Unsteady characteristics of low-Re flow past two tandem cylinders

This study investigated the two-dimensional flow past two tandem circular or square cylinders at Re = 100 and D / d = 4–10, where D is the center-to-center distance and d is the cylinder diameter. Numerical simulation was performed to comparably study the effect of cylinder geometry and spacing on the aerodynamic characteristics, unsteady flow patterns, time-averaged flow characteristics and flow unsteadiness. We also provided the first global linear stability analysis and sensitivity analysis on the physical problem for the potential application of flow control. The objective of this work is to quantitatively identify the effect of the cylinder geometry and spacing on the characteristic quantities. Numerical results reveal that there is wake flow transition for both geometries depending on the spacing. The characteristic quantities, including the time-averaged and fluctuating streamwise velocity and pressure coefficient, are quite similar to that of the single cylinder case for the upstream cylinder, while an entirely different variation pattern is observed for the downstream cylinder. The global linear stability analysis shows that the spatial structure of perturbation is mainly observed in the wake of the downstream cylinder for small spacing, while moves upstream with reduced size and is also observed after the upstream cylinder for large spacing. The sensitivity analysis reflects that the temporal growth rate of perturbation is the most sensitive to the near-wake flow of downstream cylinder for small spacing and upstream cylinder for large spacing.     

Flow field in the wake of a bluff body driven through a steady recirculating flow

The wake produced by a bluff body driven through a steady recirculating flow is studied experimentally in a water facility using particle image velocimetry. The bluff body has a rectangular cross section of height, \(H\), and width, \(D\), such that the aspect ratio, AR = H/D, is equal to 3. The motion of the bluff body is uniform and rectilinear, and corresponds to a Reynolds number based on width, Re _D  = 9,600. The recirculating flow is confined within a hemicylindrical enclosure and is generated by planar jets emanating from slots of width, \(h\), such that \(Re_h=500\). Under these conditions, experiments are performed in a closed-loop facility that enables complete optical access to the near-wake. Velocity fields are obtained up to a distance of \(13D\) downstream of the moving body. Data include a selection of phase-averaged velocity fields representative of the wake for a baseline case (no recirculation) and an interaction case (with recirculation). Results indicate that the transient downwash flow typically observed in wakes behind finite bodies of small aspect ratio is significantly perturbed by the recirculating flow. The wake is displaced from the ground plane and exhibits a shorter recirculation zone downstream of the body. In summary, it was found that the interaction between a bluff body wake and a recirculating flow pattern alters profoundly the dynamics of the wake, which has implications on scalar transport in the wake.     

Application of the γ-Reθ Transition Model to Simulations of the Flow Past a Circular Cylinder

Based on the finite volume method, the flow past a two-dimensional circular cylinder at a critical Reynolds number (Re = 8.5 × 10⁵) was simulated using the Navier-Stokes equations and the γ-Re_θ transition model coupled with the SST k ? ω turbulence model (hereinafter abbreviated as γ-Re_θ model). Considering the effect of free-stream turbulence intensity decay, the SST k ? ω turbulence model was modified according to the ambient source term method proposed by Spalart and Rumsey, and then the modified SST k ? ω turbulence model is coupled with the γ-Re_θ transition model (hereinafter abbreviated as γ-Re_θ-SR model). The flow past a circular cylinder at different inlet turbulence intensities were simulated by the γ-Re_θ-SR model. At last, the flow past a circular cylinder at subcritical, critical and supercritical Reynolds numbers were each simulated by the γ-Re_θ-SR model, and the three flow states were analyzed. It was found that compared with the SST k ? ω turbulence model, the γ-Re_θ model could simulate the transition of laminar to turbulent, resulting in better consistency with experimental result. Compared with the γ-Re_θ model, for relatively high inlet turbulence intensities, the γ-Re_θ-SR model could better simulate the flow past a circular cylinder; however the improvement almost diminished for relatively low inlet turbulence intensities The γ-Re_θ-SR model could well simulate the flow past a circular cylinder at subcritical, critical and supercritical Reynolds numbers.     

