Taylor's Hypothesis Research Articles

Skin-friction from temperature and velocity data around a wall-mounted cube

This paper reports an algorithm for measuring the time-averaged skin friction vector field τ¯(X)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\overline{\\pmb {\ au }}(\\pmb {X})$$\\end{document} starting from time-resolved temperature maps, acquired by a functional coating of temperature-sensitive paint. The algorithm is applied to a large area around a wall-mounted cube, immersed in the turbulent boundary layer over a flat plate. The method adopts a relaxed version of the Taylor Hypothesis operating on time-resolved maps of temperature fluctuations T′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T'$$\\end{document} measured on the slightly warmer bounding surface. The procedure extracts U¯T(X)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\overline{U}}_T(\\pmb {X})$$\\end{document}, the celerity of displacement of T′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T'$$\\end{document}, as the best approximation of the forecasting provided by the frozen turbulence assumption near the wall, where its rigorous application is inappropriate. The τ¯(X)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\overline{\\pmb {\ au }}(\\pmb {X})$$\\end{document} estimation is based on the hypothesis of a linear relationship between U¯T(X)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\overline{U}}_T(\\pmb {X})$$\\end{document} and U¯U(X)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\overline{U}}_U(\\pmb {X})$$\\end{document}, chained to the one between U¯U(X)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\overline{U}}_U(\\pmb {X})$$\\end{document} and U¯τ(X)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\overline{U}}_\ au (\\pmb {X})$$\\end{document}. We assess the outcomes of the proposed algorithm against those derived by the 2D and 3D Lagrangian particle tracking (LPT) methodology ’Shake-The-Box’, whose advent has made available high-quality near-wall flow field information. Furthermore, data from high-density 2D time-resolved LPT allows exploring the suitability of the linear relationships chain between U¯T(X)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\overline{U}}_T(\\pmb {X})$$\\end{document} and U¯τ(X)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\overline{U}}_\ au (\\pmb {X})$$\\end{document} in the proposed context.

Instantaneous Pressure Reconstruction From PIV In Compressible Launcher Environments

Modern launcher configurations, often characterized by a larger diameter in the payload fairing than the rest of the launch vehicle (hammerhead configuration), face significant challenges during transonic operations, given their susceptibility to flow separation and intense pressure fluctuations. This experimental study aims to reconstruct pressure from PIV under transonic conditions using Taylor's hypothesis. The focus is on the ESA VEGA-E hammerhead launcher model, investigated in the transonic regime at Ma=0.8 and at α=0°. Initially, the methodology of the pressure reconstruction algorithm is described and the validity of Taylor's hypothesis is established through validation with numerical data. Subsequently, the experimental data are first used to provide a general characterization of the flow phenomenon, highlighting key features such as an oscillating shockwave, separated and reattached flows. Later, the reconstruction of pressure from velocity data is compared to unsteady pressure transducer data, for instantaneous, average and standard deviation values, obtaining a very good agreement (ΔCpAvg~0.01-0.02 and ΔCpStd~0.02). The experimental set-up is also designed to showcase the impact of neglecting the out-of-plane velocity component on pressure reconstruction, showing comparable data for CpAvg, while larger discrepancies in terms of CpStd in particular in the separated area region.

A finite strain micromechanical-based constitutive model: Application to porous polycrystal

A finite strain micromechanical-based constitutive model is developed for multi-phase polycrystal to characterize the interplay among strain hardening, texture evolution, and stress-strain relation. The phases are regarded as ellipsoidal inhomogeneities within the polycrystalline matrix, which can be considered as an aggregation of different orientated grains. At the grain level, the crystal plasticity model is applied to physically describe the inelastic deformation results from crystallographic slipping. At the polycrystalline level, an algorithmic finite strain self-consistent model is proposed to associate the strain and rotation rate at the grain level with the corresponding terms of the polycrystalline matrix rigorously. At the representative volume element level, the phases with different properties are investigated by extending the Mori–Tanaka model at finite strain. The algorithmic self-consistent model is validated by comparing the calculated normalized stress-strain curves and textures with those obtained by the model adopting extended Taylor hypothesis and the experimental data of stainless steel. Moreover, the grain and polycrystalline level behaviors calculated by the algorithmic self-consistent model are compared to those derived from the full-field model. The effects of void and elastic particles on overall mechanical behavior are analyzed by the extended Mori–Tanaka model, which is then verified by predicting the mechanical behavior of sintered nano-silver stub columns under stress-controlled compression loads.

