Flow Path Geometry Research Articles

An Adaptive Drug Infusion System

In order to reduce the overall size and power consumption of ambulatory drug infusion systems, and to provide higher delivery accuracy, faster start-up, and more rapid occlusion detection, a non-contacting, low-power thermal time-of-flight technology has been used to provide a pressure-based miniature wearable drug infusion system that automatically compensates in real time for changes in pressure, viscosity, and flow path geometry. Prototypes have been designed, built, and tested on the bench and on animals. For liquid volumes ranging from 30 nL to 100 microL, the measured accuracy and precision of delivery were better than 1%. Tests on 30-kg swine showed delivery within the study accuracy. The performance of the prototypes demonstrates that real-time compensation of flow variables provides significant performance improvements in therapeutic infusion.

Nonlinear dynamics in flow through unsaturated fractured porous media: Status and perspectives

The need has long been recognized to improve predictions of flow and transport in partially saturated heterogeneous soils and fractured rock of the vadose zone for many practical applications, such as remediation of contaminated sites, nuclear waste disposal in geological formations, and climate predictions. Until recently, flow and transport processes in heterogeneous subsurface media with oscillating irregularities were assumed to be random and were not analyzed using methods of nonlinear dynamics. The goals of this paper are to review the theoretical concepts, present the results, and provide perspectives on investigations of flow and transport in unsaturated heterogeneous soils and fractured rock, using the methods of nonlinear dynamics and deterministic chaos. The results of laboratory and field investigations indicate that the nonlinear dynamics of flow and transport processes in unsaturated soils and fractured rocks arise from the dynamic feedback and competition between various nonlinear physical processes along with complex geometry of flow paths. Although direct measurements of variables characterizing the individual flow processes are not technically feasible, their cumulative effect can be characterized by analyzing time series data using the models and methods of nonlinear dynamics and chaos. Identifying flow through soil or rock as a nonlinear dynamical system is important for developing appropriate short‐ and long‐time predictive models, evaluating prediction uncertainty, assessing the spatial distribution of flow characteristics from time series data, and improving chemical transport simulations. Inferring the nature of flow processes through the methods of nonlinear dynamics could become widely used in different areas of the earth sciences.

Flow electrification through porous media

Abstract This paper deals with streaming current generated by water flow through 4 geological porous media. These experimental measurements and a theoretical model allow us to determine the space charge density ρW at the wall in these 4 cases and to compare these values to previous ones obtained with glass capillaries and glass porous samples. The results show that ρW is effectively the intrinsic parameter of the solid–liquid interface because it is not a function of the geometry of the fluid flow paths but it only depends on the physico–chemical properties of the solid and the liquid.

The influence of soil moisture content variations on heat losses from earth-contact structures: an initial assessment

An initial investigation of the influence of varying ground moisture content beneath buildings on the heat losses through ground floor slabs is presented. A range of finite element analyses have been performed that indicate that soil moisture content changes can have a significant effect on soil thermal conductivity and hence on ground heat transfer. The work is undertaken for conditions of static moisture content distributions. For the particular problems considered, the results obtained show that total heat flux to the ground can increase significantly with decreasing ground water table depth. Steady-state heat conduction analyses were performed for three test problems; a one-dimensional problem, a two-dimensional shallow earth-contact structure and a two-dimensional “deep” earth-sheltered structure. Each problem was analysed for water table depths ranging from 10 m to zero (i.e. the ground surface). The resulting increase in soil moisture content was found to cause a 60% increase in heat flux in the one-dimensional problem, a 20% increase for the two-dimensional shallow structure and 40% for the deep structure. The variation between types of analysis is due to the heat flow path geometry available in each case. The work is viewed as a further step towards a more complete understanding of the influence of ground moisture content on heat transfer problems. The conclusions drawn should be viewed as a first indication of the significance of this aspect of the problem and need to be considered separately from other work on the influence of ground water flow beneath the water table. The results also suggest that transient effects and coupling of heat and moisture transfer processes merit further attention.

Prediction of Pressure Drop in Non-Woven Filter Media Using a Hagen-Poiseuille Model

An accurate estimation of the pressure drop across filter media is not an easy task considering the randomness of pore size and shape, and complexity in geometry of flow paths, particularly for non-woven depth filters. The pioneering work of Darcy laid the foundation of pressure flow characteristics through sand beds. This was followed by the work of Kozeny who proposed a theory to determine the pore size using porosity as a parameter. Carman modified the porosity-permeability relationship further to suit experimental results more closely. The pressure drop relationship using this expression is known as Kozeny-Carman equation. In the present work, the prediction results of Kozeny and Kozeny-Carman equations have been compared with those obtained from the Hagen-Poiseuille model which include the effect of tortuosity. The results indicate that the introduction of tortuosity effect alone can improve the prediction based on the Hagen-Poiseuille model over the Kozeny model, which underestimates the pressure drop across the filter media.

