Non-circular Ducts Research Articles

Numerical Analysis of Forced Convection Heat Transfer for Turbulent Flow in a Square Duct with a Rough Wall.

Experimental and numerical studies of heat transfer for turbulent flow in noncircular duct with rough wall are few and far between. In this study, numerical analysis has been carried out on heat transfer for a developing turbulent flow in a square duct with a rough wall using Reynolds stress model and turbulent heat flux model. Calculated results are compared with the experimental data available. The present method can predict well the mean flow distribution and temperature distribution distorted by the secondary flow of the second kind. From calculations, the similarity which appeared between the mean flow distribution and temperature distribution is not observed near the smooth wall facing the rough wall, while it is observed from the experiment. Although the local Nusselt number of smooth walls are understimated by the present method, the production terms of the normal stress u23, shear stress u1u3 and turbulent heat flux u3 T' are in good agreement with the experimental data.

Numerical study of laminar heat transfer with temperature dependent fluid viscosity in a 2:1 rectangular duct

The present study investigates the influence of variable viscosity of temperature-dependent fluids on the laminar heat transfer and friction factor in a 2:1 rectangular duct. The H 1 thermal boundary condition corresponding to axially constant heat flux and peripherally constant temperature was adopted for a top-wall-heated configuration. The governing conservation equations of mass, momentum, and energy were solved using a finite volume method, and the range of the Prandtl number was from 7 to 15000. The present numerical results of local Nusselt numbers for oil showed 70—80% enhancement over those of a constant property fluid and 40—50% enhancement over water, and gave excellent agreement with recent experimental results [ Int. J. Heat Mass Transfer 35, 641—648 (1992)]. The heat transfer enhancement from the heated top wall was due to an increased velocity gradient near the wall. The study proposes a new correlation for local Nusselt numbers in the 2:1 rectangular duct, which covers both thermally developing and thermally fully developed regions. Consequently, a temperature-dependent viscous fluid with a non-circular duct is proposed for use in the design of a liquid cooling module for the computer industry and in compact heat exchangers in general.

A Comparison of the Linear and Nonlinear k–ε Turbulence Models in Combustors

In swirling turbulent flows, the structure of turbulence is nonhomogeneous and anisotropic and it has been observed that the assumptions leading to the formulation of the k-ε model, which is used very often in many engineering applications, are inadequate for highly swirling flows. Furthermore, even with the various modifications made to the k-ε model, it is still not capable of describing secondary flows in noncircular ducts and it cannot predict non-zero normal-Reynolds-stress differences. Recently Speziale (1987) has developed a nonlinar k-ε model, which extends the range of validity of the standard k-ε model while maintaining most of the interesting features of the k-ε model; for example, the ease of application in existing Computational Fluid Dynamics (CFD) codes. In this work, we will use the nonlinear k-ε closure to model the turbulence in combustors. The particular combustor geometries selected for this study are (i) the flow in a round pipe entering an expansion into another coaxial round pipe, and (ii) the flow in two confined co-axial swirling jets. The results show that there are no significant differences in the performance of the two models. It is speculated that the inlet conditions for k and ε may play as crucial a role in achieving predicted accuracy as turbulence modeling details. Also it is possible that weaknesses in the performance of the modeled equations for k and ε may have masked differences in the two models.

Numerical Analysis on Fully Developed Turbulent Flow in a Square Duct with a Rough Wall.

Experimental and numerical studies of turbulent flow in a non-circular duct with a rough wall are very scarce. Therefore, numerical analysis has been carried out in this study for fully developed turbulent flow in a square duct with a roughened wall using the Reynolds stress model. Calculated results are compared with the experimental data available. The present method can predict well a large eddy caused by the secondary flow of the second kind in a half cross section and a small eddy is observed in the upper wall corner region. However, a small eddy which appeared in the calculated results is not recognized in the experimental data. Calculated results of normal stresses and turbulent energy are in comparatively good agreement with the experimental data. These examinations suggest that the present method utilizing the Reynolds stress model, which is classified by an anisotropic turbulent model of high Reynolds number, is able to predict the turbulent flow in a square duct with roughened walls.

Geometrical aspects of secondary motion in turbulent duct flow

Fully developed turbulent flow through straight ducts is considered. An analysis in a Reynolds stress principal-axis coordinate frame is performed with the aim of clarifying the main mechanisms responsible for turbulence-driven secondary (transverse) mean flow in noncircular ducts. Together with this, some basic properties of that flow are deduced.

