Constant Boundary Layer Research Articles

Symmetry-reduced low-dimensional representation of large-scale dynamics in the asymptotic suction boundary layer

An important feature of turbulent boundary layers are persistent large-scale coherent structures in the flow. Here, we use Dynamic Mode Decomposition (DMD), a data-driven technique designed to detect spatio-temporal coherence, to construct optimal low-dimensional representations of such large-scale dynamics in the asymptotic suction boundary layer (ASBL). In the ASBL, fluid is removed by suction through the bottom wall, resulting in a constant boundary layer thickness in streamwise direction. That is, the streamwise advection of coherent structures by the mean flow ceases to be of dynamical importance and can be interpreted as a continuous shift symmetry in streamwise direction. However, this results in technical difficulties, as DMD is known to perform poorly in presence of continuous symmetries. We address this issue using symmetry-reduced DMD (Marensi et al., 2023), and find the large-scale dynamics of the ASBL to be low-dimensional indeed and potentially self-sustained, featuring ejection and sweeping events at large scale. Interactions with near-wall structures are captured when including only a few more modes.

A Sliding-Mode Control with Efficient Chattering Alleviation for Single-Phase Voltage Source Inverters

This paper presents an adaptive sliding mode control (SMC) method with a variable boundary layer for single-phase voltage source inverters. This strategy offers a very simple sliding function without any derivative term while preserving unique characteristics of the sliding mode control like fast dynamic response and robustness against parameter variations while also possessing the variable boundary layer method to reject the chattering phenomena. Chattering excites the high frequencies in the system and leads to inaccuracy and instability. It is shown that despite the conventinal approches, the proposed variable boundary layer method can both alleviate the chattering and generating the minimum steady state error. Owing to the adaptive nature of the suggested control approach which adjusts the thickness of the boundary layer, the whole mechanism can be controlled successfully under unpredictable parameter variations. The accomplishment of the suggested strategy is investigated by simulations in MATLAB/Simulink. The outcomes are compared with the outcomes obtained without boundary layer, with constant boundary layer and super twisting sliding control methods. The comparison reveals that the proposed control technique outperforms the other control methods for the voltage source inverter. The results demonstrate that while the conventional, SMC with constant boundary layer and super twisting sliding control (STSMC) methods have 50% ,8% and 10% chattering over their control input respectively, the proposed method has less than 3% chattering over the control input.

Ефективність впливу легування міддю на зношування заевтектоїдних сталей

The intensity of wear of graphitized eutectoid steels with a carbon content in the range of 1.1÷1.7%, by weight was investigated. The effectiveness of the effect of copper doping on the wear of eutectoid steels in the cast state has been determined. It was established that under conditions of dry friction by sliding and taking into account the friction parameters in the sealing units the temperature on the worn surface and in the thin near-surface layer should exceed 1100 0С, at such temperatures and copper content more than 12%, by weight, in the binary system Fe-Cu there is a two-phase region +-phase, and  - phase, exists in the state of liquid and acts as a lubricant, the wear mode goes from dry to limiting. Lines of existence of -phases in the liquid state are constructed. The results of studies of the effect of copper on the intensity of wear of steels with different carbon content, under conditions of dry friction by slipping, indicated that regardless of the amount of carbon, doping of alloys with copper significantly reduces their intensity of wear to copper content at the level of 10-12%, by weight, a further increase in copper doping equalizes the effectiveness of the impact and reduces the intensity of wear. Alloying of steels with copper of 12% or more causes the formation of a copper phase film on the friction surface. Under the condition of alloying steel with copper less than 12%, the steel structure contains -phase, as a product of a three-phase eutectoid reaction and as a decomposition product of supersaturated solid iron solution. As the copper content in steel increases, the amount of copper phase in the steel structure and its amount on the contact surface increases, after reaching the copper content in the steel sufficient to form the primary grains of the copper phase, the formation of a stable layer of copper on the contact surface begins, which is the constant boundary layer of copper -phase in the liquid state. Keywords: steel, copper, carbon, alloying, wear resistance, friction.

