Outer Layer Region Research Articles

Eddy-viscosity-improved resolvent analysis of compressible turbulent boundary layers

An improved resolvent analysis is proposed in the regime of compressible turbulent boundary layers. To better model nonlinear processes in the input, the resolvent framework is augmented by adding eddy viscosity. To this end, we propose two eddy-viscosity models: a modified Cess eddy-viscosity model coupling the compressibility transformation and outer-layer correction, and a new eddy-viscosity model based on an empirical relationship and mixing-length theory. Both are incorporated into the resolvent operator to examine the performance of the eddy-viscosity-improved resolvent-based reduced-order modelling. Results of the augmented resolvent analysis are compared qualitatively and quantitatively with the first leading mode of spectral proper orthogonal decomposition, by checking the profiles and cross-spectral densities of velocities, density and temperature in two hypersonic turbulent boundary layers under different wall conditions. Higher accuracy of the turbulence prediction is achieved by adding the proposed eddy-viscosity models, particularly for the energetic cycle in the outer-layer region where strong nonlinear energy transfer exists.

A hybrid computational scheme for singularly perturbed Burgers’-Huxley equation

This paper aims to construct and analyze a hybrid computational method for the nonlinear singularly perturbed Burgers’-Huxley equation. The presence of the perturbation parameter and non-linearity in the considered problem makes it difficult to solve the problem analytically and using classical numerical techniques on uniform step sizes as ε goes small. To elucidate such limitations, one can rely on non-classical numerical techniques. In this paper, one such parameter uniform numerical method is designed for the considered problem. The method is constructed:•Firstly, the non-linear terms are linearized via Newton-Raphson-Kantorovich technique. The linearized problem is discretized by the implicit Euler method in the temporal direction.•Secondly, the obtained equation is solved by employing the hybrid computational method comprised of the cubic spline in tension method in the inner layer region and the midpoint upwind method in the outer layer region on a piecewise uniform Shishkin mesh.•Finally, an error analysis of the method is done and observed that the proposed method is parameter uniform convergent with the order of convergence O(τ+N−2ln3N). Three examples are presented and the results are compared to some existing schemes in the literature to demonstrate the reliability of the proposed scheme.

Consistent energy-based framework of amplification mechanisms for the second mode in hypersonic boundary layers

The second mode is of general interest in hypersonic boundary layer flows due to its underlying responsibilities for transition to turbulence. However, a long-term debate exists on the detailed energy sources that sustain the modal exponential growth. Currently, three influential energy-based approaches appear to show different significant energy sources due to dissimilar mathematical formulations, including the momentum potential theory, the inviscid Lagrangian energy analysis, and the relative phase analysis. In this study, these three fundamental approaches are employed and examined in conjunction with direct numerical simulations. The purpose is to seek a possible unified explanation of the source terms that dominate the exponential evolution of the second mode. In the considered Mach 6 flow state, all three approaches consistently point to the same local energy amplification route driven by two pronounced source terms: the dilatation term in the near-wall region and the Reynolds thermal stress term or heat exchange term across the outer layer region, depending on the selection of the specific energy norm. The mathematical forms of the corresponding sources are derived or discussed explicitly. Theoretical and simulation results provide a unified understanding of the local energy amplification mechanisms of the second mode.

Hybrid Fitted Numerical Scheme for Singularly Perturbed Convection-Diffusion Problem with a Small Time Lag

In this article, a singularly perturbed convection-diffusion problem with a small time lag is examined. Because of the appearance of a small perturbation parameter, a boundary layer is observed in the solution of the problem. A hybrid scheme has been constructed, which is a combination of the cubic spline method in the boundary layer region and the midpoint upwind scheme in the outer layer region on a piecewise Shishkin mesh in the spatial direction. For the discretization of the time derivative, the Crank-Nicolson method is used. Error analysis of the proposed method has been performed. We found that the proposed scheme is second-order convergent. Numerical examples are given, and the numerical results are in agreement with the theoretical results. Comparisons are made, and the results of the proposed scheme give more accurate solutions and a higher rate of convergence as compared to some previous findings available in the literature.

