Inertial Effects

In this work, we have theoretically re-visited the capillary rise process into a circular tube for very short time scales, retaining in this manner, the physical influence of the inertial effects. We use the boundary-layer technique or matched asymptotic expansion procedure in order to treat this singular problem by identifying two appropriate time scales: one short time scale related with inertial effects, , and the other, , the large scale which is basically associated with imbibition effects. Considering that the well-known Washburn's law was derived by neglecting the inertial effects, the corresponding solution has a singular behavior for short times, which is reflected by an infinite mass flow rate. Then, for this purpose we derive a zero-order solution which is enough to avoid the singular behavior of the solution. In this manner, the Washburn's solution represents only the external solution only valid for the large time scale . The above analytical result is compared with a numerical solution including the case when the contact angle between the meniscus and the inner surface of the capillary tube becomes a dynamic contact angle. On the other hand, the presence of inertial effects can induce oscillations of the imbibition front which are controlled by the dynamic contact angle. Therefore, in the present work we predict a global asymptotic formula for the temporal evolution of the height of the liquid. In order to show the importance of the inertial terms, we present this evolution for different values of the dimensionless parameters involved in the analysis.

In this work, we have theoretically re-visited the capillary rise process into a circular tube for very short time scales, retaining in this manner, the physical influence of the inertial effects. We use the boundary-layer technique or matched asymptotic expansion procedure in order to treat this singular problem by identifying two appropriate time scales: one short time scale related with inertial effects, , and the other, , the large scale which is basically associated with imbibition effects. Considering that the well-known Washburn's law was derived by neglecting the inertial effects, the corresponding solution has a singular behavior for short times, which is reflected by an infinite mass flow rate. Then, for this purpose we derive a zero-order solution which is enough to avoid the singular behavior of the solution. In this manner, the Washburn's solution represents only the external solution only valid for the large time scale. The above analytical result is compared with a numerical solution including the case when the contact angle between the meniscus and the inner surface of the capillary tube becomes a dynamic contact angle. On the other hand, the presence of inertial effects can induce oscillations of the imbibition front which are controlled by the dynamic contact angle. Therefore, in the present work we predict a global asymptotic formula for the temporal evolution of the height of the liquid. In order to show the importance of the inertial terms, we present this evolution for different values of the dimensionless parameters involved in the analysis.

In many large-scale industrial applications dealing with particle-laden viscoelastic fluids, the ensemble-averaged behavior of the mixture is of most interest. The first step to parametrize this behavior is to develop an accurate expression to rapidly evaluate the drag coefficient over a broad range of kinematic parameters. The drag coefficient of a spherical particle translating in a viscoelastic matrix is strongly affected by the viscoelasticity of the fluid. In this study, we aim to parametrize the effects of fluid elasticity, especially the relaxation and retardation times, as well as inertia on the drag coefficient of a sphere translating in a viscoelastic fluid described by the Oldroyd-B model. To this end, we employed three-dimensional direct numerical simulations of viscoelastic flow past a stationary sphere. The accuracy of the numerical formulation is thoroughly tested against a number of benchmark problems consisting of steady flow past a sphere in a bounded circular or square domain filled with either a Newtonian or viscoelastic fluid. Initially, the numerical computations for the drag coefficient over a wide range of geometric and flow parameters are validated by comparison with existing data and drag correction models from the literature. The drag coefficient correction is then evaluated for unconfined flow past a sphere at different Reynolds number, Re , over a wide range of Deborah number, De < 9, and polymer viscosity ratio, 0 < < 1. For small Deborah number (De < 1), the drag coefficient decreases with respect to the Stokes drag coefficient, whereas, at large Deborah number (De > 1), the drag is enhanced due to the large elastic stresses that develop on both the surface and wake of the sphere. These canonical behaviors, observed in the inertia-less flow regime (Re ≤ 1) are amplified as the polymer viscosity ratio approaches unity. At higher Reynolds numbers (Re > 1), the drag coefficient correction arising from viscoelasticity is found to be always bigger than unity, but smaller than the enhancement calculated in the creeping flow limit. In this regime, the formation of an axisymmetric recirculating eddy expands the wake region behind the sphere, and shifts the maximum elastic stresses away from the rear stagnation point towards the flow separation points. Motivated by the self-similarity observed at Re < 1, we propose an approximate model for the viscoelastic drag coefficient based on rational functions, using the lowest possible degree of polynomial functions required to fit the computational data with 95% accuracy, for De ≤ 5 and 0 < < 1. This expression is a key step towards formulating a momentum-exchange model for the flow of dilute suspensions of solid particles in a viscoelastic matrix.

