Fluctuating Velocity Field Research Articles

Turbulence investigation in the roughness sub-layer of a near wall flow

The turbulence behaviour along a wall roughened by pyramidal elements was analysed in the region extending from the apex of the roughness elements up to the external limit of the roughness sub-layer. The data used for the analysis were obtained by particle image velocimetry technique. The rough wall turbulent boundary layer flow is characterized by a relatively low Reynolds number. All the results on the rough wall were compared with data referring to the canonical flow on a smooth wall turbulent boundary layer. Mean values and turbulence quantities for the two flows collapse when approaching the external limit of the roughness sublayer. The quadrant analysis of the Reynolds shear stress, in the region near the surface, shows that the contribution of the sweep motions is about equivalent for the two flows (except for wall distances lower than 40 viscous units). The contribution of the ejection motions appears to be more important over the smooth wall than over the rough wall with increasing differences approaching the wall. The probability density functions of the streamwise fluctuating velocity field for the rough wall case appear to be positively skewed in the zone very close to the pyramid apex, in contrast with the behavior observed for the smooth wall case at corresponding distances from the wall. The integral and Taylor scales for the rough wall case appear to be strongly reduced by the presence of the roughness, while the Kolmogorov microscale shows higher values.

Relative dispersion of particle pairs in turbulent channel flow

Lagrangian tracking of particle pairs is of fundamental interest in a large number of environmental applications dealing with contaminant dispersion and passive scalar mixing. The aim of the present study is to extend the observations available in the literature on relative dispersion of fluid particle pairs to wall-bounded turbulent flows, by means of particle pair tracking in direct numerical simulations (DNS) of a turbulent channel flow. The mean-square change of separation between particle pairs follows a clear ballistic regime at short times for all wall distances. The Eulerian structure functions governing this short-time separation are characterised in the channel, and allow to define a characteristic time scale for the ballistic regime, as well as a suitable normalisation of the mean-square separation leading to an overall collapse for different wall distances. Through fluid particle pair tracking backwards and forwards in time, the temporal asymmetry of relative dispersion is illustrated. At short times, this asymmetry is linked to the irreversibility of turbulence, as in previous studies on homogeneous isotropic flows. The influence of the initial separation (distance and orientation) as well as the influence of mean shear are addressed. By decomposing the mean-square separation into the dispersion by the fluctuating velocity field and by the average velocity, it is shown that the influence of mean shear becomes important at early stages of dispersion close to the wall but also near the channel centre. The relative dispersion tensor Δij is also presented and particularly the sign and time evolution of the cross-term Δxy are discussed. Finally, a ballistic cascade model previously proposed for homogeneous isotropic turbulence is adapted here to turbulent channel flows. Preliminary results are given and compared to the DNS. Future developments and assumptions in two particle stochastic models can be gauged against the issues and results discussed in the present study.

Spectral calculations for pressure–velocity and pressure–strain correlations in homogeneous shear turbulence

Theoretical analyses of pressure related turbulent statistics are vital for a reliable and accurate modeling of turbulence. In the inertial subrange of turbulent shear flow, pressure–velocity and pressure–strain correlations are affected by anisotropy imposed at large scales. Recently, Tsuji and Kaneda (2012 J. Fluid Mech. 694 50) performed a set of experiments on homogeneous shear flow, and estimated various one-dimensional pressure related spectra and the associated non-dimensional universal numbers. Here, starting from the governing Navier–Stokes dynamics for the fluctuating velocity field and assuming the anisotropy at inertial scales as a weak perturbation of an otherwise isotropic dynamics, we analytically derive the form of the pressure–velocity and pressure–strain correlations. The associated universal numbers are calculated using the well-known renormalization-group results, and are compared with the experimental estimates of Tsuji and Kaneda. Approximations involved in the perturbative calculations are discussed.