Effects of shear thinning on laminar heat transfer behavior in a rectangular duct

The fluid dynamic and heat transfer behavior of laminar non-Newtonian flow through noncircular ducts is of special interest because of their wide range of potential application to compact heat exchangers and in electronics cooling. The present study investigates the heat transfer characteristics for laminar forced convection of inelastic non-Newtonian fluids in a nonuniformly heated rectangular duct where the flow is hydrodynamically developed but thermally developing. The governing equations are solved by a finite volume method. Second-order accurate differencing schemes are employed for both the diffusion and convective terms. The effects of shear thinning, given by the Carreau equation, and the viscous dissipation, characterized by the Brinkman number, are examined via the friction factor, the Nusselt number, and the bulk fluid temperature. The results indicate that when viscous dissipation is present, the heat transfer from the heated surface of the duct is greatly enhanced with increased shear thinning of the fluid while the rate of increase of the bulk fluid temperature with axial distance will significantly decrease. Consequently, the use of a shear-thinning non-Newtonian fluid for heat transfer enhancement appears to be a very promising concept that is worthy of further study.

Convective heat transfer in the thermal entrance region of parallel-flow noncircular duct heat exchanger arrays

Convective heat transfer properties of a hydrodynamically fully developed flow, thermally developing flow in a parallel-flow, and noncircular duct heat exchanger passage subject to an insulated boundary condition are analyzed. In fact, due to the complexity of the geometry, this paper investigates in detail heat transfer in a parallel-flow heat exchanger of equilateral-triangular and semicircular ducts. The developing temperature field in each passage in these geometries is obtained seminumerically from solving the energy equation employing the method of lines (MOL). According to this method, the energy equation is reformulated by a system of a first-order differential equation controlling the temperature along each line. Temperature distribution in the thermal entrance region is obtained utilizing sixteen lines or less, in the cross-stream direction of the duct. The grid pattern chosen provides drastic savings in computing time. The representative curves illustrating the isotherms, the variation of the bulk temperature for each passage, and the total Nusselt number with pertinent parameters in the entire thermal entry region are plotted. It is found that the log mean temperature difference (ΔT LM), the heat exchanger effectiveness, and the number of transfer units (NTU) are 0.247, 0.490, and 1.985 for semicircular ducts, and 0.346, 0.466, and 1.345 for equilateral-triangular ducts.

Entrance heat transfer in isosceles and right triangular ducts

Heat transfer in noncircular ducts is an important factor in the design of compact heat exchangers. A Galerkin-based integral method is presently used to conduct the requisite computations. The fully developed velocity distribution is obtained independent of the energy equation, because the physical properties do not depend on temperature. More accurate results may be obtained for right-triangular ducts with small included angle from the isosceles triangular duct solution. 5 refs.

Numerical Analysis of Developing Turbulent Flow in an Elliptical Duct by a Reynolds Stress Model.

A numerical analysis has been performed for three-dimensional developing turbulent flow in an elliptical duct by a modified Reynolds stress equation model. Governing equations are transformed from the physical plane to the calculation plane by boundary-fitted coordinate systems. The calculated results are compared with the experimental data available. The predicted results of mean velocity along the axes and friction factor agree relatively well with the experimental data. The results of this analysis enable the prediction of the secondary flow of the second kind which characterizes noncircular duct flow. At the same time, a clear statement of the distribution of the various Reynolds stresses is made, showing their characteristic aspects. The secondary flow of the second kind reaches maximum intensity in the midst of development. This is a result of shear layer interaction effects as the boundary layer developing along the wall of the elliptical duct begin to merge.

A rate-dependent algebraic stress model for turbulence

Based on the stress transport model, a rate-dependent algebraic expression for the Reynolds stress tensor is developed. It is shown that the new model includes the normal stress effects and exhibits viscoelastic behavior. Furthermore, it is compatible with recently developed improved models of turbulence. The model is also consistent with the limiting behavior of turbulence in the inertial sublayer and is capable of predicting secondary flows in noncircular ducts. The TEACH code is modified according to the requirements of the rate-dependent model and is used to predict turbulent flow fields in a channel and behind a backward-facing step. The predicted results are compared with the available experimental data and those obtained from the standard k-ϵ and algebraic stress models. It is shown that the predictions of the new model are in better agreements with the experimental data.