Control of jet engines

Feedback control has always been an essential part of jet engines because they operate at or near their mechanical or aerothermal limitations. In this paper, the basics of controlling an engine while satisfying numerous constraints will be reviewed. The emphasis will be on commercial engines though most of the material is also applicable to military engines. In the first part, a simplified theory of engine operation is discussed in terms of the basic principles and limitations for each component. The second part of the paper discusses overall control requirements and typical sensors and actuators. Finally various control strategies are presented. It is shown that much of the complexity of the control comes from the need to operate the engine as close as possible to its limits. In a commercial engine, this results in a series of single input single output controllers. The case for multivariable control can be more strongly made for military engines especially those with additional flowpath geometry actuators such as a variable cycle or advanced short takeoff and landing engines.

The Effect of Inlet Boundary Layer Thickness on the Flow Within an Annular S-Shaped Duct

Experimental and numerical investigations were carried out to gain a better understanding of the flow characteristics within an annular S-shaped duct, including the effect of the inlet boundary layer (IBL) on the flow. A duct with six struts and the same geometry as that used to connect compressor spools on our experimental small two-spool turbofan engine was investigated. A curved downstream annular passage with a similar meridional flow path geometry to that of the centrifugal compressor has been fitted at the exit of S-shaped duct. Two types of the IBL (i.e., thin and thick IBL) were used. Results showed that large differences of flow pattern were observed at the S-shaped duct exit between two types of the IBL, though the value of “net” total pressure loss has not been remarkably changed. According to “overall” total pressure loss, which includes the IBL loss, the total pressure loss was greatly increased near the hub as compared to that for a thin one. For the thick IBL, a vortex pair related to the hub-side horseshoe vortex and the separated flow found at the strut trailing edge has been clearly captured in the form of the total pressure loss contours and secondary flow vectors, experimentally and numerically. The high-pressure loss regions on either side of the strut wake near the hub may act on a downstream compressor as a large inlet distortion, and strongly affect the downstream compressor performance. There is a much-distorted three-dimensional flow pattern at the exit of S-shaped duct. This means that the aerodynamic sensitivity of S-shaped duct to the IBL thickness is very high. Therefore, sufficient care is needed to design not only downstream aerodynamic components (for example, centrifugal impeller) but also upstream aerodynamic components (LPC OGV).

Two Constructal Routes to Minimal Heat Flow Resistance via Greater Internal Complexity

This paper shows that the geometry of the heat flow path between a volume and one point can be optimized in two fundamentally different ways. In the “growth” method of the original constructal theory the structure is optimized starting from the smallest volume element of fixed size. Growth, or optimal numbers of constituents assembled into larger volumes, is one route to resistance minimization. In the “design” method the overall volume is fixed, and the designer works “inward” by optimizing the internal features of the heat flow path. The design method is new. It is shown analytically that the two methods produce comparable geometric results in which the high-conductivity channels form constructal tree networks, and where the low-conductivity material fills the interstices. For simplicity, it is assumed that the high-conductivity channels and their tributaries make 90-deg angles. In both approaches, the overall resistance decreases as the internal complexity of the conductive composite increases. In the growth method the number of constituents in each assembly can be optimized. In the design method, some of the constituent numbers cannot be optimized: these numbers assume the roles of weak parameters. The growth method is the simplest, and provides a useful approximation of the design and performance that can be achieved using the design method. Numerical solutions of the volume-to-point optimization problem confirm the results obtained analytically, and show that the geometric features of the optimal design are robust.

