The boundary layer thickness on a compressor blade suction surface increases rapidly under a adverse pressure gradient and even separates from the blade surface. This paper proposes a novel method for developing the slot inside the blade, with the inlet of the slot located at the leading edge of the blade and the outlet located at the suction surface, using the momentum of the incoming flow to form a high velocity jet to control the boundary layer on the suction surface. For a plane cascade with a diffusion factor of 0.45, the effects of the main slot parametres (such as the shape of the slot and the positions of the slot inlet and outlet) on the flow in the slot, the flow field and the aerodynamic performance of the cascade were investigated with a numerical method. When the aerodynamic performance of cascades with slotted and unslotted blades was compared, it was found that a reasonable slot structure can effectively inhibit the development of the boundary layer on the blade suction surface and greatly improve the aerodynamic performance of the cascade. Based on the influence of the slot parametres of the above cascade, the slot of a plane cascade with a diffusion factor of 0.60 was designed. The numerical calculation results show that the slotted cascade with a diffusion factor of 0.60 outperformed the slotted cascade with a diffusion factor of 0.45. This result showed that the higher the cascade load, the greater the performance improvement from slotting. Furthermore, the unslotted and slotted cascades were tested, and the test results agreed well with the calculations. The aerodynamic performance of the slotted cascade was better than that of the unslotted cascade, which verifies the accuracy of the calculation method and the feasibility of blade slotting for suppressing the development of boundary layers on suction surfaces and reducing flow loss.

We study the asymptotic behaviour of the periodically mixed Zaremba problem. We cover the part of the boundary by a chess board with a small period (square size) $\varepsilon$ and impose the Dirichlet condition on black and the Neumann condition on white squares. As $\varepsilon \to 0$, we get the effective boundary condition which is always of the Dirichlet type. The Dirichlet data on the boundary, however, depend on the ratio between the magnitudes of the two boundary values.

This paper examines thermoacoustic effects on the propagation of non-planar sound in a circular duct subjected to an axial temperature gradient. Of particular concern are thermoviscous diffusive effects, which are taken into account by the boundary-layer approximation in a framework of the linear theory. For disturbances expanded into Fourier and Fourier–Bessel series in the azimuthal and radial directions, respectively, the pressure in each mode is described by a one-dimensional, dispersive wave equation, if non-diffusive propagation is assumed. When the diffusive effects are included, each radial mode is coupled to the other radial modes through the boundary layer. Focusing on a single azimuthal and radial mode only, the dispersion relation for the propagation along an infinite duct of a uniform gas is first derived. Effects of the temperature gradient are then examined by solving boundary-value problems for a duct of finite length in four typical cases. Assuming that the wall temperature increases exponentially along the duct, eigenfrequencies and decay rates in the lowest axial mode are obtained as well as axial distributions of the sound pressure and the axial velocity in the duct. The frequency and the decay rate increase as the temperature ratio at both ends becomes higher. It is found from the acoustic energy equation that the dispersion combined with the diffusion acts to reduce the damping and that the temperature gradient makes little contribution to the production of the energy. However, it is unveiled that the non-uniformity in temperature yields thermoacoustic sound confinement in the vicinity of the cold end.

Dynamical constraints on the wall layer in turbulent pipe flow imply both a narrow peak in the streamwise component of the turbulent Lamb vector near the wall, and a scaling of the wall layer depth proportional to the depth of the viscous sublayer. An approximation of the Lamb vector distribution, which equates to the gradient of Reynolds stress, is proposed. Hence the equation for streamwise mean flow may be integrated to obtain an expression for the velocity profile in the wall layer.

In this paper, we consider an initial-boundary value problem of Hsieh's equation with conservative nonlinearity. The global unique solvability in the framework of Sobolev is established. In particular, one of our main motivations is to investigate the boundary layer (BL) effect and the convergence rates as the diffusion parameter $\beta$ goes zero. It is shown that the BL-thickness is of the order $O(\beta ^{\gamma })$ with $0<\gamma <\frac {1}{2}$. We need to point out that, different from the previous work on nonconservative form of Hsieh's equations, the conservative nonlinearity $(\psi ^{\beta }\theta ^{\beta })_x$ implies that new nonlinear term $\psi _x^{\beta }\theta ^{\beta }$ needs to be handled. It is important that more regularities on the solution to the limit problem are required to obtain the convergence rates and BL-thickness. It is more difficult for initial-boundary problem due to the lack of boundary conditions (especially, higher-order derivatives) prevents us from applying the integration by part to derive the energy estimates directly. Thus it is more complicated than the case of nonconservative form. Consequently more subtle mathematical analysis needs to be introduced to overcome the difficulties.

