Fluid Mechanics Model Research Articles

A furtive stare at an intra-cellular flow

Rarely do intra-cellular flows amount to much: cells are small, and so are their Reynolds numbers. The extraordinarily large cells of the Characean algae provide a fascinating counter-example, as their geometry precludes the standard methods of distributing food and waste. van de Meent et al. (J. Fluid Mech., 2010, this issue, vol. 642, pp. 5–14) present nuclear magnetic resonance (NMR) velocimetry measurements of the fluid flow within individual living cells, which agree quantitatively with their fluid mechanical model and confirm a long-standing hypothesis. In addition to biomimetic parallels with microfluidic labs on chips, this work showcases NMR velocimetry as an under-appreciated but immensely powerful technique. The non-invasive tracer-free high-resolution flow measurements it enables – even in opaque and heterogeneous fluids – should find wide application.

Cooling rate-induced differentiation in anhydrous and hydrous basalts at 500 MPa: Implications for the storage and transport of magmas in dikes

Two sets of cooling experiments were run at 500 MPa conditions for one anhydrous and one hydrous (H 2O = 1.3 wt.%) starting basaltic melts: a) five cooling rates (15, 9.4, 3, 2.1, and 0.5 °C/min) between 1250 and 1000 °C, and b) a 0.5 °C/min cooling rate from 1250 to 1191, 1167, 1100, 1090, 1075, 1050, 1025 and 1000 °C final temperatures. Cooling rate plays a major role in the differentiation of run products. At the lower cooling rate, glasses of tephri-phonolitic and trachy-andesitic composition have been detected. At comparable cooling rate, the dry glasses show a larger compositional variability and degree of differentiation than the hydrous products. The amount of crystallizing solid phases is always larger in the dry products. It is strongly controlled by both cooling rate and water content and massive crystallization occurs only at lower cooling rates. At a constant cooling rate, massive crystallization is observed at lower temperatures. Clinopyroxene, plagioclase and oxide occur in the anhydrous products, whereas plagioclase crystallization is suppressed in the hydrous ones. The lack of plagioclase results from the faster crystallization kinetics for Fe- and Mg-bearing phases than for tectosilicates. Textural coarsening occurs at high cooling rate and, for a constant cooling rate, at higher temperatures. The textural and compositional variability observed at the margin of dikes may not mirror flow differentiation processes but could be due to cooling rate variations. Early homogeneous magma batches subjected to cooling rate-induced differentiation may also produce heterogeneous rocks similar to that originated by magma mingling. Cooling rate-related differentiation influences the physical properties (viscosity and density) of magmas. Dry or H 2O-poor magmas resulting from low cooling rate differentiation are not allowed to rise within dikes. Viscosity variations induced by cooling rate may be responsible for flow localization within conduits. The effects of cooling rate should be incorporated in fluid-mechanical models of magma ascent.

A Fluid Mechanics Model of Tissue Fluid Flow in Limb Connective Tissue—A Mechanism of Acupuncture Signal Transmission

This article explores the mechanisms of acupuncture meridians by determining characteristics of the tissue fluid flow in the connective tissue along meridians. Based on deep dissection of acupoints on the upper and lower limbs of the human body and micro and macro observation and measurement, a mathematical model of the flow of tissue fluid in interosseous membranes is constructed. It is shown that the signal transmission along acupuncture meridians may be determined by unique anatomical and physiological factors that govern the flow of tissue fluid in the connective tissue and involve mast cell degranulation. Our results provide a preliminary explanation of the phenomenon of the “de qi” sensation and the mechanism of acupuncture signal transmission along acupuncture meridians.

