An investigation of forced structures in turbulent jet flows

In many cases, turbulence is superimposed on an unsteady organized motion of a mean flow. In the past, these turbulent flows have been studied by time or ensemble averaging methods and some decomposition techniques such as proper orthogonal decomposition (POD). In this study, a new decomposition technique called the turbulence filter will be used to decompose the forced turbulent jet flows. By using the turbulence filtering technique, the fluctuating (turbulent) part and the more organized (forced) part of the velocity field are analyzed. Within this context several experiments on organized turbulent jet flow have been carried out. In the experiments, variable frequency and amplitude oscillation are imposed on a 1D jet. An elliptical plate was used in order to obtain sinusoidal forcing. The axial distance, Reynolds number and the forcing frequency of the signal were varied. The multiple hot wires (six probes) were used to investigate the evolution of the signal along the radial distance. The obtained results of the turbulence filter are compared with those of phase-averaging and POD techniques. The eigenmodes of the data are also evaluated by using the POD method. Received: 31 July 1998/Accepted: 19 January 2000     

An Eulerian time filtering technique to study large-scale transient flow phenomena

Unsteady fluctuating velocity fields can contain large-scale periodic motions with frequencies well separated from those of turbulence. Examples are the wake behind a cylinder or the processing vortex core in a swirling jet. These turbulent flow fields contain large-scale, low-frequency oscillations, which are obscured by turbulence, making it impossible to identify them. In this paper, we present an Eulerian time filtering (ETF) technique to extract the large-scale motions from unsteady statistical non-stationary velocity fields or flow fields with multiple phenomena that have sufficiently separated spectral content. The ETF method is based on non-causal time filtering of the velocity records in each point of the flow field. It is shown that the ETF technique gives good results, similar to the ones obtained by the phase-averaging method. In this paper, not only the influence of the temporal filter is checked, but also parameters such as the cut-off frequency and sampling frequency of the data are investigated. The technique is validated on a selected set of time-resolved stereoscopic particle image velocimetry measurements such as the initial region of an annular jet and the transition between flow patterns in an annular jet. The major advantage of the ETF method in the extraction of large scales is that it is computationally less expensive and it requires less measurement time compared to other extraction methods. Therefore, the technique is suitable in the startup phase of an experiment or in a measurement campaign where several experiments are needed such as parametric studies.     

Transient behavior of an axisymmetric turbulent jet

The prediction of the response of unsteady flows submitted to external excitation is a real challenge for the optimization of industrial processes. As the jet flow is a very basic turbulent flow related to mixing and entrainment phenomena via turbulent structure dynamic, we investigate the transient behavior of an axisymmetric jet submitted to a large and sudden decrease of its ejection velocity. The non stationary flow evolution is studied experimentally. Measurements along the jet axis based on pure ensemble averaging show clearly the convective motion of the perturbation and the adaptation of the local interaction to the local jet time scale. A transverse investigation in the non stationary region show that the mean flow and its turbulence is deeply affected during the local velocity decrease.     

A laboratory study of irregular shoaling waves

The present research aims to investigate the dynamics of a single laboratory irregular wave, characterized by a narrow-banded spectrum and developing on a sloping sand bottom, in intermediate waters up to the surf zone. Experiments focused on the wave shoaling region, in order to examine how the wave is affected by breaking induced turbulence offshore the surf zone. A 3D acoustic Doppler velocimeter was used to measure the three wave velocity components, which were all processed to evaluate the time-averaged vertical distributions of orbital velocities, wave and turbulent Reynolds shear stresses and turbulent intensities. The vertical distributions of the phase-averaged velocity components, turbulent kinetic energy and transport of turbulence were also analysed. The adopted phase-averaging technique was applied to each investigated measurement point. Therefore, the crucial element of the study is that all the analysed values derive directly from real measurements and are not approximated by any kind of interpolation. The study confirmed some dynamic behaviour in the shoaling zone already known in the literature, such as the typical cell-type flow pattern of the mean flow and the necessity to evaluate the turbulent kinetic energy with all the three velocity components, when available, which would otherwise be underestimated. Referring to the time-averaged wave and Reynolds shear stresses, a contribution was added to the open debate on their order of magnitude. The measured wave Reynolds shear stresses were also compared with the results of the model by Zou et al. (J Geophys Res 111:C09032, 2006), confirming the behaviour typical of dissipative breaking waves. The analysis of turbulence transport in the shoaling zone revealed that it is seaward directed close to the surface and landward directed close to the bottom. The results presented in the paper can be extended only to other analogous flow conditions.     

