Direct numerical simulation of the near field dynamics of a rectangular reactive plume

Spatial direct numerical simulation (DNS) is used to study the near field dynamics of a buoyant diffusion flame established on a rectangular nozzle with an aspect ratio of 2:1. Combustion is represented by a one-step finite-rate Arrhenius chemistry. Without applying external perturbations at the inflow boundary, large vortical structures develop naturally in the flow field, which interact with the flame and temporally create localized holes within the reaction zone in which no chemical reactions take place. The interaction between density gradients and gravity plays a major role in the vorticity generation of the buoyant plume. At the downstream of the reactive plume, a more disorganized flow regime characterized by small scales has been observed, following the breakdown of the large vortical structures due to three-dimensional (3D) vortex interactions. Analysis of energy spectra shows that the spatially developing reactive plume has a tendency of transition to turbulence under the effects of combustion-induced buoyancy. The buoyancy effects are found to be very important to the formation, development, interaction, and breakdown of vortices in reactive plumes. In contrast with the relaminarization effects of chemical exothermicity via viscous damping and volumetric expansion on non-buoyant jet diffusion flames, the tendency towards transition to turbulence in reactive plumes is greatly enhanced by the buoyancy effects.     

Radiation and scattering of sound from a vortex ring

The mechanisms of generation and scattering of sound by a vortex ring are investigated on the basis of fluid dynamics. The vortex ring can serve as a simple dynamic model of the large-scale structures observed in shear flows. Moreover, it is probably the most easily studied vortex element that can be created experimentally. The sound scattering investigation also served to determine the extent to which the vortex is affected by sound, its selectivity with respect to such parameters as the acoustic frequency, the angle of incidence of the wave, etc. The perturbed motion is considered against the background of the steady-state motion of the ring. The perturbed motion in the vortex core is determined on the basis of linear incompressible fluid dynamics. Two terms of the expansion in the M number of the far acoustic field generated by the perturbations in the core are found in accordance with Lighthill's theory. The acoustic power and directivity of the radiation and the acoustic instability growth rate are calculated. It is shown that the scattering of sound by the vortex ring is a resonance effect, and the scattering amplitude near resonance is determined. The acoustic action on the hydrodynamic structure of the flow in the core of the ring is especially intense near the resonances and extends over a period short as compared with the characteristic time of the acoustic instability.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 83–95, May–June, 1987.     

Dynamics of vortex rings moving counter the lift

The motion of a buoyant vortex ring counter the direction of the lift of given value is experimentally investigated on a wide range of the initial velocity of the ring. The dynamics of its parameters are determined. The experimental results are compared with the calculations according to the earlier developed theoretical model. It is established in which cases the theoretical model describes the dynamics of buoyant vortex ring in motion counter the lift.     

Analytical and numerical investigation of formation of a vortex ring in the process of rising of a thermal in the atmosphere

Formation of a vortex ring in the process of rising a heated light volume of air medium in the Earth’s gravity field is investigated. The results of calculations carried out on various computational grids are compared both with each other and with solutions of the approximate analytical theory of formation and motion of a buoyant vortex ring approved by the available experimental data. A good agreement between all the data is obtained.     

用拉格朗日相关结构研究圆盘启动过程的流体输运

利用粒子成像测速(PIV)技术,得到了圆盘启动涡环流场的速度分布和涡量分布.圆盘启动涡环流场的有限时间李雅普诺夫指数场(Finit-time Lyapunov exponents,FTLE)以及拉格朗日相关结构(Lagrangian coherent structures,LCS)被计算出来.基于圆盘启动涡环流场的有限时间李雅普诺夫指数场以及拉格朗日相关结构,通过跟踪流体质点,对圆盘启动涡环流场的输运情况进行了分析.在圆盘启动涡环形成过程中,流体发现被圆盘和相互排斥的拉格朗日相关结构分成三部分.剪切流窗口(vorticity-flux window)被发现,涡量流通过剪切流窗口进入涡核.涡环的非定常边界被确定,它由相互排斥的拉格朗日相关结构背风面、圆盘以及剪切流窗口组成.     