A generalized framework for reduced‐order modeling of a wind turbine wake

AbstractA reduced‐order model for a wind turbine wake is sought from large eddy simulation data. Fluctuating velocity fields are combined in the correlation tensor to form the kernel of the proper orthogonal decomposition (POD). Proper orthogonal decomposition modes resulting from the decomposition represent the spatially coherent turbulence structures in the wind turbine wake; eigenvalues delineate the relative amount of turbulent kinetic energy associated with each mode. Back‐projecting the POD modes onto the velocity snapshots produces dynamic coefficients that express the amplitude of each mode in time. A reduced‐order model of the wind turbine wake (wakeROM) is defined through a series of polynomial parameters that quantify mode interaction and the evolution of each POD mode coefficients. The resulting system of ordinary differential equations models the wind turbine wake composed only of the large‐scale turbulent dynamics identified by the POD. Tikhonov regularization is used to recalibrate the dynamical system by adding additional constraints to the minimization seeking polynomial parameters, reducing error in the modeled mode coefficients. The wakeROM is periodically reinitialized with new initial conditions found by relating the incoming turbulent velocity to the POD mode coefficients through a series of open‐loop transfer functions. The wakeROM reproduces mode coefficients to within 25.2%, quantified through the normalized root‐mean‐square error. A high‐level view of the modeling approach is provided as a platform to discuss promising research directions, alternate processes that could benefit stability and efficiency, and desired extensions of the wakeROM.

Numerical investigation of boundary layer flow and wall heat transfer in a gasoline direct-injection engine

Near-wall turbulent boundary-layer has a substantial impact on the wall heat transfer process in internal combustion engines, and ultimately affects the engine performance. However, the heat transfer processes are not well understood because of a lack of information on gas side velocity and temperature distribution. In the present study, the transient velocity and thermal boundary layers in a motored spark-ignition direct-injection engine are predicted using a Delay Detached Eddy Simulation Shear-stress Transport (DDES-SST) model. The near-wall ensemble-averaged and fluctuation velocity and temperature fields at the cylinder head are investigated throughout the compression stroke. The numerical results of the flow field in engine core region agree well with high-speed Two Dimensional Three Components-Particle Image Velocimetry (2D3C-PIV) experimental data. The simulated data show that boundary-layer separation occurs around the closing phase of intake valves and the turbulence in the near-wall region is anisotropic. The thickness of thermal boundary layer shows a non-monotonic variation with time. The dimensionless velocity profiles agree well with the law of the wall in the viscous sublayer but deviate from the log layer. The dimensionless temperature profiles tend to be uniform in the log-layer. The maximum local wall heat flux and heat transfer coefficient are 70kW/m2 and 200W/(m2K) at top dead center (TDC), respectively. The spatial distribution of turbulent heat flux shows a strong link between the velocity and thermal boundary layers, and the peaks in the buffer layer occupy about 70–85% of the local wall heat flux, indicating that the forced convection heat transfer is the main heat transfer mechanism in internal combustion engines.

How tracer particles sample the complexity of turbulence

On their roller coaster ride through turbulence, tracer particles sample the fluctuations of the underlying fields in space and time. Quantitatively relating particle and field statistics remains a fundamental challenge in a large variety of turbulent flows. We quantify how tracer particles sample turbulence by expressing their temporal velocity fluctuations in terms of an effective probabilistic sampling of spatial velocity field fluctuations. To corroborate our theory, we investigate an extensive suite of direct numerical simulations of hydrodynamic turbulence covering a Taylor-scale Reynolds number range from 150 to 430. Our approach allows the assessment of particle statistics from the knowledge of flow field statistics only, therefore opening avenues to a new generation of models for transport in complex flows.

Experimental investigation on the flow transition in different pin-fin arranged microchannels

The flow characteristics of water through the in-line and staggered pin-fin microchannels with length of 25 mm, width of 2.4 mm and height of 0.11 mm were studied experimentally. The flow transition was identified as a sudden increasing slope in both pressure drop versus mass flow rate curve and friction factor versus Reynolds number curve for in-line pin-fin microchannels, but it did not occur for staggered pin-fin microchannels. The effect of pin-fin arrangements on the flow transition was not reported in the previous literature. With the aid of microparticle image velocimetry (Micro-PIV) technology, the streamlines, velocity fields and velocity fluctuation fields of flow through the pin-fin microchannels were captured to explain the flow transition, and the effect of pin-fin arrangements on the flow transition was analyzed for the first time. It was found that at the critical Reynolds number where the flow transition occurred for the in-line pin-fin microchannels, the steady double-vortex wake flow changed to the unsteady vortex-shedding wake flow. The occurrence of vortex shedding caused an obvious change in main stream from straight flow to wavy flow and further induced significant increases of transversal velocity and velocity fluctuations, which induced strong flow disturbance in transversal directions and large additional pressure drop, and finally caused the flow transition in the in-line pin-fin microchannels. For the staggered pin-fin microchannels, the main stream through the pin-fin arrays was found to be already the wavy flow before the vortex shedding. Thus, the transversal velocity and velocity fluctuations induced by the vortex shedding were relatively small, and therefore, the flow transition with an abrupt pressure drop increase was not observed in the staggered pin-fin microchannels.

