Boundary Layer Phenomena Research Articles

Boundary layer problem on a hyperbolic system arising from chemotaxis

This paper is concerned with the boundary layer problem for a hyperbolic system transformed via a Cole–Hopf type transformation from a repulsive chemotaxis model with logarithmic sensitivity proposed in [23,34] modeling the biological movement of reinforced random walkers which deposit a non-diffusible (or slowly moving) signal that modifies the local environment for succeeding passages. By prescribing the Dirichlet boundary conditions to the transformed hyperbolic system in an interval (0,1), we show that the system has the boundary layer solutions as the chemical diffusion coefficient ε→0, and further use the formal asymptotic analysis to show that the boundary layer thickness is ε1/2. Our work justifies the boundary layer phenomenon that was numerically found in the recent work [25]. However we find that the original chemotaxis system does not possess boundary layer solutions when the results are reverted to the pre-transformed system.

Boundary-layer phenomena for the cylindrically symmetric Navier–Stokes equations of compressible heat-conducting fluids with large data at vanishing shear viscosity

This paper concerns the asymptotic behavior of the solution to an initial-boundary value problem of the cylindrically symmetric Navier–Stokes equations with large data for compressible heat-conducting ideal fluids, as the shear viscosity μ goes to zero. A suitable corrector function (the so-called boundary-layer type function) is constructed to eliminate the disparity of boundary values. As by-products, the convergence rates of the derivatives in L2 are obtained and the boundary-layer thickness (BL-thickness) of the value with is shown by an alternative method, compared with the results proved in Jiang and Zhang (2009 SIAM J. Math. Anal. 41 237–68) and Qin et al (2015 Arch. Ration. Mech. Anal. 216 1049–86).

Mixed convection heat transfer to modified second grade fluid in the presence of thermal radiation

The aim of the current research is to contemplate the mixed convection flow and heat transfer of the modified second grade fluid by examining the thermal radiation effects in the presence of the convective boundary conditions. The boundary layer phenomenon is adopted for the flow past a non-linearly stretching surface in consideration of assisting and opposing buoyancy effects. The reduced governing ordinary differential equations obtained by using appropriate local similarity transformations are numerically integrated by the help of shooting method. The impact of various emerging parameters on the velocity and temperature fields is graphically displayed for assisting as well as opposing flows. It is inferred that the skin friction coefficient and the heat transfer rate at the wall reduces with the progressive values of the generalized Biot number and the thermal radiation parameter.

Cattaneo-Christov heat flux model for flow of variable thermal conductivity generalized Burgers fluid

An attempt has been made to study the characteristics of generalized Burgers fluid over a stretched surface. Cattaneo-Christov heat flux model is utilized for the formulation of the energy equation instead of Fourier's law of heat conduction. This model can foresee the impacts of thermal relaxation time on the boundary layer phenomenon. Employing appropriate transformations the coupled nonlinear partial differential equations are converted into a set of coupled nonlinear ordinary differential equations. Convergent series solutions are developed for the arising governing equations through the homotopy analysis method (HAM) to explore the features of various pertinent parameters for the velocity and temperature distributions. The obtained results are presented in tabular form as well as graphically and discussed in detail. Our calculations witness that fluid temperature has converse relationship with the thermal relaxation time.

Formation of boundary layers for singularly perturbed fourth-order ordinary differential equations with the Lidstone boundary conditions

In this paper we concentrate on the aspect of the boundary layer phenomenon that represents a typical asymptotic behavior mode of singularly perturbed systems at the endpoints of the considered interval. We provide a detailed analysis of this phenomenon for the nonlinear fourth-order ordinary differential equations subject to the Lidstone boundary conditions by an analysis of the integral equation associated with an original boundary value problem.

Analysis and Design of a Scramjet Engine Inlet Operating from Mach 5 to Mach 10

This paper gives a preliminary report of the analysis and design process of a scramjet engine inlet operating over a Mach number range from 5 to 10 without the use of variable geometry (moving parts) in order to find an optimal 2D geometry. An introduction of scramjet engine as well as its first component, the inlet, is given in the beginning and a number of basic inlet configurations are proposed. Inlet efficiency parameters and various design criteria are then explained, followed by a theoretical flow analysis utilizing some simplifying assumptions and the oblique shockwave relations. Next, 2D CFD simulations are carried out for some inlet geometries that are constructed based on the results of the theoretical analysis using the K-Omega SST turbulence model in Fluent to take into consideration boundary layer phenomena that the theoretical analysis is not able to cover. Lastly, a conclusion summarizing the design process is drawn and the optimal model is recommended.