Inverse problem of fracture mechanics for a compound cylinder

We consider the plane problem of fracture mechanics for a compound cylinder. We assume that the sleeve (internal cylinder) is reinforced with negative allowance by the external cylinder and that near the sleeve surface there are N arbitrarily located rectilinear cracks of length 2l _k (k = 1, 2, ..., N). A minimax criterion is used to determine the negative allowance in the junction theoretically minimizing the fracture parameters (the stress intensity coefficients) of the compound cylinder. A simplified method for minimizing the fracture parameters of the compound cylinder is considered separately.     

Measurement of local forcing on a turbulent boundary layer using PIV

An experimental study was carried out to investigate the effect of periodic blowing and suction on a turbulent boundary layer. Particle image velocimetry (PIV) was used to probe the characteristics of the flow. Local forcing was introduced to the boundary layer via a sinusoidally-oscillating jet issuing from a thin spanwise slot. Three forcing frequencies (f⁺=0.44, 0.66 and 0.88) with a fixed forcing amplitude (A⁺=0.6) were employed at Re _θ =690. The effect of three different forcing angles (α=60°, 90° and l20°) was investigated under a fixed forcing frequency (f⁺=0.088). The PIV results showed that the wall-region velocity decreases on imposition of the local forcing. Inspection of the phase-averaged velocity profiles revealed that spanwise large-scale vortices are generated downstream of the slot and persist farther downstream. The highest reduction in skin friction was achieved at the highest forcing frequency (f⁺=0.088) and a forcing angle of α=120°. The spatial fraction of the vortices was examined to analyze the skin friction reduction.     

Mechanical Properties of Hard W-C Coating on Steel Substrate Deduced from Nanoindentation and Finite Element Modeling

Mechanical properties of a hard and stiff W-C coating on steel substrate have been investigated using nanoindentation combined with finite element modeling (FEM) and extended FEM (XFEM). The significant pile-up observed around the indents in steel substrate caused an overestimation of hardness and indentation modulus. A simple geometrical model, considering the additional contact surfaces due to pile-up, has been proposed to reduce this overestimation. The presence of W-C coating suppressed the pile-up in the steel substrate and a transition to sink-in behavior occurred. The FEM simulations adequately reproduced the surface topography of the indents in the substrate and coating/substrate systems as well. The maximum principal stresses of the indented W-C/steel coated system were tensile; they were always located in the coating and evolved in 3 stages. Cohesive cracking occurred during loading in the sink-in zone (stage III) when the ultimate tensile strength (σ _max ) of the coating was reached. The obtained hardness (H _c ), indentation modulus (E _c ), yield stress (Y) and strength (σ _max ) of the W-C coating were H _c ? =?20 GPa, E _c ? =?250 GPa, Y?=?9.0 GPa and σ _max ? =?9.35 GPa, respectively. XFEM resulted in fracture energy of the W-C coating of G?=?38.1 J?·?m^-2 and fracture toughness of K _IC ? =?3.5 MPa?·?m^0.5.     

Effects of Fuel Lewis Number on Localised Forced Ignition of Globally Stoichiometric Stratified Mixtures: a Numerical Investigation

The influences of fuel Lewis number Le_F on localised forced ignition of globally stoichiometric stratified mixtures have been analysed using three-dimensional compressible Direct Numerical Simulations (DNS) for cases with Le_F ranging from 0.8 to 1.2. The globally stoichiometric stratified mixtures with different values of root-mean-square (rms) equivalence ratio fluctuation (i.e. ?^′= 0.2, 0.4 and 0.6) and the Taylor micro-scale l_? of equivalence ratio ? variation (i.e. l_?/l_f= 2.1, 5.5 and 8.3 with l_f being the Zel’dovich flame thickness of the stoichiometric laminar premixed flame) have been considered for different initial rms values of turbulent velocity u^′. A pseudo-spectral method is used to initialise the equivalence ratio variation following a presumed bi-modal distribution for prescribed values of ?^′ and l_?/l_f for global mean equivalence ratio 〈?〉=1.0. The localised ignition is accounted for by a source term in the energy transport equation that deposits energy for a stipulated time interval. It has been observed that the maximum values of temperature and the fuel reaction rate magnitude increase with decreasing Le_F during the period of external energy deposition. The initial values of Le_F, u^′/S_b(?=1), ?^′ and l_?/l_f have been found to have significant effects on the extent of burning of the stratified mixtures following localised ignition. For a given value of u^′/S_b(?=1), the extent of burning decreases with increasing Le_F. An increase in u^′ leads to a monotonic reduction in the burned gas mass for all values of Le_F in all stratified mixture cases but an opposite trend is observed for the Le_F=0.8 homogeneous mixture. It has been found that an increase in ?^′ has adverse effects on the burned gas mass, whereas the effects of l_?/l_f on the extent of burning are non-monotonic and dependent on ?^′ and Le_F. Detailed physical explanations have been provided for the observed Le_F, u^′/S_b(?=1), ?^′ and l_?/l_f dependences.     

