Experimental investigation on turbulent flow through a circular-sectioned 180° bend

The steady, developing turbulent flow in a circular-sectioned 180° bend has been investigated. The bend had a radius of 104 mm and a curvature radius ratio of 4.0 with long, straight upstream and downstream pipes. Measurements of the longitudinal, radial and circumferential components of mean velocity, and corresponding components of the Reynolds stress were obtained with a hot wire anemometer at a Reynolds number of 6×10⁴ and at various longitudinal stations. The velocity fields of the primary and secondary flows and the Reynolds stresses were illustrated in the form of contour map or vector diagram. Moreover, the mean quantities characterizing the bend flow, i.e., the deflection of the primary flow in the cross section, the intensity of the secondary flow and the turbulence energy, were shown in a graphic form against the longitudinal distances. In the section upstream from a bend angle of about 60°, both the flows through the 180° and the 90° bend are closely similar in their behavior. In the section from the bend angle of 90°, the high-velocity regions, however, occur near the upper and lower walls as a result of strong secondary flow and the turbulence with high level emerges in the central region of the bend. Just behind the bend exit, an additional pair of vortices appears in the outer part of the cross section owing to the transverse pressure difference. In the downstream tangent, the flow returns slowly to the proper flow in a straight pipe, but it needs a longer distance for recovery than in the 90° bend. Received: 23 April 1998/Accepted: 24 April 1999     

Local Nusselt number and temperature field in turbulent flow through a heated square-sectioned U-bend

Local heat transfer coefficients and temperature distributions within the fluid for air flow around a 180° square-sectioned bend have been measured. The ratio of bend radius to hydraulic diameter of the duct is 3.35:1 and the flow entering the bend is sensibly fully developed. Measurements of air and wall temperatures span a range of Reynolds numbers from 9.9 × 10³ to 9.2 × 10⁴ with the principal emphasis given to the case of Re ? 5.6 × 10⁴. This Reynolds number and geometric configuration coincide with that of a companion LDA study carried out by Chang et al¹ which provides detailed maps of the mean and turbulent velocity fields. The data show that by 45° into the bend the heat transfer coefficients on the inner convex wall of the bend drop markedly while those on the other walls increase. By 90° the ratio of the heat transfer coefficients at the mid positions of the concave and convex walls is more than 2:1. Nevertheless this ratio is less than would be anticipated from considering two-dimensional flow on weakly curved surfaces. There is a general consistency between the velocity and the temperatyre field data in the heated fluid     

Experimental investigation on turbulent flow in a circular-sectioned 90-degree bend

 The steady, turbulent flow in a circular-sectioned 90° bend with smooth walls has been investigated experimentally. The bend had a curvature radius ratio of 4.0 with long, straight upstream and downstream pipes. The longitudinal, circumferential and radial components of mean and fluctuating velocities, and the Reynolds stresses in the pipe cross section at several longitudinal stations were obtained with the technique of rotating a probe with an inclined hot wire at a Reynolds number of 6×10⁴. The velocity fields of the primary and secondary flows, and the Reynolds stress distributions in the cross section were illustrated. Moreover, other characteristics of the bend flow, such as deviation of the primary flow and intensity of the secondary flow, were presented. Simultaneously, discussions were given on the transition of phenomena in the longitudinal direction and the structures of turbulence in the 90° bend. Received: 21 April 1997/Accepted: 14 November 1997     

Consistent Petrov–Galerkin finite element simulation of channel flows

In this paper, Navier–Stokes fluid flows in curved channels are considered. Upstream of the backward‐facing step, there exists a channel with a 90° bend and a fixed curvature of 2.5. The purpose of conducting this study was to apply a finite element code to study the effect of the distorted upstream velocity profile developing over the bend on laminar expansion flows behind the step. The size of the eddies formed downstream of the step is addressed. The present work employs primitive velocities, which stagger the pressure working variable, to assure satisfaction of the inf–sup stability condition. In quadratic elements, spatial derivatives are approximated within the consistent Petrov–Galerkin finite element framework. Use of this method aids stability in the sense that artificial damping is solely added to the direction parallel to the flow direction. Through analytical testing, in conjunction with two other benchmark tests, the integrity of applying the computer code in quadratic elements is verified. Copyright © 1999 John Wiley & Sons, Ltd.     

