Impingement heat transfer at a circular cylinder due to a submerged slot jet of water

An experimental investigation was carried out on the heat transfer due to a submerged slot jet of water impinging on a circular cylinder in crossflow. The cylinder diameter and the slot width are of the same order of magnitude, specifically D_s = 2.0 and 3.0 mm and D_c = 2.5 and 3.0 mm. The experimental apparatus allowed variation of the slot width, the cylinder diameter, and the distance from nozxle exit to heater. Conditions of impingement from the bottom (ascending flow) were taken into consideration as well as impingement from above (descending flow). The Nusselt number was determined as a function of Reynolds and Prandtl numbers in the range 1.5 × 10³ < Re < 2.0 × 10⁴, 2.7 < Pr < 7.0, and 1.5 ≤ z/D_s ≤ 10. The experimental data were correlated with a simple equation that fits 90% of the data with a precision of 20%.     

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.     

Numerical and experimental study of turbulent impinging twin-jet flow

The two dimensional impinging circular twin-jet flow with no-cross flow is studied numerically and experimentally. The theoretical predications are carried out through numerical procedure based on finite volume method to solve the governing mass, momentum, turbulent kinetic energy and turbulent kinetic energy dissipation rate. The parameters studied were jet Reynolds number (9.5 × 10⁴  Re  22.4 × 10⁴), nozzle to plate spacing (3  h/d  12), nozzle to nozzle centerline spacing (l/d = 3, 5 and 8) and jet angle (0°  θ  20°). It is concluded that the stagnation primary point moves away in the radial main flow direction by increasing the jet angle. This shift becomes stronger by increasing the nozzle to nozzle centerline spacing (l/d). A secondary stagnation point is set up between two jets. The value of pressure at this point decreases by decreasing Reynolds number and/or increasing the jet angle.

The sub atmospheric region occurs on the impingement plate. It increases strongly by increasing Reynolds number and decreases as the jet angle and/or a nozzle to plate spacing increases. The spreading of jet decreases by increasing nozzle to plate spacing. The intensity of re-circulation zone between two jets decreases by increasing of h/d and jet angle. The increase of turbulence kinetic energy occurs within high gradient velocity.     

Permeability of periodic arrays of spheres

For periodic arrays of spheres the permeability is obtained numerically as a function of the dimensionless wave number kD in the flow direction, where D is the sphere diameter, k = 2π/λ is the wave number, and λ is the distance between the spheres in the flow direction. Our numerical results for the solids fraction of 0.45 show that for kD < 6.5 the permeability increases with increasing kD. But, it decreases for 6.5 < kD < 8.5 and reaches a local minimum at kD  8.5, and then increases again with increasing kD. Since the Fourier spectrum of the area fraction is zero for kD = 8.98, this result suggests that the area fraction plays an important role in determining the dependence of permeability on the distance between the spheres in the flow direction. For smaller solids fractions, the positions of the local maximum and minimum of permeability shift to slightly smaller kD’s.     

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.     

Three-dimensional numerical study and field synergy principle analysis of wavy fin heat exchangers with elliptic tubes

Three dimensional numerical studies were performed for laminar heat transfer and fluid flow characteristics of wavy fin heat exchangers with elliptic/circular tubes by body-fitted coordinates system. The simulation results of circular tube were compared with the experiment data, then circular and elliptic (e = b/a = 0.6) arrangements with the same minimum flow cross-sectional area were compared. A max relative heat transfer gain of up to 30% is observed in the elliptic arrangement, and corresponding friction factor only increased by about 10%. The effects of five factors on wavy fin and elliptic tube heat exchangers were examined: Reynolds number (based on the smaller ellipse axis, 500  4000), eccentricity (b/a, 0.6  1.0), fin pitch (F_p/2b, 0.05  0.4), fin thickness (F_t/2b, 0.006  0.04) and tube spanwise pitch (S₁/2b, 1.0  2.0). The results show that with the increasing of Reynolds number and fin thickness, decreasing of the eccentricity and spanwise tube pitch, the heat transfer of the finned tube bank are enhanced with some penalty in pressure drop. There is an optimum fin pitch (F_p/2b = 0.1) for heat transfer, but friction factor always decreases with increase of fin pitch. And when F_p/2b is larger than 0.25, it has little effects on heat transfer and pressure drop. The results were also analyzed from the view point of field synergy principle. It was found that the effects of the five factors on the heat transfer performance can be well described by the field synergy principle.     