A hybrid numerical scheme for singularly perturbed parabolic differential‐difference equations arising in the modeling of neuronal variability

This study aims at constructing a robust numerical scheme for solving singularly perturbed parabolic delay differential equations arising in the modeling of neuronal variability. Taylor's series expansion is applied to approximate the shift terms. The obtained result is approximated by using the implicit Euler method in the temporal discretization on a uniform step size with the hybrid numerical scheme consisting of the midpoint upwind method in the outer layer region and the cubic spline in tension method in the inner layer region on a piecewise uniform Shishkin mesh in the spatial discretization. The constructed scheme is shown to be an ε -uniformly convergent accuracy of order O Λ t + N − 2 ln 3 N . Two model examples are given to testify the theoretical findings.

Improvement of the scale-adaptive simulation technique based on a compensated strategy

The original scale adaptive simulation (SAS) method can be implicitly divided into two computational regions, i.e., Reynolds-averaged Navier–Stokes (RANS) region in the inner layer and large-eddy simulation (LES) behavior region in the outer layer. In the inner layer, the small-scale fluctuations captured by RANS are suppressed. Similar as the RANS/LES hybrid methods, the excessive turbulent dissipation from RANS model may suppress the generation of LES content in the region near RANS/LES interface. To address this problem, an improved SAS technique has been proposed in the present study, i.e., the compensated SAS (CSAS) approach. The CSAS method can be also divided into two different computations. One is still the original SAS calculation in the outer layer region, and the other is the constrained LES computation in the inner layer. To achieve CSAS technique, Reynolds stress and turbulent heat flux in the inner layer are calculated by a specially treated subgrid-scale (SGS) model, i.e., both SGS stress and SGS heat flux are split into the mean and fluctuating parts. RANS conditions are naturally satisfied in the mean part, and the remains (the extra mean and fluctuating parts) can be treated as the compensated terms. Just as the original SAS, the interface of compensated and non-compensated regions is also determined by the local turbulence scales. To assess the prediction performance of CSAS technique, three test cases have been investigated, including two massively separated flows and one attached flow. Two massively separated flows are the incompressible and compressible flows past a circular cylinder. A spatially evolving supersonic turbulent boundary layer is chosen as the test case for the attached flow. The predictions of mean flow and turbulence statistics show that some improvements are obtained by CSAS.

Reaction kinetics of char-O2/H2O combustion under high-temperature entrained flow conditions

The combustion kinetics of char-O2/H2O reactions under high-temperature entrained flow conditions involving char-H2O and char-O2 reactions were investigated experimentally and numerically. A numerical model was established based on the unsteady convection-diffusion equations, and the random pore model (RPM) was adopted locally to predict the change in intraparticle pore surface area. The Langmuir-Hinshelwood form rate equation was used to consider the possible competitive relationship between char-O2 and char-H2O reactions, and the most probable intrinsic kinetics parameters were found by checking the correlation coefficient between the experimental and numerical results. For H2O gasification, the numerical results show that the enrichment of H2 inside char particles decreases the intrinsic char-H2O gasification rate, especially at the outer layer regions. For O2/H2O combustion, the experimental results show that H2O has a promotion effect on the total carbon conversion at low SRs (stoichiometric ratio of O2 to fuel) but has an inhibition effect on the total carbon conversion at high SRs. Using the common active sites assumption, the numerical results match well with the experimental results. According to the numerical results, H2O penetrates deeper inside the char particle than does O2, contributing more to the local carbon conversion at the inner layer region, while H2O inhibits the char-O2 combustion rate at the outer layer regions due to H2 formation. As a result, H2O pushes the kinetics-diffusion-controlled reaction towards the kinetics-controlled regime. As the SR increases, the char-O2 combustion contributes more, magnifying the inhibition effects of H2O on the char-O2 combustion rate; therefore, the total O2/H2O combustion is gradually inhibited by H2O.

