Rankine Vortex Research Articles

Analysis on the fluid flow in vortex tube with vortex periodical oscillation characteristics

To reveal the energy transferring mechanism in the vortex tube, which is an interesting phenomenon in the area of heat and mass transfer, numerical simulation and analysis of the dynamic fluid flow were employed. In contrast to the previous static study, the focus of this paper is the dynamic process, or the oscillation, of the secondary circulation layer. Based on the fluid flow results derived from the unsteady 3-D computation, the existence of the forced or Rankine vortex was confirmed, which also verified the certainty of reverse flow in the cold end of the vortex tube. Then, the oscillation of the boundary layer of the central recirculation zone was emphasized and the periodical vibrating of the fluid flow within the secondary circulation zone, varying of its boundary, and the typical frequencies of points on a cross section were provided. Based on these results, a novel energy transferring mechanism in the vortex tube was proposed, under the condition that stable oscillation of the boundary layer is the dominant mechanism for the heat and mass transfer process.

Performance analysis of wind turbines at low tip-speed ratio using the Betz-Goldstein model

Analyzing wind turbine performance at low tip-speed ratio is challenging due to the relatively high level of swirl in the wake. This work presents a new approach to wind turbine analysis including swirl for any tip-speed ratio. The methodology uses the induced velocity field from vortex theory in the general momentum theory, in the form of the turbine thrust and torque equations. Using the constant bound circulation model of Joukowsky, the swirl velocity becomes infinite on the wake centreline even at high tip-speed ratio. Rankine, Vatistas and Delery vortices were used to regularize the Joukowsky model near the centreline. The new formulation prevents the power coefficient from exceeding the Betz-Joukowsky limit. An alternative calculation, based on the varying circulation for Betz-Goldstein optimized rotors is shown to have the best general behavior. Prandtl’s approximation for the tip loss and a recent alternative were employed to account for the effects of a finite number of blades. The Betz-Goldstein model appears to be the only one resistant to vortex breakdown immediately behind the rotor for an infinite number of blades. Furthermore, the dependence of the induced velocity on radius in the Betz-Goldstein model allows the power coefficient to remain below Betz-Joukowsky limit which does not occur for the Joukowsky model at low tip-speed ratio.

Modeling Financial Losses Resulting from Tornadoes in European Countries

Abstract Tornadoes are a notorious, common threat to human life and property in the United States. Although less common, violent tornadoes are also reported in Europe. The authors aim for an estimation of the average annual loss ratio of European buildings due to tornadoes. An aggregated loss model is used that takes as input the tornado intensity distribution over the Fujita scale (F scale), the distribution of tornado footprint sizes per F class, the vulnerability of European buildings, and the average occurrence rate of tornadoes. Information about these variables is taken from the European Severe Weather Database and, where needed, from the U.S. Storm Prediction Center tornado database, which contains about 16 times more records. However, both databases are biased. Weak tornadoes are underrepresented. Therefore a bias-corrected tornado intensity distribution is used, with its uncertainty taken from the literature. Individual tornadoes are modeled as moving Rankine vortices creating elliptic footprints with correlated length and width. This allows for the estimation of the area fraction of a tornado footprint with lower wind speeds than the maximum wind speed, which is generally used to attribute an intensity. This approach is applied to define effective vulnerability functions of European buildings. A major result is that an expected 90% of the tornadoes contribute only about 1% to the average loss, while the rare F4 tornadoes contribute more than 40% of losses. Given that most national tornado databases in Europe contain tornado records for recent years only and few (if any) violent tornadoes, observed losses can lead to a remarkable underestimation of tornado risk in Europe.

Numerical study of acoustic radiation dynamics of a Rankine vortex

The paper continues investigations of a fundamental problem important for understanding the nature of vortex flows: sound radiation by a perturbed Rankine vortex. Results of numerical simulation are presented for both quadrupole and higher-mode radiations. The structure and dynamics of tonal acoustic radiation generated by a vortex are considered in detail. The transition of a Rankine vortex to a perturbed state under small external perturbation is considered. Calculations are performed using the EBR scheme implemented by NOISEtte software.