LES-based Study of the Roughness Effects on the Wake of a Circular Cylinder from Subcritical to Transcritical Reynolds Numbers

This paper investigates the effects of surface roughness on the flow past a circular cylinder at subcritical to transcritical Reynolds numbers. Large eddy simulations of the flow for sand grain roughness of size k/D = 0.02 are performed (D is the cylinder diameter). Results show that surface roughness triggers the transition to turbulence in the boundary layer at all Reynolds numbers, thus leading to an early separation caused by the increased momentum deficit, especially at transcritical Reynolds numbers. Even at subcritical Reynolds numbers, boundary layer instabilities are triggered in the roughness sublayer and eventually lead to the transition to turbulence. The early separation at transcritical Reynolds numbers leads to a wake topology similar to that of the subcritical regime, resulting in an increased drag coefficient and lower Strouhal number. Turbulent statistics in the wake are also affected by roughness; the Reynolds stresses are larger due to the increased turbulent kinetic energy production in the boundary layer and separated shear layers close to the cylinder shoulders.     

Evaluation of the Spectral Element Dynamic Model for Large-Eddy Simulation on Unstructured,Deformed Meshes

In this paper, the Spectral-Element Dynamic Model (SEDM), suited for Large-Eddy Simulation (LES) using Discontinuous Finite Element Methods (DFEM), is assessed using unstructured meshes. Five test cases of increasing complexity are considered, namely, the Taylor-Green vortex at Re =?5000, the turbulent channel flow at Re_τ =?587, the circular cylinder in cross-flow at Re_D =?3900, the square cylinder in cross-flow at Re_D =?22400 and the channel with periodic constrictions at Re_h =?10595. Various discretization parameters such as the grid spacing, polynomial degree and numerical flux are assessed and very accurate results are reported in all cases. This consistency in the results demonstrates the versatility of the SEDM approach and its ability to gage the actual resolution and quality of the mesh and, accordingly, to introduce an amount of sub-grid dissipation which is adapted to the spatial discretization considered.     

Effects of Permeable Cylinder on the Flow Structure in Deep Water

Flow behaviors around permeable cylinders were investigated using Particle Image Velocimetry technique in deep water. The height of deep water and free stream velocity were kept constant as h_w = 340 mm and U = 156 mm/s. To find out the effect of the permeable cylinders on the flow structure, eight different porosities (β = 0.4, 0.5, 0.6, 0.65, 0.7, 0.75, 0.8, and 0.85) were used. The results have indicated that the permeable cylinders are effective on the control of large-scale vortical structures downstream of the permeable cylinder. As the porosity increases, turbulent kinetic energy and Reynolds shear stress decrease. This means that the fluctuations in the wake region are significantly weakened by permeable cylinders. The permeable cylinders having the porosity higher than 0.6 do not pose an obstacle in the flow. Furthermore, for all diameter values of permeable cylinders, it can be concluded that the flow structures downstream of the permeable cylinder show similar trend with each other.     

