Numerical simulation of tangentially injected turbulent swirling flow in a divergent tube

This paper studies the properties of turbulent swirling decaying flow induced by tangential inlets in a divergent pipe using the realizable k–ε turbulence model and discusses the effects of the injector pressure and injection position. The results of transient solutions show that both the recirculation zone near the wall in upstream of the injectors and the vortex breakdown in downstream of the injectors increase in size during the whole period. A nearly axisymmetric conical breakdown is formed and its internal structure consists of two asymmetric spiral‐like vortices rotating in opposite directions. The stagnation point shifts slowly toward the pipe outlet over time. The maxima of the three velocity components, which are located near the wall, decrease gradually with streamwise direction. It can also be inferred that Mach number approaches 1.0 near the injector outlets. The velocities increase with the increasing injector pressure. However, its increasing trend is not significant. With the increase of the injection position, vortex breakdown moves in downstream direction and the pitch along the streamwise direction increases. Copyright © 2008 John Wiley & Sons, Ltd.     

3D tangentially injected swirling recirculating flow in a nozzle with a slotted‐tube—Effects of groove parameters

A numerical prediction for 3D swirling recirculating flow in an air‐jet spinning nozzle with a slotted‐tube is carried out with the realizable k–ε turbulence model. The effects of the groove parameters on the flow and yarn properties are investigated. The simulation results show that some factors, such as reverse flow upstream of the injector, vortex breakdown downstream of the injector, corner recirculation zone (CRZ) behind the step and vortex ring in the groove caused by the groove geometric variation, are significantly related to fluid flow, and consequently to yarn properties. With increasing groove height, the length of the CRZ increases, while the initial vortex ring in the groove decreases and a same direction rotating vortex forms in the bottom of the groove. Similarly, as the groove width increases, the extent of both vortex breakdown in downstream of the injectors and the vortex ring in the groove increases slightly, whereas the CRZ lengths in stream‐wise direction decrease. Some factors, such as the negative tangential velocities, the size of the vortex rings in the grooves and the CRZ, are constant for nozzles with different groove lengths. Copyright © 2009 John Wiley & Sons, Ltd.     

Numerical simulation of turbulent impinging jet on a rotating disk

The calculations of quasi‐three‐dimensional momentum equations were carried out to study the influence of wall rotation on the characteristics of an impinging jet. The pressure coefficient, the mean velocity distributions and the components of Reynolds stress are calculated. The flow is assumed to be steady, incompressible and turbulent. The finite volume scheme is used to solve the continuity equation, momentum equations and k–ε model equations. The flow characteristics were studied by varying rotation speed ω for 0?ω?167.6 rad/s, the distance from nozzle to disk (H/d) was (3, 5, 8 and 10) and the Reynolds number Re base on V_J and d was 1.45 × 10⁴. The results showed that, the radial velocity and turbulence intensity increase by increasing the rotation speed and decrease in the impingement zone as nozzle to disk spacing increases. When the centrifugal force increases, the radial normal stresses and shear stresses increase. The location of maximum radial velocity decreases as the local velocity ratio (α) increases. The pressure coefficient depends on the centrifugal force and it decreases as the distance from nozzle to plate increases. In impingement zone and radial wall jet, the spread of flow increases as the angular velocity decreases The numerical results give good agreement with the experiment data of Minagawa and Obi (Int. J. of Heat and Fluid Flow 2004; 25 :759–766). Copyright © 2006 John Wiley & Sons, Ltd.     

Large Eddy Simulation of the Sensitivity of Vortex Breakdown and Flame Stabilisation to Axial Forcing

The effect of axial forcing on the flame/vortex breakdown interaction is studied, with particular focus on the Precessing Vortex Core (PVC). Large Eddy Simulation (LES), together with a filtered flamelet model describing the subgrid combustion, is performed to study a lean premixed flame undergoing mass flow fluctuations in a wide range of frequencies and amplitude. In average, forcing at frequencies lower than the PVC characteristic frequency moves the recirculation zone upstream the combustor in the premixing tube, while higher frequencies do not relevantly affect the flow/flame. With the help of Proper Orthogonal Decomposition (POD) a detailed analysis of the dynamics of the central recirculation zone (CRZ) is performed showing how the excitation at lower frequencies weakens the PVC and allows the flame to propagate upstream. Extended POD is also applied to illustrate the flow/flame interactions during the excitation cycle.     