Insight on the sodium and chloride ions adsorption mechanism on the ettringite crystal: Structure, dynamics and interfacial interaction

The adsorption of water and ions on ettringite crystal, an important hydration product in the cement material, is fundamental to the durability of cement-based material. In this study, molecular dynamics was utilized to investigate the molecular structure, dynamics and interfacial bonding for the water and ions in the vicinity of ettringite crystal surface. The aluminate octahedron and sulfate ions in the surface of ettringite provide plenty of oxygen sites to accept H-bond from the water molecules in the interfacial region. The highly solvated surface calcium ions can strongly attract the neighboring water as their coordinate atoms. The hydrophilic nature of the ettringite interface results in the dramatically different feature of the water molecules on the ettringite surface, such as high dipole moment, ordered organization, good orientation preference and slow diffusivity. Furthermore, with gradually increasing simulation time, the calcium ions, aluminate and sulfate species in the crystal surface diffuse into the solution, resulting in the dissolution of the ettringite crystal and disturbance of the ordered interfacial topology. The six-coordinated aluminum hydroxyl groups transform to the aluminate tetrahedron, as they dissolve in the solution. Additionally, the chloride and sodium ions have different adsorption mechanism on the crystal surface. While the sodium ions are associated with the oxygen atoms in aluminate octahedron and sulfate ions by NaO ionic bond and immigrate into the inner region of the dissolved crystal, the chloride ions can form the ionic pairs with the calcium ions, accumulating to cluster in the outer layer region. As compared with the chloride adsorption, the ettringite crystal has better immobilization ability on the cation ions due to the stable NaO connection with long resident time.

EP28.02: Two cases of growing inwardly uterine cervical carcinoma that were diagnosed by transvaginal ultrasound guided needle biopsy

In diagnosis of uterine cervical carcinoma growing inwardly with biopsied specimens, accurate pathological diagnosis may not be provided because only an outer layer region of tumour is obtained. We report two cases of uterine cervical carcinoma that was diagnosed by transvaginal ultrasound guided needle biopsy. Two cases were cervical carcinoma which had difficulty in diagnosis by punch biopsied specimens though invasive carcinomas were suspected clinically with MRI findings. Case 1.A 49-year-old 3 gravidas 2 parous woman was referred to our hospital because of abnormal genital bleeding. MRI showed 67mm uterine cervical tumour, and cytology of uterine cervix was SCC. Subsequently, punch biopsy for cervical tumour was performed, but pathological diagnosis with obtained specimens was cervical intraepithelial neoplasia 3(CIN3). Therefore we performed transvaginal ultrasound guided needle biopsy, the result was that the diagnosis of invasive squamous cell carcinoma was obtained in grounds for the existence of atypical squamous cells infiltrating to myometrial layer. Case 2.A 38-year-old 4 gravidas 4 parous woman with past history of tubal ligation was referred to our hospital because of abnormal genital bleeding. MRI showed 38mm uterine cervical tumour, and cytology of uterine cervix was SCC. Subsequently, punch biopsy and diagnostic conisation for cervical tumour were performed, but pathological diagnosis by both examination was cervical intraepithelial neoplasia 3(CIN3). Therefore we performed transvaginal ultrasound guided needle biopsy, the result was that the diagnosis of invasive squamous cell carcinoma was obtained. It was thought that diagnosis by needle biopsied specimens was useful for growing inwardly uterine cervical carcinoma. In addition, it was thought that specimens could be obtained safely even if they were from deep region by performing needle biopsy under transvaginal ultrasound guide.