Precessing vortex core in a swirling wake with heat release

Numerical simulation of the non-stationary three-dimensional swirling flow is presented for an open tube with a paraxial heat source. In the considered type of swirling flows, it is shown that a precessing vortex core (PVC) appears. The obtained PVC is a left-handed co-rotated bending single-vortex structure. The influence of the heat release enhancement on parameters of PVC is investigated. Using various turbulence models (the Spalart–Allmaras, k–ω and SST models), it is shown that an increase in the heat-source power leads to an increase in the PVC frequency and to a decrease in the amplitude of PVC oscillations. Moreover, we conduct the linear stability analysis of the simplified flow model with paraxial heating (the Rankine vortex with the piecewise axial flow and density) and demonstrate that its results correspond to the results of numerical simulations rather well. In particular, we prove that the left-handed bending mode (m=+1) is the most unstable one in the low-density wake and its frequency increases with a decrease of density ratio that is similar to the behavior of precession frequency with an increase of heat-source power.

Modified shear stress transport model with curvature correction for the prediction of swirling flow in a cyclone separator

The paper investigates the confined swirling flow in a cyclone. The numerical simulations are performed using a proposed eddy viscosity turbulence model, which accounts for the effects of the streamline curvature and rotation. This distinguishes the current model from the conventional Eddy Viscosity Models (EVMs) that are known to fail to predict the Rankine vortex in swirling flows. Although computationally more expensive approaches, the Reynolds Stress Model (RSM) and Large Eddy Simulation (LES), have demonstrated a high capability of dealing with such flows, these techniques are often unsuited for use in complex design studies where computational speed and robustness are key factors. In the present approach, the Shear Stress Transport with Curvature Correction (SSTCC) turbulence model is modified by the introduction of the Richardson number to account for the rotation and curvature effects. The numerical predictions were validated using experimental results and also compared to the data obtained using the RSM model and various EVMs without the proposed modifications. The investigations started with a benchmark case of a flow through a channel duct with a U-turn, after which more challenging simulations of a high swirling flow within a cyclone separator device were performed. The results show that the proposed model is competitive in terms of accuracy when compared to RSM and proves to be superior to the RSM model in terms of computational cost. Furthermore, it is found that the proposed model preserves the ability to represent the Rankine vortex profile at different longitudinal levels of the cyclone. It is also more efficient in terms of the computational cost than the SSTCC model without the introduced modifications.

Storm surge hazard in Manila Bay: Typhoon Nesat (Pedring) and the SW monsoon

The Philippines has an average of twenty tropical cyclones entering the Philippine Area of Responsibility every year, with about six to nine making landfall. In September 2011, Typhoon Nesat (Pedring) passed about 200 km north of Manila Bay with maximum sustained wind speeds of 46.3 m/s (CAT 2), yet it was one of the most destructive storms to affect the coastal areas of Metro Manila. In order to further understand the storm surge hazard for Metro Manila, and why Typhoon Nesat was so destructive, both an analysis of historical records and numerical modeling were undertaken. The historical analysis revealed that neither the most intense (with intensity defined as the maximum sustained wind speed of the cyclone) nor the storms that passed closest to the site generated the largest values of surge. Numerical simulations of the storm surge were completed using wind and pressure input data from the Holland vortex model, the Rankine vortex model and reforecast data from the National Center for Environmental Prediction (NCEP) model. NCEP data were found to better represent the wind field in the vicinity of Manila Bay, as it accounted for interaction between Typhoon Nesat and the SW monsoon winds. Neglecting these interactions, the storm surge simulations with analytical vortex models underestimated predicted surge values by more than five times, while the simulations with NCEP data accurately modeled the surge. The study highlights the need for improved storm surge warning systems that account for factors other than the cyclone’s maximum sustained wind speeds, which can affect the severity and duration of surge events.

Study of the turbulent swirl flow in the pipe behind the axial fan impeller

Experimental research of the turbulent swirl flow in the pipe behind the axial fan impeller is presented in this paper. Axial fan is inbuilt without guide vanes in the installation with a free inlet and ducted outlet, like it is widely used in the ventilation systems. One-component laser Doppler anemometry and stereo particle image velocimetry (SPIV) are used in two measuring sections on the fan pressure side and for three fan rotation numbers. Non-dimensional axial velocity profile is not significantly transformed downstream, while the circumferential is, although it preserves its character. Turbulence level is the highest in the vortex core in both measuring sections for all velocities. It increases downstream in the vortex core zone and decreases in the main flow region. Determined skewness and flatness factors point out the intermittent character of the generated turbulent swirl flow, as well as the existence of the organized coherent structure. Correlation curves indicate various dynamics of fluctuating circumferential velocity fields in measuring points. The Rankine vortex structure of the turbulent swirl flow is also revealed by the SPIV measurements. Analysis shows more dominant vortex core dynamics in the downstream section. Studied flow is characterized by extensive mass, momentum and energy transfer.