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.     

Flow measurements inside a heated multiple rotating cavity with axial throughflow

This paper discusses experimental results from a multiple cavity test rig representative of a high pressure compressor internal air system. Measurements of the axial, tangential and radial velocity components are presented. These were made using a two component, laser doppler anemometry (LDA) system for a range of non-dimensional parameters representative of engine conditions (Re up to 4 × 10⁶ and Re_z up to 1.8 × 10⁵). Tests were carried out for two different sizes of annular gap between the (non-rotating) drive shaft and the disc bores.

The axial and radial velocities inside the cavities are virtually zero. The size of the annular gap between disc bore and shaft has a significant effect on the radial distribution of tangential velocity. For the narrow annular gap (d_h/b = 0.092), there is an increase of non-dimensional tangential velocity V/Ωr with radial location from V/Ωr < 1 at the lower radii to solid body rotation V/Ωr = 1 further into the cavity. For the wider annular gap (d_h/b = 0.164), there is a decrease from V/Ωr > 1 at the lower radii to solid body rotation further into the cavity. An analysis of the frequency spectrum obtained from the tangential velocity measurements is consistent with a flow structure in the r– plane consisting of pairs of contra rotating vortices.     

Pressure drop characteristics in a rotating smooth square channel with a sharp 180° bend

The results of an experimental study to investigate the local pressure drop characteristics in a square cross-sectioned smooth channel with a sharp 180° bend rotating about an axis normal to the free-stream direction are reported here. The sharp 180° turn was obtained by dividing a rectangular passage into two channels using a divider wall with a rounded tip at the location where the flow negotiates the turn. The study was carried out for three ratios of divider wall thickness to hydraulic diameter (W/D), namely, 0.24, 0.37 and 0.73 all with a rounded tip divider wall and only for a bend with a W/D ratio of 0.37, the influence of a sharp tip divider wall was studied. Experiments were conducted for a Reynolds number varying from 10 000 to 17 000 with the rotation number (ωD/V) varying from 0 to 0.38. The pressure drop distribution, normalized with the mainstream fluid dynamic pressure head, is presented for the leading, trailing and the outer surfaces. The results indicate that the local pressure drop characteristics in the bend region are significantly affected by a change in the rotation number but the influence of the Reynolds number is weak. The friction factor is less sensitive to rotation for the bend with a W/D ratio of 0.24 when compared to bends with W/D ratios of 0.37 and 0.73. Friction factor correlations are presented which fit the experimental data within 10% for the range of parameters studied.     

Local heat transfer coefficients on the circumference of a tube in a gas fluidized bed

A heated horizontal heat transfer tube was installed 14.8 cm above the distributor plate in a square fluid bed measuring 30.5 × 30.5 cm. Four different Geldart B sized particle beds were used (sand of two different distributions, an abrasive and glass beads) and the bed was fluidized with cold air. The tube was instrumented with surface thermocouples around half of the tube circumference and with differential pressure ports that can be used to infer bubble presence. Numerical execution of the transient conduction equation for the tube allowed the local time-varying heat transfer coefficient to be extracted. Data confirm the presence of the stagnant zone on top of the tube associated with low superficial velocities. Auto-correlation of thermocouple data revealed bubble frequencies and the cross-correlation of thermal and pressure events confirmed the relationship between the bubbles and the heat transfer events. In keeping with the notion of a “Packet renewal” heat transfer model, the average heat transfer coefficient was found to vary in sympathy with the root-mean square amplitude of the transient heat transfer coefficient.     