This work focuses on the stationary one-phase Newtonian flow in a class of homogeneous porous media at large enough flow rates leading to a non-linear relationship between the filtration velocity and the pressure gradient. A numerical analysis of the non linear -inertialcorrection to Darcy&#39;s law is carried out for model periodic structures made of arrays of square-section cylinders. The global aim is to determine and analyze the effective properties appearing in the macroscopic model resulting from the volume averaging of the mass and momentum (Navier-Stokes) equations at the pore scale                                     v f K v F K v c . p . . p . The effective permeability tensor, K, and the inertial tensor, F, are obtained by solving the microscopic flow and also the closure problems resulting from upscaling. From extensive analysis, general features of the tensor F and normalized correction fc for ordered structures (regular array of cyli...

Our interest in this work is the stationary one-phase Newtonian flow in a class of homogeneous porous media at large enough flow rates so that the relationship between the filtration velocity and the pressure gradient is no longer linear. The non linear -inertialcorrection to Darcy&#39;s law is investigated from a numerical point of view on model periodic structures made of regular arrays of cylinders. The starting point of the analysis is the macroscopic model resulting from the volume averaging of the mass and momentum (NavierStokes) equations at the pore scale. Identification of the macroscopic properties in this model is made by first solving the microscopic flow as well as the closure problem resulting from the upscaling. From these solutions, the inertial correction is computed and analyzed with respect to the Reynolds number and the pressure gradient orientation relative to the principal axes of the periodic unit cell. Our results indicate that, in the general case, for order...

We perform an experimental analysis of the exchange flow between an elasto-viscoplastic thixotropic material above a less dense Newtonian oil inside a vertical tube. This situation is usually found in cementing plug operations, performed in the oil industry when there is a need to abandon an oil well. The experiments show that three different flow regimes are observed, namely unstable, quasi-stable, and stable (no flow). The unstable regime is a wavy core-annular flow with the denser liquid in the core region. In the quasi-stable regime a slow plug flow starts after a time delay, which is a consequence of thixotropic and elastic effects. Through analysis of the experimental results it is possible to identify, for a given pair of fluids, the region in the governing parameter space, within which the exchange speed is sufficiently low (or zero).

We investigate the performance of the finite volume method in solving viscoplastic flows. The square lid-driven cavity flow of a Bingham plastic is chosen as the test case and the constitutive equation is regularised as proposed by Papanastasiou [J. Rheol. 31 (1987) 385-404]. The numerical results obtained for Bingham numbers up to 10 and Reynolds numbers up to 5000 compare favourably with reported results obtained through other methods. The effects of the Reynolds and Bingham numbers are also investigated. It is shown that the convergence rate of the standard SIMPLE pressure-correction algorithm, which is used to solve the algebraic equation system that is produced by the finite volume discretisation, severely deteriorates as the Bingham number increases, with a corresponding increase in the non-linearity of the equations. Using the SIMPLE algorithm in a multigrid context [Syrakos & Goulas, Int. J. Numer. Methods Fluids 52 (2006) 1215-1245] dramatically improves convergence, although the multigrid convergence rates are not as high as those for Newtonian flows.

