Flow visualization of supersonic two-phase transcritical flow of CO2 in an ejector of a refrigeration system

Supersonic two-phase flow of CO₂ in an ejector was investigated in flow visualization experiments. The ejector was installed in a transcritical CO₂ ejector-expansion refrigeration system with a convergent primary nozzle and a rectangular mixing chamber. The flow fields in the suction chamber and the mixing chamber of the ejector were visualized by direct photography for various operating conditions. The results showed that the liquid in the primary flow after the primary nozzle exit increased with increasing primary flow and secondary flow pressures. The expansion angle of the primary flow at the nozzle exit decreased with increasing secondary flow pressures. The primary flow was blocked in some cases at the mixing chamber entrance due to the large expansion angle which reduced the entrainment performance. The entrainment ratio was inversely related to the expansion angle. The primary and the secondary flows had a short mixing region in the mixing chamber with the mixed flow quickly becoming uniform.     

Generalized Couette flow in channels of irregular cross‐section

Abstract

The flow behavior of non‐Newtonian power‐law fluids in channels of irregular cross‐section is examined. The driving force of the flow may be a constant pressure gradient (Poiseuille flow), a moving boundary (Couette flow) or the combination of the two (generalized Couette flow). There are three factors that influence the fluid motion in a channel, namely, the power‐law index n, the channel geometry and a dimensionless quantity E which can be viewed as the ratio of drag flow to pressure flow. The effects of these variables on velocity distributions and volumetric flow rates for various channel geometries are analyzed. The direct application of the numerical results on extruder design and operation is discussed.     

Hydrodynamic instability of a suspension of spherical particles through a branching network of circular tubes

A numerical method is presented for computing the unsteady flow of a monodisperse suspension of spherical particles through a branching network of circular tubes. The particle motion and interparticle spacing in each tube are computed by integrating in time a one-dimensional convection equation using a finite-difference method. The particle fraction entering a descendent tube at a divergent bifurcation is related to the local and instantaneous flow rates through a partitioning law proposed by Klitzman and Johnson involving a dimensionless exponent, q ≥ 1. When q = 1, the particle stream is divided in proportion to the flow rate; as q → ∞, the particles are channeled into the tube with the highest flow rate. The simulations reveal that when the network involves two or more generations, a supercritical Hopf bifurcation occurs at a critical value of q, yielding spontaneous, self-sustained oscillations in the segment flow rates, pressure drop across the network, and particle spacing in each tube. A phase diagram is presented to establish conditions for unsteady flow. As found recently for blood flow in a capillary network, oscillations can be induced for a given network tree order by decreasing the ratio of the tube diameter from one generation to the next or by decreasing the diameter of the terminal segments. The instability is more prominent for rigid than deformable particles, such as drops, bubbles, and cells, due to strong lubrication forces between the tightly fitting particles and tube walls. Variations in the local particle spacing, therefore, have a more significant effect on the effective viscosity of the suspension in each tube and pressure drop required to drive a specified flow rate.     

涡轮流量计时间常数校准技术研究

为了校准涡轮流量计的时间常数,建立液体阶跃流量试验装置,该装置利用螺杆泵输送流体形成平台流量,采用内啮合齿轮泵输送流体形成阶跃流量分量,通过控制高速电磁阀的开启与关闭实现阶跃流量分量与平台流量的叠加,最终产生阶跃流量。利用皮托管对阶跃流量产生时间进行评估,结果表明阶跃流量上升时间小于9 ms。在不同阶跃工况下对涡轮流量计开展时间常数校准试验,结果表明：涡轮流量计时间常数并非固定值,且受平台流量影响较大,具有随前平台流量增大而减小的趋势,受阶跃流量幅度影响较小;在小流量范围内,实际测量得到的动态流量系数与理论模型推导得到的动态流量系数偏差较大,而在大流量范围内二者较为吻合。最后对时间常数校准结果进行了不确定度评估,最大扩展不确定度约为10 ms(k=2)。研究成果有助于评估流量计动态特性,有望提高非稳态流量测量的准确度。     

