Circumferential Vorticity Research Articles

Vorticity dynamics diagnosis of the internal flow field in a high-load counter-rotating compressor

AbstractA high-load counter-rotating compressor is optimised based on the method of coupling aerodynamic optimisation technology and computational fluid dynamics, and the flow structures in the passage are analysed and evaluated by vorticity dynamics diagnosis. The results show that the aerodynamic performance of optimised compressor are obviously improved at both design point and off-design point. By comparing the distribution characteristics of vorticity dynamics parameters on the blade surface before and after the optimisation, it is found that BVF (boundary vorticity flux) and circumferential vorticity can effectively capture high flow loss regions such as shock waves and secondary flow in the passage. In addition, the BEF (Boundary enstrophy flux) diagnosis method based on the theory of boundary enstrophy flux is developed, which expands the application scenario of the boundary vorticity dynamics diagnosis method. The change of vorticity dynamics parameters shows blade geometric parameters’ influence on the passage’s viscous flow field, which provides a theoretical basis for the aerodynamic optimisation design.

The Influence of a Blade-Guiding Fin on the Pneumatic Performance of an Axial-Flow Cooling Fan

An axial-flow cooling fan was taken as the research object in this paper, and a certain number of simulation models with different blade-guiding fin shapes were established. The methods of computational fluid dynamics (CFD), circumferential vorticity (CV) analysis and the response surface method (RSM) based on the design of experiments (DOE) method were all employed. The main external flow characteristics of the cooling fan, the blade surface pressure distribution, the static pressure efficiency and the fan power were obtained and compared. The relationships between the pneumatic performance and the fin shape parameters were subsequently investigated by the DOE method. The results obtained in this paper showed that a change in the fin height had a great influence on the pneumatic performance, while changes in its thickness had less of an influence. For the cooling fan studied in this paper, by adding reasonable structure-guiding fins onto the cooling fan blade, the static pressure efficiency was increased by a maximum of 7.6%. The research results have a good guiding significance regarding the srtructure design and optimization of axial cooling fans.

Recovery of radial-axial velocity in axisymmetric swirling flows of a viscous incompressible fluid in the Lagrangian consideration of vorticity evolution

Swirling laminar axisymmetric flows of viscous incompressible fluids in a potential field of body forces are considered. The study of flows is carried out in a cylindrical coordinate system. In the flows, the regions in which the axial derivative of the circumferential velocity cannot take on zero value in some open neighborhood (essentially swirling flows) and the regions in which this derivative is equal to zero (the region with layered swirl) are considered separately. It is shown that a well-known method (the method of viscous vortex domains) developed for non-swirling flows can be used for regions with layered swirling. For substantially swirling flows, a formula is obtained for calculating the radial-axial velocity of an imaginary fluid through the circumferential vorticity component, the circumferential circulation of a real fluid, and the partial derivatives of these functions. The particles of this imaginary fluid “transfer” vortex tubes of the radial-axial vorticity component while maintaining the intensity of these tubes, and also “transfer” the circumferential circulation and the product of the circular vorticity component by some function of the distance to the axis of symmetry. A non-integral method for reconstructing the velocity field from the vorticity field is proposed. It is reduced to solving a system of linear algebraic equations in two variables. The obtained result is proposed to be used to extend the method of viscous vortex domains to swirling axisymmetric flows.

Numerical simulation on role of the rotating stall on the hump characteristic in a mixed flow pump using modified partially averaged Navier-Stokes model

Insufficient understanding of flow instability interaction between hump characteristic and the rotating stall is a major problem in the application of mixed flow pumps. In this paper, the unsteady flow characteristics of a mixed flow pump are studied numerically to understand the hump characteristic generating mechanism using a modified SST k-ω partially averaged Navier-Stokes (MSST PANS) model. The predicted pump characteristic curves show good agreement with experimental data. Fundamental results on time-averaged flow pattern and energy loss distributions depict that the substantial rise of energy loss in the pump impeller is the main reason for the hump characteristic. Detailed flow structures show the peak regions of circumferential vorticity (Ωθ) and boundary vortex flux (BVF) are located at the blade tip near the trailing edge (TE) and leading edge (LE). Further analysis on the flow angle and blade loading are carried out. The results indicate that the peak region located near the LE of spanwise = 0.8 and streamwise = 0.3 is the source of the rotating stall evolution. In this process, the substantial reduction in the blade loading occurs near the LE, eventually induces the head drop. Finally, pressure fluctuations analysis depicts that low-frequency signal is observed induced by the rotating stall evolution.

