation in reversed field pinch devices, the scaling of a turbulent boundary layer width associated with a vortex structure having large shears of magnetic field and flow is obtained for reduced magnetohydrodynamics. The coherent vortex, with its flow and magnetic shears, interacts with Alfvén turbulence, forming a turbulent boundary layer at the edge of the vortex. The layer arises from the balance between turbulence diffusion rates and shearing rates and suppresses the turbulence in the structure. The suppression of turbulence impedes relaxation of the coherent vortex profiles, leading to long coherence times. The scaling of the boundary layer width reveals that both magnetic shear and flow shear can effectively suppress magnetic turbulence.

Matched Asymptotic Expansions of Unbalanced Adhesive Joints

AbstractA matched asymptotic expansion analysis is used to determine the dependence of shear stress boundary layer thickness on adhesive properties in unbalanced single-lap joints. A uniformly accurate expansion of shear stress, in a small and positive dimensionless parameter e, is shown to contain a pair of adhesive edge boundary layers and an outer zone where the stress is slowly varying between the two layers. An overlap constraint is also found, and if it can be satisfied for e≪1, then there is sufficient overlap and a single boundary layer of width the order of e1/2 at either adhesive end. The analytic results are presented in a generic format allowing their application and/or extension to similar problems. All results are numerically verified using a finite difference approximation.

A New Robust Filtering Strategy for Linear Systems

Abstract For linear and well-defined estimation problems with Gaussian white noise, the Kalman filter (KF) yields the best result in terms of estimation accuracy. However, the KF performance degrades and can fail in cases involving large uncertainties such as modeling errors in the estimation process. The smooth variable structure filter (SVSF) is a relatively new estimation strategy based on sliding mode theory and has been shown to be robust to modeling uncertainties. The SVSF makes use of an existence subspace and of a smoothing boundary layer to keep the estimates bounded within a region of the true state trajectory. Currently, the width of the smoothing boundary layer is chosen based on designer knowledge of the upper bound of modeling uncertainties, such as maximum noise levels and parametric errors. This is a conservative choice, as a more well-defined smoothing boundary layer will yield more accurate results. In this paper, the state error covariance matrix of the SVSF is used for the derivation of an optimal time-varying smoothing boundary layer. The robustness and accuracy of the new form of the SVSF was validated and compared with the KF and the standard SVSF by testing it on a linear electrohydrostatic actuator (EHA).

Statistical and physical balances in low Rossby number Rayleigh–Bénard convection

Rapidly rotating Rayleigh–Bénard convection is studied using an asymptotically reduced equation set valid in the limit of low Rossby numbers. Four distinct dynamical regimes are identified: a disordered cellular regime near threshold, a regime of weakly interacting convective Taylor columns at larger Rayleigh numbers, followed for yet larger Rayleigh numbers by a breakdown of the convective Taylor columns into a disordered plume regime characterized by reduced efficiency and finally by geostrophic turbulence. The transitions are quantified by examining the properties of the horizontally and temporally averaged temperature and thermal dissipation rate. The maximum of the thermal dissipation rate is used to define the width of the thermal boundary layer. In contrast to the non-rotating Rayleigh–Bénard convection, the temperature drop across this layer decreases monotonically with increasing Rayleigh number and does not saturate. The breakdown of the convective Taylor column regime is attributed to the onset of convective instability of the thermal boundary layer and confirmed using the explicit linear stability analysis. Horizontal spectra of the vorticity, vertical velocity and temperature fluctuations are computed and their evolution with time is elucidated. A large-scale barotropic mode evolves from random initial conditions on an extremely long time scale and leads to continued evolution of the nominally saturated Nusselt number and its variance over very long times. The results are used to provide insights into the dynamics of rapidly rotating convection outside the asymptotic regime described by the reduced equations.

Double loop control of buck-boost converters for wide range of load resistance and reference voltage

A double-loop control mechanism is developed for an inverting buck-boost converter. The robust converter is capable of operating in a wide range of reference voltage and load resistance with unmodelled parameters. The cause of the non-minimum phase behaviour is analysed. The boundary layer width of the output voltage in sliding mode is found to be dependent on the circuit and control parameters. The speeds of the inner and outer loop are quantitatively determined and compared. The transient responses of the circuit are forecastable. The controller is validated on a simulation circuit.

