Velocity Statistics Research Articles

Kinematic simulations as a subgrid-scale model for particle motion: a priori LES of homogeneous isotropic turbulence

In this work we investigated the impact of filtering and subgrid-scale modeling on particle settling velocity and collision-related statistics in a turbulent flow. To reduce the complexity of this task we first studied the motion of inertial particles in the low-pass filtered homogeneous and isotropic turbulence, which was subsequently enriched with the subgrid-scale velocity components obtained from a frozen high-pass filtered velocity field. Particular emphasis has been put on the radial distribution function and the radial relative velocity of nearly touching particles both in the presence or absence of the gravitational settling. These statistics are the key input parameters to the kinematic collision kernel which is of crucial importance in determining the collision rate of inertial particles in a turbulent flow. Furthermore, kinematic simulations were selected as a means of enhancing the fluid velocity at particle locations. We analyzed a wide range of Stokes numbers, i.e. a measure of particle inertia, and, in contrast to scientific premises found in the literature, we observed no improvement of particle statistics when the low-pass filtered fluid velocity was enriched with both a synthetic or spectrally-filtered small-scale structures. We discuss the shortages of any frozen-velocity-based subgrid-scale model in predicting both single- and two-point particle statistics. We also indicate that in some cases, particularly concerning the collision rate of particles suspended in homogeneous and isotropic turbulence, subgrid-scale contribution in the particle equation of motion can be neglected.

Battery screen print defect detection based on stationary velocity fields neural network matching and optical flow rectification.

In this study, an automatic defect detection method is proposed for screen printing in battery manufacturing. It is based on stationary velocity field (SVF) neural network template matching and the Lucas-Kanade (L-K) optical flow algorithm. The new method can recognize and classify different defects, such as lacking, skew, and blur, under the condition of irregular shape distortion. Three critical processing stages are performed during detection: (1) Image preprocessing was performed to acquire the printed region of interest and then image blocking was carried out for template creation. (2) The SVF network for image registration was constructed and the corresponding dataset was built based on oriented fast and rotated brief feature matching. (3) Irregular print distortion was rectified and defects were extracted using L-K optical flow and image subtraction. Software and hardware systems have been developed to support this method in industrial applications. To improve environment adaptation, we proposed a dynamic template updating mechanism to optimize the detection template. From the experiments, it can be concluded that the method has desirable performance in terms of accuracy (97%), time efficiency (485ms), and resolution (0.039mm). The proposed method possesses the advantages of image registration, defect extraction, and industrial efficiency compared to conventional methods. Although they suffer from irregular print distortions in batteries, the proposed method still ensures a higher detection accuracy.

An efficient model for subgrid-scale velocity enrichment for large-eddy simulations of turbulent flows

In some applications of large-eddy simulation (LES), in addition to providing a closure model for the subgrid-scale stress tensor, it is necessary to also provide means to approximate the subgrid-scale velocity field. In this work, we derive a new model for the subgrid-scale velocity that can be used in such LES applications. The model consists in solving a linearized form of the momentum equation for the subgrid-scale velocity using a truncated Fourier-series approach. Solving within a structured grid of statistically homogeneous sub-domains enables the treatment of inhomogeneous problems. It is shown that the generated subgrid-scale velocity emulates key properties of turbulent flows, such as the right kinetic energy spectrum, realistic strain–rotation relations, and intermittency. The model is also shown to predict the correct inhomogeneous and anisotropic velocity statistics in unbounded flows. The computational costs of the model are still of the same order as the costs of the LES.

Modeling and analyzing the motion of a 2DOF dynamical tuned absorber system close to resonance

This work investigates the planar motion of a dynamical model with two degrees-of-freedom (DOF) consisting of a connected tuned absorber with a simple pendulum. It is taken into account that the pendulum’s pivot moves in a Lissajous trajectory with stationary angular velocity in the presence of a harmonic excitation moment. In terms of the model’s generalized coordinates, Lagrange’s equations are used to derive the motion’s controlling system. The approximate solutions of this system, up to a higher order of approximation, are achieved utilizing the approach of multiple scales (AMS). Resonance cases are all classified, in which two of them are examined simultaneously to gain the corresponding equations of modulation. The solutions at the steady-state are studied in terms of solvability conditions. According to the Routh-Hurwitz criteria, all potential fixed points at steady and unsteady states are determined and graphed. The dynamical behavior of the motion's time-histories and the curves of resonance are drawn. Regions of stability are examined by inspecting their graphs in order to assess the favorable impact of various parameters on the motion. The achieved outcomes are regarded as novel because the used methodology is applied to a specific dynamical system. The importance of this model under study can be seen from its numerous applications in disciplines like engineering and physics. Furthermore, pendulum vibration absorbers are commonly employed to reduce the vibrations in engineering constructions such as chimneys, bridges, television towers, high buildings, auto-balancing shafts, and antennas.

