Incompressible flows with combustion simulated by a preconditioning method using multigrid acceleration and MUSCL reconstruction

A numerical algorithm for the steady state solution of three‐dimensional incompressible flows is presented. A preconditioned time marching scheme is applied to the conservative form of the governing equations. The preconditioning matrix multiplies the time derivatives of the system and circumvents the eigenvalue‐caused stiffness at low speed. The formulation is suitable for constant density flows and for flows where the density depends on non‐passive scalars, such as in low‐speed combustion applications. The k–ε model accounts for turbulent transport effects. A cell‐centred finite volume formulation with a Runge–Kutta time stepping scheme for the primitive variables is used. Second‐order spatial accuracy is achieved by developing for the preconditioned system an approximate Riemann solver with MUSCL reconstruction. A multi‐grid technique coupled with local time stepping and implicit residual smoothing is used to accelerate the convergence to the steady state solution. The convergence behaviour and the validation of the predicted solutions are examined for laminar and turbulent constant density flows and for a turbulent non‐premixed flame simulated by a presumed probability density function (PDF) model. Copyright © 2001 John Wiley & Sons, Ltd.     

Spatially correlated precision error in digital particle image velocimetry measurements of turbulent flows

The purpose of the current paper is to describe an experimental study of the spatially correlated precision errors associated with particle image velocimetry (PIV) measurements made in turbulent flows. A free jet was used as the base flow for the study. The precision error of time-averaged statistics of the mean and turbulent flowfield is governed by the probability distribution function of the various quantities and the finite sample size of the data sets. Spatial measurements that are separated by a distance that is shorter than the size of the large turbulent scales will not be independent, resulting in a correlated precision error. The characteristics of the precision error for various statistics will be described. It is found that mean vorticity has a correlated precision error that is limited to a much smaller length scale. The results demonstrate the importance of understanding the role of error correlation in the interpretation of PIV data.     

PIV study of large-scale flow organisation in slot jets

The paper reports on particle image velocimetry (PIV) measurements in turbulent slot jets bounded by two solid walls with the separation distance smaller than the jet width (5–40%). In the far-field such jets are known to manifest features of quasi-two dimensional, two component turbulence. Stereoscopic and tomographic PIV systems were used to analyse local flows. Proper orthogonal decomposition (POD) was applied to extract coherent modes of the velocity fluctuations. The measurements were performed both in the initial region close to the nozzle exit and in the far fields of the developed turbulent slot jets for Re ⩾ 10,000. A POD analysis in the initial region indicates a correlation between quasi-2D vortices rolled-up in the shear layer and local flows in cross-stream planes. While the near-field turbulence shows full 3D features, the wall-normal velocity fluctuations day out gradually due to strong wall-damping resulting in an almost two-component turbulence. On the other hand, the longitudinal vortex rolls take over to act as the main agents in wall-normal and spanwise mixing and momentum transfer. The quantitative analysis indicates that the jet meandering amplitude was aperiodically modulated when arrangement of the large-scale quasi-2D vortices changed between asymmetric and symmetric pattern relatively to the jet axis. The paper shows that the dynamics of turbulent slot jets are more complex than those of 2D, plane and rectangular 3D jets. In particular, the detected secondary longitudinal vortex filaments and meandering modulation is expected to be important for turbulent transport and mixing in slot jets. This issue requires further investigations.     

Speckle tomography of turbulent flows with density fluctuations

The speckle tomography technique is used for reconstructing both large-scale structures in turbulent flows and the microstructure of turbulence. The technique is based on multi-projectional line-of-sight speckle photography measurements with a subsequent computer-assisted tomographic reconstruction of the interior structure of the flowfield. The large-scale structure is reconstructed using the Radon integral equation, and the microstructure is analysed using a statistical approach and a novel Erbeck-Merzkirch integral transform. Digital speckle photography and speckle tomography methods are described. Numerical simulation of the optical technique is performed using digital ray tracing through a turbulent flowfield. The methods are illustrated by the 3D "averaged" temperature fields in turbulent convective flows obtained earlier and by the recent reconstruction of 3D correlation functions of density variations in turbulent flows. Local values of turbulence (Kolmogorov) microscale are evaluated using these correlation functions and the Erbeck-Merzkirch integral transform The precision of the reconstruction and the spatial resolution achieved are analysed.     

Particle drag in a dilute turbulent two-phase suspension flow

The drag between phases plays an important role in the study of a turbulent two-phase suspension flow and its physical understanding will greatly promote progress in theoretical treatments of a whole range of important industrial and technical problems involving such a flow. The conventional practice of using the results of measurements based on a single particle in a laminar stream for the case of a turbulent flow of a dilute suspension is questioned. An analysis of the results of local measurements of upward turbulent flows of a solid particle-air two-phase suspension leads to the determination of the realistic particle drag coefficient over a wide range of flow conditions. It is established that the particle drag can be described by the simple Stokes law, based on an apparent turbulent viscosity of the fluid for the particles in the suspension flow. A correlation is provided for this apparent turbulent viscosity in terms of the particle size and concentration in the suspension, the local flow turbulence Reynolds number and the particle-to-fluid density ratio.     

