Shear Flow Distribution Research Articles

Analytical Method of the Shear Lag Effect in Thin-Walled Box Girders Based on the Shear Flow Distribution Law

This paper presents an analytical method based on the shear flow distribution law to study the shear lag effect of thin-walled single- and double-cell box girders. The first step in this method is to determine the box girder’s shear flow distribution. Subsequently, a series of novel improved longitudinal displacement functions mathematically expressed as cubic parabolas are established. The parabolic origin of these functions is located at the zero point of the shear flow corresponding to each plate; the unknown parameters used to describe the function form can be determined according to the shear flow distribution, the continuity conditions, and the axial force balance condition. Then, the variational energy method is adopted to derive the governing differential equations. The shear lag effect in thin-walled single- and double-cell box girders under several boundary conditions and load cases is studied and analytical expressions for the shear lag coefficient are derived. Finally, results obtained using the proposed method are validated via comparison with numerical results. The results show that the proposed method can provide reasonable predictions for the shear lag effect of single- and double-cell box girders, and that this method is more straightforward and practical. In addition, the shear lag coefficients at different webs are not entirely equal, which is related to the distance from the web to the zero point of the shear flow.

Multiphase flow characteristics and gas loss in the shear layer on a ventilated supercavity wall

The shear flow on the large-scale gas–water wall inside a ventilated supercavity exhibits gas entrainment mode and determines the change law of the supercavity's gas loss, significantly impacting the shape and dynamics of the supercavity. Therefore, to develop an accurate prediction model and a ventilation control method for a supercavity under complex motion conditions, it is required to systematically and quantitatively study the shear flow characteristics and rules. This study calculates and comparatively analyzes the shear layers on either side of the supercavity wall based on numerical simulations of ventilated supercavitating flows in an unbounded field using the gas–vapor–water multi-fluid model. It is shown that the external shear layer with a very irregular outer boundary is considerably thinner than the internal shear layer. We further analyze the flow and distribution characteristics of all the phases in the shear layers with and without the influence of gravity. Our analysis confirms that all the phases exhibit a similar velocity change rule along the supercavity radial direction in the shear layer, whereas gas and water phases exhibit opposite radial phase distribution trends. It was also seen when natural cavitation occurs that the vapor phase is mainly distributed in the head of the supercavity. Moreover, at the same radial position, it was seen that the vapor velocity was higher than the gas velocity and slightly lower than the water velocity. Using the shear flow and phase distribution characteristics, a shear-layer gas loss model is established and validated for ventilated supercavitating flows.

Computation of dimensional variations on the structural analysis of multi-cell aircraft box beams with python scripting

PurposePython codes are developed for the versatile structural analysis on a 3 spar multi-cell box beam by means of idealization approach.Design/methodology/approachShear flow distribution, stiffener loads, location of shear center and location of geometric center are computed via numpy module. Data visualization is performed by using Matplotlib module.FindingsPython scripts are developed for the structural analysis of multi-cell box beams in lieu of long hand solutions. In-house developed python codes are made available to be used with finite element analysis for verification purposes.Originality/valueThe use of python scripts for the structural analysis provides prompt visualization, especially once dimensional variations are concerned in the frame of aircraft structural design. The developed python scripts would serve as a practical tool that is widely applicable to various multi-cell wing boxes for stiffness purposes. This would be further extended to the structural integrity problems to cover the effect of gaps and/or cut-outs in shear flow distribution in box-beams.

Internal Gravity Waves in a Stratified Medium with Model Shear Flow Distributions

The problem of the field of internal gravity waves in a stratified medium of finite depth is considered for model distributions of background shear flows. The constant distribution of the buoyancy frequency and various linear dependences of background shear flow on the depth are used to solve the problem analytically. The dispersion relations expressed in terms of the modified Bessel function of imaginary index are obtained. In satisfying the Miles–Howard stability condition in the case of large Richardson numbers, the Debye asymptotics of the modified Bessel function of imaginary index are used to construct the analytical solutions. The properties of the dispersion relation are studied and the basic analytical characteristics of the dispersion curves are investigated as functions of the parameters of background shear flows. The phase patterns of the excited fields are calculated numerically for various wave generation models.