Impact of spanwise effective slope upon rough-wall turbulent channel flow

Whereas streamwise effective slope ( $ES_{x}$ ) is accepted as a key topographical parameter in the context of rough-wall turbulent flows, the significance of its spanwise counterpart ( $ES_{y}$ ) remains largely unexplored. Here, the response of turbulent channel flow over irregular, three-dimensional rough walls with systematically varied values of $ES_{y}$ is studied using direct numerical simulation. All simulations were performed at a fixed friction Reynolds number 395, corresponding to a viscous-scaled roughness height $k^{+}\approx 65.8$ (where $k$ is the mean peak-to-valley height). A surface generation algorithm is used to synthesise a set of ten irregular surfaces with specified $ES_{y}$ for three different values of $ES_{x}$ . All surfaces share a common mean peak-to-valley height and are near-Gaussian, which allows this study to focus on the impact of varying $ES_{y}$ , since roughness amplitude, skewness and $ES_{x}$ can be eliminated simultaneously as parameters. Based on an analysis of first- and second-order velocity statistics, as well as turbulence co-spectra and the fractional contribution of pressure and viscous drag, the study shows that $ES_{y}$ can strongly affect the roughness drag penalty – particularly for low- $ES_{x}$ surfaces. A secondary observation is that particular low- $ES_{y}$ surfaces in this study can lead to diminished levels of outer-layer similarity in both mean flow and turbulence statistics, which is attributed to insufficient scale separation between the outer length scale and the in-plane spanwise roughness wavelength.

Simulation of stationary and nonstationary wind velocity field along a long-span bridge using a numerical truncation method

The spectral representation method (SRM) has been extensively utilized to generate inhomogeneous stochastic wind velocity fields of long-span bridges. However, the simulation process usually needs a large number of computing resources, particularly when plenty of simulation points/samples are required. To address this issue, this study proposes a numerical truncation approach with the aid of a closed-form solution of Cholesky decomposition regarding the coherence matrix. First, the double summation of SRM is optimized as two separate inner and outer summations. Then, the closed-form solution of Cholesky decomposition is cut off to simplify the inner summation by setting an appropriate threshold. Since this inner summation dispenses with the participation of the truncated elements, the computational efforts are reduced significantly. As for the outer summation, it can be fast completed via introducing the fast Fourier transform technique. Finally, numerical examples are used to verify the effectiveness of the proposed method in terms of accuracy and efficiency. The results show that this method possesses a satisfactory accuracy and high efficiency with a given threshold. Therefore, it presents a high potential in simulating large-scale stochastic fluctuating wind velocity fields.

Full-Scale Reynolds Number Testing of Rotor Hub Drag and Wake Turbulence

A 1:4.25-scale model of a generic helicopter rotor hub was tested at Reynolds numbers ranging from 1. 75× 106 to 7×106 at advance ratio of 0.2 in The Pennsylvania State University Applied Research Laboratory Garfield Thomas 48-inch diameter water tunnel. Measurements including drag and wake characteristics were performed up to full-scale Reynolds number with respect to an industry-representative helicopter rotor hub. In particular, the variation of drag and flow field with Reynolds number was characterized. Load measurements were conducted using an improved load cell design, with greater accuracy than in previous experiments. Wake velocity was measured using laser Doppler velocimetry at two downstream planes, yielding velocity statistics to the second order. Improved load measurement accuracy and wake velocity spatial resolution, at full-scale Reynolds number, provide a unique dataset for computational fluid dynamics validation as part of the Penn State Rotor Hub Flow Prediction Workshops and physical insight into rotor hub flows.

