Local Swirl Number Research Articles

Linear global stability analysis of a transient swirling flow leading to the formation of a helical precessing vortex breakdown in a straight diffuser

Vortex breakdown occurs in highly swirling flows in various engineering applications, such as hydraulic turbines working in either high-load or part-load conditions, leading to pressure pulsations and performance degradation. In the present study, the formation of a helical vortex breakdown having rotational and plunging components (axial oscillation) in a straight diffuser is investigated with transient simulation from its columnar state to a helical vortex breakdown state. It is similar to the helical precessing vortex rope occurring in hydraulic turbines operating at part-load condition. In addition, considering vortex breakdown as a global instability, a linear global stability analysis of the time-averaged turbulent flow field is conducted for different flow states. The main objective is to understand the role of plunging mode in vortex rope formation in straight draft tubes and identify its differences with the one observed in hydraulic turbines with elbow draft tubes operating at part-load condition. Results showed that in contrast to the elbow draft tubes where the plunging mode appears earlier than the rotating mode, the transient simulation showed that the plunging mode appears after several vortex rope rotations in the straight draft tube. This is confirmed by the stability analysis showing that the flow is unstable to the asymmetrical disturbances with a frequency close to the rotating frequency not the plunging ones. Finally, the stability analysis showed a higher critical flow rate than the one obtained from the contour of local swirl number and time history of pressure and velocity.

Effect of swirl on premixed flame response at high forcing amplitudes

The response of a lean premixed flame subjected to acoustic perturbations is a complex phenomenon that depends highly on the type of flame and the operating conditions. Swirl introduces additional complexities due to the azimuthal component of the flow. In this work, a bluff body stabilised burner is studied under non-swirling and highly swirling conditions by placing a removable axial swirl upstream of the burner. The influence of swirl is assessed in terms of the flame describing function which is the ratio of heat release rate fluctuations response to incoming velocity oscillations and the spatial flame dynamics at high forcing amplitudes. The effect of flame interaction with the wall on the flame response is also explored by considering an enclosure with a larger diameter. It is found that swirl can affect the non-linear characteristics of the flame at medium frequencies (Strouhal numbers around unity) by altering the flame roll-up mechanisms. This is related to the variation of the local swirl number in space and time. For Strouhal numbers that are considerably lower than unity, the effect of swirl is small due to the high convective wavelengths. The size of the enclosure can also change the flame response characteristics, specifically for large forcing frequencies. With a small enclosure, where the flame interacts with the wall, the flame break-up is more significant and the vortex formation is interrupted. This does not happen when the enclosure is enlarged and it can affect the non-linear behaviour of the flame.

Optimization of axial water injection to mitigate the Rotating Vortex Rope in a Francis turbine

Rotating Vortex Rope (RVR) resulting from flow instabilities inside draft tube affects the hydraulic turbine's efficiency and wear. Among the passive and active RVR mitigation methods, the water injection method has been widely investigated lately. The present research focuses on the dynamics of RVR mitigation using the water injection method and the optimization of exergy loss during the water injection. The numerical simulations are performed using a reduced turbine geometry consisting of one stay vane, two guide vanes, one runner passage by applying periodic boundary conditions at side boundaries, and a complete draft tube. The pressure fluctuations, velocity field, and the RVR structure are well captured using the Shear Stress Transport - Scale Adaptive Simulation (SST-SAS) turbulence model. The results of the local swirl number during the load variation show that the onset of flow instabilities and RVR formation are created due to a decrease of the axial momentum below the runner cone. The required axial momentum flux of water injection is calculated for a stable swirl number and the local minimum ratio of dimensionless loss to the pressure recovery factor. The numerical results show that the rotating and plunging components of the pressure fluctuations inside the draft tube reduce during the water injection. The pressure recovery of the draft tube improves. The dynamics of RVR mitigation are visualized using λ2 criterion and the spectrogram of pressure probes on the draft tube wall. An optimum water flow rate and jet velocity for a fixed axial momentum are proposed. The results show that a water jet with a large radius and low velocity is more effective to mitigate the RVR and minimizing the draft tube losses.

Optimizing swirl in compact uniflow cyclones

This paper presents an experimental examination of the velocity field distribution in the separation chamber of a uniflow cyclone with closed particle outlet to evaluate the swirl characteristics in the vortex finder region based on stereoscopic particle image velocimetry. A cold flow model with a closed particle outlet was used to assess different angles of attack and core size ratios at typical Reynolds numbers for the separation of low loaded gas‐solid flows. The focus of the study was on the relationship between swirl strength as well as performance data. At higher angles, the parabolic swirl strength distribution changed to a region with constant high acceleration of the particles in the separation zone. Integral and differential swirl numbers were correlated with the ratio of tangential to radial velocity and to the calculated cut size diameter. At low angles of attack, implying a strong redirection of flow perpendicular toward the main flow direction and small core size ratios, defined by the radial distance between hub and tip, the local differential swirl number can be more than twice as large as in the base configuration. Yet, the integral swirl number hardly changed. The velocity fields showed mean tangential to radial velocity ratios ranging from 0.73 to 6.85 at swirl vane angles of 15 °–60 °; core size ratios between 0.125 and 0.625 at vortex finder diameter were measured and calculated cut size diameters between 10 and 90 μm were derived. This data provides the foundation for further validation studies and the development of new design criteria. © 2018 American Institute of Chemical Engineers AIChE J, 65: 766–776, 2019