Analytical Solutions of the Internal Gravity Wave Equation in a Stratified Medium with Shear Flows

The problem of constructing internal gravity wave fields generated by an oscillating localized point source of disturbances in a stratified medium with an average shear flow is considered. A model distribution of shear flow over depth is considered, and an analytical solution of the problem is obtained in the form of a characteristic Green function expressed in terms of modified Bessel functions of imaginary index. Analytical expressions for the dispersion relations are obtained using Debye asymptotics of the modified Bessel functions. Integral representations of solutions are constructed. The wave characteristics of the excited fields are investigated depending on the basic parameters of the used stratification models, shear flows, and generation modes.

Shear-rate-dependent transport coefficients in granular suspensions.

A recent model for monodisperse granular suspensions is used to analyze transport properties in spatially inhomogeneous states close to the simple (or uniform) shear flow. The kinetic equation is based on the inelastic Boltzmann (for low-density gases) with the presence of a viscous drag force that models the influence of the interstitial gas phase on the dynamics of grains. A normal solution is obtained via a Chapman-Enskog-like expansion around a (local) shear flow distribution which retains all the hydrodynamic orders in the shear rate. To first order in the expansion, the transport coefficients characterizing momentum and heat transport around shear flow are given in terms of the solutions of a set of coupled linear integral equations which are approximately solved by using a kinetic model of the Boltzmann equation. To simplify the analysis, the steady-state conditions when viscous heating is compensated by the cooling terms arising from viscous friction and collisional dissipation are considered to get the explicit forms of the set of generalized transport coefficients. The shear-rate dependence of some of the transport coefficients of the set is illustrated for several values of the coefficient of restitution.

Tracer diffusion coefficients in a sheared inelastic Maxwell gas

We study the transport properties of an impurity in a sheared granular gas, in the framework of the Boltzmann equation for inelastic Maxwell models. We investigate here the impact of a nonequilibrium phase transition found in such systems, where the tracer species carries a finite fraction of the total kinetic energy (ordered phase). To this end, the diffusion coefficients are first obtained for a granular binary mixture in spatially inhomogeneous states close to the simple shear flow. In this situation, the set of coupled Boltzmann equations are solved by means of a Chapman–Enskog-like expansion around the (local) shear flow distributions for each species, thereby retaining all the hydrodynamic orders in the shear rate a. Due to the anisotropy induced by the shear flow, three tensorial quantities Dij, Dp,ij, and DT,ij are required to describe the mass transport process instead of the conventional scalar coefficients. These tensors are given in terms of the solutions of a set of coupled algebraic equations, which can be exactly solved as functions of the shear rate a, the coefficients of restitution and the parameters of the mixture (masses and composition). Once the forms of Dij, Dp,ij, and DT,ij are obtained for arbitrary mole fraction (where nr is the number density of species r), the tracer limit () is carefully considered for the above three diffusion tensors. Explicit forms for these coefficients are derived showing that their shear rate dependence is significantly affected by the order-disorder transition.

Computational haemodynamic analysis of left pulmonary artery angulation effects on pulmonary blood flow.

To study the effect of the angulation between the left pulmonary artery (LPA) and the main pulmonary artery on pulmonary haemodynamics. A 3D model of patient-specific pulmonary artery (PA) was reconstructed as an original model. Four models with descendent LPA angulation equalled to 120°, 110°, 100° and 90°, were reconstructed by computer-aided design for the virtual simulation of the pulmonary flow under different surgical strategies. Computational fluid dynamics was introduced to calculate the pulmonary blood flow in five models. Streamlines, wall shear stress, energy loss and flow distribution ratio were calculated and compared to determine the better haemodynamics in the pulmonary artery. Vortices were formed at the lower wall of the opening of right PA and LPA in models with LPA angles equal to or less than 100° (Models 3 and 4). Relative high wall shear stress areas at the lateral and lower wall of LPA opening had an ascendant tendency as the angle declined. Decreased flow distribution ratio to left lung (original model: 0.58, Model 1: 0.63, Model 2: 0.586, Model 3: 0.564, Model 4: 0.55) and increased energy loss (original model: 385.2 mV, Model 1: 239.4 mV, Model 2: 384.3 mV, Model 3: 430.9 mV, Model 4: 439.8 mV) in a cardiac cycle were noted as the angle reduced. Acute LPA angulation is associated with adverse haemodynamic performance. This should be particularly addressed during the reconstruction of pulmonary artery in the repair of tetralogy of Fallot.