Approaches for Improved Doppler Estimation in Lidar Remote Sensing of Atmospheric Dynamics

Laser radar (Lidar) has been used extensively for remote sensing of wind patterns, turbulence in the atmospheric boundary layer and other important atmospheric transport phenomenon. As in most narrowband radar application, radial velocity of remote objects is encoded in the Doppler shift of the backscattered signal relative to the transmitted signal. In contrast to many applications, however, the backscattered signal in atmospheric Lidar sensing arises from a multitude of moving particles in a spatial cell under examination rather than from a few prominent “target” scattering features. This complicates the process of extracting a single Doppler value and corresponding radial velocity figure to associate with the cell. This paper summarizes the prevalent methods for Doppler estimation in atmospheric Lidar applications and proposes a computationally efficient scheme for improving Doppler estimation by exploiting the local structure of spectral density estimates near spectral peaks.

A Mesoscale Model-Based Climatography of Nocturnal Boundary-Layer Characteristics over the Complex Terrain of North-Western Utah.

Nocturnal boundary-layer phenomena in regions of complex topography are extremely diverse and respond to a multiplicity of forcing factors, acting primarily at the mesoscale and microscale. The interaction between different physical processes, e.g., drainage promoted by near-surface cooling and ambient flow over topography in a statically stable environment, may give rise to special flow patterns, uncommon over flat terrain. Here we present a climatography of boundary-layer flows, based on a 2-year archive of simulations from a high-resolution operational mesoscale weather modelling system, 4DWX. The geographical context is Dugway Proving Ground, in north-western Utah, USA, target area of the field campaigns of the MATERHORN (Mountain Terrain Atmospheric Modeling and Observations Program) project. The comparison between model fields and available observations in 2012–2014 shows that the 4DWX model system provides a realistic representation of wind speed and direction in the area, at least in an average sense. Regions displaying strong spatial gradients in the field variables, thought to be responsible for enhanced nocturnal mixing, are typically located in transition areas from mountain sidewalls to adjacent plains. A key dynamical process in this respect is the separation of dynamically accelerated downslope flows from the surface.

Proper accounting of mass transfer resistances in forward osmosis: Improving the accuracy of model predictions of structural parameter

This work demonstrates a more accurate method for calculating structural parameter (S) of asymmetric osmotic membranes using experimental data and a theoretical flux model which encapsulates all significant boundary layer phenomena. External boundary layer effects on the porous side of the membrane have been neglected in many current models. In these models, external concentration polarization (ECP) effects get combined with internal concentration polarization (ICP), resulting in inflated S values. In this study, we proposed a mathematical flux model in which ECP effects are accounted for, so that S can be more accurately measured. This model considered the in-series resistances for solute transport based on intrinsic properties of the membrane, as well as boundary layers at membrane surfaces and within the support layer. We therefore introduced new equations to define total resistance to solute transport and reflection coefficient of membranes in FO. The results indicate that ICP is less severe than previously predicted and that cross-flow velocity, temperature and concentration of the draw and the feed solutions impact both external and internal concentration polarization. Our calculations surprisingly show that changes in cross-flow velocity impact internal concentration polarization due to induced mixing within the support layer. Also, we suggest that it is critical to consider the “residence time” of solutes in the vicinity of the selective layer when determining the membrane selectivity.

Homogenization of the boundary value for the Neumann problem

In this paper, we study the convergence rates for homogenization problems for solutions of partial differential equations with rapidly oscillating Neumann boundary data. Such a problem raised due to its importance for higher order approximation in homogenization theory. High order approximation gives rise to the so-called boundary layer phenomenon. As a consequence, we obtain the pointwise and W1,p convergence results. Our techniques are based on Fourier analysis.

Two-scale nonlocal shear rate formulation of Bingham plastic fluid

This paper deals with a phenomenological model based on a nonlocal Bingham constitutive law. This nonlocal viscoplastic law accounts for possible microstructured effects of a heterogeneous fluid. Thermodynamic arguments are presented for the justification of this two-scale nonlocal shear rate law, which can be specialized either as a purely nonlocal or a gradient-type Bingham law. Plane shearing and uniaxial flow assumptions between parallel walls are basic and tractable hypotheses for a first investigation of nonlocal and gradient shear rate law. Analytical solutions are presented for the plane Poiseuille stationary flow inside a straight smooth channel of infinite width. Two higher boundary conditions at the walls are assumed for this so-called micromorphic medium, a static higher-order boundary condition and a kinematic one. A boundary layer phenomenon can be observed for such nonlocal problems. Parametric studies show the key role of the characteristic lengths of the nonlocal model on the shear flow phenomena. Consequently, the heterogeneous nature of microstructured yield-stress fluids may significantly affect velocity profiles, maximum velocity and total flow rate, which have been recently reported in literature.