We provide benchmark results for a transient variant of the lid-driven cavity problem, where the lid motion is suddenly stopped and the flow is left to decay under the action of viscosity. Results include Newtonian as well as Bingham flows, the latter having finite cessation times, for Reynolds numbers Re ∈ [1, 1000] and Bingham numbers Bn ∈ [0, 10]. The finite-volume method and Papanastasiou regularisation were employed. A combination of Re and Bn, the effective Reynolds number, is shown to convey more information about the flow than either Re or Bn alone. A time scale which characterises the flow independently of the geometry and flow parameters is proposed.

We extend our recent work on the creeping flow of a Bingham fluid in a lid-driven cavity, to the study of inertial effects, using a finite volume method and the Papanastasiou regularisation of the Bingham constitutive model [J. Rheology 31 (1987) 385-404]. The finite volume method used belongs to a very popular class of methods for solving Newtonian flow problems, which use the SIMPLE algorithm to solve the discretised set of equations, and have matured over the years. By regularising the Bingham constitutive equation it is easy to extend such a solver to Bingham flows since all that this requires is to modify the viscosity function. This is a tempting approach, since it requires minimum programming effort and makes available all the existing features of the mature finite volume solver. On the other hand, regularisation introduces a parameter which controls the error in addition to the grid spacing, and makes it difficult to locate the yield surfaces. Furthermore, the equations become stiffer and more difficult to solve, while the discontinuity at the yield surfaces causes large truncation errors. The present work attempts to investigate the strengths and weaknesses of such a method by applying it to the lid-driven cavity problem for a range of Bingham and Reynolds numbers (up to 100 and 5000 respectively). By employing techniques such as multigrid, local grid refinement, and an extrapolation procedure to reduce the effect of the regularisation parameter on the calculation of the yield surfaces (Liu et al. J. Non-Newtonian Fluid Mech. 102 (2002) 179-191), satisfactory results are obtained, although the weaknesses of the method become more noticeable as the Bingham number is increased.

In this work, we have theoretically re-visited the capillary rise process into a circular tube for very short time scales, retaining in this manner, the physical influence of the inertial effects. We use the boundary-layer technique or matched asymptotic expansion procedure in order to treat this singular problem by identifying two appropriate time scales: one short time scale related with inertial effects, , and the other, , the large scale which is basically associated with imbibition effects. Considering that the well-known Washburn's law was derived by neglecting the inertial effects, the corresponding solution has a singular behavior for short times, which is reflected by an infinite mass flow rate. Then, for this purpose we derive a zero-order solution which is enough to avoid the singular behavior of the solution. In this manner, the Washburn's solution represents only the external solution only valid for the large time scale. The above analytical result is compared with a numerical solution including the case when the contact angle between the meniscus and the inner surface of the capillary tube becomes a dynamic contact angle. On the other hand, the presence of inertial effects can induce oscillations of the imbibition front which are controlled by the dynamic contact angle. Therefore, in the present work we predict a global asymptotic formula for the temporal evolution of the height of the liquid. In order to show the importance of the inertial terms, we present this evolution for different values of the dimensionless parameters involved in the analysis.

Our interest in this work is dedicated to the dependence upon the filtration velocity (or Reynolds number) of the inertial correction to Darcy&#39;s law for one-phase flow in homogeneous porous media. The starting point of our analysis is the averaged flow model operating at Darcy&#39;s scale. It shows that the inertial correction to Darcy&#39;s law involves a second order tensor that can be determined from the solution of the associated closure problem requiring the microscopic (pore-scale) velocity field. Numerical solutions achieved on 2D model structures are presented. The accent is laid upon the role of the Reynolds number, pressure gradient orientation and structural parameters such as porosity and structural disorder. The Forchheimer type of correction, exhibiting a quadratic dependence upon the filtration velocity, is discussed in different situations.