Investigation on gas-solids hydrodynamics and matching enhancement in feedstock injection zone of double-level nozzle riser

With the development of current energy economy, it is necessary to improve the product distribution of fluid catalytic cracking process, which is achieved by a riser reactor with double-level of nozzles. The new riser is constructed by adding a level of secondary nozzle 0.5 m below the main nozzle of traditional riser. This paper investigates the gas-solids flow and oil-catalyst matching feature based on the optical fiber and tracer technologies. According to the distribution of solids holdup, particle velocity and dimensionless jet concentration, the feedstock injection zone can be divided into the upstream flow control region, the main flow control region, and the secondary flow control region in the radial direction. The size of the regions is changed by the jet gas velocity and axial height. There is a poor match of secondary nozzle jet to particles below the main nozzle. The jet gas from secondary nozzles can improve the matching effect of oil-catalyst near the wall and reduce the probability of coking above the main nozzle.     

Computation of field structure and aerodynamic characteristics of delta wings at high angles of attack

A numerical investigation of the structure of the vortical flowfield over delta wings at high angles of attack in longitudinal and with small sideslip angle is presented. Three-dimensional Navier-Stokes numerical simulations were carried out to predict the complex leeward-side flowfield characteristics that are dominated by the effect of the breakdown of the leading-edge vortices. The methods that analyze the flowfield structure quantitatively were given by using flowfield data from the computational results. In the region before the vortex breakdown, the vortex axes are approximated as being straight line. As the angle of attack increases, the vortex axes are closer to the root chord, and farther away from the wing surface. Along the vortex axes, as the adverse pressure gradients occur, the axial velocity decreases, that is, A is negativee, so the vortex is unstable, and it is possible to breakdown. The occurrence of the breakdown results in the instability of lateral motion for a delta wing, and the lateral moment diverges after a small perturbation occurs at high angles of attack. However, after a critical angle of attack is reached the vortices breakdown completely at the wing apex, and the instability resulting from the vortex breakdown disappears.     

Compressible and confined vortex flow

The internal compressible flow of a thin vortex chamber was investigated experimentally by measuring the radial distribution of temperature and pressure, from which the velocity field was calculated. The bulk of the internal vortex was found to be described by u_θr^0.69 = constant. The total resistance of the vortex chamber to the flow was also investigated in the context of fluidic vortex diode behavior under conditions of compressible and choked flow. It was found that the vortex chamber choked at an upstream-to-downstream pressure ratio of about 6 and in doing so passed a mass flow rate of 28% of the equivalent one-dimensional ideal nozzle. The resistance of vortex chambers is known to be strongly influenced by the presence of reversed flow in the exit due to vortex breakdown. Schlieren photography of the swirling exhaust flow was used to show that, while vortex breakdown does occur, it can only do so after the flow has become subsonic downstream of the exit and cannot therefore influence the vortex chamber resistance.     

Numerical and experimental study of turbulent impinging twin-jet flow

The two dimensional impinging circular twin-jet flow with no-cross flow is studied numerically and experimentally. The theoretical predications are carried out through numerical procedure based on finite volume method to solve the governing mass, momentum, turbulent kinetic energy and turbulent kinetic energy dissipation rate. The parameters studied were jet Reynolds number (9.5 × 10⁴  Re  22.4 × 10⁴), nozzle to plate spacing (3  h/d  12), nozzle to nozzle centerline spacing (l/d = 3, 5 and 8) and jet angle (0°  θ  20°). It is concluded that the stagnation primary point moves away in the radial main flow direction by increasing the jet angle. This shift becomes stronger by increasing the nozzle to nozzle centerline spacing (l/d). A secondary stagnation point is set up between two jets. The value of pressure at this point decreases by decreasing Reynolds number and/or increasing the jet angle.

The sub atmospheric region occurs on the impingement plate. It increases strongly by increasing Reynolds number and decreases as the jet angle and/or a nozzle to plate spacing increases. The spreading of jet decreases by increasing nozzle to plate spacing. The intensity of re-circulation zone between two jets decreases by increasing of h/d and jet angle. The increase of turbulence kinetic energy occurs within high gradient velocity.     