Upstream and downstream influence of pipe curvature on the flow through a bend

Experiments were carried out to determine the upstream and downstream influence of a 180° pipe bend on the flow through the bend. A laser Doppler anemometer was used to measure the axial velocity at various locations before and after the bend. Two bends, of radius ratios 0.08 and 0.30, were studied at a Reynolds number of about 400, corresponding to Dean numbers of 110 and 220, respectively. Results indicate that the bend influence extended to one diameter upstream for a Dean number of 220, but no upstream influence was observed for a Dean number of 110. The corresponding downstream influence of the bend was 14 and 11 diameters, respectively. These results compare well to a recent analysis on entry flow into a pipe bend.     

Prediction of developing turbulent flow in 90°‐curved ducts using linear and non‐linear low‐Re k–ε models

This paper reports the outcome of applying two different low‐Reynolds‐number eddy‐viscosity models to resolve the complex three‐dimensional motion that arises in turbulent flows in ducts with 90^° bends. For the modelling of turbulence, the Launder and Sharma low‐Re k–ε model and a recently produced variant of the cubic non‐linear low‐Re k–ε model have been employed. In this paper, developing turbulent flow through two different 90^° bends is examined: a square bend, and a rectangular bend with an aspect ratio of 6. The numerical results indicate that for the bend of square cross‐section the curvature induces a strong secondary flow, while for the rectangular cross‐section the secondary motion is confined to the corner regions. For both curved ducts, the secondary motion persists downstream of the bend and eventually slowly disappears. For the bend of square cross‐section, comparisons indicate that both turbulence models can produce reasonable predictions. For the bend of rectangular cross‐section, for which a wider range of data is available, while both turbulence models produce satisfactory predictions of the mean flow field, the non‐linear k–ε model returns superior predictions of the turbulence field and also of the pressure and friction coefficients. Copyright © 2006 John Wiley & Sons, Ltd.     

Analysis of upstream,double-row,cylindrical holes on primary and secondary effects of endwall flow and film cooling

Flow features and film cooling performance of five configurations of double-row, cylindrical holes, upstream of an E3 vane, in a linear cascade are numerically investigated. This simulation is completed using a verified turbulence model at four blowing ratios (M = 0.5, 1.0, 1.5, 2.0). The first three configurations have two rows of cylindrical holes, each row with the same compound angle (β=-45°, 0° or 45°), while the other two have two rows with opposite compound angles (β=-45°, 45° and β=45°, -45°), which are also referred to as double-jet film cooling (DJFC) holes. The primary effects on the downstream endwall and the secondary effects on the nearby airfoil of the cooled passage are analyzed and discussed in detail. Results show that at low blowing ratios the movement of the coolant is denominated by the interaction between the jets and vortices resulting in similar film coverage on both the endwall and airfoil. The effect of vortices is reduced at high blowing ratios. It is also shown that the movement of the coolant is determined by the initial velocity direction, as well as the film cooling configuration.     

Distinctive features of the transonic flow past a cone-cylinder body at large angles of the bend in the body generator at the leading corner edge

The results of an experimental investigation of the flow past cone-cylinder bodies with small angles of the bend in the body generator at the leading corner edge (θ_s ≤ 20°) and the available data on the flow past cone-cylinder and segment-cylinder bodies with large angles of the bend in the generator (θ_{s, c} ≥ 30°) are generalized. On the basis of these data, the distinctive features of the transonic flow past these bodies and, primarily, the flow restructuring downstream of the leading corner edge at θ_s ≥ 30° are established and the characteristic gasdynamic parameters are determined. Emphasis is placed on the critical stage of flow restructuring, the nature of the stationary aerodynamic hysteresis, and the effect of the Reynolds number and wave disturbances.     

In-Situ SEM J-Testing and Crack-Tip Micromechanics of Zircaloy-4 by Three-Point Bending

A three-point bend fixture has been designed, fabricated, and utilized to demonstrate the feasibility of performing in-situ J-testing at ambient and elevated temperatures inside a scanning electron microscope (SEM). Using the three-point bend test technique, in-situ SEM J-testing has been performed to measure the crack mouth opening displacement and crack extension as a function of the applied load in order to generate J-R curves for Zircaloy-4 at 25°C and 316°C. Once the J-R curve is determined, an equivalent K_J-resistance (K_J-R) curve is computed on the basis of a relationship between the J-integral (J) and the stress intensity factor (K). The J-R and K_J-R curves of Zircaloy-4 exhibit a rising R-curve behavior, while the elastic K-R curve underestimates the fracture resistance of Zircaloy-4 once substantial crack extension has occurred. For the specimen dimensions considered, the J-R curves generated by in-situ SEM J-tests are not sensitive to the specimen geometry and measure the actual fracture resistance of the material. Furthermore, the onset of crack extension is dictated by the emission of one or more slipbands from the crack tip, and a change in the crack-tip displacement field, followed by void formation along the slipband, and linkage of the voids with the main crack.     