Radiation convection in a thermally developing duct flow of noncircular cross section

In this paper the interaction of thermal radiation and laminar forced convection in the thermal entrance region of noncircular ducts is numerically investigated. In particular, because of their complex geometry, the paper investigates in detail the combined modes of heat transfer in right triangular and semicircular ducts. The velocity in these geometries is considered fully developed and the temperature of an absorbing-emitting gas is developing in an isothermal duct with nonblack walls. The method of moments is used to describe the radiation contribution that circumvents the partial intergro-differential equation typical of this kind of problem. Also, the methodology using the method of lines (MOL) involving differential and difference formulations and coarse grids is applied to these ducts of noncircular cross section. The results based on 36 lines or less are computed numerically using a Runge-Kutta subroutine. They are presented in terms of axial bulk temperature and mean Nusselt number and are plotted as a function of the optical thickness, wall emissivity, and radiation-conduction parameter. The results compare very well with those for pure convection available in the literature. In addition, it is observed that radiation influences the thermal development of noncircular ducts in a complicated way.

Turbulent flow measurements in a 30/60 degree right triangular duct

Experimental data are reported for fully developed turbulent flow in a right triangular duct with internal angles of 60 and 30 deg. This duct geometry has no symmetry planes and as such generates a type of non-circular duct flow for which data are scarce. Measurements are made with hot-wire anemometry in an air flow rig specifically constructed for the tests. The friction factor characteristic and axial velocity contours and profiles are presented, together with contours and/or profiles of turbulence intensity, turbulence kinetic energy and the Reynolds shear stresses. Where appropriate, comparisons of the profiles are made with data from measurements in other duct geometries. The presence and influence of turbulence driven cross-plane secondary flow is clearly evident and the implied circulations follow the pattern expected from previous measurements in other ducts.

Noncircular Inlet Duct Cross-Section to Reduce Combustion Instabilities

Abstract The unique shear-flow characteristics of a triangular jet were used to suppress longitudinal pressure oscillations in a coaxial dump combustor. The asymmetric flow configuration enhanced fine-scale mixing in the corner flow, while maintaining large-scale mixing at the flat sides, as demonstrated in air and water flows with and without forcing. In a forced annular diffusion flame it was shown that the flat-side shear layers were dominated by reacting vortices which lead to periodic heat release and possible driving of pressure oscillations, while the combustion at the corners was more intense and free of periodicity because of highly three-dimensional flow with enhanced molecular mixing between the fuel and oxidizer. For a coaxial dump, the pressure oscillations were significantly reduced with a triangular inlet duct and corner injection, compared to a triangular inlet duct with flat-side injection and to a circular inlet duct.

Nonlinear Reynolds stress models and the renormalization group

The renormalization group is applied to derive a nonlinear algebraic Reynolds stress model of anisotropic turbulence in which the Reynolds stresses are quadratic functions of the mean velocity gradients. The model results from a perturbation expansion that is truncated systematically at second order with subsequent terms contributing no further information. The resulting turbulence model applies to both low and high Reynolds number flows without requiring wall functions or ad hoc modifications of the equations. All constants are derived from the renormalization group procedure; no adjustable constants arise. The model permits inequality of the Reynolds normal stresses, a necessary condition for calculating turbulence-driven secondary flows in noncircular ducts.

Effect of Wall Conduction on Combined Free and Forced Laminar Convection in Horizontal Tubes

Combined free and forced laminar convection in ducts is encountered in a wide variety of engineering applications, including heat exchangers designed for viscous fluids in chemical processes, solar collectors, food industries, and biomedical engineering. In many engineering applications, the boundary conditions for thermal convection in ducts cannot be considered uniform either for wall temperature or heat flux. In the thermally fully developed flow, the effect of peripheral wall conduction may be introduced by the nonuniform peripheral wall heat flux in noncircular ducts and also introduced simultaneously by the secondary flow in rectangular channels, or by the secondary flow alone in circular tubes. This paper investigates the effect of peripheral wall conduction on combined free and forced laminar convection in hydrodynamically and thermally fully developed flow in horizontal circular tubes with uniform heat input axially. A finite-difference power-law scheme is employed to solve the problem.