Synthesis and electrical characteristics of (1 − x)BaTiO3–xK0.5Bi0.5TiO3 PTCR ceramics

Solid solutions of (1 − x)BaTiO3–xK0.5Bi0.5TiO3 were prepared by the solid state reaction technique. Samples were sintered in reducing atmosphere of N2/H2 in the temperature range 1100–1240 °C with subsequent oxidation at 700 °C. Phase composition and crystal structure were investigated by X-ray powder diffractometry (XRPD). It was shown that all samples of (1 − x)BaTiO3–xK0.5Bi0.5TiO3 (0 ≤ x < 0.4) exhibit a tetragonal structure at room temperature, the parameters a and c decrease with increasing x. With increasing x the Curie temperature of solid solutions (1 − x)BaTiO3–xK0.5Bi0.5TiO3 (0.1 ≤ x < 0.4) increases from 150 to 220 °C. The values of potential barriers at grain boundaries were calculated on the basis of Heywang model. With increasing x, the potential barrier at grain boundaries increases. It was shown that the grain size decreases with increasing the bismuth–potassium titanate content. The complex impedance results indicate that the grain boundary and the outer layer region, located between the boundary and the core of the grain, make a contribution to the positive temperature coefficient of resistance (PTCR) effect in (1 − x)BaTiO3–xK0.5Bi0.5TiO3 solid solutions. With increasing x ρmax increases due to an increase in potential barrier at grain boundaries.

Acoustic double layer structures in dense magnetized electron-positron-ion plasmas

The acoustic double layer structures are studied using quantum hydrodynamic model in dense magnetized electron-positron-ion plasmas. The extended Korteweg-de Vries is derived using reductive perturbation method. It is found that increase in the ion concentration in dense magnetized electron-positron plasmas increases the amplitude as well as the steepness of the double layer structure. However, increase in the magnetic field strength and decrease in the obliqueness of the nonlinear acoustic wave enhances only the steepness of the double layer structures. The numerical results have also been shown by using the data of the outer layer regions of white dwarfs given in the literature.

Determination of bed shear stress in gravel-bed rivers using boundary-layer parameters

The behaviour of velocity profiles and shear velocity for non-uniform flow in gravel-bed rivers is studied, with the objectives: (a) to test a new method of shear velocity estimation in gravel-bed rivers that is based on boundary layer parameters, and to compare it with the log law and parabolic law; (b) to consider the influence of flow non-uniformity on the outer layer region of velocity profiles; and (c) to investigate the effect of aspect ratio on velocity profiles. For the primary study river, mid-channel velocity profiles were analysed with relative submergence ranging from 9.7 to 33.3 in channel sections with aspect ratios ranging between 16.2 and 50. Velocity profiles deviated from the log law in the outer region due to flow non-uniformity or pressure gradient effects, and the vertical extent of the inner region was variable. Estimates of shear velocity using the boundary layer parameters (δ* and θ) compared well with estimates from the log law. In a second study river, boundary-layer parameter estimates of shear velocity compared well to shear velocity estimates from linear extrapolation of Reynolds stress profiles.

Reynolds number scaling in a non-equilibrium turbulent boundary layer with mild adverse pressure gradient

High resolution laser Doppler anemometer measurements were acquired in a two-dimensional turbulent boundary layer over a four degree ramp at three momentum thickness Reynolds numbers: 3300, 14,100 and 20,600. The goal was to examine an adverse pressure gradient boundary layer far from separation in order to develop turbulent stress scalings to collapse the adverse pressure gradient and flat plate stress profiles over a range of Reynolds numbers. The flow develops as a flat plate boundary layer before being subjected to a varying pressure gradient along the length of a four degree straight ramp. Mean velocity measurements show a log law region for all velocity profiles. The stresses however are perturbed by the pressure gradient with the streamwise normal stress developing an extended outer layer plateau and the wall-normal stress displaying a growing outer layer peak. Scaling parameters are proposed to collapse the inner and outer layer regions of the normal stresses for both the adverse pressure gradient and flat plate profiles over the range of Reynolds numbers examined.