Optical phase and amplitude measurements of underwater turbulence via self-heterodyne detection

The creation of underwater optical turbulence is driven by density variations that lead to small changes in the water’s refractive index, which induce optical path length differences that affect light propagation. Measuring a laser beam’s optical phase after traversing these turbulent variations can provide insight into how the water’s turbulence behaves. The sensing technique to measure turbulent fluctuations is a self-heterodyne beatnote enhanced by light’s orbital angular momentum (OAM) to obtain simultaneous optical phase and amplitude information. Experimental results of this method are obtained in a water tank that creates a thermally driven flow called Rayleigh–Bénard (RB) convection. The results show time-varying statistics of the beatnote that depend on the incident OAM mode order and the strength of the temperature gradient. Beatnote amplitude and phase power spectral densities are compared to analytic theory to obtain estimates of the turbulent length scales using the Taylor hypothesis that include mean flow speed, turbulent strength, and length scales, and flow dynamics due to intermittency in the RB process.

A physics-guided machine learning framework for real-time dynamic wake prediction of wind turbines

Efficient and accurate prediction of the wind turbine dynamic wake is crucial for active wake control and load assessment in wind farms. This paper proposes a real-time dynamic wake prediction model for wind turbines based on a physics-guided neural network. The model can predict the instantaneous dynamic wake field under various operating conditions using only the inflow wind speed as input. The model utilizes Taylor's frozen-flow hypothesis and a steady-state wake model to convert instantaneous inflow wind speed and turbine parameters into neural network input features. A deep convolutional neural network then maps these features to desired wake field snapshots, enabling dynamic wake predictions for wind turbines. To train the model, we generated approximately 255 000 instantaneous flow field snapshots of single-turbine wakes using the large eddy simulation, covering different thrust coefficients and yaw angles. The model was trained using the supervised learning method and verified on the test set. The results indicate that the model can effectively predict the dynamic wake characteristics, including the dynamic wake meandering and the wake deflection of the yawed turbines. The model can also assess both the instantaneous wake velocity and the instantaneous wake center of a wind turbine. At a thrust coefficient of 0.75, the root mean square error for the predicted instantaneous wake velocity is around 6.53%, while the Pearson correlation coefficient for the predicted instantaneous wake center can reach 0.624. Furthermore, once the model is trained, its prediction accuracy does not decrease with the increase in the time span.

Wavelet Transforms and Machine Learning Methods for the Study of Turbulence

This article investigates the applications of wavelet transforms and machine learning methods in studying turbulent flows. The wavelet-based hierarchical eddy-capturing framework is built upon first principle physical models. Specifically, the coherent vortex simulation method is based on the Taylor hypothesis, which suggests that the energy cascade occurs through vortex stretching. In contrast, the adaptive wavelet collocation method relies on the Richardson hypothesis, where the self-amplification of the strain field and a hierarchical breakdown of large eddies drive the energy cascade. Wavelet transforms are computational learning architectures that propagate the input data across a sequence of linear operators to learn the underlying nonlinearity and coherent structure. Machine learning offers a wealth of data-driven algorithms that can heavily use statistical concepts to extract valuable insights into turbulent flows. Supervised machine learning needs “perfect” turbulent flow data to train data-driven turbulence models. The current advancement of artificial intelligence in turbulence modeling primarily focuses on accelerating turbulent flow simulations by learning the underlying coherence over a low-dimensional manifold. Physics-informed neural networks offer a fertile ground for augmenting first principle physics to automate specific learning tasks, e.g., via wavelet transforms. Besides machine learning, there is room for developing a common computational framework to provide a rich cross-fertilization between learning the data coherence and the first principles of multiscale physics.

