Numerical study of hysteresis in annular swirling jets with a stepped‐conical nozzle

This study investigates the experimentally observed hysteresis in the mean flow field of an annular swirling jet with a stepped‐conical nozzle. The flow is simulated using the Reynolds‐averaged Navier–Stokes (RANS) approach for incompressible flow with a k–ε and a Reynolds stress transport (RSTM) turbulence model. Four different flow structures are observed depending on the swirl number: ‘closed jet flow’, ‘open jet flow low swirl’, ‘open jet flow high swirl’ and ‘coanda jet flow’. These flow patterns change with varying swirl number and hysteresis at low and intermediate swirl numbers is revealed when increasing and subsequently decreasing the swirl. The influence of the inlet velocity profile on the transitional swirl numbers is investigated. When comparing computational fluid dynamics with experiments, the results show that both turbulence models predict the four different flow structures and the associated hysteresis and multiple solutions at low and intermediate swirl numbers. Therefore, a good agreement exists between experiments and numerics. Copyright © 2006 John Wiley & Sons, Ltd.     

Formation of Coanda jet from sharp-edged swirl nozzle with base plate

Experiments were conducted using tufts and PIV to determine the conditions for which a swirled gas jet issuing from a sharp-edge nozzle, in flush with a base plate, would form a Coanda jet. The flow field was also simulated. The inception of the Coanda jet was observed to be associated with the formation of a recirculation bubble at the nozzle exit. A threshold value of swirl number, which increased monotonically with Reynolds number, was required for the formation of the Coanda jet. The Coanda jet was associated with hysteresis. The flow features and transition from a diverging jet to a Coanda jet are discussed.     

Effect of Spherical Recesses on the Characteristics of Coanda Flow

Sub- and supersonic flows past curvilinear surfaces with spherical recesses are investigated. The Coanda flow was created by a jet flowing out from a plane convergent nozzle into a submerged space along the tangent to a circular cylinder. The forces exerted on the cylinder and the total and static pressure profiles in Coanda jet cross-sections were measured. It is shown that the spherical recesses increase the friction drag at both sub- and supersonic velocities.     

Reynolds stress modelling of jet and swirl interaction inside a gas turbine combustor

Influences of the inlet swirl levels on the interaction between the dilution air jets and the swirling cross‐flow to the interior flow field inside a gas turbine combustor were investigated numerically by Reynolds stress transport model (RSTM). Due to the intense swirl and jet interaction, a high level of swirl momentum is transported to the centreline and hence, an intense vortex core is formed. The strength of the centreline vortex core was found to depend on the inlet swirl levels. For the higher swirling inlet, the decay of the swirling motion causes strong streamline variation of pressure; and consequently leads to an elevated level of deceleration of its axial velocity. Predictions contrasted with measurements indicate that the stress model reproduces the flow correctly and is able to reflect the influences of inlet swirl levels on the interior flow structure. Copyright © 1999 John Wiley & Sons, Ltd.     

Numerical investigation of a perturbed swirling annular two-phase jet

A swirling annular gas–liquid two-phase jet flow system has been investigated by solving the compressible, time-dependent, non-dimensional Navier–Stokes equations using highly accurate numerical methods. The mathematical formulation for the flow system is based on an Eulerian approach with mixed-fluid treatment while an adjusted volume of fluid method is utilised to account for the gas compressibility. Surface tension effects are captured by a continuum surface force model. Swirling motion is applied at the inlet while a small helical perturbation is also applied to initiate the instability. Three-dimensional spatial direct numerical simulation has been performed with parallelisation of the code based on domain decomposition. The results show that the flow is characterised by a geometrical recirculation zone adjacent to the nozzle exit and by a central recirculation zone further downstream. Swirl enhances the flow instability and vorticity and promotes liquid dispersion in the cross-streamwise directions. A dynamic precessing vortex core is developed demonstrating that the growth of such a vortex in annular configurations can be initiated even at low swirl numbers, in agreement with experimental findings. Analysis of the averaged results revealed the existence of a geometrical recirculation zone and a swirl induced central recirculation zone in the flow field.     

Jet impingement onto a cylindrical cavity: consideration of annular nozzle cone angles,and cavity diameter

In the present study, gas jet emerging from an annular nozzle and impinging onto a cylindrical cavity is considered. The geometric configuration of the nozzle is varied in the simulations. Air is used as impinging gas while stainless steel is considered as workpiece material. Reynolds turbulence model is accommodated to account for the turbulence. A numerical scheme employing a control volume approach is used to simulate the flow field. Heat transfer characteristic and shear stress distribution around the cavity are computed. It is found that outer cone angle of the annular nozzle influences the heat transfer rates from the cavity wall. The flow structure around the cavity changes significantly with increasing cavity diameter. Moreover, increasing cavity depth results in stagnation zone moving into the cavity.     

