Hot-wire method for measurements of turbulent mixing induced by Richtmyer-Meshkov instability in shock tube

A constant temperature hot-wire anemometry method is applied to the study of mixing zones induced by the interaction of a shock wave with Mach number 1.25 in air with air/helium (heavy/light), air/argon or air/krypton (light/heavy) initially plane interfaces. The single wire gauge is positioned at various locations along the shock tube axis. At the present stage of our investigation, although the analysis of the hot-wire signal is not achieved yet, we report the interesting concept of using hot-wire anemometry as a diagnostic method for shock tube studies of the Richtmyer-Meshkov instability. Based on this preliminary work, we discuss prospective experimental signal conversion, in order to provide some new results for this field of investigation, in particular for resolving characteristics of the turbulent mixing zone which is of most interest. Received 3 August 2000 / Accepted 15 February 2001     

Measurements of velocity,temperature and velocity fluctuation distributions in falling liquid films

The velocity, temperature and velocity fluctuation distributions within falling spindle oil films in an inclined rectangular channel were measured using hot-wire techniques and thin thermocouples. The interfacial shear was caused by cocurrent air flow.The results indicate that the liquid films are as a whole much more laminar-like than turbulent in a range of Reynolds numbers (4γ/μ) up to the experimental limit of 6000. Mixing motion occurs in the vicinity of the interface; however, the flow near the wall surface exhibits no sign of such eddy motions, as predicted by the wall law for single phase turbulent flow. Although velocity fluctuation is observed within films with interfacial shear, mean velocity profiles are approximately the same as those obtained by the laminar film prediction.     

Measurements of Turbulent Jet Mixing in a Turbulent Co-Flow Including the Influence of Periodic Forcing and Heating

In this work, the turbulent mixing of a confined coaxial jet in air is investigated by means of simultaneous particle image velocimetry and planar laser induced fluorescence of the acetone seeded flow injection. The jet is injected into a turbulent duct flow at atmospheric pressure through a 90 ^° pipe bend. Measurements are conducted in a small scale windtunnel at constant mass flow rates and three modes of operation: isothermal steady jet injection at a Dean number of 20000 (R e _d =32000), pulsed isothermal injection at a Womersley number of 65 and steady injection at elevated jet temperatures of ΔT=50 K and ΔT=100 K. The experiment is aimed at providing statistically converged quantities of velocity, mass fraction, turbulent fluctuations and turbulent mass flux at several downstream locations. Stochastic error convergence over the number of samples is assessed within the outer turbulent shear layer. From 3000 samples the statistical error of time-averaged velocity and mass fraction is below 1 % while the error of Reynolds shear stress and turbulent mass flux components is in the of range 5-6 %. Profiles of axial velocity and turbulence intensity immediately downstream of the bend exit are in good agreement with hot-wire measurements from literature. During pulsed jet injection strong asymmetric growing of shear layer vortices lead to a skewed mass fraction profile in comparison with steady injection. Phase averaging of single shot PLIF-PIV measurements allows to track the asymmetric shear layer vortex evolvement and flow breakdown during a pulsation cycle with a resolution of 10^°. Steady injection with increased jet temperature supports mixing downstream from 6 nozzle diameters onward.     

Investigation of interaction between reflected shocks and growing perturbation on an interface

This paper reports the result of investigation into Richtmyer–Meshkov instability (RMI) resulting from multiple interactions of shock waves with the interface between two media of different densities. The instability growth rates were measured after the interactions of the mixing zone with the refracted shock and the first and the second shocks reflected from the endwall. It was shown that for the contribution of separate shock–interface interactions to the instability growth rate, the condition of additivity is not realized. The values of the factor , accounting for the decrease in the RMI growth rate due to the thickening of the mixing zone, have been determined for a continuous interface and for a turbulent mixing zone. Received 27 January 1998 / Accepted 10 June 1998     

Silicon based flow sensors used for mean velocity and turbulence measurements

Small and directional sensitive silicon based sensors for velocity measurements have been designed and fabricated using microelectronic technology. Single-chip as well as double-chip sensors for the determination of mean velocity and turbulent stresses have been developed. To determine the performance of these silicon sensors, comparisons with conventional hot-wire sensors were done in a well-defined two-dimensional turbulent flat plate boundary layer at a constant Reynolds number of 4.2 · 10⁶. All the silicon sensors were found to have a spatial and frequency resolution that makes them suitable for turbulence measurements. In the studied flow field the measured profiles of mean velocities and Reynolds stresses of all silicon sensors show the same accuracy as corresponding hot-wire measurements. The silicon sensors are also shown to operate with good resolution even when the temperature of the heated part of the chip is reduced considerably.     

