Boundary Layer Components Research Articles

Bending fatigue performance due to different roughing-finishing sequences and post-processing of components produced by Wire EDM

The relationships between machining conditions, boundary layer and mechanical component functionality are known qualitatively for selected Wire Electrical Discharge Machining (Wire EDM/WEDM) applications and continuous further developments of this manufacturing technology minimize the thermal influences significantly. Nevertheless, the use of WEDM processes has so far been severely limited in safety-critical applications, especially in the field of turbomachinery construction and aerospace. For example, the removal of the generated surface layers is often still mandatory, although cutting processes can also leave a distinct thermo-mechanically influenced rim zone on the component. This conservative approach currently unnecessarily reduces the manufacturing potential of WEDM processes considerably and calls for an objective comparison of component function. In this paper, therefore, the flexural bending fatigue strengths of differently wire-eroded surfaces based on roughing-finishing sequences and optional post-processing treatment are compared with industrially established reference process chains.

Analysis of Numerical Differential Formulas on a Bakhvalov Mesh in the Presence of a Boundary Layer

The paper considers numerical differentiation of functions with large gradients in the region of an exponential boundary layer. This topic is important, since the application of classical polynomial difference formulas for derivatives to such functions in the case of a uniform mesh leads to unacceptable errors if the perturbation parameter is comparable with the mesh size. The numerical differentiation formula with a given number of nodes in the difference stencil is built on subintervals covering the original interval. The accuracy of numerical differentiation formulas on a Bakhvalov mesh, which is widely used in the construction of difference schemes for singularly perturbed problems, is analyzed. For the original function of one variable, a representation in the form of a sum of regular and boundary-layer components, based on the Shishkin decomposition, is used to solve a singularly perturbed problem. Previously, such a decomposition was used to prove the convergence of difference schemes. An estimate of the error of classical polynomial formulas for numerical differentiation on a Bakhvalov mesh is obtained. The error estimate on a Bakhvalov mesh is obtained in the general case, when a derivative of an arbitrarily given order is calculated and the difference stencil for this derivative contains a given number of nodes. The error estimate depends on the order of the calculated derivative and the number of nodes in difference stencil and takes into account the uniformity in the parameter . The results of numerical experiments are presented, which are consistent with the error estimates obtained.

Development and application of a 6000-meter double decelerating lander

The deep-sea lander is an important equipment for in-situ detection and monitoring. It is of great significance to understand the benthic boundary layer’s physical, chemical, and ecological environment. A 6000-meter double decelerating lander was created to meet the deployment requirements of underwater detection and monitoring, allowing for long-term in-situ monitoring of several benthic boundary layer components. Protection of the installed ocean bottom seismometer (OBS) is required due to the lander’s and OBS’s different impact resistances. The double decelerating unit enables the OBS to avoid colliding with the seabed when the lander lands and then collides with the seabed at a slow speed rather than the speed at which the lander falls, which is intended to safeguard OBS from damage. To ensure a safe deployment, the lander’s static analysis and simulation were performed using ANSYS, and the motion characteristics of the application process were derived. Numerous data have been obtained after the lander’s successful application in the South China Sea. The lander provides an investigation approach for marine science and geochemistry, complementing a technical approach to marine environmental investigations.

Quantitative Comparison of a Hierarchy of Commonly Used Planetary Climate Energy Balance Models