Numerical simulation of cloud rise phenomena associated with nuclear bursts

We present numerical simulations of cloud evolution from nuclear explosions using high-resolution numerical methods. Our numerical approach includes a fluid mechanical model that is a combination of a compressible code (GEODYN) and a low Mach code (LMC). Early stages of nuclear explosions that are characterized by the blust wave propagation are simulated with an explicit code (GEODYN) that solves the compressible Navier–Stokes equations via a high-order Godunov scheme. As soon as the blust wave weakens (≈10 s) the subsequent cloud rise due to buoyancy forces can be effectively simulated by the LMC code. LMC is an implicit code based on a pressure projection technique, and derived from the compressible Navier–Stokes equations using an asymptotic analysis in Mach number. It analytically eliminates time step restrictions based on sound wave propagation and it is computationally efficient and accurate for simulations of cloud rise dynamics at later stages. We perform a series of cloud rise scenarios ranging from an idealized bubble rise problem to realistic air bursts. We analyze effects of compressible dynamics on cloud evolution at different stages. It is found that in a realistic configuration, interaction of the reflected shock wave from the ground with the fireball significantly affects cloud evolution, in contrast to the equivalent idealized bubble rise simulations. We validate the code predictions against available experimental data. It is demonstrated that, by providing the initial source from the compressible GEODYN code, late time flow evolution can be successfully simulated with the fast, efficient and accurate LMC code.

Effect of fluid application conditions on grinding behaviour

Applying copious amounts of fluid to ensure adequate lubrication and cooling during grinding creates environmental and safety hazards. The present investigation was undertaken to explore the prospects for reducing the amount of applied fluid without having a deleterious effect on grinding performance. Straight surface grinding experiments were conducted to determine the effect of fluid flowrate and nozzle set-up conditions on the grinding behaviour for both up grinding and down grinding. A high-speed camera was used to observe fluid access to the grinding zone. For up grinding at low flowrates, lack of fluid reaching the wheel and workpiece caused an increase in the forces and surface roughness. The effect of a low flowrate was much less pronounced for down grinding due to the presence of residual fluid, which had collected on the workpiece top surface. A simple fluid mechanics model was developed to determine the flowrate and nozzle set-up condition required for the fluid to reach the wheel and the workpiece.

Diffusive Limit of a Kinetic Model for Cometary Flows

A kinetic equation with a relaxation time model for wave-particle collisions is considered. Similarly to the BGK-model of gas dynamics, it involves a projection onto the set of equilibrium distributions, nonlinearly dependent on the moments of the distribution function. Under a diffusive and low Mach number scaling the macroscopic limit is a generalization of the incompressible Navier-Stokes equations, where the momentum equations are coupled to a diffusive equation for an energy distribution function. By a moment approximation, this system can be related to a low Mach number model of fluid mechanics, which already appeared in the literature. Finally, for a linearized version corresponding to Stokes flow an existence result for initial value problems is proved.

Simulation-supported measurements in large circulating fluidized bed combustors

The concept of simulation-supported measurement is suggested for the elucidation of processes occurring in the combustion chambers of large-scale circulating fluidized bed combustors where the desired information cannot be obtained by direct measurements. The concept is illustrated with the example of secondary air injection where the way the air is released, the penetration depth and the evenness of air distribution over the cross-sectional area of the combustion chamber are of interest. The measured information consists of lateral profiles of oxygen concentrations measured with gas sampling probes at two ports which were located 5 and 9 m, respectively, above the level of secondary air injection. The simulation is carried out on the basis of a 3D semi-empirical fluid-mechanical model of the circulating fluidized bed which is combined with models of gas and solids mixing, fuel distribution, devolatilization and combustion of char and volatiles. The combination of the simulation with the measurements yields a clear picture of the mechanism of secondary air injection, its penetration into the combustion chamber and its effect on the local combustion processes. The results confirm the usefulness of the concept of simulation-supported measurement for this application.