The effects of swirling decaying flow towards pipe entry length and heat transfer in an annular pipe

The hydrodynamic entry length of axial pipe flow has been studied extensively over the years. Entry length is used to identify range of fully developed flows as commonly used in many practical engineering applications (e.g. Moody’s chart). For laminar axial pipe flow, the hydrodynamic entry length has been investigated by Kays, Shah and Bhatti (KSB) (Lh = 0.056 ReDh). In contrast, several approximations exist for fully turbulent flows (i.e. 10 Dh–150 Dh). Through theoretical and numerical investigations, the hydrodynamic entry length for swirling decaying pipe flow in the laminar regime is investigated. It is found that, the development length Lh for the axial velocity profile is reduced when a rotational component is added to the mean flow. The reduction in the hydrodynamic length is found to be proportional to the inlet swirl angle θ and the magnitude of the rotational component. Results indicate that a modification can be made on the KSB equation for two-dimensional swirling annular pipe flow. This research also investigates the effect of the local swirl number and Reynolds number on the steady and unsteady heat transfer inside an annular pipe. The existence of the jet effect near the exit of the swirl vane altered the behaviour of the local heat transfer coefficient in the axial direction (along the pipe) for z = 0 mm to z = 40 mm. The heat transfer coefficient for the 30° vane angle is found to increase after z = 0 mm to a maximum value before decaying nonlinearly, whereas, for the 45° and 60° vane angles, the heat transfer coefficient decreases nonlinearly starting from the vane exit. It is found that, for low Re, Ts changes linearly over the course of the cooling zone for all vane angles. With increasing Reynolds number, the behaviour of the cooling curve changes from linear to nonlinear. Overall, the cooling time is found to be inversely proportional to Re. With increasing vane angle, the overall swirl number S along the pipe decreases, thus, reducing the overall swirling momentum in the annular pipe, leading to a lower heat diffusion rate. It is found that the dependency of the temperature of the solid rod Ts on Re is decreasing as Re increases.

Large Eddy Simulation of Low Swirl Flames Under External Flow Excitations

Low swirl flame characteristics under external flow excitations are numerically investigated using large eddy simulations with a dynamically thickened flame combustion model. A finite volume scheme on a Cartesian grid with a dynamic one equation eddy viscosity subgrid scale model is used for large eddy simulations. The excitations are imposed on inlet velocity profiles by a sinusoidal forcing function over a wide range of amplitudes and frequencies. Present investigation shows that although, the swirling motion of the low swirl flame is not intense enough to induce a recirculation zone in ensemble averaged results, external flow excitations increase the local swirl number upstream of the flame front. Such increase in the local swirl number is at maximum value when the low swirl flame is excited at the dominant frequency of the flow field, which in turn induces a vortex breakdown and hence a central recirculation zone. The strength and size of the time averaged recirculation zone depend on both the amplitude and frequency of the excitations. Moreover, phase-locked results indicate that external flow excitations induce local swirl fluctuations ahead of the flame front which alter the strength of the recirculation zone at different phase angles of the excitations.

Large Eddy Simulations of Unconfined Non-reacting and Reacting Turbulent Low Swirl Jets

The low swirl flow is a novel method for stabilizing lean premixed combustion to achieve low emissions of nitrogen oxides. Understanding the characteristics of low swirl flows is of both practical and fundamental interest. In this paper, in order to gain better insight into low swirl stabilized combustion, large eddy simulation and dynamically thickened flame combustion modeling are used to characterize various features of non-reacting and reacting low swirl flows including vortex breakdown, shear layers’ instability, and coherent structures. Furthermore, four test cases with different equivalence ratios are studied to evaluate the effects of equivalence ratio on the flame and flow characteristics. A finite volume scheme on a Cartesian grid with a dynamic one equation eddy viscosity subgrid model is used for large eddy simulations. The obtained results show that the combustion heat release and increase in equivalence ratio toward the stoichiometric value decrease the local swirl number of the flow field, while increasing the flow spreading at the burner outlet. Results show that the flame becomes W shaped as the equivalence ratio increases. Moreover, the combination of the swirling motion and combustion heat release temporally imposes a vortex breakdown in the post-flame region, which leads to occurrence of a transient recirculation zone. The temporal recirculation zone disappears downstream of the burner outlet due to merging of the inner shear layer from all sides at the centerline. Also, various analyses of shear layers’ wavy and vortical structures show that combustion heat release has the effect of decreasing the instability amplitude and vortex shedding frequency.