Nonlinear vortex structures with perpendicular shear flow, hot ions, and nonthermal distribution of electrons

Coupling of drift vortex and the ion acoustic modes in the linear and nonlinear regimes are investigated with sheared ion flow perpendicular to the ambient magnetic field in a plasma comprising of hot ions and nonthermal population of electrons. In this regard, generation of nonlinear vortex structures in the presence of kappa, Cairns, and q-nonextensive electron distributions are investigated in detail, and comparison with the Maxwellian distribution is also made. The appositeness of the present investigation in the matter of auroral F-region is also pointed out.

Generalized transport coefficients for inelastic Maxwell mixtures under shear flow.

The Boltzmann equation framework for inelastic Maxwell models is considered to determine the transport coefficients associated with the mass, momentum, and heat fluxes of a granular binary mixture in spatially inhomogeneous states close to the simple shear flow. The Boltzmann equation is solved by means of a Chapman-Enskog-type expansion around the (local) shear flow distributions f(r)(0) for each species that retain all the hydrodynamic orders in the shear rate. Due to the anisotropy induced by the shear flow, tensorial quantities are required to describe the transport processes instead of the conventional scalar coefficients. These tensors are given in terms of the solutions of a set of coupled equations, which can be analytically solved as functions of the shear rate a, the coefficients of restitution α(rs), and the parameters of the mixture (masses, diameters, and composition). Since the reference distribution functions f(r)(0) apply for arbitrary values of the shear rate and are not restricted to weak dissipation, the corresponding generalized coefficients turn out to be nonlinear functions of both a and α(rs). The dependence of the relevant elements of the three diffusion tensors on both the shear rate and dissipation is illustrated in the tracer limit case, the results showing that the deviation of the generalized transport coefficients from their forms for vanishing shear rates is in general significant. A comparison with the previous results obtained analytically for inelastic hard spheres by using Grad's moment method is carried out, showing a good agreement over a wide range of values for the coefficients of restitution. Finally, as an application of the theoretical expressions derived here for the transport coefficients, thermal diffusion segregation of an intruder immersed in a granular gas is also studied.

Torsion strength of single-box multi-cell concrete box girder subjected to combined action of shear and torsion

A model has been proposed that can predict the ultimate torsional strength of single-box multi-cell reinforced concrete box girder under combined loading of bending, shear and torsion. Compared with the single-cell box girder, this model takes the influence of inner webs on the distribution of shear flow into account. According to the softening truss theory and thin walled tube theory, a failure criterion is presented and a ultimate torsional strength calculating procedure is established for single-box multi-cell reinforced concrete box girder under combined actions, which considers the effect of tensile stress among the concrete cracks, Mohr stress compatibility and the softened constitutive law of concrete. In this paper the computer program is also compiled to speed up the calculation. The model has been validated by comparing the predicted and experimental members loaded under torsion combined with different ratios of bending and shear. The theoretical torsional strength was in good agreement with the experimental results.

Turbulent Characteristics of the Stratified Flow in the Braided River with Two Symmetrical Anabranches

The turbulent characteristics of stratified shear flow in braided rivers have not been known until now. The physical model experiment was conducted to study the turbulence kinetic energy distribution of stratified shear flow in the typical braided rivers with a mid-bar between two symmetrical anabranches. Firstly, the distributions of depth-averaged turbulence intensity components in different sections of the anabranch were analyzed. The turbulent intensity peak occurs at the boundary of the separation zone near outer bank and the high velocity zone near inner bank in the entrance region of the anabranch. In the outlet section of the anabranch, turbulent intensity increased at the inner bank. Secondarily, Lateral-averaged turbulence intensity components were compared between different sections. There was obvious high turbulence appearing at the interface of hot and cold water in the inlet section of the anabranch. Finally, the distributions of total turbulence intensity were analyzed by the sectional contours.