可压缩各向同性衰减湍流直接数值模拟研究

采用五阶有限差分WENO格式直接模拟了高初始湍流Mach数的可压缩均匀各向同性湍流,主要分析了湍流的统计特性 和压缩性的影响,包括能谱特征、激波串、耗散率、标度律等. 研究表明,湍动能主要来自于速度场螺旋分量的贡献;各向同性湍流的小尺度脉动对压缩性更为敏感,并且压缩性的增强加快了湍流大 尺度脉动向小尺度脉动的湍动能输运;随着湍流Mach数的升高,胀量(压缩)耗散率所占比率也显著增长. 标度律分析表明,强可压缩湍流的横向速度结构函数仍然具有扩展自相似性;当阶数较高(p ≥ 5)时,纵向速度结构函数的扩展自相似性则不再成立. 对于压缩性较弱的湍流,与不可压缩湍流一致,横向湍流脉动的间歇性要强于纵向湍流脉动;而对于强可压缩湍流,纵向湍流脉动的 间歇性要强于横向湍流脉动.     

Statistical structure of the velocity field in cavitating flow around a 2D hydrofoil

Transformation of flow turbulence structure with cavitation occurrence, determination of the flow conditions favorable for nucleation of cavitation bubbles, influence of the statistical structure of turbulence on this process and the inverse effect of cavitation on the flow dynamics are challenging problems in modern fluid mechanics. The paper reports on the results of statistical processing of the velocity fields measured by a PIV technique in cavitating flow over a 2D symmetric hydrofoil for four flow conditions, starting from a cavitation-free regime and finishing by unsteady cloud cavitation. We analyze basic information on the statistical structure of velocity fluctuations in the form of histograms and Q-Q diagrams along with profiles of the mean velocity and turbulent kinetic energy. The research reveals that the flow turbulence pattern and distributions of turbulent fluctuations change significantly with the cavitation development. Under unsteady cloud cavitation conditions, the probability density function of the fluctuating velocity has a two-mode distribution, which indicates switching of two alternating flow conditions in a region above the hydrofoil aft part due to periodic passing of cavitation clouds. Behaviors of the mean and most probable velocities unexpectedly appear to be different with a monotonous increase of the incoming flow velocity. This finding must be caused by modification of the skewness coefficient of the fluctuating velocity.     

Fourier averaging: a phase-averaging method for periodic flow

A new phase-averaging method, denoted as Fourier averaging, is presented for the investigation of periodic flows. In such flows, the moments of velocity, as estimated from a small number of samples, show fluctuations in their phasewise development. In previous methods these fluctuations are reduced by calculating moments from large phase intervals. Fourier averaging, in contrast, neglects high-frequency fluctuations and assumes that they are of no physical relevance. This method supplies additional information on amplitudes and phase angles of discrete frequencies, which may then be used for visualizations of flow fields at any desired phase increment. The Fourier averaging method was verified empirically by LDA measurements and compared to other methods. It is shown that the results obtained by Fourier averaging are more accurate than for previously known methods. Received: 15 June 1998/Accepted: 15 April 1999     

Planar velocity measurements of a two-dimensional compressible wake

The present study describes the application of particle image velocimetry (PIV) to investigate the compressible flow in the wake of a two-dimensional blunt base at a freestream Mach number M_X=2. The first part of the study addresses specific issues related to the application of PIV to supersonic wind tunnel flows, such as the seeding particle flow-tracing fidelity and the measurement spatial resolution. The seeding particle response is assessed through a planar oblique shock wave experiment. The measurement spatial resolution is enhanced by means of an advanced image-interrogation algorithm. In the second part, the experimental results are presented. The PIV measurements yield the spatial distribution of mean velocity and turbulence. The mean velocity distribution clearly reveals the main flow features such as expansion fans, separated shear layers, flow recirculation, reattachment, recompression and wake development. The turbulence distribution shows the growth of turbulent fluctuations in the separated shear layers up to the reattachment location. Increased velocity fluctuations are also present downstream of reattachment outside of the wake due to unsteady flow reattachment and recompression. The instantaneous velocity field is analyzed seeking coherent flow structures in the redeveloping wake. The instantaneous planar velocity and vorticity measurements return evidence of large-scale turbulent structures detected as spatially coherent vorticity fluctuations. The velocity pattern consistently shows large masses of fluid in vortical motion. The overall instantaneous wake flow is organized as a double row of counter-rotating structures. The single structures show vorticity contours of roughly elliptical shape in agreement with previous studies based on spatial correlation of planar light scattering. Peak vorticity is found to be five times higher than the mean vorticity value, suggesting that wake turbulence is dominated by the activity of large-scale structures. The unsteady behavior of the reattachment phenomenon is studied. Based on the instantaneous flow topology, the reattachment is observed to fluctuate mostly in the streamwise direction suggesting that the unsteady separation is dominated by a pumping-like motion.     