Effects of initial geometry on the development of thermals

A series of experiments were performed in a water tank to examine the effects of the initial geometry on the development of buoyant thermals in the near field. The flows were produced by releasing buoyant fluid from cylindrical tubes of aspect ratios 2 to 8 into a uniform density environment. In the near field, a vortical cap forms, followed by a column of buoyant fluid, for the larger aspect ratios. The flow development can be divided into two phases; an initial acceleration phase and a subsequent phase where the flow decelerates and displays thermal-like characteristics. In the first phase, the leading edge of the flow accelerates and the length and time scales are dependent on the initial geometry. In the second phase, the flow attains a constant circulation and the appropriate length and time scales are the cube root of the initial volume and a buoyant time scale. Circulation due to baroclinic torques and the hydrodynamic impulse in the second phase are correlated with the initial buoyant force. The data indicate that the self-similar thermal characteristics are applicable to the buoyant flows in the near field beyond the initial phase, even though the flow may not resemble a spherical thermal.     

Direct Numerical Simulation of the Puffing Phenomenon of an Axisymmetric Thermal Plume

A spatial direct numerical simulation of an axisymmetric buoyant thermal plume is presented. The governing flow field equations at the centerline are put into a special form to circumvent the axis singularity associated with the cylindrical coordinates and the high order accuracy of the numerical scheme is preserved at the centerline. Boundary conditions associated with the spatial DNS of open-boundary buoyant flows and compatible with the modern nondissipative high-order finite difference schemes have been developed. The fluid exhibits a periodic oscillatory motion known as the puffing phenomenon, which is the formation and convection of vortex at the near field of the plume. Budgets of the vorticity transport are determined to examine the mechanisms leading to the puffing phenomenon. The analysis on vorticity transport shows that vorticity is created mainly by the gravitational term which is due to the interaction between the radial density gradients and gravity at the initial stage of the establishment of the puffing structure, while the baroclinic torque dominates the vorticity transport when the flow is established. Density stratification in the radial direction close to the plume base is found to be essential to the development of the buoyant flow instability. Simulations with different initial temperature ratios reveal that entrainment close to the plume base is enhanced at a higher temperature ratio despite the fact that the puffing structures and the plume pulsation frequency only vary very weakly with the initial temperature ratio. The predicted puffing frequencies are in agreement with the values from experimental correlations for fire and isothermal helium/air plumes. Received 12 May 1999 and accepted 9 December 1999     

Analytical model of motion of turbulent vortex rings in an incompressible fluid

An analytical model describing the motion of vortex rings in an incompressible fluid is constructed. The model is valid both for homogeneous and inhomogeneous vortices buoyant in the gravity field, as well as for combined vortices. The expansion angle of a buoyant vortex is found from the characteristic parameters that define the flow rather than specified on the basis of experiments. Significant differences in the expansion angles of homogeneous and buoyant vortex rings are explained. The calculation results for the proposed model are compared with the results of laboratory experiments and data on the rise of the cloud produced by an atomic explosion.     

The pinch-off process in a starting buoyant plume

The vortex ring formation process of a starting buoyant plume was studied experimentally using digital particle image thermometry and velocimetry (DPITV). The vortex ring was observed to pinch-off, or become disconnected, from the trailing plume. Pinch-off occurred at non-dimensional times, or formation numbers, between 4.4 and 4.9. The observed pinch-off process is consistent with an explanation based upon the Kelvin–Benjamin variational principle. This is analogous to the pinch-off of a vortex ring generated using a piston–cylinder apparatus, suggesting that pinch-off is a general component of the vortex ring formation process for various generation mechanisms.     

Experimental observation of the straining field responsible for vortex ring instabilityObservation expérimentale du champ responsable de l'instabilité du tourbillon torique

The aim of this work is to show experimentally the straining field responsible for the vortex ring instability. To do so, the velocity field in the neighbourhood of the core is measured with Particle Image Velocimetry. This field is compared with the one coming from theoretical work on a thin vortex ring in an ideal fluid. Theoretical and experimental data fit well. This indicates that the linear phase of the instability is weakly influenced by viscosity. To cite this article: A. Dazin et al., C. R. Mecanique 332 (2004).     

Dynamics of prolate jellyfish with a jet-based locomotion

Swimming jellyfish deliver momentum to the surrounding fluid in the form of vortices. A three-dimensional computational model was adopted to investigate the characteristic flow patterns produced by jellyfish with a jet-based locomotion and the process of vortex generation. The interaction between jellyfish and the surrounding fluid may be simulated using the immersed boundary method. The vortex structures generated in the wake were elucidated in detail. The vortices were formed due to the contraction and expansion of the elastic bell. A dimensionless temporal parameter was employed to analyze the vortex formation process. During the early stage of contraction, the vortices were dominantly generated by the stroke. The ejected fluid from the inside of the bell was then entrained into the vortices, thereby decreasing the vorticity at the core and increasing the total circulation within the vortex ring. The Froude propulsion efficiency increased as the vortex formation number increased, implying that the propulsion in the way of growing the vortex structures was favorable in terms of the efficiency.     

