Laminar flow in the inlet region of a porous tube

Integral forms of the boundary layer equations, coupled with an assumed n-th degree boundary layer velocity profile, are used to study the effect of injection on the laminar flow in the inlet region of a circular tube. Results are illustrated graphically for a fourth degree velocity profile. It is found that the length of the inlet region decreases with the injection parameter and also that, at a given distance from the entry, the pressure drop in the inlet region increases with the injection parameter.     

Numerical study on the effect of initial flow velocity on liquid film thickness of accelerated slug flow in a micro tube

Numerical simulation of air–water slug flows accelerated from steady states with different initial velocities in a micro tube is conducted. It is shown that the liquid film formed between the gas bubble and the wall in an accelerated flow is significantly thinner than that in a steady flow at the same instantaneous capillary number. Specifically, the liquid film thickness is kept almost unchanged just after the onset of acceleration, and then gradually increases and eventually converges to that of an accelerated flow from zero initial velocity. Due to the flow acceleration, the Stokes layer is generated from the wall, and the instant velocity profile can be given by superposition of the Stokes layer and the initial parabolic velocity profile of a steady flow. It is found that the velocity profile inside a liquid slug away from the bubble can be well predicted by the analytical solution of a single-phase flow with acceleration. The change of the velocity profile in an accelerated flow changes the balance between the inertia, surface tension and viscous forces around the meniscus region, and thus the resultant liquid film thickness. By introducing the displacement thickness, the existing correlation for liquid film thickness in a steady flow (Han and Shikazono, 2009) is extended so that it can be applied to a flow with acceleration from an arbitrary initial velocity. It is demonstrated that the proposed correlation can predict liquid film thickness at Re < 4600 within the range of ±10% accuracy.     

Analytical investigation of boundary layer growth and swirl intensity decay rate in a pipe

In this research, the developing turbulent swirling flow in the entrance region of a pipe is investigated analytically by using the boundary layer integral method. The governing equations are integrated through the boundary layer and obtained differential equations are solved with forth-order Adams predictor-corrector method. The general tangential velocity is applied at the inlet region to consider both free and forced vortex velocity profiles. The comparison between present model and available experimental data demonstrates the capability of the model in predicting boundary layer parameters (e.g. boundary layer growth, shear rate and swirl intensity decay rate). Analytical results showed that the free vortex velocity profile can better predict the boundary layer parameters in the entrance region than in the forced one. Also, effects of pressure gradient inside the boundary layer is investigated and showed that if pressure gradient is ignored inside the boundary layer, results deviate greatly from the experimental data.     

A STUDY ON DROPLET VELOCITY OF ETHANOL DURING ELECTROSPRAYING PROCESS AT CONE-JET MODE

研究液滴在静电喷雾下的速度特性是理解喷雾形态的形成及演化的关键.结合锥射流模式下乙醇静电喷雾实验数据,建立了静电喷雾二维轴对称模型.基于离散相液滴运动方程、连续相空气运动方程、电场方程以及用户自定义函数,进行了数值求解,获得了锥射流模式下的乙醇静电喷雾形态、空间电场分布以及液滴速度场分布.考虑了不同空气入口流速的影响,得到了乙醇/空气同轴射流静电喷雾形态的变化规律.结果表明,喷雾外围液滴与空气流场有较强的相互作用,导致喷雾中轴线附近的液滴速度分布变化较小,而在喷雾外围处的液滴速度分布沿径向剧烈变化;随着空气入口速度的增大,乙醇/空气同轴射流静电喷雾形态先趋于发散,当空气入口速度大于喷雾外围液滴轴向速度时,喷雾形态则趋于聚拢.因此,除改变施加电压、液体流量和电极结构外,通过控制空气入口速度来影响喷雾液滴速度场,也可获得不同的静电喷雾效果.     

Theoretical and numerical studies on the flow multiplicity phenomenon for gas–solids two-phase flows in CFB risers

The dependence of the fully-developed flow profiles on the inlet flow conditions for gas–solids two-phase flows, i.e. the flow multiplicity phenomenon, in circulating fluidized bed (CFB) risers was proposed and discussed in this article. The flow multiplicity phenomenon for gas–solids two-phase flows was first proved mathematically based on the conservation equations of mass and momentum. Then the CFD model using Eulerian–Eulerian approach with k–ε turbulence model for each phase was further adopted to analyze the details of this flow multiplicity phenomenon. It is theoretically and numerically revealed that for gas–solids two-phase flows, the flow profiles in the fully-developed region are always dominated by the flow profiles at the inlet. The solids concentration profile is closely coupled with the velocity profile, and the inlet solids concentration and velocity profiles can largely influence the fully-developed concentration and velocity profiles.     