Effect of Roughness on Wall-Bounded Turbulence

Direct numerical simulation of turbulent incompressible plane-channel flow between a smooth wall and one covered with regular three-dimensional roughness elements is performed. While the impact of roughness on the mean-velocity profile of turbulent wall layers is well understood, at least qualitatively, the manner in which other features are affected, especially in the outer layer, has been more controversial. We compare results from the smooth- and rough-wall sides of the channel for three different roughness heights of h + = 5.4, 10.8, and 21.6 for Reτ of 400, to isolate the effects of the roughness on turbulent statistics and the instantaneous turbulence structure at large and small scales. We focus on the interaction between the near-wall and outer-layer regions, in particular the extent to which the near-wall behavior influences the flow further away from the surface. Roughness tends to increase the intensity of the velocity and vorticity fluctuations in the inner layer. In the outer layer, although the roughness alters the velocity fluctuations, the vorticity fluctuations are relatively unaffected. The higher-order moments and the energy budgets demonstrate significant differences between the smooth-wall and rough-wall sides in the processes associated with the wall-normal fluxes of the Reynolds shear stresses and turbulence kinetic energy. The length scales and flow dynamics in the roughness sublayer, the spatially inhomogeneous layer within which the flow is directly influenced by the individual roughness elements, are also examined. Alternative mechanisms involved in producing and maintaining near-wall turbulence in rough-wall boundary layers are also considered. We find that the strength of the inner/outer-layer interactions are greatly affected by the size of the roughness elements.

Spanwise Mean Flow Properties of Turbulent Boundary Layer through Gaps between Roughness Elements.

The off-centerline development of a turbulent boundary layer flow through a gap in an isolated wall-mounted roughness element has been studied experimentally in order to examine the effect of gap size on the spanwise mean flow properties. All measurements were made when the ratio of roughness height to boundary layer thickness is 0.135 at a Reynolds number of 3300, based on obstacle height and free stream velocity. From the off-centerline features in the horizontal plane at y+=125, the present flow field can be divided into two regions : the outer layer region and internal mixing region. The internal mixing region, furthermore, can be divided into four small groups : center region, interaction region, weak interaction region and mixing region. The interaction is more intense for a large gap than for a small one. The classification of gap size as mentioned in our previous paper is clearly related to the division of present flow field.

Double row vortical structures in the near field region of a plane wall jet

The qualitative and quantitative behaviour of double row vortical structures in the near field region of a plane wall jet are studied experimentally by flow visualization and hot-wire measurements. Ensemble averaging is employed to investigate the interaction of vortices with the wall. In the flow visualization study, a double row vortical structure, which includes a primary vortex formed in the outer layer region and a secondary vortex induced in the inner layer region, and the vortex lift-off phenomenon are clearly observed during the development of the wall jet. The phase averaged results of the velocity measurements show that the instability leading to induction of the secondary vortex is stimulated by the primary vortex. In the early stage of wall jet transition, the inflection point of the inner layer velocity profile moves transversely from the wall surface to the inner layer region due to passage of the well-organized primary vortex in the outer layer region. The inner layer instability is thus induced and the instability wave rolls up to form the secondary vortex. Furthermore, the secondary vortex will convect downstream faster than the primary vortex, and this difference in convective speed will lead to the subsequent phenomenon of vortex lift-off from the wall surface.

Turbulent Boundary Layers with Injection and Suction through a Slit : 1st Report, Mean and Turbulence Characteristics

An experimental investigation is performed on turbulent boundary layers with injection and suction through a slit. The velocity profile, turbulent energy, auto-correlation function, energy spectrum, and energy balance are measured in detail, and the influence of injection and suction through a slit on the turbulent boundary layers is presented. The process of recovery to an equilibrium state from non-equilibrium state is investigated. Main results are summarized as follows. The effects of injection and suction on velocity profiles and turbulence characteristics are small in the vicinity of the wall. On the other hand, the effects of injection clearly appear in the outer layer region of the turbulent boundary layer. Convection, production, and dissipation of turbulence energy increase with injection and decrease with suction.