Direct Numerical Simulation of Transitional Noncircular Buoyant Reactive Jets

The near field dynamics of transitional buoyant reactive jets established on noncircular geometries, including a rectangular nozzle with an aspect ratio of 2:1 and a square nozzle with the same cross-sectional area, are investigated by three-dimensional spatial direct numerical simulations. Without applying external perturbations at the inflow boundary, large vortical structures develop naturally in the flow field due to buoyancy effects. Simulation results and analysis describe the details and clarify mechanisms of vortex dynamics of the noncircular buoyant reactive jets. The interaction between density gradients and gravity initiates the flow vorticity. Among the major vorticity transport terms, the gravitational term mainly promotes flow vorticity in the cross-streamwise direction. For the baroclinic torque, it can either create or destroy flow vorticity depending on the local flow structure. The vortex stretching term has different effects on the streamwise and cross-streamwise vorticity. Streamwise vorticity is mainly created by vortex stretching, while this term can either create or destroy cross-streamwise vorticity. Under the coupling effects of buoyancy and noncircular nozzle geometry, three-dimensional vortex interactions lead to the transitional behavior of the reactive jets. Simulations also show that the rectangular jet is more vortical than the square jet. The rectangular jet has a stronger tendency of transition to turbulence at the downstream due to the aspect ratio effect. Mean flow property calculations show that the rectangular buoyant reactive jet has a higher entrainment rate than its square counterpart. Received 13 December 2000 and accepted 24 July 2001     

Three-dimensional flow structure in highly buoyant jet by scanning stereo PIV combined with POD analysis

The flow characteristics and the structure of highly buoyant jet of low density fluid issuing into a stagnant surrounding of high density fluid is studied by scanning stereo PIV combined with proper orthogonal decomposition (POD) analysis. The experiment is carried out at Froude number of 0.3 and Reynolds number of 200, which satisfies the inflow condition due to the unstable density gradient near the nozzle exit. An increase in the maximum mean velocity occurs and the vertical velocity fluctuation is highly amplified near the nozzle exit, which suggests the influence of inflow due to the unstable density gradient. The POD analysis indicates that the vertical velocity fluctuation is the major source of fluctuating energy contributing to the development of the highly buoyant jet. The examination of the POD modes show that the longitudinal structure of the vertical velocity fluctuation is generated along the jet axis having the opposite sign of velocity fluctuation on both sides of the jet axis. The vertical scale of the POD mode decreases with increasing the mode number and results in the frequent appearance of cross-flow across the buoyant jet. The reconstruction flow from the POD modes indicates that the vortex structure is caused by the highly sheared layer between the upward and downward velocity and the inflow is induced by the vortex structure. The magnitude of the vortex structure seems to be weakened with an increase in the distance from the nozzle and the buoyant jet approaches to an asymptotic state in the further downstream.     

Momentum evolution of ejected and entrained fluid during laminar vortex ring formation

The evolution of total circulation and entrainment of ambient fluid during laminar vortex ring formation has been addressed in a number of previous investigations. Motivated by applications involving propulsion and fluid transport, the present interest is in the momentum evolution of entrained and ejected fluid and momentum exchange among the ejected, entrained fluid and added mass during vortex ring formation. To this end, vortex rings are generated numerically by transient jet ejection for fluid slug length-to-diameter (L/D) ratios of 0.5–3.0 using three different velocity programs [trapezoidal, triangular negative slope (NS), and positive slope (PS)] at a jet Reynolds number of 1,000. Lagrangian coherent structures (LCS) were utilized to identify ejected and entrained fluid boundaries, and a Runge-Kutta fourth order scheme was used for advecting these boundaries with the numerical velocity data. By monitoring the center of mass of these fluid boundaries, momentum of each component was calculated and related to the total impulse provided by the vortex ring generator. The results demonstrate that ejected fluid exchanges its momentum mostly with added mass during jet ejection and that the momentum of the entrained fluid at jet termination was < 11% of the total ring impulse in all cases except for the triangular NS case. Following jet termination, momentum exchange was observed between ejected and entrained fluid yielding significant increase in entrained fluid’s momentum. A performance metric was defined relating the impulse from over-pressure developed at the nozzle exit plane during jet ejection to the flow evolution, which increased preferentially with L/D over the range considered. An additional benefit of this study was the identification of the initial (i.e., before jet initiation) location of the fluid to be entrained into the vortex ring.     

