Fluid flow and heat transfer around circular cylinder – flat and curved plates combinations

Experimental studies were carried out to investigate the fluid flow and heat transfer around a heated circular cylinder which was placed at various distances of a wall boundary with different geometries (flat or curved plate) with subcritical Reynolds number ranging from 3.5×10³ to 10⁴. The effects of plate geometry (aspect ratio: W|H=1.0,1.5 and 2.0, and rim angle, φ=0°,60°,90°, and 120°) and gap ratio, (G|D=0.0,0.86,2.0,7.0,10.0) on the fluid flow and heat transfer characteristics (static pressure around cylinder surface, wake width, base pressure, pressure drag coefficients, velocity distribution, and both local and mean Nusselt numbers) were presented. Also flow visualization was carried out to illustrate the flow patterns around the cylinder at various gap ratios (G|D). It was found that the heat transfer and fluid flow characteristics are dependent on the plate geometry at all tested gap ratios, except for G|D=7.0 and 10.0, they are independent of the plate geometry.     

Wall pressure and shear stress measurements beneath an impinging jet

This paper presents comprehensive measurements of wall pressure and surface shear stress beneath a plane, two-dimensional, turbulent jet impinging normally onto a flat surface. The results cover a wider range of Reynolds number and ratio of impingement height (H) to nozzle gap (D) than do previous studies. The pressure distributions are nearly Gaussian, independent of Reynolds number, and closely balance the momentum flux from the jet nozzle as H/D varies. Particular attention was paid to probe size in measuring the wall shear stress because this has a significant effect on the results. A range of Preston tubes and Stanton probes were tested from which it was found that a 0.05-mm-high Stanton probe—the smallest that we could make—appeared to give accurate results. As expected, the shape of the wall shear stress distributions depended both on H/D and on Reynolds number. Furthermore, the relation between wall pressure and shear stress from Hiemenz's theoretical solution for stagnation flow is not in agreement with the results. It is postulated that the discrepancy is due to the relatively high free-stream turbulence level in the jet. Future papers will document the mean flow field and turbulence and the time dependence of the surface pressure.     

Pressure drop and heat transfer comparison for both microfin tube and twisted-tape inserts in laminar flow

Experiments were carried out to compare pressure drop and heat transfer coefficients for a plain, microfin, and twisted-tape insert-tubes. The twisted-tape experiments include three different twist ratios each with two different widths. The data were taken at Reynolds numbers well in the laminar region. The heat transfer data were obtained in a single shell-and-tube heat exchanger where steam is used as a heat source to obtain a uniform wall temperature and the working fluid in the tube is oil. The twist ratio and the width of the tape seem to have a large effect on the performance of the twisted-tape insert. The results demonstrate that as the twist ratio decreases, the twisted-tape will give better heat transfer enhancement. The loose-fit (W=10.8 mm) is recommended to be used in the design of heat exchanger where low twist ratios (Y=5.4, and Y=3.6) and high pressure drop situations are expected since it is easier to install and remove for cleaning purposes. Other than these situations, the tight-fit tape gives a better performance over the loose-fit tape. For the microfin tube tested in this paper, the data shows a small increase in both heat transfer and pressure drop. This type of microfin tube is not recommended to be used in laminar flow conditions.     

Laser-Doppler measurements of laminar and turbulent flow in a pipe bend

Laser-Doppler measurements are reported for laminar and turbulent flow through a 90° bend of circular cross-section with mean radius of curvature equal to 2.8 times the diameter. The measurements were made in cross-stream planes 0.58 diameters upstream of the bend inlet plane, in 30, 60 and 75° planes in the bend and in planes one and six diameters downstream of the exit plane. Three sets of data were obtained: for laminar flow at Reynolds numbers of 500 and 1093 and for turbulent flow at the maximum obtainable Reynolds number of 43 000. The results show the development of strong pressure-driven secondary flows in the form of a pair of counter-rotating vortices in the streamwise direction. The strength and character of the secondary flows were found to depend on the thickness and nature of the inlet boundary layers, inlet conditions which could not be varied independently of Reynolds number. The quantitative anemometer measurements are supported by flow visualization studies. Refractive index matching at the fluid-wall interface was not used; the measurements consist, therefore, of streamwise components of mean and fluctuating velocities only, supplemented by wall pressure measurements for the turbulent flow. The displacement of the laser measurement volume due to refraction is allowed for in simple geometrical calculations. The results are intenden for use as benchmark data for calibrating flow calculation methods.     

