Unsteady laminar flow developing in a curved duct

The flow developing in a tightly curved U-bend of square cross section has been investigated experimentally and via numerical simulation. Both long-time averages and time histories of the longitudinal (streamwise) component of velocity were measured using a laser-Doppler velocimeter. The Reynolds number investigated was Re = 1400. The data were obtained at different bend angles, θ, and were confined to the symmetry plane of the bend. At Re = 1400, the flow entering the bend is steady, but by θ = 90° it develops an oscillatory component of motion along the outer-radius wall. Autocorrelations and energy spectra derived from the time histories yield a base frequency of approximately 0.1 Hz for these oscillations. Flow-visualization studies showed that the proximity of the outer-radius wall served to damp the amplitude of the spanwise oscillations.

Numerical simulations of the flow were performed using both steady and unsteady version of the finite-difference elliptic calculation procedure of Humphrey et al. (1977). Although the unsteadiness observed experimentally does not arise spontaneously in the calculations, numerical experiments involving the imposition of a periodic time-dependent perturbation at the inlet plane suggest that the U-bend acts upon the incoming flow so as to damp the amplitude of the imposed oscillation while altering its frequency.

The oscillations observed experimentally, and numerically as a result of the periodic perturbation, have been linked to the formation of Goertler-type vortices of the outer-radius wall in the developing flow. The vortices, which develop as a result of the centrifugal instability of the flow on the outer-radius wall, undergo a further transition to an unsteady regime at higher flow rates.     

Slip flow in an annular sector duct using radial eigenfunctions

The fully developed slip flow in an annular sector duct is solved by expansions of eigenfunctions in the radial direction and boundary collocation on the straight sides. The method is efficient and accurate. The flow field for slip flow differs much from that of no-slip flow. The Poiseuille number increases with increased inner radius, opening angle, and decreases with slip.     

Unsteady unidirectional flow of a Voigt fluid in the circular duct with different prescribed volume flow rate conditions

In the present study, the velocity profile and pressure gradient of the unsteady state unidirectional flow of a Voigt fluid in a circular duct with different prescribed volume flow rate are investigated. The flow motion in the duct is induced by a prescribed inlet volume flow rate which varies with time. Based on the flow conditions prescribed, two basic flow situations are solved; these are a suddenly started, and a constant accelerated, flow respectively. These two results are then applied to a practical case that is a trapezoidal motion which contains three phases of piston motion, the constant acceleration from the rest to a fixed velocity, then maintaining at this velocity, following with the constant deceleration to a stop. In addition, oscillatory flow is also considered.     

Unsteady unidirectional flow of an Oldroyd-B fluid in a circular duct with different given volume flow rate conditions

In this paper, the velocity profile and pressure gradient of the unsteady state unidirectional flow of an Oldroyd-B fluid in a circular duct are considered. The flow motion in the duct is induced by a given but arbitrary inlet volume flow rate which varies with time. Based on the flow conditions described, two basic flow situations are solved, which are a suddenly started, and a constant acceleration, flow respectively. These two results are applied to a practical case that is a trapezoidal piston motion which contains three phases of piston motion, the constant acceleration from the rest to a fixed velocity, then keeping at this velocity, following with the constant deceleration to a stop. In addition, oscillatory flow is also considered.     

Development characteristics of drag-reducing surfactant solution flow in a duct

Development characteristics of dilute cationic surfactant solution flow have been studied through the measurements of the time characteristics of surfactant solution by birefringence experiments and of the streamwise mean velocity profiles of surfactant solution duct flow by a laser Doppler velocimetry system. For both experiments, the concentration of cationic surfactant (oleylbishydroxymethylethylammonium chloride: Ethoquad O/12) was kept constant at 1000 ppm and the molar ratio of the counter ion of sodium salicylate to the surfactants was at 1.5. From the birefringence experiments, dilute surfactant solution shows very long retardation time corresponding to micellar shear induced structure formation. This causes very slow flow development of surfactant solution in a duct. Even at the end of the test section with the distance of 112 times of hydraulic diameter form the inlet, the flow is not fully developed but still has the developing boundary layer characteristics on the duct wall. From the time characteristics and the boundary layer development, it is concluded that the entry length of 1000 to 2000 times hydraulic diameter is required for fully developed surfactant solution flow.List of abbreviations and symbols A₁, A₂ Coefficients for time constant fitting [-] - B Breadth of the test duct [m] - C₁, C₂ Coefficients for time constant fitting [-] - D Pipe diameter [m] - D_H Hydraulic diameter [m] - g Impulse response function [Pa] - H Width of the test duct [m] - n Index of Bird-Carreau model [-] - Re Reynolds number (=U_mD_H/) - Re_D Pipe Reynolds number (=U_mD/) - Re_x Streamwise distance Reynolds number (=U₀x/) - T Absolute temperature [K] - t Time [s] - t_a Retardation time [s] - t_b Build-up time [s] - t_x Relaxation time [s] - t_x1, t_x2 Relaxation time for double time constant fitting [s] - t Time constant in Bird-Carreau model [s] - U Time mean velocity [m/s] - U_m Bulk mean velocity [m/s] - U_max Maximum velocity in a pipe [m/s] - U₀ Main flow velocity [m/s] - u Friction velocity [m/s] - x, y Coordinates [m] - Shear rate [s^–1] - Mean shear rate [s^–1] - n Birefringence [-] - 99% boundary layer thickness [m] - Solution viscosity [Pa·s] - _P, _S Surfactant and solvent viscosity [Pa·s] - ₀, Zero and infinite viscosity of Bird-Carreau model [Pa·s] - Characteristic time in Maxwell model [s] - Water kinematic viscosity [m²/s] - Density [kg/m³] - Solution shear stress [Pa] - _P, _S Surfactant and solvent shear stress [Pa] - Time in convolution [s]     

