Viscoelastic flow in a two-dimensional collapsible channel

We compute the flow of three viscoelastic fluids (Oldroyd-B, FENE-P, and Owens blood model) in a two-dimensional channel partly bounded by a tensioned membrane, a benchmark geometry for fluid–structure interactions. The predicted flow patterns are compared to those of a Newtonian liquid. We find that computations fail beyond a limiting Weissenberg number. Flow fields and membrane shape differ significantly because of the different degree of shear thinning and molecular extensibility underlying the three different microstructural models.     

Separation of flow over a diaphragm in a two-dimensional channel

A study is made of the hydrodynamic problem of the flow with separation over a diaphragm with sharp edges. The vorticity of the fluid in The separation region is determined by means of the Zhukovskii—Chaplygin condition of finiteness of the velocity at the sharp edge, and the extension of the separation region is found from the condition of vanishing of the velocity of the fluid at the point of closure of the separation region.Translated from Izvestiya Akademii Nauk SSSE, Mekhanika Zhidkosti i Gaza, No. 4, pp. 134–137, July–August, 1981.I thank L. I. Sedov and N. A. Slezkin, and also the participants of the seminars run by them for helpful discussion of the work.     

二维细胞在剪切流中的运动特性

主要模拟二维细胞在剪切流中的运动特性.计算过程采用浸入边界法,将细胞模化成Navier-Stokes方程中的力源,而不是真实物体.假设细胞的初始形状为椭圆,细胞内外流体粘性相同,细胞膜的弹性力模型选用E-S模型.本文模拟四种不同真圆度情况下细胞的形变情况,观测到初始阶段细胞沿着长轴方向做拉伸和旋转运动,达到稳定状态后细胞作类坦克履带式运动;并且发现细胞达到稳定状态所需要的时间随真圆度的增加而增加,而细胞的稳态倾角随真圆度的增加而减少.     

Fluid flow and heat transfer in a two-dimensional wavy channel

A numerical study is presented for the laminar fully developed flow and heat transfer in a two-dimensional wavy channel. The effects of the geometry, Reynolds and Prandtl number on the flow field and heat transfer are investigated. The channel is characterized by a wavy wall, heated at uniform heat flux, and an opposite wall, being plane and adiabatic. The extent of the wall waviness and the distance between the channel walls are found to significantly affect the streamlines contours as well as the heat transfer coefficients. Comparisons with the straight channel, in the same flow rate and heat transfer conditions, have been performed. Pressure drop of the wavy channel is found to be always larger than the value characteristic of a straight channel, while heat transfer performance decreases or increases depending on the values of the parameters (geometry, Reynolds and Prandtl numbers).     

Electrohydrodynamic flow in a two-dimensional channel with an axially disposed electrode-emitter

A study is made of the flow of an incompressible nonviscous unipolar charged liquid in a two-dimensional channel ¦ x ¦ <, ¦ y ¦ h with conducting walls and an axially disposed electrode-emitter (along y = 0). The charged particles have an arbitrary constant mobility. The charge distribution on the emitter is approximated as a unit step function. The problem is solved by linearizing the equations with respect to the electrohydrodynamic interaction. The behavior of the electrical parameters is determined, and the deformed profiles of velocity and pressure downstream of the zone in which the electrostatic forces are rotational in character are calculated. These profiles can be determined without having to solve the linearized partial differential hydrodynamic equations in the entire region occupied by the flow, although the profiles then depend on the distribution of the electrical parameters along the entire length of the channel.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 35–40, November–December, 1970.In conclusion the author wishes to thank A. B. Vatazhin for suggesting the problem and for his constant attention throughout the work.     

Quasi-steady deformation of a two-dimensional bubble placed within a potential viscous flow

The shape evolution of a two-dimensional bubble, bounded by a simple closed curve, which is initially placed within a potential viscous flow, is analysed. It is assumed that the influence of gravity and inertia forces is negligible, so the quasi-steady approximation can be applied. Reformulating the problem for Stokes equations with relevant boundary conditions at the free surface in terms of the bianalytic stress-stream function, and using the time-dependent conformal mappingz(,t) of a unit disk onto an unbounded flow domain sought, an infinite system of ordinary differential equations for the Laurent coefficients ofz(,t) is derived. A class of exact solutions is found for the case when the principal part of the complex velocity of the dominant flow at infinity is a polynomial, and the problem of formation of a pointed bubble is discussed.