Re-entrant corner behavior of the PTT fluid

We integrate the constitutive equation of the Phan-Thien-Tanner (PTT) fluid near a re-entrant 270° corner. The velocity field is assumed given (Newtonian). In contrast to the case of the upper convected Maxwell (UCM) fluid, we find the following features: (1) The elastic stresses near the corner are less singular than Newtonian stresses; (2) Boundary layers near the walls are much less sharp than for the UCM fluid; (3) There are no spurious stresses due to downstream instabilities.     

Buckling analysis of woven fabric under uniaxial tension in arbitrary direction

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Airfoil flow instabilities induced by background flow oscillations

 The effect of background flow oscillations on transonic airfoil (NACA 0012) flow was investigated experimentally. The oscillations were generated by means of a rotating plate placed downstream of the airfoil. Owing to oscillating chocking of the flow caused by the plate, the airfoil flow periodically accelerated and decelerated. This led to strong variations in the surface pressure and the airfoil loading. The results are presented for two angles of attack, α=4° and α=8.5°, which correspond to the attached and separated steady airfoil flows, respectively. Received: 6 June 2000 / Accepted: 18 October 2001     

Vortical patterns in turbulent flow downstream a 90° curved pipe at high Womersley numbers

The present experimental work focuses on highly pulsatile, i.e. inertia dominated, turbulent flow downstream a curved pipe and aims at investigating the vortical characteristics of such a flow. The flow parameters (Dean and Womersley number) investigated are of the same order as those met in the internal combustion engine environment. The technique employed is time-resolved stereoscopic particle image velocimetry at different cross-sections downstream the pipe bend. These measurements allow the large-scale structures that are formed to be analyzed by means of proper orthogonal decomposition. The flow field changes drastically during a pulsatile cycle, varying from a uniform flow direction across the pipe section from the inside to the outside of the bend to vortical patterns consisting of two counter-rotating cells. This study characterizes and describes pulsatile curved pipe flow at Womersley numbers much higher than previously reported in the literature. Furthermore, the oscillatory behaviour of the Dean cells for the steady flow – the so-called ‘swirl switching’ – is investigated for different downstream stations from the bend exit and it is shown that this motion does not appear in the immediate vicinity of the bend, but only further downstream.     

On flow structure, heat transfer and pressure drop in varying aspect ratio two-pass rectangular channel with ribs at 45°

To increase the thermal efficiency of gas turbines, inlet temperature of gas is increased. This results in the requirement of cooling of gas turbine blades and vanes. Internal cooling of gas turbine blades and vanes is one of several options. Two-pass channels are provided with ribs to enhance heat transfer at the expense of an increased pressure drop. The space in the blade is limited and requires channels with small aspect ratios. Numerical simulations have been performed to investigate heat transfer, flow field and pressure loss in a two-pass channel equipped with 45° ribs with aspect ratio (W_in/H) equal to 1:3 in the inlet pass and 1:1 in the outlet pass with both connected together with a 180° bend. The results are compared with a higher aspect ratio channel (W_in/H = 1:2, inlet pass). In the ribbed channel, a decrease in pressure drop was observed with a decrease in the aspect ratio of the channel. The smaller aspect ratio channel not only allows using more cooling channels in the blade, but also results in more heat transfer enhancement. The divider-to-tip wall distance (W_el) has influence on the pressure drop, as well as on the heat transfer enhancement at the bend and outlet pass. Heat transfer decreases with decrease in aspect ratio of the inlet pass of the two-pass channel. With increase in divider-to-tip wall distance, heat transfer tries to attain a constant value.     

Turbulent flow past a transverse cavity with inclined side walls. 1. Flow structure

The process of vortex formation in a cavity with inclined walls, which has a moderate aspect ratio, is experimentally studied, and the distribution of pressure coefficients is measured. The angle of inclination of the side walls ϕ is varied from 30 to 90°. It is found that the flow in the cavity becomes unstable in the range of inclination angles ϕ = 60–70°. Flow reconstruction occurs, which substantially alters the surface-temperature and static-pressure distributions. Large changes in these characteristics and their nonuniform distributions for these angles are observed across the cavity on its frontal wall and on the bottom. For small angles (ϕ = 30 and 45°), the pressure on the rear wall drastically increases, which leads to a small increase in pressure averaged over the entire cavity surface. __________ Translated from PrikladnayaMekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 68–76, September–October, 2006.     