Steady Vortex Ring with Isochronous Flow in the Vortex Core

Steady-state solutions to the problem of a thin vortex ring in an inviscid incompressible fluid in infinite space are investigated. The Fraenkel procedure is used to construct the steady-state solutions. In this procedure a given vorticity distribution in plane flow with circular streamlines is transformed into a steady vortex ring using an expansion in the ring thinness parameter. For example, a two-dimensional vortex of constant vorticity is transformed into a steady vortex ring with the uniform distribution in which the absolute value of vorticity is proportional to the distance from the axis of symmetry. The principal aim of our study is to construct the algorithm of finding the flow for an isochronous vortex ring in which the periods of revolution are the same for all the liquid particles in the vortex core. The problem is that the two-dimensional distribution which goes over in the isochronous ring in accordance with the Fraenkel procedure is unknown in advance. In particular, the ring with the uniform distribution is not isochronous despite the isochronism of the initial two-dimensional flow. In this connection the Fraenkel procedure is significantly modified so that the initial two-dimensional vorticity distribution is determined in each of the steps of the iteration procedure. The solution for the vortex ring with the uniform distribution obtained in the present study is significantly used to construct the isochronous solution. The necessary corrections to the former solution are calculated in each step. Obtaining of the isochronous flow is the key step for the investigation of stability of three-dimensional oscillations of the vortex ring since the oscillation spectrum of this flow is discrete.     

Visualization of coherent structure in scalar fields of unsteady jet flows with interferometric tomography and proper orthogonal decomposition

Proper orthogonal decomposition (POD) is a method of examining spatial coherence in unsteady flow fields from an ensemble of multidimensional measurements. When applied to experimental data, the proper orthogonal decomposition is generally restricted to data sets with low spatial resolution. This is because of the inherent difficulties in generating an ensemble of measurements that contain a large number of data points. In this paper, a system for obtaining a large ensemble of three-dimensional scalar measurements using interferometric tomography is presented. The proper orthogonal decomposition is applied in three spatial dimensions to experimental data of two jet-like flows. The coherent structure present in the near field of a neutrally buoyant, helium–argon jet and the far field of a buoyant helium jet into air is visualized. The POD results of the helium–argon jet clearly reveal the breakdown region of a sequence of vortex rings and a large-scale flapping motion in the jet far field. The POD of the buoyant helium jet shows a number of competing modes with varying degrees of helicity. Received: 14 January 2000/Accepted: 26 September 2000     

Visualization of compressible vortex rings using the background-oriented schlieren method

In this article, we attempt to validate flow visualization using the high-speed background-oriented schlieren (HiBOS) method, which is the BOS technique combined with a high-speed video camera as the recording device in the experiment. The method has been applied to shock-induced flow near the open end of a shock tube. Three incident shock Mach numbers were examined so that the BOS measurements could be compared with results given in the literature of particle-image velocimetry (PIV) measurements. Using the HiBOS technique, we were able to clearly view developing, compressible vortex rings and diffracted shock waves discharged from the open end of the shock tube. From the BOS images, we extracted the history of the propagation velocity, the diameter of the vortex ring, and the diameter of the vortex core, all of which agree with the corresponding PIV values reported in the literature.     

Acoustic emission from interaction of a vortex ring with a sphere

Acoustic waves emitted by a vortex ring interacting with a fixed solid sphere are studied experimentally and theoretically. The experiments are carried out for two kindsof vortex-sphere arrangement: (A) a vortex ring passes over the sphere, and (B) a vortex ring passes by the sphere. The vortex motion is examined optically by means of a photosensor system, and the pressure signals of the emitted wave are detected by 1/2-inch microphones in the far field. In case A, the measured diameter of the vortex ring after passing the sphere increases from its initial diameter. The observed acoustic wave is dominated mainly by a dipole emission, and some contribution from a quadrupole radiation is present. In case B, the emitted wave is characterized by a rotating dipole emission in which the dipole axis rotates as the vortex position changes relative to the sphere.     

Experiment on Vortex Formation in a Fluid Flowing out of a Reservoir

Experimental data on vortex formation near the sinkhole in a fluid flowing out of a reservoir are analyzed. An experimental facility which makes it possible to study the influence of various factors on vortex formation near a sinkhole has been designed and built. In the experiments performed, a vortex was observed only if before the sinkhole was opened a rotating disk was immersed in the fluid. In the steady-state flow regime, a brief rotation of the disk resulted in the formation and subsequent damping of a vortex. For a preswirled fluid, the formation of a vortex crater depends on the sinkhole location.