Integral methods of calculation of heat transfer and drag under conditions of turbulent pipe flow of liquid of variable properties: Steady-state and quasi-steady-state flows in a round pipe with constant density of heat flux to the wall

Integral relations are derived for the calculation of the Nusselt number and coefficients of hydraulic drag and friction drag under conditions of pipe flow of dropping liquid and gas of temperature-dependent physical properties. In the limiting case of steady-state flow of liquid of constant properties, the expression for the Nusselt number transforms to the well-known Lyon integral. The results of calculation of heat transfer and drag by an integral method are compared with more exact results obtained using the numerical solution of the set of differential equations of convective heat transfer. An inference is made about the conditions under which integral methods may be employed. An algorithm is developed for the calculation by an integral method of heat transfer and drag under conditions of quasi-steady-state pulsating flow. It is demonstrated that the flow rate oscillations superposed on the flow in the pipe enhance the effect of the variability of the properties on heat transfer, and for gas on friction drag. For a dropping liquid under conditions of pulsating flow, the friction drag depends less significantly on the variability of the properties (viscosity) than in the case of steady-state flow. The degree of manifestation of the effects identified above is the higher, the higher the oscillation amplitude and the lower the value of the Reynolds number of averaged flow.     

Laminar Flow Past a Circular Cylinder under the Effect of Nonstationary Jet Efflux to the Near‐Wake Region

Changes in a laminar flow past a circular cylinder under the effect of jets blowing out to its rare region have been studied numerically. Jet efflux was caused by a return flow of a part of the incoming flow in the inner channels of the cylinder due to the pressure difference between its front and end stagnation points. The channels connected the inlet window formed in the zone of the front stagnation point with two outlet windows on the backside surface of the cylinder. The influence of the coordinates of the jets issuing through the outlet windows and dimensions of the inlet and outlet windows on variation of the drag and lift coefficient and distribution of the coefficients of pressure and friction on the cylinder surface has been considered. It is shown that under the effect of blowing out the cylinder drag decreased by 4% and the amplitude of buoyancy force oscillations decreased by 40%.     

Stokes flow with slip caused by the axisymmetric motion of a sphere bisected by a free surface bounding a semi-infinite micropolar fluid

The first part of this paper investigates the motion of a solid spherical particle in an incompressible axisymmetric micropolar Stokes flow. A linear slip, Basset-type, boundary condition has been used. Expressions for the drag force and terminal velocity has been obtained in terms of the parameter characterizing the slip friction. In the second part, we consider the flow of an incompressible axisymmetrical steady semi-infinite micropolar fluid arising from the motion of a sphere bisected by a free surface bounding a semi-infinite micropolar fluid. Two cases are considered for the motion of the sphere: perpendicular translation to the free surface and rotation about a diameter which is also perpendicular to the free surface. The speed of the translational motion and the angular speed for the rotational motion of the sphere are assumed to be small so that the nonlinear terms in the equations of motion can be neglected under the usual Stokesian approximation. Also a linear slip, Basset-type, has been used. The analytical expressions for velocity and microrotation components are determined in terms of modified Bessel functions of second kind and Legendre polynomials. The drag for the translation case and the couple for the rotational motion on the submerged half sphere are calculated and expressed in terms of nondimensional coefficients whose variation is studied numerically. The variations of the drag and couple coefficients with respect to the micropolarity parameter and slip parameter are tabulated and displayed graphically.     

Suction of splash after impact on dry quick sand

It is well known that a splash occurs when an object impacts at high velocity on a liquid??s surface. If the impact is fast enough, surface tension and air pressure gradients pull the crown-shape splash all the way towards the axis of symmetry, making it to collapse and seal the surface. In this paper we show that splash and surface sealing are also observed in impacts on soft, dry sand. We observe influence of air pressure and grains size on the shape of the splash. By tracking individual grains using high-speed imaging we calculate their acceleration, which results from gravity and drag forces. Assuming friction drag parallel, and pressure drag perpendicular to the direction of motion of grains we estimate the friction and pressure drag contributions to the drag force. Our results support the idea that pressure drag from Bernoulli effect is at the origin of the surface seal.     

