Dynamics of swirling jet flows

Experimental investigations of near-field structure of coaxial flows are presented for four different configurations: coaxial jets without rotation (reference case), outer flow rotating only (OFRO), inner-jet rotating only (IJRO) and corotating jets (CRJ). The investigations are performed in a cylindrical water tunnel, with an independent rotation of two coaxial flows. Laser tomography is used to document the flow field, and photographs are shown for different configurations. Time mean velocity profiles obtained by PIV, with and without swirl, are also presented. The dynamics of the swirling jets in the initial region (i.e. near the exit of the jets) is described. The effects of azimuthal velocity and axial velocity ratio variations on flow dynamics are examined. The appearance and growth of the first instabilities are presented and compared with some theoretical results, as is the influence of the rotation (inner or outer) on the dominating structures.     

Elastic wedge impact onto a liquid surface: Wagner's solution and approximate models

The problem of elastic wedge impact onto the free surface of an ideal incompressible liquid of infinite depth is considered. The liquid flow is two-dimensional, symmetric and potential. The side walls of the wedge are modelled as Euler beams, which are either simply supported or connected to the main structure by linear springs. The liquid flow, the deflection of wedge walls and the size of wetted region are determined simultaneously within the Wagner theory of water impact. We are concerned with the impact conditions of strong coupling between the hydrodynamic loads and the structural response. The coupling is well pronounced for elastic wedges with small deadrise angles. This is the case when the fully nonlinear models fail and approximate models based on the Wagner approach are used. In contrast to the existing approximate models, we do not use any further simplifications within the Wagner theory. Calculations of the velocity potential are reduced to analytical evaluation of the added-mass matrix. Hydrodynamic pressures are not evaluated in the present analysis. In order to estimate the maximum bending stresses, both stages when the wedge surface is partially and totally wetted are considered.Three approximate models of water impact, which are frequently used in practical computations, are examined and their predictions are tested against the present numerical solution obtained by the normal mode method within the Wagner theory. It is shown that the decoupled model of elastic wedge impact, which does not account for the beam inertia, provides a useful formula for estimating the maximum bending stress in thick wedge platings.     

Drag reduction on the 25° slant angle Ahmed reference body using pulsed jets

This paper highlights steady and unsteady measurements and flow control results obtained on an Ahmed model with slant angle of 25° in wind tunnel. On this high-drag configuration characterized by a large separation bubble along with energetic streamwise vortices, time-averaged and time-dependent results without control are first presented. The influence of rear-end periodic forcing on the drag coefficient is then investigated using electrically operated magnetic valves in an open-loop control scheme. Four distinct configurations of flow control have been tested: rectangular pulsed jets aligned with the spanwise direction or in winglets configuration on the roof end and rectangular jets or a large open slot at the top of the rear slant. For each configuration, the influence of the forcing parameters (non-dimensional frequency, injected momentum) on the drag coefficient has been studied, along with their impact on the static pressure on both the rear slant and vertical base of the model. Depending on the type and location of pulsed jets actuation, the maximum drag reduction is obtained for increasing injected momentum or well-defined optimal pulsation frequencies.     

Wavepacket models for subsonic twin jets using 3D parabolized stability equations

An extension of the classical parabolized stability equations to flows strongly dependent on the two cross-stream spatial directions and weakly dependent on the streamwise one is applied to model the large-scale structures present in twin-jet configurations. The existence of these unsteady flow structures, usually referred to as wavepackets, has been demonstrated in the literature for both subsonic and supersonic round jets, along with their relation to the generation of highly directional noise emitted in the aft direction. The present study considers twin-jet configurations with different separations at high Reynolds number and subsonic conditions. The existing instability modes for the twin-jet mean flow, their dependence on the separation of the two jets, and the interaction between the wavepackets originating from the two jets is investigated here. Arising from the axisymmetric mode for single round jets, two dominant modes are found for twin jets: a varicose one, relatively insensitive to jets' proximity, but likely to be efficient in radiating noise; a sinuous one, whose amplification is strongly dependent on the jets' distance, and which can be expected to produce weaker acoustic signatures.     

