4D Magnetic resonance velocimetry for mean velocity measurements in complex turbulent flows

An adaptation of a medical magnetic resonance imaging system to the noninvasive measurement of three-component mean velocity fields in complex turbulent engineering flows is described. The aim of this paper is to evaluate the capabilities of the technique with respect to its accuracy, time efficiency and applicability as a design tool for complex turbulent internal geometries. The technique, called 4D magnetic resonance velocimetry (4D-MRV), is used to measure the mean flow in fully developed low-Reynolds number turbulent pipe flow, Re=6400 based on bulk mean velocity and diameter, and in a model of a gas turbine blade internal cooling geometry with four serpentine passages, Re=10,000 and 15,000 based on bulk mean velocity and hydraulic diameter. 4D-MRV is capable of completing full-field measurements in three-dimensional volumes with sizes on the order of the magnet bore diameter in less than one hour. Such measurements can include over 2 million independent mean velocity vectors. Velocities measured in round pipe flow agreed with previous experimental results to within 10%. In the turbulent cooling passage flow, the average flow rates calculated from the 4D-MRV velocity profiles agreed with ultrasonic flowmeter measurements to within 7%. The measurements lend excellent qualitative insight into flow structures even in the highly complex 180° bends. Accurate quantitative measurements were obtained throughout the Re=10,000 flow and in the Re=15,000 flow except in the most complex regions, areas just downstream of high-speed bends, where velocities and velocity fluctuations exceeded MRV capabilities for the chosen set of scan parameters. General guidelines for choosing scanning parameters and suggestions for future development are presented.     

Comparison of magnetic resonance concentration measurements in water to temperature measurements in compressible air flows

Magnetic resonance imaging (MRI) measurements in liquid flows provide highly detailed 3D mean velocity and concentration data in complex turbulent mixing flow applications. The scalar transport analogy is applied to infer the mean temperature distribution in high speed gas flows directly from the MRI concentration measurements in liquid. Compressibility effects on turbulent mixing are known to be weak for simple flows at high subsonic Mach number, and it was not known if this would hold in more complex flows characteristic of practical applications. Furthermore, the MRI measurements are often done at lower Reynolds number than the compressible application, although both are generally done in fully turbulent flows. The hypothesis is that the conclusions from MRI measurements performed in water are transferable to high subsonic Mach number applications. The present experiment is designed to compare stagnation temperature measurements in high speed airflow (M = 0.7) to concentration measurements in an identical water flow apparatus. The flow configuration was a low aspect ratio wall jet with a thick splitter plate producing a 3D complex downstream flow mixing the wall-jet fluid with the mainstream flow. The three-dimensional velocity field is documented using magnetic resonance velocimetry in the water experiment, and the mixing is quantified by measuring the mean concentration distribution of wall-jet fluid marked with dissolved copper sulfate. The airflow experiments are operated with a temperature difference between the main stream and the wall jet. Profiles of the stagnation temperature are measured with a shielded thermocouple probe. The results show excellent agreement between normalized temperature and concentration profiles after correction of the temperature measurements for the effects of energy separation. The agreement is within 1 % near the edges of the mixing layer, which suggests that the mixing characteristics of the large scale turbulence structures are the same in the two flows.     

Three-dimensional magnetic resonance velocimetry measurements of turbulence quantities in complex flow

A magnetic resonance velocimetry (MRV) experimental technique based on magnetic resonance imaging and capable of measuring the turbulent Reynolds stresses in a 3D flow domain is described. Results are presented in backward facing step flow in a square channel with a Reynolds number of 48,000 based on step height and freestream velocity at the step. MRV results are compared to particle image velocimetry (PIV) measurements in the centerplane containing the streamwise and cross-stream axes. MRV and PIV mean velocity measurements show excellent agreement. MRV measurements for Reynolds normal stresses compare to within ±20% of the PIV results while results for the turbulent shear are less accurate.     

湍流扩散多相流

湍流扩散多相流在许多工程和环境科学实际应用中十分常见.流体相中的湍流和扩散相的随机本质使得湍流扩散多相流中遇到的问题远比单一流体中遇到的湍流现象复杂得多.首先评述了湍流扩散多相流研究中实验技术和数值计算方面的现状、各自的优点与局限性,以及该领域研究中未来面临的挑战.主要关注湍流扩散多相流研究中以下3方面重点内容:颗粒、液滴和气泡的选择性聚积;湍流对流体相和扩散相耦合作用的影响以及颗粒物和气泡的存在对流体相中湍流的调节机制.     