Swirling flow structures in electrostatic precipitator

Stereoscopic digital Particle Image Velocimetry (PIV) has been used to make a three-dimensional flow mapping of a volume of approximately 0.1 × 0.1 × 0.15 m in a laboratory model electrostatic precipitator (ESP). The mapped volume covers about two unit cells determined by the 100 mm electrode spacing in the 0.2 × 0.2 × 1.0 m ESP test section of the negative corona, barbed wire, smooth-plate kind. The barbs act as corona fix points, yielding a three-dimensional electrostatic field. The induced large-scale secondary gas velocity structures in the form of unsteadily undulating axial rolls have been analyzed for swirlnumber and location of instantaneous swirl center in 11 axial planes. The flow possesses high levels of turbulence and axial vorticity. Measured particle velocities are corrected for electrical drift to produce gas velocities. Subsequently experimental results are compared to Large Eddy Simulation (LES) results.     

Velocity distributions in a hydrocyclone separator

 The internal three-dimensional flow field in a hydrocyclone was studied using laser velocimetry. Seven axial planes were investigated for three different inlet flow rates and three independent and different rejects rates. Results at each measurement plane showed that the measured tangential velocity profile behaves like a forced vortex at the region near the air core, and like a free vortex in the outer portion of the flow. The peak nondimensional tangential velocity decreases as the distance from the inlet region increases, however, the peak dimensional tangential velocity increases as the distance from the inlet region increases. The nondimensional peak tangential velocities are approximately equal for all of the flow rates. The magnitude of the tangential velocity increased in the inner forced vortex region as the rejects rate was increased. Backflows exist in the axial velocity profile near the inlet region, but these reversed flows disappear in the exit region. The dimensional vorticity is proportional to inlet flow rate and decreases with increasing rejects flow rates. Received: 27 February 2001/Accepted: 19 June 2001     

连铸结晶器内部流场及熔渣卷入的数值模拟

针对连铸结晶器内部流场及熔渣卷入过程 ,提出了两方程k -ε湍流模型和充填法数值计算模型 ,并采用硅油 /水模拟体系代替熔渣 /钢液体系 ,进行了模拟试验和数值计算。对充气造成的浸入式水口水流脉动的影响进行分析。计算结果与试验结果符合良好 ,表明本文所采用的数值模拟方法是适用的     

Characteristics of developing vertical bubbly flow under normal and microgravity conditions

The axial development of the void fraction profile, interfacial area concentration and Sauter mean bubble diameter of adiabatic nitrogen-water bubbly flows in a 9 mm-diameter pipe were measured using stereo image processing under normal and microgravity conditions. The flow measurements were performed at four axial locations (axial distance from the inlet, z normalized by the pipe diameter, D, z/D = 5, 20, 40 and 60) and with various flows: superficial gas velocity of 0.00840-0.0298 m/s, and superficial liquid velocity of 0.138-0.914 m/s. The effect of gravity on radial distribution of bubbles and the axial development of two-phase flow parameters is discussed in detail based on the obtained database and visual observation. Following Serizawa-Kataoka’s phase distribution pattern criteria under normal gravity conditions, the phase distribution pattern map was developed. Similar to normal gravity two-phase flows, wall, core and intermediate void peak patterns are observed under microgravity conditions but a transition void distribution pattern is not observed in the current experimental conditions. The data obtained in the current experiment are expected to contribute to the benchmarking of CFD simulation of phase distribution pattern and interfacial area concentration in forced convective pipe flow under microgravity conditions.     

Modeling of convective structures in a thin layer of silicone oil in air flow under heating

Numerical simulation was performed to study convective structures in a thin silicone oil layer heated from below, whose free surface is exposed to air flow generating drift flow. The basic equations are transformation to a form suitable for spectral methods. The steady flow velocity profile obtained in a laboratory experiment is calculated. It is shown that increasing the Reynolds number leads to the transition from polygonal convective cells to longitudinal rolls (elongated along the flow). The dependence of the transition Reynolds number on the temperature on the lower boundary of the layer is obtained. The calculation results are compared with experimental data.     