Experimental study on the effect of unsteadiness on boundary layer development on a linear turbine cascade

 The results from an experimental investigation of unsteady boundary layer behavior on a linear turbine cascade are presented in this paper. To perform a detailed study on unsteady cascade aerodynamics and heat transfer, a new large-scale, high-subsonic research facility for simulating the periodic unsteady flow has been developed. It is capable of sequentially generating up to four different unsteady inlet flow conditions that lead to four different passing frequencies, wake structures, and freestream turbulence intensities. For a given Reynolds number, two different unsteady wake formations are utilized. Detailed unsteady boundary layer velocity. turbulence intensity, and pressure measurements are performed along the suction and pressure surfaces of one blade. The results display the transition and development of the boundary layer, ensemble-averaged velocity, and turbulence intensity. Received: 23 September 1996/Accepted: 19 February 1997     

Mean and fluctuating components of drag and lift forces on an isolated finite-sized particle in turbulence

We perform fully resolved direct numerical simulations of an isolated particle subjected to free-stream turbulence in order to investigate the effect of turbulence on the drag and lift forces at the level of a single particle, following Bagchi and Balachandar’s work (Bagchi and Balachandar in Phys Fluids 15:3496–3513, 2003). The particle Reynolds numbers based on the mean relative particle velocity and the particle diameter are Re?=?100, 250 and 350, which covers three different regimes of wake evolution in a uniform flow: steady axisymmetric wake, steady planar symmetric wake, and unsteady planar symmetric vortex shedding. At each particle Reynolds number, the turbulent intensity is 5–10% of the mean relative particle velocity, and the corresponding diameter of the particle is comparable to or larger than the Kolmogorov scale. The simulation results show that standard drag values determined from uniform flow simulations can accurately predict the drag force if the turbulence intensity is sufficiently weak (5% or less compared to the mean relative velocity). However, it is shown that for finite-sized particles, flow non-uniformity, which is usually neglected in the case of the small particles, can play an important role in determining the forces as the relative turbulence intensity becomes large. The influence of flow non-uniformity on drag force could be qualitatively similar to the Faxen correction. In addition, finite-sized particles at sufficient Reynolds number are inherently subjected to stochastic forces arising from their self-induced vortex shedding in addition to lift force arising from the local ambient flow properties (vorticity and strain rate). The effect of rotational and strain rate of the ambient turbulence seen by the particle on the lift force is explored based on the conditional averaging using the generalized representation of the quasi-steady force proposed by Bagchi and Balachandar (J Fluid Mech 481:105–148, 2003). From the present study, it is shown that at Re?=?100, the lift force is mainly influenced by the surrounding turbulence, but at Re = 250 and 350, the lift force is affected by the wake structure as well as the surrounding turbulence. Thus, for a finite-sized particle of sufficient Reynolds number supporting self-induced vortex shedding, the lift force will not be completely correlated with the ambient flow. Therefore, it appears that in order to reliably predict the motion of a finite-sized particle in turbulence, it is important to incorporate both a deterministic component and a stochastic component in the force model. The best deterministic contribution is given by the conditional average. The influence of ambient turbulence at the scale of the particle, which are not accounted for in the deterministic contribution, can be considered in stochastic manner. In the modeling of lift force, additional stochastic contribution arising from self-induced vortex shedding must also be included.     