Gas turbine engines for fixed-wing or rotary-wing aircraft are operated in a variety of harsh weather environments ranging from arctic, volcanic zones, to desert conditions. Operation under these degraded conditions leads to the undesired entrainment of complex particulates resulting in drastic performance losses. Hence, there is a critical need to understand the governing mechanisms to inform the development of durable thermal and environmental barrier coatings. The objective of the current work is to present a novel multiscale physics-based approach to study two-phase flows that take into account the underpinning particle transport and deposition dynamics. Sessile droplet models are presented and used to compute the contact angle at high temperatures and compared with experiments. The study also investigates the sensitivity of deposition patterns to the Stokes number and the results identify local vulnerability regions. The analysis suggests that particle size distributions and the initial trajectories of the particles are critically important in predicting the final deposition pattern.

In this work, consideration is given to a novel concept for aerofoil lift enhancement and delaying flow separation. Here, lift enhancement is attained by preventing the growth of the boundary layer through the elimination of the zero-slip condition between the wing surface and the air stream. The concept would simulate all the effects of a moving wall, leading to the appearance of a slip velocity at the gas–fluid interface, including the injection of momentum into the air boundary layer, but with one exception: here there is no moving wall but instead a ferrofluid thin film pumped parallel and attached to the wall by a magnetic field. Utilising a simplified physical model for the velocity profile of the ferrofluid film and based on ferrohydrodynamic stability considerations, an analytical expression for the interfacial velocity is derived. Finally, from the available experimental data on moving walls, the expected lift and angle-of-attack enhancement are found as well as the weight penalty per unit surface area of the wing is estimated. Additional research and development is required to explore the possibilities of using ferrofluid thin films.

In 2008, the atmospheric CO2 measurements at the Hegyhátsál rural tower station were extended further by 14CO2 air sampling from two elevations (115 and 10 m a.g.l.), in cooperation with HEKAL (ICER). Since then, a complete six-year-long (2008–2014) dataset of atmospheric CO2, Δ14C, fossil, and modern CO2 excess (relative to Jungfraujoch) has been assembled and evaluated. Based on our results, the annual mean CO2 mole fraction rose at both elevations in this period. The annual mean Δ14CO2 values decreased with a similar average annual decline. Based on our comparison, planetary boundary layer height obtained by modeling has a larger influence on the variation of mole fraction of CO2 (relative to Jungfraujoch), than on its carbon isotopic composition, i.e. the boundary layer rather represents a physical constraint. Fossil fuel CO2 excess at both elevations can rather be observed in wintertime and mainly due to the increased anthropogenic emission of nearby cities in the region. The mean modern CO2 excess at both elevations was even larger in winter, but it drastically decreased at 115 m by summer, while it remained at the winter level at 10 m.

In this article, we study theoretically and numerically the interaction of a vortex induced by a rotating cylinder with a perpendicular plane. We show the existence of weak solutions to the swirling vortex models by using the Hopf extension method, and by an elegant contradiction argument, respectively. We demonstrate numerically that the model could produce phenomena of swirling vortex including boundary layer pumping and two-celled vortex that are observed in potential line vortex interacting with a plane and in a tornado.

The beginning of the transition from the laminar to a turbulent flow is usually the generation of instability Tollmien-Schlichting (T-S) waves in the boundary layer. Previously, most numerical and experimental researches focused on generating instability T-S waves through the external disturbances such as acoustic waves and vortical disturbances interacting with wall roughness or at the leading-edge of flatplate, whereas only a few paid attention to the excitation of the T-S waves directly by free-stream turbulence (FST). In this study, the generating mechanism of the temporal mode T-S waves under free-stream turbulence is investigated by using direct numerical simulation (DNS) and fast Fourier transform. Wave packets superposed by a group of stability, neutral and instability T-S waves are discovered in the boundary layer. In addition, the relation between the amplitude of the imposed free-stream turbulence and the amplitude of the excited T-S wave is also obtained.

