Search

Investigation of unsteady flow characteristics through a curved duct is widely used in many engineering applications such as in fluid transportation, rotating machinery and metallic industry. Fluid behavior depends not only on the rotation of the duct but also on physical properties such as fluid pressure, curvature and aspect ratio of the duct. The present paper focuses on the time-dependent flow behavior through a rotating curved square duct. The bottom wall of the duct is heated while cooling from the ceiling, the inner and outer sidewalls being thermally insulated. Numerical calculations are carried out by using a spectral technique, where function expansion and collocation methods are applied for constant Dean number, Dn = 1000, the Grashof number, Gr = 100 and curvature, δ = 0.01 over a wide range of the Taylor number, −1500≤Tr≤1500. In this paper, we investigated flow characteristics for both positive and negative rotation of the duct. Due to combined action of the centrifugal, Coriolis and buoyancy forces various types of physically realizable transient solutions such as steady-state, periodic, multi-periodic and chaotic solutions have been obtained. Flow transitions are well determined by obtaining the power spectrum of the solutions. Typical contours of axial flow, secondary flow and temperature profiles have also been obtained and it is found that time-dependent solutions are comprised of two-to six-vortex solutions. The present study shows that convective heat transfer is significantly enhanced by the secondary flow and there is a strong interaction between the heating-induced buoyancy force and the centrifugal-Coriolis instability in the rotating curved duct that stimulates fluid mixing and consequently enhances heat transfer in the fluid. Finally, our numerical results have been compared with the experimental investigations and it is found that there is a good agreement between the numerical and experimental investigations. [ABSTRACT FROM AUTHOR]

Time-dependent flow behavior through a curved duct is widely encountered in engineering and cell sorting sections. In this article, we have numerically investigated time-dependent fluid flow and dynamic heat transfer related to the stationary curved square duct, paying particular attention to the dependence of velocity and temperature fields on Dean number (Dn), Grashof number (Gr), curvature (δ) and aspect ratio. Here, the outer and bottom walls of the duct are maintained at high temperature whereas the inner and upper walls adiabatically segregated. In the first instance, time evolution calculation of the unsteady solutions has been performed for an extensive range of the Dean number (100 ≤ Dn ≤ 1000) and the Grashof number (100 ≤ Gr ≤ 1000) while other parameters have been considered to be fixed. Time-dependent solutions show that the flow undergoes through various flow instabilities regarding the range of parameters. It has been seen that three types of flow characters, steady-state, periodic, multi-periodic oscillations have been constructed in the time vs. Nusselt number for cooling wall plane. To point out the periodic and multi-periodic flow more clearly, power spectrum has been accomplished. Typical contours of two types of flow velocity such as axial and secondary flow and isotherm (temperature profiles) have been obtained for various values of Dn and Gr. It is found that only two-vortex asymmetric solutions appear for the steady-state solution whereas two- to four-vortex for the periodic and multi-periodic flows. Heat transfer has been demonstrated and it is found that heat transfer is enhanced by the secondary flow particularly when the Dean vortices emerge at outer concave wall. The present investigation reveals that there is a sharp influence amidst the ardor-induced buoyancy compulsion and the centrifugal instability in the curved duct that stimulates fluid composition and consequently enhances heat transfer in the fluid. [ABSTRACT FROM AUTHOR]

