Equilateral Triangular Ducts Research Articles

Numerical investigation of flow through a triangular duct: The coexistence of laminar and turbulent flow

Experimental studies of turbulent flow through a triangular duct with small apex angle of 11.5° performed by Eckert and Irvine (1956) show flow laminarisation in the corner region of the duct. This effect is re-investigated using direct numerical simulation (DNS). In order to analyze the impact of duct corners on the flow behavior, results for the friction factor and the mean velocity profiles arising from different non-circular duct geometries, namely a square duct, an equilateral triangular duct and isosceles triangular ducts with an apex angle of 11.5° and 4° are compared with the results for circular pipe flow. Within the cross-sections of the ducts with the small apex angles, regions of essentially laminar and turbulent properties are found to exist simultaneously. From analysis of the turbulent quantities performed exemplary for the 11.5°-triangle we gain further insights into the mechanisms responsible for flow laminarization which are supported by analytical considerations for statistically axisymmetric turbulence.

Benchmark Solutions for Slip Flow and H1 Heat Transfer in Rectangular and Equilateral Triangular Ducts

Accurate analytic solutions for the fully developed slip flow and H1 heat transfer in rectangular and equilateral triangular ducts are presented. Both velocity slip and temperature jump have significant influences on the Poiseuille and Nusselt numbers. These exact solutions serve as benchmark cases for other methods, whether analytic, approximate, or numerical.

The study of laminar convective heat transfer of CuO/water nanofluid through an equilateral triangular duct at constant wall heat flux

AbstractThe present paper focuses on the heat transfer of an equilateral triangular duct by employing the CuO/water nanofluid in a laminar flow and under constant heat flux condition. The triangular ducts were used due to their ease of creation and high compaction. They have less pressure drop when compared to the circular and non‐circular ducts and their other attributes are very useful in industrial applications. These reasons cause their heat transfer characteristics to be very important. In this paper, to improve the heat transfer of an equilateral triangular duct, a CuO/water nanofluid was employed. The nanofluid was conducted through an equilateral triangular duct with a constant wall heat flux. Results show that the experimental heat transfer coefficient of the CuO/water nanofluid is more than that of distilled water. Also, the experimental heat transfer coefficient of a CuO/water nanofluid is greater than the theoretical one. The heat transfer enhancement of the equilateral triangular duct increases with the nanofluid volume concentration as well as the Peclet number. So a 41% enhancement in the convective heat transfer coefficient for a 0.8% CuO/water nanofluid can be seen when compared to pure water. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21011

Flow past confined delta-wing type vortex generators

This paper presents the results of an experimental study of flow structure in horizontal equilateral triangular ducts having double rows of half delta-wing type vortex generators mounted on the duct’s slant surfaces. The test ducts have the same axial length and hydraulic diameter of 4 m and 58.3 mm, respectively. Each duct consists of double rows of half delta wing pairs arranged either in common flow-up or common flow-down configurations. Flow field measurements were performed using a Particle Image Velocimetry Technique for hydraulic diameter based Reynolds numbers in the range of 1000–8000. The secondary flow field differences generated by two different vortex generator configurations were examined in detail. The secondary flow is found stronger behind the second vortex generator pair than behind the first pair but becomes weaker far from the second pair in the case of Duct1. However, the strength of the secondary flow is found nearly the same behind the first and the second vortex generator pair as well as far from the second vortex generator pair in the case of Duct2. Both ducts are able to create a counter-rotating and a second set of twin foci. Duct2 is able to create the second set of twin foci in an earlier streamwise location than Duct1, as these foci are well-known to their heat transfer augmentation. A larger vortex formation area and a greater induced vorticity field between vortex pairs are observed for Duct2 compared with Duct1. As the induced flow field between the vortex pairs increases the heat transfer, and as the flow field between the vortex cores is found larger in the case of Duct2, therefore, it is expected to obtain better heat transfer characteristics for Duct2 compared with Duct1.