An Enhanced SMO-Based Permanent-Magnet Synchronous Machine Sensorless Drive Scheme With Current Measurement Error Compensation

This article establishes an enhanced sliding-mode observer (SMO) with current measurement error compensators for the speed and position estimation in the permanent-magnet synchronous machine (PMSM) sensorless drive scheme. First, hyperbolic tangent switching function-based SMO with a self-adjusted shape coefficient is realized using a fuzzy logic controller (FLC) to not only eliminate the low-pass filter (LPF) and angular compensator in the conventional SMO, but also to reduce chatter caused by the constant boundary layer thickness. On the basis of Lyapunov's second theory, reachable and stable conditions of the enhanced SMO are founded. Then, as the current controller in the PMSM sensorless drive system needs to detect phase currents using current sensors, inevitable measurement errors exist. Two major kinds of current measurement errors, namely, the offset error and the scaling error, are analyzed. Their influences on the current fluctuations and corresponding compensation strategies are given in detail. By integrating current compensators into the enhanced SMO, a practical PMSM sensorless field-oriented control (FOC) scheme is constructed. The effectiveness of the enhanced SMO and current compensators is validated separately by comparative experiments. Final results indicate satisfactory chatter reduction and current ripple suppression performance of the proposed method.

Simulation of Mesoscale Cellular Convection in Marine Stratocumulus: 2. Nondrizzling Conditions

AbstractThis is the second of two large‐eddy simulation studies on the mechanisms of mesoscale cellular organization in drizzling (open cells) and nondrizzling marine stratocumulus (closed cells). This study uses a hard nudging approach which maintains fixed horizontal‐mean temperature and humidity profiles for a well‐mixed boundary layer with a constant boundary layer depth. For the case studied, closed cells develop and broaden by 32 hr to an aspect ratio of 25. Simulations show that the closed‐cell mesoscale cellular convection is driven by positive feedback from cloud‐induced mesoscale perturbations of longwave radiative cooling. A conceptual model for closed‐cell stratocumulus as a mesoscale wavelength hydrodynamic instability in which mesoscale moist and dry anomalies spontaneously grow is presented. In simulations in which long‐wavelength sinusoidal moisture anomalies are initially imposed, these anomalies evolve into amplifying closed cells. The cell structure is visualized with a compositing approach based on sorting grid columns by their mesoscale‐smoothed total water path. A thermally direct mesoscale circulation pattern develops in the interior of the boundary layer with buoyant mesoscale updrafts, thicker cloud, and a slightly higher capping inversion in the moister columns. There is a mesoscale flow of above‐inversion air down the slightly sloping capping inversion from the moist to the dry regions, reinforced by cloud top radiative cooling. This strengthens the mesoscale anomalies by preferentially cooling and drying the already dry regions. The sloping inversion flow is not driven as efficiently if the radiative cooling is artificially horizontally homogenized, partly disrupting this positive feedback and the resulting closed‐cell development.

Modeling of turbulent cross flow microfiltration of pomegranate juice using hollow fiber membranes

A mathematical analysis of the permeate flux decline during microfiltration of fruit juice with hollow fibers under turbulent flow is presented. Impact of complex fluid flow phenomena on mass transfer is analyzed. A comprehensive analytical model for developing concentration boundary layer was formulated from first principles using integral method. Attempts to model the system considering constant boundary layer thickness (film theory) is inaccurate for developing boundary layer. Gel resistance parameter depending on juice characteristics has significant impact on permeate flux. Specific gel layer concentration has insignificant effect on system performance under total recycle mode but important for batch mode. Theoretical results were compared with experiments in clarification of pomegranate juice with poly(ether ether ketone) and polysulfone hollow fiber membranes. The physical parameters of complex mixture were evaluated by optimizing of the flux profiles in total recycle mode of operation and were successfully applied for prediction of batch mode performance. © 2014 American Institute of Chemical Engineers AIChE J 60: 4279–4291, 2014

The Role of Extreme Agitation in Accelerating the Removal Rate of Advanced Packaging Photoresists