Second-Law Analysis: A Powerful Tool for Analyzing Computational Fluid Dynamics (CFD) Results

Second-law analysis (SLA) is an important concept in thermodynamics, which basically assesses energy by its value in terms of its convertibility from one form to another.[...]

Influence of velocity fluctuations on the Kelvin‐Helmholtz instability and its associated mass transport

AbstractKelvin‐Helmholtz instability (KHI) and associated magnetic reconnection and diffusion processes provide plasma transport from solar wind into the magnetosphere. The efficiency of this transport depends on the magnetosheath and magnetospheric plasma and field properties at the vicinity of the magnetopause. Our recent statistical study using data from the Time History of Events and Macroscale Interactions during Substorms spacecraft indicates that the amplitude of the magnetosheath velocity fluctuations perpendicular to the magnetopause can be substantial. We have performed a series of local macroscale 2.5‐dimensional magnetohydrodynamic simulations of the KHI during strongly northward interplanetary magnetic field and with the initial plasma parameters typical to the dayside magnetopause by perturbing the initial equilibrium with time‐dependent perpendicular velocity field fluctuations. The effect of the single‐mode and multimode seed spectrums at different frequencies and amplitudes is studied. The plasma transport in Kelvin‐Helmholtz vortices is quantified. The results show that when large‐amplitude, low‐frequency seed velocity fluctuations exist in the magnetosheath, the resulting KH waves grow faster, get larger in size, and can transport more plasma through magnetic boundary, resulting in diffusion coefficient of the order 109 m2/s. The relevance of these findings to the solar wind‐magnetosphere coupling is discussed.

Magnetic and velocity fluctuations from nonlinearly coupled tearing modes in the reversed field pinch with and without the reversal surface

We investigate the role of poloidal mode number m = 0 fluctuations on m = 1 velocity and magnetic field fluctuations in the Reversed Field Pinch (RFP). Removing the m = 0 resonant surface in the Madison Symmetric Torus (MST), results in suppressed m = 0 activity without a reduction in m = 1 magnetic activity. However, the m = 1 velocity fluctuations and fluctuation-induced mean emf are reduced as m = 0 modes are suppressed. Velocity fluctuations are measured directly using fast Doppler spectroscopy. Similar results are seen in visco-resistive MHD simulation with the DEBS code. An artificial line-averaged velocity diagnostic is developed for DEBS simulations to facilitate direct comparisons with experimental measurements. The sensitivity of the m = 1 velocity fluctuations and corresponding emf to changes in m = 0 mode activity is a feature of tearing modes in the nonlinear regime with a spectrum of interacting modes. These results have implications for RFP sustainment strategies and inform our understanding of the role of magnetic turbulence in astrophysical contexts.

Large eddy simulations of blood dynamics in abdominal aortic aneurysms

We study the effects of transition to turbulence in abdominal aortic aneurysms (AAA). The presence of transitional effects in such districts is related to the heart pulsatility and the sudden change of diameter of the vessels, and has been recorded by means of clinical measures as well as of computational studies. Here we propose, for the first time, the use of a large eddy simulation (LES) model to accurately describe transition to turbulence in realistic scenarios of AAA obtained from radiological images. To this aim, we post-process the obtained numerical solutions to assess significant quantities, such as the ensemble-averaged velocity and wall shear stress, the standard deviation of the fluctuating velocity field, and vortical structures educed via the so-called Q-criterion. The results demonstrate the suitability of the considered LES model and show the presence of significant transitional effects around the impingement region during the mid-deceleration phase.