Heat/mass transfer and pressure drop in a triangular-rib-roughened rectangular channel

In this paper, the heat/mass transfer analogy was used to investigate the heat transfer and pressure drop in a square channel with triangular ribs on its two opposite walls. Reynolds number varied from 1 × 10⁴ to 7 × 10⁴; the dimensionless heights of the triangular ribs H/W were 0.04, 0.07, and 0.1; and their dimensionless pitches S/W were 0.45, 0.63, 1.0, 1.37, 1.55, and 2.1. Experimental results showed that the heat transfer coefficients of the wall with triangular rib were about 1 to 2.3 times larger than those of a smooth-channel wall, and the pressure drops along this roughened channel were about 1 to 10 times larger than those for a smooth channel. Correlations of heat transfer and pressure drop were obtained, which are useful for practical designs.     

Enhancement of heat transfer in compact heat exchanger by different type of rib with holographic interferometry

An experimental study was carried out to investigate enhancement of heat transfer in compact heat exchanger by keeping pressure drop constant in a given range. Two different test matrices, cylindrical and triangular, used to find the optimum ribs were compared with a smooth channel. The investigation was performed with both laminar and turbulent forced flow for Reynolds numbers from 250 to 7000. The geometric parameters, in order to satisfied manufacturer demands, were fixed at p/e=6.67 and the wall temperature was held constant at 50°C. The technique of holographic interferometry was used to determine the temperature distribution in the test duct. Velocity distribution was measured using laser doppler anemometer techniques. For comparison the technique of global measurement was also used. The results revealed that cylindrical ribs are optimum heat transfer for conversion of pressure drop. An 8% experimental error was found in global measurement compared to holographic interferometry.     

Experimental investigation of heat transfer and pressure drop characteristics of flow through spirally fluted tubes

Spirally fluted tubes are used extensively in the design of tubular heat exchangers. In previous investigations, results for tubes with flute depths e/D_vi < 0.2 were reported, with most correlations applicable for Re ≥ 5000. This paper presents the results of an experimental investigation of the heat transfer and pressure drop characteristics of spirally fluted tubes with the following tube and flow parameter ranges: flute depth e/D_vi = 0.1−0.4, flute pitch p/D_vi = 0.4−7.3, helix angle θ/90° = 0.3−0.65, Re = 500−80,000, and Pr = 2−7. The heat transfer coefficients inside the fluted tube were obtained from measured values of the overall heat transfer coefficient using a nonlinear regression scheme. The friction factor data obtained consisted of 507 data points. The proposed correlation for the friction factor predicts 96% of the database within ±20%. The heat transfer correlation for the range 500 ≤ Re ≤ 5000 predicts 76% of the database (178 data points) within ±20%, and the correlation for the higher Re range predicts 97% of the 342 data points within ±20%. Comparison of heat transfer and friction data show that these tubes are most effective in the laminar and transition flow regimes. The present results show that the increase of flute depth in the range considered does not improve heat transfer.     

Experimental study of turbulent round jet flow impinging on a square cylinder laid on a flat plate

A turbulent axisymmetric air jet impinging on a square cylinder mounted on a flat plate has been studied experimentally. Turbulence statistics and flow’s topology were investigated. When the surface was heated through uniform heat flux, local heat transfer coefficient was measured. The jet from a long round pipe, 75 pipe diameters (D) in length, at Reynolds number of 23,000, impinged vertically on the square cylinder (3D × 3D × 43D). Measurements were performed using particle image velocimetry, flow visualization using fluorescent dye and infrared thermography. The flow’s topology demonstrated a three-dimensional recirculation after separating from the square cylinder and a presence of foci between the bottom corner and the recirculation’s detachment line. The distribution of heat transfer coefficient was explained by the influence of these flow’s structures and the advection of kinetic energy. On the impingement wall of the square cylinder, a secondary peak in heat transfer coefficient was observed. Its origin can be attributed to very pronounced shear production coupled with the external turbulence coming from the free jet.     