Experimental study of coherent wall-pressure fluctuations associated with the turbulent near wake of a cylinder

The objective of this work is to present a coherent detection method to determine relationships between pressure fluctuations and wake velocity in the case of the flow past a cylinder in a turbulent regime. We report experimental results and pressure–velocity statistics measured simultaneously on the surface boundary layer and the near wake in the range of Reynolds numbers (2×103<Re<3.5×104). The novelty of the analysis lies in the application of a coherent mean method to determine conditioned wall pressure statistics to velocity events observed in the turbulent cylinder wake. The method allows one to associate wake turbulent events with a corresponding wall-pressure signal profile on the cylinder surface performing discrete angular measurements with a minimum number of pressure sensors. Simultaneous measurements of both time series of wake velocity and wall pressure allow us to characterize the mutual influence of hydrodynamic perturbations from the boundary layer surface pressure with the near wake velocity fluctuations. Large scale turbulent vortex shedding is well correlated with surface pressure fluctuations as expected in the low frequency range. Near wake velocity signals were used as timing signals to determine the coherent influence of a representative velocity pattern on the statistical properties of wall pressure fluctuations. The dynamics of low-frequency large-scale structures is consistent with the presence of counter-rotating vortices and is well correlated with a great part of the pressure fluctuations of the boundary layer. Conditional statistics using the velocity pattern obtained from the coherent averaging method provided the instantaneous pressure fluctuating profile associated with the large-scale vortex shedding cycle, thus, enabling a coherent estimation of the fluctuating lift and drag forces. Conditional statistics on wake velocity are well influenced by the phase of the vortex life-cycle.

Distinct Dynamical and Structural Properties of Marine Stratocumulus and Shallow Cumulus Clouds in the Eastern North Atlantic

AbstractLow‐level clouds in a marine environment are examined using multiple ground‐based instruments. We used Doppler radar and Doppler lidar measurements (a) to examine cloud properties including cloud base and top height and thickness and (b) to investigate vertical velocity (w) statistics throughout the subcloud and in‐cloud layers. Marine stratocumulus (Sc) and shallow cumulus (Cu) clouds have distinct properties in their horizontal and vertical extent. We also find that the two cloud types have different thermodynamic (coupled and decoupled conditions) and dynamical characteristics for the first four moments of the w distributions (mean, variance, skewness, and kurtosis). We identify a strong dependence of subcloud mean w on near‐surface horizontal wind direction, implying that topographic effects exert a substantial impact on boundary layer dynamics and cloud properties at Graciosa Island. Our findings strongly suggest that care must be taken when interpreting island‐based observations as representative of a generic marine dynamical environment. This information also can be useful for guiding and constraining the future global model development using an observational data set.

Electrically Induced Hydrodynamic Effect in Nematics Caused by Volume Reduction

A pressure gradient caused by the local field-induced reduction of the effective molecular volume results in a flow of the nematic liquid crystal (NLC). Here, the hydrodynamics of homeotropically aligned NLC molecules under the influence of this pressure gradient was studied theoretically. The equations describing the system were written and solved in the steady-state case using analytical methods, and the stationary velocity of the observed flow was found. We discussed the obtained results and compared them with existing experimental results.

RANS CFD modeling of the flow around a thin windbreak fence with various porosities: Validation using wind tunnel measurements

In computational fluid dynamics (CFD) simulations of airflow in built environments, the porous-jump model is commonly used to represent extremely thin porous windbreak fences, which have much smaller sizes than the neighborhood computational cells. However, owing to the limited quantitative validation studies that include turbulence characteristics, no clear guidelines exist on modeling such thin porous fences in CFD simulations. In this study, pressure loss coefficients of porous materials with various porosity values and opening shapes were determined using a small wind tunnel while the velocity and turbulence statistics behind the fences were measured in an atmospheric boundary layer wind tunnel. Two separate CFD models based on the Reynolds-averaged Navier–Stokes equation and porous-jump models were used to mimic the airflow in each wind tunnel and then they were validated using the experimental results. The results showed that the pressure loss was accurately predicted by CFD simulations. For wire-mesh fences, a good agreement was obtained between experimental and numerical results for the mean streamwise velocity and turbulent kinetic energy (TKE), whereas the velocity deficit and TKE were overestimated and underestimated, respectively, for the non-wire-mesh fences. This study can be used to improve the performance of thin porous windbreak fences.