Intermittency at Earth's bow shock: Measures of turbulence in quasi-parallel and quasi-perpendicular shocks

Turbulent plasmas such as the solar wind and magnetosheath exhibit an energy cascade that is present across a broad range of scales, from the stirring scale at which energy is injected, down to the smallest scales where energy is dissipated through processes such as reconnection and wave–particle interactions. Recent observations of Earth's bow shock reveal a disordered or turbulent transition region exhibiting features of turbulent dissipation, like reconnecting current sheets. We used observations from magnetospheric multiscale (MMS) over four separate bow shock crossings of varying shock normal angle to characterize turbulence in the shock transition region and how it evolves toward the magnetosheath. These cases studies have been chosen to ensure validity of Taylor's hypothesis, which we discuss in depth. We observe the magnetic spectrum evolving by fitting power laws over many short intervals, finding that the power-law index in the shock transition region is separable from the upstream and downstream plasma, for both quasi-perpendicular and quasi-parallel shocks. Across the shock, we see a change in the breakpoint location between inertial and ion power-law slopes. We also observe the evolution of scale-independent kurtosis of magnetic fluctuations across the shock, finding a reduction of high kurtosis intervals downstream of the shock. Finally, we adapt a method for calculating correlation length to include a high-pass filter, allowing estimates for changes in correlation length across the shock. In a quasi-perpendicular shock, we find the correlation length to be significantly smaller in the magnetosheath than in solar wind; however, the opposite can occur for quasi-parallel shocks.

Generation of turbulent inflow data from realistic approximations of the covariance tensor

This study presents a novel synthetic inflow generator capable of producing a random field matching a realistic set of two-point statistics with minimal input. The method is based on two main elements. The first element is a procedure to infer realistic two-point covariance tensors from readily available data (e.g., freestream velocity, boundary layer thickness, and turbulence intensity) by a preliminary Reynolds-averaged Navier–Stokes simulation with an explicit algebraic Reynolds stress model closure. The second element is an efficient eigen-decomposition step of the two-point correlation tensor, which determines a set of modes. The modal decomposition guarantees the spatial correlation in transversal directions, while the temporal correlation/streamwise spatial correlation is obtained by digital filters based on longitudinal and transversal spectra of a realistic shape and Taylor's hypothesis. The instantaneous inlet flow field is obtained by a linear combination of the modes via uncorrelated random weights with unit variance. The modes are generated in a computationally inexpensive pre-processing step. Compared to existing inflow generation methods that try to match given two-point statistics, the proposed method relieves the burden of obtaining data from direct numerical simulation (DNS) or experiments, while the complexity of the eigenvalue problem that needs to be solved is reduced. The proposed method is shown to produce a realistic turbulent channel flow and a realistic turbulent boundary layer by the large-eddy simulation, which contains statistics that are in good agreement with results from DNS. The proposed inflow generator features, cost-effectiveness, robustness, and potential for generalization to complex geometries.

Exchange rate pass‐through to consumer prices in India – nonlinear evidence from a smooth transition model

AbstractUsing a backward‐looking Philips curve framework and a Logistic Smooth Transition Regression (STR) model, this article examined the exchange rate pass‐through (ERPT) to final consumer prices in the case of India. Specifically, the nonlinearity of ERPT has been investigated with respect to the level of economic activity and the rate of inflation by considering two alternative measures of exchange rate. For the first transition variable, results are markedly different between high and low‐activity regimes and signify the favourable impact of economic activity on the extent of pass‐through. In the short run, 1% exchange rate appreciation would decrease the price level by 0.244% when the economy is in a low‐activity regime; however, the same appreciation increases the price level by 0.485% when there is a boom in the economy. In the long run, ERPT in the low‐activity regime is −0.358, and in the high‐activity regime, it is 0.039. In both regimes, pass‐through coefficients differ from zero and one, implying that neither local currency pricing nor producer currency pricing characterizes the ERPT mechanism. The impact of other important determinants of inflation is also well according to theoretical expectations. Finally, for the rate of inflation, we did not report any evidence favouring the Taylor hypothesis in the case of India.

