Swirl Velocity Research Articles

Analytical Equilibrium Swirling Inflow Conditions for Computational Fluid Dynamics

T HE specification of swirling inflow conditions is an integral and important part of computational fluid dynamics (CFD) of swirling flows, which are complex flows with many practical applications [1], for instance, in turbulent combustion [2]. To specify a swirling velocity profile with a desired swirl number in a traditional CFDanalysis based on aReynolds-averagedNavier–Stokes (RANS) modeling approach is not an easy task, which becomes even more difficult in advanced CFD approaches such as direct numerical simulation (DNS) or large-eddy simulation (LES). DNS or LES of spatially inhomogeneous turbulent flows requires turbulent inflow boundary conditions [3], which may be generated either from an auxiliary simulation, from a proper orthogonal decomposition and linear stochastic estimation [4], from a digital filter reproducing specified statistical data [5], or simply taken as the mean velocity profile with superimposed fluctuations [6], which is essentially a perturbed inflow. With the presence of swirling, inflow conditions are difficult to specify. For RANS-based CFD, an appropriate mean velocity profile is needed. For DNS and LES, apart from the mean velocity profile, information on an appropriate “turbulent” component is needed as well. Pierce and Moin [7] developed a method for generating equilibrium swirling inflow conditions, which represents a logical, idealized starting point for generating swirling velocity profiles. In their method, the swirling inflow is obtained numerically by solving for the flow driven by fictitious axial and azimuthal body forces, where the axial body force represents themean pressure gradient that drives the physical flow. The azimuthal body force is not physically producible and may be thought of as existing only to overcome drag from the walls. This technique was used in LES of a coaxial jet combustor and good agreement with the experimental data was observed [7]. The method can be regarded as an effective and simple means of generating realistic swirling inflow conditions. In this study, efforts have beenmade to derive an analytical formof the equilibrium swirling inflow conditions. The analytical swirling inflow is easy to implement, as it does not require solving for the flow numerically [7]. The particular forms of the analytical equilibrium swirling velocity profiles have been obtained for swirling annular and round jets, which can be directly applied in the specification of swirling inflow conditions for RANS approaches and further explored for the specification of swirling inflow conditions for DNS and LES, regardless of the turbulent component needed in the timedependent simulations. A desired swirl number at the inflow can also be conveniently achieved by adjusting a constant.

Simplified Turbulence Models for Confined Swirling Flows

Turbulent flow in a stirred vessel is distinguished by the domination of the swirl velocity component, which makes the flow turbulence highly anisotropic. As a result, conventional turbulence models based on the eddy viscosity hypothesis provide poor predictions for not only turbulence characteristics, but also velocity distributions. Many suggestions to modify the conventional turbulence models that take into account the effect of flow swirl have been made. Even though a reasonable distribution of the velocity field can be obtained with the modified k-ε turbulence model proposed by Launder, Priddin and Sharma (1977), the approach fails to provide a good prediction for the turbulence characteristics, especially at the core region. The Reynolds stress transport model based on a second-order closure scheme seems to be able to provide much better prediction results without any ad hoc modification. However, the computational complexity with this model is considerable. The ordinary algebraic stress model, which stems from the Reynolds stress transport model, was found not working for the swirling flows in a stirred vessel. In this work, a modification to the algebraic stress model is proposed, which takes into account additional terms arising from the production terms of the Reynolds stress transport equations during the transformation of these equations from Cartesian to cylindrical coordinate system. Comparisons of the prediction results are made with available experimental data and with the results obtained by means of the differential Reynolds stress turbulence model.

Benchmarking Particle Image Velocimetry with Laser Doppler Velocimetry for Rotor Wake Measurements

An experiment was conducted to identify and measure the sources of uncertainty that are associated with the application of particle image velocimetry to the measurement of the vortical wakes trailing from helicopter rotor blades. Phase-resolved, three-component particle image velocimetry measurements were performed in the wake of a subscale rotor operating in hover, and were compared with high-resolution three-component laser Doppler velocimetry measurements obtained with the same rotor under identical operating conditions. This helped formulate the essential experimental conditions that need to be satisfied for particle image velocimetry to accurately resolve the high-velocity gradient, high streamline curvature flows that are present inside the rotor wake and in the blade tip vortices. Uncertainties associated with the calibration, acquisition, and processing of the particle image velocimetry images were analyzed in detail. It was shown that the optimization of laser pulse separation time is fundamental to reduce the errors associated with acceleration and curvature effects. Similarly, the interrogation window size was shown to play a critical role in determining the velocity gradient bias errors. The correlation between the laser Doppler velocimetry and particle image velocimetry measurements of the tip vortex characteristics, such as core radius and peak swirl velocity, were found to be excellent.