The Influence of Downstream Passage on the Flow Within an Annular S-Shaped Duct

Experimental and numerical investigations were carried out to gain a better understanding of the flow characteristics within an annular S-shaped duct, including the influence of the shape of the downstream passage located at the exit of the duct on the flow. A duct with six struts and the same geometry as that used to connect the compressor spools on our new experimental small two-spool turbofan engine was investigated. Two types of downstream passage were used. One type had a straight annular passage and the other a curved annular passage with a meridional flow path geometry similar to that of the centrifugal compressor. Results showed that the total pressure loss near the hub is large due to instability of the flow, as compared with that near the casing. Also, a vortex related to the horseshoe vortex was observed near the casing. In the case of the curved annular passage, the total pressure loss near the hub was greatly increased compared with the case of the straight annular passage, and the spatial position of this vortex depends on the passage core pressure gradient. Furthermore, results of calculation using an in-house-developed three-dimensional Navier–Stokes code with a low-Reynolds-number k–ε turbulence model were in good qualitative agreement with experimental results. According to the simulation results, a region of very high pressure loss is observed near the hub at the duct exit with the increase of inlet boundary layer thickness. Such regions of high pressure loss may act on the downstream compressor as a large inlet distortion, and strongly affect downstream compressor performance.

Constructal tree networks for the time-dependent discharge of a finite-size volume to one point

This paper shows that the time needed to discharge a volume to a concentrated sink can be minimized by making appropriate changes in the geometry of the flow path. The time-dependent flow of heat between a volume and one point is chosen for illustration, however, the same geometric optimization method (the constructal principle) holds for other transport processes (fluid flow, mass transfer, conduction of electricity). There are two classes of geometric degrees of freedom in designing the flow path: the external shape of the volume, and the distribution (amount, location, orientation) of high-conductivity inserts that facilitate the volumetric collection of the discharge. The optimization of flow path geometry is executed in a sequence of steps that starts with the smallest volume elements and proceeds toward larger and more complex volume sizes (first constructs, second constructs, etc.). Every geometric feature is the result of minimizing the time of discharge, or the resistance in volume-to-point flow. The innermost details of the structure have only a minor effect on the minimized time of discharge. The high-conductivity inserts come together into a tree-network pattern which is the result of a completely deterministic principle. The interstices are equally important in this optimal design, as they are occupied by the low-conductivity material in which the energy charge was stored initially. The paper concludes with a discussion of the relevance on this deterministic principle—the constructal law—to predicting structure in natural flow, and to understanding why the geometry of nature is not fractal.

Linear scale ultrafiltration

Tangential flow filtration has traditionally been scaled up by maintaining constant the filtrate volume to membrane surface area ratio, membrane material and pore size, channel height, flow path geometry and retentate and filtrate pressures. Channel width and the number of channels have been increased to provide increased membrane area. Several other parameters, however, have not been maintained constant. A new comprehensive methodology for implementation of linear scale up and scale down of tangential flow filtration processes has been developed. Predictable scale up can only be achieved by maintaining fluid dynamic parameters which are independent of scale. Fluid dynamics are controlled by operating parameters (feed flow rate, retentate pressure, fed batch ratio and temperature), geometry (channel length, height, turbulence promoter and entrance/exit design), materials (membrane, turbulence promoter, and encapsulant compression), and system geometry (flow distribution). Cassette manufacturing procedures and tolerances also play a significant role in achieving scale independent performance. Extensive development work in the aforementioned areas has resulted in the successful implementation of linear scale up of ultrafiltration processes for recovery of human recombinant DNA derived pharmaceuticals. A 400-fold linear scale up has been achieved without intermediate pilot scale tests. Scale independent performance has a direct impact on process yield, protein quality and product economics and is therefore particularly important in the biotechnology industry. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 737-746, 1997.

Design and Test of a New Axial Compressor for the Nuovo Pignone Heavy-Duty Gas Turbines

This axial compressor design was primarily focused to increase the power rating of the current Nuovo Pignone PGT10 Heavy-Duty gas turbine by 10 percent. In addition, the new 11-stage design favorably compares with the existing 17-stage compressor in terms of simplicity and cost. By scaling the flowpath and blade geometry, the new aerodynamic design can be applied to gas turbines with different power ratings as well. The reduction in the stage number was achieved primarily through the meridional flowpath redesign. The resulting higher blade peripheral speeds achieve larger stage pressure ratios without increasing the aerodynamic loadings. Wide chord blades keep the overall length unchanged thus assuring easy integration with other existing components. The compressor performance map was extensively checked over the speed range required for two-shaft gas turbines. The prototype unit was installed on a special PGT10 gas turbine setup, that permitted the control of pressure ratio independently from the turbine matching requirements. The flowpath instrumentation included strain gages, dynamic pressure transducers, and stator vane leading edge aerodynamic probes to determine individual stage characteristics. The general blading vibratory behavior was proved fully satisfactory. With minor adjustments to the variable stator settings, the front stage aerodynamic matching was optimized and the design performance was achieved.