The objective of this paper is to examine the effect of the various simplifications inherent in commonly-used planetary energy balance climate models (EBMs). Specifically, we look at the zero-dimensional (0-d) radiative equilibrium model, the 1-d radiative equilibrium model, and the 1-d radiative-convective equilibrium (RCE) model. Each of these models make fundamental steps towards a well-represented Earth system model, and make different simplifications and assumptions in the process. We seek to evaluate the effects these assumptions have on key thermal quantities of the system (OLR / outgoing longwave radiation, surface temperature, etc.). These evaluations lead us to identify contexts for each model wherein it remains a valid option to accurately replicate a system. The 0-d model fails to account for the greenhouse effect’s impact on energetics, thus predicting an erroneously-low surface temperature and low OLR. It instead requires an emissivity coefficient ~ 0.619 to balance OLR and temperature and model the Earth system. The 1-d radiative equilibrium model is a significant improvement on its predecessor, creating a stratospheric thermal profile reasonably similar to that of the Earth. The strong low-altitude temperature lapse rate and convective instability near the surface, however, slightly diminishes the validity of the low-level thermal profile – a drawback the RCE model appears to resolve with the addition of convective and boundary layer components. We conclude that the 0-d radiative equilibrium is best suited to isothermal atmospheres, the 1-d radiative equilibrium model to non-isothermal atmospheres where convection is suppressed, and the 1-d RCE model to convectively-active atmospheres.

A Bayesian approach to eliminate correlated noise using an independent reference-Application to supersonic jet noise extraction.

A Bayesian method to remove correlated noise from multi-channel measurements is introduced. It is based on Bayesian factor analysis coupled with prior but uncertain knowledge of the correlation structure of the noise. This technique is well suited to denoise cross-spectral matrices measured in the frame of aeroacoustic experiments when background noise measurements are available, because it allows separating the engine noise contribution from the turbulent boundary layer and uniform noise components that are all sensed by in-flow microphones. In-flight data measured on flush-mounted microphones on an aircraft fuselage are denoised using this method. It is shown that it has a significant benefit for studying the broadband shock-associated noise generated by the engines in realistic flight conditions.

Sustainable aircraft design — A review on optimization methods for electric propulsion with derived optimal number of propulsors

The high environmental impact of conventional aircraft can be considerably reduced using hybrid- or fully-electrical propulsion systems with distributed propulsors. It results in an increased efficiency for a higher number of propulsors, where different effects like boundary layer ingestion, propulsors-structure interactions, or component failures affect the overall design decisions. Hence, a distributed electric propulsion layout leads to an increasing demand for an overall integrated system design process in which optimization methods play an important role. In this review study, first, we give an overview of embedded propulsion, where boundary layer ingestion was heavily examined. Second, we present distributed propulsion and its combination with embedded propulsion. Third, we give a detailed overview of optimization methods in the conceptual and preliminary design stage. We illustrate the benefits of the usage of integrated optimization methods by presenting a study and answer the question of how many propulsors would be optimal for a distributed electric aircraft to maximize the overall efficiency in cruise. The formulated constrained optimization model is derived from the application of first principles, allometric scaling, and dimensional analysis. The solution of the optimization problem yields the design rule that the optimal number of propulsors increases with the aircraft mass to the power of 0.29. As uncertainty is always present in the design process and especially in earlier design stages, we explicitly present approaches to master this uncertainty by presenting an overview of sensitivity analysis methods.

Non-Polynomial Interpolation of Functions with Large Gradients and Its Application

Interpolation of a function of one variable with large gradients in the boundary layer region is studied. The problem is that the use of classical polynomial interpolation formulas on a uniform mesh to functions with large gradients can lead to errors of the order of $$O(1)$$ , despite a small mesh size. An interpolation formula based on fitting to the component that defines the boundary-layer growth of the function is investigated. An error estimate, which depends on the number of interpolation nodes and is uniform over the boundary layer component and its derivatives, is obtained. It is shown how the interpolation formula derived can be used to construct formulas for numerical differentiation and integration and in the two-dimensional case. The corresponding error estimates are obtained.

Asymptotic solution of Sturm-Liouville problem with periodic boundary conditions for relativistic finite-difference Schrödinger equation