Laminar fully developed flow through square and equilateral triangular ducts with rounded corners subjected to H1 and H2 boundary conditions

The present paper deals with the evaluation of pressure drop and heat transfer characteristics of laminar fully-developed flow through ducts of square and equilateral triangular cross sections with rounded corners, for both H1 and H2 boundary conditions. The dimensionless radius of curvature ( R c ) of both type of ducts is varied from zero to the maximum possible value (1 for square duct and 1 / 3 for triangular duct). The solutions for velocity and temperature are considered in the form of a harmonic series. The constants of the series are evaluated by ‘least square technique’. From the velocity and temperature solutions, fRe and Nu are calculated. The results show that for square duct, at lower values of R c , both fRe and Nu increase rapidly with R c and for higher values of R c , both fRe and Nu asymptotically assume their values corresponding to that for the circular duct. For triangular ducts, Nu shows a similar behaviour. fRe, on the other hand, shows a similar behaviour only for lower values of R c . At moderate R c , fRe attains its maximum value around R c ≈ 0.35 and with further increase in R c , fRe drops slightly and finally tends to its value corresponding that of a circular ducts in an asymptotic manner. For both type of ducts, Nu for H1 boundary condition is always higher than that for H2 boundary condition. It is also observed that the straight portion of the duct is always more effective than the circular duct, where as, the effectiveness of the rounded portion, which is always less than the circular duct, increases with the increase in R c . Correlations, in two different forms, are obtained for all the cases and they show excellent agreement with the computed data.

Experimental Investigations on Natural Convection Heat Transfer Around Horizontal Triangular Ducts

Experimental investigations have been reported on steady-state natural convection from the outer surfaces of horizontal ducts with triangular cross sections in air. Two different horizontal positions are considered; in the first position, the vertex of the triangle faces up, while in the other position, the vertex faces down. Five equilateral triangular cross-section ducts have been used with cross-section side length of 0.044, 0.06, 0.08, 0.10, and 0.13 m. The ducts are heated using internal constant-heat-flux heating elements. The temperatures along the surface and peripheral directions of the duct wall are measured. Longitudinal (perimeter-averaged) heat transfer coefficients along the side of each duct are obtained for natural convection heat transfer. Total overall averaged heat transfer coefficients are also obtained. Longitudinal (perimeter-averaged) Nusselt numbers and the modified Rayleigh numbers are evaluated and correlated using different characteristic lengths. Furthermore, total overall averaged Nusselt numbers are correlated with the modified Rayleigh numbers. Moreover, a dimensionless temperature group was developed and correlated with the modified Rayleigh number. For the upward-facing case, laminar and transition regimes are obtained and characterized. However, for the downward-facing vertex case, only the transition regime is observed. The local (perimeter-averaged) or the overall total Nusselt numbers increase as the modified Rayleigh numbers increase in the transition regime. However, Nusselt numbers decrease as the modified Rayleigh numbers increase in the laminar regime.

Approximate method of determining the optimum cross section of microhannel heat sink

Microchannels are at the forefront of today’s cooling technologies. They are widely being considered for cooling of electronic devices and in micro heat exchanger systems due to their ease of manufacture. One issue which arises in the use of microchannels is related to the small length scale of the channel or channel cross-section. In this work, the maximum heat transfer and the optimum geometry for a given pressure loss have been calculated for forced convective heat transfer in microchannels of various cross-section having finite volume for laminar flow conditions. Solutions are presented for 10 different channel cross sections: parallel plate channel, circular duct, rectangular channel, elliptical duct, polygonal duct, equilateral triangular duct, isosceles triangular duct, right triangular duct, rhombic duct and trapezoidal duct. The model is only a function of the Prandtl number and the geometrical parameters of the cross-section, i.e., area and perimeter. This solution is performed with two exact and approximate methods. Finally, in addition to comparison and discussion of these two methods, validation of the relationship is provided using results from the open literature.

EFFECT OF VORTEX GENERATORS ON A FRICTION FACTOR IN AN EQUILATERAL TRIANGULAR DUCT

The main objective of this study is to determine the effect of vortex generators on a friction factor for fully developed flow of a fluid such as air. Longitudinal vortices can be generated in a channel flow by punching or mounting protrusions in the channel wall. Such vortex generators (VGs) can be classified into delta wing, rectangular wing, pair of delta-winglet and pair of rectangular winglet. These longitudinal vortices disrupt the growth of the boundary layer and lead to enhance the heat transfer rate between the working fluid and the conductor channel wall, but this enhancement is associated with increasing in a pressure gradient along the axial length of the channel. So, the friction factor for fully developed air flow in an equilateral triangular duct is investigated experimentally with Reynolds number ranging from (31,000) to (53,000) and the size of the generators was kept constant for three cases which are single, double, and triple pairs of delta–winglet type of vortex generators embedded in the turbulent boundary layer for attack angle of generator of (30, 40, and 50 ) degree. The results show that the friction factor increases by about (43.5 %) when the angle of attack is varied from (30 deg) to (50 deg) for the triple pairs case compared with the base case (without VG).

