Simple Vortex Model Research Articles

Mitigation mechanism of torsional vortex-induced vibrations using aerodynamic countermeasures: Case study on a typical closed-box girder

In this paper, a torsional simplified vortex model (SVM) framework is deduced from the time-frequency characteristics of the aerodynamic forces and related vortex drift patterns obtained by numerical flow visualization. With the SVM, the mechanism of torsional vortex-induced vibrations (VIVs) in a typical closed-box bridge girder is investigated, and then the mechanism for the mitigation of these VIVs with aerodynamic countermeasures, such as spoilers on handrails or guide vanes near maintenance rails, is analysed. The results reveal that large-amplitude torsional VIVs occur in the bridge girder at an initial angle of attack (AOA) of + 3°. The spoilers can almost eliminate VIVs, whereas the guide vanes can moderately suppress them. The contributions of distributed aerodynamic moment to the global vortex-excited moment (VEM) on the upper surface of both the original and guide vane girders are much larger than those on the lower surface, implying that the aerodynamic behaviour over the upper surface is predominant in exciting and sustaining VIVs. The contributions of distributed aerodynamic moment to the global VEM on the improved girder with spoilers are much smaller than those on the original girder, particularly on the upper surface, which cannot trigger VIVs. Thus, VIVs disappear when the spoilers are installed on handrails. Subsequently, the flow fields during VIVs are obtained by numerical flow visualization. For both the original and guide vane girders, the torsional VIVs are mainly excited by the separated vortices forming at the windward barriers over the upper surface, while the separated vortices over the lower surface also make slight contribution to VIVs. After the guide vanes are installed near the maintenance rails, the scales of vortices over both the upper and lower surfaces are reduced, resulting in a weaker impact on the girder, which is fundamentally responsible for the mitigation effect of the guide vanes.

Aerodynamic force distribution and vortex drifting pattern around a double-slotted box girder under vertical vortex-induced vibration

Double-slotted box girder is a novel type of main girder for long-span bridges. To investigate the vertical vortex induced vibration (VIV) performance and aerodynamic effect of double-slotted box girder, wind tunnel tests were conducted on a spring-suspended sectional model. The results showed that the aerodynamic forces on the upper and lower surfaces of upstream box, the upper surface of middle box, and the rear regions of upper and lower surfaces of downstream box contribute positively to the VIV, becoming the main excitation source. Compared with streamlined closed-box and central-slotted box girders, the regions with obvious contribution values on double-slotted box girder surface significantly increase. This indicates that double slots allow the aerodynamic forces acting on larger areas of girder surface to participate in VEF generation and potentially affect the VIV performance. A vortex-related flow pattern around the double-slotted box girder was described by combining the vortex drifting theory and simplified vortex model, which provide insight into the mechanism of vertical VIV. Periodic vortex drifting exists on the upper surface of downstream box. The aerodynamic forces from the windward side to the front area of the lower surface of middle box appear to be significantly affected by vortices in windward slot.

A simple vortex model applied to an idealized rotor in sheared inflow

Abstract. A simple analytical vortex model is presented and used to study an idealized wind turbine rotor in uniform and sheared inflow, respectively. Our model predicts that 1D momentum theory should be applied locally when modelling a non-uniformly loaded rotor in a sheared inflow. Hence the maximum local power coefficient (expressed with respect to the local, upstream velocity) of an ideal rotor is not affected by the presence of shear. We study the interaction between the wake vorticity generated by the rotor and the wind shear vorticity and find that their mutual interaction results in no net generation of axial vorticity: the wake effects and the shear effects exactly cancel each other out. This means that there are no resulting cross-shear-induced velocities and therefore also no cross-shear deflection of the wake in this model.

