Two-phase flow in bends

An equation is developed for use in predicting the two-phase multiplier for pressure drop in bends; the equation simplifies the use of an existing method. The method is also compared for the first time with data at high density ratios ($\text{?l/?g = 560}$).     

Detonation interaction with wedges and bends

The paper reports the results of a series of studies on the interaction of gaseous detonations with obliquely inclined surfaces. Interactions of increasing complexity are described in turn: at a planar inclined wall, two-dimensional propagation in a curved channel and finally three-dimensional interaction with a bend in a cylindrical pipe. The role of detonation structure is discussed as well as the magnitude and duration of potentially damaging overpressures. Received 15 December 2000 / Accepted 15 January 2002     

Effects of riblet bends on pipe flows

Four riblet bends were tested to investigate the effects of riblets on pipe flows including the secondary flow on the Reynolds numbers; Re _D =6×10³–4×10⁴. The pressure gradients on the smooth pipe downstream from the riblet bends were measured, and also the pressure losses of the bends only were measured. All riblet bends reduced the pressure gradient on the smooth pipe downstream from them, which means a drag reduction. Two of the riblet bends showed the maximum drag reduction of about 4 percent at Re _D = 6500; this reduction rate was significant considering the uncertainty of the present experiments. Since the pressure losses of these two riblet bends were almost identical to that of the smooth bend at Re _D = 6500, they could cause a net drag reduction of about 4 percent on the piping system including these bends at that Reynolds number. Furthermore, the velocity profiles measured by LDV indicated that the secondary flow becomes weaker downstream from the riblet bends when a drag reduction is recognized there.Nomenclature D pipe diameter - D ₀ the distance from the valley to the valley passing through the pipe center - H height of groove - P nondimensional static pressure (p/it/(U ₀ ² ):p is gauge pressure) - dP/dX nondimensional pressure gradient - Rc curvature of bend - Re _D Reynolds number based on bulk velocity and pipe diameter - s spacing of groove - U mean streamwise velocity along the horizontal diameter - U ₀ bulk velocity - V mean vertical velocity along the horizontal diameter - x streamwise direction along the pipe axis (see Fig. 1) - X nondimensionalx (=x/D) - y radial direction in the horizontal plane which is perpendicular to the plane including the bend (see Fig. 1) - yUV swirl intensity (nondimensional swirl intensity:yUV/(DU ₀ ² ))     

Prediction of nanoparticle transport and deposition in bends

Nanoparticle transport and deposition in bends with circular cross-section are solved for different Reynolds numbers and Schmidt numbers. The perturbation method is used in solving the equations. The results show that the particle transport patterns are similar and independent of the particle size and other parameters when suspended nanoparticles flow in a straight tube. At the outside edge, particle deposition is the most intensive, while deposition at the inside edge is the weakest. In the upper and lower parts of the tube, depositions are approximately the same for different Schmidt numbers. Curvatures of tube, Reynolds number, and Schmidt number have second-order, forth-order, and first-order effects on the relative deposition efficiency, respectively.     

Studies on low viscous oil-water flow through return bends

In the present work, investigations have been carried out on the hydrodynamics of kerosene-water flow through return bends connecting two horizontal conduits. Extensive experiments are performed on two bend geometry (U and rectangular) and three flow directions through the bend (up, down and horizontal flow). It is observed that bend geometry has a strong influence on the downstream phase distribution while the direction of flow through the bend does not significantly affect the same. The pressure drop has been observed to be higher in the rectangular as compared to the U bend. The loss coefficients have been estimated for each of the cases. They have been found to be independent of flow patterns for all cases. Two different pressure drop correlations have also been proposed for each bend geometry to estimate liquid-liquid pressure drop across bend.     

A note on secondary flow in bends and bend combinations

 In this paper an explanation for the formation of swirl past three-dimensional bend combinations in pipe flows is given. Supportive and comparative swirl measurements past a double bend combination and past a combination of an asymmetric diaphragm and a following angle bend are presented and discussed. Received: 21 August 1996 / Accepted: 12 February 1997     