Experimental analysis of preferential flow in dry snowpack

Preferential flow in snowpack is an important phenomenon and influences snowpack modeling, avalanche forecasting and runoff forecasting for snow-covered basins. However, the theoretical foundation is not sufficient to develop a snowpack model that includes a water movement process including preferential flow. The water ponding process, which is caused by the water-entry value of capillary pressure, is a key process for capillary pressure overshoot, water saturation overshoot and the formation of preferential flow in other porous media like homogeneous dry sand. We attempted to apply theories of preferential flow in homogeneous dry soil to initially dry snow. Infiltration experiments into homogeneous dry snow and theoretical analysis were carried out to reveal the developing process of preferential flow during infiltration into a homogeneous dry snowpack and to obtain critical conditions for that process. The capillary pressure was measured just above the interface between the dry/wet snow layer by the tensiometer. Concurrently we conducted experiments with a dye-tracer in order to observe the flow patterns. The capillary pressure overshoot and the water-entry value were observed in experiments for samples of a large grain diameter (> 0.25 mm). The capillary pressure overshoot was directly linked to the formation of preferential flow. The velocity criterion and the pressure head criterion which are used to predict preferential flow for dry sand were able to predict the preferential flow for three out of our four different samples. The velocity criterion failed, however, to predict the stable case (no occurrence of preferential flow) for the experiment with the smallest grain diameter and pore size. Good agreement experimental results and both criterions were obtained from the analysis. These results showed some similarities between the developing process of preferential flow in dry sand and in dry snowpack.     

Dynamical characteristics of wave-excited channel flow

This paper is part of a study on the receptivity characteristics of the shear flow in a channel whose walls are subjected to a wave-like excitation. The small amplitude forced wavy wall motion is characterised by a wave number vectorλ ₁,λ ₂ and a frequencyω _g . The basic flow in the problem is a superposition of the Poiseuille flow and a periodic component that corresponds to the wave excitation of the wall. The aim of the study is to examine the susceptibility of this flow to transition. The problem is approached through studying the stability characteristics of the basic flow with respect to small disturbances. The theoretical framework for this purpose is Floquet theory. The solution procedure for solving the eigenvalue problem is the spectral collocation method. Preliminary results showing the influence of the amplitude and the wave number of the wall excitation on the stability boundary of the flow are presented.     

Development of constitutive equations for modelling of hot rolling

Abstract

Constitutive equations which describe the flow stress behaviour of materials during hot deformation are used to model forming processes. Since the flow stress depends on both temperature and strain rate, the Zener–Hollomon parameter which combines these factors, is frequently used to describe the shape of such curves. For materials which dynamically recover, (only) the flow stress reaches a steady state value at high strains and methodologies which enable such behaviour to be modelled have previously been presented. Beyond the onset of dynamic recrystallisation, the flow stress of materials, such as steels, reach a peak in flow stress before gradual softening. The relative position of the peak in the flow stress shifts as a function of the Zener–Hollomon parameter further complicating such analyses. The present paper describes the development and application of a methodology for modelling the flow stress of microalloyed steels: materials which exhibit dynamic recrystallisation behaviour.     

Practical mathematical representation of the flow due to a distribution of sources on a steadily advancing ship hull

A practical mathematical representation of the flow velocity due to a distribution of sources on the mean wetted hull surface and the mean waterline of a ship that steadily advances along a straight path in calm water, of large depth and lateral extent, is presented. A main feature of this flow representation is a simple analytical approximation—valid within the entire flow region—to the local flow component in the expression for the gradient of the Green function associated with the classical Kelvin–Michell linearized free-surface boundary condition. Another notable feature of the flow representation is that the singularity associated with the gradient of the Green function is removed, using a straightforward regularization technique. The flow representation only involves elementary continuous functions (algebraic, exponential and trigonometric) of real arguments. These functions can then be integrated using ordinary Gaussian quadrature rules. Thus, the flow representation is particularly simple and well suited for practical flow calculations. The specific case of a low-order panel method—in which the hull geometry, the source density, and the flow velocity are consistently represented via piecewise linear approximations within flat triangular hull panels or straight waterline segments—is considered.     