Multiple-order vertical vortex-induced vibration mechanism of a typical streamlined closed-box girder

Multiple-order vertical vortex-induced vibrations (VIVs) have been frequently observed in prototype bridges as well as tested models in wind tunnels, but VIV excitation and VIV suppression mechanisms need further investigation. In this study, a simplified vortex model (SVM) derived from the spatial distribution characteristics of the wind pressure around the girder surface was developed to elucidate the multiple-order vertical VIV phenomena of a typical streamlined closed-box girder with additional attachments. The results showed that there are three potential lock-in ranges of vertical VIVs. The 1st lock-in range is excited and sustained by the separated vortex formation at the trailing edge, which is referred to as trailing-edge-vortex-dominated VIV. In the 2nd and 3rd lock-in ranges, the contribution of local aerodynamic forces to the general vortex-excited forces (VEFs) over the upper surface varies with the local positions in the form of simple harmonic curves. Therefore, the local aerodynamic force can be simplified by a concentrated force with an approximately constant loading amplitude and drift velocity, which is illustrated as a simplified moving vortex; based on this, an SVM can be established and utilized to associate the vortex-drift pattern with multiple vertical VIVs in terms of Strouhal number of the separated vortex. With the help of the SVM, the 2nd and 3rd lock-in ranges are excited and sustained by the separated vortex formation at the leading edge and then by a regular vortex drift pattern over the upper surface of the bridge girder, referred to as impinging-edge-vortex-dominated VIVs. Spoilers installed on the handrails can effectively suppress the separated vortex formation both at the trailing edge and leading edge; thus, vertical VIVs in all lock-in ranges can be mitigated.

On the relationships between different vortex identification methods based on local trace criterion

Vortical flow is generally considered to be a flow with a rotational trend, but vortex regions vary depending on the vortex identification methods by which they are extracted. In this paper, theoretical relationships between commonly used Q series vortex criteria, eigenvalue-based vortex criteria, and the Rortex method are analytically derived and built based on the local trace (LT) criterion (LTcri). The projections of vortex regions extracted by different vortex criteria onto the LT-plane constructed by LTcri are presented to graphically discuss their physical meanings and interrelations. The LTcri-based method reflects the local swirling patterns of flow and provides new interpretations of various vortex criteria in terms of local flow patterns. The simple vortex models, including Rankin vortex and Burgers' vortex, forced isotropic turbulence flow, and a compressor corner separation flow case with a practical Mach number, are tested and analyzed. The potential of the LTcri-based method is shown both by analyzing vortex dynamic properties and by distinguishing the different swirling patterns of complex vortices in tangle. This contributes to the exploration of flow mechanisms and furthers investigations into vortex dynamics.

A Numerical Investigation of the Influence of the Blade–Vortex Interaction on the Dynamic Stall Onset

Recently, fluid–structure coupling simulations of helicopter rotors in high-thrust forward flight suggested that dynamic stall might be triggered by the blade–vortex interaction. However, no clear evidence of a correlation between dynamic stall and blade–vortex interaction has yet been given. We propose in this paper a simplified two-dimensional numerical model that can be used to indicate the role that the blade–vortex interaction plays in dynamic stall onset for different flight conditions. In this model, the rotor blade element is considered in pitching oscillation motion with a nonuniform translation, and a simplified vortex model can be introduced or not in the simulation to highlight the effect of blade–vortex interaction. All flow parameters of this simplified model are deduced from data provided by previous three-dimensional high-fidelity fluid–structure simulations. The method is used for validation and analysis of three flight conditions. The results show that, for the two cases with moderate advance ratio, the dynamic stall event is only triggered when a blade–vortex interaction occurs in the stall region. For the high-speed test case, the dynamic stall event seems to be only triggered by the very high angle of attack due to the motion of the blade.

A simplified vortex model for the mechanism of vortex-induced vibrations in a streamlined closed-box girder

A simplified vortex model for the mechanism of vortex-induced vibrations in a streamlined closed-box girder

A vortex model for forces and moments on low-aspect-ratio wings in side-slip with experimental validation.

This paper studies low-aspect-ratio ([Formula: see text]) rectangular wings at high incidence and in side-slip. The main objective is to incorporate the effects of high angle of attack and side-slip into a simplified vortex model for the forces and moments. Experiments are also performed and are used to validate assumptions made in the model. The model asymptotes to the potential flow result of classical aerodynamics for an infinite aspect ratio. The [Formula: see text] → 0 limit of a rectangular wing is considered with slender body theory, where the side-edge vortices merge into a vortex doublet. Hence, the velocity fields transition from being dominated by a spanwise vorticity monopole ([Formula: see text] ≫ 1) to a streamwise vorticity dipole ([Formula: see text] ∼ 1). We theoretically derive a spanwise loading distribution that is parabolic instead of elliptic, and this physically represents the additional circulation around the wing that is associated with reattached flow. This is a fundamental feature of wings with a broad-facing leading edge. The experimental measurements of the spanwise circulation closely approximate a parabolic distribution. The vortex model yields very agreeable comparison with direct measurement of the lift and drag, and the roll moment prediction is acceptable for [Formula: see text] ≤ 1 prior to the roll stall angle and up to side-slip angles of 20°.