Pressure-Gradient Turbulent Boundary Layers Developing Around a Wing Section

A direct numerical simulation database of the flow around a NACA4412 wing section at R e _c = 400,000 and 5^° angle of attack (Hosseini et al. Int. J. Heat Fluid Flow 61, 117–128, 2016), obtained with the spectral-element code Nek5000, is analyzed. The Clauser pressure-gradient parameter β ranges from ? 0 and 85 on the suction side, and from 0 to ? 0.25 on the pressure side of the wing. The maximum R e _?? and R e _τ values are around 2,800 and 373 on the suction side, respectively, whereas on the pressure side these values are 818 and 346. Comparisons between the suction side with zero-pressure-gradient turbulent boundary layer data show larger values of the shape factor and a lower skin friction, both connected with the fact that the adverse pressure gradient present on the suction side of the wing increases the wall-normal convection. The adverse-pressure-gradient boundary layer also exhibits a more prominent wake region, the development of an outer peak in the Reynolds-stress tensor components, and increased production and dissipation across the boundary layer. All these effects are connected with the fact that the large-scale motions of the flow become relatively more intense due to the adverse pressure gradient, as apparent from spanwise premultiplied power-spectral density maps. The emergence of an outer spectral peak is observed at β values of around 4 for λ _z ? 0.65δ ₉₉, closer to the wall than the spectral outer peak observed in zero-pressure-gradient turbulent boundary layers at higher R e _?? . The effect of the slight favorable pressure gradient present on the pressure side of the wing is opposite the one of the adverse pressure gradient, leading to less energetic outer-layer structures.     

Linearized Stability for Semiflows Generated by a Class of Neutral Equations,with Applications to State-Dependent Delays

We prove a principle of linearized stability for semiflows generated by neutral functional differential equations of the form x′(t) = g(? x _t , x _t ). The state space is a closed subset in a manifold of C ²-functions. Applications include equations with state-dependent delay, as for example x′(t) = a x′(t + d(x(t))) + f (x(t + r(x(t)))) with \({a\in\mathbb{R}, d:\mathbb{R}\to(-h,0), f:\mathbb{R}\to\mathbb{R}, r:\mathbb{R}\to[-h,0]}\).     

Aerodynamic characteristics of a thin airfoil cascade in an ideal incompressible flow with separation from the leading edges

A new method of solving the problem of separation flow past a cascade of thin airfoils is proposed. The method is based on the model of separated flow past a single airfoil in which vortex wakes shed from the airfoil edges are modeled by vortex layers with time-averaged intensities. Under the assumption of a small deviation of the freestream angle α from the “impactless entry” angle α ₀ the singular integral equation governing the flow kinematics is closed by a dynamic equation. It is shown that the separation effect on the time-averaged aerodynamic characteristics of the cascade is associated with the total pressure loss due to the flow energy expenditure on the vortex wake formation. The aerodynamic characteristics of the cascade calculated with and without account for flow separation differ by the second-order quantity ? = α ? α ₀.     

Spray-Flame Dynamics in a Rich Droplet Array

We numerically study spray-flame dynamics. The initial state of the spray is schematized by alkane droplets located at the nodes of a face-centered 2D-lattice. The droplets are surrounded by a gaseous mixture of alkane and air. The lattice spacing s reduced by the combustion length scale is large enough to consider that the chemical reaction occurs in a heterogeneous medium. The overall spray equivalence ratio is denoted by ?_T, with ?_T = ?_L + ?_G, where ?_G corresponds to the equivalence ratio of the gaseous surrounding mixture at the initial saturated partial pressure, while ?_L is the so-called liquid loading. To model such a heterogenous combustion, the retained chemical scheme is a global irreversible one-step reaction governed by an Arrhenius law, with a modified heat of reaction depending on the local equivalence ratio. ?_T is chosen in the range 0.9 ≤ ?_T ≤ 2. Three geometries (s = 3, s = 6, s = 12) and four liquid loadings, ?_L = 0.3, ?_L = 0.5, ?_L = 0.7, ?_L = 0.85 are studied. In the rich sprays, our model qualitatively retrieves the recent experimental measurements: the rich spray-flames can propagate faster than the single-phase flames with the same overall equivalence ratio. To analyse the conditions for this enhancement, we introduce the concept of “spray Peclet number”, which compares the droplet vaporization time with the combustion propagation time of the single-phase flame spreading in the fresh surrounding mixture.     

