旋转方形截面螺旋管内流动与传热特性

利用数值计算方法研究了旋转矩形截面螺旋管内的粘性流动，分析了在离心力，科氏力共同作用下曲线管道中的二次流动结构、轴向流速分布、截面温度分布、摩擦系数比以及管道Nusselt数比随各参数的变化情况。计算结果表明：当旋转方向和主流方向相同时，旋转的作用与增大Dean数的作用相同，使得管道摩擦系数变大，管道换热效果增强，而当旋转方向和主流方向相反时，管道内流动结构变化十分明显，当F≈-1．2时(F为科氏力与离心力之比)，二次流出现类似于直扭管内的鞍状流动结构，轴向速度类似于静止直管内的流动结构，管道内的摩擦系数与静止直管内的摩擦系数大约相等，换热效果减至最弱；挠率对流动结构以及摩擦系数比和Nusselt系数比的影响效果与F有关。     

A criterion for detection of the onset of Dean instability in Newtonian fluids

Dean instability for Newtonian fluids in laminar secondary flow in 180° curved channels was studied experimentally and numerically. The numerical study used Fluent CFD code to solve the Navier–Stokes equations, focusing on flow development conditions and the parameters influencing Dean instability. An accurate criterion based on the radial gradient of the axial velocity was defined that allows detection of the instability threshold, and this criterion is used to optimize the grid geometry. The effects on Dean instability of the curvature ratio (from 5.5 to 20) and aspect ratio (from 0.5 to 12) are studied. In particular, we show that the critical value of the Dean number decreases with the increasing duct curvature ratio. The variation of the critical Dean number with duct aspect ratio is less regular.In the experimental study, flows were visualized in several tangential positions of a 180° curved channel with aspect ratio 8 and curvature ratio 10. The flow is hydrodynamically developed at the entrance to the curved channel. The critical Dean number is detected and the development of secondary flow vortices by additional counter-rotating vortex pairs is observed. A diagram of different critical Dean numbers is established.     

A numerical investigation of developing flow in an eccentric curved annulus in the presence of gravity

In this article developing incompressible viscous flow in an eccentric curved annulus in the presence of gravity is numerically studied using a second order finite difference method based on the projection algorithm to solve the governing equations including the continuity and full Navier–Stokes equations. The equations written in a bipolar–toroidal coordinate system are discretized in a three dimensional staggered grid. The effects of governing non-dimensional parameters including the eccentricity, non-dimensional curvature ratio, Dean number, Froude number, aspect ratio, and the Reynolds number on the flow field in the entrance and fully developed region are investigated. The numerical results indicate that at the small Froude numbers, the flow field distorts from the symmetrical condition due to the larger body force effect and the axial velocity formation mostly takes place at the lower half of the annulus. In addition, at the constant Froude number, by decreasing the curvature radius, the peak axial velocity and its sharp gradient appear on the outer curvature region due to the larger centrifugal forces and by increasing the eccentricity the flow rate intensifies at the wider region and weakens at the narrower region due to the larger flow resistance. Furthermore, the friction factor increases by decreasing the Froude number and increasing the Dean number.     

Thermally developing flow in curved square ducts with internal fins

The laminar incompressible hydrodynamically fully developed and thermally developing flow is studied in a curved square duct with four longitudinal fins. The duct is successively subjected to constant wall temperature, to circumferentially uniform temperature and axially linearly or exponentially varying temperature. The local and fully developed Nusselt numbers are examined for various values of the Dean number and it is found that the heat transfer rate increases for high fins. The parameters that affect the entry length are studied and the fluctuations of the local Nu that appear in the entrance region are investigated. Temperature contour plots are presented for the visualization of the temperature field and functional relations for the Nusselt number are proposed in terms of the Dean and Prandtl numbers.     

Experimental study on the pressure drop and heat transfer characteristics of tubes with internal wave-like longitudinal fins

Experiments were performed to determine the heat transfer and pressure drop characteristics in the entrance and fully developed regions of tubes with internal wave-like longitudinal fins. The test tube has a double-pipe structure, with the inner tube as an insertion. The wave-like fins are in the annulus and span its full width. Experiments were conducted for two cases: one with the inner tube blocked (no air flowing through it) and the other with the inner tube unblocked. The outer tube was electrically heated. Local and average heat transfer coefficients and friction factors were measured. The friction factor and Nusselt number correlations in the fully developed region were obtained in the Reynolds number range of 9×10² to 3.5×10³. It has been found that the wave-like fins enhance heat transfer significantly with the blocked case being superior. In addition, the in-tube heat transfer process is characterized by an earlier transition from laminar to turbulent flow and Reynolds number-dependent thermal entrance length. Received on 12 May 1998     

Forced convection in tightly coiled ducts: Bifurcation in a high Dean number region

The present numerical study is on the fully developed bifurcation structure of forced convection in a tightly coiled duct of square cross-section and curvature ratio of 0.5 in a high Dean number region. Ten solution branches, two symmetric and eight asymmetric, are found. Among them, one symmetric branch and seven asymmetric branches have not been reported in the literature. On these new branches, the flow has a structural 2-, 4-, 5-, 6-, 7- or 8-cell. The mean friction factor and Nusselt number are different on various solution branches. In tightly coiled ducts, the secondary flow enhances the heat transfer more significantly than the friction increase.     