A numerical technique for laminar swirling flow at the interface between porous and homogenous fluid domains

There have been a few recent numerical implementations of the stress‐jump condition at the interface of conjugate flows, which couple the governing equations for flows in the porous and homogenous fluid domains. These previous demonstration cases were for two‐dimensional, planar flows with simple geometries, for example, flow over a porous layer or flow through a porous plug. The present study implements the interfacial stress‐jump condition for a non‐planar flow with three velocity components, which is more realistic in terms of practical flow applications. The steady, laminar, Newtonian flow in a stirred micro‐bioreactor with a porous scaffold inside was investigated. It is shown how to implement the interfacial jump condition on the radial, axial, and swirling velocity components. To avoid a full three‐dimensional simulation, the flow is assumed to be independent of the azimuthal direction, which makes it an axisymmetric flow with a swirling velocity. The present interface treatment is suitable for non‐flat surfaces, which is achieved by applying the finite volume method based on body‐fitted and multi‐block grids. The numerical simulations show that a vortex breakdown bubble, attached to the free surface, occurs above a certain Reynolds number. The presence of the porous scaffold delays the onset of vortex breakdown and confines it to a region above the scaffold. Copyright © 2008 John Wiley & Sons, Ltd.     

The effect of vortex angle on the efficiency of the Ranque–Hilsch vortex tube

A Ranque–Hilsch vortex tube is a long hollow cylinder with tangential nozzle placed near one end for injection of compressed air. The flow inside the vortex tube can be described as rotating air, which moves as a helical vortex flow. The peripheral flow moves toward the hot end, where the central part of the tube is blocked by a plug. The axial flow, which is forced back by the central part of the hot end plug, moves in the opposite direction toward the cold end. This paper focuses on the effect of the angle of rotating flow on the performance and efficiency of the Ranque–Hilsch vortex tube. To find the effect of vortex angle, different vortex angle generators were used and the best configuration was found.     

Flow regimes and frequency selection of a cylinder oscillating in an upstream cylinder wake

This paper describes flow around a pair of cylinders in tandem arrangement with a downstream cylinder being fixed or forced to oscillate transversely. A sinusoidal parietal velocity is applied to simulate cylinder oscillation. Time-dependent Navier-Stokes equations are solved using finite element method. It is shown that there exist two distinct flow regimes: ‘vortex suppression regime’ and ‘vortex formation regime’. Averaged vortex lengths between the two cylinders, pressure variations at back and front stagnant points as well as circumferential pressure profiles of the downstream cylinder are found completely different in the two regimes and, thus, can be used to identify the flow regimes. It is shown that frequency selection in the wake of the oscillating cylinder is a result of non-linear interaction among vortex wakes upstream and downstream of the second cylinder and its forced oscillation. Increasing cylinder spacing results in a stronger oscillatory incident flow upstream of the second cylinder and, thus, a smaller synchronization zone.     

An investigation of adiabatic spiral vortex flow by means of cross-wire probes

Flow transitions occurring with increase in the Taylor number in an annular gap of radius ratio 0.8, having an imposed axial flow of air of Reynolds number 500 have been studies using the output from a cross-wire probe in a complex digital analysis. Cross and phase spectra, together with auto and cross correlograms, are presented for four Taylor numbers from 10 620 to 12.2 × 10⁶, covering the onset of vortex flow, chaotic flow and turbulent vortex flow. As the Taylor number increases, there is little alteration in the spiral vortex flow in the axial and tangential directions, which oscillates in phase in these two directions. The tangential velocity gradient was seen to become increasingly dominant, with increase in the Taylor number     

Obstacle-induced spiral vortex breakdown

An experimental investigation on vortex breakdown dynamics is performed. An adverse pressure gradient is created along the axis of a wing-tip vortex by introducing a sphere downstream of an elliptical hydrofoil. The instrumentation involves high-speed visualizations with air bubbles used as tracers and 2D Laser Doppler Velocimeter (LDV). Two key parameters are identified and varied to control the onset of vortex breakdown: the swirl number, defined as the maximum azimuthal velocity divided by the free-stream velocity, and the adverse pressure gradient. They were controlled through the incidence angle of the elliptical hydrofoil, the free-stream velocity and the sphere diameter. A single helical breakdown of the vortex was systematically observed over a wide range of experimental parameters. The helical breakdown coiled around the sphere in the direction opposite to the vortex but rotated along the vortex direction. We have observed that the location of vortex breakdown moved upstream as the swirl number or the sphere diameter was increased. LDV measurements were corrected using a reconstruction procedure taking into account the so-called vortex wandering and the size of the LDV measurement volume. This allows us to investigate the spatio-temporal linear stability properties of the flow and demonstrate that the flow transition from columnar to single helical shape is due to a transition from convective to absolute instability.     