An experimental investigation of heat transfer characteristics for turbulent flow over staggered ribs in a square duct

An experimental study of developing and fully developed turbulent air flow in a square duct with two opposite rib-roughened walls in which the ribs are attached in a staggered fashion was conducted to determine the heat transfer characteristics. The rib height-to-hydraulic diameter ratio (e/D_H) was 0.19, the rib pitch-to-height ratio (p/e) was 5.31. The streamwise temperature distribution was measured, and a law of the wall for the thermal boundary layer at each free-stream turbulence level was obtained. The effects of free-stream turbulence intensity with variations of 4–11% on heat transfer coefficients were also examined. Finally, the relationship between Nusselt number and Reynolds number was correlated. The results might be used in the design of turbine blade cooling channels.     

The influence of tube bundle geometry on cross-flow boiling heat transfer and pressure drop

An experimental investigation was performed to compare the boiling heat transfer coefficients and two-phase pressure drops from a square inline and a staggered tube bundle having the same tube pitch-to-diameter ratio (P/D = 1.30) and from two square inline tube bundles having different pitch-to-diameter ratios (P/D = 1.30 and 1.70). Except at the highest heat fluxes the heat transfer coefficients generally were higher in the staggered tube bundle than in the inline tube bundle and higher in the larger P/D tube bundle than in the smaller. As the heat flux increased, the differences decreased. The differences were attributed to the tradeoff between nucleation and convection. The staggered tube bundle had higher pressure drops than the inline bundle except at low mass velocities; the larger pressure drop in the staggered bundle was attributed to the combination of a larger void fraction and a larger friction multiplier, with the frictional component dominating at higher mass velocities. Comparing the inline tube bundle pressure drops, it was concluded that the larger P/D bundle had a larger void fraction than the smaller P/D tube bundle; no conclusions could be drawn regarding the relative magnitude of the two-phase fraction multiplier.     

Friction characteristics of compressible gas flows in microtubes

The characteristics of a gaseous flow of nitrogen in commercial stainless steel microtubes for gas chromatography having a nominal inner diameter of 762, 508, 254 and 127 μm are experimentally investigated. The friction factor is calculated as a function of the Reynolds number and plotted in a Moody chart. A comparison among three different methods to calculate the friction factor is made in order to evidence limitations and advantages of each method. It was observed that in the laminar regime the Poiseuille law correctly predicts the value of the pressure drop. It has been evidenced that in order to make accurate experiments on the frictional characteristics of commercial microtubes the value of the inner diameter given by the manufacturer has to be always verified. The experimental data presented in this work remark how in microtubes the compressibility effects related to the axial variation of the gas density tend to become important at large Reynolds numbers and small diameters even if the average Mach number is low. The effects due to the gas acceleration on the laminar-to-turbulent transition in microtubes are investigated by evidencing the role of the L/D (length to diameter) ratio on the transition to turbulence. No early transition to turbulence has been evidenced in the tests, instead it takes place at Reynolds numbers ranging between 1800 and 2900.     

Vortex shedding and surface pressures on a square cylinder at incidence to a uniform air stream

This article describes results of experiments on vortex-shedding frequencies and surface pressures of a square cylinder at non-zero angle of incidence. The range of Reynolds numbers was 2000–21 000, but the lower range was emphasized. For Reynolds numbers greater than 5300, the Strouhal number shows a similar trend with changing angle of incidence; that is, a rapid rise in Strouhal number occurs at an angle of around 13°. The occurrence of such a jump in Strouhal number was found to be associated with onset of the flow reattachment, bringing in a strong pressure recovery on the lower side face of the cylinder. For lower Reynolds numbers Re=2000–3300, the maximum Strouhal number occurs at a relatively higher angle of 17°. Around this angle, the pressure measurements exhibit a rather weak pressure recovery, suggesting a less firm shear-layer reattachment to the side face of the cylinder. The nature of the reattaching flow was further examined by spectral analysis of the fluctuating pressure coefficients measured on the lower side face of the cylinder.     