Nanosecond (ns) pulsed dielectric barrier discharge (DBD) actuator in a laminar flat plate boundary layer is investigated numerically in an attempt to gain some new insights into the understanding of ns DBD actuation mechanism. Special emphasis is put on the examination, separation and comparison of behaviors of discharge induced micro shock wave and residual heat as well as on the investigation of response of external flow to the two effects. The shock wave is found to introduce highly transient, localized perturbation to the flow and be able to significantly alter the flow pattern shortly after its initiation. The main flow tends to quickly recover to close to its undisturbed state due to the transient nature of perturbation. However, with the shock decay and final disappearance, another perturbation source in the vicinity of discharge region, which contains contribution from both residual heat and shock, becomes increasingly pronounced and eventually develops into a perturbation wave train in the boundary layer. The perturbation is relatively weak and may not be a Tollmien-Schlichting (TS) wave and not trigger the laminar-turbulent transition of boundary layer. Instead, it is more likely to manipulate the flow stability to achieve the strong control authority of this kind of actuation in the case of flow separation control. In addition, a parametric study over the different electrical and hydrodynamic parameters is also conducted.

This paper presents a relatively simple numerical method to investigate the flow and heat transfer of laminar power-law fluids over a semi-infinite plate in the presence of viscous dissipation and anisotropy radiation. On one hand, unlike most classical works, the effects of power-law viscosity on velocity and temperature fields are taken into account when both the dynamic viscosity and the thermal diffusivity vary as a power-law function. On the other hand, boundary layer equations are derived by Taylor expansion, and a mixed analytical/numerical method (a pseudosimilarity method) is proposed to effectively solve the boundary layer equations. This method has been justified by comparing its results with those of the original governing equations obtained by a finite element method. These results agree very well especially when the Reynolds number is large. We also observe that the robustness and accuracy of the algorithm are better when thermal boundary layer is thinner than velocity boundary layer.

In this paper, we propose a novel and simple technique to construct effective difference schemes for solving systems of singularly perturbed convection-diffusion-reaction equations, whose solutions may display boundary or interior layers. We illustrate the technique by taking the Il'in-Allen-Southwell scheme for 1-D scalar equations as a basis to derive a formally second-order scheme for 1-D coupled systems and then extend the scheme to 2-D case by employing an alternating direction approach. Numerical examples are given to demonstrate the high performance of the obtained scheme on uniform meshes as well as piecewise-uniform Shishkin meshes.

This paper deals with a more general class of singularly perturbed boundary value problem for a differential-difference equations with small shifts. In particular, the numerical study for the problems where second order derivative is multiplied by a small parameter ε and the shifts depend on the small parameter ε has been considered. The fitted-mesh technique is employed to generate a piecewise-uniform mesh, condensed in the neighborhood of the boundary layer. The cubic B-spline basis functions with fitted-mesh are considered in the procedure which yield a tridiagonal system which can be solved efficiently by using any well-known algorithm. The stability and parameter-uniform convergence analysis of the proposed method have been discussed. The method has been shown to have almost second-order parameter-uniform convergence. The effect of small parameters on the boundary layer has also been discussed. To demonstrate the performance of the proposed scheme, several numerical experiments have been carried out.

We apply the multiscale basis functions for the singularly perturbed reaction-diffusion problem on adaptively graded meshes, which can provide a good balance between the numerical accuracy and computational cost. The multiscale space is built through standard finite element basis functions enriched with multiscale basis functions. The multiscale basis functions have abilities to capture originally perturbed information in the local problem, as a result our method is capable of reducing the boundary layer errors remarkably on graded meshes, where the layer-adapted meshes are generated by a given parameter. Through numerical experiments we demonstrate that the multiscale method can acquire second order convergence in the L2 norm and first order convergence in the energy norm on graded meshes, which is independent of ɛ. In contrast with the conventional methods, our method is much more accurate and effective.