Development characteristics of fluctuating velocity field of drag-reducing surfactant solution flow in a duct

Development behavior of the fluctuating velocity of surfactant solution in a duct has been studied experimentally. The concentration of surfactants was kept constant at 1,000 ppm, mean velocity at 0.78 m/s and fluid temperature at 15 °C. Using laser Doppler velocimetry, the fluctuating streamwise velocity distributions at six cross sections, which ranged from 14 to 112 times of hydraulic diameter of the duct, were measured. From the results, the fluctuating structures of surfactant solution flow are observed to have structures different from that of turbulent water flow in the developing field. The wavelet analysis reveals that the high-level fluctuation of surfactant solution flow is characterized by periodicity rather than irregularity around the position where the fluctuation intensity takes a peak value and that the period and the scale of periodic flow structures are related to the relaxation times of the fluid. This indicates that the high-level fluctuation is deeply related to the elastic instability and has a different generation mechanism from that of turbulence observed in a Newtonian turbulent flow.     

Numerical simulation of flow in a circular duct fitted with air‐jet vortex generators

Most of the fundamental studies of the use of air‐jet vortex generators (AJVGs) have concentrated on their potential ability to inhibit boundary layer separation on aerofoils. However, AJVGs may be of use in controlling or enhancing certain features of internal duct flows. For example, they may be of use in controlling the boundary layer at the entrance to engine air intakes, or as a means of increasing mixing and heat transfer. The objective of this paper is to analyse the flow field in the proximity of an air‐jet vortex generator array in a duct by using two local numerical models, i.e. a simple flat plate model and a more geometrically faithful sector model. The sector model mirrors the circular nature of the duct's cross‐section and the centre line conditions on the upper boundary. The flow was assumed fully turbulent and was solved using the finite volume, Navier–Stokes Code CFX 4 (CFDS, AEA Technology, Harwell) on a non‐orthogonal, body‐fitted, grid using the k–ε turbulence model and standard wall functions. Streamwise, vertical and cross‐stream velocity profiles, circulation and peak vorticity decay, peak vorticity paths in cross‐stream and streamwise direction, cross‐stream vorticity profiles and cross‐stream wall shear stress distributions were predicted. Negligible difference in results was observed between the flat plate and the sector model, since the produced vortices were small relative to the duct diameter and close to the surface. The flow field was most enhanced, i.e. maximum thinning of the boundary layer, with a configuration of 30° pitch and 75° skew angle. No significant difference in results could be observed between co‐ and counter‐rotating vortex arrays. Copyright © 2002 John Wiley & Sons, Ltd.     

On Stokes slip flow through a transversely wavy channel

The Stokes flow through a wavy or corrugated channel with surface slip is studied. The correct Navier's partial slip condition is applied and perturbation solutions about the small amplitude to channel width ratio are obtained. As in Stokes slip flow over a sphere, the resistance is not zero even when slip is infinite. The resistance (due to the interaction of waviness and slip) is larger when the corrugations of the two plates are out of phase than that when they are in phase.     

Unsteady circulatory flow about a circular cylinder with suction

Summary The complete Navier-Stokes equations which describe the unsteady flow of a viscous incompressible fluid when an infinite circular cylinder is given an impulsive twist, and simultaneously a constant suction velocity is imposed on the cylinder, are integrated using Laplace transforms. It is found that points which are at a greater distance from the cylinder are nearer to steadiness than points which are closer to the cylinder. Unsteady flow through a concentric annulus has also been considered.     