Volumetric intake flow measurements of an IC engine using magnetic resonance velocimetry

Magnetic resonance velocimetry (MRV) measurements are performed in a 1:1 scale model of a single-cylinder optical engine to investigate the volumetric flow within the intake and cylinder geometry during flow induction. The model is a steady flow water analogue of the optical IC-engine with a fixed valve lift of $9.21$  mm to simulate the induction flow at crank-angle $270^{\circ }$ bTDC. This setup resembles a steady flow engine test bench configuration. MRV measurements are validated with phase-averaged particle image velocimetry (PIV) measurements performed within the symmetry plane of the optical engine. Differences in experimental operating parameters between MRV and PIV measurements are well addressed. Comparison of MRV and PIV measurements is demonstrated using normalized mean velocity component profiles and showed excellent agreement in the upper portion of the cylinder chamber (i.e., $y \ge -20$  mm). MRV measurements are further used to analyze the ensemble average volumetric flow within the 3D engine domain. Measurements are used to describe the 3D overflow and underflow behavior as the annular flow enters the cylinder chamber. Flow features such as the annular jet-like flows extending into the cylinder, their influence on large-scale in-cylinder flow motion, as well as flow recirculation zones are identified in 3D space. Inlet flow velocities are analyzed around the entire valve curtain perimeter to quantify percent mass flow rate entering the cylinder. Recirculation zones associated with the underflow are shown to reduce local mass flow rates up to 50 %. Recirculation zones are further analyzed in 3D space within the intake manifold and cylinder chamber. It is suggested that such recirculation zones can have large implications on cylinder charge filling and variations of the in-cylinder flow pattern. MRV is revealed to be an important diagnostic tool used to understand the volumetric induction flow within engine geometries and is potentially suited to evaluate flow changes due to intake geometry modifications.     

In-hole and mainflow velocity measurements of low-momentum jets in crossflow emanating from short holes

Discrete hole film cooling utilizes jet-in-crossflow geometry where the jet is supplied through a short hole which may be pitched relative to the main flow. Typically, the velocity ratio is near one. Under these conditions, the mean flow structure of the jet/mainstream interaction may be strongly affected by the characteristics of the flow within the hole. Magnetic resonance velocimetry (MRV) is used to measure the 3-dimensional mean velocity field for various jets in crossflow with short holes of varied inclination angles and blowing ratios typically of gas turbine applications. Novel measurements of the flow within inclined feed holes are captured using MRV. Secondary flows within the hole are found to be strongly dependent on the inclination of the hole. The traditional counter-rotating vortex pair is observed in the mainstream, as well as high levels of wall-normal vorticity. The 3D vorticity field is used to modify traditional jet-in-crossflow vortex ring theory to apply to low-momentum jets which remain attached to the ejection surface.     

Sensitivity of an asymmetric 3D diffuser to vortex-generator induced inlet condition perturbations

Modifications of the turbulent separated flow in an asymmetric three-dimensional diffuser due to inlet condition perturbations were investigated using conventional static pressure measurements and velocity data acquired using magnetic resonance velocimetry (MRV). Previous experiments and simulations revealed a strong sensitivity of the diffuser performance to weak secondary flows in the inlet. The present, more detailed experiments were conducted to obtain a better understanding of this sensitivity. Pressure data were acquired in an airflow apparatus at an inlet Reynolds number of 10,000. The diffuser pressure recovery was strongly affected by a pair of longitudinal vortices injected along one wall of the inlet channel using either dielectric barrier discharge plasma actuators or conventional half-delta wing vortex generators. MRV measurements were obtained in a water flow apparatus at matched Reynolds number for two different cases with passive vortex generators. The first case had a pair of counter-rotating longitudinal vortices embedded in the boundary layer near the center of the expanding wall of the diffuser such that the flow on the outsides of the vortices was directed toward the wall. The MRV data showed that the three-dimensional separation bubble initially grew much slower causing a rapid early reduction in the core flow velocity and a consequent reduction of total pressure losses due to turbulent mixing. This produced a 13% increase in the overall pressure recovery. For the second case, the vortices rotated in the opposite sense, and the image vortices pushed them into the corners. This led to a very rapid initial growth of the separation bubble and formation of strong swirl at the diffuser exit. These changes resulted in a 17% reduction in the overall pressure recovery for this case. The results emphasize the extreme sensitivity of 3D separated flows to weak perturbations.     