배연탈황설비 흡수탑 내 연소가스 및 슬러리의 거동에 관한 수치해석적 연구

Numerical analysis had been performed to understand flow characteristics of the flue gas and slurry in the absorber of a flue gas desulphurization (FGD) system using computational fluid dynamics (CFD) technique. Two-fluid(Euler-Lagrangian) model had been employed to simulate physical phenomenon, which slurry particles injected through slurry spray nozzles fall down and bump into the flue gas inflowing through inlet duct. It was not necessary to adopt pre-defined pressure drop inside the absorber because interaction between flue gas and slurry particles was considered. Hundreds of slurry spray nozzles were considered with the spray velocity at the nozzles, swirl velocity and spreading angle. The results note that the flow disturbance of flue gas is found at the bottom of the absorber, and the current rising with high speed stream is observed in the opposite region of the inflow duct. The high speed stream is reduced as the flue gas goes up, because the high speed stream of flue gas dumps falling slurry particles due to momentum exchange between flue gas and slurry particles. In spite of some disproportion in slurry distribution inside the absorber, escape of slurry particles from the absorber facility is not observed. The pressure drop inside the absorber is mainly occurred at the bottom section.

Heat transfer process under a film-cooled surface with presence of weak swirling flow in the mainstream

Experiments have been performed in a relatively large circular pipe to study and obtain the heat transfer data over a film-cooled surface, with the presence of weak swirling flow in the mainstream. The swirling flow is generated by a flat-vaned swirler situated upstream. A cooling film is injected from an annular slot formed by the pipe wall and the circular cover plate. The radial temperature distribution measurements at several axial locations were used to infer the film jet structure and the rate of mixing of the film jet with the swirling flow. The nondimensional parameters governing the heat transfer process under the film are derived from the system of governing equations. Experiments demonstrate that the swirl number, increasing with turbulence intensity and swirl velocity in the mainstream, can rapidly destroy the film jet structure and enhance the heat transfer process. During the course of the experiments, the blowing parameter ranged from 0.5 to 2 and the swirl number ranged from 0 to 0.6. Correlations for the Nusselt number which account for the effect of swirling flow are presented.

Near-Surface Intensification of Tornado Vortices

Abstract An idealized analytical model and numerical large-eddy simulations are used to explore fluid-dynamic mechanisms by which tornadoes may be intensified near the surface relative to conditions aloft. The analytical model generalizes a simple model of Barcilon and Fiedler and Rotunno for a steady supercritical end-wall vortex to more general vortex corner flows, angular momentum distributions, and time dependence. The model illustrates the role played by the corner flow swirl ratio in determining corner flow structure and intensification; predicts an intensification of near-surface swirl velocities relative to conditions aloft of Iυ ∼ 2 for supercritical end-wall vortices in agreement with earlier analytical, numerical, and laboratory results; and suggests how larger intensification factors might be achieved in some more general corner flows. Examples of the latter are presented using large-eddy simulations. By tuning the lateral inflow boundary conditions near the surface, quasi-steady vortices exhibiting nested inner and outer corner flows and Iυ ∼ 4 are produced. More significantly, these features can be produced without fine tuning, along with an additional doubling (or more) of the intensification, in a broad class of unsteady evolutions producing a dynamic corner flow collapse. These scenarios, triggered purely by changes in the far-field near-surface flow, provide an attractive mechanism for naturally achieving an intense near-surface vortex from a much larger-scale less-intense swirling flow. It is argued that, applied on different scales, this may sometimes play a role in tornadogenesis and/or tornado variability. This phenomenon of corner flow collapse is considered further in a companion paper.