入口速度比对射流拟序结构的影响

为了深入了解湍流流动机理以及湍流拟序结构发现过程的影响因素，本文采用大涡模拟方法对不同入口射流伴流速度比的平面湍射流流动进行了数值模拟。采用分步投影法求解动量方程，亚格子项采用标准Smagorinsky亚格子模式模拟，压力泊松方程采用修正的循环消去法快速求解，空间方程采用二阶精度的差分格式，在时间方向上采用二阶精度的显式差分格式。模拟结果给出了平面射流中湍流拟序结构的瞬态发展演变过程，分析了入口速度比对射流拟序结构发展演化过程及宏观流场形态的影响。为进一步研究射流拟序结构及其在湍流流动中的作用提供了基础。     

Assessment of PIV-based analysis of water entry problems through synthetic numerical datasets

The phenomenon of hull-slamming, that is, the sudden impact of a solid body on the water surface, is critical in the design of naval structures. Thus, the development and validation of schemes to predict the slamming load and elucidate energy exchange during water entry are of fundamental importance in a wide range of engineering applications. Recent studies have demonstrated the possibility of using direct flow measurements from particle image velocimetry (PIV) to investigate the kinetics of water entry. Specifically, these efforts have contributed a first characterization of the hydrodynamic loading on impacting wedges and of the energy imparted to the water pile-up and the spray jets. Here, we seek to provide a thorough assessment of such a PIV-based approach through synthetic datasets, in which PIV parameters, such as the camera acquisition rate and the size of the interrogation area, are systematically varied, without experimental confounds. We implement a direct computational framework to study the two-dimensional flow physics generated during the water entry of a rigid wedge. Water and air are treated as immiscible phases and their relative motion is utilized to track the free surface dynamics. Our results show that the PIV-based methodology allows for an accurate reconstruction of the pressure field from the measured velocity field, except for early stages of the impact and for a small region close to the free surface. We also demonstrate that the reconstruction is only marginally affected by the spatial resolution, while a sufficiently high acquisition frequency is required to correctly predict the pressure field in the pile-up region. The proposed computational framework can also find application in the analysis of less studied aspects of water entry problems, such as cycling loading, flow transitions and separation, and formation of spray jets.     

刚性球体三维高速垂直自由入水载荷

入水结构体在从空中弹道转入水下弹道的入水阶段,其周围的流体将呈现出强非线性性质,本文针对传统基于Wagner理论的结构体入水载荷计算模型不能很好描述流体三维流动的情况,基于无黏不可压流体流动模型,考虑流体弹性,采用微元边界运动等效方法对运动边界进行分段分析,计及入水过程中系统的动能损失,根据能量守恒,对刚性球体高速垂直自由入水过程中流体的三维流动进行了理论分析,建立了基于无黏不可压弹性流体的刚性球体垂直高速入水载荷计算模型,并与基于多介质任意拉格朗日欧拉方法的有限元模型进行了对比分析,验证了该方法的可行性。基于此模型,本文进一步分析了入水载荷的影响因素。该方法提供了一种计算结构体垂直高速入水载荷的思路,具有一定的理论意义和工程应用价值。     

Flow visualisation studies on growth of area of deflected jets

 Laser light sheet visualisation, coupled with image processing, was utilised to understand the effect of exit geometry on the integral properties of jets in cross flow. The study involved jets emanating from circular and rectangular nozzles of different aspect ratios deflected by a uniform free-stream. The investigation considers incompressible momentum jets with exit Reynolds number in the range of 4400–9200, the velocity ratios being 3.9, 5.9 and 7.8. In contrast to a deflected circular jet, those jets emanating from blunt configurations tend to have higher growth rates initially and are devoid of the horse-shoe or the bound vortex system in their cross section. Received: 30 May 1996 / Accepted: 27 November 1996     

Density and compressibility effects in turbulent subsonic jets part 1: mean velocity field