Swirling and Impinging Effects in an Annular Nonpremixed Jet Flame

The effects of swirl and downstream wall confinement on an annular nonpremixed flame were investigated using direct numerical simulation (DNS). Fully three-dimensional parallel DNS was performed employing high-order numerical methods and high-fidelity boundary conditions to solve governing equations for variable-density flow and finite-rate Arrhenius chemistry. Three swirl numbers have been examined: 0 (without swirl), 0.4 and 0.8, while the effects of downstream wall confinement have been examined for swirl numbers 0 and 0.4. Results have been presented in terms of instantaneous and time-averaged flow quantities, which have also been analysed using energy spectra and proper orthogonal decomposition (POD). Effects of swirl on the fluid dynamic behaviour of the annular nonpremixed flame were found to be significant. The fluid dynamic behaviour of the flame is greatly affected by the interaction between the geometrical recirculation zone (GRZ) near the jet nozzle exit due to the annular configuration, the central recirculation zone (CRZ) associated with swirl, the unsteady vortical structures in the jet column due to the shear instability, and the downstream wall confinement. Depending on the degree of swirl, the GRZ near the burner mouth and the CRZ may co-exist or one zone may be overwhelmed by another. At a moderate swirl number, the co-existence leads to a flame with strong reaction attached to the burner mouth; while at a high swirl number, the CRZ dominates over the GRZ. The precessing vortex core was observed to exist in the swirling flow fields. The Nusselt number distribution of the annular impinging flames differs from that of round impinging jets. The POD analysis revealed that wall effects on the flow field are mainly associated with the higher mode numbers.     

Numerical simulations of negatively buoyant jets in an immiscible fluid using the Particle Finite Element Method

Negatively buoyant jets consist in a dense fluid injected vertically upward into a lighter ambient fluid. The numerical simulation of this kind of buoyancy‐driven flows is challenging as it involves multiple fluids with different physical properties. In the case of immiscible fluids, it requires, in addition, to track the motion of the interface between fluids and accurately represent the discontinuities of the flow variables. In this paper, we investigate numerically the injection of a negatively buoyant jet into a homogenous immiscible ambient fluid using the Particle Finite Element Method and compare the two‐dimensional numerical results with experiments on the injection of a jet of dyed water through a nozzle in the base of a cylindrical tank containing rapeseed oil. In both simulations and experiments, the fountain inlet flow velocity and nozzle diameter have been varied to cover a wide range of Froude Fr and Reynolds Re numbers ( 0.1 < Fr < 30, 8 < Re < 1350), reproducing both weak and strong laminar fountains. The flow behaviors observed for the different numerical simulations fit in the regime map based on the Re and Fr values of the experiments, and the maximum fountain height is in good agreement with the experimental observations, suggesting that particle finite element method is a useful tool for the study of immiscible two‐fluid systems. Copyright © 2011 John Wiley & Sons, Ltd.     

Correlation of swirl number for a radial-type swirl generator

An experimental investigation was undertaken to derive a new correlation for the swirl number of a radial-type swirl generator under various Reynolds numbers and various vane angle conditions. A radial-type swirl generator with 16 rotary guide vanes was used to generate an annular swirling jet flow. The Reynolds numbers ranged from 60 to 6000, and the vane angles from 0° to 56°. Quantitative measurements for the velocities were made by using an optical method of laser-Doppler anemometry (LDA). Three-component velocity profiles of axial, radial, and azimuthal components at the swirling jet exit were measured for various flow conditions. A flow visualization method using smoke-wire and still photography was also applied to observe the flow patterns of the recirculation region behind the circular bluff body. Under low Reynolds number conditions, the swirl strength was found to be strongly dependent on the Reynolds number as well as on the guide vane angle. Based on the experimental results, a modified swirl number S is derived to characterize the swirling flow, which is useful for the design of a swirl generator.     

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.     