Macro‐scale topology optimization for controlling internal shear stress in a porous scaffold bioreactor

Shear stress is an important physical factor that regulates proliferation, migration, and morphogenesis. In particular, the homeostasis of blood vessels is dependent on shear stress. To mimic this process ex vivo, efforts have been made to seed scaffolds with vascular and other cell types in the presence of growth factors and under pulsatile flow conditions. However, the resulting bioreactors lack information on shear stress and flow distributions within the scaffold. Consequently, it is difficult to interpret the effects of shear stress on cell function. Such knowledge would enable researchers to improve upon cell culture protocols. Recent work has focused on optimizing the microstructural parameters of the scaffold to fine tune the shear stress. In this study, we have adopted a different approach whereby flows are redirected throughout the bioreactor along channels patterned in the porous scaffold to yield shear stress distributions that are optimized for uniformity centered on a target value. A topology optimization algorithm coupled to computational fluid dynamics simulations was devised to this end. The channel topology in the porous scaffold was varied using a combination of genetic algorithm and fuzzy logic. The method is validated by experiments using magnetic resonance imaging readouts of the flow field.

Elastic shear buckling characteristics of LiteSteel beams

LiteSteel beam (LSB) is a new cold-formed steel hollow flange channel beam. The unique LSB section is produced by a patented manufacturing process involving simultaneous cold-forming and dual electric resistance welding. To date, limited research has been undertaken on the shear buckling behaviour of LSBs with torsionally rigid, rectangular hollow flanges. For the shear design of LSB web panels, their elastic shear buckling strength must be determined accurately including the potential post-buckling strength. Currently the elastic shear buckling coefficients of web panels are determined by assuming conservatively that the web panels are simply supported at the junction between the flange and web elements. Therefore finite element analyses were carried out to investigate the elastic shear buckling behaviour of LSB sections including the effect of true support conditions at the junction between their flange and web elements. An improved equation for the higher elastic shear buckling coefficient of LSBs was developed and included in the shear capacity equations of Australian cold-formed steel codes. Predicted ultimate shear capacity results were compared with available experimental results, both of which showed considerable improvement to the shear capacities of LSBs. A study on the shear flow distribution of LSBs was also undertaken prior to the elastic buckling analysis study. This paper presents the details of this investigation and the results including the shear flow distribution of LSBs.

グラフ理論を用いた薄肉断面構造の剪断流解析法に関する研究（第１報） − 解析法−

The authors are developing the simple and easy structural design system which investigates rapidly the design spiral in the stage of early design. In this system, initial scantlings and dimensions are determined through the total strength analysis system before performing FE analysis. The shear flow analysis is carried out by identifying the cross-section shape of hull girder using the number of representative points in a cross-section, the shape of closed circuits and the property of the shear flow on each member.The coefficients of the expression to shear flow distribution are automatically calculated. However, to apply this analysis to more complicated and various cross-sections within fore and aft portion of ships, it is important to develop a more generalized shear flow analysis method.In this paper, the authors propose a new shear flow analysis method using the basic concept of graph theory, where a pattern of networks is expressed by connections between points and edges, mainly applied to electric circuit network.In this first report, the authors give a concrete description for the formulation of the new analysis and the analytical procedure using a cross-section with three closed circuits.