Field-scale colloid migration experiments in a granite fracture

An understanding of particle migration in fractured rock, required to assess the potential for colloid-facilitated transport of radionuclides, can best be evaluated when the results of laboratory experiments are demonstrated in the field. Field-scale migration experiments with silica colloids were carried out at AECL's Underground Research Laboratory (URL), located in southern Manitoba, to develop the methodology for large-scale migration experiments and to determine whether colloid transport is possible over distances up to 17 m. In addition, these experiments were designed to evaluate the effects of flow rate and flow path geometry, and to determine whether colloid tracers could be used to provide additional information on subsurface transport to that provided by conservative tracers alone. The colloid migration studies were carried out as part of AECL's Transport Properties in Highly Fractured Rock Experiment, the objective of which was to develop and demonstrate methods for evaluating the solute transport characteristics of zones of highly fractured rock. The experiments were carried out within fracture zone 2 as two-well recirculating, two-well non-recirculating, and convergent flow tests, using injection rates of 5 and 10 1 min −1. Silica colloids with a 20 nm size were used because they are potentially mobile due to their stability, small size and negative surface charge. The shapes of elution profiles for colloids and conservative tracers were similar, demonstrating that colloids can migrate over distances of 17 m. The local region of drawdown towards the URL shaft affected colloid migration and, to a lesser extent, conservative tracer migration within the flow field established by the two-well tracer tests. These results indicate that stable colloids, with sizes as small as 20 nm, have different migration properties from dissolved conservative tracers. - 1997 Atomic Energy of Canada.

Analysis of colloid and tracer breakthrough curves

We consider the dispersion and elution of colloids and dissolved nonsorbing tracers within saturated heterogeneous porous media. Since flow path geometry in natural systems is often ill-characterized macroscopic (mean) flow rates and dispersion tensors are utilized in order to account for the sub-model scale microscopic fluctuations in media structure (and the consequent hydrodynamic profile). Even for tracer migration and dispersal this issue is far from settled. Here we consider how colloid and tracer migration phenomena can be treated consistently. Theoretical calculations for model flow geometries yield two quantitative predictions for the transport of free (not yet captured) colloids with reference to a non-sorbing dissolved tracer within the same medium: the average migration velocity of the free colloids is higher than that of the tracer; and that the ratio of the equivalent hydrodynamic dispersion rates of colloids and tracer is dependent only upon properties of the colloids and the porous medium, it is independent of pathlengths and fluid flux, once length scales are large enough. The first of these is well known, since even in simple flow paths free colloids must stay more centre stream. The second, if validated suggests how solute and colloid dispersion may be dealt with consistently in macroscopic migration models. This is crucial since dispersion is usually ill-characterized and unaddressed by the experimental literature. In this paper we present evidence based upon an existing Drigg field injection test for the validity of these predictions. We show that starting from experimental data the fitted dispersion rates of both colloids and non-sorbing tracers increase with the measured elution rates (obeying slightly different rules for tracers and colloids); and that the ratio of colloid and nonsorbing tracer elution rates, and the ratio of colloid and nonsorbing tracer dispersion rates may be dependent upon properties of the colloids and the medium (not the flow regime). It is important to realize that even for unretarded species, an earlier peak in the breakthrough curve does not necessarily correspond to a faster mean elution rate, or vice versa. But rather that a colloid may elute faster but disperse less than an equivalent tracer. Hence its peak may be retarded compared to that of the tracer, even assuming no retardation. Hence one must consider a combination of mean elution rate and mean dispersion rate, and not rely on “peak times” to corroborate chromatographic effects. The importance of this lies in the fact that these processes are not independent and yet upscale differently. Thus realistic estimates of effective colloid dispersion rates should be upscaled in a way consistent with that adopted for tracers within the same system.