Study of aerodynamic forces acting on a train using a tornado simulator

A novel experiment was conducted to investigate the aerodynamic forces acting on a train traveling through a tornado, in which we developed a moving model rig with a tornado simulator. The flow field generated by the tornado simulator was validated by comparison with those of real tornadoes and the Rankine vortex model. Using this setup, we measured unsteady surface pressures on a model train as it passed through the vortex center. The side force, lift force, and yawing moment were estimated from the pressure data. The results were as follows: 1) the side force acting on the train changed its direction from negative to positive while passing through the tornado-like swirling flow; 2) the lift force increased as the train approached the flow and became maximum around the vortex center; 3) the yawing moment first decreased slightly and then reached its maximum around the vortex center. Asymmetric wave forms of the forces and moment at the center of the tornado simulator suggested that the train itself may have affected the vortex structure of the flow.

Numerical Analysis of Tip Cavitation on Marine Propeller with Wake Alignment Using a Simple Surface Panel Method “SQCM”

This paper presents the calculation method of tip cavitation with wake alignment. Tip cavitation consists of tip vortex cavitation and tip super cavitation which means the undeveloped and local super cavitation around blade tip. The feature of this study is that the method applies the wake alignment model in order to express the realistic phenomena of tip cavitation and predict the pressure fluctuation more accurately. In the present method, the wake sheet is deformed according to the induced velocity vector on the vortex lines. The singularity of the potential vortex can be removed by using the Rankine Vortex model. This paper shows the calculated results regarding cavitation pattern, pressure fluctuation etc. comparing with published experimental data and calculated results without wake alignment.

Long-wave instability of a helical vortex

We investigate the instability of a single helical vortex filament of small pitch with respect to displacement perturbations whose wavelength is large compared to the vortex core size. We first revisit previous theoretical analyses concerning infinite Rankine vortices, and consider in addition the more realistic case of vortices with Gausssian vorticity distributions and axial core flow. We show that the various instability modes are related to the local pairing of successive helix turns through mutual induction, and that the growth rate curve can be qualitatively and quantitatively predicted from the classical pairing of an array of point vortices. We then present results from an experimental study of a helical vortex filament generated in a water channel by a single-bladed rotor under carefully controlled conditions. Various modes of displacement perturbations could be triggered by suitable modulation of the blade rotation. Dye visualisations and particle image velocimetry allowed a detailed characterisation of the vortex geometry and the determination of the growth rate of the long-wave instability modes, showing good agreement with theoretical predictions for the experimental base flow. The long-term (downstream) development of the pairing instability leads to a grouping and swapping of helix loops. Despite the resulting complicated three-dimensional structure, the vortex filaments surprisingly remain mostly intact in our observation interval. The characteristic distance of evolution of the helical wake behind the rotor decreases with increasing initial amplitude of the perturbations; this can be predicted from the linear stability theory.

Wind pressure features of large-span flat roof in different wind fields induced by conical vortex

The wind pressure features on a large-span flat roof in uniform flow field and turbulent field induced by conical vortex were studied, through wind tunnel tests. From the comparison of the mean and fluctuating wind pressure distributions on a flat roof in different wind fields induced by conical vortex, results indicate that the mean suction dominates in the smooth flow, whereas the fluctuating suction is more obvious in the turbulent flow. The probability density function for the pressure fluctuations under different approaching flows is analyzed. The two-peaked distribution, peculiar to turbulent flow field, is observed on the curve of probability density. The fluctuating pressures at reattachment points are larger under the turbulent flow. This indicates a more intense reattachment, which may cause overturning moment for roof-mounted items. Point vortex, RanKine vortex, and simplified Cook expression are applied to fit the pressure profiles beneath conical vortices, respectively. The results have shown that the RanKine vortex model and simplified Cook expression were applicable to forecast the wind pressure profiles beneath conical vortices, while point vortex underestimated the real wind suction. The wind pressure distributions in turbulent fields induced by different wind angles were contrasted, when the approaching flow is along the diagonal of the roof, the intensity of the vortex pairs is almost equal, with obvious reattachment. When the approaching flow deviate from the diagonal of the roof, the lateral turbulent component spins the vortex more quickly; this induces larger mean suctions beneath windward vortices. Smaller suctions are observed beneath the leeward vortex, due to less vorticity being converted to vortex motion from the freestream.