Experimental investigation of two-phase flow characteristics of HFC-134a through short-tube orifices

The two-phase flow characteristics of HFC-134a, including flow pattern, mass flow rate, pressure distribution and temperature distribution through short-tube orifices are experimentally investigated. Short tube diameters ranging between 0.605 and 1.2 mm with length-to-diameter ratios ranging between 8.3 and 33 are used in the experiments. The test runs are performed at upstream pressure ranging between 900 and 1300 kPa, downstream pressure ranging between 300 and 400 kPa, and degree of subcooling ranging between 1 and 12 °C. Two groups of short-tube orifices are used in the experiment. The first is used to visualise the flow pattern. The second is used to measure temperature and pressure distributions along the tube. The results from the present experiment show that metastable flow and choked flow phenomena exist inside the short-tube orifices over the whole range of experimental conditions. The metastable liquid flow region increases with increasing degree of subcooling and upstream pressure. The mass flow rate is directly proportional to upstream pressure and degree of subcooling. The results of pressure distribution inside the short-tube orifices indicate that accelerational pressure drop at the inlet and outlet has a significant effect on the total pressure drop across the short-tube orifice.     

Momentum transfer of ice slurry flows in tubes, modeling

In this paper we present results of the studies of ice slurry flow in horizontal tubes. The possibility of treating the rheological parameters of ice slurry as being those of Bingham fluid was confirmed. The values of parameters (mass fraction, flow velocity) corresponding to the laminar, intermediate and turbulent flow were determined which permits to optimize the flow in the systems working with this cooling agent. Critical flow velocity and mass fraction of ice values were determined thereby; they correspond to a change in character of an ice slurry flow from a laminar to turbulent motion. Experimental results were compared to the analytical results, based on the Hedström and Tomita algorithms (the laminar and turbulent flow, respectively). The comparison showed a very good agreement between these data.     

Effect of pulsations on two-layer channel flow

The effect of vertical wall vibrations on two-phase channel flow is examined. The basic flow consists of two superposed fluid layers in a channel whose walls oscillate perpendicular to themselves in a prescribed, time-periodic manner. The solution for the basic flow is presented in closed form for Stokes flow, and its stability to small periodic perturbations is assessed by means of a Floquet analysis. It is found that the pulsations have a generally destabilizing influence on the flow. They tend to worsen the Rayleigh–Taylor instability present for unstably stratified fluids; the larger the amplitude of the pulsations, the greater the range of unstable wave numbers. For stably stratified fluids, the pulsations raise the growth rate of small perturbations, but are not sufficient to destabilize the flow. In the latter part of the paper, the basic flow for arbitrary Reynolds number is computed numerically assuming a flat interface, and the motion of the interface in time is predicted. The existence of a time-periodic flow is demonstrated in which the ratio of the layer thicknesses remains constant throughout the motion.     

Stability of magnetohydrodynamic stratified shear flows

Summary A study is made of the stability of a stratified shear flow in a perfectly conducting fluid in the presence of an external magnetic field aligned with the flow. A semi-circle theorem for the present hydromagnetic case is proved. The magnetic field is found to have a stabilizing effect on the flow. The Rayleigh-Taylor instability problem in a stratified conducting fluid is discussed. Finally, a study is made of the absorption of wave energy by the mean flow in the hydromagnetic case by considering a shear flow with an anti-symmetric velocity profile given byU=tanhz. Unlike the hydrodynamic case, it is found that, in the critical layer atU=0, the transfer of the wave energy to the mean flow occurs for any value of the Richardson number. This result implies again the stabilizing effect of the magnetic field on the shear flow.     