The effect of a discrete window offset on the accuracy of cross-correlation analysis of digital PIV recordings

 This paper describes how the accuracy for estimating the location of the displacement-correlation peak in (digital) particle image velocimetry (PIV) can be optimized by the use of a window offset equal to the integer-pixel displacement. The method works for both cross-correlation analysis of single-exposure image pairs and multiple-exposure images. The effect is predicted by an analytical model for the statistical properties of estimators for the displacement, and it is observed in the analysis of synthetic PIV images of isotropic turbulence, and in actual measurements of grid-generated turbulence and of fully-developed turbulent pipe flow. Received: 29 April 1996/Accepted: 29 October 1996     

Response of the streaks, the active and passive eddies in an unsteady channel flow

Spanwise space–time correlations of the wall shear stress and the longitudinal velocity fluctuations in the low buffer layer of an unsteady channel flow are reported. The imposed amplitude is 20% of the centerline velocity and the imposed frequency covers a large range going from the quasi-steady limit to the bursting frequency of the corresponding steady flow. The unsteady spanwise correlation coefficient is investigated both through its own modulation characteristics (amplitude and phase shifts) and those of the resulting streak spacing. A good correspondence is found between the modulation of the streak spacing and that of the ejection period. The data is further analyzed by temporal filtering of the wall shear stress and streamwise velocity fluctuations. It is shown that the large outer-layer structures play a “passive” role in the unsteady response of the near wall turbulence. The inner wall eddies, in return, are amply responsible for the unsteady reaction of both the turbulent wall shear stress and the streamwise velocity intensities in the buffer layer.     

Assessment of dual plane PIV measurements in wall turbulence using DNS data

Experimental dual plane particle image velocimetry (PIV) data are assessed using direct numerical simulation (DNS) data of a similar flow with the aim of studying the effect of averaging within the interrogation window. The primary reason for the use of dual plane PIV is that the entire velocity gradient tensor and hence the full vorticity vector can be obtained. One limitation of PIV is the limit on dynamic range, while DNS is typically limited by the Reynolds number of the flow. In this study, the DNS data are resolved more finely than the PIV data, and an averaging scheme is implemented on the DNS data of similar Reynolds number to compare the effects of averaging inherent to the present PIV technique. The effects of averaging on the RMS values of the velocity and vorticity are analyzed in order to estimate the percentage of turbulence intensity and enstrophy captured for a given PIV resolution in turbulent boundary layers. The focus is also to identify vortex core angle distributions, for which the two-dimensional and three-dimensional swirl strengths are used. The studies are performed in the logarithmic region of a turbulent boundary layer at z ⁺ = 110 from the wall. The dual plane PIV data are measured in a zero pressure gradient flow over a flat plate at Re _τ = 1,160, while the DNS data are extracted from a channel flow at Re _τ = 934. Representative plots at various wall-normal locations for the RMS values of velocity and vorticity indicate the attenuation of the variance with increasing filter size. Further, the effect of averaging on the vortex core angle statistics is negligible when compared with the raw DNS data. These results indicate that the present PIV technique is an accurate and reliable method for the purposes of statistical analysis and identification of vortex structures.     

PIV measurements of turbulent flow in planar mixing layer

A turbulent mixing layer consists of two different flow types, i.e. shear layer (shear-flow turbulence) and free stream regions (nearly homogeneous turbulence). The inherent non-uniform seeding tracer distributions observed around the interfaces between the shear layer and two free stream regions usually lead to a difficulty in particle image velocimetry (PIV) measurements. A parametric study on the application of PIV to the measurement of velocity field in a planar mixing layer is made by means of six factors, including interrogation window size, aspect ratio of interrogation window, interrogation window offset, threshold of data validation, sharpening spatial filters (Prewitt and Sobel masks), and smoothing spatial filter (median mask). The objective of this study is to obtain accurate turbulent measurements in both mean and fluctuating velocities using PIV under an appropriate parametric setting. The optimal levels, which are trade-off in between the accuracy and fine spatial resolution of velocity field measurements, are determined with the aid of the Taguchi method. It is shown that the PIV measurements made with this optimal set of parameters are in good agreement with the measurements made by a two-component hot-wire anemometer. Case independency of the proposed optimal set of parameters on the flow condition of the mixing layer is validated through the applications to two additional tests under the different experimental conditions in changing solely either velocity ratio of high-speed to low-speed free stream velocities or Reynolds number.     