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.     

Opposed round jets issuing into a small aspect ratio channel cross flow

Round jets (diameter D) discharging into a confined cross flow (dimension 3.16D × 21.05D) are investigated experimentally. Two configurations are considered: (1) a single jet (momentum flux ratio, J = 155) and (2) two opposed jets with two different momentum flux ratios (J = 60, and 155). A two-component laser-Doppler anemometer is used to make a detailed map of the normal stresses and mean velocities in the symmetry plane of the jets. In addition, smoke-wire and laser-sheet visualization are used to study the flow.

The rate of bending of the single confined jet is found to be higher than the rate of bending of an unconfined jet with the same momentum flux ratio. In the far field, the jet centerline velocity is observed to decay more slowly than the unconfined jet, indicating poor turbulent diffusion of linear momentum. Annular shear layer vortices are visualized on the upstream edge of the jet in the near field. In the far field, the flow visualization suggests that the jet loses its integrity and fragments into independent regions that are convected by the cross flow.

In the opposed jet configuration at the high momentum flux ratio (J = 155), the jets impinge in the center of the duct, and a pair of vortices is observed upstream of the impingement region. The flow visualization implies that the impingement vortices form quasi periodically and have a finite life span. In the impingement region, the jets are observed to penetrate alternately beyond the symmetry plane of the duct. In the two-jet configuration with J = 60, the jets do not impinge on each other owing to the higher rate of bending. Instead, the flow visualization indicates that the shear layers of the jets penetrate to the central region and periodically pinch off regions of the potential-like cross-flow fluid where they meet. The pinch-off regions of cross-flow fluid are convected by the turbulent flow for large distances, yet remain essentially unmixed.     

Dynamics of interaction modes in excited annular jets

Evolution of coherent structures and their interaction dynamics are educed in the near field of an acoustically excited basic annular jet using conditional sampling technique based on a multiple triggering criterion to detect the two dominating modes of structure pattern. Acoustic excitation is applied with an aim to better organize the phase alignment of initial rolling and pairing process in the outer shear layer. Negligible modification of the time-averaged flow field results from the excitation. The educed coherent vorticities show that the two modes of evolution are due to the corresponding two modes of shedding pattern of the wake structures from the centerbody, namely the mode one wake and the mode zero wake. In both modes, the shear-layer mode jet vortex rings in the outer layer are perturbed by the shedding of wake structures in the inner region and interaction involving primary merging of three successive jet vortex rings or their partial circumferential sections is found. This results in the formation of wake-induced structures of the corresponding mode pattern, which possesses concentration of coherent vorticity and fluid circulation over a large spatial extent at 1 < x/D < 2. Secondary interactions, such as vortex tearing, are also observed.     

Experimental investigations of fluid flow and heat transfer characteristics of a slot jet impinging on a square cylinder

Experimental investigations on pressure distributions and average heat transfer on square cylinders due to slot jet impingement have been carried out for different parameters such as, slot jet-width, distance of the square cylinder from the nozzle exit, angle of inclination of the cylinder to the jet axis and Reynolds numbers. The minimum value of the pressure coefficient is obtained on the lower face at an angle of inclination of 15° for all distances of the square cylinder from the nozzle exit. At the lowest Reynolds number the maximum average heat transfer rate is obtained at a distance of eight times the jet width from the nozzle exit. An increasing trend of the heat transfer rate is observed for higher Reynolds numbers. The maximum value of the heat transfer rate is obtained between the angles of inclination of 15° and 30° of the square cylinder to the jet axis. A correlation for the average Nusselt number is proposed in terms of the relevant non-dimensional parameters.