A boundary vorticity diagnosis of the flows in a model pump-turbine in turbine mode

In the present study, the internal flow field in a model pump-turbine operating in turbine mode was numerically studied. By recognizing that appearance of boundary vorticity flux (BVF)’s peaks might act as the precursors of flow separation in turbomachines, flow diagnosis based on the boundary vorticity dynamics was then performed. It was shown that the effect of the BVF distribution at the condition in design operating zone is to weaken the axial vorticity component ωz, as well as to enhance the radial and circumferential vorticity components ωr and ωθ. Thus, the peaks of the axial BVF component σz led to the strong weakening of ωz, which is responsible for the flow separations. Geometric optimization for the runner was then achieved by modifying the inlet angle of the blade from 14° to 16°. The optimization successfully suppressed the occurrence of the flow separations and improved the moment on the runner at design operating condition by 4%, which was achieved by the redistribution of the axial BVF component generated by pressure σpz on the pressure side. The fact that only an accurate steady simulation is required for the analysis indicates the great potential application of this method in engineering practice.

Entropy and Vorticity Wave Generation in Realistic Gas Turbine Combustors

Understanding the nature of the unsteady flow at the combustor exit is required to accurately simulate time-dependent phenomena in the turbine entry, such as indirect noise generation. Using large-eddy simulations of the combustion process in a realistic geometry, the flow at its exit is analyzes. Two realistic near-ground certification operating conditions are considered. Different mechanisms for large-scale flow and thermal structure generation are described, which are ejected into the turbine. Modal decomposition methods are used to extract the spatial and temporal scales at the turbine entry. It is found that, depending on the operating condition, the entropy waves convect as elongated streaks in the core of the combustor annulus or the proximity of the walls. The dominant unsteady character of the fluctuations exhibits different spectral properties: that is, low frequency in the core and high frequency toward walls. At the combustor exit, the vortical field is dominated by the swirl in the air inlet, which is found to have little influence on the entropy perturbations. Furthermore, the importance of considering the interaction of multiple fuel injectors and combustion zones in an annular combustor is investigated. It is shown that pulsating circumferential vorticity modes can occur in multisector annular combustors, but these do not affect the entropy wave distribution.

Flow field behind a complex total pressure distortion screen

The flow field behind a complex total pressure distortion screen is investigated experimentally and numerically. The distortion screen is designed using an established design methodology and fabricated by water-jet cutting technique. The distorted total pressure field behind the screen is quantified by a distortion index parameter, which is evaluated from computations and experiments for several values of inlet Mach number. The root-mean-square error between the target total pressure values and that achieved by the screen design at the aerodynamic interface plane is 4.75%. The evolution of the distorted total pressure field downstream of the screen is presented in detail in terms of radial and circumferential total pressure distributions and their gradients. An alternative interpretation of the distorted total pressure field is made by means of defining a total pressure flux existing behind the screen and expanding it using derivative-moment transformation technique. It is seen that the circumferential vorticity is a major contributing factor to the total pressure flux.

Optimization design of annular axial cooling fan based on circumferential vorticity analysis

As complex axial flow machinery, lots of vortex distributes around engine cooling fan. Negative circumferential vorticity (CV) leads to low efficiency and power loss. In order to investigate the adverse effects of CV on aerodynamic performances of the fan, a mathematical physical relationship between CV and aerodynamic performances is established, and the location of the negative CV is found by the method of vorticity analysis. An outer ring is designed for annular cooling fan, and the parameter of aperture rate is defined in this paper. Both static pressure and power loss is overall considerate during the optimization process of the outer ring, and putting forward that optimum range of the aperture rate is different for various annular fans.