A subsurface warm‐eddy off northern Baja California in July 2004

Upper‐ocean eddies are commonly observed from remote sensing, but submerged eddies are more difficult to detect. During July 2004, a 21‐day hydrographic survey in the southern region of the California Current was carried out to investigate the mesoscale variability. We observed for the first time a subsurface anticyclonic eddy off northern Baja California with the same water mass characteristics as the California Undercurrent. The core of the eddy was quasi‐circular with radii of 35 km and thickness of 250 m. The maximum swirl velocity was ∼3 cms−1. The water mass of the core of the eddy was characterized by potential temperature of 11°C, salinity of 34.5, and dissolved oxygen of 1.4 mll−1. The eddy propagated westward. The subsurface warm‐eddy could transport relatively saline water into the North Pacific subtropical gyre.

Computation of rotordynamic coefficients associated with leakage steam flow through labyrinth seal

A mathematical model of calculating rotordynamic coefficients associated with leakage steam flow through labyrinth seals was presented. Particular attention was given to incorporating thermal properties of the steam fluid into prediction of leakage flow and subsequent derivation of rotordynamic coefficients, which quantitatively characterize influence of aerodynamic forcing of the leakage steam flow on the rotordynamics. By using perturbation analysis, we determined periodic and analytic solutions of the continuity and circumferential momentum equations for the time-dependent flow induced by non-axisymmetric rotation of the rotor encompassed by a labyrinth seal. Pressure distributions along labyrinth seal cavities and rotordynamic coefficients were compared at the same condition for air and steam flows. Influence of steam flow through the labyrinth seal cavities on rotordynamic coefficients was analyzed in terms of inlet pressure, inlet swirl velocity and rotor speed.

On the refracted patterns produced by liquid vortices

A theoretical analysis of the refracted shadows produced by steady and time-decaying liquid vortices under uniform illumination from above is given in this article. An expression for the induced shadow intensity is derived and found to be a function of the vortex’s free surface profile, i.e., function of the static pressure distribution. The patterns for different focusing depth are given and compared with previous visualization results from the literature. The phenomenon is examined and illustrated as a bench mark case by using both steady and time-decaying algebraic vortex models. However, this study can be extended to check the feasibility of recovering the main flow properties by analyzing the luminous image intensity of the refracted patterns. The present analysis is valid only when the swirl velocity is order of magnitude higher than the meridional flow components and the vorticity is concentrated within the core region and of intense conditions.

Large Eddy Simulation on Flow Structure in Centrifugal Flow Tundish

Centrifugal flow tundish which the molten steel is horizontally rotated by electromagnetic force has been developed to produce high quality steel with high productivity. Because the swirling flow in the rotation chamber is crucial for the effectiveness of centrifugal flow tundish, it is beneficial to search the way to enhance the swirling flow and understand the flow structure in centrifugal flow tundish. Large Eddy Simulation (LES) technique is developed to simulate the complicated flows. LES is computationally much more intensive than k-e and cost less than direct numerical simulation (DNS), but offers a new level of insight into transient phenomena. In the present works, flow structures in three cases are simulated and analyzed, i.e. the swirling flow is produced by (a) electromagnetic force with the direct nozzle, (b) bending nozzle using height potential energy of molten steel, (c) combination of electromagnetic force and bending nozzle. The swirling flow and vortices are clearly displayed. The effectiveness of bending nozzle is validated by 17% increment of maximum swirling velocity in rotation chamber.

Influence of the inlet swirl velocity profile shape on swirl decay in laminar pipe flow

Role of the inlet swirl velocity profile shape on swirl decay in steady-state, incompressible, laminar pipe flow is computationally analysed. Two different integral parameters, namely the circulation and the swirl number are investigated as measures of the swirl level. It is observed that swirl decays at different rates along the pipe length, if the shape of the inlet swirl velocity profile is changed, although the inlet value of the integral parameter is kept constant. Even though this result is obtained for the laminar flow, it implies that a similar dependency may exist for the turbulent flow, and the accuracy of the swirl decay correlations may be increased, if they are additionally sensitised to the shape of the swirl velocity profile.