The purpose of this work is to propose a derivation of a macroscopic model for a certain class of inertial two-phase, incompressible, Newtonian fluid flow through homogenous porous media. The starting point of the procedure is the pore-scale boundary value problem given by the continuity and Navier–Stokes equations in each phase β and γ along with boundary conditions at interfaces. The method of volume averaging is employed subjected to a series of constraints for the development to hold. These constraints are on the lengthand time-scales, as well as, on some quantities involving capillary, Weber and Reynolds numbers that define the class of two-phase flow under consideration. The development also assumes that fluctuations of the curvature of the fluid–fluid interfaces are unimportant over the unit cell representing the porous medium. Under these circumstances, the resulting macroscopic momentum equation, for the -phase ( = , ) relates the gradient of the phase-averaged pressure p t...

We perform an experimental analysis of the exchange flow between an elasto-viscoplastic thixotropic material above a less dense Newtonian oil inside a vertical tube. This situation is usually found in cementing plug operations, performed in the oil industry when there is a need to abandon an oil well. The experiments show that three different flow regimes are observed, namely unstable, quasi-stable, and stable (no flow). The unstable regime is a wavy core-annular flow with the denser liquid in the core region. In the quasi-stable regime a slow plug flow starts after a time delay, which is a consequence of thixotropic and elastic effects. Through analysis of the experimental results it is possible to identify, for a given pair of fluids, the region in the governing parameter space, within which the exchange speed is sufficiently low (or zero).

In this work, we have theoretically re-visited the capillary rise process into a circular tube for very short time scales, retaining in this manner, the physical influence of the inertial effects. We use the boundary-layer technique or matched asymptotic expansion procedure in order to treat this singular problem by identifying two appropriate time scales: one short time scale related with inertial effects, , and the other, , the large scale which is basically associated with imbibition effects. Considering that the well-known Washburn's law was derived by neglecting the inertial effects, the corresponding solution has a singular behavior for short times, which is reflected by an infinite mass flow rate. Then, for this purpose we derive a zero-order solution which is enough to avoid the singular behavior of the solution. In this manner, the Washburn's solution represents only the external solution only valid for the large time scale. The above analytical result is compared with a numerical solution including the case when the contact angle between the meniscus and the inner surface of the capillary tube becomes a dynamic contact angle. On the other hand, the presence of inertial effects can induce oscillations of the imbibition front which are controlled by the dynamic contact angle. Therefore, in the present work we predict a global asymptotic formula for the temporal evolution of the height of the liquid. In order to show the importance of the inertial terms, we present this evolution for different values of the dimensionless parameters involved in the analysis.

The present analytical work discusses the outcomes of a series of 1-g shaking table experimental tests that were carried out to validate numerical models formulated for kinematic and inertial interaction effects on pile-supported systems. Towards this aim, pile models in layered sand deposits were built in the laboratory; such models were subjected to several cyclic tests and an ensemble of earthquake loading. The piles were densely instrumented with accelerometers and strain gauges; therefore, earthquake response, including bending strains along their length, could be measured directly. Different configurations were considered for the shake-table tests; the latter configurations include free-head piles and single-degree-offreedom (SDOF) systems with short and long caps at foundation level. The experimental data have been assessed accurately to estimate the period elongation of the SDOF structures, if any. Additionally, comparisons between the soil free-field response derived experimentally and advanced numerical simulations are also included. The results of the analyses show that the period elongations of the SDOF structure caused by pile-soil-interactions may be significant, thus affecting the evaluation of structural response under earthquake loading. Implications on the assessment of existing structures and the design of new ones are discussed.

In this work, we have theoretically re-visited the capillary rise process into a circular tube for very short time scales, retaining in this manner, the physical influence of the inertial effects. We use the boundary-layer technique or matched asymptotic expansion procedure in order to treat this singular problem by identifying two appropriate time scales: one short time scale related with inertial effects, , and the other, , the large scale which is basically associated with imbibition effects. Considering that the well-known Washburn's law was derived by neglecting the inertial effects, the corresponding solution has a singular behavior for short times, which is reflected by an infinite mass flow rate. Then, for this purpose we derive a zero-order solution which is enough to avoid the singular behavior of the solution. In this manner, the Washburn's solution represents only the external solution only valid for the large time scale. The above analytical result is compared with a numerical solution including the case when the contact angle between the meniscus and the inner surface of the capillary tube becomes a dynamic contact angle. On the other hand, the presence of inertial effects can induce oscillations of the imbibition front which are controlled by the dynamic contact angle. Therefore, in the present work we predict a global asymptotic formula for the temporal evolution of the height of the liquid. In order to show the importance of the inertial terms, we present this evolution for different values of the dimensionless parameters involved in the analysis.

