Statistical and eddy structure approaches to turbulent mixing

Turbulent scalar mixing processes are of significant interest to a broad range of fields within the fluid and thermal sciences. An improved understanding of the underlying physics of how two independent fluid streams mix under turbulent flow conditions is important for a multitude of engineering systems and natural processes ranging from the mixing of a fuel and oxidizer in combustion chambers to the dispersal of pollutants within the atmosphere. The dispersion and mixing of scalars is dependent on the local three-dimensional velocity field, which for turbulent flows, fluctuates in both space and time. In this manner, it is important to have both scalar and velocity measurements with high spatial and temporal resolution across a large dynamic range of scales. Laser-based imaging diagnostics have made it possible to investigate the underlying structure of turbulent flows with high spatial resolution; however, the majority of commonlyused scalar measurement techniques have been limited to low acquisition rates in gas-phase flows. Typically, gasphase measurements utilize techniques which rely upon high laser pulse energies (i.e., 100’s mJ/pulse) due to the relatively “weak” signals collected from the scalar of interest. Such levels of output pulse energy are not currently possible with commercially-available high-speed laser systems. In the present work we demonstrate simultaneous acetone planar laser-induced fluorescence (PLIF) and stereoscopic particle imaging velocimetry (sPIV) at 10 kHz. The acetone acts as a tracer to mark the conserved scalar field and the sPIV measurements yield all three components of the turbulent velocity field. The PLIF measurements are facilitated by a High-Energy Pulse-Burst Laser System (HEPBLS), which can generate 266-nm pulse trains for burst durations exceeding 20 ms at 10 kHz with >140 mJ/pulse. The fourth-harmonic output of the HEPBLS is approximately an order of magnitude higher than any previously-reported kHz-rate 266-nm output. The high pulse energies available from the HEPBLS allows our preliminary measurements to be performed with low tracer seed levels (4% acetone in the main jet and 0.75% acetone in the co-flow) which significantly reduces absorption effects and facilitates quantitative measurements. A sample image set of the scalar field, where the velocity field is left off for visual clarity, is shown in Fig. 1 demonstrating the detail in both time and space that is possible with the current measurements. The sPIV measurements are made with an EdgeWave IS80-2-LD double-pulsed PIV laser capable of 40 Watts of average power per laser head. While PIV measurements are possible using the HEPBLS, an independent laser system is employed for the PIV measurement to allow for an optimization of the temporal spacing between the PIV double pulses and an accurate temporal placement of the PIV laser pulses in reference to the scalar measurement. Both of these considerations are important when attempting to accurately correlate an inferred velocity field to an instantaneous scalar measurement. The two laser systems are coupled with two Vision Research VR710 (sPIV) and one VR711 (PLIF) cameras for the data collection. The PLIF imaging system includes a 240-mm focal length acromat lens coupled with an 85 focal length f#1.4 Nikkor camera lens to maximize the signal while maintaining the desired resolution of 55 um x 55 um per pixel. The sPIV cameras are each mounted with a scheimpflug adapter and a 200-mm focal length Nikkor Macro lens leading to a resolution of 28 um x 28 um per pixel. For the given repetition rate of 10 kHz the fields of view of the PLIF and PIV cameras are 27.5 mm x 60.5 mm and 11 mm x 25 mm, respectively. The current work is centered on developing a new measurement capability for examining the time-dependent coupling between the turbulent velocity field and conserved scalar mixing in non-reacting gas-phase axisymmetric jets over a broad range of Reynolds number. Our preliminary results show significant promise for the methods described above. Simultaneous 3-component velocity and 2-D scalar imaging will provide the necessary data (both visualization and spatio-temporal statistics) to study the complex interaction between the velocity and scalar fields. Beyond an increased understanding of the underlying physics, new spatiallyand temporally-resolved data will provide new, detailed information for assessing and validating turbulence models.