Simultaneous concentration and velocity field measurements in a shock-accelerated mixing layer

A novel technique to obtain simultaneous velocity and concentration measurements is applied to the Richtmyer–Meshkov instability. After acceleration by a Mach 2.2 shock wave, the interface between the two gases develops into a turbulent mixing layer. A time-separated pair of acetone planar laser-induced fluorescence images are processed to yield concentration and, through application of the Advection-Corrected Correlation Image Velocimetry technique, velocity fields. This is the first application of this technique to shock-accelerated flows. We show that when applied to numerical simulations, this technique reproduces the velocity field to a similar quality as particle image velocimetry. When applied to the turbulent mixing layer of the experiments, information about the Reynolds number and anisotropy of the flow is obtained.     

低密度流体界面不稳定性大涡模拟

采用拉伸涡亚格子尺度应力模型对湍流输运中的亚格子作用项进行模式化处理,发展了适用于可压多介质黏性流动和湍流的大涡模拟方法和代码MVFT（multi-viscous flow and turbulence）。利用MVFT代码对低密度流体界面不稳定性及其诱发的湍流混合问题进行了数值模拟。详细分析了扰动界面的发展,流场中冲击波的传播、相互作用、湍流混合区边界的演化规律,以及流场瞬时密度和湍动能的分布和发展。数值模拟获得的界面演化图像和流场中波系结构与实验结果吻合较好。三维和二维模拟结果的比较显示,两者得到的扰动界面位置、波系及湍流混合区边界基本一致,只是后期的界面构型有所不同,这也正说明湍流具有强三维效应。     

Experimental study of the interaction of shock waves with the contact boundary and zone of turbulent mixing of different gases

The interaction of a shock wave with turbulent flow was experimentally investigated. The case where a shock wave formed at one end of the tube, passed through the interface between two quiescent gases with different densities (air–CO2 or air–Ar), was reflected from the end of the tube, and interacted with the zone of turbulent mixing formed at the interface. The Mach number of the shock wave incident on the interface in air was M ≈ 2.37–2.57. The flow field was recorded using the schlieren method and high-speed video recording. It was found that after passing the mixing zone, the shock-wave front was deformed and became unstable.     

Detonation interaction with a diffuse interface and subsequent chemical reaction

We have investigated the interaction of a detonation with an interface separating a combustible from an oxidizing mixture. The ethylene-oxygen combustible mixture had a fuel-rich composition to promote secondary combustion with the oxidizer in the turbulent mixing zone that resulted from the interaction. Diffuse interfaces were created by the formation of a gravity current using a sliding valve that initially separated the test gas and combustible mixture. Opening the valve allowed a gravity current to develop before the detonation was initiated. By varying the delay between opening the valve and initiating the detonation it was possible to achieve a wide range of interface conditions. The interface orientation and thickness with respect to the detonation wave have a profound effect on the outcome of the interaction. Diffuse interfaces result in curved detonation waves with a transmitted shock and following turbulent mixing zone. The impulse was measured to quantify the degree of secondary combustion, which accounted for 1–5% of the total impulse. A model was developed that estimated the volume expansion of a fluid element due to combustion in the turbulent mixing zone and predicted the resulting impulse increment.      

Velocity–pressure correlation measurements in complex free shear flows

Simultaneous measurements of fluctuating velocity and pressure were performed in various turbulent free shear flows including a turbulent mixing layer and the wing-tip vortex trailing from a NACA0012 half-wing. Two different methods for fluctuating static pressure measurement were considered: a direct method using a miniature Pitot tube and an indirect method where static pressure was calculated from total pressure. The pressure obtained by either of these methods was correlated with the velocity measured by an X-type hot-wire probe. The results from these two techniques agreed with each other in the turbulent mixing layer. In the wing-tip vortex case, however, some discrepancies were found, although overall characteristics of the pressure-related statistics were adequately captured by both methods.     

柱形汇聚激波冲击球形重气体界面的实验研究

采用高速纹影法实验研究了柱形汇聚激波与球形重气体界面相互作用的 Richtmyer-Meshkov不稳定性问题. 激波管实验段基于激波动力学理论设计, 将马赫数为1.2 的平面激波转化为柱形汇聚激波, 气体界面由肥皂膜分隔六氟化硫(内)和空气(外)得到. 采用高速摄影机在单次实验中拍摄激波运动的全过程, 对柱形激波的形成进行了实验验证, 并进一步观测了汇聚激波与球形气体界面相互作用过程中的波系发展和气体界面变形以及反射激波同已变形界面二次作用的流场演化. 结果表明: 当柱形汇聚激波穿过气泡界面以后, 气泡左侧界面极点沿激波传播方向保持匀速运动, 气泡右侧界面发展成为射流结构, 气泡主体发展成为涡环结构; 在反射激波的二次作用下, 流场中无序运动显著增强并很快进入湍流混合阶段.     