Determination of Incompressible Flow Friction in Smooth Circular and Noncircular Passages: A Generalized Approach Including Validation of the Nearly Century Old Hydraulic Diameter Concept

It has been demonstrated conclusively that the widely observed differences in data for frictional pressure coefficient between circular and noncircular passages derive from the inseparably connected effects of transition and the choice of a length scale. A relatively simple approach, the critical friction method (CFM), has been developed and when applied to triangular, rectangular, and concentric annular passages, the reduced data lie with remarkable consistency on the circular tube relations. In accordance with the theory of dynamical similarity, it has also been shown that noncircular duct data can be reduced using the hydraulic diameter or any arbitrarily defined length scale. The proposed method is what is needed to reconcile such data with those for circular tubes. With the hydraulic diameter, the critical friction factor almost converges to a universal value for all passages and the correction is simply that required to account for the difference in critical Reynolds number. By contrast, with any other linear parameter, two corrections are needed to compensate for variations in critical friction factor and Reynolds number. Application of the method to roughened passages is discussed.

Generalized Explicit Equation for the Friction Factor for Newtonian and Non‐Newtonian Fluids in Both Circular and Non‐Circular Ducts

Chemie Ingenieur TechnikVolume 60, Issue 4 p. 304-306 Article Generalized Explicit Equation for the Friction Factor for Newtonian and Non-Newtonian Fluids in Both Circular and Non-Circular Ducts Prof. Dr. A. R. Mansour, Prof. Dr. A. R. Mansour Departments of Chemical & Mechanical Engineering, Yarmouk University, Irbid – JordanSearch for more papers by this authorO. T. Rajie, O. T. Rajie Departments of Chemical & Mechanical Engineering, Yarmouk University, Irbid – JordanSearch for more papers by this author Prof. Dr. A. R. Mansour, Prof. Dr. A. R. Mansour Departments of Chemical & Mechanical Engineering, Yarmouk University, Irbid – JordanSearch for more papers by this authorO. T. Rajie, O. T. Rajie Departments of Chemical & Mechanical Engineering, Yarmouk University, Irbid – JordanSearch for more papers by this author First published: April 1988 https://doi.org/10.1002/cite.330600413Citations: 2AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Citing Literature Volume60, Issue4April 1988Pages 304-306 RelatedInformation

Electromagnetic scattering from ducts with irregular edges. II. Noncircular case

For pt.I see ibid., vol.AP-36, no.3, p.383-97 (1988). Electromagnetic scattering from finite noncircular ducts terminated with irregular edges is investigated. An edge-dependent entire-domain Galerkin expansion is proposed for the current variation on the duct wall, rigorously satisfying the edge conditions. The electric field integral equation is solved using this expansion for arbitrary noncircular ducts. Convergence of these solutions is examined and compared to results obtained with a simpler edge-independent formulation. The solutions are shown to agree with previously published results for circular ducts and recently obtained experimental data.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A GENERALIZED BLASIUS EQUATION FOR POWER LAW FLUIDS

Making use of a generalized turbulent velocity distribution for power law fluids, a Blasius type equation was derived which explicitly relates the friction factor to a generalized Reynolds number in fully developed pipe flow. Comparison of the equation with experimental data shows an agreement of approximately ± 8% A modification of the equation to account for geometry appears to allow its application to non-circular duct flow.

TAYLOR DISPERSION IN CONDUITS OF LARGE ASPECT RATIO†

The Taylor dispersion coefficient D¯C (above and beyond the purely molecular contribution D) arising during Poiseuille-like flow through noncircular cylindrical ducts of large aspect ratio (but otherwise arbitrary cross section) is theoretically calculated. Our study is motivated by an attempt to rationalize the remarkable fact that D¯C for a rectangular duct does not reduce to its well-known flat-plate value, D¯ ∞ C = 202H2/105D, in the limit where the aspect ratio tends to infinity [V¯ = mean velocity in duct, H = distance between plates]. Slender-body theory is used to express both the fluid velocity and concomitant Taylor dispersion fields as perturbation expansions in the small parameter e = (aspect ratio)−1 ≪ 1, following which D¯C is computed to the lowest order in e. This dispersivity is found to scale with the longer of the two characteristic duct dimensions for all cross sections save the rectangular, for which D¯C scales with the shorter dimension. This surprising result is explained by noting ...