Effect of Delta–Winglet Vortex Generators on a Forced Convection Heat Transfer in an Asymmetrically Heated Triangular Duct

An experimental investigation is performed to study the friction factor ( f ) and convection heat transfer coefficient (h) behavior in an asymmetrically heated equilateral triangular duct by using delta–winglets vortex generators which are embedded in a turbulent boundary layer. Two side walls of the heated test section are electrically heated with a constant heat flux, whereas the lower wall is indirectly heated. Reynolds number (Re) is ranged from (23,000) to (58,000). Two sizes and three attack angles of vortex generators are studied here for three cases; single, double, and treble pairs of generators. Each pair was supported in one wall of the test section at the various locations from the leading edge. The indicated results that friction factor ( f )and Nusselt number (Nu) are relatively proportion with the size, number and the inclination angle of the generators. The ( f ) decreases as airflow rate increases whereas Nu number increases. The present data of ( f ) is less than the data of Chegini by about (6.5 %) and overpredicts the data of Altemani by about (1.7 %).

Thermohydraulic performance of a periodic trapezoidal channel with a triangular cross-section

Simulations are performed to study the heat transfer behaviour of an equilateral triangular section duct following a tortuous path for fully-developed laminar flows with Reynolds numbers below 200. The enhancement of heat transfer and the increase in pressure drop are compared with those for ducts of circular, semi-circular and square section following the same serpentine path. For this flow regime, the triangular duct is shown to be the optimum choice (best heat transfer augmentation compared with increased pressure drop) amongst those studied. The effects of changing the path shape, the apex angle for an isosceles triangular cross-section and rounding of a corner of the equilateral triangular duct are also considered.

An integrated 2-D Navier–Stokes equation and its application to 3-D internal flows

An efficient two-dimensional (2-D) analytical and numerical procedure has been proposed to investigate three-dimensional (3-D) internal flows through a passage with a spatially variable depth, in which the viscous forces act significantly on both upper and lower walls. The integral 2-D version of the Navier–Stokes equation was obtained by integrating the full Navier–Stokes equation in a 3-D form over the depth of the passage. In order to examine the validity of the integrated momentum equations, fully-developed flows in straight noncircular ducts were investigated analytically prior to numerical investigations. It has been shown that the exact solutions for circular, elliptical and equilateral triangular ducts are obtainable from the integrated Navier–Stokes equation. Having confirmed its wide applicability to internal flows, numerical computations were conducted to investigate the oscillation mechanism of a fluidic oscillator. Comparison of the present prediction and experiment reveals the validity of the present treatment.

Simulation of Turbulent Flow and Forced Convection in a Triangular Duct with Internal Ribbed Surfaces

ABSTRACT A three-dimensional problem of fully developed turbulent flow through an equilateral triangular duct with internal ribbed surfaces has been simulated numerically through two two-dimensional approaches: turbulent forced convection between two parallel plates with ribbed bottom surface and that in an equilateral triangular duct with smooth internal surfaces. Effects of the complicated geometry on the turbulent forced convection, as well as the formation of the secondary flows around the ribs and in the triangular duct's corners, are analyzed in detail. Comparisons between the calculated and experimental results have been carried out and it has been found that the geometry effect from the attached uniformly spaced ribs on the triangular duct's thermal performance is more significant than that from the duct's corners.

Forced convection and flow friction characteristics of air-cooled horizontal equilateral triangular ducts with ribbed internal surfaces

Experimental studies have been conducted to examine the forced convection and flow friction characteristics of air-cooled horizontal equilateral triangular ducts whose internal surfaces have been fabricated with uniformly spaced square ribs. Effects of duct geometry (i.e. relative rib height ( H/ D) and relative rib-to-rib spacing ( S/ W)) as well as the hydraulic-diameter based Reynolds number ( Re D ) on heat transfer coefficient and friction factor of a fully developed turbulent air flow in a horizontal triangular duct with ribbed internal surfaces have been fully investigated. The ranges of experimental parameters under consideration are: H/ D from 0.11 to 0.21, S/ W from 3.41 to 13.93, and Re D from 4000 to 23,000. Optimum relative rib height and relative rib-to-rib spacing corresponding to maximum thermal performance of this system have been determined, which are equal to 0.18 and 7.22, respectively. Flow friction in the triangular duct increases rather linearly with the relative rib height, but a maximum flow friction factor is obtained at the relative rib-to-rib spacing of 7.22. Non-dimensional expressions for prediction of average Nusselt number and friction factor in terms of Re D , H/ D and S/ W have been developed correspondingly, which correlate well with the experimental data with maximum deviations of ±3.5% and ±8.7%, respectively.