A CHANNEL NETWORK MODEL FOR CHEMICAL MIGRATION IN SUBSURFACE MEDIA

We consider the migration of chemical species through saturated heterogeneous media, where the scale of the flow path geometry is large enough to invalidate a Fickian based, representative elementary volumes, approach to dispersal. Channel network models combine the effects of channeling over small spatial scales with network mixing which gives rise to an equivalent dispersion effect over large spatial scales. We extend equations and solutions given previously for ideal nonabsorbing tracers, to include the retardation of chemically active species. The primary aim is to derive explicit solutions for future calibration purposes, and illustrate scale dependent dispersive behavior with and without chemical absorption processes. In this paper we develop a twin channel model allowing for various specification of the retardation process. This allows the retardation to be either positively or negatively correlated with pathway apertures (which are in turn related directly to flow rates of the respective channels). We show that if absorption is controlled by specific surface area, then a scaling argument infers that highly transmissive paths are also less retarding. We illustrate the model’s applicability to such cases. We shall discuss the scale dependence of calculated (observed) equivalent dispersivities obtained by analyzing the moments of breakthrough curves at various distances. For a range of parameter values we exhibit scaling behavior similar to that observed in the field and laboratory. This does not necessarily imply any validity to the approach: it is a direct consequence of deferring the network — mixing effect to large length scales. An important point of consideration is that wherever conceptual model choices must be made, in modeling natural processes such as chemical migration, there is a possibility of biasing calculations by sole reliance on a particular approach. Channel network models marry channeling models and classical Fickian models. Thus in calibrating a model such as the Twin Channel model from given experimental behavior, we can immediately estimate over which scales channeling or Fickian dispersive effects are likely to be dominant.

不連続性岩盤内の透水性の不均一性と流れの局所化について

This paper describes a relationship between heterogeneous permeability profile and the geometry of localized flow paths based on a laboratory experiment. A 30cm cube of chert containing multiple sets of natural fractures is used for the study. Each of the six faces of the block is divided into 25 hydraulically isolated subpanels, i.e. 150 subpanels in total, which are connected to a separate flow line for control or monitoring. The pressure and flow responses under different boundary conditions are inverted to provide information on the spatial variation of hydraulic conductivity. It has been shown that, because of the wide variation in permeability, the limited number of high permeability zones are creating localized flow paths which controll the overall flow characteristics in a fractured chert block.

Steady groundwater flow as a dynamical system

Dynamical systems describe the time evolution of moving spatial points under the influence of a smooth, bounded vector field. The theory of these systems is focused on the global properties of their flow paths, not on their integration, and so gives general, qualitative information that does not depend on the details of the spatial variability of the vector field. This approach was applied to describe the global consequences of the Darcy law for steady groundwater flows in isotropic, heterogeneous aquifers. No particular model of the spatial variability of the hydraulic conductivity (K) was assumed. Vorticity in the flow paths was shown to exist wherever isoconductivity and equipotential surfaces intersect transversely, and the importance of the Lamb vector (the vector product of vorticity and specific discharge) for the geometry of flow paths was established. Because steady groundwater flows governed by the Darcy law have zero helicity, they cannot exhibit tangled vorticity lines or become chaotic. The absence of chaos is related closely to the impossibility of closed flow paths, the asymptotic stability of isolated minima of the hydraulic head (H), and the existence of a function ℋ(K, H) on whose level surfaces all flow paths are confined. This last function also permits groundwater flows to be represented by moving points in the K, H plane, with motion there generated by a form of Hamilton's equations. The results obtained are not related to any stochastic approach to aquifer spatial variability, but instead may be applied to constrain stochastic models on purely dynamical grounds.

Geometry of flow paths for fluid transport in rocks : David, C J Geophys ResV98, NB7, July 1993, P12267–12278

Geometry of flow paths for fluid transport in rocks : David, C J Geophys ResV98, NB7, July 1993, P12267–12278

Geometry of flow paths for fluid transport in rocks

Results from numerical simulations on two‐dimensional networks used as an analog to pore space in porous rocks are presented to emphasize the existence of preferential paths for transport processes in heterogeneous media. The simulations show that hydraulic flow and electrical current are mostly driven in the so‐called “critical paths” when the pore size distribution has a decreasing exponential‐like shape in opposition to nearly homogeneous or uniform like distributions. The geometry of these flow paths is controlled by spatially correlated large conductances and can be described by a tortuosity factor, τ2. The amount of flow carried by the critical paths is higher than that predicted by statistical or effective medium models which do not take into account the role of spatial correlation. Another interesting result is that the geometry of the critical paths may change in response to alterations in the properties of the pore space, like, for example, the reduction in connectivity due to pressure‐induced pore closure. The simulations also show that the critical paths for hydraulic flow are different from those for electrical current. A statistical analysis shows that the hydraulic tortuosity is higher than the electrical tortuosity by a factor of 1.5 on the average which implies that one must be cautious in using the electrical tortuosity in the equivalent channel model for determining the permeability of rocks. As the numerical simulations have been done on distributions of pore or crack geometries typically encountered in rocks, the existence of critical paths highlighted in this paper is likely to play an important role in the phenomenology of transport processes in the Earth's crust.

The fractal geometry of flow paths in natural fractures in rock and the approach to percolation

The fractal geometry of flow paths in natural fractures in rock and the approach to percolation