Role of permeability and storage in the initiation and propagation of natural hydraulic fractures

Joint sets within sedimentary basins are commonly interpreted to have formed by tensile failure in conditions where pore fluid pressure was elevated. Such tensile fractures are inferred to be a part of the process that relieves high fluid pressure by locally increasing rock permeability. In spite of the importance of this feedback mechanism, the detailed mechanics of hydraulic fracture genesis remain poorly understood. We describe the results of both experimental and numerical studies of hydraulic fracture genesis on the basis of an experimental protocol that combines rock extension with elevated pore fluid pressure such that the hydraulic fracture criterion is met in the sample interior. This is achieved by simultaneously dropping both minimum stress and external pore fluid pressure, inducing a large fluid pressure drop between the sample interior and its ends. Poroelastic modeling suggests that the pore fluid pressure is highest close to, but not at, the sample ends and is locally maintained at levels that meet the hydraulic fracture criterion for up to 50 s. Application of this experimental protocol to an impure sample of sandstone resulted in the generation of several hydraulic fractures subparallel to the maximum principal stress. Fracturing did not occur in a drained test on the same sample, demonstrating that the elevated pore fluid pressure was critical to fracture formation. To better understand the experimental results, we explore the role of rock permeability and storage on fracture processes using a numerical model that directly couples a lattice‐Boltzmann model for fluid mechanics with a discrete element model for solid mechanics. Like the experiment, the numerical simulations produced opening mode fractures when operated to replicate the conditions of the experiment. Fractures preferentially occur in portions of the model inferred to be mechanically weak. Local fluid pressure gradients strongly influence the state of stress in the solids and thereby fracture growth. Increasing the model permeability increases fracture propagation rate, decreases sample deformation, and increases fracture spacing. Sample deformation increases, and fracture spacing decreases, with increasing overpressure. It appears that bulk forcing of the solid via fluid seepage forces is important in fracture genesis, explaining the key roles of permeability and diffusivity in the hydrofracture process.

Load-Independent Spin Power Losses of a Spur Gear Pair: Model Formulation

A physics-based fluid mechanics model is proposed to predict spin power losses of gear pairs due to oil churning and windage. While the model is intended to simulate oil churning losses in dip-lubricated conditions, certain components of it apply to air windage losses as well. The total spin power loss is defined as the sum of (i) power losses associated with the interactions of individual gears with the fluid, and (ii) power losses due to pumping of the oil at the gear mesh. The power losses in the first group are modeled through individual formulations for drag forces induced by the fluid on a rotating gear body along its periphery and faces, as well as for eddies formed in the cavities between adjacent teeth. Gear mesh pumping losses will be predicted analytically as the power loss due to squeezing of the lubricant, as a consequence of volume contraction of the mesh space between mating gears as they rotate. The model is applied to a unity-ratio spur gear pair to quantify the individual contributions of each power loss component to the total spin power loss. The influence of operating conditions, gear geometry parameters, and lubricant properties on spin power loss are also quantified at the end. A companion paper (Seetharaman et al., 2009, “Oil Churning Power Losses of a Gear Pair: Experiments and Model Validation,” ASME J. Tribol., 131, p. 022202) provides comparisons to experiments for validation of the proposed model.

Boiling Lake of Dominica, West Indies: High‐temperature volcanic crater lake dynamics

The Boiling Lake of Dominica has exhibited stable high‐temperature behavior for at least 150 a. This stability is punctuated by occasional crises involving rapid filling and draining of the lake and changes in water temperature. The most recent such crisis occurred in December 2004 to April 2005. Using the results of previous theoretical and experimental work on analogue models, we present a combined thermal, hydrological, and fluid mechanical model of the Boiling Lake. This reveals that the lake appears to be suspended above the local water table by a constant supply of rising steam bubbles sourced from the boiling of groundwater near an igneous intrusion. The bubbles condense in the Boiling Lake, maintaining the temperature at ∼90°C. The geometry of the lake‐conduit system provides a mechanism for instability, with a denser liquid lake overlying a bubbly fractured permeable conduit. Following a sufficiently large perturbation, the whole lake rapidly drains until the surface is at the local water table level. The persistent gas supply then reinitiates filling. We propose that local seismic activity may have caused shock nucleation of bubbles within the conduit and triggered the instability of the Boiling Lake.