Operator method for solving the plane elasticity problem for a strip with periodic cuts

In the present paper, we use the conformal mapping z/c = ζ?2a sin ζ (a, c?const, ζ = u + iv) of the strip {|v| ≤ v ₀, |u| < ∞} onto the domain D, which is a strip with symmetric periodic cuts. For the domain D, in the orthogonal system of isometric coordinates u, v, we solve the plane elasticity problem. We seek the biharmonic function in the form F = C ψ ₀ + S ψ*₀ + x(C ψ ₁ ? S ψ ₂) + y(C ψ ₂ + S ψ ₁), where C(v) and S(v) are the operator functions described in [1] and ψ ₀(u), …, ψ ₂(u) are the desired functions. The boundary conditions for the function F posed for v = ±v ₀ are equivalent to two operator equations for ψ ₁(u) and ψ ₂(u) and to two ordinary differential equations of first order for ψ ₀(u) and ψ*₀(u) [2]. By finding the functions ψ _j (u) in the form of trigonometric series with indeterminate coefficients and by solving the operator equations, we obtain infinite systems of linear equations for the unknown coefficients. We present an efficient method for solving these systems, which is based on studying stable recursive relations. In the present paper, we give an example of analysis of a specific strip (a = 1/4, v ₀ = 1) loaded on the boundary v = v ₀ by a normal load of intensity p. We find the particular solutions corresponding to the extension of the strip by the longitudinal force X ^∞ and to the transverse and pure bending of the strip due to the transverse force Y ^∞ and the constant moment M ^∞, respectively. We also present the graphs of normal and tangential stresses in the transverse cross-section x = 0 and study the stress concentration effect near the cut bottom.     

Characterization of Viscoelasticity Due to Shear Wave Propagation: a Comparison of Existing Methods Based on Computational Simulation and Experimental Data

Shear wave propagation causes microvibrations within a medium; measuring the wave attenuation coefficient, α, and phase velocity, c _s , the medium shear modulus, μ, and shear viscosity, η, are determined based on a viscoelastic model that includes both c _s and α. The present work compares the performances of nine processing methods, based on cross-correlation and quadrature demodulation, used to extract the motion waveform from a sequence of radio-frequency (RF) echo signals from the medium. Kalman filtering determined the amplitude and the phase of the extracted motion waveform. The comparisons were done with regard to computational simulation and experiments with a gel phantom. Estimates obtained for μ and η of the medium considered different conditions for the vibration amplitude and the signal-to-noise ratio (SNR) of the RF echo signals and the waveform extracted by means of single frequency and shear wave dispersion ultrasound vibration (SDUV) methods. According to the simulated results, the cross-correlation-based processing techniques are more precise and accurate in comparison to quadrature demodulation techniques. The results for c _s , α, μ and η of the phantom and those obtained under the same setup conditions for experimental and computational tests agree with each other. Comparing the estimates based on single frequency and SDUV techniques, they presented similar performances at high SNR of the RF echo signal. On the other hand, the former technique prevailed for low SNR.     

Effects of Fuel Lewis Number on Localised Forced Ignition of Turbulent Mixing Layers

The influences of fuel Lewis number Le _F on localised forced ignition of inhomogeneous mixtures are analysed using three-dimensional compressible Direct Numerical Simulations (DNS) of turbulent mixing layers for Le _F  = 0.8, 1.0 and 1.2 and a range of different root-mean-square turbulent velocity fluctuation u′ values. For all Le _F cases a tribrachial flame has been observed in case of successful ignition. However, the lean premixed branch tends to merge with the diffusion flame on the stoichiometric mixture fraction isosurface at later stages of the flame evolution. It has been observed that the maximum values of temperature and reaction rate increase with decreasing Le _F during the period of external energy addition. Moreover, Le _F is found to have a significant effect on the behaviours of mean temperature and fuel reaction rate magnitude conditional on mixture fraction values. It is also found that reaction rate and mixture fraction gradient magnitude \(\vert \nabla \xi \vert \) are negatively correlated at the most reactive region for all values of Le _F explored. The probability of finding high values of \(\vert \nabla \xi \vert \) increases with increasing Le _F . For a given value of u′, the extent of burning decreases with increasing Le _F . A moderate increase in u′ gives rise to an increase in the extent of burning for Le _F  = 0.8 and 1.0, which starts to decrease with further increases in u′. For Le _F  = 1.2, the extent of burning decreases monotonically with increasing u′. The extent of edge flame propagation on the stoichiometric mixture fraction ξ = ξ _st isosurface is characterised by the probability of finding burned gas on this isosurface, which decreases with increasing u′ and Le _F . It has been found that it is easier to obtain self-sustained combustion following localised forced ignition in case of inhomogeneous mixtures than that in the case of homogeneous mixtures with the same energy input, energy deposition duration when the ignition centre is placed at the stoichiometric mixture. The difficultly to sustain combustion unaided by external energy addition in homogeneous mixture is particularly prevalent in the case of Le _F  = 1.2.     