Unsteady compressible flow in long pipelines following a rupture

The unsteady frictional flow of a compressible fluid generated in a long pipeline after an accidental rupture is of considerable interest to the offshore gas industry. It answers several important questions concerning safety and pollution, e.g. the flow rate at the broken pipe end. Laboratory tests cannot simulate the rather complex phenomenon satisfactorily. The problem is highly non-linear and no general analytical solution is yet known. In this study, based on computational fluid dynamics, the simplifying assumptions of isothermal and low Mach number flow often applied in the case of unsteady compressible flows in pipelines, have not been used. Owing to the choking condition (Ma=1) which prevails for some time at the broken end. and the cumulative effect of friction over the 145 km long pipeline, we obtain (?p/?x)^t→?∞. This analytically established singularity leads to numerical difficulties which seriously affect the accuracy. For short tubes (such as shock tubes) this negative feature is much less severe. Special procedures were necessary to keep the accuracy within the chosen limit of 1 per cent.     

Effect of radius of toroidal square duct on the transition of electromagnetically driven liquid metal flow

Toroidal magnetohydrodynamic flows are important for fusion technology because of the blanket surrounding the core of the fusion machine. The effect of the radius of toroidal square ducts on flow transition of an electromagnetically driven liquid metal is assessed. The flow governing equations are solved numerically using direct numerical simulation. Critical Reynolds (Re) numbers where transition occurs are obtained for Hartmann (Ha) numbers in the range of 3 < Ha < 500. The results are compared with previous experimental and numerical results of toroidal square ducts of various radii. It is shown that, independent of the toroidal duct mean radius (r), the transition occurs in three regimes: in the sub-magnetohydrodynamic regime for very low Ha numbers, in a plateau regime for 10 < Ha < 20 and in a higher Ha regime. By increasing the radius of the torus, a transition occurs at higher Reynolds numbers as turbulent fluctuations are developing inside the boundary layers of the cylindrical side walls. The results indicate that transition occurs at $\frac{Re}{\sqrt{r}}H̃a^{-3.39}$ in the sub-magnetohydrodynamic regime and at $\frac{Re}{\sqrt{r}}H̃a^{-1.4}$ in the magnetohydrodynamic one. The boundary layer thickness at the Hartmann walls were found to scale as ${\mathit{Ha}}^{-0.8}$.     

Numerical analysis of the developing fluid flow in a circular duct rotating steadily about a parallel axis

A numerical analysis of the flow pattern in the inlet region of a circular pipe rotating steadily about an axis parallel to its own is presented. Both finite cell and finite element methods are used to analyse the problem and they give qualitatively similar results which show that a swirling fluid motion is induced in the pipe inlet region. The analyses show that the direction of swirl is opposite to that of the pipe rotation when viewed along the flow axis and that its magnitude depends on the speed of pipe rotation and throughflow Reynolds number. Neither numerical analysis predicts the marked upturn in friction factor (or pressure drop) which has been observed experimentally. However, a dependence on the pipe inlet boundary conditions is demonstrated.     

Turbulent flow in a duct with cusped corners

An orthogonal-cuvilinear-mesh-based finite volume calculation method has been applied to the problem of fully developed turbulent flow in the tri-cusped cornered duct formed when parallel circular rods touch in triangular array. Algebraic stress relations combined with the k-? turbulence model are used for calculation of the required stresses. A single circulation of turbulence-driven cross-plane secondary flow from the core into the duct corner has been predicted in a one-sixth symmetry region of the duct and the convective transport effects of this flow are seen to have much influence on local mean flow distributions. The turbulence field predicted by the k-? model showed significant damping in the cusped corner region where turbulent viscosities approached the laminar value. Satisfactory agreement was obtained with the limited local and overall mean flow measurements available.     

Two-phase flow of R-134a refrigerant during flow boiling through a horizontal circular mini-channel

This research focuses on heat transfer to R-134a during flow boiling in a 1.75 mm internal diameter tube. Flow visualisation and heat transfer experiments are conducted to obtain heat transfer coefficients for different flow patterns. The measured data in each flow regime are compared with predictions from a three-zone flow boiling model. The calculations are in fair agreement with the experimental results which correspond in particular to slug flow, throat-annular flow and churn flow regimes under conditions of low heat flux.     