Effect of blade tip geometry on tip leakage vortex dynamics and cavitation pattern in axial-flow pump

A series of blade tip geometries, including original plain tip, rounded tip on the pressure side and diverging tip towards the suction side, were adopted to investigate the effect of blade geometry on tip leakage vortex dynamics and cavitation pattern in an axial-flow pump. On the basis of the computation, it clearly shows the flow structure in the clearance for different tip configurations by the detailed data of axial velocity and turbulent kinetic energy. The in-plain trajectory, in aspects of the angle between the blade suction side and vortex core and the initial point of tip leakage vortex, was presented using the maximum swirling strength method. The most striking feature is that the inception location of tip leakage vortex is delayed for chamfered tip due to the change of blade loading on suction side. Some significant non-dimensional parameters, such as pressure, swirling strength and turbulent kinetic energy, were used to depict the characteristics of tip vortex core. By the distribution of circumferential vorticity which dominates the vortical flows near the tip region, it is observed that the endwall detachment as the leakage flow meets the mainstream varies considerably for tested cases. The present study also indicates that the shear layer feeds the turbulence into tip leakage vortex core, but the way is different. For the chamfered tip, high turbulence level in vortex core is mainly from the tip clearance where large turbulent kinetic energy emerges, while it is almost from a layer extending from the suction side corner for rounded tip. At last, the visualized observations show that tip clearance cavitation is eliminated dramatically for rounded tip but more intensive for chamfered tip, which can be associated with the vortex structure in the clearance.

Numerical simulations of the internal flow pattern of a vortex pump compared to the Hamel-Oseen vortex

We did a numerical study of the internal flow field of a vortex pump. Five operating points were considered and validated through a measured characteristic curve. The internal flow pattern of a vortex pump was analyzed and compared to the Hamel-Oseen vortex model. The calculated flow field was assessed with respect to the circumferential velocity, the vorticity and the axial velocity. Whereas the trajectories of the circumferential velocity were largely in line with the Hamel-Oseen vortex model, the opposite was true for vorticity. Only the vorticity at strong part load was in line with the predictions of the Hamel-Oseen vortex model. We therefore compared the circumferential velocity and vorticity for strong part load operation to the analytical predictions of the Hamel-Oseen vortex model. The simulated values were below the analytical values. The study therefore suggests that a vortex similar to the Hamel-Oseen vortex is only present at the strong part load operation.

Three-dimensional flow structures and associated turbulence in the tip region of a waterjet pump rotor blade

Stereo particle image velocimetry measurements focus on the flow structure and turbulence within the tip leakage vortex (TLV) of an axial waterjet pump rotor. Unobstructed optical access to the sample area is achieved by matching the optical refractive index of the transparent pump with that of the fluid. Data obtained in closely spaced planes enable us to reconstruct the 3D TLV structure, including all components of the mean vorticity and strain-rate tensor along with the Reynolds stresses and associated turbulence production rates. The flow in the tip region is highly three-dimensional, and the characteristics of the TLV and leakage flow vary significantly along the blade tip chordwise direction. The TLV starts to roll up along the suction side tip corner of the blade, and it propagates within the passage toward the pressure side of the neighboring blade. A shear layer with increasing length connects the TLV to the blade tip and initially feeds vorticity into it. During initial rollup, the TLV involves entrainment of a few vortex filaments with predominantly circumferential vorticity from the blade tip. Being shed from the blade, these filaments also have high circumferential velocity and appear as swirling jets. The circumferential velocity in the TLV core is also substantially higher than that in the surrounding passage flow, but the velocity peak does not coincide with the point of maximum vorticity. When entrainment of filaments stops in the aft part of the passage, newly forming filaments wrap around the core in helical trajectories. In ensemble-averaged data, these filaments generate a vortical region that surrounds the TLV with vorticity that is perpendicular to that in the vortex core. Turbulence within the TLV is highly anisotropic and spatially non-uniform. Trends can be traced to high turbulent kinetic energy and turbulent shear stresses, e.g., in the shear layer containing the vortex filaments and the contraction region situated along the line where the leakage backflow meets the throughflow, causing separation of the boundary layer at the pump casing. Upon exposure to adverse pressure gradients in the aft part of the passage, at 0.65–0.7 chord fraction in the present conditions, the TLV bursts into a broad turbulent array of widely distributed vortex filaments.