The effect of inflow conditions on the transition to turbulence in large eddy simulations of spatially developing mixing layers

Large Eddy Simulations (LES) of spatially developing turbulent mixing layers have been performed for flows of uniform density and Reynolds numbers of up to 50,000 based on the visual thickness of the layer and the velocity difference across it. On a fine LES grid, a validation simulation performed with a hyperbolic tangent inflow profile produces flow statistics that compare extremely well with reference Direct Numerical Simulation (DNS) data. An inflow profile derived from laminar Blasius profiles produces a flow that is significantly different to the reference DNS, particularly with respect to the initial development of the flow. When compared with experimental data, however, it is the boundary layer-type inflow simulation produces the better prediction of the flow statistics, including the mean transition location. It is found that the boundary layer inflow condition is more unstable than the hyperbolic tangent inlet profile. A suitably designed coarse LES grid produces good predictions of the mean transition location with boundary layer inflow conditions at a low computational cost. The results suggest that hyperbolic tangent functions may produce unreliable DNS data when used as the initial condition for studies of the transition in the mixing layer flow.     

Stability of motion of the plane boundary separating two fluids

The effect of viscosity on the disintegration of liquid jets can be considered in two ways. First, viscous forces alter the basic flow: they form a boundary layer whose presence necessarily alters wave formation. Second, viscous forces can have a direct effect on the development of perturbations for a given velocity profile of the basic flow. In this case the study of stability must be based on the Navier-Stokes equations instead of the equations of an ideal fluid. This complicates analysis considerably. Available data [1] indicate that this influence is very minor in the case of moderately viscous fluids. It appears, therefore, that the principal role is played by changes in the velocity profile alone, and that the behavior of the perturbations is described by the equations of an ideal fluid.In the present study we investigated the stability of motion and wave formation at the boundary between two fluids in order to determine the effect of viscosity on the drop formation mechanism. The simplest case of oscillation of the boundary is chosen in order to keep the analysis as simple as possible.     

一类平衡大气边界层边界条件研究

基于标准k-ε湍流模型,首先利用湍流粘度方程和剪切应力在整个边界层内恒定的假设,推导出一类耗散率表达式,并根据常用的湍动能入口剖面方程以及平均风速剖面方程,计算获得相应的耗散率方程;然后在输运方程中添加自定义源项,通过已经确定的平均速度方程、湍动能方程、耗散率方程计算得到相应输运方程的自定义源项表达式,并进行空风洞数值模拟,从而得到了一类满足平衡大气边界层的来流边界条件．通过将这种边界条件与由湍流平衡条件得到的边界条件进行比较,表明本方法获得的边界条件更适用．并且,本方法无需考虑修正壁面函数和修正湍流模型常数,因而计算更为简单,可为平衡大气边界层的研究提供一种新的思路．     

Exit-flow velocity survey of two single-tangential-inlet vaneless turbine volutes

The most cited analytical technique for designing turbine volutes is to assume the throughflow is free from torque, although for this assumption to hold, the volute walls must lie near what would be streamlines in an unbounded free vortex-plus-sink flow. The single tangential inlet design, with inlet offset decreased and diameter increased to attain the weak exit swirl required by high specific speed turbines, deviates from such a shape, and the volute’s internal geometry is no longer torque-free. It is desired to know the actual time-averaged flow leaving such a volute, so that a rotor can be designed to compliment it.For two existing single tangential inlet volutes, time-averaged radial and tangential velocity and static pressure measurements of exit flow have been obtained on a cylindrical cut plane through the radial-inflow section using a three-port yawmeter in air. The Reynolds numbers based on inlet pipe mean conditions, around 10⁵, are well into the fully-turbulent regime and on the order of comparable water turbines.A comprehensive map of time-averaged exit flow of both volutes is presented. The integrated values of gross angular momentum flux change and total pressure loss coefficient are tabulated. Circumferential variation of flowrate and swirl strength highlight unexpected differences in outlet flow between the two volute designs. Results are presented alongside corresponding numerical results from the commercial package Fluent (Fluent, Inc., Lebanon, NH, USA) using Reynolds stress, k-ω, and inviscid flow models.In both volutes, measured gross exit angular momentum flux was more than 1.7 times what the zero-torque assumption would predict when blindly applied to the volute as a whole. This discrepancy is attributed to significant turning near the volute’s inlet region leading to an updated view of what an appropriate control volume is when applying the zero-torque assumption. Additionally, variation of both radial and tangential velocity in both the circumferential and axial directions on the order of 15% of the mean value reveal that volute swirl characterization by a single measurement would have a significant associated uncertainty.     

The use of perforated plates to control the flow emerging from a wide-angle diffuser,with application to electrostatic precipitator design

The flow through a wide-angle, pyramidal diffuser of area ratio 6.8, in which two perforated plates are used to control the emergent velocity distribution was investigated. (Wide-angle diffusers combined with perforated plates find application in electrostatic precipitator flow systems. The efficacy of these systems depends critically on the uniformity of the gas flow within the collection chamber downstream of the diffuser outlet plane.) The main results of the study are (i) the establishment of the main factor influencing the flow at the diffuser exit plane, (ii) the determination of plate characteristics which produce a uniform velocity profile in the collection chamber, and (iii) the establishment of the corresponding pressure drop characteristics of the plate—diffuser combinations. The results also extend the range of diffuser geometries for which two perforated plates provide uniform velocity profiles at exit.     