Capillary drawing for fabrication of photonic crystal fibers: theoretical calculation and experiments

A simplified fluid-mechanics model is developed for the drawing of silica capillaries. Calculations are carried out to predict the influence of the technical parameters on the final geometry of the capillaries. Geometrical collapse is inevitable when drawing capillaries, and active control of the parameters only helps to some extent in tuning the final structures. Drawing experiments were performed to check the theoretical calcualtions. Good agreement was obtained, which certified the validity of the model. The predictions provide valuable practical information for the fabrication of photonic crystal fibers.

Inertially driven transient response in polymeric liquids

We report here a computational study, with inertial contributions included, of the time-dependent velocity and shear stress profiles following flow start-up from rest for a polymeric liquid. Earlier workers solved similar fluid-mechanical start-up problems with viscoelastic character represented by a single Maxwell element. They found significant oscillatory departures from the steady-state velocity profile that persist throughout the entire period of stress growth to steady state. Such results are unsettling since they imply that the usual assumptions about velocity fields for transient tests of polymeric liquids are seriously in error. It turns out, however, that such oscillations are rapidly suppressed when a broad distribution of relaxation times is employed, the physically appropriate situation for polymeric liquids. The initial shear wave oscillations decay quickly compared with the time to reach the stress steady state when realistic descriptions of their viscoelastic character are employed. We note that a combination of inertial contributions with sparse relaxation spectra in fluid-mechanical modeling can lead to spurious velocity and stress field predictions for polymeric liquid flows.

Choice of In Vivo Versus Idealized Velocity Boundary Conditions Influences Physiologically Relevant Flow Patterns in a Subject-Specific Simulation of Flow in the Human Carotid Bifurcation

Accurate fluid mechanics models are important tools for predicting the flow field in the carotid artery bifurcation and for understanding the relationship between hemodynamics and the initiation and progression of atherosclerosis. Clinical imaging modalities can be used to obtain geometry and blood flow data for developing subject-specific human carotid artery bifurcation models. We developed subject-specific computational fluid dynamics models of the human carotid bifurcation from magnetic resonance (MR) geometry data and phase contrast MR velocity data measured in vivo. Two simulations were conducted with identical geometry, flow rates, and fluid parameters: (1) Simulation 1 used in vivo measured velocity distributions as time-varying boundary conditions and (2) Simulation 2 used idealized fully-developed velocity profiles as boundary conditions. The position and extent of negative axial velocity regions (NAVRs) vary between the two simulations at any given point in time, and these regions vary temporally within each simulation. The combination of inlet velocity boundary conditions, geometry, and flow waveforms influences NAVRs. In particular, the combination of flow division and the location of the velocity peak with respect to individual carotid geometry landmarks (bifurcation apex position and the departure angle of the internal carotid) influences the size and location of these reversed flow zones. Average axial wall shear stress (WSS) distributions are qualitatively similar for the two simulations; however, instantaneous WSS values vary with the choice of velocity boundary conditions. By developing subject-specific simulations from in vivo measured geometry and flow data and varying the velocity boundary conditions in otherwise identical models, we isolated the effects of measured versus idealized velocity distributions on blood flow patterns. Choice of velocity distributions at boundary conditions is shown to influence pathophysiologically relevant flow patterns in the human carotid bifurcation. Although mean WSS distributions are qualitatively similar for measured and idealized inlet boundary conditions, instantaneous NAVRs differ and warrant imposing in vivo velocity boundary conditions in computational simulations. A simulation based on in vivo measured velocity distributions is preferred for modeling hemodynamics in subject-specific carotid artery bifurcation models when studying atherosclerosis initiation and development.