Seal-Inlet Disturbance Boundary Condition Correlations for Rotordynamics Models, Part 1: Correlation Development

Systematic parametric studies were performed to better understand seal-inlet rotordynamics. A CFD-perturbation model was employed to compute the seal-inlet flow disturbance quantities. Seal inlet disturbance boundary condition correlations were proposed from the computed seal-inlet quantities using the important parameters. It was found that the cosine component of the seal-inlet swirl velocity disturbance W 1C has a substantial impact on cross-coupled stiffness, and that the correlations for W 1C and W 1S should be used to replace the historical guess that seal inlet W 1C = 0 and W 1S = 0. Also, an extremely precise relationship was found between the cross-coupled stiffness and the seal-inlet swirl velocity (ω R sh −[Wbar] 0 ). Thus, the number of experiments or computer runs needed to determine the effect of spin speed, shaft radius, and/or inlet swirl velocity on cross-coupled stiffness could be greatly reduced by plotting the simplified relationship of the cross-coupled stiffness against the swirl slip velocity. In addition, the upstream chamber size and shape were found to have a substantial influence on the seal-inlet swirl disturbance velocity W 1S which plays a significant role in determining the direct stiffness. Final manuscript approved June 2, 2006 Review led by Tom Lai

Seal-Inlet Disturbance Boundary Condition Correlations for Rotordynamics Models, Part 2: Assessment

Nearly all seal rotordynamics models were forced to assume that the seal-inlet swirl velocity disturbance boundary condition components (W 1C and W 1S ) are zero. The companion (Part 1) paper employs an extensive parametric study to develop a complete set of widely applicable seal-inlet disturbance boundary condition correlations that will alleviate this shortcoming. The benefits of using the new seal-inlet boundary condition correlations were assessed by implementing them into a CFD-perturbation model. Two widely different test cases were employed. Case 1 is a test of the correlations for large upstream chambers using a simple liquid smooth-plain seal, and Case 2 is a test for small, as well as radial injection, upstream chambers using a complicated gas labyrinth seal. For both cases, consistently improved agreement with measurements was obtained for the options with non-zero W 1C and W 1S compared to the option with W 1C = W 1S = 0. Specifically, the correlation set using the W 1C -profile option gave a clearly better prediction of the effective damping and the cross-coupled stiffness than did the set using the W 1C -bulk option for the higher spin speed case of the challenging gas labyrinth. For the smooth-plain liquid seal case, the correlations with the W 1C -profile and W 1C -bulk options gave nearly the same level of agreement with measurements. Final manuscript approved June 2, 2006 Review led by Tom Lai

A new cyclone separator-based pre-filter design for internal combustion engine applications. Part 2: Parametric study and optimization

In a previous paper a new design was presented of a cyclone separator based pre-filter along with validation of a numerical model with experimental data. The validated model is used to evaluate certain designs with varying inlet air entry configurations. Furthermore, several cases as part of a detailed parametric study on the new pre-filter design are simulated in terms of geometrical parameters to optimize the performance with respect to overall pressure drop and dust collection efficiency. The results of the parametric study are used to derive a final optimized pre-filter configuration. In addition, based on the results of some of the simulations, a new concept of air filtration which could potentially replace the conventional air filter plus pre-filter configuration is introduced and assessed numerically. This design utilizes the high swirl velocities of air to separate particles as small as 4-5 μm with almost 100 per cent efficiency. More importantly, it offers much lower pressure drop than the total pre-filter plus main filter configuration.

Hybrid lattice Boltzmann finite‐difference simulation of axisymmetric swirling and rotating flows

AbstractThe axisymmetric flows with swirl or rotation were solved by a hybrid scheme with lattice Boltzmann method for the axial and radial velocities and finite‐difference method for the azimuthal (or swirl) velocity and the temperature. An incompressible axisymmetric lattice Boltzmann D2Q9 model was proposed to solve the axial and radial velocities through inserting source terms into the two‐dimensional lattice Boltzmann equation. Present hybrid scheme was firstly validated by simulations of Taylor–Couette flows between two concentric cylinders. Then the benchmark problems of melt flow in Czochralski crystal growth were studied and accurate results were obtained. Numerical experiment demonstrated that present axisymmetric D2Q9 model is more stable than the previous axisymmetric D2Q9 model (J. Comp. Phys. 2003; 186(1):295–307). Hence, compared with the previous model, present numerical method provides a significant advantage in simulation melt flow cases with high Reynolds number and high Grashof number. Copyright © 2006 John Wiley & Sons, Ltd.