Negative Dry Film and Negative Spin-On photoresists are widely adopted as the prime choice in wafer-scale packaging processes such as bumping, TSV, and copper pillars. High transparency of negative resist produces vertical profiles with no footing at low exposure energy, resulting in a robust, high throughput lithography process (Doki, 2005). In plating applications, the 3-D cross-linking of negative resist provides good adhesion to wide range of substrates, enabling high-current ECD processes with high throughput. The main challenge of negative photoresist has always been its removal difficulty. Aggressive remover chemistries consisting of DMSO, NMP, and TMAH have been used to cleave, swell, and dissolve the material (Moore, 2002). This paper demonstrates the capabilities of a novel immersion-based strip technology that maintains a constant boundary layer at the wafer surface by providing high-speed agitation to each individual wafer. Results show an acceleration of the removal process, while reduced exposure to remover chemistries reduces risks of bump corrosion. Removal rates of negative dry film and negative spin-on resist materials have been studied across variety of commercially available strip chemistries.

Position Control for Interior Permanent Magnet Synchronous Motors using an Adaptive Integral Binary Observer

An approach to control the position for an interior permanent magnet synchronous motor (IPMSM) based on an adaptive integral binary observer is described. The binary controller with a binary observer is composed of a main loop regulator and an auxiliary loop regulator. One of its key features is that it alleviates chatter in the constant boundary layer. However, steady state estimation accuracy and robustness are dependent upon the thickness of the constant boundary layer. In order to improve the steady state performance of the binary observer and eliminate the chattering problem of the constant boundary layer, a new binary observer is formed by adding extra integral dynamics to the existing switching hyperplane equation. Also, the proposed adaptive integral binary observer applies an adaptive scheme because the parameters of the dynamic equations such as the machine inertia and the viscosity friction coefficient are not well known. Furthermore, these values can typically be easily changed during normal operation. However, the proposed observer can overcome the problems caused by using the dynamic equations, and the rotor position estimation is constructed by integrating the rotor speed estimated with a Lyapunov function. Experimental results obtained using the proposed algorithm are presented to demonstrate the effectiveness of the approach.

VARIABLE-THICKNESS BOUNDARY LAYERS FOR SLIDING MODE CONTROL

Sliding mode control is a nonlinear feedback control technique which provides good robustness against modeling uncertainties and external disturbances. However, as the uncertainties or disturbances increase, a greater control input is required, and the control signal may cause an undesirable chattering phenomenon. In general, the further the system trajectory from the origin, the more violent the chattering effect. However, as the trajectory moves closer to the origin, the degree of chattering gradually reduces. As a result, even if an attempt is made to eliminate chattering by introducing a small constant boundary layer around the sliding surface, the chattering phenomenon may still take place during the transient stage. Furthermore, if the thickness of the boundary layer is increased in order to suppress chattering completely, control accuracy may be lost. Accordingly, this study proposes four different variable-thickness boundary layers designed to achieve a compromise between the desire to eliminate the chattering phenomenon and the need to retain control accuracy. In two of these boundary layers, the thickness is approximately proportional to the norm of the normalized state vector; while in the other two layers, the thickness tends toward a saturated value as the trajectory moves further from the origin. The feasibility and effectiveness of the proposed approaches are verified through their application to several representative numerical examples.

Evaluating Spectral Models and the X‐Ray States of Neutron Star X‐Ray Transients

We analyze the X-ray spectra of the neutron star (NS) X-ray transients Aql X-1 and 4U 1608-52, obtained with RXTE during more than 20 outbursts. We test commonly used spectral models and evaluate their performance against desirability criteria, including LX ∝ T4 evolution for the multicolor disk (MCD) component and similarity to black holes (BHs) for correlated timing/spectral behavior. None of the classical models for thermal emission plus Comptonization perform well in the soft state. Instead, we devise a hybrid model: for the hard state, a single-temperature blackbody (BB) plus a broken power law (BPL), and for the soft state, two thermal components (MCD and BB) plus a constrained BPL. This model produces LX ∝ T4 tracks for both the MCD and BB, and it aligns the spectral/timing correlations of these NSs with the properties of accreting BHs. The visible BB emission area is very small (~1/16 of the NS surface), but it remains roughly constant over a wide range of LX that spans both the hard and soft states. We discuss implications of a small and constant boundary layer in terms of the presence of an innermost stable circular orbit that lies outside the NS. Finally, if the BB luminosity tracks the overall accretion rate, then we find that the Comptonization in the hard state has surprisingly high radiative efficiency compared to MCD emission in the soft state. Alternatively, if we assume that the radiative efficiency of a jet in the hard state must be less than the MCD efficiency in the soft state, while relaxing presumptions about the accretion rate, then our results may suggest substantial mass outflow in the jet.