Optimum rib size to enhance forced convection in a horizontal triangular duct with ribbed internal surfaces

The optimum rib size to enhance heat transfer had been proposed through an experimental investigation on the forced convection of a fully developed turbulent flow in an air-cooled horizontal equilateral triangular duct fabricated on its internal surfaces with uniformly spaced square ribs. Five different rib sizes (B) of 5 mm, 6 mm, 7 mm, 7.9 mm and 9 mm, respectively, were used in the present investigation, while the separation (S) between the center lines of two adjacent ribs was kept at a constant of 57 mm. The experimental triangular ducts were of the same axial length (L) of 1050 mm and the same hydraulic diameter (D) of 44 mm. Both the ducts and the ribs were fabricated with duralumin. For every experimental set-up, the entire inner wall of the duct was heated uniformly while the outer wall was thermally insulated. From the experimental results, a maximum average Nusselt number of the triangular duct was observed at the rib size of 7.9 mm (i.e. relative rib size \(\frac{B}{D} = 0.1795\) ). Considering the pressure drop along the triangular duct, it was found to increase almost linearly with the rib size. Non-dimensional expressions had been developed for the determination of the average Nusselt number and the average friction factor of the equilateral triangular ducts with ribbed internal surfaces. The developed equations were valid for a wide range of Reynolds numbers of 4,000 < ReD < 23,000 and relative rib sizes of \( 0.11 \leqslant \frac{B} {D} \leqslant 0.21 \) under steady-state condition.

HEAT TRANSFER AND PRESSURE DROP IN THE ROUGHENED EQUILATERAL TRIANGULAR DUCT

Experimental investigations were conducted to study the forced convection of fully developed turbulent flow in the horizontal equilateral triangular duct fabricated with different surface roughness pitch ratio (P/e) of 4, 8, and 16 on the one side wall only. The entire bottom wall of the duct was heated uniformly and the other surfaces were thermally insulated. To understand the mechanism of the heat transfer enhancement, measurements of heat transfer were done to investigate the contributive factor of heat transfer promotion, namely, the fin effect. Smooth triangular ducts were also tested for benchmark purposes. The results were compared with those of previous investigations for similarly configured channels, at which they were roughened by regularly spaced transverse ribs in the rectangular and circular channels

FORCED-CONVECTION AUGMENTATION OF TURBULENT FLOW IN A TRIANGULAR DUCT WITH ARTIFICIALLY ROUGHENED INTERNAL SURFACES

Use of artificially roughened internal surfaces to enhance the steady-state forced convection in an air-cooled horizontal equilateral triangular duct (apex angle of 60°) has been investigated experimentally under a hydrodynamic fully developed turbulent flow condition with hydraulic diameter-based Reynolds numbers ranging from 4,300 to 15,000. The test duralumin triangular ducts were fabricated with the same axial length of 2.4 m and hydraulic diameter of 0.44 m, but four kinds of internal surface finishing. In addition to a smooth surface with an average surface roughness of less than 1 w m, the internal surfaces of the triangular ducts were roughened artificially either by milling/shaping processes, by cutting V-grooves, or by fixing square ribs with a uniform spacing along their axial length. The artificial surface roughness was fabricated in parallel and essentially in the orthogonal direction to the mean flow. By comparing the thermal performance of triangular ducts with the same geometry but different kinds of surface finishing, it was found that forced-convection augmentation could be achieved by the internally roughened surfaces. A much greater enhanced forced convection was obtained by cutting V-grooves or fixing square ribs at uniform spacing, rather than fabricating random roughness on the internal surfaces by machining processes. In addition, the best thermal performance was achieved with the ribbed surface. Nondimensional expressions for the determination of the steady-state heat transfer coefficient of the equilateral triangular ducts, which were internally fabricated with various kinds of artificial surface roughness under consideration, have also been developed.

