Interpolation Schemes for Three-Dimensional Velocity Fields from Scattered Data Using Taylor Expansions

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.

Two methods are investigated to simultaneously obtain both three-dimensional (3D) velocity field and free surface elevations (FSEs) measurements near a surface piercing foil, while limiting the equipment. The combined velocity field and FSE measurements are obtained specifically for the validation of numerical methods requiring simultaneous field data and free surface measurements for a slender body shape. Both methods use stereo particle image velocimetry (SPIV) to measure three component velocities in the flow field and both methods use an off the shelf digital camera with a laser intersection line to measure FSEs. The first method is performed using a vertical laser sheet oriented parallel to the foil chord line. Through repetition of experiments with repositioning of the laser, a statistical representation of the three-dimensional flow field and surface elevations is obtained. The second method orients the vertical laser sheet such that the foil chord line is orthogonal to the laser sheet. A single experiment is performed with this method to measure the three-dimensional three component (3D3C) flow field and free surface, assuming steady flow conditions, such that the time dimension is used to expand the flow field in 3D space. The two methods are compared using dynamic mode decomposition and found to be comparable in the primary mode. Utilizing these methods produces results that are acceptable for use in numerical methods verification, at a fraction of the capital and computing cost associated with two plane or tomographic particle image velocimetry (PIV).

Three-dimensional velocity fields were measured using tomographic particle image velocimetry (Tomo-PIV) on a model of the blade of a small-scale horizontal axis wind turbine (HAWT) to study the effects of rotation on separated turbulent flows during stall delay at a global tip speed ratio (TSR) of 3 and a Reynolds number of 4800. The flow fields on a static airfoil were also measured at a similar angle-of-attack (AOA) and Reynolds number for comparison. It was observed that the blade’s rotation in the streamwise direction significantly affected both the mean flow and the turbulence statistics over the suction surface. The mean velocity fields revealed that, different from the airfoil flow at large AOA, the recirculation region with reversed flow did not exist on the suction surface of the blade and the flow was rather attached. Mean spanwise flow from blade’s root to its tip was also generated by the rotation. The mean vorticity vector of the blade flow was found to be tilted in the rotational direction of the blade, as well as in the wall-normal direction. Of particular effects of the rotation on Reynolds stresses were the enhancement of 〈w 2〉 and the creation of strong 〈v w〉. The production of Reynolds stresses was also affected by blade’s rotation directly through the rotational production terms and indirectly by dramatically changing the fluctuating velocity fields. The distribution of enstrophy was observed to be modified by rotation, too.

On the fast fluid dynamics and fractional step methods to predict the coupled indoor temperature and velocity fields

In microimprint lithography, the resist deformation directly influences the quality of the final imprinted patterns. The resist velocity field was investigated through numerical simulations and visualization experiments. A numerical model based on the computational fluid dynamics was built to predict the resist filling behavior. Meanwhile, a 3D defocusing digital particle image velocimetry (DDPIV) system was developed to achieve the microscale velocity field of resist. The spatial coordinates of the fluorescent tracer particles were derived from their defocused images, and then the three-dimensional particle field and velocity field inside the resist were obtained according to the particles' spatial coordinates and time interval recording the particle images. The investigation of the velocity field, including the horizontal and vertical velocity history, was performed to help describe the filling mode and flow behavior of the resist. The experimental results agreed well with the simulation prediction, which justified the use of the micro DDPIV system to investigate the resist filling behavior and verified the numerical model. The combined effect of the mold's local asymmetric geometries and resist's initial thickness on its own deformation was further analyzed by numerical simulation.

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.

Particle image velocimetry (PIV) techniques have a limited field of view of the flow field and can only capture high-resolution flow fields in localized areas. To obtain a larger measurement range, multiple cameras must be used to capture the flow field simultaneously and then stitch the parts together. However, this method can be expensive. We propose the local-global fusion convolutional neural network (LGF-CNN) for reconstructing large-field flow fields with high spatial resolution based only on two flow data types: local small-field high spatial resolution wake velocity fields and global large-field low spatial resolution velocity fields. The core of the model consists of convolutional neural network (CNN) architecture to learn the mapping relationship between the small field of view with high spatial resolution and the large field of view with low spatial resolution. Using the effectively trained LGF-CNN model, we demonstrate its ability to reconstruct high-resolution velocity fields around the circular cylinder. The LGF-CNN is rigorously validated on a number of representative datasets, including simulated data for Reynolds numbers of 200 and 500, as well as experimental data for a Reynolds number of 3.3 × 104 with the steady jet at the rear stagnation point of the cylinder. The results demonstrate the ability of LGF-CNN to generate accurate velocity fields with high spatial resolution, including reliable detection of high-frequency components. The proposed method could reduce the number of cameras required for large-field, high spatial resolution PIV measurements, thereby reducing experimental costs.