Due to ample engineering applications, flow in a curved duct has become one of the most challenging research fields of fluid mechanics. In this paper, a computational numerical study of flow and heat transfer through a curved rectangular duct of various aspect ratios has been analyzed by using a spectral method and covering a wide range of the pressure gradient parameter, the Dean number 0 < Dn ≤ 1000 for the Grashof number Gr=1000. Unsteady solutions are obtained by time evolution calculations for the aspect ratios ranging from 1 to 3 with constant curvature 0.5. The outer wall of the duct is heated while the inner wall is in normal temperature, the top and bottom walls being thermally insulated. The main concern of this paper is to investigate the effects of aspect ratios on time-dependent solutions such as steady-state, periodic, multi-periodic or chaotic solution, if Dn is increased. For square duct flow, it is observed that there appears steady-state solution whether Dn is small or large. For rectangular duct of aspect ratio 2, however, the steady-state solution turns into chaotic solution, if Dn is increased. For aspect ratio 3, on the other hand, the steady-state solution turns into chaotic solution via periodic or multi-periodic flows. To justify the flow transition from one state to another, phase portrait of the time evolution results are obtained. Secondary flow patterns and temperature profiles on the flow characteristics are also obtained. Nusselt numbers are calculated as an index of convective heat transfer, and it is found that convective heat transfer is significantly enhanced by the secondary flow and as the flow becomes chaotic heat transfer occurs substantially. Finally, our numerical results are validated with experimental investigations and it is found that there is a good agreement between the numerical and experimental data. [ABSTRACT FROM AUTHOR]

In this paper, a viscous incompressible fluid flow through a tightly coiled rectangular duct of large aspect ratio has been studied numerically by using a spectral method and covering a wide range of the pressure gradient parameter, the Dean number, Dn (0 < Dn ≤ 1000) for both isothermal and non-isothermal flow. For non-isothermal flow, a temperature difference is applied across the vertical sidewalls for the Grashof number Gr =1000, where the outer wall is heated and the inner wall cooled. The main concern of this paper is to investigate effects of aspect ratio on time-dependent solutions such as steady-state, periodic, multi-periodic or chaotic. To investigate non-linear behavior of the unsteady solutions, time evolution calculations are performed and flow transition between two types of solutions is determined by drawing the phase space of the time-dependent solutions. The study shows that if Dn is small, the flow is steady-state whether the flow is isothermal or non-isothermal. However, as Dn increases, the flow undergoes in the scenario 'steady-state ⃗ periodic ⃗chaotic'. Secondary flow patterns, axial flow distribution and temperature profiles on the unsteady flow characteristics are also obtained and it is found that the time-dependent flow consists of asymmetric two- to eight-vortex solutions. Distribution of the time dependent solutions is shown in the Dean number vs. vortex-structure plane for both isothermal and non-isothermal flows. Finally, our numerical results are validated with the experimental investigations obtained so far. [ABSTRACT FROM AUTHOR]

Due to engineering application and its intricacy, flow in a curved duct has become one of the most challenging research fields of fluid mechanics. In this paper, a computational numerical study is presented for the flow through a curved rectangular duct of aspect ratio 4 with strong curvature δ = 0.5 for the pressure gradient, the Dean number, 100 ≤ Dn ≤1000. A spectral method is employed as the basic tool to solve the system of nonlinear partial differential equations while function expansion and collocation method as the secondary tools. First, solution structure of the steady solutions is investigated. As a result, three branches of symmetric/asymmetric steady solutions with multi-vortex solutions are obtained by the path continuation technique. Then, in order to investigate non-linear behavior of the unsteady solutions, time evolution calculations as well as their phase portraits are obtained, and it is found that typical transition occurs from a steady flow to a chaotic state through periodic or multi-periodic flows if Dn is increased no matter what the curvature is. Finally, distribution of the time dependent solutions is shown in the Dean number vs. curvature (Dn ∓ δ) plane with vortex structure of secondary flows. [ABSTRACT FROM AUTHOR]

The present paper investigates a spectral-based numerical study for fully developed two-dimensional flow of viscous incompressible fluid through a curved square duct for the constant curvature δ = 0.1. The bottom wall of the duct is heated while cooling from the ceiling; the inner and outer sidewalls being thermally insulated. Flow characteristics are investigated over a wide range of the Dean number 0 < Dn ≤ 5000 for the Grashof number Gr = 100. First, we investigated solution structure of the steady solutions by using Newton-Raphson iteration method. As a result, four branches of steady solutions are obtained with a bifurcating relationship among the branches. Then, we studied unsteady solutions by time evolution calculations justified by their phase spaces, and it is found that the unsteady flow undergoes in the scenario “steady-state→periodic (multi-periodic)→chaotic”, if Dn is increased. The present study demonstrates the role of secondary vortices on convective heat transfer and it is found that convective heat transfer is significantly enhanced by the secondary flow; and the chaotic flow, which occurs at large Dn’s, enhances heat transfer more effectively than the steady-state or periodic solutions. [ABSTRACT FROM AUTHOR]