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Sommario E analizzata l'evoluzione di una bolla bi-dimensionale, limitata da una curva chiusa semplice, inizialmente posta in un flusso potenziale viscoso. Si assume che l'influenza della gravità e delle forze inerziali sia trascurabile, cosicchè si può applicare l'approssimazione quasi-stazionaria. Riformulando il problema per le equazioni di Stokes con le opportune condizionial contorno sulla superficie libera in termini della funzione stress-stream bianalitica, e usando la tecnica delle trasformazioni conformi dipendenti dal tempoz(,t) di un disco unitario su un dominio di flusso non limitato incognito, viene derivato un sistema infinito di equazioni differenziali ordinarie per i coefficienti di Laurent diz(,t). Viene trovata una classe di soluzioni esatte per il caso in cui la parte principale della velocità complessa del flusso dominante all'infinito è una polinomiale, ed è discusso il problema della formazione di una bolla lenticolare.

     

Steady two-dimensional merging flow from two channels into a single channel

Two-dimensional steady symmetric merging flow from two channels into a single one is investigated. The geometry of the configuration has been chosen such that it can be mapped conformally onto a rectangular geometry, thus facilitating the numerical solution procedure for the governing Navier-Stokes equations. Computed velocity profiles and streamline patterns are presented in graphical form. Furthermore, results concerning the inlet length are given.     

Viscous flow in a rotating channel with permeable walls (two-dimensional approximation)

Laminar flow in a rotating rectangular channel with suction through one or more of the permeable walls is studied. The conditions under which a two-dimensional formulation of the flow core calculations is possible are discussed and the corresponding problem is formulated. Calculation results illustrating the combined effect of suction and rotation about the transverse axis are presented for a channel with a stopped end. Leningrad. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 30–34, September–October, 1988.     

Heat transfer associated with viscous two-dimensional channel flow in a transverse acoustic field

An analytic solution is proposed for the problem of the effect of a transverse resonant acoustic field on the heat transfer process in laminar two-dimensional channel flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 41–49, May–June, 1985.The author wishes to thank V. E. Nakoryakov for formulating the problem and discussing the results.     

Numerical calculation of two-dimensional flow in the channel with a partially compliant wall

The present paper is concerned with the flow in a two-dimensional channel whose wall is partially compliant. The flow field is calculated by the finite-difference method. Results are as follows: (1) When the upstream condition is given by steady flow (Reynolds number Re = 50), a compliant part of the wall oscillates with a frequency nearly equal to the characteristic frequency of the elastic wall. Absolute values of the pressure drop across the compliant part become small compared with those of the plane Poiseuille flow with wholly rigid walls. This ensures under physiological conditions that the blood can be transported more easily toward distal parts due to the compliance of vessel walls. (2) When the upstream condition is given by a pulsatile flow (Womersley number α = 8), interaction arises between characteristic frequency of the wall and basic frequency of the main stream near the compliant wall. As the basic frequency of pulsatile flow decreases, absolute values of mean pressure, which drop across the compliant wall, also become small compared with those of pulsatile flow between wholly rigid walls.     

Simulation of flux expulsion and associated dynamics in a two-dimensional magnetohydrodynamic channel flow

We consider a plane channel flow of an electrically conducting fluid which is driven by a mean pressure gradient in the presence of an applied magnetic field that is streamwise periodic with zero mean. Magnetic flux expulsion and the associated bifurcation in such a configuration are explored using direct numerical simulations (DNS). The structure of the flow and magnetic fields in the Hartmann regime (where the dominant balance is through Lorentz forces) and the Poiseuille regime (where viscous effects play a significant role) are studied, and detailed comparisons to the existing one-dimensional model of Kamkar and Moffatt (J Fluid Mech 90:107–122, 1982) are drawn to evaluate the validity of the model. Comparisons show good agreement of the model with DNS in the Hartmann regime, but significant differences arising in the Poiseuille regime when nonlinear effects become important. The effects of various parameters like the magnetic Reynolds number, imposed field wavenumber etc. on the bifurcation of the flow are studied. Magnetic field line reconnections occurring during the dynamic runaway reveal a specific two-step pattern that leads to the gradual expulsion of flux in the core region.     