The effect of sub-filter scale dynamics in large eddy simulation of turbulence

We study the effect of sub-filter scale (SFS) dynamics on the accuracy of direct deconvolution models (DDM) in large eddy simulation of isotropic turbulence at different filter-to-grid ratios (FGR), by using several types of invertible filters including the Gaussian, Helmholtz I and II, Butterworth, Chebyshev I and II, Cauchy, Pao, and rapidly decaying filters. We show that the FGR is crucial in controlling errors to ensure an accurate prediction of SFS stresses. In the case of FGR of 1, the DDM models cannot accurately reconstruct SFS stress, since the effect of SFS dynamics on SFS stress is not properly resolved by the coarse grid. The prediction abilities of most DDM models are significantly improved at FGR of 2, giving rise to quite an accurate reconstruction of SFS stresses, except for the situation of Helmholtz I and II filters. All the DDM models give very accurate results at FGR of 4. Moreover, the DDM models are comprehensively compared against various traditional SFS models, including the velocity gradient model, dynamic Smagorinsky model (DSM), dynamic mixed model (DMM), and the approximate deconvolution model. In the a priori study, the correlation coefficients of SFS stress for the DDM are much larger than those of the traditional models. In the a posteriori study, DDM outperforms DSM and DMM models in the prediction of various velocity statistics and instantaneous flow structures. These results indicate that the DDM framework with an appropriate FGR has much potential in developing high-fidelity SFS models in the LES of turbulence.

Organization Development in Precipitating Shallow Cumulus Convection: Evolution of Turbulence Characteristics

Abstract Horizontal organization or mesoscale variability is an important mechanism in the interaction of the boundary layer with the large-scale conditions. The development of organization in a precipitating cumulus trade wind boundary layer is studied using large-eddy simulations with extensive horizontal domains, up to 160 × 160 km2 and fine grid resolution (40 m). The cloud fields vary between different computational domain sizes. Mean profiles and vertical velocity statistics do not vary significantly, both with respect to the domain size and when large-scale organization develops. Turbulent kinetic energy (TKE) rapidly increases when organization develops. The increase of TKE is attributed to the horizontal component, whereas the vertical velocity variance does not change significantly. The large computational domains blend the boundary between local convective circulations and mesoscale horizontal motions leading to the dependence of horizontal TKE on the LES domain size. Energy-containing horizontal length scales are defined based on the premultiplied spectra. When large-scale organization develops, the premultiplied spectra develop multiple peaks corresponding to the characteristic horizontal scales in the boundary layer. All flow variables have a small length scale of 1–2 km, which corresponds to local convective motions, e.g., updrafts and cumulus clouds. Organization development creates additional larger length scales. The growth rate of the large length scale is linear and it is about 3–4 km h−1, which agrees well with the growth rate of the cold pool radii. A single energy containing length scale is observed for vertical velocity for the entire run (even after organized convection develops) that is fairly constant with height.

Outer-layer coherent structures from the turbulent/non-turbulent interface perspective at moderate Reynolds number

This study reports the observation of outer-layer coherent structures in turbulent boundary layer from the turbulent/non-turbulent interface perspective at moderate Reynolds number. The observation relies on time-resolved particle image velocimetry measurements with a large field-of-view. The local turbulent kinetic energy is used to detect the turbulent/non-turbulent interface. In the reference frame of turbulent/non-turbulent interface, raw velocity is decomposed into three components: time average of raw velocity, conditionally averaging components and turbulent fluctuations. The triple velocity decomposition eliminates the bias of Reynolds decomposition fluctuations in the intermittent region. The conditional statistics based on the turbulent/non-turbulent interface is considered to discuss the turbulence characteristics. The basic statistics of mean raw velocity, Reynolds stresses, and swirling strength are observed in conditional statistics. And the results are compared with the results based on the traditional wall surface reference frame. Quadrant analysis is introduced to extract ejections & sweeps and reflect the statistical characteristics of the outer-layer structure. The contribution of ejections and sweeps to the Reynolds shear stresses exhibits significantly different characteristics. Then, the configuration of the turbulent fluctuations and instantaneous structures is presented relied on the uniform momentum zones in the instantaneous frames. The spatial characteristics of coherent structures are reflected by two-point correlation of the streamwise turbulent fluctuations. In addition, the spatial scale of the outer-layer structures is revealed from the turbulent/non-turbulent interface perspective.