Analytical Solutions for Circular Stratified Eddies of the Reduced-Gravity Shallow-Water Equations

Abstract A set of new analytical nonstationary solutions of the nonlinear, reduced-gravity shallow-water equations on an f plane in a vertically stably stratified active environment is presented. The solutions, which describe the dynamics of inertially pulsating surface as well as intermediate lens-like stratified vortices, represent an extension of previous analytical solutions to more realistic vortex shapes and structures of the vortex swirl velocity fields in the presence of an arbitrary stable vertical stratification within the active environment. To elucidate aspects of the novelty of the new set of solutions, examples are presented referring to a vertically stratified surface vortex and to a vertically stratified intermediate vortex, both characterized by azimuthal velocity fields that are nonlinear functions of the radius and by layer shapes that largely deviate from paraboloidal shapes. First, a solution describing a five-layer surface “warm core” eddy is analyzed and characteristics resembling characteristics observed in geophysical surface vortices are revealed: Within each layer, the obtained azimuthal velocity shows a realistic distribution, as its maximum is located far from the vortex rim, where it is negligible. Moreover, the obtained azimuthal velocity is largest in the surface layer and decreases monotonically toward the deeper layers. Integral properties of the new stratified solutions significantly differ from the corresponding properties of equivalent, known homogeneous solutions. Significant differences are found, for instance, between the shape of a five-layer vortex and that of its homogenous counterpart having the same mean azimuthal velocity structure. Second, a solution referring to a five-layer intermediate “meddy like” vortex is analyzed: while in each layer the obtained azimuthal velocity is maximum in the interior part of the vortex and decreases toward its center and its periphery, its magnitude is largest in the intermediate layer and it decreases toward the surface and toward the bottom layer, which are characteristics resembling characteristics of observed meddies. The quoted examples demonstrate that the new solutions add substantial realism to the analytical description of oceanic nonlinear geophysical vortices. In the context of the nonlinear reduced-gravity shallow-water equations on an f plane they seem to represent the most general analytical features achievable, which refer to vertically stratified circular vortices characterized by linear radial velocity fields.

Simple Model for Turbulent Tip Vortices

V ORTICES are interwoven into the fabric of fluid mechanics transporting mass momentum and energy in the majority of natural and industrial flows. In technology these are either produced deliberately to accomplish the task, improve the function of devices, or emerge as a parasitic by-product of fluid motion. Aeronautical applications are very susceptible to these flow manifestations. Consequences of lift, tip vortices cause considerable drag, noise, and/or hazard in fixedand/or rotating-wing aircraft. Although complicated in nature simple mathematical models are routinely used to elaborate on some of their fundamental properties [1,2]. It is a well-known fact that, irrespective of the host flowfield, intense vortices are analogous. Theoretically, intense (or strong) vortices are those where the tangential velocity component is orders of magnitude larger than the radial and axial. In practice, however, the property is also maintained by vortices where the swirl velocity component is dominant, but not necessarily of a magnitude enormously greater than the other two. Under these conditions the vortex appears to develop in amanner that the swirling action ignores the secondarylike flow in the azimuthal plane. Consequently, simple Rankine-like formulations have been used widely to model a variety of geophysical, wingtip, cyclone chamber, ship propeller, intake, and other types of vortices. The physics of laminar vortices is relatively well known. Simple exact solutions of the Navier–Stokes equations are due to Rankine [3], Oseen [4], Lamb [5], Burgers [6], and others. Every one of them represents a possible solution, applicable to low vortex Reynolds numbers (Re ) defined as the total circulation divided by the kinematic viscosity. In antithesis, our grasp reduces exponentially for turbulent vortices. Certainly this is not accidental. Turbulent flows are considerably more complex both analytically and experimentally. Even today the turbulent vortex is among the not very well-explored territories in aerodynamics. Not long ago, Ramasamy and Leishman [7] examined turbulent helicopter tip vortices using state of the art instruments and experimental techniques. Their high-resolution visualizations revealed that these types of whirls display the already familiar path to turbulence (probably slow, through spectral development). Inside the core, they have confirmed that helicopter tip vortices do enjoy laminarlike conditions. Approaching the core from the origin, past the laminar core and when a critical local Reynolds number is reached, the flow enters a transition region. This condition persists until a second critical Reynolds number where the flowfield changes into the “turbulent state” at larger radii. Most important of all, the accompanied high-fidelity velocity data (at Re 48; 000) exposed the following particular behavior for the azimuthal velocity component. In the region where the vortex is turbulent, the velocity decreases at a rate noticeably smaller than that of a laminar vortex. As a consequence of the new experimental evidence it became amply evident that high Re helicopter tip vortices cannot be modeled by the laminar formulations of the past. Instead one has to seek analytical representations of the phenomenon where at least the most fundamental effects of turbulence are included. Previous, theoretically more involved developments on the subject are those of Newman [8], Inversen [9], Tang [10], and Ramasamy and Leishman [7]. Here we present a new simple mathematically convenient formulation that accounts for the flattening effect in the tangential velocity profile.