Measurements in the flow around a marine propeller at the stern of an axisymmetric body

An experimental study of the flow around and behind an axisymmetric body driven by a marine propeller is reported. Experiments were performed in a wind tunnel to document this complex, unsteady, three-dimensional, turbulent shear flow. Measurements were made in the boundary layer and wake of the bare body with a fixed dummy hub for the propeller, with the dummy hub rotating, and finally, with the propeller in operation. A five-hole yaw probe was employed for the mean-flow measurements, and two- and threesensor hotwires were used to obtained the mean and turbulent velocity fields. Part 1 of this two-part paper describes the experimental arrangement and circumferentially-averaged results which clarify certain overall aspects of the flow when it is viewed as a rotationally-symmetric flow. These are of special interest in marine hydrodynamics. In Part 2, the triple-sensor hotwire data are analyzed using phase-averaging techniques to reconstruct the instantaneous velocity and Reynolds-stress fields downstream of the propeller to show the evolution of the wakes of individual blades, blade-tip vortices, and the complex flow associated with vortices generated at hub-blade junctions.     

Velocity statistics along the stagnation line of an axi- symmetric stagnating turbulent flow

 Velocity statistics along the stagnation line of an axi-symmetric wall stagnating turbulent flow are studied experimentally. A low turbulence, uniform air flow from a nozzle type air supply with an exit diameter of 50 mm stagnates at a wall located 50 mm downstream. A flow velocity is set to 3 m/s, 10 mm downstream from the exit of the air supply. Instantaneous values of streamwise and radial velocities are measured by laser-Doppler velocimetry. The turbulence level in the air flow is changed by use of turbulence generator. When the turbulence generator is not installed in the air supply, the mean velocity profile in the streamwise direction fits well with that of a laminar viscous flow with the rms value of velocity fluctuations low near the wall. With the turbulence generator installed, a significant turbulence structure appears near the wall. When the wall is approached, the rms value of velocity fluctuations in the streamwise direction decreases monotonically while the profile of the rms value in the radial direction reaches a maximum near the wall. The increase in the rms value of velocity fluctuations in the radial direction near the wall is attributed to the bi-modal histogram of the fluctuating velocity in the radial direction. Near the wall, the instantaneous stagnation streamline fluctuates and the probability of the mean location of the stagnation point reaches a maximum not at the stagnation line but on a circle around the stagnation line, resulting in the bi-modal histogram. Turbulence statistics, the rms value of velocity fluctuation and the turbulent kinetic energy, can be normalized successfully by similarity parameters based on the strain rate and the reference turbulent kinetic energy introduced by Champion and Libby. Received: 7 April 1995/Accepted: 27 September 1996     

Generalized detection of a turbulent front generated by an oscillating grid

This report presents experimental results on the propagation of a turbulent front induced by an oscillating grid starting from rest. The purpose of this preliminary investigation is to implement and validate detection methods of the turbulent/non-turbulent interface, which are based on flow measurements (velocity and vorticity) and scalar intensity, for oscillating grid turbulence. This is done using particle image velocimetry (PIV) and fluorescent dye visualization, separately. The results of both techniques describe the spreading of the turbulent front, confirming the known dependency of the front location, H, on time, t. It is demonstrated, that the level-based detection of a turbulent front can be applied to an unsteady flow, such as grid turbulence advancing into a fluid at rest.     

Velocity measurements in a precessing jet flow using a three dimensional LDA system

 The turbulent, three dimensional and time dependent flow field of a precessing jet is investigated. In the present case the jet precession is generated by mechanically rotating a round jet inclined relative to the axis of rotation. A conditional flow visualisation technique is used to complement three dimensional laser Doppler velocity data, time-averaged and phase-averaged at the frequency of precession. The conditional phase-averaging technique enables phase-averaged velocity contours and vectors to be obtained which reveal flow patterns and structures within the flow field. Time-averaging of the velocity data shows that these structures are significant in that they generate a reverse flow (recirculation) region between the jet and its spinning axis. They are found also to cause a rapid decay of the mean velocity. The characteristics of the precessing jet found here are compared with previous investigations of the same flow and with investigations of other turbulent jets. Received: 17 March 1995/Accepted: 7 December 1995     

Applications of URANS on predicting unsteady turbulent separated flows

Accurate prediction of unsteady separated turbulent flows remains one of the toughest tasks and a practi cal challenge for turbulence modeling. In this paper, a 2D flow past a circular cylinder at Reynolds number 3,900 is numerically investigated by using the technique of unsteady RANS （URANS）. Some typical linear and nonlinear eddy viscosity turbulence models （LEVM and NLEVM） and a quadratic explicit algebraic stress model （EASM） are evaluated. Numerical results have shown that a high-performance cubic NLEVM, such as CLS, are superior to the others in simulating turbulent separated flows with unsteady vortex shedding.