On the three-dimensional nature of the orthogonal blade–vortex interaction

An orthogonal blade–vortex interaction has been visualised using stereo particle image velocimetry. Significant changes to the vortex axial flow w component velocity are observed during the interaction, with a deceleration on the lower surface of the blade where the vortex axial flow is towards the blade surface. Over this surface the interaction process close to the blade surface spreads the vorticity out to the areas of oppositely signed blade w component, and the results suggest a non-uniform spreading over the leading edge region of the blade, with a tendency for a spanwise transport of vorticity. Over the upper surface of the blade, the vortex axial flow velocity increases and the vortex core shrinks slightly. During the lower surface interaction the vorticity and velocity vectors become significantly realigned with respect to one another, while this is not observed for the upper surface interaction.     

Numerical and experimental study of an axially induced swirling pipe flow

In-line flow segregators based on axial induction of swirling flow have important applications in chemical, process and petroleum production industries. In the later, the segregation of gas bubbles and/or water droplets dispersed into viscous oil by swirling pipe flow may be beneficial by either providing a pre-separation mechanism (bubble and/or drop coalescer) or, in the case of water-in-oil dispersions, by causing a water-lubricated flow pattern to establish in the pipe (friction reduction). Works addressing these applications are rare in the literature. In this paper, the features and capabilities of swirling pipe flow axially induced by a vane-type swirl generator were investigated both numerically and experimentally. The numerical analysis has been carried out using a commercial CFD package for axial Reynolds numbers less than 2000. Pressure drop, tangential and axial velocity components as well as swirl intensity along a 5 cm i.d. size and 3 m long pipe were computed. Single phase flow experiments have been performed using a water–glycerin solution of 54 mPa s viscosity and 1210 kg/m³ density as working fluid. The numerical predictions of the pressure drop were compared with the experimental data and agreement could be observed within the range of experimental conditions. The experiments confirmed that swirl flow leads to much higher friction factors compared with theoretical values for non-swirl (i.e. purely axial) flow. Furthermore, the addition of a conical trailing edge reduces vortex breakdown. Visualization of the two-phase swirling flow pattern was achieved by adding different amounts of air to the water–glycerin solution upstream the swirl generator.     

Stability of flow past a cylinder: Energy budget of eigenmodes

Global linear stability analysis of the flow past a circular cylinder at the onset of primary wake instability is carried out. The real and imaginary parts of the most unstable eigenmode, responsible for vortex shedding, are very similar but associated with a spatial shift in the vortex structures. This shift results in the convection of vortices that are observed in the unsteady flow, which is actually a consequence of global absolute instability. The kinetic energy density, associated with the most unstable eigenmode, is studied. At the onset of the instability the energy density of the disturbance field is found to be stronger in the far wake compared with the near wake. With increase in Re the region where the disturbance is strong moves upstream closer to the cylinder. However, the maximum value of the kinetic energy density of the disturbance lies outside the recirculation zone even for Re upto 100. A linearized mechanical energy equation for the time evolution of the kinetic energy density of the disturbance is utilized to examine the energy budget of the most unstable eigenmode at various Re. It is found that the most significant contribution to the growth rate of the disturbance arises from the transfer of the energy due to the strain rate of the base flow to the perturbation. The stabilizing effect of the viscous dissipation increases with increase in Re, but saturates for Re beyond ～70. Copyright © 2009 John Wiley & Sons, Ltd.     

Numerical modeling of vortex/shock wave interaction and its transformation by localized energy deposition

Three-dimensional unsteady Euler simulations are presented for the interaction of a streamwise vortex with an oblique shock of angle β = 23.3° at Mach 3 and 5. The flowfield features are analyzed for weak, moderate and strong interaction regimes. The details of the free recirculation zone at conditions of subsonic and supersonic flow on the vortex axis are considered. The vortex breakdown under conditions of a subsonic vortex core is characterized by a continuous growth and gradual degeneration of the region, unlike the supersonic core condition wherein a steady recirculation zone is achieved. The possibility of using a localized steady and pulsed periodic energy deposition on the vortex axis for stimulating the breakdown is demonstrated for various interaction regimes. It is shown that the formation of a subsonic wake downstream of an energy source lying on the vortex axis contributes to a more significant growth of the dimensions of the recirculation zone compared to the case when the vortex core remains supersonic. The possibility of achieving the effects similar to the steady case is demonstrated by the effect of a pulsed periodic energy source on the flow under consideration for corresponding equivalence parameters.      