Purpose This study aims to introduce a novel machine learning feature vector (MLFV) method to bring machine learning to overcome the time-consuming computational fluid dynamics (CFD) simulations for rapidly predicting turbulent flow characteristics with acceptable accuracy. Design/methodology/approach In this method, CFD snapshots are encoded in a tensor as the input training data. Then, the MLFV learns the relationship between data with a rod filter, which is named feature vector, to learn features by defining functions on it. To demonstrate the accuracy of the MLFV, this method is used to predict the velocity, temperature and turbulent kinetic energy fields of turbulent flow passing over an innovative nature-inspired Dolphin turbulator based on only ten CFD data. Findings The results indicate that MLFV and CFD contours alongside scatter plots have a good agreement between predicted and solved data with R2 ≃ 1. Also, the error percentage contours and histograms reveal the high precisions of predictions with MAPE = 7.90E-02, 1.45E-02, 7.32E-02 and NRMSE = 1.30E-04, 1.61E-03, 4.54E-05 for prediction velocity, temperature, turbulent kinetic energy fields at Re = 20,000, respectively. Practical implications The method can have state-of-the-art applications in a wide range of CFD simulations with the ability to train based on small data, which is practical and logical regarding the number of required tests. Originality/value The paper introduces a novel, innovative and super-fast method named MLFV to address the time-consuming challenges associated with the traditional CFD approach to predict the physics of turbulent heat and fluid flow in real time with the superiority of training based on small data with acceptable accuracy.

Turbulent jet flows require significant computational resources at high Reynolds numbers when simulated using large-eddy simulation (LES). To address this challenge, a convolutional neural network (CNN) was used to reproduce small-scale fluctuations from large-scale velocity fields in turbulent jet flows. High-resolution LES data were used as ground truth, and the fast Fourier transform was applied to separate large-scale and subgrid-scale (SGS) components. The CNN was trained to predict SGS velocity fields using the large-scale components extracted from coarse-grid LES data. The performance of the model was evaluated under a 20% and 40% decrease in data resolution, and with a 50% increase in Reynolds number. The CNN-generated velocity fields reproduced energy spectra and turbulent kinetic energy, which closely agreed with those of the high-resolution LES. Although turbulence production and dissipation were less accurately predicted, due to complex energy transfer mechanisms, the CNN outputs demonstrated physical consistency in terms of mass and momentum conservation.

Temperature and velocity fields in high-temperature lead coolant flows in a circular clearance for controlled oxygen impurity content in a flow were experimentally studied at the Nizhny Novgorod State Technical University by R.E. Alekseev (NNSTU). Temperature and velocity fields were simultaneously studied in “cold” and “hot” parts of the circuit in the following operating conditions: the lead temperature is t = 400–550 °C, the thermodynamic activity of oxygen is a = 10−5–100; the Peclet number is Pe = 500–7000, the coolant flow velocity is w = 0.1–1.5 m/s, and the average heat flux is q = 50–160 kW/m2. It has been found that the oxygen impurity content and characteristics of protective oxide coatings affect temperature and velocity fields in round and circular channels. This is due to the fact that oxygen in a coolant and oxide coatings on the surfaces limiting a liquid metal flow influence characteristics of the wall boundary region. The heat transfer process that occurs when HLMC transversely flows around heat exchange pipes is investigated now at the NNSTU. The experimental facility is a combination of two high-temperature liquid-metal stands, i.e., FT-2 with the lead coolant and FT-1 with the lead-bismuth coolant combined with an experimental section. The temperature of a heat-exchange surface is measured by thermocouples of diameter 1 mm mounted in walls of heat-exchange pipes. Velocity and temperature fields in a high-temperature HLMC flow are measured by special sensors placed in the flow cross section between rows of heat-exchange pipes. Heat transfer characteristics and temperature and velocity fields in a high-temperature lead coolant flow are studied in the following operating conditions: the lead temperature is t = 450–500 °C, the thermodynamic activity of oxygen is a = 10−5–100, and the coolant flow rate through the experimental setup is Q = 3–6 m3/h, which corresponds to coolant flow velocities of V = 0.4–0.8 m/s. Integrated experimental studies of characteristics of the heat transfer that occurs when the lead coolant transversely or obliquely flows around pipes have been carried out for the first time and the dependences Nu = f(Pe) for controlled content of thermodynamically active oxygen impurity and sediments of impurities have been obtained. It is assumed that the obtained experimental data on distribution of velocity and temperature fields in a HLMC flow will permit to study heat transfer processes and to use them for developing program codes for engineering calculations of heat exchange surfaces (steam generators) with a HLMC flow around them.