On Robust, Multi-Input Sliding-Mode Based Control with a State-Dependent Boundary Layer

This paper proposes a nonlinear multi-input control law using sliding mode concepts for continuous-time, uncertain, linear systems. The control law introduces a state-dependent layer around the sliding mode plane to remove chattering. This layer combines two types of boundary layers: a constant layer and a sector-shaped layer. The states will always enter the state-dependent boundary layer and the choice of the sliding mode will be seen to determine the ultimate system performance. A proof of stability shows ultimate boundedness. The controller is applied to a nonlinear simulation model of a cart-pendulum and exhibits a high degree of robustness. The new boundary layer in connection with a novel dynamically changing, state-dependent gain can be used to obtain a narrow boundary-layer shape in the operating region of interest. This permits rejection of disturbances without chattering of the control and improves on the performance expected of a sliding-mode control with constant boundary layer.

Experimental study of rotating disk flow instability. II. Forced flow

The destabilization of the rotating disk flow subject to a forcing is experimentally investigated. An isolated roughness element of size of order δ (the constant boundary layer thickness) is placed under the linear threshold of the cross-flow instability in order to create a hydrodynamic pattern of finite amplitude and localized in space. The experimental neutral stability curve is first established. The resulting double parabolic curve exhibits two minima: one of which is due to the amplification of fundamental modes, the other one is linked to the emergence of superharmonic modes. Dispersion curves determined by means of two-point measurements appear to be shifted away from those measured in the natural case (without forcing). We show that this discrepancy is due to the presence of weak nonlinear effects which can be described by a Ginzburg–Landau amplitude equation. Lastly, we present an original method that enables to determine both components of the group velocity vector using the measured dispersion relations and wave packet propagation angle.

An electrical sensor for potential transpiration: Principle and prototype

SummaryTheoretical treatment showed that evaporation rate from a physical model of a hypo- stomatous leaf can be estimated by measuring the degree of evaporative cooling relative to a dry reference ‘leaf but that proportionality depends on constant boundary layer conditions and therefore constant wind speed. The significance of this and other possible sources of error involved in the application of this principle to the development of an electrical sensor to monitor environments used for rooting cuttings were examined. A prototype sensor was created by incorporating thermocouples into the ‘leaf of an existing volumetric evaporimeter. Calibration of evaporation rate against the electrically measured temperature difference was much less sensitive to wind speed than expected from the theory. However, measurements with replicate evaporimeters in a wet and humid environment showed that there could be unexpectedly large variations in calibration coefficient from one hour-long measurement interval to another. Po...

Modeling of extrusion with slip boundary conditions

AbstractSlip at boundaries is possible in viscous flows; for instance, in the extrusion of foodstuffs, water‐containing materials, and some polymers. There are two phenomenological descriptions of slip: The first is based on the presence of a very thin, low viscosity boundary layer and has been derived for capillary flow and extrusion; the second is based on a Coulomb‐friction mechanism and has been derived for capillary flow only. After a survey of these results, the friction model is derived for the extrusion process. All calculations are as simple as possible: two‐dimensional, Newtonian, isothermal, and with constant boundary layer parameters of coefficients of friction. A strong dependence of pumping characteristics and efficiency on the slip boundary conditions, and also on the extruder length in the case of friction, was found, especially when slip is only allowed for at the screw surface. Exercises like these may help in understanding abnormal extrusion behavior of slippery materials in practice.