A Smoothed Particle Hydrodynamics axisymmetric solver was developed in order to simulate the collapse of a single cavitation bubble close to an elastic-plastic material and study plasticity formation and hence material erosion. Findings indicate the relative importance of the material deformation due to the impact of the micro-jet and the shock wave that develop during collapse. A shock-wave dominated impact has a much higher material erosion ability compared to a micro-jet impact. Strain rate is found to have a significant effect on plastic deformation, with an overestimation of the plastic deformation up to 60% if strain rate effects are neglected in the case of stainless steel A2205. We also demonstrate that, although the impact pressure is maximum just below the collapsing bubble, maximum plastic strain occurs at a radial offset from the symmetry axis. This is the result of inertial effects that have an impact on both the magnitude and the position of the plastic domain in the material. A new non-dimensional parameter called effective pressure is introduced that can predict plastic strain location accurately for higher stand-off ratios. Alternatively, a characteristic time analysis also shows that it can be used for prediction of plastic strain zone in the solid for detached cavities.

In this work, we have theoretically re-visited the capillary rise process into a circular tube for very short time scales, retaining in this manner, the physical influence of the inertial effects. We use the boundary-layer technique or matched asymptotic expansion procedure in order to treat this singular problem by identifying two appropriate time scales: one short time scale related with inertial effects, , and the other, , the large scale which is basically associated with imbibition effects. Considering that the well-known Washburn's law was derived by neglecting the inertial effects, the corresponding solution has a singular behavior for short times, which is reflected by an infinite mass flow rate. Then, for this purpose we derive a zero-order solution which is enough to avoid the singular behavior of the solution. In this manner, the Washburn's solution represents only the external solution only valid for the large time scale. The above analytical result is compared with a numerical solution including the case when the contact angle between the meniscus and the inner surface of the capillary tube becomes a dynamic contact angle. On the other hand, the presence of inertial effects can induce oscillations of the imbibition front which are controlled by the dynamic contact angle. Therefore, in the present work we predict a global asymptotic formula for the temporal evolution of the height of the liquid. In order to show the importance of the inertial terms, we present this evolution for different values of the dimensionless parameters involved in the analysis.

Primary cementing is the well construction operation where drilling fluid is displaced from the annular space behind the casing string, and replaced by a cement slurry. The annular cement sheath is a critical barrier element that should provide zonal isolation along the well and prevent uncontrolled flow of formation fluids to the environment. We present a combined experimental and computational study of reverse circulation displacement of the annulus, corresponding to operations where cementing fluids are pumped down the annulus from the surface. We focus on iso-viscous displacements in a vertical and concentric annulus, and vary the density hierarchy among the fluids to study both stable and density-unstable displacement conditions. While the interface between the two fluids is advected according to the laminar annular velocity profile for density-stable and iso-dense displacements, considerable secondary flows and fluid mixing is observed for density-unstable cases. Increasing th...