Surface quasi-geostrophic (SQG) theory describes the two-dimensional active transport of a scalar field, such as temperature, which – when properly rescaled – shares the same physical dimension of length/time as the advecting velocity field. This duality has motivated analogies with fully developed three-dimensional turbulence. In particular, the Kraichnan – Leith – Batchelor similarity theory predicts a Kolmogorov-type inertial range scaling for both scalar and velocity fields, and the presence of intermittency through multifractal scaling was pointed out by Sukhatme & Pierrehumbert (2002 Chaos 12 , 439–450), in unforced settings. In this work, we refine the discussion of these statistical analogies, using numerical simulations with up to $16\,384^2$ collocation points in a steady-state regime dominated by the direct cascade of scalar variance. We show that mixed structure functions, coupling velocity increments with scalar differences, develop well-defined scaling ranges, highlighting the role of anomalous fluxes of all the scalar moments. However, the clean multiscaling properties of SQG transport are blurred when considering velocity and scalar fields separately. In particular, the usual (unmixed) structure functions do no follow any power-law scaling in any range of scales, neither for the velocity nor for the scalar increments. This specific form of the intermittency phenomenon reflects the specific kinematic properties of SQG turbulence, involving the interplay between long-range interactions, structures and geometry. Revealing the multiscaling in single-field statistics requires us to resort to generalised notions of scale invariance, such as extended self-similarity and a specific form of refined self-similarity. Our findings emphasise the fundamental entanglement of scalar and velocity fields in SQG turbulence: they evolve hand in hand and any attempt to isolate them destroys scaling in its usual sense. This perspective sheds new lights on the discrepancies in spectra and structure functions that have been repeatedly observed in SQG numerics for the past 20 years.

Multiple-resolution scheme in finite-volume code for active or passive scalar turbulence

A combined theoretical and experimental investigation is conducted with the objective of evaluating the lift aerodynamic admittances of an airfoil in various turbulent flow fields. Current theoretical approaches and concepts are reviewed and extended, enabling us to use a strategy to measure the one-wavenumber aerodynamic admittance in the turbulent flow field. The key of the strategy is to separate the spanwise effect from the generalized aerodynamic admittances which can be directly determined by the one-dimensional lift spectrum and one-dimensional turbulent velocity spectrum. With this strategy, the experimental values of one-wavenumber aerodynamic admittances of a two-dimensional airfoil with a NACA 0015 profile in three turbulent flow fields are obtained. As expected, due to the influence of the spanwise effect, the generalized aerodynamic admittances vary with different turbulent flow fields, exhibiting a significant dependence on flow field, and are much less than the Sears function. Contrarily, the one-wavenumber aerodynamic admittances, which are obtained in three turbulent flow fields, are generally consistent, confirming that the one-wavenumber aerodynamic admittance is mainly related to the cross-sectional shape itself. The experimental values of one-wavenumber aerodynamic admittances are compared with the Sears function. The results of all cases indicate that the experimental results agree well with the Sears function at low frequencies, while decaying faster at high frequencies.

In this paper, we consider the reconstruction of 3D turbulent flow fields from a time series of lidar data in a conventionally neutral atmospheric boundary layer (CNBL). For the reconstruction we use the maximum a posteriori estimate of the flow field. This corresponds to an optimization problem, with a cost function that has two contributions; a first term originating from the prior belief on the probability of having a certain turbulent flow field without any observations. Flow field fluctuations are assumed normally distributed and thus statistically fully determined by the mean and two-point covariance of the velocity field. The second term, is related to the likelyhood of the observations, influenced by model and measurement uncertainties. The two-point covariance is computed and found to be significantly altered by the Coriolis force, breaking up longer streamwise velocity streaks and veering spanwise structures by ∼ 45° with respect to the mean flow direction. For the reconstruction, we consider two different scanning modes, a plan position indicator (PPI) mode and a trajectory which is based on a Lissajous curve. For the PPI scanning mode we find that the mean squared error of the reconstructed velocity field is around 10% of the background variance in the scanning plane, and quickly increases outside this region. The Lissajous curve on the other hand attains an average error of 40% over the scanning region, which spans almost the whole BL height.