Lagrangian-based investigation of multiphase flows by finite-time Lyapunov exponents

Multiphase flows are ubiquitous in our daily lifeand engineering applications.It is important to investigatethe flow structures to predict their dynamical behaviors effectively.Lagrangian coherent structures(LCS) defined bythe ridges of the finite-time Lyapunov exponent(FTLE) isutilized in this study to elucidate the multiphase interactionsin gaseous jets injected into water and time-dependent turbulent cavitation under the framework of Navier-Stokes flowcomputations.For the gaseous jets injected into water,the highlightedphenomena of the jet transportation can be observed by theLCS method,including expansion,bulge,necking/breaking,and back-attack.Besides,the observation of the LCS revealsthat the back-attack phenomenon arises from the fact that theinjected gas has difficulties to move toward downstream region after the necking/breaking.For the turbulent cavitatingflow,the ridge of the FTLE field can form a LCS to capturethe front and boundary of the re-entraint jet when the adverse pressure gradient is strong enough.It represents a barrier between particles trapped inside the circulation regionand those moving downstream.The results indicate that theFTLE field has the potential to identify the structures of multiphase flows,and the LCS can capture the interface/barrieror the vortex/circulation region.     

Three-dimensional concentration field measurements in a mixing layer using magnetic resonance imaging

Magnetic resonance imaging (MRI) was used to measure the three-dimensional, time-averaged concentration distribution in a turbulent two-stream mixing layer. Test fluids and MRI scanning parameters were chosen to give good signal linearity, and a calibration/normalization procedure was developed to reduce the concentration measurement uncertainty. Plain deionized water mixing with a solution of 0.8% gadopentetate dimeglumine in deionized water were selected as test fluids. The concentration of the marked water was measured on an array of 220,000 0.69 mm³ voxels covering the entire flow apparatus. Planar laser-induced fluorescence experiments were performed on the flow centerplane to provide validation data. The uncertainty of a single voxel measurement was estimated to be less than 12% with the largest source of uncertainty being turbulent dephasing. Averaging two runs in which the marked water was switched between the two streams reduced the uncertainty to only 4%. The complete magnetic resonance concentration (MRC) procedure including the adjustment of scanning parameters, a background run, two reference/calibration runs, and multiple concentration measurement runs can be completed in 2–3 h. This work establishes MRC as a viable technique for studying the mixing in complex turbulent liquid flows.     

Experimentally informed optimization of turbulent diffusivity for a discrete hole film cooling geometry

A process has been developed by which mean velocity and concentration measurements can be used to determine optimal turbulent diffusivity values for an angled jet in cross-flow configuration. This configuration has applications in film cooling for gas turbine blades. The measurements, obtained by magnetic resonance imaging techniques, provide 3D time-averaged velocity and concentration fields. The mean velocity field is fed into a Reynolds-Averaged Advection Diffusion solver, which uses a turbulent diffusivity model to solve for the mean coolant concentration distribution. This distribution can be compared to the experimentally-obtained concentration field by means of an error metric that quantifies the difference between the computational and experimental concentration fields. By minimizing this error, an optimal value of the turbulent diffusivity can be determined. This optimized distribution is then compared to a RANS simulation to evaluate the relative contribution to error of the turbulent momentum flux model versus the turbulent scalar flux model.     

A multiblock operator‐splitting algorithm for unsteady flows at all speeds in complex geometries

This paper describes a non‐iterative operator‐splitting algorithm for computing all‐speed flows in complex geometries. A pressure‐based algorithm is adopted as the base, in which pressure, instead of density, is a primary variable, thus allowing for a unified formulation for all Mach numbers. The focus is on adapting the method for (a) flows at all speeds, and (b) multiblock, non‐orthogonal, body‐fitted grids for very complex geometries. Key features of the formulation include special treatment of mass fluxes at control volume interfaces to avoid pressure–velocity decoupling for incompressible (low Mach number limit) flows and to provide robust pressure–velocity–density coupling for compressible (high‐speed) flows. The method is shown to be robust for all Mach number regimes for both steady and unsteady flows; it is found to be stable for CFL numbers of order ten, allowing large time steps to be taken for steady flows. Enhancements to the method which allow for stable solutions to be obtained on non‐orthogonal grids are also discussed. The method is found to be very reliable even in complex engineering applications such as unsteady rotor–stator interactions in turbulent, all‐speed turbomachinery flows. Copyright © 2004 John Wiley & Sons, Ltd.     