Taylor's frozen-in hypothesis for magnetohydrodynamic turbulence and solar wind

In hydrodynamics, Taylor's frozen-in hypothesis connects the wavenumber spectrum to the frequency spectrum of a time series measured in real space. In this paper, we generalize Taylor's frozen-in hypothesis to magnetohydrodynamic turbulence. We analytically derive one-point two-time correlation functions for Elsässer variables whose Fourier transform yields the corresponding frequency spectra, E±(f). We show that for isotropic turbulence, E±(f)∝|U0 ∓ B0|2/3 in the Kolmogorov-like model and E±(f)∝(B0|U0 ∓ B0|)1/2 in the Iroshnikov–Kraichnan model, where U0 and B0 are the mean velocity and mean magnetic fields, respectively, and f±=k|U0 ∓ B0|/(2π) are the respective frequencies for a wavenumber k. However, for anisotropic magnetohydrodynamic turbulence, E±(f)∝B02/3 when U0≪B0. These results are important for the analysis of solar wind, in particular, those measured by Parker Solar Probe.

Modeling probability density functions of velocity fluctuations in wind farms

SummaryThe flow in large wind farms is a complex multiscale phenomenon, making comprehensive analytical or computational studies of velocity fluctuations challenging. Motivated by the need for simple, physics‐based analytical approaches to short‐time wind velocity prediction, we derive a statistical model for the spatio‐temporal evolution of streamwise velocity fluctuations in wind farms. Here, we show that the one‐point—one‐time probability density function of velocity fluctuations can be modeled by a weighted superposition of two Ornstein‐Uhlenbeck processes. The model is extended to a one‐particle advection model assuming Taylor's hypothesis of frozen turbulence. We find that our advection model captures the decorrelation process of streamwise velocity fluctuations observed in experiments.

Three-level model based on physical theories of plasticity: Formulation, implementation algorithms, results of application to the study of cyclic loading

The physical and mechanical properties of metals and alloys, as well as, the operational characteristics of products made of them, are known to be significantly determined by the meso- and microstructure of materials. Therefore, physically oriented models that can be used to analyze the material structure evolution have been intensively developed and widely applied in recent decades for the study of thermomechanical processing of metals and alloys. These models are based on the introduction of internal variables, theories of crystal plasticity (elastoviscous plasticity), and a multilevel approach. In this paper, we consider the structure, mathematical formulation and algorithm for implementing a three-level (macro-, meso-1, and meso-2 levels) dislocation-oriented model designed to study the behavior of a representative macrovolume (macrosample) of mono- and polycrystalline alloys under cyclic deformation paths. The loading is given, and the Voigt (Taylor) hypothesis is used to connect the macro- and mesolevel-1. The mesolevel-2 submodel operates with the densities and velocities of full and split edge dislocations on slip systems. Interactions of dislocations of various systems, such as annihilation, hardening due to forest dislocations, formation of barriers of a dislocation nature (Lomer–Cottrell, Hirt) are taken into account. At mesolevel-1, the description is carried out in terms of shear stresses and shear rates along slip systems, determined by the Orowan equation using the mesolevel-2 data. A rigid moving coordinate system associated with a crystal lattice is introduced to evaluate the rotation of crystallites. The response of the material at the macro level is determined by averaging the stresses in crystallites. The results of applying the model to the study of deformation of alloy macrosamples with different values of stacking fault energy along simple and complex deformation trajectories are presented. It is shown that the materials with low stacking fault energy demonstrate the effect of additional cyclic hardening when loaded along complex deformation trajectories.

On the applicability of Taylor's hypothesis, including small sampling velocities

Taylor's hypothesis, or the frozen turbulence approximation, can be used to estimate also the specific energy dissipation rate $\epsilon$ by comparing experimental results with the Kolmogorov–Obukhov expression. The hypothesis assumes that a frequency detected by an instrument moving with a constant large velocity $V$ can be related to a wavenumber by $\omega = k V$ . It is, however, not obvious how large the translational velocity has to be in order to make the hypothesis valid, or at least applicable with some acceptable uncertainty. Using the space–time-varying structure function for homogeneous and isotropic conditions, this question is addressed in the present study with emphasis on small velocities $V$ . The structure function is obtained using results from numerical solutions of the Navier–Stokes equation. Particular attention is given to the $V$ variation of the estimated specific energy dissipation, $\epsilon _{est}$ , compared with the actual value, $\epsilon$ , used in the numerical calculations. In contrast to previous studies, the results emphasize velocities $V$ less than or comparable to the one-component root-mean-square velocity, $u_{rms}$ . We find that $\epsilon$ can be determined to an acceptable accuracy for $V \geq 0.3\,u_{rms}$ . A simple analytical model is suggested to explain the main features of the observations, both Eulerian and Lagrangian. The model assumes that the observed time variations are solely due to eddies moving past the observer, thus ignoring eddy deformation and intermittency effects. In spite of these simplifications, the analysis accounts for most of the numerical results when also eddy-size-dependent velocities are accounted for.