Analysis of the horizontal two‐dimensional near‐surface structure of a winter tornadic vortex using high‐resolution in situ wind and pressure measurements

AbstractThe horizontal two‐dimensional near‐surface structure of a tornadic vortex within a winter storm was analyzed. The tornadic vortex was observed on 10 December 2012 by the high‐resolution in situ observational linear array of wind and pressure sensors (LAWPS) system in conjunction with a high‐resolution Doppler radar. The 0.1 s maximum wind speed and pressure deficit near the ground were recorded as 35.3 m s−1 and −3.8 hPa, respectively. The horizontal two‐dimensional distributions of the tornadic vortex wind and pressure were retrieved by the LAWPS data, which provided unprecedented observational detail on the following important features of the near‐surface structure of the tornadic vortex. Asymmetric convergent inflow toward the vortex center existed. Total wind speed was strong to the right and rear side of the translational direction of the vortex and weak in the forward part of the vortex possibly because of the strong convergent inflow in that region. The tangential wind speed profile of the vortex was better approximated using a modified Rankine vortex rather than the Rankine vortex both at 5 m above ground level (agl) and 100 m agl, and other vortex models (Burgers‐Rott vortex and Wood‐White vortex) were also compared. The cyclostrophic wind balance was violated in the core radius R0 and outside the core radius in the forward sector; however, it was held with a relatively high accuracy of approximately 14% outside the core of the vortex in the rearward sector (from 2 R0 to 5 R0) near the ground.

On the trivial solutions for the rotating patch model

In this paper, we study the clockwise simply connected rotating patches for Euler equations. By using the moving plane method, we prove that Rankine vortices are the only solutions to this problem in the class of slightly convex domains. We discuss in the second part of the paper the case where the angular velocity $${\varOmega=\frac{1}{2}}$$ , and we show without any geometric condition that the set of the V-states is trivial and reduced to the Rankine vortices.

Numerical simulation of observed flow phenomena in the supply and control ports and associated feed channels of a mini-vortex amplifier

The trajectory and reach of jets issuing from tangential control ports at the periphery of a vortex amplifier's swirl chamber depend largely on design geometry, size and pressures applied. Excessive control port pressure causes these jets to extend too far across the face of the radial supply ports, to impact on the opposing supply port wall whereupon, they bifurcate to create back diffusion of control port flow along the supply port channels. Flow through vortex amplifier geometry is simulated using a baseline Reynolds stress turbulence model with Computational Fluid Dynamics (CFX) automatic wall treatment. Anisotropic stress and vortex stretching in the swirl chamber and outlet have not prevented convergence (based on normalised vortex amplifier residuals). Known flow structures are reproduced. This paper is focussed on simulation close to pressures needed for bifurcation. Just before the point on an operating characteristic at which bifurcated tangential flow appears, the recirculation zone crossing most of the radial supply stretches to intermittently cut off the radial flow. The steady state results indicate asymmetry between the four ports, as smoke visualisation tests also imply. The transient results are sufficient to demonstrate time-dependent structures and suggest periodicity of flow structures. The model can be used to inform design and operability studies. Moreover, a curious near-wall structure of spinning flow not previously reported has been predicted close to the axis and hugging the swirl chamber wall opposite the outlet, at radii within the forced part of the Rankine vortex.

On the Vortex Detection Method Using Continuous Wavelet Transform with Application to Propeller Wake Analysis

The method based on the continuous wavelet transformation to detect and characterize two-dimensional vortex is analyzed for a synthetic flow and applied to vortex detection of propeller wake. The characteristics of a vortex, such as center location, core radius, and circulation, are extracted based on the Lamb-Oseen and Rankine vortex models, the latter of which is a novel attempt. The effects of various factors such as the difference scheme, the grid and scale discretization, transform variable, and vortex model on vortex detection have been investigated thoroughly. The method is further applied to identify the tip vortex in a propeller wake.