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.

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

In the present study, a digital holography microscope has been developed to study instantaneous 3D velocity field in a square channel of 1000 × 1000 μm2 cross-section. The flow field is seeded with polystyrene microspheres of size dp = 2.1 μm. The volumetric flow rate is set equal to 20 μl/min. The instantaneous 3D velocity field is obtained by correlating the particles obtained from the 3D numerical reconstruction of holograms using particle tracking velocimetry (PTV).

Experimental study on acoustic vector tomography of 2-D flow field in an experiment-scale furnace

The three-dimensional velocity field of a propeller-driven liquid metal flow is reconstructed by a contactless inductive flow tomography. The underlying theory is presented within the framework of an integral equation system that governs the magnetic field distribution in a moving electrically conducting fluid. For small magnetic Reynolds numbers this integral equation system can be cast into a linear inverse problem for the determination of the velocity field from externally measured magnetic fields. A robust reconstruction of the large scale velocity field is already achieved by applying the external magnetic field alternately in two orthogonal directions and measuring the corresponding sets of induced magnetic fields. Kelvin's theorem is exploited to regularize the resulting velocity field by using the kinetic energy of the flow as a regularizing functional. The results of this technique are shown to be in satisfactory agreement with ultrasonic measurements.

Rotating air-water ring in the vaneless gap of a pump-turbine operating in condenser mode

For industrial and environmental purposes there is a need for broad concepts and general models to describe many types of mixing processes and situations. These concepts arise from exact conversation results,1 and the similarity of the velocity fields and the particle displacements in turbulent fields at high Reynolds number, especially in the presence of shear. However, the design and control of mixing, like other kinds of turbulent problems, is usually improved by considering quasideterministic models of how turbulent eddies affect the process. Such models are changing with new computations and experimental studies of turbulence structure. Mixing involves continuously bringing together volumes of fluid with different concentrations on small enough scales to effect mixing between molecules. The Lagrangian statistical analysis of the displacements of fluid elements enables joint moments of concentration to be calculated in terms of initial concentration distributions in the absence of diffusion and reaction.2 This macromixing analysis in conjunction with simple concepts of small-scale mixing leads to models and a new understanding for many mixing processes, e.g., concentration fluctuations, simple chemical reactions, and the effects of varying the mean shear, the velocity spectra and the molecular diffusivity.3–7 Since extreme pollution concentrations and many complex chemical and physical processes can only be understood in a given scalar field, rather than from statistics of scalar fields, it is necessary to understand and model where and how mixing occurs in a single realization of the flow. This requires computing and/or measuring the evolving velocity and scalar fields in turbulent flows. Recent direct numerical simulations8–10 and kinematic simulations,11,12 i.e., velocity fields constructed from random Fourier modes, with observed or idealized two-point, two-time Eulerian and Lagrangian spectra, have shown (i) how surface areas expand exponentially, and volumes elongate only slightly;8,13 (ii) how scalar surfaces are deformed quite differently in different characteristic regions of turbulent flows; viz., vortical, eddy regions (rolling up into ‘‘fractal’’ surfaces), convergent–divergent, stagnating regions (stretching out, and nonfractal), and streaming regions (where tendrils form);14 (iii) how large volumes of matter disperse in particular events (which cannot be obtained from ensemble average statistics obtained from stochastic models based on displacements of one or two particles).15

The Evershed flow (EF), since its discovery in 1909, represents a longstanding issue in solar physics, with its three-dimensional velocity fields and underlying physical mechanisms still not fully understood. We present a comprehensive analysis of the velocity fields for 20 sunspots, using the full-disk spectroscopic observations from the Chinese H α Solar Explorer (CHASE). The height-dependent velocity fields are derived from the bisector analysis of the Si i 6560.58 Å, Fe i 6569.21 Å, and H α 6562.81 Å spectral lines, which are formed from the deep photosphere (∼70 km) to the upper chromosphere (∼1340 km). The statistical results based on CHASE observations reveal that the photospheric EF manifests as a nearly horizontal outflow with the maximum radial flow velocities of 2.5–2.9 km s −1 at the outer penumbral boundaries, and the inverse EF (IEF) at the chromosphere shows predominant inward flows of 1.6–3.5 km s −1 , with substantial downward flows. EF-like flows above the penumbra are found in all sunspots in the H α far wings, with a velocity reversal shown by the bisector analysis at H α ±0.65 Å (corresponding to a normalized line depth intensity of ∼0.6) in the limb-side region, and a small reversal in the center-side region, suggesting the coexistence of the EF outflows and IEF downflows at the flow reversal layers. We finally construct a three-dimensional schematic of the EF and IEF above sunspots, depicting the height-dependent flows from the deep photosphere to the upper chromosphere.