Simultaneous measurements of velocity and density in buoyancy-driven mixing

A variant of the particle image velocimetry (PIV) technique is described for measuring velocity and density simultaneously in a turbulent Rayleigh-Taylor mixing layer. The velocity field is computed by the usual PIV technique of cross-correlating two consecutive images, and deducing particle displacements from correlation peaks of intensity fields. Different concentrations of seed particles are used in the two streams of different temperature (density) fluids, and a local measure of the density is obtained by spatially averaging over an interrogation window. Good agreement is reported between the first- and second-order statistics for density obtained from this technique and from a thermocouple. Velocity-density correlations computed by cross-correlating individual time series are presented. The errors in the density measurements are quantified and analyzed, and the issue of spatial resolution is also discussed. Our purpose for this paper is to introduce the PIV-S method and validate its accuracy against corresponding thermocouple measurements.     

A sensitivity analysis of the point reference global correlation (PRGC) technique for spatio-temporal correlations in turbulent flows

The point reference global correlation (PRGC) technique which combines single and global measurements as proposed by Chatellier and Fitzpatrick (Exp Fluids 38(5):563–757, 2005) is of significant interest for the analysis of the turbulent statistics for noise source modeling in jet flows as it allows the 2D spatio-temporal correlation functions to be obtained over a region of the flow. This enables the statistical characteristics including inhomogeneous and anisotropic features to be determined. The sensitivity of the technique is examined in some detail for the specific case of laser doppler velocimetry (LDV) and particle image velocimetry (PIV). Simulated data are used to enable a parametric study of the accuracy of the PRGC technique to be determined as a function of the various measurement parameters. The sample frequencies and the number of samples of both the LDV and PIV signals are shown to be critical to errors associated with the estimated spatio-temporal correlations and that low data rates can lead to significant errors in the estimates. Measurements performed in single stream and co-axial jet flows at Mach 0.24 using PIV and LDV systems are reported and the 2D space–time correlation functions for these flows are determined using the PRGC technique. The results are discussed in the context of noise source modeling for jet flows.     

Measurements of admixture concentration fluctuations in a turbulent shear flow using an averaged Talbot image

The present study is concerned with adopting of a Talbot effect-based technique for analyzing flows with random phase inhomogeneities. It is shown that this method is a powerful tool for diagnostics of turbulent flows. The potential of the technique is illustrated by measuring mean and fluctuating values of admixture concentration of two-dimensional turbulent helium jet issuing into the ambient air. Averaged air and helium concentrations throughout the flow field are determined using local light refraction measurements with a high spatial resolution from a long-exposed Talbot image of the jet. The analysis of light intensity distributions in light spots of a Talbot-image shows that the jet turbulence is inhomogeneous and anisotropic. Quantitative information on rms fluctuations of concentration gradients throughout the flow field is obtained from local photometric measurements at the Talbot light spots.     

Uncertainty analysis of four-sensor hot-wires and their data-reduction schemes used in the near field of a turbulent jet

Four data-reduction schemes were implemented and applied to measurements taken in the near field of a free, round jet with single-, cross- and four-wire probes from the Auspex Corporation. The results of these three databases were compared with experimental data from the literature and large eddy simulation computations. Comparisons between reduction techniques were also made to examine their respective characteristics and assess how they affected the accuracy of measurements made in a turbulent jet flow. Estimates of the accuracy of each scheme are given as a function of velocity direction and magnitude. It is concluded that four-wire probes, while a useful addition to the experimenters arsenal, remain limited to low and moderate turbulence intensity flows.     

Extended proper orthogonal decomposition: a tool to analyse correlated events in turbulent flows

A tool to analyse correlated events in turbulent flows based on an extended proper orthogonal decomposition (POD) is proposed in this paper. A general definition of extended POD modes is presented and their properties are demonstrated. If the initial POD analysis in a spatio-temporal domain S concerns, for example, velocity—the concept of extended modes can be applied to study the correlation of any physical quantity in any domain with the projection of the velocity field on POD modes in S. The link with particular associations of POD and linear stochastic estimation (LSE) recently proposed is demonstrated at the end of the paper. The method is believed to provide a valuable tool to extend the well-documented POD analysis of eddy structures in turbulent flows, for example, in boundary layers or free shear flows. If extended modes are velocity modes, spatial and temporal interactions between eddy structures can be detected and studied. The rapid development of experimental diagnostic techniques now permit measurements of the concentration in the domain, the velocity of a dispersed phase in the domain or the static pressure at the boundary together with the fluid velocity field. Using this method we are then able to extract objectively the link between the representative groups of velocity modes and the correlated part of the concentration, particle motion or pressure signals.     