Sensors for physical fluxes at the sea surface: energy, heat, water, salt

Abstract. The current status of meteorological sensors used aboard ships and buoys to measure the air-sea fluxes of momentum, heat, and freshwater is reviewed. Methods of flux measurement by the bulk aerodynamic, inertial dissipation and eddy-correlation methods are considered; and areas are identified where improvements are needed in measurement of the basic variables. In some cases, what is required is the transition from emergent to operational technology, in others new technologies are needed. Uncertainties in measured winds caused by flow distortion over the ship are discussed; and the possible role of computational fluid mechanics models to obtain corrections is considered. Basic studies are also needed on the influence of waves and rain on the fluxes. The issues involved in the specification of sea surface temperature are described, and the relative merits of the available sensors are discussed. The improved capability of buoy-mounted systems will depend on the emergence of low-power instruments, and/or new means of increasing the available power capacity. Other issues covered include the continuing uncertainty about the performance of rain gauges and short-wave radiometers. Also, the requirements for new instruments to extend the range of observations to extreme wind conditions are outlined, and the latest developments in the measurement of aerosol fluxes by eddy-correlation are presented.

Influence of cortical canal architecture on lacunocanalicular pore pressure and fluid flow

Bone is a dynamic tissue that undergoes structural modification in response to its mechanical environment, but how bone cells sense and respond to loading conditions remains incompletely understood. Current theories focus on strain-induced fluid flow for the primary means of mechanotransduction. To examine the influence of age-related cortical rarefaction on lacunocanalicular fluid characteristics, coupled fluid flow and mechanical computational models of bone specimens representing young, mid-age and aged samples were derived artificially from the same original micro-computed tomography image data. Simulated mechanical loading was applied to the bone models to induce pressure-driven interstitial fluid flow. Results demonstrated a decrease in pore pressure and fluid velocity magnitudes with age as a result of increased cortical porosity. Mean canal separation, as opposed to canal size, was implicated as a primary factor affecting age-related fluid dynamics. Future investigations through refinement of the model may implicate fluid stasis or inadequate nutrient transport experienced by osteocytes as a key factor in the initiation of cortical remodelling events.

Unsteady, three-dimensional fluid mechanic analysis of blood flow in plaque-narrowed and plaque-freed arteries

Fluid mechanic analysis is used to create and implement a metric to quantify the effectiveness of plaque removal (i.e., debulking) modalities in small arteries. The quantification is based on a three-dimensional, unsteady model of blood flow in complex tubular geometries which characterizes plaque-narrowed arteries. Blood flow unsteadiness is due to the heart-imposed temporal variations which occur during the cardiac cycle. The arterial geometries used for the analysis were determined by the reconstruction of ultrasonic images which were captured before and after debulking. Numerical simulation was used to implement the fluid mechanic model, and separate consideration is given to Newtonian and non-Newtonian constitutive equations. The results of the analysis indicates that the removal of the plaque led to an increase in the rate of blood flow of approximately 2.5, both during the systole and diastole portions of the cardiac cycle. This increase corresponds to the application of the same time-varying, end-to-end pressure difference across the artery segments. The shear stress on the artery wall, a major determinant of the buildup of plaque, is found to be higher for a debulked artery than for a plaque-narrowed artery. This outcome is favorable in that the higher the wall shear, the lower the rate of plaque formation.

Evaluation of Microgravity Heat Conductivity Measurements with FLUENT System

Microgravity experiments were executed to measure the convection free, pure heat conductivity and heat diffusivity parameters in molten metals. The application of well known numerical methods to evaluate the data collected under low gravity conditions was only partially successful. None of the methods (Crank-Nicolson, error function fitting or simple FEM model) could be used over the whole measured temperature range. The purpose of this work was to alleviate the previously experienced problems by using a commercially available finite value method package on high performance computers, to simulate the coupled thermal and fluid mechanical model in order to accurately determine the heat transport properties of Ga, Sn-Bi, Sn and Zn melts, and by incorporating device geometry data, compare the results to the values gathered from short time microgravity experiments.