Detailed measurement of heat/mass transfer and pressure drop in a rotating two-pass duct with transverse ribs

The present study investigates the convective heat/mass transfer and pressure drop characteristics in a rotating two-pass duct with and without transverse ribs. The Reynolds number based on the hydraulic diameter is kept constant at 10,000 and the rotation number is varied from 0.0 to 0.2. When rib turbulators are installed, heat/mass transfer and friction loss are respectively augmented 2.5 times and 5.8 times higher than those of the smooth duct since the main flow is turbulated by reattaching and separating on the vicinity of the duct surfaces. Differences of heat/mass transfer and pressure coefficient between leading and trailing surfaces result from the rotation of duct, so that Sherwood number ratios and pressure coefficients are high on the trailing surface in the first-pass and on the leading surface in the second-pass. In the turning region, a pair of Dean vortices shown in the stationary case transform into one large asymmetric vortex cell, and subsequently heat/mass transfer and pressure drop characteristics also change. As the rotation number increases, the discrepancies of the heat/mass transfer and the pressure coefficient enlarge between the leading and trailing surfaces.     

Experimental investigation of various turbulator inserts in gas-heated channels

This experimental research was focused on the investigation of the heat transfer augmentation by various turbulator inserts in gas-heated channels. The work was conducted directly in a convective part of a two fire-tube boiler. The flue ducts were positioned vertically and horizontally for various design applications. Twisted-tape insert (with the twist ratio y=4.12), the straight-tape insert, and the combined turbulator insert (the internal twisted tape with the twist ratio of 180° y=2.16 and an external tape, which spirally winded on an internal tape, with longitudinal pitch H_360°=110 mm and the relative height of a tape (rib) e/D₀=0.098;0.2) were investigated. The working fluids were the combustion products of light oil fuel and wood pellets. In addition, the experiments were conducted in the two fire-tube boiler without any inserts. Despite of relatively large data scattering obtained in these experiments some qualitative and quantitative conclusions were drawn.     

Numerical analysis of turbulent flow separation in a rectangular duct with a sharp 180‐degree turn by algebraic Reynolds stress model

Turbulent flow in a rectangular duct with a sharp 180‐degree turn is difficult to predict numerically because the flow behavior is influenced by several types of forces, including centrifugal force, pressure‐driven force, and shear stress generated by anisotropic turbulence. In particular, this type of flow is characterized by a large‐scale separated flow, and it is difficult to predict the reattachment point of a separated flow. Numerical analysis has been performed for a turbulent flow in a rectangular duct with a sharp 180‐degree turn using the algebraic Reynolds stress model. A boundary‐fitted coordinate system is introduced as a method for coordinate transformation to set the boundary conditions next to complicated shapes. The calculated results are compared with the experimental data, as measured by a laser‐Doppler anemometer, in order to examine the validity of the proposed numerical method and turbulent model. In addition, the possibility of improving the wall function method in the separated flow region is examined by replacing the log‐law velocity profile for a smooth wall with that for a rough wall. The analysis results indicated that the proposed algebraic Reynolds stress model can be used to reasonably predict the turbulent flow in a rectangular duct with a sharp 180‐degree turn. In particular, the calculated reattachment point of a separated flow, which is difficult to predict in a turbulent flow, agrees well with the experimental results. In addition, the calculation results suggest that the wall function method using the log‐law velocity profile for a rough wall over a separated flow region has some potential for improving the prediction accuracy. Copyright © 2007 John Wiley & Sons, Ltd.     