Wall shear stress measurement in a turbulent pipe flow using ultrasound Doppler velocimetry

A turbulent boundary layer of a water flow is investigated by means of pulsed ultrasound Doppler velocimetry. The advantage of this method is the acquisition of complete velocity profiles along the sound propagation line within very short time intervals. The shear stress velocity, used for normalizing the velocity profiles, was determined by fitting the profiles to the universal profiles in a turbulent boundary layer obtained from Prandtl's mixing length theory. A coordinate transformation in the near-wall region is proposed to allocate the velocity data to "true" wall distances. From the experimental values of the wall shear stress velocity, the friction factors for a turbulent pipe flow are calculated and compared to the Blasius law. The overall error in measurement was estimated to NJ.4%.     

Shock train generated turbulence inside a nozzle with a small opening angle

The flow inside an over expanding rectangular nozzle with a small opening angle of 1.6° is investigated by means of high-speed schlieren and shadowgraph photography, pressure probes and hot-wire anemometry on the nozzle centre line in order to measure the turbulent fluctuations generated by the occurring shock wave/boundary layer interaction. Additionally, an optical shock capturing tool is deployed to measure the amplitude and frequency of the shock train oscillation. Varying the back pressure, the pre-shock Mach number is changed between Ma ₁ = 1.1 and 2.1. Two different modes of turbulence generation and distribution are detected. For a single normal shock and a normal shock train, the normal Reynolds stress [`(u^￠2 )] \overline{{u^{\prime 2} }} on the channel axis is only slightly increased compared to the free stream value, whereas for the cases of a lambda foot shock train and an x-type shock train, a strong intensification by forming a turbulent mixing zone can be observed.     

Direct measurement of mixture fraction in reacting flow using Rayleigh scattering

The mixture fraction variable, , is very useful in describing reaction zone structure in nonpremixed flames. Extinction limits and turbulent mixing are often described as a function of this variable. Experimental evaluation of is critical for improving our understanding of the influence of turbulent mixing on the chemistry process. Heretofore, the evaluation of mixture fraction in combusting flow required multiple simultaneous concentration measurements. In this paper we present a fuel designed to permit measurements of mixture fraction by Rayleigh scattering technique only. A Rayleigh intensity/mixture fraction correspondence has been obtained experimentally in a laminar coflow flame. The influence of strain rate and differential diffusion effects have been investigated using laminar counterflow diffusion flame and shifting equilibrium chemistry models. The results obtained from comparisons between experiments and these models are very encouraging and suggest that the Rayleigh/mixture fraction correspondence established is valid under both the turbulent mixing and laminar strained flamelet combustion regimes.     

Development of steady-state mixing in an aerodynamic wake

We consider the unsteady, isothermal flow in the wake behind a body on which a shock wave has impinged. This flow is studied for sufficiently large distance from the body, when the effect of the latter on the external flow, as in the corresponding steady problem [1, 2], may be neglected. The analysis is performed for laminar and turbulent mixing with planar and axial symmetry.In § 1 we use the characteristics of the system of equations consisting of the momentum equation written on the wake centerline and an integral equation to determine approximately the boundary separating the steady and unsteady flows. It is noted that the unsteady flow takes place between this boundary and the tagged particle line, which at the moment of detachment of the shock wave from the body coincided with it.In §2 we show the possibility of calculating the flow in this region using the characteristics of the system of equations noted above. Some particular solutions of the latter are obtained.Then, in §§ 3 and 4 the exact solutions corresponding to the flow regions identified in §§1 and 2 are presented.Section 3 presents the exact solutions of the linear system of equations for large values of the time, when the velocity in the wake is close to the velocity of the particles behind the shock wave.On the basis of the analysis made in §2, and previously in [3], §4 obtains the exact solution of the nonlinear system of equations which describes the development of the mixing near the tagged particle line for planar turbulent flow. This solution is compared with the corresponding approximate solution of §2. The accuracy of the latter is noted. Comparison of the horizontal component velocity profiles with the profiles obtained in the preceding section and used in [4] in the method of integral relations shows satisfactory agreement between them     

Single-shot laser Mie scattering measurements of the scalar profiles in the near field of turbulent jets with variable densities

A single-shot laser Mie scattering technique is used to measure the instantaneous radial distributions of seed particles in the early development zone of turbulent jets with various bulk densities issuing into a slow coflowing air stream. Instantaneous radial profiles of mixture fraction are derived from the measured distributions with either the jet fluid or only the coflow air seeded, depending on the investigated zone. Radial gradients and autocorrelation profiles are analyzed to study the scalar dissipation and the mixing length scale respectively. Self-similar behaviour is investigated by plotting the centreline scalar decay as a function of a reduced abscissa, which accounts for the axial variation of the jet density in its early development. As the density is simultaneously derivable from the mixture fraction data, direct comparisons between Favre and Reynolds averaged values are obtained which show very significant differences in the near field.     