Comparison of the near‐wake between actuator‐line simulations and a simplified vortex model of a horizontal‐axis wind turbine

AbstractThe flow around an isolated horizontal‐axis wind turbine is estimated by means of a new vortex code based on the Biot–Savart law with constant circulation along the blades. The results have been compared with numerical simulations where the wind turbine blades are replaced with actuator lines. Two different wind turbines have been simulated: one with constant circulation along the blades, to replicate the vortex method approximations, and the other with a realistic circulation distribution, to compare the outcomes of the vortex model with real operative wind‐turbine conditions (Tjæreborg wind turbine). The vortex model matched the numerical simulation of the turbine with constant blade circulation in terms of the near‐wake structure and local forces along the blade. The results from the Tjæreborg turbine case showed some discrepancies between the two approaches, but overall, the agreement is qualitatively good, validating the analytical method for more general conditions. The present results show that a simple vortex code is able to provide an estimation of the flow around the wind turbine similar to the actuator‐line approach but with a negligible computational effort. Copyright © 2015 John Wiley & Sons, Ltd.

Confinement effects in wind-turbine and propeller measurements

AbstractA new model to account for the presence of the test-section wall in wind-turbine or propeller measurements is proposed. The test section, here assumed to be cylindrical, is modelled by means of axisymmetric source panels, while the wind turbine (or the propeller) is modelled with a simplified vortex model (Segalini & Alfredsson, J. Fluid Mech., vol. 725, 2013, pp. 91–116). Combining both models in an iterative scheme allows the simulation of the effect of the test-section wall on the flow field around the rotor. Based on this novel approach, an analysis of the flow modification due to blockage is conducted together with a comparison of actuator-disk theory results. Glauert’s concept of equivalent unconfined turbine is reviewed and extended to account for the angular velocity of the rotor. It is shown that Glauert’s equivalent free-stream velocity concept is beneficial and can correct most of the systematic error introduced by the presence of the test-section wall, although some discrepancies remain, especially in the power coefficient. The effect of the confinement on the wake structure is also discussed in terms of wake expansion/contraction, pitch of the tip vortices and forces at the rotor.

A simplified vortex model of propeller and wind-turbine wakes

AbstractA new vortex model of inviscid propeller and wind-turbine wakes is proposed based on an asymptotic expansion of the Biot–Savart induction law to account for the finite vortex core size. The circulation along the blade is assumed to be constant from the blade root to the tip approximating a turbine with maximum power production for given operating conditions. The model iteratively calculates the tip-vortex path, allowing the wake to expand/contract freely, and is afterward able to evaluate the velocity field in the whole domain. The ‘roller-bearing analogy’, proposed by Okulov and Sørensen (J. Fluid Mech., vol. 649, 2010, pp. 497–508), is used to determine the vortex core size. A comparison of the main outcomes of the present model with the general momentum theory is performed in terms of the operating parameters (namely the number of blades, the tip-speed ratio, the blade circulation and the vortex core size), demonstrating good agreement between the two. Furthermore, experimental data have been compared with the model outputs to validate the model under real operating conditions.

Comparison of Mobile-Radar Measurements of Tornado Intensity with Corresponding WSR-88D Measurements

Abstract In the United States, visual observations of tornadoes and/or the existence of tornado damage currently provide the sole evidence of tornadogenesis in association with a mesocyclone or other radar-detected storm-scale vortex. The severity of the tornado damage is currently the only means of estimating the intensity of tornadoes, radar detected or otherwise. The limitations of the damage-based record of tornado occurrence and intensity are well known and motivated this research. Weather Surveillance Radar-1988 Doppler (WSR-88D) measurements of the translating tornadic flow were compared with (semi-) coordinated measurements obtained near the surface with mobile radar. On the basis of a small yet fairly broad sample of tornadoes, high linear correlation was found between the vortex intensity (rotation plus translation) quantified using WSR-88D data and that quantified using Doppler on Wheels data. The possible effects of Doppler radar sampling on these results were explored through experiments with a simple vortex model. These experiments argued that the likelihood is high that a tornado would be sampled in a favorable way during at least one radar scan. Hence, the suggestion from this work is that WSR-88Ds (or similar operational radars) can potentially be used in isolation to estimate low-level tornado intensity. The proposed estimation is by way of a linear regression model, and application of this model is relevant only once a tornado is already confirmed.