A numerical study on unsteady fluid flow and heat transfer through a rotating curved square channel with variable curvatures (0.1≤δ≤ 0.5) is presented numerically by using a spectral method. The bottom wall of the duct is heated while cooling from the ceiling. A rotation of the channel about the center of curvature is imposed in the positive and negative direction for the Taylor number -500≤Tr≤2000, and combined effects of the centrifugal, Coriolis and buoyancy forces are investigated. At first, steady solutions are obtained by using Newton-Raphson iteration method with path continuation technique. As a result, two branches of steady solutions with two- to six-vortex solutions are obtained. Then, in order to study the non-linear behavior of the unsteady solution, time evolution calculation as well as their phase spaces are obtained, and it is found that for positive rotation Coriolis force enforces the curvature effect that results in to turn the chaotic flow into steady-state flow through periodic or multi-periodic flows. For negative rotation, however, it is found that Coriolis force exhibits an opposite effect to that of the curvature so that the unsteady flow undergoes through various flow instabilities. The present study elucidates the role of secondary vortices on convective heat transfer and it is found that convective heat transfer is significantly enhanced by the secondary flow. [ABSTRACT FROM AUTHOR]

In this paper, a comprehensive numerical study on viscous incompressible fluid flow and heat transfer through a loosely coiled square duct has been presented. Spectral method is used as a basic tool to solve the system of non-linear partial differential equations. Numerical calculations are carried out for the Dean number Dn = 1000 with a temperature difference across the vertical sidewalls for the Grashof number Gr = 100, where the outer wall is heated and the inner wall cooled. A rotation of the duct about the center of curvature is imposed in the positive direction for the Taylor number 0 ≤Tr ≤ 2000 and combined effects of the centrifugal, Coriolis and buoyancy forces are investigated. First, steady solutions are obtained by the Newton-Raphson iteration method. As a result, three branches of asymmetric steady solutions with two- to four-vortex solutions are obtained. Then, time evolution calculations as well as power spectrum density of the unsteady solutions are obtained and it is found that the unsteady flow undergoes through various flow instabilities, if Tr is increased in the positive direction. Nusselt numbers are calculated as an index of convective heat transfer, and it is found that convective heat transfer is significantly enhanced by the secondary flow. Finally, a comparison between the numerical and experimental investigations has been provided. It is found that there is a good agreement between the numerical and experimental investigations. [ABSTRACT FROM AUTHOR]

In this paper, a spectral-based numerical result is presented for the fully developed two-dimensional flow of viscous incompressible fluid through a rotating curved rectangular duct. The bottom wall of the duct is heated while cooling from the ceiling. A rotation of the duct about the centre of curvature is imposed in the positive direction for the constant Dean number Dn = 1000 over a wide range of the Taylor number 0 ≤ Tr ≤ 2000 . First, solution structure of the steady solutions is obtained by the Newton-Raphson iteration method. Then, we investigated unsteady solutions by time evolution calculations justified by power spectrum of the solutions, and it is found that when there is no rotation, the flow is chaotic but as the rotational speed increases, the chaotic flow turns into steady-state flow through periodic or multi-periodic flows. This study shows that combined effects of the centrifugal and Coriolis forces counteract each other in a nonlinear manner which results in to turn the chaotic flow into steady-state flow. The present study demonstrates the role of secondary vortices on convective heat transfer which shows that secondary flow enhances heat transfer in the flow. Typical contours of secondary flow patterns and temperature distribution are also obtained at several values of Tr, and it is found that the unsteady flow consists of two- to eight-vortex solutions if the duct rotation is involved in the present case. [ABSTRACT FROM AUTHOR]