Unsteady flow dynamics reconstruction from mean flow and point sensors: an experimental study

This article presents a reconstruction of the unsteady behaviour of a round jet at a Reynolds number equal to 3300, from the sole knowledge of the time-averaged flow field and one pointwise unsteady measurement. The reconstruction approach is an application of the work of Beneddine et al. (J. Fluid Mech., vol. 798, 2016, pp. 485–504) and relies on the computation of the dominant resolvent modes of the flow, using a parabolised stability equations analysis. To validate the procedure, the unsteady velocity field of the jet has been characterised by time-resolved particle image velocimetry (TR-PIV), yielding an experimental reference. We first show that the dominant resolvent modes are proportional to the experimental Fourier modes, as predicted by Beneddine et al. (J. Fluid Mech., vol. 798, 2016, pp. 485–504). From these results, it is then possible to fully reconstruct the unsteady velocity and pressure fluctuation fields, yielding a flow field that displays good agreement with the experimental reference. Finally, it is found that the robustness of the reconstruction mainly depends on the location of the pointwise unsteady measurement, which should be within energetic regions of the flow, and this robustness as well as the quality of the reconstruction can be greatly improved by considering a few pointwise measurements instead of a single one. The effects of other experimental parameters on the reconstruction, such as the size of the interrogation window used for the TR-PIV processing and the accuracy of the positioning of the sensors, are also investigated in this paper.

Correlation of flow field and acoustic output from hearing aids under influence of wind

Wind noise in hearing aids occurs even at low wind speeds and is a confounding factor for hearing aid wearer, hence leading to a reduction of speech intelligibility. In this submission, a study on the correlation of the flow field around a hearing aid to its acoustic output is made. The BTE (behind the ear) hearing aid is mounted on an artificial head with three different ear geometries. The flow field is captured using a two component PIV (particle image velocimetry) system. For exposing critical flow phenomena, a POD (proper orthogonal decomposition) of the PIV measurement data is made. The hearing aid output is measured with a microphone inside the artificial head. On the one hand, wind noise in hearing aids is generated by the fluctuating velocity field of the boundary layer on the hearing aid. On the other hand, based on the PIV data and the POD results, flow patterns around the artificial head and the hearing aid are detected, which cause further noise, that is captured by the hearing aid microphones. With these findings, modifications on the hearing aid geometry are deduced, that lead to a decrease in wind noise and hence to a better speech intelligibility.

Invariants of the velocity-gradient tensor in a spatially developing inhomogeneous turbulent flow

Tomographic particle image velocimetry experiments were performed in the near field of the turbulent flow past a square cylinder. A classical Reynolds decomposition was performed on the resulting velocity fields into a time invariant mean flow and a fluctuating velocity field. This fluctuating velocity field was then further decomposed into coherent and residual/stochastic fluctuations. The statistical distributions of the second and third invariants of the velocity-gradient tensor were then computed at various streamwise locations, along the centreline of the flow and within the shear layers. These invariants were calculated from both the Reynolds-decomposed fluctuating velocity fields and the coherent and stochastic fluctuating velocity fields. The range of spatial locations probed incorporates regions of contrasting flow physics, including a mean recirculation region and separated shear layers, both upstream and downstream of the location of peak turbulence intensity along the centreline. These different flow physics are also reflected in the velocity gradients themselves with different topologies, as characterised by the statistical distributions of the constituent enstrophy and strain-rate invariants, for the three different fluctuating velocity fields. Despite these differing flow physics the ubiquitous self-similar ‘tear drop’-shaped joint probability density function between the second and third invariants of the velocity-gradient tensor is observed along the centreline and shear layer when calculated from both the Reynolds decomposed and the stochastic velocity fluctuations. These ‘tear drop’-shaped joint probability density functions are not, however, observed when calculated from the coherent velocity fluctuations. This ‘tear drop’ shape is classically associated with the statistical distribution of the velocity-gradient tensor invariants in fully developed turbulent flows in which there is no coherent dynamics present, and hence spectral peaks at low wavenumbers. The results presented in this manuscript, however, show that such ‘tear drops’ also exist in spatially developing inhomogeneous turbulent flows. This suggests that the ‘tear drop’ shape may not just be a universal feature of fully developed turbulence but of turbulent flows in general.