Hysteresis phenomena in a plane rotatable nozzle

The flow in a rotatable nozzle is calculated within the framework of the Reynolds equations and the Spalart-Allmaras turbulence model on the pressure difference range 1.1 < π < 5 for four configurations of the nozzle with the area ratio ε = 1.52 and two angles of the nozzle axis rotation. The flow structure is determined and the thrust characteristics and the angles of the thrust vector rotation are obtained. It was found that in the overexpansion regime the flows in plane symmetric and rotatable nozzles involve hysteresis phenomena due the Coanda effect and the interaction between the boundary layer and a shock generated within the nozzle on its supersonic walls. The hysteresis phenomena detected provide an up-to-4% divergence in the thrust coefficient for the same problem parameters. The results of the numerical modeling are compared with the experimental data and the results of calculations in accordance with Sekundov’s model.     

Parametric Study of Alternating Flow Patterns in Non-Reacting Multiple-Swirl Flows

Multiple nozzle combustors, under certain conditions, may result in flowfields that differ between nozzles in an alternating pattern. Previous work has provided some clues on the parameters which govern the appearance of this behavior, but there is a lack of systematic studies. A series of non-reacting simulations of adjacent swirling flows is used to investigate the effect of nozzle exit flare angle and swirl number on the presence of the alternating flow pattern. Two-nozzle simulations are shown to accurately predict if an asymmetric flow characteristic appears and are therefore used in the parametric investigation. Alternating flow patterns are predicted at nozzle exit flare angles of 105 degrees (for a swirl number of 0.79) and 120 degrees (for a swirl number of 0.69 and 0.79). Under conditions close to the stability boundary between symmetric and asymmetric flows, the nozzle exit flare and increased swirl number push the shear layers against the dome wall so that the flows between each nozzle are largely opposite in direction. An increase in nozzle exit flare above 120^° results in separated flows exiting from the inlet and a return to a symmetric flow state. This is consistent with a proposed physical mechanism based on hydrodynamic stability in turbulent opposed jets.     

On coherent structures and mixing characteristics in the near field of a rotating-pipe jet

Mixing characteristics and coherent structures populating the near-nozzle area of a rotating-pipe jet at the Reynolds number of 5300 were studied by Large-eddy simulation (LES). The swirl rate, defined as the ratio of the tangential velocity of the inner pipe wall to the bulk axial velocity, varied from 0 to 1, corresponding to a weak-to-moderate swirl intensity, insufficient to induce reverse flow near the nozzle. The visualization shows that for the non-swirling jet the near-wall streaky structures generated in the pipe interact with the shear layer, evolving into hairpin-like structures that become tilted at low rotation rates. For higher swirl, they cannot be recognized as they are destroyed at the nozzle exit. No large-scale coherent structures akin to Kelvin–Helmholtz vortical rings in the ‘top-hat’ jets are identifiable close to the nozzle. Using the single and joint probability density functions of velocity and passive scalar (temperature) fields we quantify the events responsible for the intensive entrainment at various swirl numbers. The isosurface of the temperature field indicates the meandering and precessing motion of the rotating jet core at the axial distance of 6D downstream, where D is the diameter of the pipe. The Fourier analysis with respect to the azimuthal angle and time reveals an interplay between the co- and counter-rotating modes. These findings explain the previously detected but not fully clarified phenomenon of the weakly counter-rotating jet core at low swirl rates.     

Flow in a simple swirl chamber with and without controlled inlet forcing

Results are presented from a swirl chamber with and without controlled inlet forcing. The controlled inlet forcing is induced using arrays of vortex generators placed along one wall of the swirl chamber inlet duct. Flow visualization results are given, along with surveys of circumferential mean velocity, static pressure, and total pressure, at Reynolds numbers (based on inlet duct characteristics) as high as 8000. The controlled inlet forcing provides means to alter and control: (i) the spacing and number of Görtler vortices across the span of the swirl chamber, (ii) the amount of vortex development at a particular Reynolds number and circumferential location, (iii) the circumferential location and Reynolds number of initial Görtler vortex development, and (iv) the circumferential location and Reynolds number of Görtler vortex breakup into more chaotic flow.     

A numerical study of an annular liquid jet in a compressible gas medium

An annular liquid jet in a compressible gas medium has been examined using an Eulerian approach with mixed-fluid treatment. The governing equations have been solved by using highly accurate numerical methods. An adapted volume of fluid method combined with a continuum surface force model was used to capture the gas–liquid interface dynamics. The numerical simulations showed the existence of a recirculation zone adjacent to the nozzle exit and unsteady large vortical structures at downstream locations, which lead to significant velocity reversals in the flow field. It was found that the annular jet flow is highly unstable because of the existence of two adjacent shear layers in the annular configuration. The large vortical structures developed naturally in the flow field without external perturbations. Surface tension tends to promote the Kelvin–Helmholtz instability and the development of vortical structures that leads to an increased liquid dispersion. A decrease in the liquid sheet thickness resulted in a reduced liquid dispersion. It was identified that the liquid-to-gas density and viscosity ratios have opposite effects on the flow field with the reduced liquid-to-gas density ratio demoting the instability and the reduced liquid-to-gas viscosity ratio promoting the instability characteristics.     