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Experimentelle Untersuchung der Strömungs- und Wärmeübergangscharakteristik bei Schlitzdüsenanblasung eines quadratischen Zylinders

Zusammenfassung Druckverteilung und gemittelter Wärmeübergang bei Schlitzanblasung eines quadratischen Zylinders wurden experimentell für folgende Parameter untersucht: Schlitzbreite; Abstand Düsenmündung vom Zylinder; Neigungswinkel des Zylinders zur Strahlachse; Reynoldszahl. Den Minimalwert des Druckkoeffizienten erhält man für alle Abstände an der Unterseite (bei einem Neigungswinkel von 15°). Bei der niedrigsten Reynoldszahl tritt der höchste Wert des gemittelten Wärmestroms in einem Abstand Düsenmündung/Zylinder von 8 Strahlbreiten auf. Mit steigender Reynoldszahl nimmt der Wärmestrom zu. Dessen höchster Wert tritt im Bereich 15 bis 30° des Neigungswinkels zwischen Zylinder und Strahlachse auf. Eine die Meßwerte korrelierende Nusscltbeziehung als Funktion dimensionsloser Parameter wird angegeben.

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Nomenclature A surface area of the square cylinder - a width of the square cylinder - C _p pressure coefficient=(p–p _a )/ - C _pb base pressure coefficient=(p _b –p _a )/ - h _f free convection heat transfer coefficient - average heat transfer coefficient - k thermal conductivity of air - L distance of the axis of the square cylinder from the nozzle exit - l length of the square cylinder - Pr Prandtl number - p static pressure - p _a atmospheric pressure - p _b base pressure on the rear face - Nu _f free convection Nusselt number - average Nusselt number - q heat loss - q _f heat loss due to free convection - Re Reynolds number=u _j W/v _a - T _a ambient air temperature - average surface temperature - u _j average jet velocity at the nozzle exit - W nozzle width - angle of inclination of the square cylinder to the jet axis in degrees - _a kinematic viscosity of air - _a density of air     

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.     

Heat transfer to air–water annular flow in a horizontal pipe

Two-phase air–water flow and heat transfer in a 25 mm internal diameter horizontal pipe were investigated experimentally. The water superficial velocity varied from 24.2 m/s to 41.5 m/s and the air superficial velocity varied from 0.02 m/s to 0.09 m/s. The aim of the study was to determine the heat transfer coefficient and its connection to flow pattern and liquid film thickness. The flow patterns were visualized using a high speed video camera, and the film thickness was measured by the conductive tomography technique. The heat transfer coefficient was calculated from the temperature measurements using the infrared thermography method. It was found that the heat transfer coefficient at the bottom of the pipe is up to three times higher than that at the top, and becomes more uniform around the pipe for higher air flow-rates. Correlations on local and average Nusselt number were obtained and compared to results reported in the literature. The behavior of local heat transfer coefficient was analyzed and the role of film thickness and flow pattern was clarified.     

Experimental and numerical investigations on slot air jet impingement cooling of a heated cylindrical concave surface

Experimental and numerical studies have been carried out for slot air jet impingement on a heated concave surface of a partially opened-top horizontal cylinder of length L = 20 cm. The slot jet is situated at the symmetry line of the partially opened-top cylinder along the gravity vector and impinges to the bottom of the cylinder which is designated as θ = 0°. The width of the opening at the top of the horizontal cylinder is W = 3 cm which corresponds to a circumferential angle Δθ = 50.8°. The experiments are performed by a Mach–Zehnder interferometer which enables to measure the local convection heat transfer coefficient. Also, a finite volume method based on the SIMPLE algorithm and non-orthogonal grid discretization scheme is used to solve the continuity, momentum, and energy equations. The Poisson equations are solved for (x, y) to find the grid points which are distributed in a non-uniform manner with higher concentration close to the solid regions. The effects of jet Reynolds number (Re _j) in the range from 190 to 1,600 and the ratio of spacing between nozzle and cylinder surface to the jet width from H = 1.5 to H = 10.7 on the local and average Nusselt numbers are examined. It is observed that maximum Nusselt number occurs at the stagnation point at (θ = 0°) and the local heat transfer coefficient decreases on the circumferential surface of the cylinder with increase of θ as a result of thermal boundary layer thickness growth. Also results show that the local and average heat transfer coefficients are raised by increasing the jet Reynolds number and by decreasing the nozzle-to-surface spacing.     