Coherent structures and mixing enhancement in a confined impinging-jet mixer

This study attempted to apply improved delayed detached-eddy simulation (IDDES) method to the prediction of the turbulent mixing in a confined impinging-jet mixer (a simplified model of a side-dump combustor). It was found that the time-averaged velocity and second-order statistics were in good agreement with available experimental data, demonstrating the reliability of IDDES for the numerical study of impinging jets. We visualized all discovered coherent structures and revealed the existence of two arrays of quasi-two-dimensional spanwise vortices in the jet shear layers and the continuous rolling-up of large-scale counter-rotating spanwise vortices in the downstream region with the aid of conditional sampling method. We provided insights on the generation and evolution mechanisms of both discovered and newly-discovered coherent structures. Furthermore, the effects of coherent structures on phase-averaged turbulence statistics were evaluated. The improvements of mixing efficiency associated with coherent structures were elaborated through the phase-averaging analysis on heat flux components.

Dataset of Wall-Resolved Large-Eddy Simulations Turbulent Pseudoboiling in Cryogenic Hydrogen Pipe Flows

In this paper, a dataset of wall-resolved large-eddy simulations of cryogenic hydrogen at supercritical pressure and different values of wall heat flux is presented. The aim is to provide a reference dataset for wall-function development under trans- and supercritical conditions, such as those found in liquid rocket engine applications. The employed numerical framework is a pressure-based segregated low-Mach-number approach based on an equation-of-state independent formulation. The wall-adapting local eddy-viscosity subgrid model is used for turbulence closure. Real-gas effects are taken from the National Institute for Standards and Technology database and stored as a function of a nondimensional temperature at the considered pressure. A validation and a grid-convergence analysis are first performed on an incompressible case without imposed heat flux. The effect of axial, radial, and azimuthal refinements on first- and second-order velocity statistics is discussed and compared with direct numerical simulation data from the literature. A parametric analysis at different wall heat fluxes is then performed by keeping the inlet mass flux, temperature, and Reynolds number constant. Particular attention is devoted to turbulent pseudoboiling and its effect on the wall temperature. The latter shows a more pronounced increment as the heat flux increases, which is attributed to the pseudochange of the phase in the core flow. Correspondingly, a flattening of the probability density function of the temperature is observed, and it is associated with the pseudoboiling interface forming close to the wall and causing a more intense stratification. First- and second-order statistics for velocity and selected scalars are then presented, and the effect of pseudoboiling is discussed. The effect of the wall heat flux on the viscous and thermal resolution of the computational grid is also assessed, and considerations on the relation between turbulent pseudoboiling and near-wall gradients is finally provided.

Spatial correlations and relative velocities of polydisperse droplets in homogeneous isotropic turbulence

We investigate the motions of polydisperse droplets in homogeneous and isotropic turbulence at Reynolds numbers Reλ=200–300. The emphasize is put on the parameter dependences of spatial velocity correlations (SVCs) and relative velocities (RVs) of droplets, which are relevant to particle transport and dispersion in turbulence and have been less studied in experiments. The Kolmogorov-scale Stokes number is Stp=10−1–101, and the settling parameter, i.e., the ratio of particle settling velocity to fluid velocity fluctuations, is SvL=0.5–2.0. Using high-resolution measurements, we can resolve the motions of turbulence and droplet over a wide range of scales (10−1η to 102η, η is Kolmogorov length). The parabolic behavior in droplet SVCs near the origin is observed, similar to turbulence. The droplet SVCs are smaller than turbulence for all scales and decrease with both Stp and SvL. At large scales, the droplet RVs, smaller than those of turbulence due to the inertial filtering effect, also decrease with Stp and SvL. At small scales, the path-history effect leads to larger droplet RVs than fluid RVs. Interestingly, we find RVs present a non-monotonic trend with Stp and reach a valley at Stp≈1.0. It may originate from particle clustering and preferential sweeping effects, which both prevail at Stp≈1.0. It is also found that droplet motions are less intermittent than turbulence. This is in contrast to the previous observations by simulations with the gravity effect being ignored. The intermittency of droplet RVs decreases with SvL due to the diminished droplet–turbulence interactions, and it presents opposite trends with Stp for small and large scales. Finally, the balance between the effects of path histories and turbulent structures makes the velocity statistics of droplets quasi-independent from the scale in the range of the dissipative scale (r≲5η).