Experimental Determination of Lagrangian Velocity Statistics in Turbulent Pipe Flow

The calculation of Lagrangian statistics out of experimentally determined data from homogeneously seeded inhomogeneous turbulent flows is far from straightforward since statistical properties are position-dependent, necessitating local sampling. Two solutions for the preferential sampling of faster particles at a certain position in the flow are proposed. The performance of both methods was tested using DNS calculations for turbulent pipe flow. Both methods show a good performance for various statistical properties, thus providing two reliable ways to analyze experimental data from inhomogeneous turbulent flows.     

Analysis of high-order velocity moments in a strained channel flow

In the current study, model expressions for fifth-order velocity moments obtained from the truncated Gram-Charlier series expansions model for a turbulent flow field probability density function are validated using data from direct numerical simulation (DNS) of a planar turbulent flow in a strained channel. Simplicity of the model expressions, the lack of unknown coefficients, and their applicability to non-Gaussian turbulent flows make this approach attractive to use for closing turbulent models based on the Reynolds-averaged Navier-Stokes equations. The study confirms validity of the model expressions. It also shows that the imposed flow deformation improves an agreement between the model and DNS profiles for the fifth-order moments in the flow buffer zone including when the flow reverses its direction. The study reveals sensitivity of particularly odd velocity moments to the grid resolution. A new length scale is proposed as a criterion for the grid generation near the wall and in the other flow areas dominated by high mean velocity gradients when higher-order statistics have to be collected from DNS.     

A model for tracking inertial particles in a lattice Boltzmann turbulent flow simulation

A computationally inexpensive model for tracking inertial particles through a turbulent flow is presented and applied to the turbulent flow through a square duct having a friction Reynolds number of Re_τ = 300. Prior to introducing particles into the model, the flow is simulated using a lattice Boltzmann computation, which is allowed to evolve until a steady state turbulent flow is achieved. A snapshot of the flow is then stored, and the trajectories of particles are computed through the flow domain under the influence of this static probability field. Although the flow is not computationally evolving during the particle tracking simulation, the local velocity is obtained stochastically from the local probability function, thus allowing the dynamics of the turbulent flow to be resolved from the point of view of the suspended particles. Particle inertia is modeled by using a relaxation parameter based on the particle Stokes number that allows for a particle velocity history to be incorporated during each time step. Wall deposition rates and deposition patterns are obtained and exhibit a high level of agreement with previously obtained DNS computational results and experimental results for a wide range of particle inertia. These results suggest that accurate particle tracking through complex turbulent flows may be feasible given a suitable probability field, such as one obtained from a lattice Boltzmann simulation. This in turn presents a new paradigm for the rapid acquisition of particle transport statistics without the need for concurrent computations of fluid flow evolution.     

An Error Criterion in Digital Image Correlation for Unknown Deformation Fields and Its Application of Parameters Selection

Digital image correlation (DIC) is a widely used optical metrology for surface deformation measurement. In DIC, the square root of the mean square error (RMS error) and standard deviation error (SD error) are used as quantitative criteria in order to evaluate the accuracy and robustness of a DIC method\algorithm. However, RMS and SD error criteria are computed from prescribed and measured displacements, which indicates that the prescribed displacement fields must be precisely generated. Therefore, it is difficult to quantitatively evaluate the accuracy and robustness of an algorithm\method in practical DIC measurements because imposed displacements are unknown (that’s why DIC measurements are needed). Moreover, the accuracy of DIC measurements highly relies on parameters selection, especially the selections of subset size and shape function. In practice, the subset size and shape function are usually selected according to experience because there are numerous factors (e.g. the quality of speckle image, local displacement field) and uncertainties (e.g. noise level, out-of-plane motion, illumination lighting fluctuation during image capturing) that affect the parameters selection, which makes it difficult to select optimal parameters based on previous works which mainly focused on theoretical deduction in ideal condition. In this paper, an error criterion for evaluating the accuracy of practical DIC measurements with unknown displacements is proposed. Numerical experiments are used to validate the effectiveness and feasibility of the proposed criterion for accuracy evaluation. It is concluded that the square root of the sum of squared forward and backward displacements difference (SFBD) error has a significant positive linear correlation with the widely used SD error in most practical DIC measurements where the mismatch between the frequently-used first- and second-order shape functions and the actual field is usually small. Also, an application of the proposed criterion is presented by real experiments for subset size and shape function selections, which verifies that the proposed error criterion can be effectively used for DIC parameters selection.     

