Fluid Mechanics Research Articles

Development of an object-oriented finite element program with adaptive mesh refinement for multi-physics applications

In this paper, an object-oriented framework for numerical analysis of multi-physics applications is presented. The framework is divided into several basic sets of classes that enable the code segments to be built according to the type of problem to be solved. Fortran 2003 was used in the development of this finite element program due to its advantages for scientific and engineering programming and its new object-oriented features. The program was developed with h-type adaptive mesh refinement, and it was tested for several classical cases involving heat transfer, fluid mechanics and structural mechanics. The test cases show that the adaptive mesh is refined only in the localization region where the feature gradient is relatively high. The overall mesh refinement and the h-adaptive mesh refinement were justified with respect to the computational accuracy and the CPU time cost. Both methods can improve the computational accuracy with the refinement of mesh. The overall mesh refinement causes the CPU time cost to greatly increase as the mesh is refined. However, the CPU time cost does not increase very much with the increase of the level of h-adaptive mesh refinement. The CPU time cost can be saved by up to 90%, especially for the simulated system with a large number of elements and nodes.

Symmetry justification of Lorenz’ maximum simplification

In 1960 Edward Lorenz (1917-2008) published a pioneering work on the `maximum simplification' of the barotropic vorticity equation. He derived a coupled three-mode system and interpreted it as the minimum core of large-scale fluid mechanics on a `finite but unbounded' domain. The model was obtained in a heuristic way, without giving a rigorous justification for the chosen selection of modes. In this paper, it is shown that one can legitimate Lorenz' choice by using symmetry transformations of the spectral form of the vorticity equation. The Lorenz three-mode model arises as the final step in a hierarchy of models constructed via the component reduction by means of symmetries. In this sense, the Lorenz model is indeed the `maximum simplification' of the vorticity equation.

Validation of computational models in biomechanics

The topics of verification and validation have increasingly been discussed in the field of computational biomechanics, and many recent articles have applied these concepts in an attempt to build credibility for models of complex biological systems. Verification and validation are evolving techniques that, if used improperly, can lead to false conclusions about a system under study. In basic science, these erroneous conclusions may lead to failure of a subsequent hypothesis, but they can have more profound effects if the model is designed to predict patient outcomes. While several authors have reviewed verification and validation as they pertain to traditional solid and fluid mechanics, it is the intent of this paper to present them in the context of computational biomechanics. Specifically, the task of model validation will be discussed, with a focus on current techniques. It is hoped that this review will encourage investigators to engage and adopt the verification and validation process in an effort to increase peer acceptance of computational biomechanics models.

Combined local microchannel-scale CFD modeling and global chip scale network modeling for electronics cooling design

Microchannel cold plates enjoy increasing interest in liquid cooling of high-performance computing systems. Fast and reliable design tools are required to comply with the fluid mechanics and thermal specifications of such complex devices. In this paper, a methodology accounting for the local as well as the device length scales of the involved physics is introduced and applied to determine the performance of a microchannel cooler. A unit cell of the heat transfer microchannel system is modeled and implemented in conjugate CFD simulations. The fluidic and thermal characteristics of three different cold plate mesh designs are evaluated. Periodic boundary conditions and an iteration procedure are used to reach developed flow and thermal conditions. Subsequently, two network-like models are introduced to predict the overall pressure drop and thermal resistance of the device based on the results of the unit cell evaluations. Finally, the performance figures from the model predictions are compared to experimental data. We illustrate the cooling potential for different channel mesh porosities and compare it to the required pumping power. The agreement between simulations and experiments is within 2%. It was found that for a typical flow rate of 250 ml/min, the thermal resistance of the finest microchannel network examined is reduced by 7% and the heat transfer coefficient is increased by 25% compared to the coarsest channel network. On the other hand, an increase in pressure drop by 100% in the case of densest channel network was found.

Experimental study and analytical model of the cavitation ring region with small diameter ultrasonic horn

Experiments of cavitation erosion are performed on a surface using the “stationary specimen method”. A small diameter horn of 5 mm is selected instead of using the standard horn of 15.9 mm. The experiments are performed according to these parameters: an excitation frequency of the horn of 20 kHz, a gap between the horn and the specimen within the range from 0.05 to 0.5 mm and the displacement amplitude of the horn within a range of 15–50 μm. After examination of the samples, two erosion patterns can be clearly distinguished, one circular shape centred in the origin and a ring shape around. Moreover, it has been observed that the diameter of this ring shape, the cavitation ring region, is a function that depends on the amplitude and the gap. Existence of the cavitation ring region under the mentioned conditions is explained using a theoretical model based on the combination of Fluid Mechanics and Analytical Mechanics. Results after application of this model reveal the satisfactory agreement between the numerical output and the experimental data.