Lagrangian particle statistics in turbulent flows from a simple vortex model

The statistics of Lagrangian particles in turbulent flows is considered in the framework of a simple vortex model. Here, the turbulent velocity field is represented by a temporal sequence of Burgers vortices of different circulation, strain, and orientation. Based on suitable assumptions about the vortices' statistical properties, the statistics of the velocity increments is derived. In particular, the origin and nature of small-scale intermittency in this model is investigated both numerically and analytically. We critically compare our results to experimental studies.

Baroclinic Vorticity Production in Protoplanetary Disks. II. Vortex Growth and Longevity

The factors affecting vortex growth in convectively stable protoplanetary disks are explored using numerical simulations of a two-dimensional anelastic-gas model that includes baroclinic vorticity production and radiative cooling. The baroclinic feedback, in which anomalous temperature gradients produce vorticity through the baroclinic term and vortices then reinforce these temperature gradients, is found to be an important process in the rate of growth of vortices in the disk. Factors that strengthen the baroclinic feedback include fast radiative cooling, high thermal diffusion, and large radial temperature gradients in the background temperature. When the baroclinic feedback is sufficiently strong, anticyclonic vortices form from initial random perturbations and maintain their strength for the duration of the simulation, for over 600 orbital periods. Based on both simulations and a simple vortex model, we find that the local angular momentum transport due to a single vortex may be inward or outward, depending on its orientation. The global angular momentum transport is highly variable in time and is sometimes negative and sometimes positive. This result is for an anelastic-gas model and does not include shocks that could affect angular momentum transport in a compressible-gas disk.

Lagrangian Measurements of Inertial Particle Accelerations in Grid Generated Wind Tunnel Turbulence

We describe Lagrangian measurements of water droplets in grid generated wind tunnel turbulence at a Taylor Reynolds number of R(lambda)=250 and an average Stokes number (St) of approximately 0.1. The inertial particles are tracked by a high speed camera moving along the side of the tunnel at the mean flow speed. The standardized acceleration probability density functions of the particles have spread exponential tails that are narrower than those of a fluid particles (St approximately 0) and there is a decrease in the acceleration variance with increasing Stokes number. A simple vortex model shows that the inertial particles selectively sample the fluid field and are less likely to experience regions of the fluid undergoing the largest accelerations. Recent direct numerical simulations compare favorably with these first measurements of Lagrangian statistics of inertial particles in highly turbulent flows.

Maximum Likelihood Estimates of Vortex Parameters from Simulated Coherent Doppler Lidar Data

Abstract The performance of pulsed coherent Doppler lidar in estimating aircraft trailing wake vortices by scanning across the aircraft flight track is evaluated using Monte Carlo lidar simulations of a simple vortex pair in both a nonturbulent and turbulent environment. The performance estimates are based on maximum likelihood estimates of aircraft wake vortex parameters and provide a measure of the ability of the lidar to detect and track wake vortices under the best possible conditions. Two aircraft types are considered: the Boeing 737 and the Boeing 747. Rigorous error analyses are produced by comparing the estimated parameters from numerical simulations of raw lidar data with the known input parameters of the simulation. It is shown that the probability density functions for the estimates are approximately Gaussian and the bias is very small. The main source of the bias was determined to be the movement of the vortex during the lidar scan. The estimation error is increased by the effects of a background turbulent velocity field. The trade-off between lidar pulse energy and pulse repetition frequency for the standard condition of constant laser power is also presented. It is shown that these maximum likelihood estimates provide accurate detection and tracking of the key vortex parameters for a simple vortex model, with and without background turbulence.