The quasi-potential approach is very famous in modern relativistic particles physics. This approach is based on the so-called covariant single-time formulation of quantum field theory in which the dynamics of fields and particles is described on a space-like three-dimensional hypersurface in the Minkowski space. Special attention in this approach is paid to methods for constructing various quasi-potentials. The quasipotentials allow to describe the characteristics of relativistic particles interactions in quark models such as amplitudes of hadron elastic scatterings, mass spectra, widths of meson decays and cross sections of deep inelastic scatterings of leptons on hadrons. In this paper SturmLiouville problems with periodic boundary conditions on a segment and a positive half-line for the 2m-order truncated relativistic finite-difference Schrdinger equation (LogunovTavkhelidzeKadyshevsky equation, LTKT-equation) with a small parameter are considered. A method for constructing of asymptotic eigenfunctions and eigenvalues in the form of asymptotic series for singularly perturbed SturmLiouville problems with periodic boundary conditions is proposed. It is assumed that eigenfunctions have regular and boundary-layer components. This method is a generalization of asymptotic methods that were proposed in the works of A. N. Tikhonov, A. B. Vasilyeva, and V. F Butuzov. We present proof of theorems that can be used to evaluate the asymptotic convergence for singularly perturbed problems solutions to solutions of degenerate problems when 0 and the asymptotic convergence of truncation equation solutions in the case m. In addition, the SturmLiouville problem on the positive half-line with a periodic boundary conditions for the quantum harmonic oscillator is considered. Eigenfunctions and eigenvalues
 are constructed for this problem as asymptotic solutions for 4-order LTKT-equation.

Structures of wing-tip vortices at low Reynolds numbers and their modelling

The structures of wing-tip vortices at a low Reynolds number () are studied by direct numerical simulation. After confirming the basic features of the wing-tip vortices, the distributions of axial vorticity and velocity are investigated in detail. The vorticity distribution consists of a dominant symmetric component, quadrupole components responsible for elliptical deformation of the vortex core and the other small components. The symmetric component of vorticity is in reasonable agreement with the Moore-Saffman model (Moore & Saffman 1973 Proc. R. Soc. Lond. 333, 491) for the three types of wing planform considered: the rectangular, elliptic and delta wings. The agreement between numerical results and the Moore-Saffman model is not good for the symmetric component of axial velocity since the boundary layer component is small owing to the incomplete roll-up of the vortex sheet shed from the boundary layer. However, the vortex component of the axial velocity is correctly predicted by the Moore-Saffman model. The elliptical deformation of the vortex core is characterized by the aspect ratio and the direction of the major axis. It is found that the elliptical deformation is not uniform in the streamwise direction, which implies that the wing-tip vortices cannot be always modelled by a two-dimensional vortex pair. The evolution of the elliptical deformation along the streamwise direction is shown to be described by two-dimensional vortex dynamics under the boundary-layer approximation. The equations of motion of an elliptic vortex patch in a straining field predicts correctly the rate of change of the direction, but fails to predict that of the aspect ratio, for which the equation derived for axisymmetrization of vortices gives a good prediction.

Andronov–Hopf Bifurcation in Logistic Delay Equations with Diffusion and Rapidly Oscillating Coefficients

A logistic delay equation with diffusion, which is important in applications, is studied. It is assumed that all of its coefficients, as well as the coefficients in the boundary conditions, are rapidly oscillating functions of time. An averaged equation is constructed, and the relation between its solutions and the solutions of the original equation is studied. A result on the stability of the solutions is formulated, and the problem of local dynamics in the critical case is studied. An algorithm for constructing the asymptotics of the solutions and an algorithm for studying their stability are proposed. It is important to note that the corresponding algorithm contains both a regular and a boundary layer component. Meaningful examples are given.

Seismic Response Analysis for Ordinary State-Based Peridynamics in a Linear Isotropic Elastic Material

Earthquakes may induce the failure of soil-structures built with a geo-material. It is therefore a crucially important aspect to study how a crack initiates and propagates in these soil-structures to analyze and improve their earthquake resistance. Peridynamics, although a powerful method for such an analysis, has not been applied to seismic response analysis of soil-structures on a viscous boundary surface that can consider an input seismic wave. To apply seismic response analysis to ordinary state-based peridynamics (OSB-PD), this paper proposed a fictitious viscous boundary layer and Rayleigh damping components constructed with time derivative of force density vectors. OSB-PD was semi-verified through the comparison of calculated response acceleration via the proposed method and via the dynamic finite element method (FEM). The discussions were stressed on the effect of Poisson’s ratio, the frequency, and the Rayleigh damping components relative to the calculated response acceleration in both methods. Moreover, the seismic response acceleration at the top of the analysis model was calculated through the proposed method using an actual seismic acceleration time history, and then the result was compared with that calculated by the dynamic FEM. The results of both methods in the seismic response analysis agreed well with each other. From these results, we verified that the fictitious viscous layer can represent incoming/outgoing acceleration wave from the bottom of the analysis domain, and that Rayleigh damping can be expressed using the time derivative of force density vectors.