Formation of tidal starting-jet vortices through idealized barotropic inlets with finite length

This paper presents a surface particle image velocimetry study to investigate the dynamics of shallow starting-jet dipoles formed by tidal flow through inlets and their interaction with vorticity formed at the inlet channel lateral boundaries. Vortical structure in the flow field is identified using a local swirl strength criterion evaluated from the two-dimensional flow field. The starting jet dipole vortices and vortices formed as the lateral boundary layers are expelled during flow reversal are characterized by their trajectory, size, and circulation. Using these quantities, a model is developed to predict the size and strength of the expelled lateral boundary layer vortices based on the inlet velocity, channel length, and width of the lateral boundary layer. The expelled boundary layer vortices are found to disrupt the formation of the primary tidal jet dipole through two mechanisms. First, because the boundary layer vortices themselves form a dipole with each half of the starting-jet dipole, the starting-jet vortices are pulled apart and advected away from the inlet mouth early in the tidal cycle, resulting in a reduction in the spin-up time and the amount of vorticity input during starting-jet vortex formation. Second, the advection of each dipole away from the inlet disconnects each starting-jet vortex from the starting jet; hence, the vortices are not fed by fluid in the jet or energized by shear in the jet boundary layers. These influences of the lateral boundary layer on the starting-jet vortices’ formation and propagation are found to be a function of the channel length L, maximum velocity U, and tidal period T, resulting in a predictive value to characterize their trajectory, strength, and evolution.

Boundary layers in stochastic thermodynamics

We study the problem of optimizing released heat or dissipated work in stochastic thermodynamics. In the overdamped limit these functionals have singular solutions, previously interpreted as protocol jumps. We show that a regularization, penalizing a properly defined acceleration, changes the jumps into boundary layers of finite width. We show that in the limit of vanishing boundary layer width no heat is dissipated in the boundary layer, while work can be done. We further give an alternative interpretation of the fact that the optimal protocols in the overdamped limit are given by optimal deterministic transport (Burgers equation).

Elastic turbulence in a curvilinear channel flow

We report detailed quantitative studies of elastic turbulence in a curvilinear channel flow in a dilute polymer solution of high molecular weight polyacrylamide in a high viscosity water-sugar solvent. Detailed studies of the average and rms velocity and velocity gradients profiles reveal the emergence of a boundary layer associated with the nonuniform distribution of the elastic stresses across the channel. The characteristic boundary width is independent of the Weissenberg number Wi and proportional to the channel width, which is consistent with the findings our early investigations of the boundary layer in elastic turbulence in different flow geometries. The nonuniform distribution of the elastic stresses across the channel and appearance of the characteristic spatial scales of the order of the boundary layer width of both velocity and velocity gradient in the correlation functions of the velocity and velocity gradient fields in a bulk flow may suggest that excessive elastic stresses, concentrated in the boundary layer, are ejected into the bulk flow similar to jets observed in passive scalar mixing in elastic turbulence observed recently. Finally, the experimental results show that one of the main predictions of the theory of elastic turbulence, namely, the saturation of the normalized rms velocity gradient in the bulk flow of elastic turbulence contradicts the experimental observations both qualitatively and quantitatively in spite of the fact that the theory explains well the observed sharp power-law decay of the velocity power spectrum. The experimental findings call for further development of theory of elastic turbulence in a bounded container, similar to what was done for a passive scalar problem.