Turbulence Modulation by Slender Fibers

In this paper, we numerically investigate the turbulence modulation produced by long flexible fibres in channel flow. The simulations are based on an Euler–Lagrangian approach, where fibres are modelled as chains of constrained, sub-Kolmogorov rods. A novel algorithm is deployed to make the resolution of dispersed systems of constraint equations, which represent the fibres, compatible with a state-of-the-art, Graphics Processing Units-accelerated flow-solver for direct numerical simulations in the two-way coupling regime on High Performance Computing architectures. Two-way coupling is accounted for using the Exact Regularized Point Particle method, which allows to calculate the disturbance generated by the fibers on the flow considering progressively refined grids, down to a quasi-viscous length-scale. The bending stiffness of the fibers is also modelled, while collisions are neglected. Results of fluid velocity statistics for friction Reynolds number of the flow Reτ=150 and fibers with Stokes number St = 0.01 (nearly tracers) and 10 (inertial) are presented, with special regard to turbulence modulation and its dependence on fiber inertia and volume fraction (equal to ϕ=2.12·10−5 and 2.12·10−4). The non-Newtonian stresses determined by the carried phase are also displayed, determined by long and slender fibers with fixed aspect ratio λtot=200, which extend up to the inertial range of the turbulent flow.

Experimental quantification of interfacial convections at the water–nonaqueous‐phase liquid interface in microfluidic systems

AbstractMass transfer rates at liquid–liquid interfaces are relevant for a broad range of processes in natural and technical systems. The objective of this study was to characterize and quantify convective flow along the interface between water and nonaqueous‐phase liquids (NAPLs). Three NAPLs with different water solubility were used: 1‐heptanol, 1‐octanol, and 1‐nonanol. The convective flow was visualized and recorded in a micromodel setup with fluorescent particles and an epifluorescence microscope. Individual trajectories were evaluated to obtain the statistics of the particle velocities. We observed a fast‐rotating convection current along the NAPL–water interface with a maximum velocity of approximately 1,000 μm s−1 after 10 min. The fluid motion showed a persistent movement in the form of a rolling cell for at least 99 h, but a decreasing rotation speed over time. We attributed the convective flow dynamics to three mechanisms following different kinetic rates: (a) a short‐lived Marangoni flow, (b) a medium‐lived dissolution‐driven flow, and (c) a long‐lived evaporation‐driven flow. Upon initial contact between water and NAPLs, the differences in surface tension caused a rapid Marangoni flow along the interface, which died out quickly as the surface tensions were equilibrated. The Marangoni flow was superseded by a dissolution‐driven flow as the NAPLs dissolved in the aqueous phase. The dissolution‐driven flow dissipated according to a first‐order rate law and died out when the liquids were mutually saturated. Evaporation of water and NAPLs caused a long‐term but slow convective flow. The interaction of these three mechanisms caused enhanced mixing during multiphase transport.

Drag reduction by a superhydrophobic surface with longitudinal grooves: the effects of the rib surface curvature

We have investigated the effects of rib surface curvature of a superhydrophobic wall in both laminar and turbulent channel flows. Direct numerical simulation is performed for laminar flows and large eddy simulation is performed for turbulent flows. The parametric study shows that a convex rib surface leads to a lower flow ratethan a flat rib for all Reynolds numbers. A concave rib surface firstly increases and then decreases the flow rate as the curvature angle becomes larger, where an optimal curvature angle exists to maximise flow rate. The value of the optimal curvature angle varies with the Reynolds number. A curved rib surface can modify the distribution of the mean velocity and turbulent statistics near the SH wall. Analysis shows that the overall effect of a curved rib surface on the flow rate is the combination of the wetted area augmentation and the change to the spanwise flow interaction, which depends on the curvature angle and the Reynolds number. The SH wall does not change the fundamental structures of near-wall vortices in turbulent flows. The ridge-groove pattern formed by the curved rib surface can provide additional drag reduction similar to that arising from the surface riblets.