The flow in three-dimensional fibrous porous media is studied in the inertial regime by first simulating for the motion in unit, periodic cells, and then solving successive closure problems leading-after applying an intrinsic averaging procedure-to the components of the apparent permeability tensor. The parameters varied include the orientation of the driving pressure gradient, its magnitude (which permits to define a microscopic Reynolds number), and the porosity of the medium. All cases tested refer to situations for which the microscopic flow is steady. When the driving force is oriented in a direction which lies on the plane perpendicular to the fibers' axis, the results found agree with those available the literature. The fact that the medium is composed by bundles of parallel fibers favours a deviation of the mean flow towards the fibers' axis when the driving pressure gradient has even a small component along it, and this is enhanced by a decreasing porosity; this phenomenon is well quantified by the knowledge of the components of the permeability. Contrary to our initial expectations, for the over one hundred cases which we have simulated, the apparent permeability tensor remains, to a very good approximation, diagonal, a fact mainly related to the transversely isotropic nature of the medium. To obtain a complete, albeit approximate, database of the diagonal components of the apparent permeability tensor we have developed a metamodel, based on kriging interpolation, and carefully calibrated it. The resulting response surfaces can be invaluable in determining the force caused by the presence of inclusions in macroscopic simulations of the flow through bundles of fibers whose orientations and dimensions can vary in space and/or time.

The flow in three-dimensional fibrous porous media is studied in the inertial regime by first simulating for the motion in unit, periodic cells, and then solving successive closure problems leading-after applying an intrinsic averaging procedure-to the components of the apparent permeability tensor. The parameters varied include the orientation of the driving pressure gradient, its magnitude (which permits to define a microscopic Reynolds number), and the porosity of the medium. All cases tested refer to situations for which the microscopic flow is steady. When the driving force is oriented in a direction which lies on the plane perpendicular to the fibers' axis, the results found agree with those available the literature. The fact that the medium is composed by bundles of parallel fibers favours a deviation of the mean flow towards the fibers' axis when the driving pressure gradient has even a small component along it, and this is enhanced by a decreasing porosity; this phenomenon is well quantified by the knowledge of the components of the permeability. Contrary to our initial expectations, for the over one hundred cases which we have simulated, the apparent permeability tensor remains, to a very good approximation, diagonal, a fact mainly related to the transversely isotropic nature of the medium. To obtain a complete, albeit approximate, database of the diagonal components of the apparent permeability tensor we have developed a metamodel, based on kriging interpolation, and carefully calibrated it. The resulting response surfaces can be invaluable in determining the force caused by the presence of inclusions in macroscopic simulations of the flow through bundles of fibers whose orientations and dimensions can vary in space and/or time.

In fractures where surface fluctuations are large compared to their aperture (narrow fractures) the flow is forced to move in tortuous paths that produce additional viscous friction and are subject to inertia effects. We consider the relation between the magnitude of surface roughness and the onset of inertial effects in the pressure driving the flow through a single open fracture. We performed experiments systematically varying the average aperture of the open fracture and covering a wide range of Reynolds numbers. For each aperture, we analyze the data in terms of the Forchheimer equation and show that the critical Reynolds number, defined as the Reynolds number at which inertial effects contribute 10% of the total pressure losses is highly correlated with the roughness of the surface. In particular, we show that significant inertial effects appear early as the relative importance of surface roughness increases. Finally, we present results showing that the magnitude of the deviations in the pressure field compared to a linear profile, taken at different points in the fracture along the flow direction, are directly related to the relative surface roughness of the fracture.

The present paper considers a new model for the formation of the dynamic error inertial component. It is very effective in the analysis and synthesis of measuring instruments positioned on moving objects and measuring their movement parameters. The block diagram developed within this paper is used as a basis for defining the mathematical model. The block diagram is based on the set-theoretic description of the measuring system, its input and output quantities and the process of dynamic error formation. The model reflects the specific nature of the formation of the dynamic error inertial component. In addition, the model submits to the logical interrelation and sequence of the physical processes that form it. The effectiveness, usefulness and advantages of the model proposed are rooted in the wide range of possibilities it provides in relation to the analysis and synthesis of those measuring instruments, the formulation of algorithms and optimization criteria, as well as the developm...