On the orders of the best approximations of integrals of functions by integrals of rank <Emphasis Type="Italic">σ</Emphasis>

We study the values e _σ(f) of the best approximation of integrals of functions from the spaces L _p (A, dμ) by integrals of rank σ. We determine the orders of the least upper bounds of these values as σ → ∞ in the case where the function ? is the product of two nonnegative functions one of which is fixed and the other varies on the unit ball U _p (A) of the space L _p (A, dμ). We consider applications of the obtained results to approximation problems in the spaces S _p ^? .     

Experimental Investigation of the Transverse Self-Oscillations of Circular Cylinders Mounted with a Narrow Clearance in a Plane Channel

The results of an investigation of the flow past and the behavior of free bluff bodies mounted in pipes and channels with a narrow clearance, conducted in the Institute of Mechanics of Moscow State University, are presented. The drag of circular cylinders of different size and mass in a circulation-free water flow in a plane channel of rectangular cross-section was studied in the transverse self-oscillation regime. The experiments were conducted for Reynolds numbers based on the cylinder diameter 1.7 ? 10⁴ ≤ Re ≤ 7.2 ? 10⁴, relative clearances \(\bar S\) based on a cross-sectional area ranging from 0.76 to 0.9, and cylinder-to-water density ratios ρ _c /ρ ranging from 1.29 to 8.2. Only the case of intense transverse self-oscillations accompanied by impact interaction with the channel wall was considered. The dependence of the period-average cylinder drag coefficient C _x on the basic dimensionless relevant parameters is obtained. The dependence of the dimensionless self-oscillation frequency determined in [1] is refined. The kinematic and dynamic features of the flows past spheres in cylindrical pipes and cylinders in plane channels are compared in the transverse self-oscillation regime.     

Miscible Thermo-Viscous Fingering Instability in Porous Media. Part 1: Linear Stability Analysis

The development of the thermo-viscous fingering instability of miscible displacements in homogeneous porous media is examined. In this first part of the study dealing with stability analysis, the basic equations and the parameters governing the problem in a rectilinear geometry are developed. An exponential dependence of viscosity on temperature and concentration is represented by two parameters, thermal mobility ratio β _T and a solutal mobility ratio β _C , respectively. Other parameters involved are the Lewis number Le and a thermal-lag coefficient λ. The governing equations are linearized and solved to obtain instability characteristics using either a quasi-steady-state approximation (QSSA) or initial value calculations (IVC). Exact analytical solutions are also obtained for very weakly diffusing systems. Using the QSSA approach, it was found that an increase in thermal mobility ratio β _T is seen to enhance the instability for fixed β _C , Le and λ. For fixed β _C and β _T , a decrease in the thermal-lag coefficient and/or an increase in the Lewis number always decrease the instability. Moreover, strong thermal diffusion at large Le as well as enhanced redistribution of heat between the solid and fluid phases at small λ is seen to alleviate the destabilizing effects of positive β _T . Consequently, the instability gets strictly dominated by the solutal front. The linear stability analysis using IVC approach leads to conclusions similar to the QSSA approach except for the case of large Le and unity λ flow where the instability is seen to get even less pronounced than in the case of a reference isothermal flow of the same β _C , but β _T  = 0. At practically, small value of λ, however, the instability ultimately approaches that due to β _C only.