Hydrodynamics and heat transfer in pulsating turbulent flow of gas in a heated pipe

The paper deals with the investigation of the effect produced by the dependence of the physical properties on temperature and flow rate fluctuations on heat transfer and drag under conditions of turbulent pipe flow of gas. The method of finite differences is used to solve numerically a set of equations of motion, continuity, and energy written in a narrow channel approximation. A model of turbulence is used which takes into account the effect of the variability of the properties and of the nonstationarity of flow on turbulent transfer. In the particular case of steady-state flow of gas being heated, the calculation results fit well the available experimental data. It is found that the heat transfer depends on the heating rate more significantly than the friction drag. In the case of pulsating flow, the part of hydraulic drag is estimated which is spent for the variation of longitudinal velocity along the pipe and is due to the thermal acceleration of gas. It is demonstrated that the main features of pulsating flow, which were previously investigated for a liquid of constant properties and for a dropping liquid of variable viscosity, are retained for the gas being heated as well. Comparison is made for the gas and dropping liquid of the effect made by various process parameters such as the Reynolds, Stokes, and Prandtl numbers, the heating rate, and the form of thermal condition on the wall on the period average Nusselt number and coefficient of friction drag.     

The flow of liquid past a plate with boiling and injection of gas

A classical model boundary layer problem is considered for the flow of liquid past a plate in view of injection of a vapor-gas mixture from its surface. The obtained self-similar solutions enable one to estimate the typical values of thickness of the vapor-gas layer, the value of heat-transfer coefficient as a function of temperature of liquid, intensity of injection and composition of mixture being injected, and the velocity of flow past the plate. In addition, the problem is considered of reducing the hydrodynamic drag owing to vapor and vapor-gas “lubrication” because of boiling of liquid and injection of vapor-gas mixture from the plate surface. The possibility is analyzed of the emergence of vapor film due to viscous friction forces in the case where the liquid is in the vicinity of the boiling point.     

Integral methods of calculation of heat transfer and drag under conditions of turbulent pipe flow of liquid of variable properties: Pulsating high-frequency flow

An integral method is suggested for approximate calculation of oscillation-period average heat transfer and drag under conditions of pulsating high-frequency flow of gas in a pipe with constant density of heat flux to the wall. It is found that the flow rate oscillation superimposed on the flow has little effect on the period average Nusselt number and coefficient of friction drag; these quantities may be calculated by the method developed for a steady-state flow of liquid of variable properties. The oscillation affects significantly the period average coefficient of hydraulic drag whose values increase with the amplitude of superimposed oscillation.     

Heat transfer in boundary layer flow of a micropolar fluid past a curved surface with suction and injection

Van Dyke's singular perturbation technique has been used to study the heat transfer in the flow of a micropolar fluid past a curved surface with suction and injection. The conditions for similar solutions of the thermal boundary layer equations have been obtained. In addition to the usual “no slip” condition for velocity, the two types of boundary conditions used for microrotation are: (i) no relative spin on the boundary; (ii) the anti-symmetric part of the stress tensor vanishes at the boundary. The effect of suction or injection on velocity, microrotation, temperature, skin friction coefficient, wall couple stress coefficient, displacement and momentum thicknesses, rate of heat transfer and adiabatic wall temperature have been studied. It is observed that with the increase of injection velocity, the thickness of the boundary layer is increased and the local drag is reduced. A comparison with the results obtained for a Newtonian fluid reveals that the microelements present in the fluid reduce the velocity and frictional drag, and cool the boundary.     

The effects of nonmonotonicity of energy flux and of normal momentum flux in transient mode in the Couette problem at high values of Mach number

The numerical solution of Boltzmann equation is used for investigating the Couette flow in a wide range of values of Knudsen number and velocity of the upper plate. The Knudsen number dependences of the energy flux to the lower plate, of the friction drag of the lower plate, and of the flux of normal momentum transferred to the lower plate are considered. It is demonstrated that the effect of nonmonotonicity at high values of Mach number is observed both for the friction drag and for the energy flux and normal momentum flux.     