The cell-free layer in microvascular blood flow

This review discusses the cell-free layer at the wall of the microcirculatory vessels with emphasis on the influence of blood rheological parameters on its formation as well as its possible effects on microvascular functions. Understanding cell-free layer characteristics in the microcirculation has been of increased interest for its possible influence on physiological function. The availability of better imaging and measurement techniques in recent years has created an excellent opportunity for researchers to examine the cell-free layer in much greater detail than possible previously. The most recent approach enables capturing spatial and temporal information of cell-free layer characteristics which can provide new insights to how cell-free layer width and its variations can impact physiological function. Cell-free layer formation is dependent on diameter of the vessel, flow rate, and rheological properties of blood including hematocrit, red blood cell aggregation, and deformability. Specifically in microvessels, its formation can also be affected by the presence of the glycocalyx layer that lines the luminal surface of the vessel wall. As the cell-free layer is omnipresent in microcirculatory vessels, its formation at the vessel wall could affect function throughout the microvascular network by altering wall shear stress, local hematocrit, flow distribution, effective viscosity and nitric oxide production as well as its scavenging by red blood cells.

Shear buckling of thin-walled channel sections

The elastic buckling stresses of channel sections with and without lips and subject to shear forces parallel with the web are determined, where computational modelling of the thin-walled steel sections is implemented by means of a spline finite strip analysis. Both unlipped and lipped channels are studied, where the main variables are flange width, different boundary conditions and shear flow distribution. The channel sections are also analysed at different lengths, to investigate the effect of length/width ratio on the critical shear buckling stresses. Comparisons between cases and with classical solutions are included in this paper.

Mass flux of a binary mixture of Maxwell molecules under shear flow

Transport coefficients associated with the mass flux of a binary mixture of Maxwell molecules under uniform shear flow are exactly determined from the Boltzmann kinetic equation. A normal solution is obtained via a Chapman–Enskog-like expansion around a local shear flow distribution that retains all the hydrodynamics orders in the shear rate. In the first order of the expansion the mass flux is proportional to the gradients of mole fraction, pressure, and temperature but, due to the anisotropy induced in the system by the shear flow, mutual diffusion, pressure diffusion and thermal diffusion tensors are identified instead of the conventional scalar coefficients. These tensors are obtained in terms of the shear rate and the parameters of the mixture (particle masses, concentrations, and force constants). The description is made both in the absence and in the presence of an external thermostat introduced in computer simulations to compensate for the viscous heating. As expected, the analysis shows that there is no simple relationship between the results with and without the thermostat. The dependence of the three diffusion tensors on the shear rate is illustrated in the tracer limit case, the results showing that the deviation of the generalized transport coefficients from their equilibrium forms is in general quite important.

Shear-rate-dependent transport coefficients for inelastic Maxwell models

The Boltzmann equation for d-dimensional inelastic Maxwell models is considered to analyse transport properties in spatially inhomogeneous states close to the simple shear flow. A normal solution is obtained via a Chapman–Enskog-like expansion around a local shear flow distribution f(0) that retains all the hydrodynamic orders in the shear rate. The constitutive equations for the heat and momentum fluxes are obtained to first order in the deviations of the hydrodynamic field gradients from their values in the reference state and the corresponding generalized transport coefficients are exactly determined in terms of the coefficient of restitution α and the shear rate a. Since f(0) applies for arbitrary values of the shear rate and is not restricted to weak dissipation, the transport coefficients turn out to be nonlinear functions of both parameters a and α. A comparison with previous results obtained for inelastic hard spheres from a kinetic model of the Boltzmann equation is also carried out.

Mass transport of an impurity in a strongly sheared granular gas

Transport coefficients associated with the mass flux of an impurity immersed in a granulargas under simple shear flow are determined from the inelastic Boltzmann equation. Anormal solution is obtained via a Chapman–Enskog-like expansion around a local shearflow distribution that retains all the hydrodynamic orders in the shear rate. Due to theanisotropy induced by the shear flow, tensorial quantities are required to describe thediffusion process instead of the conventional scalar coefficients. The mass flux isdetermined to first order in the deviations of the hydrodynamic fields from theirvalues in the reference state. The corresponding transport coefficients are given interms of the solutions of a set of coupled linear integral equations, which areapproximately solved by considering the leading terms in a Sonine polynomialexpansion. The results show that the deviation of these generalized coefficients fromtheir elastic forms is in general quite important, even for moderate dissipation.