Space-time energy spectra in turbulent shear flows

This article reviews the recent theories and models of space-time energy spectra in turbulent shear flows. The review is based on the picture of turbulent passage proposed by Taylor's frozen-flow hypothesis and Kraichnan-Tennekes random sweeping hypothesis: convection of small-scale eddies by large-scale eddies with a certain distortion, which determines the peaks and bandwidths of space-time energy spectra. The data-refined stochastic models and data-based reconstruction models are examined. The linearized Navier-Stokes equations with random forcing for space-time energy spectra are also discussed.

The structure of a highly decelerated axisymmetric turbulent boundary layer

Experiments were performed over a body of revolution at a length-based Reynolds number of 1.9 million. While the lateral curvature parameters are moderate ( $\delta /r_s < 2, r_s^+>500$ , where $\delta$ is the boundary layer thickness and r s is the radius of curvature), the pressure gradient is increasingly adverse ( $\beta _{C} \in [5 \text {--} 18]$ where $\beta_{C}$ is Clauser’s pressure gradient parameter), representative of vehicle-relevant conditions. The mean flow in the outer regions of this fully attached boundary layer displays some properties of a free-shear layer, with the mean-velocity and turbulence intensity profiles attaining self-similarity with the ‘embedded shear layer’ scaling (Schatzman & Thomas, J. Fluid Mech., vol. 815, 2017, pp. 592–642). Spectral analysis of the streamwise turbulence revealed that, as the mean flow decelerates, the large-scale motions energize across the boundary layer, growing proportionally with the boundary layer thickness. When scaled with the shear layer parameters, the distribution of the energy in the low-frequency region is approximately self-similar, emphasizing the role of the embedded shear layer in the large-scale motions. The correlation structure of the boundary layer is discussed at length to supply information towards the development of turbulence and aeroacoustic models. One major finding is that the estimation of integral turbulence length scales from single-point measurements, via Taylor's hypothesis, requires significant corrections to the convection velocity in the inner 50 % of the boundary layer. The apparent convection velocity (estimated from the ratio of integral length scale to the time scale), is approximately 40 % greater than the local mean velocity, suggesting the turbulence is convected much faster than previously thought. Closer to the wall even higher corrections are required.

A high-efficiency simulation method of wind field and its application on transmission line

Generally, the fluctuating wind is simplified as several independent one-dimensional multivariate stationary Gaussian processes in simulating a natural wind field. The correlation in the lateral, longitudinal and vertical directions should all be considered in the simulation of longitudinal wind field for the large-span spatial structures. In fact, this type of structure has lots of simulation points. The calculation amount of wind field simulation by the harmonic superposition method depends on the scale of cross-spectral density matrix, which is directly related to the number of simulated points, leading to a low efficiency when generating the time-varying wind speed. This paper innovatively proposes a high-efficiency simulation method for the longitudinal wind field based on Taylor's hypothesis. Subsequently, the effectiveness of the proposed wind field method was verified by the numerical simulation. Finally, the dynamic responses of a transmission tower-line system under the wind loadings generated with the new method and traditional method are calculated and compared. The percentages difference of the mean and maximum axial force at the main tower members are less than 0.02% and 1%, respectively, indicating the effectiveness of the proposed time delay method. The results also show that the proposed simulation method of wind field can not only ensure the simulation accuracy, but also significantly improve the efficiency of wind speed generation, which is suitable for the wind load simulation of large-span spatial structures.

Statistical properties of two-dimensional elastic turbulence.