Energy loss at bends in the pneumatic conveying of fly ash

An accurate estimation of the total pressure drop of a pipeline is important to the reliable design of a pneumatic conveying system.The present paper presents results from an investigation into the modelling of the pressure drop at a bend in the pneumatic conveying of fly ash.Seven existing bend models were used(in conjunction with solids friction models for horizontal and vertical straight pipes,and initial acceleration losses) to predict the total pipeline pressure drop in conveying fly ash(median particle diameter:30 μm;particle density:2300 kg/m~3;loose-poured bulk density:700 kg/m~3) in three test rigs(pipelines with dimensions of 69 mm inner diameter(I.D.) × 168 m length:105 mm I.D.× 168 m length;69 mm I.D.× 554 m length).A comparison of the pneumatic conveying characteristics(PCC) predicted using the seven bend models and experimental results shows that the predicted total pipeline PCC and trends depend on the choice of bend model.While some models predict trends that agree with the experimental results,other models predicted greater bend pressure drops for the dense phase of fly ash than for the dilute phase.Models of Pan,R.(1992).Improving scale-up procedures for the design of pneumatic conveying systems.Doctoral dissertation,University of Wollongong,Australia.Pan,R., Wypych,P.W.(1998).Dilute and dense phase pneumatic conveying of fly ash.In Proceedings of the sixth International Conference on Bulk Materials Storage and Transportation(pp.183-189),Wollongong,NSW,Australia and Chambers,A.J., Marcus,R.D.(1986).Pneumatic conveying calculations.In Proceedings of the second International Conference on Bulk Materials Storage and Transportation(pp.49-52).Wollongong,Australia reliably predicted the bend losses for systems conveying fly ash over a large range of air flows.     

Energy loss at bends in the pneumatic conveying of fly ash

An accurate estimation of the total pressure drop of a pipeline is important to the reliable design of a pneumatic conveying system. The present paper presents results from an investigation into the modelling of the pressure drop at a bend in the pneumatic conveying of fly ash. Seven existing bend models were used (in conjunction with solids friction models for horizontal and vertical straight pipes, and initial acceleration losses) to predict the total pipeline pressure drop in conveying fly ash (median particle diameter: 30 μm; particle density: 2300 kg/m³; loose-poured bulk density: 700 kg/m³) in three test rigs (pipelines with dimensions of 69 mm inner diameter (I.D.) × 168 m length; 105 mm I.D. × 168 m length; 69 mm I.D. × 554 m length). A comparison of the pneumatic conveying characteristics (PCC) predicted using the seven bend models and experimental results shows that the predicted total pipeline PCC and trends depend on the choice of bend model. While some models predict trends that agree with the experimental results, other models predicted greater bend pressure drops for the dense phase of fly ash than for the dilute phase. Models of Pan, R. (1992). Improving scale-up procedures for the design of pneumatic conveying systems. Doctoral dissertation, University of Wollongong, Australia, Pan, R., & Wypych, P.W. (1998). Dilute and dense phase pneumatic conveying of fly ash. In Proceedings of the sixth International Conference on Bulk Materials Storage and Transportation (pp. 183–189), Wollongong, NSW, Australia and Chambers, A.J., & Marcus, R.D. (1986). Pneumatic conveying calculations. In Proceedings of the second International Conference on Bulk Materials Storage and Transportation (pp. 49–52), Wollongong, Australia reliably predicted the bend losses for systems conveying fly ash over a large range of air flows.     

Measurement and calculation of guide vane performance in expanding bends for wind-tunnels

 The design of guide vanes for use in expanding bends was investigated both experimentally and numerically. The primary application in mind is the use of expanding corners in wind-tunnels for the purpose of constructing compact circuits with low losses. To investigate the performance of guide vanes in realistic situations expansion ratios between 1 and 53 were tested in the experiments. These were carried out in an open wind-tunnel specially built for the present purpose. The experimental results demonstrated that suitably designed guide vanes give very low losses and retained flow quality even for quite substantial expansion ratios. For wind-tunnel applications expansion ratios around 1.3 seem appropriate, Optimization of a guide vane design was done using a two-dimensional cascade code, Mises. A new vane optimized for an expansion ratio of 43 gave a two-dimensional total pressure-loss coefficient as low as 0.041 for a chord Reynolds number of 200,000. Received: 7 April 1997/Accepted: 11 August 1997     

小型水洞拐角导流片的数值设计

拐角是回流式水洞的重要组成部分,对实验段流场的品质有着重要的影响。本文针对某小型高速水洞中的第四拐角,利用RNGk-ε湍流模型,对比模拟了导流片对拐角流场的影响。针对一种等厚圆弧形导流片的长度、布置等进行了对比计算。结果表明导流片的安装对提高流场均匀性、降低湍动能和减弱二次流等具有非常大的意义,其中半径/边长比为0.2、间距/弦长为0.15~0.25的导流片效果最为明显;文中两种非等间距的导流片分布方式以及-4°和+4°攻角的情形对流场影响较小。     