Friction factor and heat transfer in equilateral triangular ducts with surface roughness

Experimental investigations were conducted to study forced convection of fully developed turbulent flows in horizontal equilateral triangular ducts with different surface roughness pitch ratios (P/e) of 4, 8, and 16 on one side. The duct’s bottom wall was heated uniformly and the other surfaces were thermally insulated. To understand heat transfer enhancement mechanism, heat transfer rates were measured. Smooth triangular ducts were also tested for benchmark purposes. The results were compared with previous results for similarly configured channels, at which they were roughened by regularly spaced transverse ribs in the rectangular and circular channels.

Enhanced forced-convection from ribbed or machine-roughened inner surfaces within triangular ducts

An experimental investigation has been conducted to study the steady-state forced-convection heat-transfer characteristics of the hydrodynamic fully-developed turbulent flow in air-cooled horizontal equilateral triangular ducts (i.e. of 60° apex angle), which were each fabricated with the same length of 2.4 m and hydraulic diameter of 0.44 m. The inner surfaces of the triangular ducts were roughened by a milling process, shaping process or fixing uniformly-spaced parallel square ribs orthogonal to the mean air flow. The average surface roughness of the inner surfaces, which were produced by milling and shaping processes, were 3.0 and 11.5 μm, respectively. The square-sectioned ribs, adopted to produce the roughened surface, had different protrusions of 6.35, 9.525 and 12.7 mm, and the uniform separation between the centre lines of two successive ribs was kept constant at 57.15 mm. Both the triangular ducts and the square ribs were fabricated out of duralumin. The experiments were performed with the hydraulic-diameter based Reynolds numbers ranging from 4000 to 15000. The entire inner wall of the duct was heated uniformly, while its outer surfaces were thermally well insulated. By comparing the heat-transfer performances with those of a smooth triangular duct (i.e. average inner-surface roughness of less than 1.0 μm) having the same geometry, it was found that forced convection was enhanced by the roughened surfaces. In addition, a much enhanced forced convection was obtained by fixing uniformly-spaced parallel square ribs, rather than by fabricating random roughness on its inner surfaces by machining. However, the heat-transfer enhancement was not proportional to the rib size; the maximum forced convection heat-transfer augmentation was obtained using the smallest (i.e. 6.35 mm) ribs of those tested. Non-dimensional expressions for the determination of the steady-state heat-transfer coefficient of the equilateral triangular ducts, which were fabricated with the various kinds of artificial inner-surface roughness, were also developed.

Shape Factor and Hydraulic Conductance in Noncircular Capillaries: I. One-Phase Creeping Flow

We use the Mason–Morrow shape factor, i.e., a dimensionless hydraulic radius, and corner half-angles to capture the geometry of noncircular capillaries pertinent to a physically adequate pore network description of porous media. We give analytic expressions for random corner half-angles that satisfy a given shape factor calculated from the microscopic images of pore space. We demonstrate that use of the shape factor leads to particularly simple expressions for the hydraulic conductance in single-phase flow through noncircular capillaries. In particular, we obtain the hydraulic conductances of arbitrary triangular ducts semianalytically, using conformal mapping. The conductances of equilateral triangular, rectangular, and elliptic ducts are calculated analytically.

Forced convection and friction in triangular duct with uniformly spaced square ribs on inner surfaces

Experimental investigation had been conducted to study the steady-state forced convection heat transfer and pressure drop characteristics of the hydrodynamic fully-developed turbulent flow in the air-cooled horizontal equilateral triangular ducts, which were fabricated with the same length and hydraulic diameter. Inner surfaces of the ducts were fixed with square ribs with different side lengths of 6.35, 9.525 and 12.7 mm, respectively, and the uniform separation between the centre lines of two adjacent ribs was kept constant at 57.15 mm. Both the triangular ducts and the ribs were fabricated with duralumin. The experiments were performed with the hydraulic diameter based Reynolds number ranged from 3100 to 11300. The entire inner wall of the duct was heated uniformly, while the outer surface was thermally insulated. It was found that the Darcy friction factor of the duct was increasing rather linearly with the rib size, and forced convection could be enhanced by an internally ribbed surface. However, the heat transfer enhancement was not proportional to the rib size but a maximum forced convection heat transfer augmentation was obtained at the smallest rib of 6.35 mm. Non-dimensional expressions for the determination of the steady-state heat transfer coefficient and Darcy friction factor of the equilateral triangular ducts, which were internally fabricated with uniformly spaced square ribs of different sizes, were also developed.