We numerically investigate the spatial and temporal statistical properties of a dilute polymer solution in the elastic turbulence regime, i.e., in the chaotic flow state occurring at vanishing Reynolds and high Weissenberg numbers. We aim at elucidating the relations between measurements of flow properties performed in the spatial domain with the ones taken in the temporal domain, which is a key point for the interpretation of experimental results on elastic turbulence and to discuss the validity of Taylor's hypothesis. To this end, we carry out extensive direct numerical simulations of the two-dimensional Kolmogorov flow of an Oldroyd-B viscoelastic fluid. Static pointlike numerical probes are placed at different locations in the flow, particularly at the extrema of mean flow amplitude. The results in the fully developed elastic turbulence regime reveal large velocity fluctuations, as compared to the mean flow, leading to a partial breakdown of Taylor's frozen-field hypothesis. While second-order statistics, probed by spectra and structure functions, display consistent scaling behaviors in the spatial and temporal domains, the third-order statistics highlight robust differences. In particular the temporal analysis fails to capture the skewness of streamwise longitudinal velocity increments. Finally, we assess both the degree of statistical inhomogeneity and isotropy of the flow turbulent fluctuations as a function of scale. While the system is only weakly nonhomogenous in the cross-stream direction, it is found to be highly anisotropic at all scales.

Temperature and skin-friction maps on a lifting hydrofoil in a propeller wake

There are at least two direct links between the friction acting on the surface of a (slightly warmer or colder) body under the influence of an incompressible flow and the temperature distribution on the surface of the body itself. The first relies on the energy equation, which connects the evolution of the temperature distribution at the wall to the action of the skin-friction field. On the other hand, the equation of passive transport of temperature perturbations at the wall unveils a direct relationship between the celerity of propagation of thermal blobs and the friction velocity. Grounding on these relationships, this paper reports about the application of different methodologies, developed to determine skin-friction fields from surface temperature maps, to the analysis of the complex flow evolution on a lifting NACA 0015 hydrofoil immersed in a non-uniform, unsteady wake induced by a marine propeller. The adopted temperature-sensitive paint technique allows obtaining the global temperature data with the appropriate, high resolution in space and time. The approach based on the energy equation leads to an unconventional, single-snapshots optical-flow-like methodology, which allows obtaining time-resolved, relative skin-friction fields. The two approaches based on the displacement of the wall temperature perturbations enable the determination of time- and phase-averaged, quantitative skin-friction fields. One approach grounds on a classical tracking of the thermal disturbances via optical flow, the other one relies on minimizing the discrepancy between the celerity of propagation of thermal fluctuations and the behavior expected according to the Taylor hypothesis. The analysis of the skin-friction fields obtained via the three uncorrelated, complementary approaches discloses the evolution and the mutual interaction of different flow structures (manifolds) over the hydrofoil surface at lifting and zero-lift conditions: the hub and tip vortices, the blade wake, the laminar separation bubble, and the separation at trailing edge.

3D pressure field reconstruction from time-resolved stereoscopic PIV measurements by relaxation of Taylor's hypothesis

This work presents reconstructions of 3D pressure fields starting from 2D3C stereoscopic-PIV (SPIV) measurements. In Fratantonio et al. (2021), we presented a new reconstruction algorithm, the “Instantaneous convection” method, capable of producing 3D velocity fields from time-resolved SPIV measurements. For reconstructions in flows with strong shear layers and high turbulence intensity, this method is able to provide time-resolved 3D velocity volumes that are more accurate than those that can be obtained from the more frequently employed reconstruction method based on the Taylor’s hypothesis and on the use of a mean convective field. Here we investigate the possibility of reconstructing the 3D pressure field from the timeresolved series of reconstructed 3D velocity data. A pseudo-tracking method is employed for computing the velocity material derivative, and the pressure field is then reconstructed by solving the 3D Poisson equation. The velocity and pressure reconstructions are validated on the Direct Numerical Simulation data of the turbulent channel flow taken from the John Hopkins Turbulence Database (JHTDB), and an application to experimental SPIV measurements of an air jet flow in coflow carried out at the Turbulent Mixing Tunnel (TMT) facility at Los Alamos National Laboratory is presented.

Large-to-small scale frequency modulation analysis in wall-bounded turbulence via visibility networks

Abstract