Velocity measurements of flow through a step stenosis using Magnetic Resonance Imaging

 Magnetic resonance imaging (MRI) is a versatile noninvasive tool for achieving full-field quantitative visualization of complex fluid flows. The MRI signal results from the interaction of radio-frequency (RF) pulses with nuclear spins exposed to a strong static magnetic field. The two main techniques of MRI velocimetry are time-of-flight and phase contrast techniques. Time-of- flight techniques involve tagging and tracking a material volume of fluid, whereas phase contrast techniques use magnetic field gradients to encode velocity information into the phase of the MRI signal. In this study, both techniques are used to probe the pressure-driven steady flow of water in a pipe with a step stenosis. The velocity measurements were then compared with computational results obtained using the FIDAP software package. The experiments show that the phase contrast method gives more accurate results, with 90% of the measurements within 10% of the local computational fluid dynamics (CFD) velocity predictions at Re = 100 and 94% of the measurements within 10% of the local CFD predictions at Re = 258. Although the time-of-flight experiments were not as accurate, they provide a good qualitative image of the flow field. Sources of the discrepancies between the MRI data and the CFD results are also discussed, including acceleration and spin flow-through artifacts. Received: 7 April 1999/Accepted: 20 December 1999     

Method of Lines for Transient Flow Fields

A computational fluid dynamics (CFD) code based on the method of lines (MOL) approach was developed for the solution of transient, two-dimensional Navier-Stokes equations for incompressible separated internal flows in complex rectangular geometries. The predictive accuracy of the code was tested by applying it to the prediction of flow fields in both laminar and turbulent channel flows with and without sudden expansion, and comparing its predictions with either measured data or numerical results available in the literature. The predicted flow fields were found to be in favorable agreement with those available in the literature for laminar channel flow with sudden expansion and turbulent channel flow with Re=6600. The code was then applied to the prediction of the highly turbulent flow field in the inlet flue of a heat recovery steam generator (HRSG). The predicted flow field was found to display the same trend with the experimental findings and numerical solutions reported previously for a turbulent diverging duct. As the code uses the MOL approach in conjunction with (i) an intelligent higher-order spatial discretization scheme, (ii) a parabolic algorithm for pressure, and (iii) an elliptic grid generator using a body-fitted coordinate system for complex geometries, it provides an efficient algorithm for future direct numerical simulation (DNS) applications in complex rectangular geometries.     

入口速度比对射流拟序结构的影响

为了深入了解湍流流动机理以及湍流拟序结构发现过程的影响因素，本文采用大涡模拟方法对不同入口射流伴流速度比的平面湍射流流动进行了数值模拟。采用分步投影法求解动量方程，亚格子项采用标准Smagorinsky亚格子模式模拟，压力泊松方程采用修正的循环消去法快速求解，空间方程采用二阶精度的差分格式，在时间方向上采用二阶精度的显式差分格式。模拟结果给出了平面射流中湍流拟序结构的瞬态发展演变过程，分析了入口速度比对射流拟序结构发展演化过程及宏观流场形态的影响。为进一步研究射流拟序结构及其在湍流流动中的作用提供了基础。     

Multi-scale magnetic resonance measurements and validation of Discrete Element Model simulations

This short review describes the capabilities of magnetic resonance (MR) to image opaque single- and two-phase granular systems, such as rotating cylinders and gas-fluidized beds operated in different fluidization regimes. The unique capability of MR to not only image the solids’ distribution (voidage) but also the velocity of the particulate phase is clearly shown. It is demonstrated that MR can provide measurements over different length and time scales. With the MR equipment used for the studies summarized here, temporal and spatial scales range from sub-millisecond to hours and from a few hundred micrometres to a few centimetres, respectively. Besides providing crucial data required for an improved understanding of the underlying physics of granular flows, multi-scale MR measurements were also used to validate numerical simulations of granular systems. It is shown that predictions of time-averaged properties, such as voidage and velocity of the particulate phase, made using the Discrete Element Model agree very well with MR measurements.     