Generalized Spline Interpolation of Functions with Large Gradients in Boundary Layers

The spline interpolation of functions of one variable with large gradients in boundary layers is studied. It is well known that applying polynomial splines to interpolate functions of this kind leads to significant errors when the small parameter is comparable with the grid step size. A generalized spline that is an analogue of a cubic spline is constructed. The spline is exact on the component responsible for large gradients of the function in the boundary layer. The boundary-layer component is considered as a function of a general form; in particular, the case of an exponential boundary layer is treated. The existence, uniqueness, and accuracy of the constructed spline are analyzed.

Asymptotic behaviour of a boundary layer solution to a stationary partly dissipative system with a multiple root of the degenerate equation

We construct asymptotics with respect to a small parameter of a boundary layer solution of the boundary value problem for a system of two ordinary differential equations, one second order and the other first order, with a small parameter multiplying the derivatives in both equations. Systems of this type arise in chemical kinetics as stationary processes in models of fast reactions in the absence of diffusion for one of the reactants. An essential feature of the problem under study is a double root of one of the equations of the degenerate system. This leads to a qualitative change in the boundary layer component of the solution by comparison with the case when all the roots are simple. The boundary layer becomes multizoned, while the standard algorithm for constructing boundary layer series is no longer suitable and has to be replaced by a new one. Bibliography: 13 titles.

Momentum Drag Effect Over Urbanized Areas in the ACM2 PBL Component of the WRF model

AbstractMesoscale meteorology models, such as the Weather Research and Forecasting (WRF) model, typically use land use categorization data to specify surface characteristics by grid cells. In commonly used land use schemes, such as the 24‐class U.S. Geological Survey land use classification system or the Moderate Resolution Imaging Spectroradiometer landcover product, cities are placed in single urban categories that are characterized by a high roughness length. Monin‐Obunkov similarity theory is commonly used to simulate boundary layer dynamics based on surface energy and momentum fluxes which resulted in an overprediction of wind speed in weather forecasts for urban areas. It is thus crucial to include the momentum drag effects of the buildings, including walls and roofs, in the prediction models. The WRF model contains several momentum flux parameterizations, including the single‐layer urban canopy model, building effect parameterization, and building energy model. The building energy model and building effect parameterization schemes are limited to the Mellor‐Yamada‐Janjic or BouLac planetary boundary layer models and are computationally costly. In this study, a realistic multilayer urban approach is introduced into the Asymmetric Convective Model version 2 planetary boundary layer component of the WRF model. Sensitivity tests are applied to a range of urban morphological parameters in idealized simulations, and the impact of building morphology on atmospheric conditions is examined. The modified Asymmetric Convective Model version 2 is implemented in two real cases in the forecast mode, resulting in significant improvements in wind speed prediction.

Bigleaf-An R package for the calculation of physical and physiological ecosystem properties from eddy covariance data.