雷诺数对沟槽减阻特性影响的数值分析

采用雷诺平均N—S方程和RNG κ-ε湍流模型计算V型沟槽面的湍流边界层流动和黏性阻力，通过改变来流速度大小和沟槽面布置位置，研究了雷诺数对沟槽减阻特性的影响规律。计算结果表明，来流速度对沟槽减阻率的影响很大，对于一种尺度的V型沟槽，存在着一个具有较好减阻效果的来流速度范围，最大减阻率可迭8．6％；沟槽面在沿来流方向上的布置位置对其减阻效果的影响则非常小。     

The initial boundary-layer flow past a translating and spinning rotational symmetric body

The boundary-layer flow on an impulsively started translating and spinning rotational symmetric body is considered. The stream function and the swirl component of the velocity are expanded in series in powers of time. Leading and first order solutions are obtained analytically and the second order solutions are determined numerically. The results are applied to a translating and spinning sphere and the rotation is found to reduce the friction drag and facilitate flow separation.     

Drag reduction of turbulent flow over thin rectangular riblets

Direct numerical simulations of low-Reynolds number turbulent channel flow are carried out where thin rectangular riblets are distributed uniformly at only one of the channel walls. A second-order accurate finite volume code is modified in order to reconstruct the adjacent cells to the riblets at Cartesian coordinates. A quadratic interpolation scheme is used to estimate the fluxes at the reformed cells. The riblets height/spacing ratio is fixed at 0.5 which doubles the surface area at the ribbed wall and the thickness/spacing ratio is set to 0.02. The riblet spacing ranges from 13 to 41 viscous units. Comparison with experiments shows excellent agreement in detecting both reduction and the increase of drag at the studied range of spacings. The maximum drag reduction obtained is about 11% which occurs at a spacing of 18 viscous units. The increase of drag is addressed when the spacing is larger than 30 wall units. Wide spacing permits the near-wall eddies to reside inside the riblet-to-riblet span which in turn makes them interacting with larger wetted area and increases the friction drag.     

泡沫型多孔介质中非达西流动特性的研究

本文通过将泡沫材料复杂结构进行几何简化，形成立方框架结构，利用简化的等效单元流道，提出一种数理模型，它既考虑固体网架表面对流体的摩擦阻力作用，也考虑网架迎着流向的迎风阻力（形状阻力），得到了在多孔介质中非达西流的压力降与流速的关系式。并用简化的框架结构导出了预估泡沫材料渗透率ｋ和Ｆ－Ｗ关系式中流速平方项的系数Ｆ。另外，还通过专用的实验装置测定了四种不同孔径泡沫陶瓷的ｋ和Ｆ。结果表明，根据所给模型理论预测的结果与实验值一致性较好，在泡沫型多孔材料的应用中能够提供流动特性的相关数据。     

Flow properties of granular materials with large overburden loads

Summary For the rapid shear flow of granular materials with large overburden loads, an action involving the simultaneous impact of more than two particles is shown to provide a mechanism for reducing the effective drag force acting on the flowing material. The drag is reduced below both the static friction value and the drag due only to binary collisions. Since the frequency of multiparticle collisions increase as the bulk density of the flowing material decreases, larger overburdens result in more multiparticle collisions giving rise to greater decreases in the effective drag force. It is hypothesized that this mechanism may account for the extraordinarily long runout distances observed for large rockslides and avalanches. A simple numerical model of interacting inelastic disks in a quasi-two dimensional flow was used to guide the investigation and verify the proposed mechanism.With 5 Figures     

Aerodynamic drag of a plate in an ionized gas flow induced by a near-surface high-frequency barrier discharge

We have made an experimental study of the dependence of the total drag of a flat plate on the incident flow velocity and electrical parameters of discharge in the presence of a high-frequency barrier discharge on the surface. It has been shown that the use of a near-surface barrier discharge permits decreasing the profile drag coefficient by 3–7%.     