OPERATOR–SPLITTING COMPUTATION OF TURBULENT FLOW IN AN AXISYMMETRIC 180° NARROWING BEND USING SEVERAL k—ϵ MODELS AND WALL FUNCTIONS

This paper describes a finite element implementation of an operator-splitting algorithm for solving transient/steady turbulent flows and presents solutions for the turbulent flow in an axisymmetric 180° narrowing bend, a benchmark problem dealt with at the 1994 WUA-CFD annual meeting. Three k–ϵ based models are used: the standard linear k–ϵ model, a non-linear k–ϵ model and an RNG k–ϵ model. Flow separation after the bend, as observed in the experiment, is predicted by the RNG model and by both the linear and non-linear k–ϵε models with van Driest mixing length wall functions. Good agreement with experimental data of pressure distribution on bending walls is obtained by the present numerical simulation. Results show that there is very little difference between the linear and non-linear k–ϵε models in terms of predicted velocity fields and that the non-linearities mainly affect the distribution of turbulent normal stress and pressure, in analogy to the effect of second-order viscoelastic fluid models on laminar flow. Both the linear and non-linear k–ϵε models fail to predict any flow separation if logarithmic wall functions are used.     

NUMERICAL MODELLING OF THREE-DIMENSIONAL FLY-ASH FLOW IN POWER UTILITY BOILERS

A two-fluid Eulerian model in combination with a particle–wall collision model and generalized Eulerian boundary conditions for the particulate phase is employed to predict complex three- dimensional fly-ash flows which often cause severe erosion to boiler tubes located in power utility boilers. Mean momentum and mass conservation equations are solved for each phase using a finite volume scheme with two-way coupling and a modified renormalization group (RNG)-based k –ϵ turbulence model. Comparison of predicted particle concentration with measured data is made and excellent agreement is obtained. The detailed character of the particulate velocity field and concentration just downstream of the 180° bend shows a marked dependence on the Stokes number not previously reported. © 1997 by John Wiley & Sons, Ltd.     

An upstream flux‐splitting finite‐volume scheme for 2D shallow water equations

An upstream flux‐splitting finite‐volume (UFF) scheme is proposed for the solutions of the 2D shallow water equations. In the framework of the finite‐volume method, the artificially upstream flux vector splitting method is employed to establish the numerical flux function for the local Riemann problem. Based on this algorithm, an UFF scheme without Jacobian matrix operation is developed. The proposed scheme satisfying entropy condition is extended to be second‐order‐accurate using the MUSCL approach. The proposed UFF scheme and its second‐order extension are verified through the simulations of four shallow water problems, including the 1D idealized dam breaking, the oblique hydraulic jump, the circular dam breaking, and the dam‐break experiment with 45° bend channel. Meanwhile, the numerical performance of the UFF scheme is compared with those of three well‐known upwind schemes, namely the Osher, Roe, and HLL schemes. It is demonstrated that the proposed scheme performs remarkably well for shallow water flows. The simulated results also show that the UFF scheme has superior overall numerical performances among the schemes tested. Copyright © 2005 John Wiley & Sons, Ltd.     

Advection upwinding splitting method to solve a compressible two‐fluid model

In this study, the advection upwinding splitting method (AUSM) is modified for the resolution of two‐phase mixtures with interfaces. The compressible two‐fluid model proposed by Saurel and Abgrall is chosen as the model equations. Dense and dilute phases are described in terms of the volume fraction and equations of state to represent multi‐phase mixtures. Test cases involving an air–water shock tube, water faucet, and dilute particulate turbulent flows through a 90° bend are used to verify the current work. It is shown that the AUSM based on flux differences (AUSMD) contains the mechanism to correctly capture the contact discontinuity and interfaces between phases. In addition, a successful application to dilute particulate turbulence flows by the AUSMD is demonstrated. Copyright © 2001 John Wiley & Sons, Ltd.     

Convective heat transfer in a square channel with angled ribs on two opposite walls

Detailed quantitative maps of the heat transfer distribution in a square channel with angled rib turbulators are measured by means of infrared (IR) thermography associated with the heated-thin-foil technique. Air flows in the channel where square ribs are mounted on two opposite walls at an angle of either 30° or 45° with respect to the duct axis. Two rib pitches, two different rib arrangements and two heating conditions are investigated. Results are presented in terms of local and averaged Nusselt numbers, which are normalised with the classical Dittus and Boelter correlation, for three different Reynolds numbers.