Fluid flow in a rotating curved rectangular duct

The fluid flowing in a rotating curved duct is subjected to both the Coriolis force due to a rotation and the centrifugal force due to a curvature. In this paper, the combined effects of the two forces on the flows in rotating curved rectangular ducts are examined numerically. According to the aspect ratio of the cross-section, the rectangular ducts are divided into three types: η>1, η=1, η<1, where η is the aspect ratio. The variations of the flow structures with the force ratio F (the ratio of the Corislis force to the centrifugal force) are studied in detail and many hitherto unknown flow patterns are found. The effects of the force ratio and the aspect ratio of the cross-section on the friction factor are also examined. Present results show both the characteristics of the secondary flow, axial flow and the natures of the friction factor.     

An exact analytical solution for creeping Dean flow of Bingham plastics through curved rectangular ducts

In this paper, an exact analytical solution for creeping flow of Bingham plastic fluid passing through curved rectangular ducts is presented for the first time. The closed form of axial velocity distribution, flow resistance ratio, and wall shear stress are derived using bounded Fourier transformation. An extensive investigation on mutual effects of Hedstrom number, curvature ratio, and aspect ratio is conducted. The results indicate that a drag reduction is caused in the flow field by increasing the Hedstrom number. It is shown that unlike the Newtonian creeping Dean flow, the critical aspect ratio (an aspect ratio in which the flow resistance ratio is independent from curvature ratio) does not exist at large enough Hedstrom numbers. Analytical solution also indicated that as Hedstrom number is increased, the value of Poiseuille number is enhanced, and unlike the Newtonian flows, the value of Poiseuille number is not zero at edges of cross section.     

Effects of aspect ratio on unsteady solutions through curved duct flow

The effects of the aspect ratio on unsteady solutions through the curved duct flow are studied numerically by a spectral based computational procedure with a temperature gradient between the vertical sidewalls for the Grashof number 100 ≤ Gr ≤ 2 000. The outer wall of the duct is heated while the inner wall is cooled and the top and bottom walls are adiabatic. In this paper, unsteady solutions are calculated by the time history analysis of the Nusselt number for the Dean numbers Dn = 100 and Dn = 500 and the aspect ratios 1≤γ≤ 3. Water is taken as a working fluid （Pr =7.0）. It is found that at Dn = 100, there appears a steady-state solution for small or large Gr. For moderate Gr, however, the steady-state solution turns into the periodic solution if γ is increased. For Dn = 500, on the other hand, it is analyzed that the steady-state solution turns into the chaotic solution for small and large Gr for any γ lying in the range. For moderate Gr at Dn = 500, however, the steady-state flow turns into the chaotic flow through the periodic oscillating flow if the aspect ratio is increased.     

Vortex shedding and structural loading characteristics of finned cylinders

The flow development and structural loading characteristics of cylinders with equispaced circular fins were studied experimentally for a range of fin pitches with constant fin thickness and diameter. The experiments were performed for a range of Reynolds numbers, corresponding to the shear layer transition turbulent shedding regime. Time-resolved planar Particle Image Velocimetry and direct mean drag and fluctuating lift measurements are employed to relate spatio-temporal flow development to structural loading. The results show that wake development is dominated by vortex shedding for all the cases examined. However, the fin pitch ratio has a significant effect on vortex shedding characteristics. The addition of fins increases the characteristic spatial and temporal scales of the main spanwise vortices forming in the near wake. As the fin pitch is decreased to a critical value, the coalescence of boundary layers between the adjacent fins leads to a significant enlargement of the vortex formation region. A modified vortex shedding frequency scaling is proposed, based on the effective diameter, that incorporates a Reynolds number dependence associated with the lateral boundary layers developing on the fin surfaces. A detailed analysis is conducted to characterize the strength of the vortical structures forming in the near wake. The addition of the fins is shown to produce a stabilizing effect on the roll-up process, associated with a reduction in the generation of smaller scale, three-dimensional structures. The results demonstrate that the addition of fins leads to an increase in the mean drag, which is driven primarily by the associated increase in skin friction. The significant effect of the fin pitch ratio on the characteristics of the shed vortices as well as the size of the vortex formation region is shown to lead to substantial variations in the fluctuating loads.     