A Case Study of Mid-Atlantic Nocturnal Boundary Layer Events during WAVES 2006

AbstractThe Water Vapor Variability-Satellite/Sondes (WAVES) 2006 field campaign provided a contiguous 5-day period of concentrated high-resolution measurements to examine finescale boundary layer phenomena under the influence of a summertime subtropical high over the mid-Atlantic region that is characterized by complex geography. A holistic analytical approach to low-level wind observations was adopted to identify the low-level flow structures and patterns of evolution on the basis of airmass properties and origination. An analysis of the measurements and the other available observations is consistent with the classic depiction of the daytime boundary layer development but revealed a pronounced diurnal cycle that was categorized into three stages: (i) daytime growth of the convective boundary layer, (ii) flow intensification into a low-level jet regime after dusk, and (iii) interruption by a downslope wind regime after midnight. The use of the field campaign data allows for the differentiation of the latter two flow regimes by their directions with respect to the orientation of the Appalachian Mountains and their airmass origins. Previous studies that have investigated mountain flows and low-level jet circulations have focused on regions with overt geographic prominence, stark gradients, or frequent reoccurrences, whereby such meteorological phenomena exhibit a clear signature and can be easily isolated and diagnosed. The results of this study provide evidence that similar circulation patterns operate in nonclassic locations with milder topography and atmospheric gradients, such as the mid-Atlantic region. The new results have important implications for the understanding of the mountain-forced flows and some air quality problems during the nocturnal period.

Application of atmospheric CVD for internal surface coating of graphite conduit by silicon carbide

Mechanism of silicon carbide coating on the internal surface of the graphite tube of dimension ϕ 3mm ID×ϕ 10mm OD×ϕ 235mm and surface area ∼24.5cm2 has been investigated. Atmospheric pressure chemical vapor deposition (APCVD) method in mass controlled domain has been applied. Methyltrichlorosilane (MTS) as precursor was used in the present investigation. The coating was characterized by X-ray micro tomography (μCT). The coating thickness and composition were analyzed by scanning electron microscopy energy-dispersive spectroscopy (SEM–EDS). The coating phase analyzed by X-ray diffraction (XRD). It has been concluded that silicon carbide coating is a predominantly boundary layer phenomena and the engineering of the same could open up the prospects to accomplish SiC coating on complex pipe line structures on macro scale.

Static analysis of deepwater lazy-wave umbilical on elastic seabed

Lazy wave configuration is considered as an appropriate approach for deepwater umbilical installation due to its advantages of accommodating large vessel offsets, decoupling the vessel motions from the touchdown point of the umbilical and reducing the hang-off tension. However, the introduction of buoyancy modules system brings about the great nonlinearity of lazy wave configuration, and the configuration is also significantly affected by the change of buoyancy modules. This paper presents an analytical model to analyze the static behavior of deepwater lazy-wave umbilical on the elastic seabed. Taking the environmental loads, elastic seabed and boundary-layer phenomenon into consideration, this lazy-wave model is divided into three parts: cable segment suspended in the water, boundary-layer segment in the neighborhood of the touchdown point and touchdown segment laid on the seabed. FEM by OrcaFlex was employed to verify the accuracy of the analytical model. The results from the two methods show excellent consistency. As well, a series of sensitivity analyses are also presented to highlight the influencing parameters in lazy wave configuration. The proposed method will provide a practical reference for deepwater lazy-wave umbilical installation.

Asymptotic Analysis of Acoustic Waves in a Porous Medium: Microincompressible Flow

This is the second in a series of three papers that studies acoustic waves governed by the linearized compressible Stokes equations in a porous medium. In particular, we want to analyze the simultaneous inviscid and high frequency limits of fluid flows in a porous medium. The presence of time-space boundary layers decouples the flow into an incompressible (that we call microincompressible) and an acoustic part (that we call micro-acoustic) on the microscopic scale. While this paper employs the two-scale methods used in our first paper [10], the present boundary layer phenomenon requires additional weak convergence tools. Using the Bloch decomposition, we introduce modified Helmholtz operators, enabling us to split the flow into its microincompressible and microacoustic parts. Closed equations for the microincompressible flow are obtained using two-scale convergence, while closed equations for the microacoustic flow are given in our forthcoming paper.