An algorithm for rotating axisymmetric flows: model,validation and industrial applications

The study of axisymmetric flows is of interest not only from an academic point of view, due to the existence of exact solutions of Navier–Stokes equations, but also from an industrial point of view, since these kind of flows are frequently found in several applications. In the present work the development and implementation of a finite element algorithm to solve Navier–Stokes equations with axisymmetric geometry and boundary conditions is presented. Such algorithm allows the simulation of flows with tangential velocity, including free surface flows, for both laminar and turbulent conditions. Pseudo‐concentration technique is used to model the free surface (or the interface between two fluids) and the k–ε model is employed to take into account turbulent effects. The finite element model is validated by comparisons with analytical solutions of Navier–Stokes equations and experimental measurements. Two different industrial applications are presented. Copyright © 2005 John Wiley & Sons, Ltd.     

Reconstruction of velocity fields from wall pressure measurements in a shock wave/turbulent boundary layer interaction

We present here experimental results in a shock wave/turbulent boundary layer interaction at Mach number of 2.3 impinged by an oblique shock wave, with a deflection angle of 9.5°, as installed in the supersonic wind tunnel of the IUSTI laboratory, France. For such a shock intensity, strong unsteadiness are developing inside the separated zone involving very low frequencies associated with reflected shock motions.The present work consists in simultaneous PIV velocity fields and unsteady wall pressure measurements. The wall pressure and PIV measurements were used to characterize the pressure distribution at the wall in an axial direction, and the flow field associated. These results give access for the first time to the spatial-time correlation between wall pressure and velocity in a shock wave turbulent boundary layer interaction and show the feasibility of such coupling techniques in compressible flows. Linear Stochastic Estimation (LSE) coupled with Proper Orthogonal Decomposition (POD) has been applied to these measurements, and first results are presented here, showing the ability of these techniques to reproduce both the unsteady breathing of the recirculating bubble at low frequency and the Kelvin–Helmholtz instabilities developing at moderate frequency.     

湍流冲击射流流动与传热的数值研究进展

湍流冲击射流由于其冲击表面时具有很高的局部传热率和冲击力,被广泛应用于如表面的加热、电子元件的冷却、纸张的干燥和材料的切割等工程应用和工业过程中.由于其流动的复杂性,也常被作为一种理想的测试实例来评价湍流模型的性能.此外,湍升力射流与地面之间的空气动力作用对V/STOL (垂直或短距离起落)飞机的性能具有很大的影响.长期以来,人们从理论分析、实验测量和数值模拟方面对冲击射流进行了广泛而系统的研究,积累了丰富的资料.本文在分析了湍流冲击射流的数值研究现状的基础上,对近年来有关湍流冲击射流流动与传热的数值研究方面的文献有选择地进行了综述,重点评述了不同湍流模型对冲击射流流动与传热的预测能力,讨论了存在的问题并对该领域今后的研究方向进行了展望.      

Determination of correlation functions of turbulent velocity and sound speed fluctuations by means of ultrasonic technique

An experimental study of the propagation of high-frequency acoustic waves through grid-generated turbulence by means of an ultrasound technique is discussed. Experimental data were obtained for ultrasonic wave propagation downstream of heated and non-heated grids in a wind tunnel. A semi-analytical acoustic propagation model that allows the determination of the spatial correlation functions of the flow field is developed based on the classical flowmeter equation and the statistics of the travel time of acoustic waves traveling through the kinematic and thermal turbulence. The basic flowmeter equation is reconsidered in order to take into account sound speed fluctuations and turbulent velocity fluctuations. It allows deriving an integral equation that relates the correlation functions of travel time, sound speed fluctuations and turbulent velocity fluctuations. Experimentally measured travel time statistics of data with and without grid heating are approximated by an exponential function and used to analytically solve the integral equation. The reconstructed correlation functions of the turbulent velocity and sound speed fluctuations are presented. The power spectral density of the turbulent velocity and sound speed fluctuations are calculated.     

Tomographic PIV measurements in a turbulent lifted jet flame

Measurements of instantaneous volumetric flow fields are required for an improved understanding of turbulent flames. In non-reacting flows, tomographic particle image velocimetry (TPIV) is an established method for three-dimensional (3D) flow measurements. In flames, the reconstruction of the particles location becomes challenging due to a locally varying index of refraction causing beam-steering. This work presents TPIV measurements within a turbulent lifted non-premixed methane jet flame. Solid seeding particles were used to provide the 3D flow field in the vicinity of the flame base, including unburned and burned regions. Four cameras were arranged in a horizontal plane around the jet flame. Following an iterative volumetric self-calibration procedure, the remaining disparity caused by the flame was less than 0.2 pixels. Comparisons with conventional two-component PIV in terms of mean and rms values provided additional confidence in the TPIV measurements.