Influence of Rim Seal Purge Flow on the Performance of an Endwall-Profiled Axial Turbine

Nonaxisymmetric endwall profiling is a promising method to reduce secondary losses in axial turbines. However, in high-pressure turbines, a small amount of air is ejected at the hub rim seal to prevent the ingestion of hot gases into the cavity between the stator and the rotor disk. This rim seal purge flow has a strong influence on the development of the hub secondary flow structures. This paper presents time-resolved experimental and computational data for a one-and-1/2-stage high work axial turbine, showing the influence of purge flow on the performance of two different nonaxisymmetric endwalls and the axisymmetric baseline case. The experimental total-to-total efficiency assessment reveals that the nonaxisymmetric endwalls lose some of their benefit relative to the baseline case when purge is increased. The first endwall design loses 50% of the efficiency improvement seen with low suction, while the second endwall design exhibits a 34% deterioration. The time-resolved computations show that the rotor dominates the static pressure field at the rim seal exit when purge flow is present. Therefore, the purge flow establishes itself as jets emerging at the blade suction side corner. The jet strength is modulated by the first vane pressure field. The jets introduce circumferential vorticity as they enter the annulus. As the injected fluid is turned around the rotor leading edge, a streamwise vortex component is created. The dominating leakage vortex has the same sense of rotation as the rotor hub passage vortex. The first endwall design causes the strongest circumferential variation in the rim seal exit static pressure field. Therefore, the jets are stronger with this geometry and introduce more vorticity than the other two cases. As a consequence the experimental data at the rotor exit shows the greatest unsteadiness within the rotor hub passage with the first endwall design.

Vorticity Dynamics in Axial Compressor Flow Diagnosis and Design—Part II: Methodology and Application of Boundary Vorticity Flux

In a companion paper (2008, “Vorticity Dynamics in Axial Compressor Flow Diagnosis and Design,” ASME J. Fluids Eng., 130, p. 041102), a study has been made on the critical role of circumferential vorticity (CV) in the performance of axial compressor in through-flow design (TFD). It has been shown there that to enhance the pressure ratio, the positive and negative CV peaks should be pushed to the casing and hub, respectively. This criterion has led to an optimal TFD that indeed improves the pressure ratio and efficiency. The CV also has great impact on the stall margin as it reflects the end wall blockage, especially at the tip region of the compressor. While that work was based on inviscid and axisymmetric theory, in this paper, we move on to the diagnosis and optimal design of fully three-dimensional (3D) viscous flow in axial compressors, focusing on the boundary vorticity flux (BVF), which captures the highly localized peaks of pressure gradient on the surface of the compressor blade, and thereby signifies the boundary layer separation and dominates the work rate done to the fluid by the compressor. For the 2D cascade flow we show that the BVF is directly related to the blade geometry. BVF-based 2D and 3D optimal blade design methodologies are developed to control the velocity diffusion, of which the results are confirmed by Reynolds-averaged Navier–Stokes simulations to more significantly improve the compressor performance than that of CV-based TFD. The methodology enriches the current aerodynamic design system of compressors.

Volumetric three-component velocimetry measurements of the turbulent flow around a Rushton turbine

Volumetric three-component velocimetry measurements have been taken of the flow field near a Rushton turbine in a stirred tank reactor. This particular flow field is highly unsteady and three-dimensional, and is characterized by a strong radial jet, large tank-scale ring vortices, and small-scale blade tip vortices. The experimental technique uses a single camera head with three apertures to obtain approximately 15,000 three-dimensional vectors in a cubic volume. These velocity data offer the most comprehensive view to date of this flow field, especially since they are acquired at three Reynolds numbers (15,000, 107,000, and 137,000). Mean velocity fields and turbulent kinetic energy quantities are calculated. The volumetric nature of the data enables tip vortex identification, vortex trajectory analysis, and calculation of vortex strength. Three identification methods for the vortices are compared based on: the calculation of circumferential vorticity; the calculation of local pressure minima via an eigenvalue approach; and the calculation of swirling strength again via an eigenvalue approach. The use of two-dimensional data and three-dimensional data is compared for vortex identification; a ‘swirl strength’ criterion is less sensitive to completeness of the velocity gradient tensor and overall provides clearer identification of the tip vortices. The principal components of the strain rate tensor are also calculated for one Reynolds number case as these measures of stretching and compression have recently been associated with tip vortex characterization. Vortex trajectories and strength compare favorably with those in the literature. No clear dependence of trajectory on Reynolds number is deduced. The visualization of tip vortices up to 140° past blade passage in the highest Reynolds number case is notable and has not previously been shown.