The behavior of compressible jets originated from initially turbulent pipe flows issuing in still air has been investigated at three different subsonic Mach numbers, 0.3, 0.6 and 0.9. Helium, nitrogen and krypton gases were used to generate the jet flows and investigate the additional effects of density on the flow structure. Particle image velocimetry, high-frequency response pressure transducers and thermocouples were used to obtain velocity, Mach number and total temperature measurements inside the flow field. The jets were formed at the exit of an adiabatic compressible frictional turbulent pipe flow, which was developing toward its corresponding sonic conditions inside the pipe, and continued to expand within the first four diameters distance after it exited the pipe. Theoretical considerations based on flow self-similarity were used to obtain the decay of Mach number along the centerline of the jets for the first time. It was found that this decay depends on two contributions, one from the velocity field which is inversely proportional to the distance from the exit and one from the thermal field which is proportional to this distance. As a result, a small non-linearity in the variation of the inverse Mach number with downstream distance was found. The decay of the Mach number at the centerline of the axisymmetric jets increases by increasing the initial Mach number at the exit of the flow for all jets. The decay of mean velocity at the centerline of the jets is also higher at higher exit Mach numbers. However, the velocity non-dimensionalized by the exit velocity seems to decrease faster at low exit Mach numbers, suggesting a reduced mixing with increasing exit flow Mach numbers. Helium jets were found to have the largest spreading rate among the three different gas jets used in the present investigation, while krypton jets had the lowest spreading rate. The spreading rate of each gas decreases with increasing its kinetic energy relatively to its internal energy.     

Elongational-flow predictions of the Leonov constitutive equation

The basic thermodynamic ideas from rubber-elasticity theory which Leonov employed to derive his constitutive model are herein summarized. Predictions of the single-mode version are presented for homogeneous elongational flows including stress growth following start-up of steady flow, stress decay following sudden stretching and following cessation of steady flow, elastic recovery following cessation of steady flow, energy storage in steady-state flow, and the velocity profile in constantforce spinning. Using parameters of the multiple-mode version which fit the linearviscoelastic data, the Leonov-model predictions of elongational stress growth during, and elastic recovery following, steady elongation are calculated numerically and compared to the experimental results for Melt I and to the Wagner model. It is found that the Leonov model, as originally formulated, agrees qualitatively with the data, but not quantitatively; the Wagner model gives quantitative agreement, but requires much nonlinear data with which to fit model parameters. Quantitative agreement can be obtained with the Leonov model, if the nonequilibrium potential which relates recoverable strain to strain rate is adjusted empirically. This can most simply be done by making each relaxation time dependent upon the recoverable strain. The Leonov model, unlike the Wagner model, is derived from an entropic constitutive equation, which is advantageous for calculating stored elastic energy or viscous dissipation. The Leonov model also has an appealingly simple differential form, similar to the upper-convected Maxwell model, which, in numerical calculations, may be an important advantage over the integral Wagner model.     

Investigation of flows induced by subsonic turbulent jets and their relation with the effect of static pressure reduction in a jet

The interaction between turbulent jets, both swirling and nonswirling, and the ambient medium is studied on the basis of the results of measurements and numerical simulation. It is shown that the turbulent flow and the swirl give rise to induced ejection flow toward the jet. The mechanism of the jet action on the ambient medium is connected with a decrease in the static pressure in the jet, which, in turn, is due to either the flow swirl or the fluctuating flow in the mixing layer, when the static pressure reduces owing to the presence of velocity fluctuations. The former rarefaction mechanism is predominant in swirling jets and the latter predominates in jets without swirling. It is shown that the ambient medium inflow into the jet due to the rarefaction is independent in nature of the mechanism of the lowered pressure generation and that it is the kinetic energy of the jet that is the energy source for the induced flow.     

Opposed round jets issuing into a small aspect ratio channel cross flow

Round jets (diameter D) discharging into a confined cross flow (dimension 3.16D × 21.05D) are investigated experimentally. Two configurations are considered: (1) a single jet (momentum flux ratio, J = 155) and (2) two opposed jets with two different momentum flux ratios (J = 60, and 155). A two-component laser-Doppler anemometer is used to make a detailed map of the normal stresses and mean velocities in the symmetry plane of the jets. In addition, smoke-wire and laser-sheet visualization are used to study the flow.