Effects of upstream bends and valves on oriffice plate pressure distributions and discharge coefficients

An extensive series of tests has been carried out to determine the effect of upstream fittings (bends, valves, bend-bend and bend-valve combinations) on the discharge coefficients of orifice plates. The pressure data acquired during these tests have been studied in detail and a number of general recommendations for reducing the errors associated with using orifice plates in disturbed flow conditions are presented in this paper. It is noteworthy that other tapping combinations in place of the standard D and D/2, flange and corner combinations were less sensitive to disturbances in the flow so that their use could result in smaller errors. Of more direct practical use, as the internationally standardized tapping arrangements are unlikely to be changed, it was established that the use of a further pressure measurement would allow the change in the discharge coefficient for corner and flange taps to be estimated with reasonable accuracy for most adverse flow conditions     

On the vorticity distribution over a normal diffracted shock for small and large bends

Vorticity distributions over the diffracted shock both from Lighthill’s theory (Proc R Soc A 198:454–470, 1949) applicable for small bends and Sakurai and Takayama’s theory (Shock Waves 4:225–230, 2005) applicable for larger bends have been investigated for Mach numbers 1.80 and 1.95. Furthermore, Mach reflection effects for both theories for the same Mach numbers 1.80 and 1.95 have been investigated.     

Theoretical analyses on bed topography responses in large depth-to-width ratio river bends with constant curvatures

Bed morphology is the result of a dynamic response to a complex meandering river system. It is an important factor for the further development of river. Based on the meandering river characterized by a large depth-to-width ratio, a theoretical model is established with the coupling of Navier-Stokes (N-S), sediment transport, and bed deformation equations. The flow characteristics and bed response of river are obtained with the perturbation method. The research results show that, under the effect of two-dimensional flow disturbance, the bars and pools present the regular response. For a given sinuousness, the amplitude of the bed response can be used as a criterion to judge the bedform stability. The effects of the Reynolds number, disturbance wavenumber, sinuousness, and bed morphology gradient on the bed response development are described.     

Effect of local pipe bends on pump performance of a small air-lift system in transporting solid particles

The pump performance of a small air-lift system in transporting solid particles is investigated experimentally. Three types of riser pipe were used to examine the effect of local bends of riser pipes on the flow characteristics of a three-phase air–water–solid particles mixture. Two of them were locally S-shaped either below or above a gas injector. The other was vertically straight. Alumina particles of 3 or 5 mm diameter were used as solid particles. It is indicated that the pump performance is appreciably reduced when the pipe bend is above the gas injector. The critical condition under which solid particles are vertically lifted is discussed from a practical viewpoint. In addition, the particle motion in the region of a pipe bend is investigated by photographic observations.     

Flow regime visualization and pressure drops of HFO-1234yf,R-134a and R-410A during downward two-phase flow in vertical return bends

This paper provides a qualitative visual observation of the two-phase flow patterns for HFO-1234yf and R-134a during downward flow in a vertical 6.7 mm inner diameter glass return bend. The different flow regimes observed are: slug, intermittent and annular flows. Bubble and vapor slug dynamical behaviors in downward slug flow are reported for HFO-1234yf. In addition, to determine the perturbation lengths up- and downstream of the return bend, the total pressure drop has been measured at different pressure tap location up- and downstream of the singularity. Furthermore, 285 pressure drop data points measured for two-phase flow of HFO-1234yf, R-134a and R-410A in vertical downward flow return bends are presented. The flow behavior in the return bend, which is subjected to the complex combined actions of gravity and centrifugal force was expressed in terms of the vapor Froude number. This experimental pressure drop database, which is included in the appendix, is compared to four well-known prediction methods available in the literature.     

Numerical and experimental investigation of the gas dynamics of flat symmetric nozzles with a section of constant height and two bends of the profile in the region of the critical section

On the basis of a numerical and experimental investigation the pressure distributions are obtained along the walls of contracting and expanding flat symmetric nozzles having a section of constant, height in the region of the critical section. It is shown that a calculation in the approximation of two-dimensional flow of an ideal gas makes it possible to obtain basically reliable data. The flow is basically determined by the inviscid core of the flow, and the influence of the boundary layers is relatively small and manifested only at points of abrupt change of the pressure. The presence of a contracting part with straight walls and a section of constant height in the critical section gives rise to an appreciable disturbance of the flow at the start of the expanding part of the nozzle, but the disturbances are rapidly damped in the longitudinal direction.