Inlet flow disturbance effects on direct numerical simulation of incompressible round jet at Reynolds number 2500

This letter reports inlet flow disturbance effects on direct numerical simulation of incompressible round jet at Reynolds number 2500.The simulation employs an accurate projection method in which a sixth order biased upwind difference scheme is used for spatial discretization of nonlinear convective terms,with a fourth order central difference scheme used in the discretization of the divergence of intermediate velocity.Carefully identifying reveals that the inlet flow disturbance has some influences on the distribution pattern of mean factor of swirling strength intermittency.With the increase of inlet disturbance magnitude jet core cone slightly shortens,observable differences occur in the centerline velocity and its fluctuations,despite the negligible impacts on the least square fitted centerline velocity decay constant(B_u)and distribution parameter(K_u)for velocity profile in self-similar region.     

Analysis of gaseous flow in a micropipe with second order velocity slip and temperature jump boundary conditions

In this paper, second order velocity slip and temperature jump boundary conditions are used to solve the momentum and energy equations along with isoflux thermal boundary condition at the surface of the micropipe. The flow is assumed to be hydrodynamically and thermally fully developed inside the micropipe and viscous dissipation is included in the analysis. The solution yields closed form expressions for the temperature field and Nusselt number (Nu) as a function of various modeling parameters, namely, Knudsen number and Brinkman number (Br). For the given values of Br, the maximum difference of Nu between continuum flow with first order slip model and continuum and, second order slip model is found to be 35.67 and 34.62 %, respectively. Present solution exhibits good agreement with the other theoretical models.     

孔板空调风口送风射流的数值模拟

介绍Ｎ点风口模型用于数值模拟室内空气流动时描述孔板类送风口的入流边界条件．然后采用该风口模型对不同的孔板风口出流条件算例进行数值计算，并就轴心速度衰减、射流扩展角以及断面流速分布等射流特性与实验数据进行了对比．比较结果表明，Ｎ点风口模型用于描述数值模拟室内空气流动的孔板类风口入流边界条件，可以获得工程上足够满意的结果．     

Precise flow rate measurements of natural gas under high pressure with a laser Doppler velocity profile sensor

This paper reports about the first application of a laser Doppler velocity profile sensor for precise flow rate measurements of natural gas under high pressure. The profile sensor overcomes the limitations of conventional laser Doppler anemometry (LDA) namely the effect of spatial averaging and the effect of fringe spacing variation (virtual turbulence). It uses two superposed, fan-like interference fringe systems to determine the axial position of a tracer particle inside the LDA’s measurement volume. Consequently, a spatial resolution of about 1 μm can be achieved and the effect of virtual turbulence is nearly eliminated. These features predestine the profile sensor for flow rate measurements with high precision. Velocity profile measurements were performed at the German national standard for natural gas, one of the world′s leading test facilities for precision flow rate measurements. As a result, the velocity profile of the nozzle flow could be resolved more precisely than with a conventional LDA. Moreover, the measured turbulence intensity of the core flow was of 0.14% mean value and 0.07% minimum value, which is significantly lower than reference measurements with a conventional LDA. The paper describes the performed measurements, gives a discussion and shows possibilities for improvements. As the main result, the goal of 0.1% flow rate uncertainty seems possible by an application of the profile sensor.     

Near-wall measurements of turbulence statistics in a fully developed channel flow with a novel laser Doppler velocity profile sensor

This paper reports on the measurements of the near-wall turbulence statistics in a fully developed channel flow. The flow measurements were carried out with a novel laser Doppler velocity profile sensor with a high spatial resolution. The sensor provides both the information of velocity and position of individual tracer particles inside the measurement volume. Hence, it yields the velocity profile inside the measurement volume, in principle, without the sensor being mechanically traversed. Two sensor systems were realized with different techniques. Typically the sensor has a relative accuracy of velocity measurement of 10⁻³ and the spatial resolution of a few micrometers inside the measurement volume of about 500 μm long. The streamwise velocity was measured with two independent sensor systems at three different Reynolds number conditions. The resulting turbulence statistics show a good agreement with available data of direct numerical simulations up to fourth order moment. This demonstrates the velocity profile sensor to be one of the promising techniques for turbulent flow research with the advantage of a spatial resolution more than one magnitude higher than a conventional laser Doppler technique.