深水悬链锚泊线阻尼计算

深水悬链锚泊线的阻尼主要包括流体动力阻尼、内阻尼和海床摩擦阻尼。除内阻尼由材料特性决定以外,流体动力阻尼和海床摩擦阻尼受上部浮体运动的影响比较显著。利用单根锚泊线由于上部浮体运动而吸收的能量来计算锚泊阻尼。锚泊线和海床之间的接触作用基于刚性海床假定,利用Morrison公式计算锚泊线的惯性力和拖曳力荷载。用有限元方法进行非线性时域动力分析,计算在不同流速分布条件下,上部浮体分别发生慢漂运动和波频运动时的锚泊线动力响应,比较不同工况下锚泊线的最大张力和流体动力阻尼。考虑锚泊线与海床之间的接触摩擦,比较不同摩擦系数时锚泊线的最大张力,并对摩擦阻尼进行计算。     

Effect of drag force modeling on the flow of electrostatically charged particles

In CFD simulations of two-phase flows, accurate drag force modeling is essential for predicting particle dynamics. However, a generally valid formulation is lacking, as all available drag force correlations have been established for specific flow situations. In particular, these correlations have not been evaluated for particle-laden flows subjected to electrostatic forces. The paper reports the effect of drag force modeling on the flow of electrically charged particles. To this end, we implemented different drag force correlations to the open-source CFD tool pafiX. Then, we performed highly-resolved Direct Numerical Simulations (DNS) using the Eulerian–Lagrangian approach of a particle-laden channel flow with the friction Reynolds number of 180. The simulations generally revealed a strong influence of the precise drag correlation on particles in the near-wall region and a minor effect on the particles far from the walls. Due to their turbophoretic drift, particles accumulate close to the channel walls. For uncharged particles, the simulations show large deviations of the particle concentration profile in the near-wall region depending on the drag force correlation. Therefore, the disturbance of the flow surrounding a particle by a nearby wall or other particles is important for its drag. Driven by electrostatic forces, charged particles accumulate even closer to the wall. Contrary to the uncharged cases, when the particles carry a high charge (in our case one femto-coulomb), we found minor effects of drag force modeling on particle concentration profiles. In conclusion, for the investigated conditions, we propose to account for the effect of nearby particles and walls on the drag of low- or uncharged particles.     

Modeling of vortex structures on the lateral surface of a cylinder in a longitudinal flow

The problem of generation of vortex structures by ejection of a jet through an annular slot on a cylindrical surface in a longitudinal flow is considered. Results of modeling of large-scale vortices and their effect on local characteristics of the wall boundary layer are presented. The modeling is based on numerical integration of the Navier-Stokes equations in an axisymmetric formulation. An unsteady-state flow with separation and entrainment of vortices by the main stream is obtained. The decrease in the friction drag achievable in devices of this kind is estimated.Academic Scientific Complex A. V. Luikov Heat and Mass Transfer Institute, Academy of Sciences of Belarus, Minsk, Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 66, No. 5, pp. 527–533, May, 1994.     

Non-equilibrium linearized magnetogasdynamic flow over a wavy wall (aligned)

Summary A steady, linearized flow of a conducting fluid withn non-equilibrium processes in parallel has been considered and neglecting the effects due to viscosity, heat conduction and diffusion and assuming the electrical conductivity to be infinite, a single equation for the flow variables has been derived when the undisturbed uniform magnetic field is aligned to the undisturbed uniform fluid stream. The solution of the equation has been obtained for a flow over a two-dimensional wavy wall. The pressure, net pressure i.e. the difference between the local static, pressure and force per unit area arising from the surface current, drag coefficient and total drag coefficient have been calculated and the results have been discussed. It is found that for certain values of the equilibrium Mach number and the magnetic pressure number negative drag coefficient as well as negative total drag coefficient occur in the flow.With 6 Figures