Diabatically Induced Secondary Flows in Tropical Cyclones. Part II: Periodic Forcing

Abstract The linearized equation for the time-varying, axially symmetric circumferential component of the vorticity in a hurricane-like vortex closely resembles the classical Sawyer–Eliassen equation for the quasi-steady, diabatically induced secondary-flow streamfunction. The salient difference lies in the coefficients of the second partial derivatives with respect to radius and height. In the Sawyer–Eliassen equation, they are the squares of the buoyancy and isobaric local inertia frequencies; in the circumferential vorticity equation they are the differences between these quantities and the square of the frequency with which the imposed forcing varies. The coefficient of the mixed partial derivative with respect to radius and height is the same in both equations. Thus, for low frequencies the response to periodic forcing is a slowly varying analog to steady Sawyer–Eliassen solutions. For high frequencies, the solutions are radially propagating inertia-buoyancy waves. Since the local inertia frequency, which approximately defines the boundary between quasi-steady and propagating solutions, decreases with radius, quasi-steady solutions in the vortex core transform into radiating ones far from the center. Periodic forcing will always lead to some wave radiation to the storm environment unless the period of the forcing is longer than a half-pendulum day.

Distribution of non-plane strain in experimental compression of short cylinders of Solnhofen limestone

Axi-symmetric compression experiments on short cylinders (radius>length) have great potential for the investigation of different non-plane strain geometries. In such experiments strain geometry and intensity are heterogeneously distributed throughout the specimens due to the effects of friction at the contact surface between the pistons and the specimen. We ran a series of tests on Solnhofen limestone at constant confining pressure (200 MPa), temperature (600 °C) and displacement rate (5.2×10 −6 m s −1), conditions at which this material deforms predominantly by crystal plasticity. Using shape and crystallographic preferred orientation (SPO and CPO) patterns of calcite grains, the latter measured by electron back-scattered diffraction techniques (EBSD), we can discriminate areas in the deformed specimens with distinct non-plane strain geometries. SPO and CPO patterns record differences in the orientation of the finite stretching direction with respect to the external reference frame. It is radial in the vicinities of the rigid loading pistons, but circumferential outside the periphery of the pistons. As shortening progressed, the middle part of the specimen was extruded with respect to the contacts with the rigid end pieces, imparting a non-coaxial component to the flow with a circumferential vorticity axis in both upper and lower halves of the specimen. This component was recorded in the microstructure as an asymmetric CPO. The aim of the experiments is to improve the interpretation of naturally deformed rock bodies when strain departs from plane strain conditions by using the CPO as a 3D kinematic indicator, providing not only shearing direction but also information about the shape in 3D of the strain ellipsoid.

Enhanced performance of a gas-turbine combustor using miniature vortex generators

Several modes of instabilities were identified in an experimental combustor. The axisymmetric lowfrequency instabilities were associated with the external recirculation zone downstream of the dump plane. The helical low-frequency instabilities were related to the central recirculation zone formed by vortex breakdown. High-frequency helical instabilities were excited when the power level was increased or when the air inlet temperature was reduced. At these conditions, the high-frequency mode dominated the thermoacoustic instability. The high-frequency oscillations were excited by the small-scale vortices that are shed at the initial separating shear layer and are related to the Kelvin-Helmholtz flow instability in this region. Miniature vortex generators were installed at the circumference of the burner's exit to interfere with the rollup of these vortices through the induction of streamwise vorticity. The streamwise vorticity interacted with the circumferential vorticity, causing azimuthal deformation and excitation of high-order azimuthal modes that disrupted the formation of coherent circumferential vortices. The tests showed that in addition to the effect on the initial vortices, the entire process that leads to the formation of large-scale vortices through pairing and vortex merging was disrupted. Thermoacoustic instabilities that are excited by the periodic heat release due to the presence of coherent vortices were thus avoided in both the high-and low-frequency ranges. The effect was particularly significant in the high-frequency oscillations, which reached high-amplitude level in the plain burner and were suppressed by up to 28 dB by the miniature vortex generators. At the same time, low-frequency instabilities were reduced by 50%. Emissions of NOx were reduced by a factor of 2 in a wide range of operating conditions and CO and unburned hydrocarbons were slightly reduced.