Bounded solutions in a T-shaped waveguide and the spectral properties of the Dirichlet ladder

The Dirichlet problem is considered on the junction of thin quantum waveguides (of thickness h ≪ 1) in the shape of an infinite two-dimensional ladder. Passage to the limit as h → +0 is discussed. It is shown that the asymptotically correct transmission conditions at nodes of the corresponding one-dimensional quantum graph are Dirichlet conditions rather than the conventional Kirchhoff transmission conditions. The result is obtained by analyzing bounded solutions of a problem in the T-shaped waveguide that the boundary layer phenomenon.

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.

Low Ozone Episodes at Amphitrite Point Marine Boundary Layer Observatory, British Columbia, Canada

ABSTRACTAt Amphitrite Point, ozone (O3) mixing ratios are observed to drop steadily to 5–15 ppb over a period of 12 hours or less with a frequency approaching one event per week (with highest frequencies occurring in summer and fall). Analysis of 47 such O3 depletion events reveals that low O3 episodes are a predominantly nocturnal phenomenon associated with anticyclonic conditions characterized by light onshore or alongshore winds and an absence of fog and mist. Back-trajectories show air carried to the Amphitrite Point Observatory (APO) during depletion events remains in the marine boundary layer and is not brought to the surface from aloft. There is no strong correlation with other “criteria” pollutants (CO, NOx, SO2, PM2.5) that might be indicative of a mechanism for O3 destruction linked to human, terrestrial, or marine pollutant sources. However, CO2 mixing ratios are observed to increase, coincident with O3 depletion. Together, these results point to a natural marine boundary layer phenomenon in which O3 destruction dominates O3 production and/or replenishment by vertical mixing. While there are several candidate mechanisms, the conditions for O3 depletion (and CO2 buildup) to occur are set by meteorology and, in particular, development of a stable marine boundary layer in which vertical mixing is suppressed. Support for this interpretation is provided by simultaneous increases in CO2 in the stable marine boundary that are indicative of an important role played by marine biogenic processes (respiration). Future research should be directed at elucidating the chemical mechanisms responsible for O3 destruction in the coastal zone, which means that there would be a need for a much broader range of measurements at APO (including halogenated species) as well as offshore measurements of both chemical and marine boundary layer meteorological variables.

Implementation of a generalized actuator disk wind turbine model into the weather research and forecasting model for large-eddy simulation applications

A generalized actuator disk (GAD) wind turbine parameterization designed for large-eddy simulation (LES) applications was implemented into the Weather Research and Forecasting (WRF) model. WRF-LES with the GAD model enables numerical investigation of the effects of an operating wind turbine on and interactions with a broad range of atmospheric boundary layer phenomena. Numerical simulations using WRF-LES with the GAD model were compared with measurements obtained from the Turbine Wake and Inflow Characterization Study (TWICS-2011), the goal of which was to measure both the inflow to and wake from a 2.3-MW wind turbine. Data from a meteorological tower and two light-detection and ranging (lidar) systems, one vertically profiling and another operated over a variety of scanning modes, were utilized to obtain forcing for the simulations, and to evaluate characteristics of the simulated wakes. Simulations produced wakes with physically consistent rotation and velocity deficits. Two surface heat flux values of 20 W m−2 and 100 W m−2 were used to examine the sensitivity of the simulated wakes to convective instability. Simulations using the smaller heat flux values showed good agreement with wake deficits observed during TWICS-2011, whereas those using the larger value showed enhanced spreading and more-rapid attenuation. This study demonstrates the utility of actuator models implemented within atmospheric LES to address a range of atmospheric science and engineering applications. Validated implementation of the GAD in a numerical weather prediction code such as WRF will enable a wide range of studies related to the interaction of wind turbines with the atmosphere and surface.

Forced Convection Across Horizontal Hot Cylinder Using Slotted Deflector Plate

According to Kirchoff–Helmhotlz solution for flow across a horizontal cylinder, the boundary layer separates at an angle of 55° from horizontal plane, so due to this separation phenomenon of boundary layer, the heat transfers from the upper side of a hot cylinder is minimum. Heat transfer from upper side can be increased by preventing the separation of boundary layer. Here we delay the separation of boundary layer by using a slotted deflector plate. Due to this accelerated air passes over upper side of the cylinder. The optimum distance at which the plate is to be kept from the cylinder is found out through this experiment. This experiment is also carried out by varying the width of the slot, the heat input to the cylinder and the velocity of flow of the air. We find that this method is more effective at higher temperatures and the highest temperature difference achieved was 20 % which is significant for cooing industrial equipments.