Effects of two-dimensional V-shaped grooves on turbulent channel flow

Detailed Laser Doppler velocimeter (LDV) measurements have been carried out in a turbulent rectangular channel flow with one rough wall. The roughness elements of two-dimensional spanwise 120° V-shaped grooves are periodically arranged with different depths and pitches. The Reynolds number based on the centerline velocity, and the channel half height ranges from 2,740 to 20,000. The comparisons of turbulence statistics over smooth and rough walls indicate that the present roughness leads to a significant change in the turbulence both in the inner and in the outer flow. Particularly, the distribution density of the grooves is a key parameter to evaluate the effect of roughness. The low-Reynolds-number dependence of turbulence statistics is also observed. The rough walls with the same pitch-to-depth ratio exhibit the equivalent roughness function under the corresponding Reynolds numbers. The disagreement of velocity defect profiles between smooth and rough walls challenges the defect universal law. The variations of the turbulence stresses and Reynolds shear stress decomposition in the outer layer suggest that the turbulent motions may be modified by the present grooves. The importance of sweep events for the present groove-roughened walls is reflected by the differences in relative contribution to Reynolds shear stress from each quadrant and the higher-order moments over smooth and rough walls.     

二维槽道湍流数值模拟与白组织特性

从流体力学基本方程出发,讨论了二维槽道湍流的衰减特性,通过对流场施加合适的体积力,采用拟谱方法对二维槽道强制湍流进行了数值模拟.研究了二维槽道衰减湍流的自组织与逆能量级串特性,再现了二维槽道衰减湍流中湍涡的自组织过程,以及不同波数湍流结构所携能量在自组织过程中的变化,并解释了二维槽道湍流平均速度曲线特征以及海洋环流所特有的自然现象.     

Structure of turbulent two-dimensional channel flow with strongly heated wall

A laser Doppler velocimeter and a resistance thermometer were used to study velocity and temperature statistics in a strongly heated turbulent two-dimensional channel flow, with the wall temperature up to 700 °C and a Reynolds number of 14,000. Normalized mean velocity and mean temperature profiles were not significantly affected by the wall heating. Turbulent intensities of temperature fluctuation were also insensitive to the heat flux. However, turbulent intensities of velocity fluctuation were suppressed in the region away from the wall, whereas those near the wall were not changed noticeably by the wall heating. This phenomenon was explained by the balance of three parameters: turbulent production, viscous dissipation and intermittency.     

Simulation of two-dimensional turbulence in a planar channel

A study is made of the two-dimensional flow of an incompressible viscous fluid in a planar channel at supercritical Reynolds number Re = 10⁴. Calculation of the flow over an appreciable time interval leads to the establishment of a statistically steady flow regime and stabilization of its averaged characteristics (the profile of the mean velocity, the mean pressure gradient, the pulsation energy, etc.). The calculations show that numerical simulation of turbulent flow of an incompressible fluid on the basis of the Navier-Stokes equations leads to qualitatively correct characteristics of this flow regime.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 26–35, November–December, 1982.We are very grateful to Yu. L. Levitan, B. D. Moiseenko, V. K. Sidorova, and I. N. Simakin, collaboration with whom helped us to do this work.     

Hydromagnetic flow in a rotating channel

The steady flow in a parallel plate channel rotating with an angular velocity Ω and subjected to a constant transverse magnetic field is analysed. An exact solution of the governing equations is obtained. The solution in the dimensionless form contains two parameters: the Hartmann number, M ², and K ² which is the reciprocal of the Ekman number. The effects of these parameters on the velocity and magnetic field distributions are studied. For large values of the parameters, there arise thin boundary layers on the walls of the channel.     

Magnetohydrodynamic entrance flow in a channel

A MHD entrance flow in a channel is studied in the Prandtl approximation. It is shown that consistency with the approximation requires an appropriate change in the boundary conditions which hold for the original, unsimplified equations. The correct boundary conditions are established and used to repete the numerical calculations in a few cases studied by other authors with the unmodified boundary conditions. In the cases here considered the numerical differences do not amount in practice to more than 10%, though they grow with increasing Hartmann number. Gabinete de Aplicaciones Nucleares de O.P. and Centro Coordinado de Fisica (C.S.I.C.-U.A.M.). Present address: Departamento de Física, Facultad de Ciencias, Universidad Autónoma de Madrid.     

Two-fluid oscillatory flow in a channel

The validity of Navier's partial slip condition is investigated by studying the oscillatory flow in a coated channel. The two-fluid model is used to solve the unsteady viscous equations exactly. Partial slip is experienced by the core fluid. It is found that Naviers condition does not hold for an unsteady core fluid.