Structure of the low‐latitude boundary layer

Observations at high temporal resolution of the frontside magnetopause and plasma boundary layer, made with the Los Alamos Scientific Laboratory/Max‐Planck‐Institut, Institut für Extraterrestrische Physik, fast plasma analyzer on board the Isee 1 and 2 spacecraft, have revealed a complex quasi‐periodic structure of some of the observed boundary layers: cool tailward streaming boundary layer plasma is seen intermittently, with intervening periods of hot tenuous plasma which has properties similar to the magnetospheric population. While individual encounters with the boundary layer plasma last only a few minutes, the total observation time may extend over 1 hour or more. One such crossing, at 0800 hours local time and 40° northern GSM latitude, is examined in detail, including a quantitative comparison of the boundary layer entry and exit times of the two spacecraft. The data are found to be compatible with a boundary layer that is always attached to the manetopause but where the layer thickness has a large‐scale spatial modulation pattern which travels tailward past the spacecraft. Included are periods when the thickness is essentially zero and others when it is of the order of 1 RE. The duration of these periods is highly variable but is typically in the range of 2–5 min, corresponding to a distance along the magnetopause of the order of 3–8 RE. The observed boundary layer features include a steep density gradient at the magnetopause, with an approximately constant boundary layer plasma density amounting to about 25% of the magnetosheath density, and a second abrupt density decrease at the inner edge of the layer. It also appears that the purely magnetospheric plasma is occasionally separated from the boundary layer by a halo region in which the plasma density is somewhat higher, and the temperature somewhat lower, than in the magnetosphere. A tentative model is proposed in which the variable boundary layer thickness is produced by the Kelvin‐Helmholtz instability of the inner edge of the layer and in which eddy motion provides effective mixing within the layer.

The acoustical impedance of holes in the wall of flow ducts

The radiation impedance of circular and oblong holes in the wall of a flow duct has been measured as a function of the flow velocity. The boundary layer at the wall of the duct is thin compared to the dimensions of the orifices. At low Strouhal numbers (quasi-static case) and constant boundary layer thickness, the flow resistance of the orifice (real part of the impedance) increases in proportion to the flow velocity. The imaginary part of the impedance corresponds to a constant, negative attached mass above the orifice, i.e. the impedance is spring-like. In the transition range from air at rest to the quasi-static case (high Strouhal numbers) the impedance as a function of the flow velocity describes a spiral in the complex plane. The mechanism causing the flow dependence of the impedance is illustrated by a simple model of the flow above the orifice. As a practical example of the flow-dependent impedance of orifices, the flow-dependent sensitivity of a probe microphone used in flowing media is discussed.

An analytical model for mass transfer in an electrodialysis cell with spacer of finite mesh

The proposed “mesh step” model represents the mass transfer process as a laminar concentration boundary layer whose development is periodically interrupted. The boundary layer develops along a given characteristic length at the end of which it undergoes partial mixing, i.e., it regresses to an earlier, less developed stage, from which the development starts again, etc. Thus the mixing effect of the spacer is represented by two parameters: The mesh size and mixing efficiency. This is compared with a “constant boundary layer” model which assumes a laminar diffusion layer of constant thickness with perfectly mixed bulk flow.

The effect of convergent and divergent flow patterns on infrared and optical radiation from the sea

The thermal, and some optical effects, of divergence and convergence are calculated both for steady and periodic in time flow. The former corresponds to stationary sources and sinks or convection cells, the latter to travelling surface and internal waves. Thermal effects are primarily calculated for radiation loss, the effects of evaporation and conduction are estimated. The total thermal effects of surface waves are of order 0.1 to 0.01°C, and the frequency spectrum of temperature fluctuations is related quantitatively to the wave height spectrum at the same time and position on the sea. The general thermal effects of an oscillating divergence associated with wave motion can be divided into two parts depending upon whether the period of wave motion is large (slow) or small (rapid) compared to the cooling time of the boundary layer. For rapid variations the temperature variation is independent of boundary layer thickness and is proportional to the static, normal thermal gradient at the surface. This case includes most surface waves. For slow variations, the temperature variation is proportional to the total temperature drop through the boundary layer, and varies with some power of the boundary layer thickness. This case includes most internal waves. For this slow case, the temperature fluctuation is much smaller for a constant boundary layer thickness, than for a layer of thickness varying periodically with the divergence. The theory is inadequate to describe thermal effects over internal waves, primarily due to the effects of surface contaminants. A simple experiment is proposed to resolve some of the numerous uncertainties in the calculations.