On the early evolution in the transient Bénard–Marangoni problem

We focus on the early evolution of small (linear) perturbations following the sudden (step-function) exposure of a liquid layer to a cold adjacent atmosphere. On a time scale short relative to that characterizing thermal relaxation across the liquid layer, the temperature distribution is nonlinear and highly transient. Thus, the conduction reference state may not be regarded quasi steady. We accordingly consider the initial-value problem and obtain a Volterra-type integral equation governing the evolution of surface-temperature perturbations. Assuming an O(1) Biot number we study the effects on perturbations evolution of the wavenumber, the Prandtl number (Pr) and the effective Marangoni number (Ma¯, which, from the dominant balance in the thermal perturbation equation, is based on the current values of the width of the thermal boundary layer and the temperature difference across it, respectively). Explicit results are first presented in the limit of Pr>>1 wherein the hydrodynamic perturbation problem is quasi steady. The dominant perturbations correspond to large wavenumbers and convection effectively confined to the thermal boundary layer. Typical of the results is the nonmonotonic temporal evolution of perturbations which initially diminish and only after some finite delay time start to grow. These trends are rationalized in terms of the Marangoni mechanism by observing that while the magnitude of the reference-state temperature gradients remain essentially constant, they extend over a widening thermal boundary layer allowing for enhanced convective effects. Thus, since perturbations may be introduced at all positive times, those evolving on the favourable background of further developed (wider) thermal boundary layers may take over perturbations introduced earlier. This suggests the existence of a nonzero “optimal” appearance time of perturbations which will eventually dominate the instability process. We study the effects of finite O(1) values of Pr on the evolution of the hydrodynamic perturbation problem which is no longer quasi steady. Increasing Pr at a constant Ma¯ is destabilizing which reflects the dual role of liquid viscosity in the transient Bénard-Marangoni problem. It is further demonstrated that with increasing wavenumber convergence to the asymptotic Pr>>1 limit is practically achieved at smaller Pr.

Effects of sub-millimeter-bubble injection on transition to turbulence in natural convection boundary layer along a vertical plate in water

Temperature and velocity measurements are performed to clarify the effects of sub-millimeter-bubble injection on the transition to turbulence in the natural convection boundary layer along a vertical plate in water. In particular, we focus on the relationship between the bubble injection position L and the transition to turbulence in the natural convection boundary layer. The bubble injection positions used in our experiments are L = 1.6 and 3.6 mm. Bubble injection at L = 1.6 mm delays the transition to turbulence in the natural convection boundary layer, while that at L = 3.6 mm accelerates the transition to turbulence in the boundary layer. In the case of L = 1.6 mm, the appearance region of the liquid velocity fluctuation in the bubble-induced upward flow in the upstream unheated section is restricted to near the wall, although the peak of the liquid velocity fluctuation is high. In contrast, in the case of L = 3.6 mm, the relatively large liquid velocity fluctuation is distributed widely over the laminar boundary layer width. These results suggest that the effect of the liquid velocity fluctuation on the laminar boundary layer is quite different between L = 1.6 and 3.6 mm. It is therefore expected that the transition to turbulence in the natural convection boundary layer for the case with bubble injection is dependent on the magnitude and appearance region of the liquid velocity fluctuation in the bubble-induced upward flow in the upstream unheated section.

Reaction-layer asymptotics and the electrochemical pickling of steel

Asymptotic methods are used to explore the role of one of the homogeneous chemical reactions, water protolysis, in a recent numerical model for the electrochemical pickling of steel. The analysis helps to interpret the somewhat surprising results of the original numerical model: that the local current density profile at the pickled strip does not depend on whether the water protolysis reaction is included in the model or not. The analysis also gives a useful systematic approach for determining qualitative estimates for the width of reaction boundary layers at cell electrodes, which can be of help when designing a computational mesh for the numerical solution of electrochemical models that have such layers.

On the interactions between planetary geostrophy and mesoscale eddies

Abstract Multiscale asymptotics are used to derive three systems of equations connecting the planetary geostrophic (PG) equations for gyre-scale flow to a quasigeostrophic (QG) equation set for mesoscale eddies. Pedlosky (1984), following similar analysis, found eddy buoyancy fluxes to have only a small effect on the large-scale flow; however, numerical simulations disagree. While the impact of eddies is relatively small in most regions, in keeping with Pedlosky’s result, eddies have a significant effect on the mean flow in the vicinity of strong, narrow currents. First, the multiple-scales analysis of Pedlosky is reviewed and amplified. Novel results of this analysis include new multiple-scales models connecting large-scale PG equations to sets of QG eddy equations. However, only introducing anisotropic scaling of the large-scale coordinates allows us to derive a model with strong two-way coupling between the QG eddies and the PG mean flow. This finding reconciles the analysis with simulations, viz. that strong two-way coupling is observed in the vicinity of anisotropic features of the mean flow like boundary currents and jets. The relevant coupling terms are shown to be eddy buoyancy fluxes. Using the Gent-McWilliams parameterization to approximate these fluxes allows solution of the PG equations with closed tracer fluxes in a closed domain, which is not possible without mesoscale eddy (or other small-scale) effects. The boundary layer width is comparable to an eddy mixing length when the typical eddy velocity is taken to be the long Rossby wave phase speed, which is the same result found by Fox-Kemper and Ferrari (2009) in a reduced gravity layer.