Rollup region of a turbulent trailing vortex issued from a blade with flow separation

This paper presents the results of an experimental investigation on the near field of a tip vortex generated by a blade at moderate incidence. The experiments were conducted at Re=15 000 and the boundary layer over the blade separated around midchord on the upper surface. Laser-Doppler measurements of the turbulent flow (Tu=1.5%) were performed at various stations downstream of the blade. The three components of the mean velocity field and turbulent attributes were quantified at cross-planes, characterizing both the blade wake and the tip vortex structure. This allowed the analysis of the rollup and initial stages of decay of the tip vortex in the light of known theories and models. The axial velocity defect at the center of the vortex core evolved as x⁻¹ log x, without displaying any significant outgrowth imposed by the separated flow upstream. Momentum balances were also carried out at a station downstream to the conclusion of vortex rollup. The approximate axisymmetry of the flow field in the trailing vortex was used to formulate the balances in a cylindrical coordinate system. Among other observations, it was seen that an adverse axial pressure gradient developed in the vortex core, which reinforced the tenacity of the axial velocity defect. In contrast, an area influenced by a favorable pressure gradient was found outside the core.     

Influence of flow field scaling on flashback of swirl flames

In this paper, the effect of geometrical scaling on the onset of flashback into a cylindrical premixing zone of a swirl flame is investigated. We discriminate two types of flashback. In the first type of flashback the flame propagates upstream inside an already present axial recirculation zone. This flashback is caused by turbulent burning along the vortex axis (TBVA¹) and is controlled by flame extinction inside the recirculation zone. The second type of flashback is caused by combustion induced vortex breakdown (CIVB²). This type of flashback is characterised by the aerodynamic influence of the combustion heat release that leads to propagation of the axial recirculation zone and the flame in upstream direction.To study the effects of geometrical scaling on the flow fields and the two types of flashback, the operation of two geometrically scaled burners are compared at equal Reynolds number. By this method it is possible to observe the flashback phenomena in similar swirl flow fields but with different turbulent scales affecting the combustion process. To check flow field similarity and to indentify the flashback type, the non-reacting and reacting flow fields have been examined by planar particle imaging velocimetry and simultaneous recording of the flame luminescence.It is shown that geometrical scaling of the burner shifts the equivalence ratio at which flashback occurs and that this shift is different for the two types of flashback. Consistency and inconsistency with known scaling and stability criterions is discussed. Analysing the fluid dynamics and turbulent combustion gives a first explanation of why CIVB and TBVA are affected differently by geometrical scaling at constant Reynolds number which is in good agreement with the experimental observations.     

Influence of inertia,topography and gravity on transient axisymmetric thin‐film flow

This study examines theoretically the development of early transients for axisymmetric flow of a thin film over a stationary cylindrical substrate of arbitrary shape. The fluid is assumed to emerge from an annular tube as it is driven by a pressure gradient maintained inside the annulus, and/or by gravity in the axial direction. The interplay between inertia, annulus aspect ratio, substrate topography and gravity is particularly emphasized. Initial conditions are found to have a drastic effect on the ensuing flow. The flow is governed by the thin‐film equations of the ‘boundary‐layer’ type, which are solved by expanding the flow field in terms of orthonormal modes in the radial direction. The formulation is validated upon comparison with the similarity solution of Watson (J. Fluid Mech 1964; 20 :481) leading to an excellent agreement when only 2–3 modes are included. The wave and flow structure are examined for high and low inertia. It is found that low‐inertia fluids tend to accumulate near the annulus exit, exhibiting a standing wave that grows with time. This behaviour clearly illustrates the difficulty faced with coating high‐viscosity fluids. The annulus aspect is found to be influential only when inertia is significant; there is less flow resistance for a film over a cylinder of smaller diameter. For high inertia, the free surface evolves similarly to two‐dimensional flow. The substrate topography is found to have a significant effect on transient behaviour, but this effect depends strongly on inertia. It is observed that the flow of a high‐inertia fluid over a step‐down exhibits the formation of a secondary wave that moves upstream of the primary wave. Gravity is found to help the film (coating) flow by halting or prohibiting the wave growth. The initial film profile and velocity distribution dictate whether the fluid will flow downstream or accumulate near the annulus exit. Copyright © 2004 John Wiley & Sons, Ltd.