Optimal mixing in recirculation zones

Coarse-scale mixing in a recirculation zone is described with a simple vortex model. Time-dependent forcing is employed to change the vortex motion and mixing properties. An optimal mixing problem is defined in which the flux across the recirculation region shall be maximized under the side-constraints of bounded vortex motion and bounded actuation. Concepts of control theory and chaotic advection are used to achieve this goal. In particular, controllability is proven with a transformation into flat coordinates. Thus, a feedforward law for the optimal trajectory and a feedback law for its stabilization are derived. Observability of the vortex motion is indicated by a dynamic observer. Mixing in the optimized flow is studied using Poincaré maps. The low-frequency modulations to vortex motion are shown to substantially increase mixing in the average. Generalizations of the mathematical framework for mixing optimization are suggested for a larger class of models and flows.

Shock–planar curtain interactions: Strong secondary baroclinic deposition and emergence of vortex projectiles and late-time inhomogeneous turbulence

We continue our previous investigations (Yang, Zabusky, & Chern, 1990; Zabusky & Zhang, 2002) of the interaction of a shock with a planar, inclined curtain (slow/fast/slow) to a wider Mach number range (M = 1.5, 2.0, and 5.0) and longer times. In all cases, the generic features may be explained in terms of the opposite-signed vortex layers (deposited by the shock wave), which approach and collide to form a complex vortex bilayer (VBL). At M ≤ 2.0, the VBL traverses the shock tube and eventually collides with the opposite horizontal boundary and evolves into upstream and downstream moving inhomogeneous vortex projectiles (VPs) (Zabusky & Zeng, 1998). This is manifested as early-time “breakthrough” (Yang, Zabusky, & Chern, 1990). During the traversal, we observe and scale a strong secondary baroclinic circulation enhancement. We track and quantify the VPs and show that their velocities compare well to that from a simple vortex model. We also display turbulent domains and a new rapid early time turbulization at M = 5, when the VBL is narrower.

A Model for Multicomponent Spray Vaporization in a High-Pressure and High-Temperature Environment

A multicomponent droplet vaporization model including both gas and liquid phase transport processes was developed for multidimensional spray computations. This paper focuses on two effects altering vaporization in a high-pressure and high-temperature environment. One effect is on droplet surface regression caused by a higher vaporization rate. This effect is well characterized by the Lewis number and the Peclet number with the regression velocity. Formulas based on the two numbers were included to improve model accuracy. The other effect is on the nonideal behavior and was covered in the model by using the Peng-Robinson equation of state to determine phase equilibrium at the droplet surface. The model was validated by the results from an accurate simplified vortex model and experimental measurements, and excellent agreements were demonstrated. Further comparisons against the model without the two effects and an infinite diffusion model show that significant improvement was achieved by the model for single-droplet and spray computations.

CAVITATION IN VORTICAL FLOWS

▪ Abstract Cavitation in vortical structures is a common, albeit complex, problem in engineering applications. Cavitating vortical structures can be found on the blade surfaces, in the clearance passages, and at the hubs of various types of turbomachinery. Cavitating microvortices at the trailing edge of attached sheet cavitation can be highly erosive. Cavitating hub vortices in the draft tubes of hydroturbines can cause major surges and power swings. There is also mounting evidence that vortex cavitation is a dominant factor in the inception process in a broad range of turbulent flows. Most research has focused on the inception process, with limited attention paid to developed vortex cavitation. Wave-like disturbances on the surfaces of vapor cores are an important feature. Vortex core instabilities in microvortices are found to be important factors in the erosion mechanisms associated with sheet/cloud cavitation. Under certain circumstances, intense sound at discrete frequencies can result from a coupling between tip vortex disturbances and oscillating sheet cavitation. Vortex breakdown phenomena that have some commonalities are also noted, as are some differences with vortex breakdown in fully wetted flow. Simple vortex models can sometimes be used to describe the cavitation process in complex turbulent flows such as bluff body wakes and in plug valves. Although a vortex model for cavitation in jets does not exist, the mechanism of inception appears to be related to the process of vortex pairing. The pairing process can produce negative peaks in pressure that can exceed the rms value by a factor of ten, sometimes exceeding the dynamic pressure by a factor of two. A new and important issue is that cavitation is not only induced in vortical structures but is also a mechanism for vorticity generation.