Rotordynamics of Impeller Eye Seals with Wear-Damaged Teeth in Centrifugal Compressors

This paper investigates the influence of labyrinth seal teeth wear damage on the performance and the rotordynamic characteristics of impeller eye seals in centrifugal compressors. A well-established CFD-perturbation model was employed to predict the seal rotordynamic coefficients. The inclusion of at least an approximate shroud leakage path chamber is preferred for an accurate prediction of seal-inlet swirl velocity and flow-induced rotordynamic forces. It was found that impeller eye seals with teeth damage: (a) suffer significant leakage increases due to the increased seal clearance and (b) produce higher seal-inlet swirl velocity and thus larger rotordynamic forces that tend to cause the system to become unstable. It was also found that variations of the distorted teeth tip geometries have an insignificant influence on both leakage and rotordynamic coefficients for a given seal radial clearance. The impeller shroud leakage path influence on seal-inlet swirl velocity W0 and the effect of W0 were also explored to better understand the rotordynamic characteristics of the eye seal subject to various degrees of teeth damage.

Steady‐state properties and statistical distribution of atmospheric dust devils

A steady Rankine‐like vortex model of a dust devil is reported, which takes into account the sunlight absorption by airborne dust particles and the diabatic heating of a rotating dust column. For the maximum swirl velocity being a few times larger than the mean updraft velocity, the model admits significant simplifications allowing for its complete analytical treatment. The competitive effects of (i) the surface heat fluxes and (ii) the suspended‐dust‐caused diabatic heating on the vortex constitution (strength, height and shape) are examined. The second factor is found to be more influential for the strongest vortices. A reference exponential distribution of dust devils over their radius (visible diameter), which was introduced based on general arguments of mathematical information theory, is shown to fit satisfactory well the observational data on dust devils in Arizona and southern California and, in a preliminary way, on Mars.

Effect of liquid and air swirl strength and relative rotational direction on the instability of an annular liquid sheet

Instability of a swirling annular liquid sheet in swirling inner and outer air streams has been investigated by a temporal linear stability analysis. The effects of the swirling and axial motion of the liquid and the air streams, as well as the effects of relative inner and outer air swirl orientation with respect to the liquid swirl direction on the instability have been investigated. Results show that for a non-swirling liquid sheet axial inner air stream is more effective than axial outer air stream in enhancing the sheet instability. This is opposite of a swirling liquid sheet where axial outer air is more effective in promoting sheet instability compared to axially moving inner air stream. The liquid swirl has a destabilizing effect at the outer interface but has a stabilizing effect at the inner interface. At high liquid swirl Weber number, the outer air (with axial and swirl velocity components) is more effective in enhancing sheet instability compared to the inner air (with axial and swirl velocity components). To understand the effect of air swirl orientation with respect to liquid swirl direction, four possible combinations with both swirling air streams with respect to the liquid swirl direction have been considered. Results show that at high liquid swirl Weber number a combination of counter-rotating-inner air stream and co-rotating-outer air stream has the largest most unstable wave number. However, at low liquid swirl, co-inner/counter-outer combination has the largest most unstable wave number. The combination of inner and the outer air stream co-rotating with the liquid has the highest growth rate. In many combustion applications, the liquid sheet is injected in high pressure environment where the effect of high ambient pressure results in increased aerodynamic interaction due to high air density. Hence the effect of high ambient pressure is studied in terms of the dimensionless parameter of air-to-liquid density ratio. Results show significantly higher disturbance growth rates at high air pressure. However, the qualitative sheet stability behavior is similar to that at atmospheric pressure.