Non-orthogonal stagnation-point flow of a micropolar fluid

This paper considers the problem of steady two-dimensional flow of a micropolar fluid impinging obliquely on a flat plate. The flow under consideration is a generalization of the classical modified Hiemenz flow for a micropolar fluid which occurs in the boundary layer near an orthogonal stagnation point. A coordinate decomposition transforms the full governing equations into a primary equation describing the modified Hiemenz flow for a micropolar fluid and an equation for the tangential flow coupled to the primary solution. The solution to the boundary-value problem is governed by two non-dimensional parameters: the material parameter K and the ratio of the microrotation to skin friction parameter n. The obtained ordinary differential equations are solved numerically for some values of the governing parameters. The primary consequence of the free stream obliqueness is the shift of the stagnation point toward the incoming flow.     

Effect of Particle Properties on Slug Flow Conveying in a Horizontal Pneumatic Pipeline

The influence of particle properties on slug flow conveying was experimentally examined by using polyethylene particles of different densities from 825 kg/m³ to 945 kg/m³ in a horizontal pipeline 5.5 m in length, inside diameter of 32 mm, for air speeds below 8 m/s. It was found that hardness affects the slug flow conveying in such a way that for soft particles lower limiting velocity as well as boundary air velocities for suspension flow and slug flow increases. Additionally, it was found that the frictional characteristics of a particle influence its flow pattern. Also, there are two types of slug flow, that is, a solitary slug flow and a consecutive slug flow. In a solitary slug flow, there is at most only one plug in the pipeline. In a consecutive slug flow, the particles are conveyed continuously as slugs. There is always at least one slug in the pipeline.     

Setup and Test of a Laser Doppler Velocimeter for Investigations of Flow Behaviour of Polymer Melts

The flow behaviour of a low-density polyethylene melt is investigated in a specifically developed flow channel by means of Laser Doppler Velocimetry (LDV). The used flow channel is a slit die with a planar contraction of 14:1. The investigation of the velocity fields was performed in the steady state of flow. The optics of the LDV system as well as the used frequency analyser proved to be reliable for measurements of velocities down to 250μm/s. By adding TiO₂ tracer particles to the pellets the signal quality as well as the signal frequency were improved. It is demonstrated that the Laser Doppler Velocimeter is suited to detect velocities of polymer melts with an error of a few per cent by comparing the measured volume flow rate to the directly determined mass flow rate. Using simple fluid mechanics the viscosity function is obtained by measuring only one velocity profile within the fully developed flow in the slit die. Over a wide range of shear rates the viscosity function obtained via LDV measurement corresponds with the viscosity function which was determined by the classical mass-flow-rate method. Both resulting viscosity functions were additionally checked by performing measurements with a capillary rheometer. The LDV setup described in this paper is a powerful experimental tool to investigate the flow behaviour of polymer melts. Its accuracy and the high spatial and temporal resolution opens a way to get more quantitative insight into the flow of polymer melts and to check the validity of model calculations. This revised version was published online in August 2006 with corrections to the Cover Date.     

Axial and Radial Pressure Drops of Dense Phase Plugs

ABSTRACT

An improved angle droplet collection efficiency model for the intermediate flow regime is presented in this paper, taking into account both inertial impaction and interception mechanisms. This model uses the equations of motion that has been derived by performing a force balance on a particle interacting with the flow field of a spherical collector. The fluid flow field around the collector is assumed to be the approximate solution as developed by Hamielec and Johnson for Reynolds numbers ranging between 10 and 80 and Tomotika and Aoi for Reynolds numbers less than 1.0.

The results of this work indicate that the collection efficiencies calculated by using potential flow conditions may have overestimated the overall collection of particulate matter. It was identified that the transition from intermediate to potential flow occurs when the Reynolds number is about 80. The interpolation scheme for the single droplet collection efficiency proposed in this work can be used from Stokes flow to potential flow conditions including intermediate flow regime.     

