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.     

Flow pattern, mass flow rate, pressure distribution, and temperature distribution of two-phase flow of HFC-134a inside short-tube orifices

New experimental data on the influence of short-tube orifice configuration, including diameter, length, length-to-diameter ratio (L/D), and orientation on the flow pattern, mass flow rate, and pressure distribution of HFC-134a inside the short-tube orifice are presented. Short-tube orifice diameters ranging between 0.605 and 1.2 mm with L/D ranging between 1.87 and 33 are used in the experiments. Three different forms of the metastable liquid flow, which are metastable liquid core flow, conical metastable liquid core flow, and full metastable liquid flow are visually observed. The short-tube orifice diameter has a significant effect on the increase in the flow rate. Conversely, the change in the orientation of the test section has no significant effect on the flow rate. The choke flow phenomenon disappears inside the short-tube orifice when L/D is less than 2.91. Based on the present data, a correlation for predicting the mass flow rate through short-tube orifices is proposed.     

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.     

Numerical simulation of gas flow in pneumatic components

The flow through pneumatic components is characterized by very complex flow phenomina. In general the flow is viscous, transonic (0≦M≦4) and turbulent. Small geometrical dimensions of pneumatic components make flow measurement difficult or sometimes impossible. Hence the accurate numerical prediction of the flow field becomes of great importance. In this paper we present the theoretical framework and the numerical capabicities of the commercial Navier-Stokes CFD code TASC flow. We solve some test problems which reflect many features of the numerical flow simulation in pneumatic components. For the test cases considered here, TASC flow was found to be an excellent tool for fast and accurate flow simulation.     

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.     

Two-phase flow regimes in round, square and rectangular tubes during condensation of refrigerant R134a

An experimental investigation of two-phase flow mechanisms during condensation of refrigerant R134a in six small diameter round (4.91 mm), square (D_h=4 mm, α=1), and rectangular (4×6 and 6×4 mm: D_h=4.8 mm, α=0.67 and 1.5; 2×4 and 4×2 mm: D_h=2.67 mm, α =0.5 and 2) was conducted. Unique experimental techniques and test sections were developed to enable the documentation of the flow mechanisms during phase change. For each tube under consideration, flow mechanisms were recorded over the entire range of qualities for five different refrigerant mass fluxes between 150 and 750 kg m⁻² s⁻¹. The flow mechanisms were categorized into four different flow regimes: intermittent flow, wavy flow, annular flow, and dispersed flow. In addition, the large amount of data enabled the delineation of several different flow patterns within each flow regime, which provides a clearer understanding of the different modes of two-phase flow. Transition lines between the respective flow patterns and regimes on these maps were established based on the experimental data. It was found that for similar hydraulic diameters, flow regime transitions are not very strongly dependent on tube shape or aspect ratio. These maps and the transition lines can be used to predict the particular flow pattern or regime that will be established for a given mass flux, quality and tube geometry.     

基于递归图的两相流流动特性分析与流型识别

基于数字化电阻层析成像(ERT)系统采集的垂直管道气液两相流实验数据,通过计算不同时刻系统采集的数据均值,生成一维时间序列并进行相空间重构,绘制递归图。对绘制的递归图进行阈值分割,并分析了两相流流动特性。计算了不同流型对应无阈值递归图的图像信息熵范围：泡状流为0.570～0.660;泡状流到弹状流过渡流型为2.300～3.200;弹状流为3.650～4.100;段塞流为4.300～4.600;段塞流到混状流过渡流型为4.650～4.950。结果表明各流型递归图图像信息熵范围分隔明显,可有效识别这5种流型。     

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.     

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.     

Review of flow condensation of CO2 as a refrigerant

Carbon dioxide (CO₂) has emerged as an excellent substitute natural refrigerant for low temperature refrigeration applications, but a better understanding of its in-tube flow condensation is needed in order to achieve its full potential. From experimental studies in the open literature we review the effects of mass flux, vapour quality and saturation pressure on CO₂ flow condensation heat transfer, frictional pressure drop and flow regime transition inside smooth, micro-fin and microchannel tubes. Successful condensation models which were developed from experiments with other refrigerants are evaluated against the CO₂ flow condensation experimental data. Comparison between the predicted and experimental data shows that the unique thermophysical properties of CO₂ at high reduced pressure conditions lead to these correlations having high prediction errors on the flow condensation heat transfer inside smooth tubes and microchannels, but have less significant effects on the flow condensation heat transfer and two-phase frictional pressure drop under high mass flux conditions inside micro-fin tubes. Recommendations for condensation and pressure drop models to apply to CO₂ flow condensation in different tubes are made. As there is inconsistency between the experimental data in smooth tubes from different sources, and the effects of microchannel and micro-fin tube geometries, on the flow regime transition and condensation heat transfer of CO₂, are unclear, a more extensive range of the experimental data in different tubes is needed for a fully understanding of in-tube CO₂ flow condensation.     

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.     

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.     