气固两相流动的湍流脉动扩散数学模型及其应用

本文提出了气固两相流动的湍流扩展数学模型，本模型用k-ε双方程模型求解气相湍流场，并根据气流脉动的频谱、能谱曲线提出了随机富工级数来模拟气相脉动速度，用拉氏方法描述颗粒的运动，故称为脉动频谱随机颗粒轨道模型。本文还给出了本模型在气固多相射流和流化床内应用的实例。     

Fluid flow investigations within a 37 element CANDU fuel bundle supported by magnetic resonance velocimetry and computational fluid dynamics

The current work presents experimental and computational investigations of fluid flow through a 37 element CANDU nuclear fuel bundle. Experiments based on Magnetic Resonance Velocimetry (MRV) permit three-dimensional, three-component fluid velocity measurements to be made within the bundle with sub-millimeter resolution that are non-intrusive, do not require tracer particles or optical access of the flow field. Computational fluid dynamic (CFD) simulations of the foregoing experiments were performed with the hydra-th code using implicit large eddy simulation, which were in good agreement with experimental measurements of the fluid velocity. Greater understanding has been gained in the evolution of geometry-induced inter-subchannel mixing, the local effects of obstructed debris on the local flow field, and various turbulent effects, such as recirculation, swirl and separation. These capabilities are not available with conventional experimental techniques or thermal-hydraulic codes. The overall goal of this work is to continue developing experimental and computational capabilities for further investigations that reliably support nuclear reactor performance and safety.     

Turbulent particle dispersion in arbitrary wall-bounded geometries: A coupled CFD-Langevin-equation based approach

A Lagrangian continuous random walk (CRW) model is developed to predict turbulent particle dispersion in arbitrary wall-bounded flows with prevailing anisotropic, inhomogeneous turbulence. The particle tracking model uses 3D mean flow data obtained from the Fluent CFD code, as well as Eulerian statistics of instantaneous quantities computed from DNS databases. The turbulent fluid velocities at the current time step are related to those of the previous time step through a Markov chain based on the normalized Langevin equation which takes into account turbulence inhomogeneities. The model includes a drift velocity correction that considerably reduces unphysical features common in random walk models. It is shown that the model satisfies the well-mixed criterion such that tracer particles retain approximately uniform concentrations when introduced uniformly in the domain, while their deposition velocity is vanishingly small, as it should be. To handle arbitrary geometries, it is assumed that the velocity rms values in the boundary layer can locally be approximated by the DNS data of fully developed channel flows. Benchmarks of the model are performed against particle deposition data in turbulent pipe flows, 90° bends, as well as more complex 3D flows inside a mouth-throat geometry. Good agreement with the data is obtained across the range of particle inertia.     

基于滑移速度壁模型的复杂边界湍流大涡模拟

采用滑移速度壁模型实现了浸入边界方法与壁模型相结合的大涡模拟.本文首先分别采用平衡层模型和非平衡壁模型对周期山状流进行数值模拟,以考查在壁模型中考虑切向压力梯度的作用.数值结果表明,流场的压力对本文所采用的壁模型形式并不敏感,但是考虑切向压力梯度可以显著改进壁面摩擦力的计算结果,并且能够准确的预测强压力梯度区以及分离区内的流动平均统计特性.不考虑压力梯度效应的平衡层模型显著低估了壁面摩擦力的分布,同时无法准确预测分离区内的平均速度剖面.非平衡模型的修正项正比于切向压力梯度和壁面法向距离,因此在强压力梯度区或者网格较粗时,计算得到的平均压力和摩擦力分布以及流动的低阶统计量均与参考的实验和计算结果吻合.在此基础上,通过回转体绕流的大涡模拟考查了该方法用于模拟高雷诺数壁湍流的适用性,非平衡壁模型可以准确地捕捉流动的物理结构并较准确地预测其水动力学特性.结果表明,将浸入边界方法与非平衡滑移速度壁模型相结合的大涡模拟,有望成为数值模拟复杂边界高雷诺数壁湍流的工具.      

Multiphase flow model developed for simulating gas hydrate transport in horizontal pipe

The hydrate formation or dissociation in deep subsea flow lines is a challenging problem in oil and gas transport systems. The study of multiphase flows is complex while necessary due to the phase changes (i.e., liquid, solid, and gas) that occur with increasing the temperature and decreasing the pressure. A one-dimensional multiphase flow model coupled with a transient hydrate kinetic model is developed to study the characteristics of the multiphase flows for the hydrates formed by the phase changes in the pipes. The multiphase flow model is derived from a multi-fluid model, while has been widely used in modelling multiphase flows. The heat convection between the fluid and the ambient through the pipe wall is considered in the energy balance equation. The developed multiphase flow model is used to simulate the procedure of the hydrate transport. The results show that the formation of the hydrates can cause hold-up oscillations of water and gas.