The rate of bending of the single confined jet is found to be higher than the rate of bending of an unconfined jet with the same momentum flux ratio. In the far field, the jet centerline velocity is observed to decay more slowly than the unconfined jet, indicating poor turbulent diffusion of linear momentum. Annular shear layer vortices are visualized on the upstream edge of the jet in the near field. In the far field, the flow visualization suggests that the jet loses its integrity and fragments into independent regions that are convected by the cross flow.

In the opposed jet configuration at the high momentum flux ratio (J = 155), the jets impinge in the center of the duct, and a pair of vortices is observed upstream of the impingement region. The flow visualization implies that the impingement vortices form quasi periodically and have a finite life span. In the impingement region, the jets are observed to penetrate alternately beyond the symmetry plane of the duct. In the two-jet configuration with J = 60, the jets do not impinge on each other owing to the higher rate of bending. Instead, the flow visualization indicates that the shear layers of the jets penetrate to the central region and periodically pinch off regions of the potential-like cross-flow fluid where they meet. The pinch-off regions of cross-flow fluid are convected by the turbulent flow for large distances, yet remain essentially unmixed.     

Impact of a surfacewave on an elastic hull

In order to model a ship hull’s response to the impact of surface waves, the two-dimensional problem of wave impact on an elastic beam whose ends are connected by springs with a rigid structure uniformly submerged in a fluid is considered. The fluid is assumed to be ideal and incompressible and its flow symmetric; the lateral bending of the beam is described by the Euler equation. The fluid flow and the size of the wetted region are determined simultaneously with the calculation of the the beam deflection within the framework of the Wagner approach which takes into account the reshaping of the free surface of the fluid on interacting with a body. The stresses and strains arising in the beam and at its ends during impact are found. The numerical algorithm developed makes it possible to analyze the elastic effects in fluid impacts on thin-walled structures of finite length. Moreover, as the stiffness of the connecting springs tends to zero, the solution of this problem describes the impact of an elastic beam with free ends on a weakly curved fluid surface.     

Buoyant turbulent jets with mutual hindering

Vertical, round turbulent jets with combined effects of buoyancy and mutual hindering are investigated by an integral method. The method avoids application of an empirical entrainment coefficient by including the differential equations of motion and energy at the jet axis. Mutual hindering of jets in a spatially periodic arrangement is shown to give rise to significant deviations from single jet behaviour. In the absence of buoyancy forces, the flow would decay exponentially with increasing distance from the jet origin. In the case of buoyancy-enhanced jets, however, a transition to a cellular flow driven by natural convection is predicted.     

水下爆炸冲击凹陷液面诱导射流研究

利用液滴坠落冲击直管中水平液面产生半球形凹陷,并以此凹陷液面作为初始界面进行水下爆炸冲击诱导射流的实验研究。以高速摄影为主要手段,结合Fluent数值模拟,揭示了凹陷液面在水下爆炸冲击作用下的变形过程和机理。实验结果表明,随着爆炸的发生,液面凹陷中心会汇聚形成纤细光滑的射流,同时在管壁附近会产生附加环状射流,这明显区别于冲击直管中水平液面诱导射流的现象。进一步研究发现,中心射流的产生主要源于液面凹陷对爆炸能量的汇聚作用,而附加射流的产生受到液面初始形状和管壁剪切阻力的共同影响,二者经历短暂的加速过程之后均以一个近似恒定的速度向上抬升。通过考察能量对射流的影响发现,中心射流与附加射流的速度均与充电电压(爆炸能量的1/2次方)呈线性正相关;中心射流形态特征基本不变,附加射流则随能量的变化呈现不同的形态。     

One-dimensional turbulence modeling for cylindrical and spherical flows: model formulation and application