Stochastic dispersion of ellipsoidal fibers in various turbulent fields

Extensive recent work has demonstrated that predictive under-resolved simulations of the velocity fields in turbulent flows are possible without resorting to explicit subgrid models. When using a class of physics-capturing high-resolution finite-volume numerical algorithms. This strategy is denoted implicit large eddy simulation (ILES, MILES). The performance of ILES in the substantially more difficult problem of under-resolved material mixing driven by under-resolved velocity fields and initial conditions (ICs) is a focus of the present work. Progress is presented in analyzing the effects of IC combined spectral content and thickness parametrizations. In the large eddy simulation (LES). the large energy containing structures are resolved, the smaller, presumably more isotropic, structures are filtered out, and effects of subgrid scales (SGS) are modeled. ILES effectively addresses the seemingly insurmountable issues posed to LES by under-resolution. by relying on the use of SGS modeling and filtering provided implicitly by a class of physics capturing numerics; extensive verification and validation in areas of engineering. geophysics. and astrophysics has been reported. In many areas of interest such as. inertial confinement fusion. understanding the collapse of the outer cores of supernovas. and supersonic combustion engines, vorticity is introduced at material interfaces by the impulsive loading of shock waves.more » and turbulence is generated via Richtmyer-Meshkov instabilities (RMI). Given that ILES is based on locally-adaptive, non-oscillatory. finite-volume methods it is naturally suited to emulate shock physics. The unique combination of shock and turbulence emulation capabilities supports direct use of ILES as an effective simulation anzatz for RMI. Here, we further test this approach using a particular strategy based on a nominally-inviscid, Schmidt number {approx} 1, simulation model that uses the LANL RAGE code to investigate planar RMI. Issues of initial material interface characterization and modeling difficulties, and effects of IC resolved spectral content on transitional and late-time turbulent mixing were examined in our previous work. The focus here is to carry out a systematic analysis of effects of combined IC spectral content and thickness.« less

Simultaneous measurements of the velocity and concentration field in fully developed turbulent flows over a wavy wall are described. The concentration field originates from a low-momentum plume of a passive tracer. PLIF and digital particle image velocimetry are used to make spatially resolved measurements of the structure of the scalar distribution and the velocity. The measurements are performed at three different Reynolds numbers of Re b = 5,600, Re b = 11,200 and Re b = 22,400, respectively, based on the bulk velocity u b and the total channel height 2h. The velocity field and the scalar field are investigated in a water channel with an aspect ratio of 12:1, where the bottom wall of the test section consists of a train of sinusoidal waves. The wavy wall is characterized by the amplitude to wavelength ratio α = 0.05 and the ratio β between the wave amplitude and the half channel height where β = 0.1. The scalar is released from a point source at the wave crest. For the concentration measurements, Rhodamine B is used as tracer dye. At low to moderate Reynolds number, the flow field is characterized through a recirculation zone which develops after the wave crest. The recirculation zone induces high intensities of the fluctuations of the streamwise velocity and wall-normal velocity. Furthermore, large-scale structures are apparent in the flow field. In previous investigations it has been shown that these large-scale structures meander laterally in flows over wavy bottom walls. The investigations show a strong effect of the wavy bottom wall on the scalar mixing. In the vicinity of the source, the scalar is transported by packets of fluid with a high scalar concentration. As they move downstream, these packets disintegrate into filament-like structures which are subject to strong gradients between the filaments and the surrounding fluid. The lateral scale of the turbulent plume is smaller than the lateral scale of the large-scale structures in the flow field and the plume dispersion is dominated by the structures in the flow field. Due to the lateral meandering of the large-scale structures of the flow field, also the scalar plume meanders laterally. Compared to turbulent plumes in plane channel flows, the wavy bottom wall enhances the mixing effect of the turbulent flow and the spreading rate of the scalar plume is increased.