ICONE19-43569 STUDY ON FLOW INDUCED VIBRATION EVALUATION FOR A LARGE SCALE JSFR PIPING : (4) UNSTEADY FLOW CHARACTERISTICS IN 1/10 SCALE HOT-LEG PIPING EXPERIMENTS UNDER UNDEVELOPED AND SWIRL INFLOW CONDITIONS

LDV measurements in a 90 degrees elbow were examined for the cases of inflow from a long pipe, short pipe and swirl generator. The elbow is considered as a 1/10 scale hot-leg piping model of a Japanese sodium-cooled fast breeder reactor (JSFR). Time-averaged flow distribution for the Reynolds number of 320000, based on the inner pipe diameter and bulk velocity, shows that shortening the upstream pipe length to 4.9D from 10D induces the flow separation downstream of the elbow. Detailed observation shows that shortening upstream pipe weakens the Prandtl's secondary flow of the first kind. This suppresses the kinetic energy transport from the outer to inner side of the elbow. Swirl generator in the present experimental setting generates the swirling inflow with the non-dimensional angular momentum of 0.12, based on the inner pipe diameter and bulk velocity. The circumferential velocity distribution formed a shape like Rankin's combined vortex in the elbow inlet, and the accelerated axial velocity at the vortex center is observed. The axial velocity distribution however is found to be almost the same as that of the non-swirl inflow case in the latter half of the elbow. Frequency analyses shows that the Strouhal number by vortex shedding from the boundary layer occurring at the inner side became 0.5, except for 0.6 in the case of the long pipe case. This might be related with the boundary layer width and the local flow velocity.

Conformational Ordering in Growing Spherulites of Isotactic Polypropylene

The conformational ordering in spherulites of isotactic polypropylene during growing process is studied with in situ infrared microspectroscopic imaging. A comparison between the intensity distribution of bands representing crystal and conformational ordering indicates that large concentration of conformational ordered segments exist in the growth boundary region of spherulites, which suggests that conformational ordering takes place before packing into crystal lattice in the growth boundary layer. The width of the growth boundary layer is sensitive to temperature but keeps relative constant during isothermal crystallization process. Though the interchain organization of the conformational ordered segments is not clear yet, conformational ordering in the growth boundary layer is assigned to be a preordering step of crystallization.

Bathymetric influences of the Emperor Seamounts upon the subarctic gyre of the North Pacific: Examining boundary current dynamics along the eastern side of the mountain ridge with an idealized numerical model

The possible influences of the Emperor Seamounts (ESs) upon the subarctic gyre of the North Pacific (NPSAG) were investigated by a series of numerical experiments. In the experiments, a two-layer ocean with a meridional mountain ridge was forced by seasonally varying wind stress. We focused on how the return ratio, the ratio of the boundary transport along the eastern side of the ridge to the interior Sverdrup transport, changes with ridge height, width and density stratification. It was found that the return ratio can be large if the ridge width is greater than the width of the viscous boundary layer. In this case, the bottom pressure torque determines the return ratio; the return ratio is almost proportional to the ridge height when the ridge height is small and some contours of planetary potential vorticity pass over the ridge. However, the return ratio is independent of the ridge height and decreases with the stratification when the ridge height is large and all the contours of planetary potential vorticity are closed. These dependences of the return ratio were understood in terms of barotropic and baroclinic components of the bottom pressure torque. Implications for the bathymetric influences of ESs on the actual NPSAG are also discussed.