Non-relativistic conformal symmetries in fluid mechanics

The symmetries of a free incompressible fluid span the Galilei group, augmented with independent dilations of space and time. When the fluid is compressible, the symmetry is enlarged to the expanded Schrödinger group, which also involves, in addition, Schrödinger expansions. While incompressible fluid dynamics can be derived as an appropriate non-relativistic limit of a conformally invariant relativistic theory, the recently discussed conformal Galilei group, obtained by contraction from the relativistic conformal group, is not a symmetry. This is explained by the subtleties of the non-relativistic limit.

TURBULENCE-INDUCED MAGNETIC FIELDS AND STRUCTURE OF COSMIC RAY MODIFIED SHOCKS

We propose a model for Diffusive Shock Acceleration (DSA) in which stochastic magnetic fields in the shock precursor are generated through purely fluid mechanisms of a so-called small-scale dynamo. This contrasts with previous DSA models that considered magnetic fields amplified through cosmic ray streaming instabilities; i.e., either by way of individual particles resonant scattering in the magnetic fields, or by macroscopic electric currents associated with large-scale cosmic ray streaming. Instead, in our picture, the solenoidal velocity perturbations that are required for the dynamo to work are produced through the interactions of the pressure gradient of the cosmic ray precursor and density perturbations in the inflowing fluid. Our estimates show that this mechanism provides fast growth of magnetic field and is very generic. We argue that for supernovae shocks the mechanism is capable of generating upstream magnetic fields that are sufficiently strong for accelerating cosmic rays up to around 10^16 eV. No action of any other mechanism is necessary.

Deposition of micron liquid droplets on wall in impinging turbulent air jet

The fluid mechanics of the deposition of micron liquid (olive oil) droplets on a glass wall in an impinging turbulent air jet is studied experimentally. The spatial patterns of droplets deposited on a wall are measured by using luminescent oil visualization technique, and the statistical data of deposited droplets are obtained through microscopic imagery. Two distinct rings of droplets deposited on a wall are found, and the mechanisms of the formation of the inner and outer rings are investigated based on global diagnostics of velocity and skin friction fields. In particular, the intriguing effects of turbulence, including large-scale coherent vortices and small-scale random turbulence, on micron droplet deposition on a wall and coalescence in the air are explored.

Synthetic turbulence using artificial boundary layers

Turbulent vortices in fluid flows are crucial for a visually interesting appearance. Although there has been a significant amount of work on turbulence in graphics recently, these algorithms rely on the underlying simulation to resolve the flow around objects. We build upon work from classical fluid mechanics to design an algorithm that allows us to accurately precompute the turbulence being generated around an object immersed in a flow. This is made possible by modeling turbulence formation based on an averaged flow field, and relying on universal laws describing the flow near a wall. We precompute the confined vorticity in the boundary layer around an object, and simulate the boundary layer separation during a fluid simulation. Then, a turbulence model is used to identify areas where this separated layer will transition into actual turbulence. We sample these regions with vortex particles, and simulate the further dynamics of the vortices based on these particles. We will show how our method complements previous work on synthetic turbulence, and yields physically plausible results. In addition, we demonstrate that our method can efficiently compute turbulent flows around a variety of objects including cars, whisks, as well as boulders in a river flow. We can even apply our model to precomputed static flow fields, yielding turbulent dynamics without a costly simulation.

Computational Fluid Dynamics of an Electrolytic Cell FM01-LC

Due to the complexity of an Electrochemical Reactor, the knowledge of the kinetics, thermodynamics, process engineering and fluid hydrodynamics is needed to achieve an optimum operation. The availability of electrolytic reactor FM01-LC has been studied lately with great interest. The fluid mechanics of the electrolyte in this type of reactors is essential to be studied because its effect modifies the mass transport to the electrodes. Computational fluid dynamics (CFD) is a novel tool to compute and understand the fluid mechanics in great detail, the software FLUENT TM 6.3.26 was used to solve the governing equations. The velocity profiles and flow paths were predicted using the k-epsilon model for turbulence closure and compared with experimental results. k-epsilon model has shown to be an adequate model to describe the flow in parallel plate reactors FM01-LC type.