Turbulence in fluids has been a popular research topic for many years due to its influence on a wide range of applications. Computational Fluid Dynamics (CFD) tools are able to provide plenty of information about this phenomenon, but their computational cost often makes the use of these tools unfeasible. For that reason, in recent years, turbulence modelling using Artificial Neural Networks (ANNs) is becoming increasingly popular. These networks typically calculate directly the desired magnitude, having input information about the computational domain. In this paper, a Convolutional Neural Network (CNN) for predicting different magnitudes of turbulent flows around different geometries by approximating the equations of the Reynolds-Averaged Navier-Stokes (RANS)-based realizable k-ε two-layer turbulence model is proposed. Using that CNN, alternative network structures are proposed to predict the velocity fields of a turbulent flow around different geometries on a rectangular channel, with a preliminary stage to predict pressure and vorticity fields before calculating the velocity fields, and the obtained results are compared with the ones obtained with the basic structure. The results demonstrate that the proposed structures clearly outperform the basic one, especially when the flow becomes uncertain. In addition, considering the results, the best network configuration is proposed. That network is tested with a domain with multiple geometries and a domain with a narrowing of the channel, which are domains with different conditions from the training ones, showing fairly accurate predictions.

ABSTRACTIn this work, with elasticity governed by the Giesekus constitutive equation, a proper orthogonal decomposition (POD) reduced-order model of viscoelastic turbulent channel flow is established for the first time. The established reduced-order model is based on small sets of basis functions from the POD of the sampling data obtained by direct numerical simulation (DNS) for the studied flow. The POD reduced-order model is tested on cases with that are different from the samplings for viscoelastic turbulent channel flow. The results show that the errors for root-mean-square (rms) velocity fluctuations are significant at the top and bottom walls. It is found that each basis function plays an important role in describing the studied turbulence which makes it unmanageable to obtain accurate velocity field (including mean velocity and velocity fluctuations) through solving the reduced-order model. It is of necessity to take all the basis functions into consideration to depict the flows more accurately. However, the mean velocity obtained from the reduced-order model is of high precision, which states that the POD-based reduced-order model is a potential approach to obtain an accurate mean velocity field for viscoelastic turbulent flow, which has great significance in academic study as well as engineering. The calculation speed of the established reduced-order model is much faster than that of DNS, which indicates that the POD is a highly efficient way of obtaining the statistic characteristics, such as mean velocity in turbulent channel flow.

The non-linear diffusion and the fourth order partial differential equations (PDEs) are used to decompose a turbulent flow field into coherent and incoherent fields. The methods are applied against the velocity fields for both forced and decaying homogeneous isotropic turbulence. The aim of this paper is to examine the ability of the partial differential equations in extracting coherent vortices from a turbulent flow field in the spatial domain without transforming the turbulent velocity field into frequency domain. The comparison against the standard methods such as the wavelet and Fourier decompositions are also considered. The three dimensional velocity fields with a resolution of 1283 are generated using the Lattice Boltzmann method (LBM) where the Taylor micro-scale Reynolds numbers are 72 and 29 for forced and decaying fields, respectively. Results show that the coherent field and the random incoherent part contribute to all scales in the inertial range. The two filtering methods approximately identify the coherent fields without any loss of the geometrical structure of the vortices. The statistical properties such as flatness, skewness and spectrum of the extracted fields (coherent and incoherent parts) are also investigated for each filtering method.

Adding vertical ribs is recognized as a useful practice for reducing wind effects on cooling towers. However, ribs are rarely used on cooling towers in China since Chinese Codes are insufficient to support the design of rough-walled cooling towers, and an “understanding” hampers the use of ribs, which thinks that increased surface roughness has limited effects on the maximum internal forces that control the structural design. To this end, wind tunnel model tests in both uniform flow field with negligible free-stream turbulence and atmospheric boundary layer (ABL) turbulent flow field are carried out in this article to meticulously study and quantify the surface roughness effects on both static and dynamic wind loads for the purpose of improving Chinese Codes first. Subsequently, a further step is taken to obtain wind effects on a full-scale large cooling tower at a high Re, which are employed to validate the results obtained in the wind tunnel. Finally, the veracity of the model test results is discussed by investigating the Reynolds number (Re) effects on them. It has been proved that the model test results for atmospheric boundary layer flow field are all obtained in the range of Re-independence and the conclusions drawn from model tests and full-scale measurements basically agree, so most model test results presented in this article can be directly applied to the full-scale condition without corrections.