Effect on the flow and heat transfer characteristics for sinusoidal pulsating laminar flow in a heated square cylinder

Two-dimensional numerical simulation is performed to understand the effect of flow pulsation on the flow and heat transfer from a heated square cylinder at Re = 100. Numerical calculations are carried out by using a finite volume method based on the pressure-implicit with splitting of operators algorithm in a collocated grid. The effects of flow pulsation amplitude (0.2 ≤ A ≤ 0.8) and frequency (0 ≤ f _p  ≤ 20 Hz) on the detailed kinematics of flow (streamlines, vorticity patterns), the macroscopic parameters (drag coefficient, vortex shedding frequency) and heat transfer enhancement are presented in detail. The Strouhal number of vortices shedding, drag coefficient for non-pulsating flow are compared with the previously published data, and good agreement is found. The lock-on phenomenon is observed for a square cylinder in the present flow pulsation. When the pulsating frequency is within the lock-on regime, time averaged drag coefficient and heat transfer from the square cylinder is substantially augmented, and when the pulsating frequency in about the natural vortex shedding frequency, the heat transfer is also substantially enhanced. In addition, the influence of the pulsating amplitude on the time averaged drag coefficient, heat transfer enhancement and lock-on occurrence is discussed in detail.     

Numerical study of the parametric evolution of bifurcations in the three-dimensional ring problem of N bodies

We study the dynamics of a massless particle in an annular configuration of N bodies, N − 1 of which have equal masses m and are located in equal distances on a fictitious circle and one has mass βm and is located at the center of the circle. Our interest is focused on the bifurcation points from planar to three-dimensional families of symmetric periodic orbits in the above problem. We study numerically the evolution of these bifurcation points with respect to the variation of the mass parameter β. In particular we investigate the continuous evolution of bifurcation points for values of β from 2 up to 1000. The two distinct cases of the system’s behavior at β = 2 and 1000 are examined comparatively and various conclusions are drawn regarding the overall dynamical evolution of the three-dimensional system as the relative mass of the central body grows.     

An experimental study on developing air-water two-phase flow along a large vertical pipe: effect of air injection method

The flow structure in a developing air-water two-phase flow was investigated experimentally along a large vertical pipe (inner diameter, D_h: 0.48 m, ratio of length of flow path L to D_h: about 4.2). Two air injection methods (porous sinter injection and nozzle injection) were adopted to realize an extremely different flow structure in the developing region. The flow rate condition in the test section was as follows: superficial air velocity: 0.02–0.87 m/s (at atmospheric pressure) and superficial water velocity: 0.01–0.2 0.01–0.2 m/s, which covers the range of bubbly to slug flow in a small-scale pipe (D_h about 0.05 m).

No air slugs occupying the flow path were recognized in this experiment regardless of the air injection methods even under the condition where slug flow is realized in the small-scale pipe. In the lower half of the test section, the axial distribution of sectional differential pressure and the radial distribution of local void fraction showed peculiar distributions depending on the air injection methods. However, in the upper half of the test section, the effects of the air injection methods are small in respect of the shapes of the differential pressure distribution and the phase distribution. The comparison of sectional void fraction near the top of the test section with Kataoka's correlation indicated that the distribution parameter of the drift-flux model should be modeled including the effect of D_h and the bubble size distribution is affected by the air injection methods. The bubble size distribution is considered to be affected also by L/D_h based on comparison of results with Hills' correlation.