Modelling the flow of power law fluids in a packed bed using a volume-averaged equation of motion

The development of a theoretical model for the prediction of velocity and pressure drop for the flow of a viscous power law fluid through a bed packed with uniform spherical particles is presented. The model is developed by volume averaging the equation of motion. A porous microstructure model based on a cell model is used. Numerical solution of the resulting equation is effected using a penalty Galerkin finite element method. Experimental pressure drop values for dilute solutions of carboxymethylcellulose flowing in narrow tubes packed with uniformly sized spherical particles are compared to theoretical predictions over a range of operating conditions. Overall agreement between experimental and theoretical values is within 15%. The extra pressure drop due to the presence of the wall is incorporated directly into the model through the application of the no-slip boundary condition at the container wall. The extra pressure drop reaches a maximum of about 10% of the bed pressure drop without wall effect. The wall effect increases as the ratio of tube diameter to particle diameter decreases, as the Reynolds number decreases and as the power law index increases.     

A Semi-empirical Correlation for Pressure Drop in Packed Beds of Spherical Particles

The effect of a confining wall on the pressure drop of fluid flow through packed beds of spherical particles with small bed-to-particle diameter ratios was investigated to develop an improved pressure drop correlation. The dependency of pressure loss on both wall friction and increased porosity near the wall was accounted for by using a theoretical approach. A semi-empirical model was created based upon the capillary-orifice model, which included a wall correction factor for the inertial pressure loss. In this model, packed beds were treated as a bundle of capillary tubes whose orifice diameter in the core region was different from that of the wall region. Using this model, a new pressure drop correlation was obtained, based on the Ergun equation and applicable for a wide range of Reynolds numbers (10⁻²–10³). The proposed correlation was compared with previous correlations, as well as with experimental data. This correlation showed close agreement with the experimental data for both low- and high-Reynolds number regimes and for a wide range of bed-to-particle diameter ratios. The ratio of the pressure drop in finite packing to that in homogeneous packing was then calculated. This ratio clearly shows how the wall effect depends on the Reynolds number and the bed-to-particle diameter ratio.     

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     

Laser-sheet flow visualization of the confined wake behind a ring

The flow over a ring model situated axisymmetrically in a circular pipe has been studied by the laser-sheet flow visualization technique. Over 25 rings of different sizes are investigated. The flow characteristics are observed and summarized into six regimes, in terms of the two geometrical parameters G/W and . Here, W is the width of the ring, is the mean diameter of the ring, and G is the gap width between the pipe wall and the outer edge of the ring. It is interesting to point out that vortex-shedding structures produced by a ring model can persist over a considerable distance downstream in three of the six regimes which correspond to different physical processes of shedding.     

Unsteady laminar flow developing in a curved duct

The flow developing in a tightly curved U-bend of square cross section has been investigated experimentally and via numerical simulation. Both long-time averages and time histories of the longitudinal (streamwise) component of velocity were measured using a laser-Doppler velocimeter. The Reynolds number investigated was Re = 1400. The data were obtained at different bend angles, θ, and were confined to the symmetry plane of the bend. At Re = 1400, the flow entering the bend is steady, but by θ = 90° it develops an oscillatory component of motion along the outer-radius wall. Autocorrelations and energy spectra derived from the time histories yield a base frequency of approximately 0.1 Hz for these oscillations. Flow-visualization studies showed that the proximity of the outer-radius wall served to damp the amplitude of the spanwise oscillations.

Numerical simulations of the flow were performed using both steady and unsteady version of the finite-difference elliptic calculation procedure of Humphrey et al. (1977). Although the unsteadiness observed experimentally does not arise spontaneously in the calculations, numerical experiments involving the imposition of a periodic time-dependent perturbation at the inlet plane suggest that the U-bend acts upon the incoming flow so as to damp the amplitude of the imposed oscillation while altering its frequency.

The oscillations observed experimentally, and numerically as a result of the periodic perturbation, have been linked to the formation of Goertler-type vortices of the outer-radius wall in the developing flow. The vortices, which develop as a result of the centrifugal instability of the flow on the outer-radius wall, undergo a further transition to an unsteady regime at higher flow rates.