Passive scalars: Mixing, diffusion, and intermittency in helical and nonhelical rotating turbulence.

We use direct numerical simulations to compute structure functions, scaling exponents, probability density functions, and effective transport coefficients of passive scalars in turbulent rotating helical and nonhelical flows. We show that helicity affects the inertial range scaling of the velocity and of the passive scalar when rotation is present, with a spectral law consistent with ∼k_{⊥}^{-1.4} for the passive scalar variance spectrum. This scaling law is consistent with a phenomenological argument [P. Rodriguez Imazio and P. D. Mininni, Phys. Rev. E 83, 066309 (2011)PLEEE81539-375510.1103/PhysRevE.83.066309] for rotating nonhelical flows, which follows directly from Kolmogorov-Obukhov scaling and states that if energy follows a E(k)∼k^{-n} law, then the passive scalar variance follows a law V(k)∼k^{-n_{θ}} with n_{θ}=(5-n)/2. With the second-order scaling exponent obtained from this law, and using the Kraichnan model, we obtain anomalous scaling exponents for the passive scalar that are in good agreement with the numerical results. Multifractal intermittency models are also considered. Intermittency of the passive scalar is stronger than in the nonhelical rotating case, a result that is also confirmed by stronger non-Gaussian tails in the probability density functions of field increments. Finally, Fick's law is used to compute the effective diffusion coefficients in the directions parallel and perpendicular to rotation. Calculations indicate that horizontal diffusion decreases in the presence of helicity in rotating flows, while vertical diffusion increases. A simple mean field argument explains this behavior in terms of the amplitude of velocity fluctuations.

Influence of the Local Cross-Streamlined Obstacles on the Velocity and Pressure Fluctuations

Background. Developing means to enhance the effectiveness of mass and heat transfer processes on streamlined surfaces and their hydroacoustic qualities in the objects of power, aerospace and marine engineering. Objective. The purpose of the research is to determine the formation features and space-time characteristics of the velocity and wall-pressure fluctuation fields in flows above and on the streamlined surfaces with local obstacles as the cross-streamlined half-cylindrical trench on a flat surface and circular obstacle on the flexible longitudinal hydroacoustic antenna surface. Methods. The research was carried out by means of hot-wire and hydroacoustic measuring in flows on streamlined obstacles and spectral analysis of statistical characteristics of the velocity and wall-pressure fluctuations in investigating systems. Results. It has been determined experimentally the zones and conditions of vortices formation by various frequency ranges, the extremes of power spectrum densities of the velocity and wall-pressure fluctuations, vortex interaction, ejections and stalls near streamlined surfaces with local obstacles at rather wide Reynolds number ranges. Conclusions. Basing on received space-time characteristics of the velocity and wall-pressure fluctuations and discovered typical features of their spectra the hydromechanical mechanisms of heat and mass exchange and hydroacoustic processes in the investigated systems have been determined. The results of the study can be used for designing of such systems and they reveal the perspective of directed control by mentioned processes for increase of their efficiency.

Simulation of size segregation in granular flow with material point method

Segregation is common in granular flows consisting of mixtures of particles differing in size or density. In gravity-driven flows, both gradients in total pressure (induced by gravity) and gradients in velocity fluctuation fields (often associated with shear rate gradients) work together to govern the evolution of segregation. Since the local shear rate and velocity fluctuations are dependent on the local concentration of the components, understanding the co-evolution of segregation and flow is critical for understanding and predicting flows where there can be a variety of particle sizes and densities, such as in nature and industry. Kinetic theory has proven to be a robust framework for predicting this simultaneous evolution but has a limit in its applicability to dense systems where collisions are highly correlated. In this paper, we introduce a model that captures the coevolution of these evolving dynamics for high density gravity driven granular mixtures. For the segregation dynamics we use a recently developed mixture theory (Fan & Hill 2011, New J. Phys; Hill & Tan 2014, J. Fluid Mech.) which captures the combined effects of gravity and fluctuation fields on segregation evolution in high density granular flows. For the mixture flow dynamics, we use a recently proposed viscous-elastic-plastic constitutive model, which can describe the multi-state behaviors of granular materials, i.e. the granular solid, granular liquid and granular gas mechanical states (Fei et al. 2016, Powder Technol.). The platform we use for implementing this model is a modified Material Point Method (MPM), and we use discrete element method simulations of gravity-driven flow in an inclined channel to demonstrate that this new MPM model can predict the final segregation distribution as well as flow velocity profile well. We then discuss ongoing work where we are using this platform to test the effectiveness of particular segregation models under different boundary conditions.