The present article views a measuring system for determining the parameters of vessels. The system has high measurement accuracy when operating in both static and dynamic mode. It is designed on a gyro-free principle for plotting a vertical. High accuracy of measurement is achieved by using a simplified design of the mechanical module as well by minimizing the instrumental error. A new solution for improving the measurement accuracy in dynamic mode is offered. The approach presented is based on a method where the dynamic error is eliminated in real time, unlike the existing measurement methods and tools where stabilization of the vertical in the inertial space is used. The results obtained from the theoretical experiments, which have been performed on the basis of the developed mathematical model, demonstrate the effectiveness of the suggested measurement approach.

An effective way to study the complex seismic soil-structure interaction phenomena is to analyse the response of physical scaled models in 1-g or n-g laboratory devices. The outcomes of an extensive experimental campaign carried out on scaled models by means of the shaking table of the Bristol Laboratory for Advanced Dynamics Engineering (BLADE), University of Bristol, UK are discussed in the present paper. The experimental model comprises an oscillator connected to a single or a group of piles embedded in a bi-layer deposit. Different pile head conditions, i.e. free head and fixed head, several dynamic properties of the structure, including different masses at the top of the single degree of freedom system, excited by various input motions, e.g. white noise, sinedwells and natural earthquake strong motions recorded in Italy, have been tested. In the present work, the modal dynamic response of the soil-pile-structure system is assessed in terms of period elongation and system damping ratio. Furthermore, the effects of oscillator mass and pile head conditions on soil-pile response have been emphasized, when the harmonic input motions are considered.

A Smoothed Particle Hydrodynamics axisymmetric solver was developed in order to simulate the collapse of a single cavitation bubble close to an elastic-plastic material and study plasticity formation and hence material erosion. Findings indicate the relative importance of the material deformation due to the impact of the micro-jet and the shock wave that develop during collapse. A shock-wave dominated impact has a much higher material erosion ability compared to a micro-jet impact. Strain rate is found to have a significant effect on plastic deformation, with an overestimation of the plastic deformation up to 60% if strain rate effects are neglected in the case of stainless steel A2205. We also demonstrate that, although the impact pressure is maximum just below the collapsing bubble, maximum plastic strain occurs at a radial offset from the symmetry axis. This is the result of inertial effects that have an impact on both the magnitude and the position of the plastic domain in the material. A new non-dimensional parameter called effective pressure is introduced that can predict plastic strain location accurately for higher stand-off ratios. Alternatively, a characteristic time analysis also shows that it can be used for prediction of plastic strain zone in the solid for detached cavities.

The production and transportation of petroleum fluids could be severely affected by deposition of suspended particles (i.e. asphaltene, paraffin/wax, sand, and/or diamondoid) in the production wells and/or transfer pipelines. In many instances the
amount of precipitation is rather large causing complete plugging of these conduits. Therefore, it is important to understand the behavior of suspended particles during flow conditions.
        In this paper we present an analysis of the diffusional effects on the rate of solid particle deposition during turbulent flow conditions (crude oil production generally falls within this regime). The turbulent boundary layer theory and the concepts of mass transfer have been utilized to calculate the particle deposition rates on the walls of the flowing conduit. The developed model accounts for the eddy and Brownian diffusivities as well as for inertial effects.
        The analysis presented in this paper shows that rates of solid particle deposition (during crude oil production) on the walls of the flowing channel due solely to diffusional effects are small. It is also shown that deposition rates decrease with increasing particle size. However, when the process is momentum controlled (large particle sizes) higher deposition rates are expected.

stationary start. Instead, the traditional 85 g kg −1 BW loading is suitable for both males and females. Keywords Anaerobic test • Wingate • Peak power • Ergometry Abbreviations WAnT Wingate anaerobic test BW Body weight TRAD Traditional load OPT Optimal load PPO Peak power output MPO Mean power output FI Fatigue index W Watts TtPP Time to peak power PD Power decline rPD Rate of power decline I Inertia Introduction Many factors can be attributed to an accurate peak power output (PPO) or mean power output (MPO) measure obtained during a maximal sprint on a cycle ergometer. The literature is largely varied in regards to the methodology, equipment and correction factors that might apply when attempting to test an individual's power output. For instance, the traditional and widely used wingate anaerobic test (WAnT) has been the subject of criticism, primarily in regards to the model of cycle ergometer used (Mickle