The one-dimensional turbulence (ODT) model resolves a full range of time and length scales and is computationally efficient. ODT has been applied to a wide range of complex multi-scale flows, such as turbulent combustion. Previous ODT comparisons to experimental data have focused mainly on planar flows. Applications to cylindrical flows, such as round jets, have been based on rough analogies, e.g., by exploiting the fortuitous consistency of the similarity scalings of temporally developing planar jets and spatially developing round jets. To obtain a more systematic treatment, a new formulation of the ODT model in cylindrical and spherical coordinates is presented here. The model is written in terms of a geometric factor so that planar, cylindrical, and spherical configurations are represented in the same way. Temporal and spatial versions of the model are presented. A Lagrangian finite-volume implementation is used with a dynamically adaptive mesh. The adaptive mesh facilitates the implementation of cylindrical and spherical versions of the triplet map, which is used to model turbulent advection (eddy events) in the one-dimensional flow coordinate. In cylindrical and spherical coordinates, geometric stretching of the three triplet map images occurs due to the radial dependence of volume, with the stretching being strongest near the centerline. Two triplet map variants, TMA and TMB, are presented. In TMA, the three map images have the same volume, but different radial segment lengths. In TMB, the three map images have the same radial segment lengths, but different segment volumes. Cylindrical results are presented for temporal pipe flow, a spatial nonreacting jet, and a spatial nonreacting jet flame. These results compare very well to direct numerical simulation for the pipe flow, and to experimental data for the jets. The nonreacting jet treatment overpredicts velocity fluctuations near the centerline, due to the geometric stretching of the triplet maps and its effect on the eddy event rate distribution. TMB performs better than TMA. A hybrid planar-TMB (PTMB) approach is also presented, which further improves the results. TMA, TMB, and PTMB are nearly identical in the pipe flow where the key dynamics occur near the wall away from the centerline. The jet flame illustrates effects of variable density and viscosity, including dilatational effects.     

Jet impingement on cylindrical cavity: Conical nozzle considerations

In laser gas-assisted processing, the assisting gas emerges from a nozzle and nozzle geometric configurations alter the flow structure and heat transfer characteristics in and around the section processed. In the present study, the influence of nozzle geometric configurations, cavity diameter and depth, on flow structure and heat transfer rates from the cavity is investigated. A cylindrical cavity with two diameters and varying depths is accommodated in the simulations. Air is used as assisting gas while steel is employed as workpiece material. A numerical scheme using a control volume approach is accommodated to discretize the flow and energy equations. It is found that flow structure changes significantly for large diameter cavity. The influence of the nozzle cone angle on heat transfer and flow structure is more pronounced as the cavity depth increases.     

水下超音速气体射流胀鼓和回击的关联性研究

阐述了水下超音速气体射流的实验研究结果. 用高速摄影仪实时记录了水下超音速气体射流喷射的状态, 清晰地演示了射流气体在上中游流域的演化过程. 具体分析了水下高速气体射流的动态不稳定性形貌, 并从实时记录的射流照片中统计测量出了胀鼓和回击随机频率.结果发现, 胀鼓频率越大, 回击频率越大; 胀鼓频率随着喷嘴的驻室压力与出口背压的比值增大而增大. 通过胀鼓与回击事件前后实验数据的对比分析表明其二者之间存在相关性: 胀鼓和回击均由射流内部压力振荡引发并且存在一定的随机性; 胀鼓是回击前的能量积聚一个前征和表现, 当胀鼓的振荡即能量积聚到一定程度后, 引发回击.      

Controlling the Parameters of a Shock Wave by Means of the Mass and Energy Supply

The process of controlling the parameters of a bow shock created by a body flying at supersonic velocity by supplying mass and thermal energy behind the shock is investigated. The mass and thermal energy were supplied by means of fan air jets flowing out from the body and hydrogen combustion in the neighborhood of the model, respectively. The flow parameters were measured in the neighborhood of the model and recalculated for greater distances. For these control methods some features of the variation of the shock intensity and momentum are presented. A generalization of the effect of the thrust of the nozzles forming the jets and their orientation on the shock wave parameters is obtained. The control methods considered are compared with each other.