Entropy generation in flow field subjected to a porous block in a vertical channel

Entropy generation in the flow field subjected to a porous block situated in a vertical channel is examined. The effects of channel inlet port height (vertical height between channel inlet port and the block center), porosity, and block aspect ratio on the entropy generation rate due to fluid friction and heat transfer in the fluid are examined. The governing equations of flow, heat transfer, and entropy are solved numerically using a control volume approach. Air is used as the flowing fluid in the channel. A uniform heat flux is considered in the block and natural convection is accommodated in the analysis. It is found that entropy generation rate due to fluid friction increases with increasing inlet port height, while this increase becomes gradual for entropy generation rate due to heat transfer for the inlet port height exceeding 0.03 m. The porosity lowers entropy generation rate due to fluid friction and heat transfer. The effect of block aspect ratio on entropy generation rate is notable; in which case, entropy generation rate increases for the block aspect ratio of 1:2.     

Comparative studies on the effect of duct height on heat transfer and flow behavior between co-angular and co-rotating type finned surface

This paper presents the comparative studies on the effect of duct height on heat transfer and flow behavior between co-angular and co-rotating type finned surface in duct. Experiments were performed to investigate the effect of duct height on heat transfer enhancement of a surface affixed with arrays (7 × 7) of short rectangular plate fins of a co-angular and a co-rotating type pattern in the duct. An infrared imaging system with the camera of TVS 8000 was used to measure the temperature distributions to calculate the local heat transfer coefficients of the representative fin regions. Pressure drop and heat transfer experiments were performed for both types of fin pattern varying the duct to fin height ratio (H _d/H _f) of 2.0–5.0. The friction factor calculated from the pressure drop shows that friction factor decreases with increasing the duct to fin height ratio (H _d/H _f) regardless of fin pattern and this is expected because the larger friction occurs for smaller duct to fin height ratios. Detailed heat transfer distribution gives a clear picture of heat transfer characteristics of the overall surface as well as the influence of the duct height. In addition, different flow behavior and flow structure developed by both patterns were visualized by the smoke flow visualization technique.     

Flow through doubly connected ducts

Fluid flow in doubly connected ducts, bounded externally by a circle and internally by a regular polygon of various shapes, is analysed using the finite element method. Hydrodynamically developed, steady, laminar flow of a constant-property fluid is considered. Velocity profiles as well as friction factors (at the inner and outer walls, and average value) are presented. These compare well to previous results available in the literature. Salient characteristics of flow are identified. Correlations for the average friction factor with aspect ratio are suggested.     

Heat transfer performance comparison of steam and air in gas turbine cooling channels with different rib angles

Using steam as working fluid to replace compressed air is a promising cooling technology for internal cooling passages of blades and vanes. The local heat transfer characteristics and the thermal performance of steam flow in wide aspect ratio channels (W/H = 2) with different angled ribs on two opposite walls have been experimentally investigated in this paper. The averaged Nusselt number ratios and the friction factor ratios of steam and air in four ribbed channels were also measured under the same test conditions for comparison. The Reynolds number range is 6,000–70,000. The rib angles are 90°, 60°, 45°, and 30°, respectively. The rib height to hydraulic diameter ratio is 0.047. The pitch-to-rib height ratio is 10. The results show that the Nusselt number ratios of steam are 1.19–1.32 times greater than those of air over the range of Reynolds numbers studied. For wide aspect ratio channels using steam as the coolant, the 60° angled ribs has the best heat transfer performance and is recommended for cooling design.     

Two-dimensional wall temperature measurements and heat transfer enhancement for top-heated horizontal channels with flow boiling

Two-dimensional (circumferential and axial) wall temperature distributions were measured for top-heated coolant channels with internal geometries that include smooth walls, spiral fins and both twisted tape and spiral fins. Freon-71 was the working fluid. The flow regimes studied were single-phase, subcooled flow boiling, and stratified flow boiling. The inside diameter of all test sections was near 10.0 mm. Circumferentially averaged heat transfer coefficients at several axial locations were obtained for selected coolant channels for a volumetric flow rate of 4.738 x 10⁻⁵m³/s, 0.19 MPa (absolute) exit pressure, and 22.2°C inlet subcooling. Overall (averaged over the entire channel) heat transfer coefficients were compared for the various channel geometries. This comparison showed that the channel with large-pitch spiral fins had higher heat transfer coefficients at all power levels. However, the results appear to indicate that if the twist ratio (ratio of the twisted tape period to the inside diameter) is decreased, the configuration employing both fins and a twisted tape will have had greater enhancements.     