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The production and transportation of petroleum fluids could be severely affected by deposition of suspended particles (i.e. asphaltene, paraffin/wax, sand, and/or diamondoid) in the production wells and/or transfer pipelines. In many instances the amount of precipitation is rather large causing complete plugging of these conduits. Therefore, it is important to understand the behavior of suspended particles during flow conditions.
              In this paper we present an analysis of the diffusional effects on the rate of solid particle deposition during turbulent flow conditions (crude oil production generally falls within this regime). The turbulent boundary layer theory and the concepts of mass transfer have been utilized to calculate the particle deposition rates on the walls of the flowing conduit. The developed model accounts for the eddy and Brownian diffusivities as well as for inertial effects.
              The analysis presented in this paper shows that rates of solid particle deposition (during crude oil production) on the walls of the flowing channel due solely to diffusional effects are small.
              It is also shown that deposition rates decrease with increasing particle size. However, when the process is momentum controlled (large particle sizes) higher deposition rates are expected.

We perform a detailed computational study of the flow of a Bingham fluid along a narrow channel, with one locally uneven wall. This uneven section of the channel represents a washed out section of an oil well about to be cemented. By studying a wide range of different washout geometries, of differing shape characterized by dimensionless height h and length L, we discover that the flows exhibit a type of self-similarity in the limit of large h and B. More specifically, in this limit we find that regardless of the washout geometry, the area of the channel that contains moving fluid is the same for each L. Essentially, uneven and distant parts of the washout become full of static fluid, below the yield stress, while the flow self-selects its own unique geometry. The washout geometry with the largest flowing region within the washout, appears to be the square wave. We show how a simple correction can be calculated that allows one to predict the flowing area for other washout geometries. Lastly, we examine the effect on the pressure drop of different washout geometries.

We study steady inertial flows of a Bingham fluid through 2D "washout" geometries, that represent longitudinal sections of an oil and gas well under construction, thus extending our previous work into the inertial regime. The washout geometry is characterised by dimensionless depth h and length δ −1 . The other dimensionless parameters of problem are the Reynolds number Re and Bingham number B.

Slow flows of Bingham fluids through wavy-walled channels have stationary fouling layers if the amplitude of the wall perturbation h exceeds some critical value h f . We have characterised the occurrence of fouling and the main characteristics of fouling layers, using Stokes flow computations performed extensively over the parameter space (h, d, B). Fouling can occur over a range of channel aspect ratios d and progressively at larger Bingham number, B. Fouling begins at a value of hd that varies mainly with B: both necessary and sufficient conditions are given. The limit of large B appears to plateau to constant values of hd. At moderate B, for h > h f the fluid appears to self-select the flowing region, i.e. the shape of the fouling layer, which can be partly understood via selection of a new length-scale for the flow in the widest part of the channel. Fouling at small B coincides with the onset of recirculation in Newtonian fluid flows.

This study assessed the effect of incorrect calculation of power output measurement on the ergogenic properties of creatine. Fifteen males performed repeated Wingate Tests, under baseline, placebo and creatine condition. Statistics showed significant differences (p<0.05) following creatine supplemented conditions compared to placebo, whilst no significant differences existed between baseline and placebo condition. However, the performance enhancement effect of creatine became significant only when the corrected (for the inertia of the flywheel) method was employed for measuring peak and minimum power. Mean±SD values across all cycle sprints for placebo versus creatine were 1033±100 Watts versus 1130±95 Watts for peak power and 385±78 Watts versus 427±70 Watts for minimum power.  No significant differences were shown using the uncorrected method for peak power (756±97 Watts versus 786±88 Watts) and minimum power 440±64 Watts pre versus 452±65 Watts post). In conclusion, the present study suggests that the potentiating effect of creatine might be underestimated, if the inertial effects of the flywheel are not considered in power output determination