The most typical shape of oceanic mesoscale eddies from global satellite sea level observations

In this research, we normalized the characteristics of ocean eddies by using satellite observation of the Sea Level Anomaly (SLA) data to determine the most typical shape of ocean eddies. This normalization is based on modified analytic functions with nonlinear optimal fitting. The most typical eddy is the Taylor vortex (∼50%), which exhibits a Gaussian-shaped exp(−r 2) SLA and a vorticity distribution of (1 − r 2)exp(−r 2) as a function of the normalized radii r. The larger the amplitude of the eddy, the more likely the eddy is to be Gaussian-shaped. Furthermore, approximately 40% of ocean eddies are combinations of two Gaussian eddies with different parameters, but the composition of these types of eddies is more like a quadratic eddy than a Gaussian one. Only a small portion of oceanic eddies are pure quadratic eddies (<10%) with the same vorticity distribution as a Rankine vortex. We concluded that the Taylor vortex is a good approximation of the typical shape of ocean eddies.

Characterizing the eddy field in the Arctic Ocean halocline

AbstractIce‐Tethered Profilers (ITP), deployed in the Arctic Ocean between 2004 and 2013, have provided detailed temperature and salinity measurements of an assortment of halocline eddies. A total of 127 mesoscale eddies have been detected, 95% of which were anticyclones, the majority of which had anomalously cold cores. These cold‐core anticyclonic eddies were observed in the Beaufort Gyre region (Canadian water eddies) and the vicinity of the Transpolar Drift Stream (Eurasian water eddies). An Arctic‐wide calculation of the first baroclinic Rossby deformation radius Rd has been made using ITP data coupled with climatology; Rd ∼ 13 km in the Canadian water and ∼8 km in the Eurasian water. The observed eddies are found to have scales comparable to Rd. Halocline eddies are in cyclogeostrophic balance and can be described by a Rankine vortex with maximum azimuthal speeds between 0.05 and 0.4 m/s. The relationship between radius and thickness for the eddies is consistent with adjustment to the ambient stratification. Eddies may be divided into four groups, each characterized by distinct core depths and core temperature and salinity properties, suggesting multiple source regions and enabling speculation of varying formation mechanisms.

Multi-objective efficiency enhancement using workload spreading in an operational data center

The cooling systems of rapidly growing Data Centers (DCs) consume a considerable amount of energy, which is one of the main concerns in designing and operating DCs. The main source of thermal inefficiency in a typical air-cooled DC is hot air recirculation from outlets of servers into their inlets, causing hot spots and leading to performance reduction of the cooling system. In this study, a thermally aware workload spreading method is proposed for reducing the hot spots while the total allocated server workload is increased. The core of this methodology lies in developing an appropriate thermal DC model for the optimization process. Given the fact that utilizing a high-fidelity thermal model of a DC is highly time consuming in the optimization process, a three dimensional reduced order model of a real DC is developed in this study. This model, whose boundary conditions are determined based on measurement data of an operational DC, is developed based on the potential flow theory updated with the Rankine vortex to account for buoyancy and air recirculation effects inside the DC. Before evaluating the proposed method, this model is verified with a computational fluid dynamic (CFD) model simulated with the same boundary conditions. The efficient load spreading method is achieved by applying a multi-objective particle swarm optimization (MOPSO) algorithm whose objectives are to minimize the hot spot occurrences and to maximize the total workload allocated to servers. In this case study, by applying the proposed method, the Coefficient of Performance (COP) of the cooling system is increased by 17%, and the total allocated workload is increased by 10%. These results demonstrate the effectiveness of the proposed method for energy efficiency enhancement of DCs.

A Hurricane Tangential Wind Profile Estimation Method for C-Band Cross-Polarization SAR

Hurricane tangential wind profiles are routinely observed by aircraft reconnaissance in order to estimate the surface winds. However, these wind profile estimates are occasionally biased because along-track aircraft observations might not determine the nonaxisymmetric hurricane structure characteristics. In this paper, we resolve this problem by calculating the mean wind speed in all radial directions using cross-polarization SAR wide-swath images. Moreover, we propose a one-half modified Rankine vortex (OHMRV) model to describe the hurricane wind profile, particularly for those wind profiles with a wind speed maximum and an inflection point possibly associated with the degeneration of the inner wind maximum in the hurricane reintensification phase. OHMRV characterizes the hurricane wind profile and represents a model that complements the previously established single-modified Rankine vortex model and the double-modified Rankine vortex model. Moreover, the OHMRV-derived wind profiles are used to estimate hurricane intensity and structure parameters, such as the maximum wind speed and the radius of maximum wind. For validation of the method, the estimated ISPs are compared with measurements by the stepped-frequency microwave radiometer on board the National Oceanic and Atmospheric Administration aircraft. These parameters contribute to a description of hurricane inner-core intensity and structure associated with eyewall replacement cycles.