A Flexible Flow Sensor System and Its Characteristics for Fluid Mechanics Measurements

In this paper, we present a novel micromachined hot-film flow sensor system realized by a technique using a film depositing processes and incorporating a standard printed circuit. Sensor electrodes and electronic circuits are preprinted on a flexible substrate of polyimide (PI), i.e., a flexible printed circuit board (FPCB). The sensing element, which is made of Cr/Ni/Pt with a temperature coefficient of resistance around 2,000 ppm/K, is fabricated on the FPCB by either magnetron sputtering technology or pulsed laser deposition (PLD). The sensor can be packed efficiently at high-density and integrated with signal processing circuits without additional pads. A simple fabrication process using mature technique and materials selection guarantees that the time and costs are greatly reduced. Both steady-state and transient characteristics of the sensors are experimentally tested, and the results presented to validate the effectiveness of the sensors.

Experimental study of the movement of control fluid in compound perforation

The interaction between the high pressure gas and the control fluid and the movement mechanism of the control fluid in compound perforation were studied by a series of large-scale experiments, where the movement behavior of the control fluid was observed. The curves of measured pressure were analyzed, a mathematical model for the rigid movement of the control fluid was established, and the movement velocity of control fluid was analyzed. Moreover, the velocity from experimental results and velocity from an analytical solution were contrasted. The movement of the control fluid in the initial stage was similar to the rigid movement; however, the propagation of the pressure wave in the control fluid should be taken into account. Experimental results are significant for research on the movement mechanism of control fluid in compound perforation.

Laboratory Testing of Downhole Gas Separators

Summary This paper provides insights on the design of downhole gas separators based on the laboratory study of various separator designs. A downhole gas separator, also known as a gas anchor, may be installed below the pump to separate free gas from the produced liquid. The free gas-produced downhole is usually separated through the casing-tubing annulus (the casing-tubing annulus acts as a natural gravity separator) while the liquid is produced through the tubing. However, inefficient gas anchor designs are widespread and an acceptable guide for their optimum design does not currently exist. Laboratory testing of downhole gas separators has been ongoing since January 2005 at The University of Texas at Austin Petroleum Production Engineering Facility (UTAPPEF) using an instrumented full-scale model of a wellbore and separator constructed with clear acrylic pipe to visualize the fluid mechanics of the separation process. An air and water mixture is injected through the well's perforations. The air and water flow rate measurements are used to measure and define a performance plot of each separator design. The separator designs tested differed in entry-port configuration, size of dip tube, and the relative position of the separator-fluid entry ports with respect to the well's perforations. Based on the results of the tests, a new separator design that includes the effect of centrifugal forces to separate the gas and liquid phases was developed. The results show that, for the conditions in the laboratory, 100% separation was achieved whenever the entry ports were located 1- to 2-feet (ft) below the bottom-most casing perforation thereby dispelling the predominant industry-held opinion that more distance is required between the separator-fluid entry ports and the bottom-most casing perforation. Similarly, laboratory results equally show that an optimum dip tube length of 5.5 ft is sufficient for the optimal separation of free gas from the produced liquid by the separator. This clearly runs contrary to the accepted industry practice, as many industry models employed for the estimation of dip-tube length were found to over-estimate the dip-tube length, and this subsequently results in the undesirable increased pressure drop across the separator. Lastly, the entry port geometry does not appear to have a significant impact on the separator performance as long as sufficient flow area is present. The efficiency of all gravity-driven separators was limited by the liquid velocity inside the separator annulus. When the liquid velocity inside the separator averaged approximately 6 in. per second or less, an almost-to-complete gas separation was achieved. On the other hand, the centrifugal separator had a liquid capacity 70% greater than any of the gravity-driven, static-downhole gas separators.