A numerical‐variational procedure for laminar flow in curved square ducts

A new numerical method is presented for the solution of the Navier–Stokes and continuity equations governing the internal incompressible flows. The method denoted as the CVP method consists in the numerical solution of these equations in conjunction with three additional variational equations for the continuity, the vorticity and the pressure field, using a non‐staggered grid. The method is used for the study of the characteristics of the laminar fully developed flows in curved square ducts. Numerical results are presented for the effects of the flow parameters like the curvature, the Dean number and the stream pressure gradient on the velocity distributions, the friction factor and the appearance of a pair of vortices in addition to those of the familiar secondary flow. The accuracy of the method is discussed and the results are compared with those obtained by us, using a variation of the velocity–pressure linked equation methods denoted as the PLEM method and the results obtained by other methods. Copyright © 2004 John Wiley & Sons, Ltd.     

Flow and heat transfer in a pipe with a fin attached to inner wall

Enhancement of heat transfer to the fluid can be done by turbulence promoters such as attached fins to the pipe walls. In this study, the flow field and the heat transfer rates were numerically investigated in a pipe with an internally attached fin. Numerical simulations were conducted for four different types of fluids and for different fin heights and locations, and as the Reynolds number was varied, the effects of the fin on Nusselt number and friction factors were investigated. For all the Reynolds numbers considered in this study, the effect of fin location on the heat transfer rate and friction factor was negligible. As the fin height was increased, the mean Nusselt number and the friction factor also increased in the turbulent flow regimes. For low Prandtl number fluids (Pr = 0.011), the main heat transfer mode is conduction, and hence the mean Nusselt number slightly affected the flow rates.     

Pressure drop and heat transfer characteristics of turbulent flow in annular tubes with internal wave-like longitudinal fins

Measured were pressure drop and heat transfer characteristics with uniform axial heat input using air as the working fluid in both the entrance and fully developed regions of annular tubes with wave-like longitudinal fins. Five series of experiments were performed for turbulent flow and heat transfer in the annular tubes with number of waves equal to 4, 8, 12, 16 and 20, respectively. The test tube has a double-pipe structure with the inner blocked tubes as an insertion. The wave-like fins are in the annulus and span its full width. The friction factor and Nusselt number in the fully developed region were obtained. The friction factor and Nusselt number can be well corrected by a power-law correction in the Reynolds number range tested. In order to evaluate the thermal performance of the longitudinal finned tubes over a plain circular tube, comparisons were made under three conditions: (1) identical pumping power; (2) identical pressure drop and (3) identical mass flow. It was found that under the three constraints all the wave-like finned tubes can enhance heat transfer with the tube with wave number 20 being superior. Finally, discussion on the enhancement mechanism is conducted and a general correlation for the fully developed heat transfer is provided, which can cover all the fifty data of the five tubes with a mean deviation of 9.3%.     

Natural convection and conduction heat transfer in open shallow cavities with bounding walls

A numerical study has been carried out on inclined open shallow cavities, which are formed by a wall and horizontal fins. Constant heat flux is applied on the surface of the wall inside the cavity while its other surface was kept isothermal. The wall and the fins are conductive. Conjugate heat transfer by natural convection and conduction is studied by numerically solving equations of mass, momentum and energy. Streamlines and isotherms are produced, heat and mass transfer is calculated. A parametric study is carried out using following parameters: Rayleigh number from 10⁶ to 10¹², conductivity ratio from 1 to 60, open cavity aspect ratio from 1 to 0.125, dimensionless end wall thickness from 0.05 to 0.20, horizontal walls from 0.01 to 0.15 and inclination of the end wall from 90° to 45°. It is found that the volume flow rate and Nusselt number are a decreasing function of the cavity aspect ratio, horizontal fin thickness and conductivity ratio. They are an increasing function of end wall thickness and inclination angle, except in the latter case optima exist at high Rayleigh numbers.     

Natural Convection Heat Transfer Augmentation Factor with Square Conductive Pin Fin Arrays

Natural convection heat transfer from a vertical isothermal plate with pin fins is numerically studied by solving the Navier–Stokes equations along with the energy equation. The average Nusselt number for the plate with different configurations of pin fins is obtained. The average Nusselt number is found to increase with increasing aspect ratio of the fin and to decrease with increasing angle of fin inclination with respect to the plate. There is only a minor difference between the average Nusselt numbers for in-line and staggered arrangement of fins for the range of parameters studied in the present work. A correlation is developed to predict the average Nusselt number of the plate as a function of fin spacing in the streamwise and spanwise directions, aspect ratio of the fin, and its angle of inclination.