Development of equine upper airway fluid mechanics model for Thoroughbred racehorses

Computational fluid dynamics (CFD) models provide the means to evaluate airflow in the upper airways without requiring in vivo experiments. The physiological conditions of a Thoroughbred racehorse's upper airway during exercise could be simulated. Computed tomography scanned images of a 3-year-old intact male Thoroughbred racehorse cadaver were used to simulate in vivo geometry. Airway pressure traces from a live Thoroughbred horse, during exercise was used to set the boundary condition. Fluid-flow equations were solved for turbulent flow in the airway during inspiratory and expiratory phases. The wall pressure turbulent kinetic energy and velocity distributions were studied at different cross-sections along the airway. This provided insight into the general flow pattern and helped identify regions susceptible to dynamic collapse. The airflow velocity and static tracheal pressure were comparable to data of horses exercising on a high-speed treadmill reported in recent literature. The cross-sectional area of the fully dilated rima glottidis was 7% greater than the trachea. During inspiration, the area of highest turbulence (i.e. kinetic energy) was in the larynx, the rostral aspect of the nasopharynx was subjected to the most negative wall pressure and the highest airflow velocity is more caudal on the ventral aspect of the nasopharynx (i.e. the soft palate). During exhalation, the area of highest turbulence was in the rostral and mid-nasopharynx, the maximum positive pressure was observed at the caudal aspect of the soft palate and the highest airflow velocity at the front of the nasopharynx. In the equine upper airway collapsible area, the floor of the rostral aspect of the nasopharynx is subjected to the most significant collapsing pressure with high average turbulent kinetic during inhalation, which may lead to palatal instability and explain the high prevalence of dorsal displacement of the soft palate (DDSP) in racehorses. Maximal abduction of the arytenoid cartilage may not be needed for optimal performance, since the trachea cross-sectional area is 7% smaller than the rima glottidis.

Arterial fluid mechanics modeling with the stabilized space–time fluid–structure interaction technique

AbstractWe present an overview of how the arterial fluid mechanics problems can be modeled with the stabilized space–time fluid–structure interaction (SSTFSI) technique developed by the Team for Advanced Flow Simulation and Modeling (T★AFSM). The SSTFSI technique includes the enhancements introduced recently by the T★AFSM to increase the scope, accuracy, robustness and efficiency of this class of techniques. The SSTFSI technique is supplemented with a number of special techniques developed for arterial fluid mechanics modeling. These include a recipe for pre‐FSI computations that improve the convergence of the FSI computations, using an estimated zero‐pressure arterial geometry, and the sequentially coupled arterial FSI (SCAFSI) technique. The recipe for pre‐FSI computations is based on the assumption that the arterial deformation during a cardiac cycle is driven mostly by the blood pressure. The SCAFSI technique, which was introduced as an approximate FSI approach in arterial fluid mechanics, is also based on that assumption. The need for an estimated zero‐pressure arterial geometry is based on recognizing that the patient‐specific image‐based geometries correspond to time‐averaged blood pressure values. In our arterial fluid mechanics modeling the arterial walls can be represented with the membrane or continuum elements, both of which are geometrically nonlinear, and the continuum element is made of hyperelastic (Fung) material. Test computations are presented for cerebral and abdominal aortic aneurysms, where the arterial geometries used in the computations are close approximations to the patient‐specific image‐based data. Copyright © 2007 John Wiley & Sons, Ltd.

Well-Posedness in Critical Spaces for Barotropic Viscous Fluids with Truly Not Constant Density

This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N ≥ 2. We address the question of well-posedness for large data having critical Besov regularity. Our sole additional assumption is that the initial density be bounded away from zero. This improves the analysis of Danchin (2001) where the smallness of for some positive constant was needed. Our result relies on a new a priori estimate for a class of parabolic systems with variable coefficients, which is likely to be useful for the investigation of other models in fluid mechanics.