An active flow control strategy for the suppression of vortex structures behind a circular cylinder

An algorithm is proposed to model, predict and control vortex shedding behind a circular cylindrical configuration. The main ingredients of the algorithm include multiple-feedback sensors, actuators (with zero net mass injection) and a control strategy. Along with the mass and momentum conservation equations, a control equation is implemented to enable the desired flow control goals. A number of sensors are chosen in the downstream of the body to report the state of the flow. The role of externally controllable actuators on the fluid flow patterns past a circular configuration is assessed. To enable, zero net mass injection, two simple rotary type mechanical actuators are located at 120°, right behind the main cylinder. The popular finite volume based SIMPLE scheme is employed for the numerical calculations. As a precursor, the scheme simulates flow past an isolated cylinder, which is validated over a moderate range of Reynolds numbers. The design parameters of interest such as Strouhal number, drag and lift coefficients etc are used for the purpose of validation. The simulated flow fields are compared against the flow visualization study, which clearly demonstrates the efficacy of the actuators at discrete levels of rotation. The basic character of the flow is completely modified at U c/ U ∞ = 2.0 and Re = 100, where a complete suppression of vortex shedding is observed. This is tantamount to complete control of all the global instability modes. Fictitious tracer particles are released to visualize the vortex structures in the form of streaklines. The results clearly demonstrate the effectiveness of a rather simple active control algorithm in suppressing the vortex structures. All the relevant fluid flow features of the bluff-body fluid mechanics under the influence of actuators are studied in the sub-critical Reynolds number range of Re = 100–300.

Evaluation of rate of cyclopentane hydrate formation in an oscillatory baffled column using laser induced fluorescence and energy balance

We report a novel method using laser induced fluorescence (LIF) for observing cyclopentane hydrate formation in an oscillatory baffled column (OBC). In LIF, a dye fluoresces in a hydrate system when induced by a laser; this highlights the areas in which hydrates are present, allowing the hydrate formation regimes to be identified and rates evaluated. Using temperature measurements of the system, the rates of hydrate formation are also determined by a thermal method. The work shows that there is a high correlation between the LIF and the thermal techniques in obtaining kinetic information on cyclopentane hydrate. The results indicate that there are possibly three mechanisms governing hydrate growth. With the absence of mixing, a film formation is observed. At high mixing intensities uniform droplet dispersion is resulted, where fluid mechanics is the controlling parameter. At low mixing conditions a combination of the two mechanisms co-exists, interfacial mechanics is thought to be the dominant factor. The trends in the rates of hydrate formation are different in each of these regimes.

Fountain flow revisited: The effect of various fluid mechanics parameters

AbstractNumerical simulations have been undertaken for the benchmark problem of fountain flow present in injection‐mold filling. The finite element method (FEM) is used to provide numerical results for both cases of planar and axisymmetric domains under laminar, isothermal, steady‐state conditions for Newtonian fluids. The effects of inertia, gravity, surface tension, compressibility, slip at the wall, and pressure dependence of the viscosity are all considered individually in parametric studies covering a wide range of the relevant parameters. These results extend previous ones regarding the shape of the front, and in particular the centerline front position, as a function of the dimensionless parameters. The pressures from the simulations have been used to compute the excess pressure losses in the system (front pressure correction or exit correction). Inertia leads to highly extended front positions relative to the inertialess Newtonian values, which are 0.895 for the planar case and 0.835 for the axisymmetric one. Gravity acting in the direction of flow shows the same effect, while gravity opposing the flow gives a reduced bulge of the fountain. Surface tension, slip at the wall, and compressibility, all decrease the shape of the front. Pressure‐dependence of the viscosity leads to increased front position as a corresponding dimensionless parameter goes from zero (no effect) to higher values of the pressure‐shift factor. The exit correction increases monotonically with inertia, compressibility, and gravity, while it decreases monotonically with slip and pressure‐dependence of the viscosity. Contour plots of the primary variables (velocity‐pressure) show interesting trends compared with the base case (zero values of the dimensionless parameters and of surface tension). © 2009 American Institute of Chemical Engineers AIChE J, 2010

Fluid dynamics based modelling of the Falcon concentrator for ultrafine particle beneficiation

Enhanced gravity separators are widely used in mineral beneficiation, as their superior gravity field enables them to separate particles within narrow classes of density and size. This study aims to shed light on the Falcon concentrator’s ability to separate particles within size and density ranges lower than usual, say 5–60 μm and 1.2–3.0 s.g. respectively. As differential particle settling is expected to be the prevailing separation mechanism under such conditions, this study presents the workings of a predictive Falcon separation model that embeds phenomenological fluid and particle flow simulation inside the Falcon’s flowing film. Adding to the novelty of modelling the Falcon concentrator using a fluid mechanics approach, one point of practical significance within this work is the derivation of the Falcon’s partition function from fluid flow simulation results.