We present the R package bigleaf (version 0.6.5), an open source toolset for the derivation of meteorological, aerodynamic, and physiological ecosystem properties from eddy covariance (EC) flux observations and concurrent meteorological measurements. A ‘big-leaf’ framework, in which vegetation is represented as a single, uniform layer, is employed to infer bulk ecosystem characteristics top-down from the measured fluxes. Central to the package is the calculation of a bulk surface/canopy conductance (Gs/Gc) and a bulk aerodynamic conductance (Ga), with the latter including formulations for the turbulent and canopy boundary layer components. The derivation of physical land surface characteristics such as surface roughness parameters, wind profile, aerodynamic and radiometric surface temperature, surface vapor pressure deficit (VPD), potential evapotranspiration (ET), imposed and equilibrium ET, as well as vegetation-atmosphere decoupling coefficients, is described. The package further provides calculation routines for physiological ecosytem properties (stomatal slope parameters, stomatal sensitivity to VPD, bulk intercellular CO2 concentration, canopy photosynthetic capacity), energy balance characteristics (closure, biochemical energy), ancillary meteorological variables (psychrometric constant, saturation vapor pressure, air density, etc.), customary unit interconversions and data filtering. The target variables can be calculated with a different degree of complexity, depending on the amount of available site-specific information. The utilities of the package are demonstrated for three single-level (above-canopy) eddy covariance sites representing a temperate grassland, a temperate needle-leaf forest, and a Mediterranean evergreen broadleaf forest. The routines are further tested for a two-level EC site (tree and grass layer) located in a Mediterranean oak savanna. The limitations and the ecophysiological interpretation of the derived ecosystem properties are discussed and practical guidelines are given. The package provides the basis for a consistent, physically sound, and reproducible characterization of biometeorological conditions and ecosystem physiology, and is applicable to EC sites across vegetation types and climatic conditions with minimal ancillary data requirements.

Interpolation Formulas for Functions with Large Gradients in the Boundary Layer and their Application

Interpolation of functions on the basis of Lagrange’s polynomials is widely used. However in the case when the function has areas of large gradients, application of polynomials of Lagrange leads to essential errors. It is supposed that the function of one variable has the representation as a sum of regular and boundary layer components. It is supposed that derivatives of a regular component are bounded to a certain order, and the boundary layer component is a function, known within a multiplier; its derivatives are not uniformly bounded. A solution of a singularly perturbed boundary value problem has such a representation. Interpolation formulas, which are exact on a boundary layer component, are constructed. Interpolation error estimates, uniform in a boundary layer component and its derivatives are obtained. Application of the constructed interpolation formulas to creation of formulas of the numerical differentiation and integration of such functions is investigated.

Interpolation of a function of two variables with large gradients in boundary layers

The paper is concerned with the interpolation of a function of two variables with large gradients in the boundary layers. An underlying function is assumed to be the sum of the regular componentwith derivatives bounded up to some order and two boundary layer components, the latter are known up to a multiplicative factor. Such a representation is typical for the solution of a singular perturbed elliptic problem. A two-dimensional interpolation formula exact on the boundary layer components is put forward. The formula has an arbitrary number of nodes in each direction. An error estimate is obtained which is uniform on the gradients of the underlying function in boundary layers. Results of numerical experiments are provided.

Analogue of Newton–Cotes formulas for numerical integration of functions with a boundary-layer component

The numerical integration of functions with a boundary-layer component whose derivatives are not uniformly bounded is investigated. The Newton–Cotes formulas as applied to such functions can lead to significant errors. An analogue of Newton–Cotes formulas that is exact for the boundary-layer component is constructed. For the resulting formula, an error estimate that is uniform with respect to the boundary-layer component and its derivatives is obtained. Numerical results that agree with the error estimates are presented.

Lagrange interpolation and Newton-Cotes formulas for functions with boundary layer components on piecewise-uniform grids

The problem of interpolation of a one-variable function considered as a solution to a boundary value problem for an equation with a small parameter ɛ in the highest derivative is investigated. The application of a Lagrange polynomial for such a function on a uniform grid may result in serious errors. For a Shishkin grid, ɛ-uniform error estimates of Lagrange polynomial interpolation are obtained. The Shishkin grid is modified to increase the interpolation accuracy. For Newton-Cotes formulas on such grids, ɛ-uniform error estimates are obtained. The results of numerical experiments confirm the theoretical estimates.

Интерполяция Лагранжа и формулы Ньютона-Котеса для функций с погранслойной составляющей на кусочно-равномерных сетках

Интерполяция Лагранжа и формулы Ньютона-Котеса для функций с погранслойной составляющей на кусочно-равномерных сетках