Investigation of a combustion driven oscillation in a refinery flare: Part B: Visualisation of a periodic flow instability in a bifurcating duct following a contraction

A flow visualisation study was performed to investigate a periodic flow instability in a bifurcating duct within the tip of the flares at the Shell refinery in Clyde, NSW, to verify the trigger of a combustion-driven oscillation proposed in Part A of this study, and to identify its features. The model study assessed only the flow instability, uncoupled from the acoustic resonance and the combustion that are also present in the actual flare. Three strong, coupled flow oscillations were found to be present in three regions of the fuel line in the flare tip model. A periodic flow separation was found to occur within the contraction at the inlet to the tip, a coupled, periodic flow oscillation was found in the two transverse “cross-over ducts” from the central pipe to the outer annulus and an oscillating flow recirculation was present in the “end-cap” region of the central pipe. The dimensionless frequency of these oscillations in the model was found to match that measured in the full-scale plant for high fuel flow rates. This, and the strength of these flow oscillations, gives confidence that they are integral to the full-scale combustion-driven oscillation and most likely the primary trigger. The evidence indicates that the periodic flow instability is initiated by the separation and roll-up of the annular boundary layer at the start of the contraction in the fuel section of the flare tip. The separation generates an annular vortex which interacts with the blind-ended pipe downstream, leading to a pressure wave which propagates back upstream, initiating the next separation event and repeating the cycle. The study also investigated flow control devices with a view to finding a practical approach to mitigate the oscillations. The shape of these devices was constrained to allow installation without removing the tip of the flare. This aspect of the study highlighted the strength and nature of the coupled oscillation, since it proved to be very difficult to mitigate the oscillation in this way. An effective configuration is presented, comprising of three individual components, all three of which were found to be necessary to eliminate the oscillation completely.     

Gas-particle two-phase turbulent flow in a vertical duct

Two-phase gas-phase turbulent flows at various loadings between the two vertical parallel plates are analyzed. A thermodynamically consistent turbulent two-phase flow model that accounts for the phase fluctuation energy transport and interaction is used. The governing equation of the gas-phase is upgraded to a two-equation low Reynolds number turbulence closure model that can be integrated directly to the wall. A no-slip boundary condition for the gas-phase and slip-boundary condition for the particulate phase are used. The computational model is first applied to dilute gas-particle turbulent flow between two parallel vertical walls. The predicted mean velocity and turbulence intensity profiles are compared with the experimental data of Tsuji et al. (1984) for vertical pipe flows, and good agreement is observed. Examples of additional flow properties such as the phasic fluctuation energy, phasic fluctuation energy production and dissipation, as well as interaction momentum and energy supply terms are also presented and discussed.

Applications to the relatively dense gas-particle turbulent flows in a vertical channel are also studied. The model predictions are compared with the experimental data of Miller & Gidaspow and reasonable agreement is observed. It is shown that flow behavior is strongly affected by the phasic fluctuation energy, and the momentum and energy transfer between the particulate and the fluid constituents.     

High speed cine observations of cavitating flow in a duct

The dynamics of cavities produced in cavitating flow confined in a duct was studied. The ultimate purpose of the work is to develop models of the flow to assist in predicting cavitation erosion and noise. Observations of the cavitating flow using high speed cine photography allowed confirmation to be made of the shedding mechanism originally described by Knapp, and measurements of the cavity dimensions to be determined as a function of time. It was found that the time for a cavity to collapse was found three times greater than expected from Rayleigh's classical theory.     

Influence of temperature dependent conductivity of a nanofluid in a vertical rectangular duct

Natural convective heat transfer and fluid flow in a vertical rectangular duct filled with a nanofluid is studied numerically assuming the thermal conductivity to be dependent on the fluid temperature. The transport equations for mass, momentum and energy formulated in dimensionless form are solved numerically using finite difference method. Particular efforts have been focused on the effects of the thermal conductivity variation parameter, Grashof number, Brinkman number, nanoparticles volume fraction, aspect ratio and type of nanoparticles on the fluid flow and heat transfer inside the cavity. It is found that the flow was enhanced for the increase in Grashof number, Brinkman number and aspect ratio for any values of conductivity variation parameter and for regular fluid and nanofluid. The heat transfer rate for regular fluid is less than that for the nanofluid for all governing parameters.     

Unsteady heat and mass transfer in MHD flow over an oscillatory stretching surface with Soret and Dufour effects

In this paper, we study the unsteady coupled heat and mass transfer of two-dimensional MHD fluid over a moving oscillatory stretching surface with Soret and Dufour effects. Viscous dissipation effects are adopted in the energy equation. A uniform magnetic field is applied vertically to the flow direction. The governing equations are reduced to non-linear coupled partial differential equations and solved by means of homotopy analysis method （HAM）. The effects of some physical parameters such as magnetic parameter, Dufour number, Soret number, the Prandtl num- ber and the ratio of the oscillation frequency of the sheet to its stretching rate on the flow and heat transfer characteristics are illustrated and analyzed.     

A review on flow energy harvesters based on flapping foils

This article presents an overview of the state of the art investigations on the recently developed oscillating foil energy converters. A summary of available knowledge and up-to-date progress in the application of such bio-inspired systems for renewable energy devices is provided. Starting from concepts and achieved results in three distinguishable categories, various parametric studies are reviewed, along with an in-depth discussion on the potential device performance enhancement via flow control mechanisms. Finally, potential future research directions are discussed.