Computational study of the drag and oscillatory movement of biofilm streamers in fast flows

Hydrodynamic conditions have a significant impact on the biofilm lifecycle. Not well understood is the fact that biofilms, in return, also affect the flow pattern. A decade ago, it was already shown experimentally that under fast flows, biofilm streamers form and oscillate with large amplitudes. This work is a first attempt to answer the questions on the mechanisms behind the oscillatory movement of the streamers, and whether this movement together with the special streamlined form of the streamers, have both a physical and biological benefit for biofilms. In this study, a state of the art two-dimensional fluid-structure interaction model of biofilm streamers is developed, which implements a transient coupling between the fluid and biofilm mechanics. Hereby, it is clearly shown that formation of a Kármán vortex street behind the streamer body is the main source of the periodic oscillation of the streamers. Additionally it is shown that the formation of streamers reduces the fluid forces which biofilm surface experiences.

Turbulence and heat excited noise sources in single and coaxial jets

The generation of noise in subsonic high Reynolds number single and coaxial turbulent jets is analyzed by a hybrid method. The computational approach is based on large-eddy simulations (LES) and solutions of the acoustic perturbation equations (APE). The method is used to investigate the acoustic fields of one isothermal single stream jet at a Mach number 0.9 and a Reynolds number 400,000 based on the nozzle diameter and two coaxial jets whose Mach number and Reynolds number based on the secondary jet match the values of the single jet. One coaxial jet configuration possesses a cold primary flow, whereas the other configuration has a hot primary jet. Thus, the configurations allow in a first step the analysis of the relationship of the flow and acoustic fields of a single and a cold coaxial jet and in a second step the investigation of the differences of the fluid mechanics and aeroacoustics of cold and hot coaxial jets. For the isothermal single jet the present hybrid acoustic computation shows convincing agreement with the direct acoustic simulation based on large-eddy simulations. The analysis of the acoustic field of the coaxial jets focuses on two noise sources, the Lamb vector fluctuations and the entropy sources of the APE equations. The power spectral density (PSD) distributions evidence the Lamb vector fluctuations to represent the major acoustic sources of the isothermal jet. Especially the typical downstream and sideline acoustic generations occur on a cone-like surface being wrapped around the end of the potential core. Furthermore, when the coaxial jet possesses a hot primary jet, the acoustic core being characterized by the entropy source terms increases the low frequency acoustics by up to 5 dB, i.e., the sideline acoustics is enhanced by the pronounced temperature gradient.

Investigation of Pulsatile Flowfield in Healthy Thoracic Aorta Models

Cardiovascular disease is the primary cause of morbidity and mortality in the western world. Complex hemodynamics plays a critical role in the development of aortic dissection and atherosclerosis, as well as many other diseases. Since fundamental fluid mechanics are important for the understanding of the blood flow in the cardiovascular circulatory system of the human body aspects, a joint experimental and numerical study was conducted in this study to determine the distributions of wall shear stress and pressure and oscillatory WSS index, and to examine their correlation with the aortic disorders, especially dissection. Experimentally, the Phase-Contrast Magnetic Resonance Imaging (PC-MRI) method was used to acquire the true geometry of a normal human thoracic aorta, which was readily converted into a transparent thoracic aorta model by the rapid prototyping (RP) technique. The thoracic aorta model was then used in the in vitro experiments and computations. Simulations were performed using the computational fluid dynamic (CFD) code ACE+((R)) to determine flow characteristics of the three-dimensional, pulsatile, incompressible, and Newtonian fluid in the thoracic aorta model. The unsteady boundary conditions at the inlet and the outlet of the aortic flow were specified from the measured flowrate and pressure results during in vitro experiments. For the code validation, the predicted axial velocity reasonably agrees with the PC-MRI experimental data in the oblique sagittal plane of the thoracic aorta model. The thorough analyses of the thoracic aorta flow, WSSs, WSS index (OSI), and wall pressures are presented. The predicted locations of the maxima of WSS and the wall pressure can be then correlated with that of the thoracic aorta dissection, and thereby may lead to a useful biological significance. The numerical results also suggest that the effects of low WSS and high OSI tend to cause wall thickening occurred along the inferior wall of the aortic arch and the anterior wall of the brachiocephalic artery, similar implication reported in a number of previous studies.