Longitudinal and transverse structure functions in high Reynolds-number magneto-hydrodynamic turbulence

We investigate the scaling behavior of longitudinal and transverse structure functions in homogeneous and isotropic magneto-hydrodynamic (MHD) turbulence by means of an exact hierarchy of structure function equations as well as by direct numerical simulations of two- and three-dimensional MHD turbulence. In particular, rescaling relations between longitudinal and transverse structure functions are derived and utilized in order to compare different scaling behavior in the inertial range. It is found that there are no substantial differences between longitudinal and transverse structure functions in MHD turbulence. This finding stands in contrast to the case of hydrodynamic turbulence which shows persistent differences even at high Reynolds numbers. We propose a physical picture that is based on an effective reduction of pressure contributions due to local regions of same magnitude and alignment of velocity and magnetic field fluctuations. Finally, our findings underline the importance of the pressure term for the actually observed scaling differences in hydrodynamic turbulence.

Experimental Measurement of the Velocity Field of Round Wall Jet in Counterflow

Experimental investigations showing the mean and fluctuating velocity fields of a three-dimensional round wall jet in counterflow are presented. The ratios of jet to counterflow velocity ranged from 2.5 to 25 and the jet Reynolds numbers were from 1,000 to 10,000. The jet penetration length, which is the axial distance that the wall jet penetrates into the counterflow before stopping, was measured and scaled with a power-law relation. The decay of the jet velocity during its penetration into the oncoming flow was analyzed with proper scaling parameters. The results show that up to 70% of the wall jet penetration length, the velocity decay, and the spreading rate are effectively identical to those of a wall jet in quiescent ambient flow. Above this distance, the velocity decay is linear and the jet spreading rate increases sharply. The mean axial velocity profiles show self-similarity between 25 and 80% of the penetration distance and are similar to the case with no counterflow. The vortical structures from the jet and the opposing turbulent boundary layer interact in the stagnation area to provide a large recirculation region with stochastic oscillations that enhance the mixing of the wall jet and counterflow. These interactions result in a region of high turbulence intensity near the upstream extents of the wall jet. The profiles of Reynolds stresses are presented and discussed. It was observed that the normalized velocity fluctuation profiles show self-similarity for the region within 30 and 70% of the wall jet penetration length, which is shorter than the region for which the axial velocity profiles are self-similar.

Numerical and experimental investigation of a beveled trailing-edge flow field and noise emission

Efficient tools and methodology for the prediction of trailing-edge noise experience substantial interest within the wind turbine industry. In recent years, the Lattice Boltzmann Method has received increased attention for providing such an efficient alternative for the numerical solution of complex flow problems. Based on the fully explicit, transient, compressible solution of the Lattice Boltzmann Equation in combination with a Ffowcs-Williams and Hawking aeroacoustic analogy, an estimation of the acoustic radiation in the far field is obtained. To validate this methodology for the prediction of trailing-edge noise, the flow around a flat plate with an asymmetric 25° beveled trailing edge and obtuse corner in a low Mach number flow is analyzed. Flow field dynamics are compared to data obtained experimentally from Particle Image Velocimetry and Hot Wire Anemometry, and compare favorably in terms of mean velocity field and turbulent fluctuations. Moreover, the characteristics of the unsteady surface pressure, which are closely related to the acoustic emission, show good agreement between simulation and experiment. Finally, the prediction of the radiated sound is compared to the results obtained from acoustic phased array measurements in combination with a beamforming methodology. Vortex shedding results in a strong narrowband component centered at a constant Strouhal number in the acoustic spectrum. At higher frequency, a good agreement between simulation and experiment for the broadband noise component is obtained and a typical cardioid-like directivity is recovered.