Turbulent mixing,induced by the Richtmyer-Meshkov instability

Turbulent mixing development, induced by passing of shock waves through the interface, has been studied on the basis of two semi-empirical models. The process of transition from random initial perturbations to turbulence is a rather complicated one, but it proceeds in a finite time. Here it is assumed that passing of shock waves through the initial zone of roughness leads to the instant development of mixing. The expression for the turbulent kinetic energy, transfered by the arriving shock wave, has been derived. The value of this energy is determined by the value of the non-dimensional parameter which is equivalent to the Richardson number. The analytical solution describing the turbulent kinetic energy decay and the mixing zone width change in time, has been obtained.The analytical form of constructed solutions allows to perform comparison between the models and to make the choice of constants on the basis of comparison with the known experiments. Comparison of the obtained theoretical results with Zaitzev's experimental data is given for the impulsive acceleration.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Experimental study of stratified jet by simultaneous measurements of velocity and density fields

Stratified flows with small density difference commonly exist in geophysical and engineering applications, which often involve interaction of turbulence and buoyancy effect. A combined particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) system is developed to measure the velocity and density fields in a dense jet discharged horizontally into a tank filled with light fluid. The illumination of PIV particles and excitation of PLIF dye are achieved by a dual-head pulsed Nd:YAG laser and two CCD cameras with a set of optical filters. The procedure for matching refractive indexes of two fluids and calibration of the combined system are presented, as well as a quantitative analysis of the measurement uncertainties. The flow structures and mixing dynamics within the central vertical plane are studied by examining the averaged parameters, turbulent kinetic energy budget, and modeling of momentum flux and buoyancy flux. At downstream, profiles of velocity and density display strong asymmetry with respect to its center. This is attributed to the fact that stable stratification reduces mixing and unstable stratification enhances mixing. In stable stratification region, most of turbulence production is consumed by mean-flow convection, whereas in unstable stratification region, turbulence production is nearly balanced by viscous dissipation. Experimental data also indicate that at downstream locations, mixing length model performs better in mixing zone of stable stratification regions, whereas in other regions, eddy viscosity/diffusivity models with static model coefficients represent effectively momentum and buoyancy flux terms. The measured turbulent Prandtl number displays strong spatial variation in the stratified jet.     

单一倾斜热线探头在三维湍流场中的应用

研究的目的是确立用单一倾斜热线探头进行三维湍流测试的基础技术．在阐明基本原理，基础方程式的基础上，对比实验结果，证明应用所阐明的方法、用单一倾斜热线探头进行三维湍流测试是切实可行的．对边界层壁面附近的测试结果表明考虑平均速度和变动速度的高次相关项后可以得到更加精确的实验结果．     

An Analysis of Turbulent Motions In and Around a Differentially Forced Density Interface

The Rapid-Distortion-Theory-based analysis proposed by Fernando and Hunt [1] is extended to study the nature of turbulence in and around a density interface sandwiched between turbulent layers with dissimilar properties. It is shown that interfacial motions consist of low-frequency, resonantly excited, nonlinear internal waves and high-frequency, linear internal waves driven by background turbulence. Based on the assumptions that (i) all resonant waves and some nonresonant waves having frequencies close to the resonant frequencies grow rapidly, break, and cause interfacial mixing, (ii) the spectral amplitude of the vertical velocity in the wave-breaking regime is constant, and (iii) kinetic energy is equipartitioned between linear and nonlinear breaking wave regimes, the r.m.s. vertical velocity at the interface and the turbulent kinetic energy flux into the interface are calculated. The migration velocity of the interface is calculated using the additional assumption that the buoyancy flux into a given turbulent layer is a fixed fraction of the turbulent kinetic energy flux supplied to the interface by the same layer. The calculations are found to be in good agreement with the entrainment data obtained in previous laboratory experiments in the parameter regime where the interface is dominated by internal wave dynamics. Received 23 July 1997 and accepted 8 January 1999