The influence of swirl on the reattachment length in an abrupt axisymmetric expansion

This paper presents a theoretical study on the influence of swirl on the reattachment length in an abrupt axisymmetric expansion. A scale analysis of the equations of motion reveals that this reattachment length decreases with increasing swirl. Moreover, it seems to suggest that there may be a singularity in the non-swirling sudden expansion flow, which disappears with increasing swirl beyond a critical value. This singularity is a possible explanation for the scatter of the data found in the literature at zero swirl. For the swirling flow, an analytical expression for the reattachment length is derived based on similarities found in experimental data between swirling and non-swirling flows. This expression shows that the reattachment length is a function of the swirl number and the expansion ratio and, to some extend, of the reattachment length at zero swirl. It is found that the local swirl number of the detaching streamline S D is a better parameter to characterise the reattachment length than the momentum flux averaged swirl number S. The theoretical model is validated based on values for the reattachment length found in the literature for expansion ratios h = R 2/ R 1 ranging from 1.5 to 2, Reynolds numbers Re from 10,000 to 100,000 and swirl numbers S from 0 to 1.23. Comparison with experiments shows a good agreement between the model and experimental data.

Topological Flow Structures of Annular Swirling Jets

AbstractThe effects of blockage and swirl on the macro flow structures of the annular jet past a circular disc are experimentally studied through the time-averaged streamline patterns. In the blockage-effect regime, the flows present multiple modes, single bubble, dual rings, vortex breakdown, and triple rings, in different regimes of blockage ratio and swirl number. The topological models of the flow structures are proposed and discussed according to the measured flow fields to manifest the complex flow structures. The single bubble is a closed recirculation bubble with a stagnation point on the central axis. The dual-ring flow is an open-top recirculsation zone, in which a pair of counter-rotating vortex rings exists in the near wake. The fluids in the dual rings are expelled downstream through a central jet-like swirling flow. A vortex breakdown may occur in the central jet-like swirling flow if the exit swirl number exceeds critical values. When the vortex breakdown interacts with the dual rings, a complex triple-ring flow structure forms. Axial distributions of the local swirl number are presented and discussed. The local swirl number increases with the increase of the exit swirl number and attains the maximum in the dual-ring mode. At large exit swirl numbers where the vortex breakdown occurs, the local swirl number decreases drastically to a low value.

Flame movement mechanisms and characteristics of gas fired cyclone combustors

Cyclone combustors are finding application in several fields, ranging from burning waste vegetable refuse, low calorific value gases, MHD applications and as highly flexible modulatable combustors. The combustor, described in this paper, is based on design experience with coal fired cyclone burners and is run on a premixed supply of natural gas and air at varying mixture ratios. Three principal modes of combustion and associated flame movement mechanisms are described. Mode I occurs at rich mixture ratios, combustion taking place partially inside the combustor, but for the most part downstream of the exit. Mode II occurs at near stoichiometric mixture ratios, the flame being located primarily in the inlet/outlet mainifold of the combustor but extending inside the cyclone chamber. Mode III occurs at weak mixture ratios, the flame is of annular form and located at 0.75 of the cyclone chamber diameter. The flame movement mechanism between Mode I and II is caused by differences in heat release rates due to the degree of flammability of the air/fuel mixture. The distinct flame movement mechanisms between Mode II and III is caused by (a) a reduction in entrainment from the descending wall flow to the exhaust flow, (b) a reduction in the annular width of the wall flow, (c) a change in angular and axial momentum flux distributions inside the combustor. The effect of combustion is seen to significantly reduce the local dynamic swirl number throughout the combustor, due to flow acceleration, and is predicted by a simple expression using spatially averaged mean densities.

Combustor Swirl Flow Modeling

CHALLENGING problem facing theoretical combustion aerodynamicists today is the prediction of turbulent reacting swirl flows. Prediction greatly facilitates economical design and operation of combustion systems, where flame size, shape, stability, and combustion intensity are often controlled by the use of, among other things, swirl.1 The degree of swirl is characterized by the swirl number S (axial flux of angular momentum divided by the axial flux of axial momentum times nozzle radius), or the local swirl number Sz (which uses the local mixing layer width). The swirl strength determines the degree of upstream influence. The flow classification of parabolic (boundary-layer type with a single predominant direction—weak swirl S 0.6), governs the type of boundary conditions required and the solution method. Marching methods are appropriate for the former; relaxation methods for the latter.2 Recent work in the simulation and solution of these flows is reviewed in Ref. 3 and the full-length paper.

Prediction of Inert Turbulent Swirl Flows

Numerical finite-difference predictions are made of inert turbulent boundary-layer swirling flows. A variety of turbulence models are considered and a nonisotropic model is found to show more realistically the effects of swirl on jet development. Gross effects may be represented by an extended Prandtl mixing length model but constants appearing do not exhibit universality. This deficit is partially overcome by the use of an algebraically-modeled, nonisotropic energy-length turbulence model. The Richardson number and the local swirl number play important parts in linking the rtf-shear with the rx-viscosity and the nonisotropy of the turbulent viscosity.