Size of annular separation bubble around the inlet corner and viscous flow structure between two parallel disks

The annular separation bubble around the inlet corner and the radial flow between two parallel disks were investigated by means of flow visualization and numerical simulations to gain an understanding of the features of axisymmetric separation and reattachment in the inlet region. For the case with a sharp corner, the radius of the reattachment point depends only on clearance ratio, independent of Reynolds number in the turbulent flow regime where the reattachment point fluctuates randomly. For the cases with a rounded corner, the radius of reattachment point and the height of the bubble decrease with increasing corner roundness. Received: 23 January 2001 / Accepted: 31 August 2001     

Transient effects of orthogonal pipe oscillations on laminar developing incompressible flow

This paper presents a numerical study of the transient developing laminar flow of a Newtonian incompressible fluid in a straight horizontal pipe oscillating around the vertical diameter at its entrance. The flow field is influenced by the tangential and Coriolis forces, which depend on the through‐flow Reynolds number, the oscillation Reynolds number and the angular amplitude of the pipe oscillation. The impulsive start of the latter generates a transient pulsating flow, whose duration increases with axial distance. In any cross‐section, this flow consists of a pair of symmetrical counter‐rotating vortices, which are alternatively clockwise and anti‐clockwise. The circumferentially averaged friction factor and the axial pressure gradient fluctuate with time and are always larger than the corresponding values for a stationary pipe. On the other hand, local axial velocities and local wall shear stress can be smaller than the corresponding stationary pipe values during some part of the pipe oscillation. The fluctuation amplitude of these local variables increases with axial distance and can be as high as 50% of the corresponding stationary pipe value, even at short distances from the pipe entrance. Eventually, the flow field reaches a periodic regime that depends only on the axial position. The results show that the transient flow field depends on the pipe oscillation pattern (initial position and/or direction of initial movement). Copyright © 2000 John Wiley & Sons, Ltd.     

环形通道内湍流旋流流动的数值模拟

本文应用一种考虑湍流－旋流相互作用及湍流脉动各向异性的新的代数Ｒｅｙｎｏｌｄｓ应力模型,对环形通道内的湍流旋流流动进行了数值模拟,研究了改主为旋流流数,进口轴向速度及半径比等参数对环形通道内湍流流动的影响,以及对强化环形通道内传热的作用。     

Flow in a viscous jet escaping through a supersonic nozzle into a semi-infinite ambient space

The problem of an axisymmetric gas flow in a supersonic nozzle and in the jet escaping from the nozzle to a quiescent gas is solved within the framework of Navier-Stokes equations. The calculated pressure distribution is compared with that measured in the jet by a Pitot tube. The influence of the jet pressure ratio, Reynolds number, and half-angle of the supersonic part of the nozzle on nozzle flow and jet flow parameters is studied. It is shown that the distributions of gas-dynamic parameters at the nozzle exit are nonuniform, which affects the jet flow. The flow pattern for an overexpanded jet shows that jet formation begins inside the nozzle because of boundary-layer displacement from the nozzle walls. This result cannot be obtained with the inviscid formulation of the problem.     

An experimental study of the under-expanded swirling jet with secondary coaxial stream

The present study addresses experimental results for investigating the details of the near field flow characteristics produced in an under-expanded, dual, coaxial, swirling jet. The under-expanded swirling jet is discharged from a sonic inner nozzle. An outer annular nozzle produces co- and counter-swirling streams relative to the inner primary swirling jet. The interaction between both the outer annular swirling stream and inner under-expanded swirling jet is quantified by impact and static pressure measurements, and visualized by using the shadowgraph method. Experiments are performed for several different pressure ratios. The results show that the outer secondary co-swirling jet significantly changes the structure of the inner under-expanded swirling jet, such as the shock structures and the recirculation region generated at the jet axis. The effect of the outer secondary stream on the major structures of the inner primary swirling jet is strongly dependent on the pressure ratio of the inner swirling jet, regardless of the swirl direction of the outer stream.Received: 17 May 2004, Accepted: 27 September 2004, Published online: 26 November 2004[/PUBLISHED]H.D. Kim: Correspondence to