Effect of a moving boundary on pulsatile flow of incompressible fluid in a tube

The pulsatile flow in a pipe with a moving boundary has been studied for a viscous, incompressible fluid by solving the Navier-Stokes equations numerically. The governing equations were formulated in boundary fitted curvilinear coordinates and a finite volume discretization procedure was used to solve the problem. This analysis is based on the assumption that the flow has a simple periodic pulsation and the shape of the wall changes according to the frequency of pulsation. The presence of the moving boundary causes unsteadiness in the flow behaviour as the vibrating wall has a nonlinear interaction with the flow. A detailed analysis of the flow field is presented here for a range of frequencies (5≤α≤10) where α is the reduced frequency parameter and a Reynolds number of 100.     

Discussion on the validity of prediction tools for two-phase flow pressure drops from experimental data obtained at high saturation temperatures

In order to evaluate the validity of prediction tools for two-phase flow pressure drops for conditions of high saturation temperatures, this paper focuses on the comparison between new experimental results and theoretical results predicted with the commonly used methods. The original dataset was obtained in a horizontal 3.00 mm inner diameter during adiabatic flow with R-245fa as working fluid. The mass velocity ranges from 100 to 1500 kg m⁻² s⁻¹, the saturation temperature varies from 60 to 120 °C and the inlet vapor quality from 0 to 1. The database is composed of 249 data points covering four flow patterns: (i) intermittent flow, (ii) annular flow, (iii) dryout flow, and (iv) mist flow regimes. The dataset is compared against 23 well-known two-phase frictional pressure drop prediction methods. The effect of the saturation temperature and of the flow pattern on the ability of the methods to predict the frictional pressure drop was pointed out.     

Temperature Dependence of Resin Flow in a Resin Film Infusion (RFI) Process by Ultrasound Imaging

Ultrasonic imaging in the C-scan mode was used in conjunction with the amplitude of the reflected signal to measure the temperature dependence of resin flow rate in single layers of woven carbon fabric. The RFI samples were vacuum-bagged and scanned in a water tank at 50°C, 60°C, 70°C, and 80°C. The measured flow rates were plotted versus inverse viscosity to determine the permeability in the thin film, non-saturated system. The permeability values determined in this work were consistent with permeability values reported in the literature. Capillary flow was not observed at the temperatures and times required for pressurized flow to occur. The flow rate at 65°C was predicted from the measured flow rates, and then measured in a 10-layer laminate. The investigation demonstrates that ultrasonic imaging in the C-scan mode in conjunction with the amplitude of the reflected signal is an effective method for measuring resin flow through fabric.     

Multi-scale study of particle flow in silos

The flow characteristics of solid particles in a silo were studied experimentally and theoretically. A multi-scale study of the particles flow was performed by means of discrete element method (DEM). The dependence of flow behaviors on the particles diameter distribution and silo geometry was analyzed to establish the spatial and statistical distributions of microdynamic variables related to flow and silo structures such as velocity, porosity, coordination number, and interaction forces between particles. The results show that the distribution of particle diameter has great effects on particles flow, and the mixing of multi-sized particles is propitious to granular flow. The geometry of silos has greater effects on granular flow than particle size distribution, and inserts can improve the flow behaviors of “funnel flow” type to “mass flow”. Linear equations can be used to describe the relationship between discharge rate and orifice size by G^2/5 vs. D_o for the same distribution of particles diameter. The flow structure of particles in the silos is spatially non-uniform, which is illustrated by spatial and statistical distributions of porosity and coordination number. Both porosity and coordination number are affected by the mode of particles packed, which is affected by the geometry of silos and particle size distribution. The distribution of contact forces between particles is spatially non-uniform too. In flat-bottomed silo, there are arched stress chains in the vicinity of the orifice under the “bridging action”, which disappeared in wedge-shaped hopper silo.