Numerical simulation of the variation of fiber orientation distribution during flow molding of Ultra High Performance Cementitious Composites (UHPCC)

In this paper, the variation of the fiber orientation distribution along the flow of fresh UHPCC was studied. In order to describe the rotational motion of a single fiber, Jeffery’s equation was adopted, in which the interaction among fibers is neglected. Two cases of flow patterns were considered: shear flow and radial flow. Starting with a three-dimensional random distribution of fibers, the fiber orientation distribution along the flow distance was simulated. These results reveal that fibers gradually become more parallel (in the case of shear flow) and perpendicular (in the case of radial flow) to the flow direction as the flow distance increases. This approach will be useful to predict flow-dependent tensile behavior considering the change of fiber orientation distribution.     

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.     

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.     

The simulation of turbulent two-phase flow after an abrupt expansion of the pipe in the presence of evaporation of droplets

The results are given of investigation of flow and heat and mass transfer of a gas-droplet flow after an abrupt expansion of the pipe using the Eulerian approach. It is demonstrated that the intensity of heat transfer significantly increases upon addition of evaporating droplets into separated flow (by a factor of more than two compared to single-phase flow at a low value of mass concentration of droplets M _L1 ≤ 0.05). The addition of dispersed phase to a turbulent gas flow leads to an insignificant increase in the length of recirculation zone. Low-inertia droplets (d ₁ ≤ 50 μm) are well entrained into circulation flow and are present in the entire cross section of the pipe. Large particles (d ₁ ≈ 100 μm) pass through the shear layer and do not enter the separated-flow region. Adequate agreement with experimental data is indicative of the adequacy of the developed model for the calculation of gas-droplet separated flow in the case of an abrupt expansion of the pipe.     

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.     

Structural changes of hot-wire CVD silicon carbide thin films induced by gas flow rates

Silicon carbide (SiC) thin films were prepared by hot-wire chemical vapor deposition in a CH₄ gas flow rate of 1 sccm, and the influence of the gas flow rates of SiH₄ and H₂ gases on the film structure and properties were investigated. In the case of a H₂ gas flow rate below 100 sccm, the SiC:H films obtained in SiH₄ gas flow rates of 3 and 4 sccm were amorphous. On the other hand, when the H₂ gas flow rate was above 150 sccm, SiH₄ gas flow rates of 4 and 3 sccm resulted in a Si-crystallite-embedded amorphous SiC:H film and a nanocrystalline cubic SiC film, respectively. It was found that gas flow rates were important parameters for controlling film structure.     

Simulations of Vortex Evolution and Phase Slip in Oscillatory Potential Flow of the Superfluid Component of 4He Through an Aperture

The evolution of semicircular quantum vortex loops in oscillating potential flow emerging from an aperture is simulated in some highly symmetrical cases. As the frequency of potential flow oscillation increases, vortex loops that are evolving so as eventually to cross all of the streamlines of potential flow are drawn back toward the aperture when the flow reverses. As a result, the escape size of the vortex loops, and hence the net energy transferred from potential flow to vortex flow in such 2π phase-slip events, decreases as the oscillation frequency increases. Above some aperture-dependent and flow-dependent threshold frequency, vortex loops are drawn back into the aperture. Simulations are performed using both radial potential flow and oblate-spheroidal potential flow.     

Prediction of two-phase pressure gradients of refrigerants in horizontal tubes

Two-phase pressure drop data were obtained for evaporation in two horizontal test sections of 10.92 and 12.00 mm diameter for five refrigerants (R-134a, R-123, R-402A, R-404A and R-502) over mass velocities from 100 to 500 kg/m² s and vapor qualities from 0.04 to 1.0. These data have then been compared against seven two-phase frictional pressure drop prediction methods. Overall, the method by Müller-Steinhagen and Heck (Müller-Steinhagen H, Heck K. A simple friction pressure drop correlation for two-phase flow in pipes. Chem. Eng. Process 1986;20:297–308) and that by Grönnerud (Grönnerud R. Investigation of liquid hold-up, flow-resistance and heat transfer in circulation type evaporators, part IV: two-phase flow resistance in boiling refrigerants. Annexe 1972-1, Bull. de l'Inst. du Froid, 1979) were found to provide the most accurate predictions while the widely quoted method of Friedel (Friedel L. Improved friction drop correlations for horizontal and vertical two-phase pipe flow. European Two-phase Flow Group Meeting, paper E2; June 1979; Ispra, Italy) gave the third best results. The data were also classified by two-phase flow pattern using the Kattan-Thome-Favrat (Kattan N, Thome JR, Favrat D. Flow boiling in horizontal tubes. Part 1: development of a diabatic two-phase flow pattern map. J. Heat Transfer 1998;120:140–7; Kattan N, Thome JR, Favrat D. Flow boiling in horizontal tubes. Part 2; new heat transfer data for five refrigerants. J Heat Transfer 1998;120:148–55; Kattan N, Thome JR, Favrat D. Flow boiling in horizontal tubes. Part 3: development of a new heat transfer model based on flow patterns. J. Heat Transfer 1998;120:156–65) flow pattern map. The best available method for annular flow was that of Müller-Steinhagen and Heck. For intermittent flow and stratified-wavy flow, the best method in both cases was that of Grönnerud. It was observed that the peak in the two-phase frictional pressure gradient at high vapor qualities coincided with the onset of dryout in the annular flow regime.