The near wake of a model horizontal-axis wind turbine: Part 3: properties of the tip and hub vortices

This paper concludes a series on the formation and development of the near-wake of a model horizontal-axis wind. The three-dimensional mean velocity and turbulence fields were obtained at six axial locations within two chord lengths of the blades for three operating conditions: stalled flow over the blades, close to optimum performance, and approaching runaway. Here we concentrate on the tip and hub vortices. For the second and third conditions, the hub vortex quickly becomes a sheet of vorticity spread over the cylindrical centrebody. It is suggested that the ‘trailing vorticity’ at the hub is formed by the skewing of the circumferential vorticity in the upstream boundary layer as it encounters the blades, so that the ‘bound’ vorticity of the blades simply passes through the centrebody surface. The tip vortices, which were shown in Part 2 to contain increasing amounts of angular momentum as the tip speed ratio increases, are associated with large variations in all velocity components and high levels of turbulence. The pitch of the helical tip vortices decreases with increasing tip speed ratio.

Bubble- and spiral-type breakdown of slender vortices

Bubble- and spiral-type breakdown and periodic transition between the two were visualizedby varying the volume flux in a transparent, low-speed, vertical water tunnel with a diffuser inset. A feedback model for the initiation and development of bubble-type breakdown is proposed, and the transition from bubble- to spiral-type breakdown is explained by an asymmetry of the circumferential vorticity distribution. Both are qualitatively confirmed by experimental flow visualizations. The initiation of the bubble-type breakdown and its transition to the spiral-type were successfully simulated by solving the Navier-Stokes equations for three-dimensional, unsteady, and incompressible flow with boundary conditions similar to those of an experimental investigation. Hence, for the first time it was possible to compare the results of numerical and experimental flow visualizations and therefore to draw a conclusion about the reliability of simulating vortex breakdown numerically.

Study of vortex breakdown by particle tracking velocimetry (PTV) Part 3: Time-dependent structure and development of breakdown-modes

This third part of the study deals with the time-dependent nature of vortex breakdown. The results show the unsteady velocity and vorticity field of the initiation and development of breakdown and transition between both predominant breakdown modes, the bubble and the spiral. During the development to breakdown, the generated amount of circumferential vorticity follows the theoretical prediction by Brown and Lopez (1990). This confirms the idea of positive feedback as the key-mechanism leading to vortex breakdown. We regard the bubble-type as the fundamental breakdown type, that is stationary and nearly axisymmetric. The circumferential vorticity is distributed in a form of an elliptical vortex-ring-like structure. Starting from this stage, an increase of volume flux to a higher Reynolds number leads to the transition to the spiral-type with an initial stretching of the vortex ring-like structure and a subsequent change to an asymmetric circumferential vorticity distribution. This in combination with the inductive effect causes the front stagnation point to be deflected radially away and later to rotate around the centerline. Consequently the approaching vortex core is radially deflected in opposite direction and evolves in a spiral path. The idea of a second positive feedback-mechanism gives a possible explanation for the transition. Following this theory the asymmetry of circumferential vorticity will trigger itself at a certain degree by the interaction with the inductively affected stagnation point and its influence on the approaching vortex core. This self-enhancing process will finally lead to the spiral-type breakdown in which the radial distance between rotating stagnation point and deflected vortex core is of the order of the characteristic vortex core radius. The reversed transition from the spiral to a stable bubble-type can be regenerated by decreasing the Reynolds number down to the value that corresponds to the stable bubble state. The flow structure evolves nearly in the time-reversed way as during transition from bubble towards the spiral.