Effect of Vertical Heterogeneity on Long-Term Migration of CO<Subscript>2</Subscript> in Saline Formations

For deep injection of CO₂ in thick saline formations, the movements of both the free gas phase and dissolved CO₂ are sensitive to variations in vertical permeability. A simple model for vertical heterogeneity was studied, consisting of a random distribution of horizontal impermeable barriers with a given overall volume fraction and distribution of lengths. Analytical results were obtained for the distribution of values for the permeability, and compared to numerical simulations of deep CO₂ injection and convection in heterogeneous formations, using multiple realizations for the permeability distribution. It is shown that for a formation of thickness H, the breakthrough times in two dimensions for deep injection scale as H ² for moderate injection rates. In comparison to heterogeneous shale distributions, a homogeneous medium with equivalent effective vertical permeability has a longer breakthrough time for deep injection, and a longer onset time for convection.     

Thermal-hydraulic performance of oval tubes in a cross-flow of air

The thermal-hydraulic performance of five oval tubes is experimentally investigated and compared with that for a circular tube in a cross-flow of air. The range of Reynolds numbers Re_D is approximately between 1,000 and 11,000. The nominal axis ratios R (major axis/minor axis) for three of the investigated oval tubes are 2, 3, and 4. Two other configurations of oval tubes are also tested, an oval tube R=3 with two wires soldered on its upper and lower top positions, and a cut-oval tube. The performance of the tubes is corrected for the effects of area blockage and turbulence intensity. The measurement results show that the mean Nusselt numbers Nu_D for the oval tubes are close to that for the circular tube for Re_D<4,000. For a higher Re_D, the Nu_D for the oval tubes is lower than that for the circular tube and it decreases with the increase in the axis ratio R. The drag coefficients C_d for the tubes are measured and the combined thermal-hydraulic performance is indicated by the ratio Nu_D/C_d, which shows a better combined performance for the oval tubes.     

Rigorous Results in Steady Finger Selection in Viscous Fingering

This paper concerns the existence of a steadily translating finger solution in a Hele-Shaw cell for small but non-zero surface tension (ɛ²). Though there are numerous numerical and formal asymptotic results for this problem, we know of no mathematically rigorous results that address the selection problem. We rigorously conclude that for relative finger width λ in the range , with small, analytic symmetric finger solutions exist in the asymptotic limit of surface tension if and only if the Stokes constant for a relatively simple nonlinear differential equation is zero. This Stokes constant S depends on the parameter and earlier calculations by a number of authors have shown it to be zero for a discrete set of values of a. The methodology consists of proving the existence and uniqueness of analytic solutions for a weak half-strip problem for any λ in a compact subset of (0, 1). The weak problem is shown to be equivalent to the original finger problem in the function space considered, provided we invoke a symmetry condition. Next, we consider the behavior of the solution in a neighborhood of an appropriate complex turning point for the restricted case , for some . This turning point accounts for exponentially small terms in ɛ, as ɛ→0⁺ that generally violate the symmetry condition. We prove that the symmetry condition is satisfied for small ɛ when the parameter a is constrained appropriately. (Accepted July 4, 2002 Published online January 15, 2003) Communicated by F. OTTO     

On simulations investigating droplet diameter–charge distributions in electrostatically atomized dielectric liquid sprays

A general procedure has been developed for the simulation of charged liquid and electrostatically atomized sprays. The procedure follows a Lagrangian approach for simulation of spray droplets and a Eulerian approach for gas‐phase variables, including the electric field generated by the charge presence on droplets. Validation of the procedure was examined through simulations of previously published charged spray experiments. Results showed that for the specification of initial droplet charge, modelling the droplet charge–diameter relationship through a scaling law is as reliable a method as using a directly obtained charge–diameter relationship from experimental measurements. The normalized root‐mean‐square errors for sprays using the two methods were shown to be within 12% of one another, for the prediction of spatially averaged profiles of mean droplet diameters, mean axial velocities and mean radial droplet velocities. Results showed that the general spatial characteristics and dynamics of a charged liquid spray can successfully be reproduced, including the axial and radial dispersal pattern of droplets and the distribution of mean droplet diameters throughout the spray plume. For all sprays with droplet charges defined through a scaling law relationship, the normalized root‐mean‐square errors range from 9.0% to 31.6% for mean droplet diameters, 10.4% to 67.9% for mean axial droplet velocities and 16.8% to 38.6% for mean radial droplet velocities. Lastly, we present a brief set of general recommendations for simulating electrostatically atomized dielectric liquid sprays.Copyright © 2013 John Wiley & Sons, Ltd.     

Fully plastic center-cracked strip under anti-plane shear

The problem of a center-cracked strip subjected to uniform remote anti-plane shear stress is transformed to a problem in a hodograph plane which is solved exactly by Mellin transform and Wiener-Hopf technique. The material of the strip satisfies a pure power hardening stress strain relation and the results are valid for both deformation and flow theories of placticity. Numerical values are given for the crack opening displacement δ and Rice's path independent J integral for several values of the power hardening exponent n and crack width to strip width ratios. Approximate asymptotic formulas are presented for J and δ for large n.     

Green’s functions for multi-phase isotropic laminated plates

This work develops a series of Green’s functions for multi-phase Kirchhoff isotropic laminated plates. First, we derive the Green’s functions for a composite laminated plate composed of two bonded dissimilar isotropic laminated semi-infinite plates. Second, the obtained results for bimaterials are judiciously applied to obtain the Green’s function solution for a circular elastic inclusion embedded in an infinite isotropic laminated plate. Third, Green’s functions for a composite space composed of an arbitrary number of wedges of different isotropic laminated plates are derived. Finally, we derive Green’s functions for a laminated plate with an elliptical and a parabolic boundary, respectively.     

The creep deformation of vibrating structures

In a recent paper [1] it was shown that the evaluation of certain bounding solutions for a structure subjected to cyclic loading was equivalent to assuming that the cycle time Δt was short compared with a stress redistribution time. Comparisons between values which are likely to occur in creep design situations indicated that Δt may often be assumed to be small and the bounding solution may be expected to closely approximate the actual stress history. In this paper the solution for the limiting case when Δt → 0 is evaluated for a class of constitutive relationships which may be expressed in terms of a finite number of state variables. Strain-hardening viscous, visco-elastic and Bailey-Orowan equations are discussed and particular solutions for which the residual stresses remain constant in time are derived. The solution for a non-linear visco-elastic model indicates that, for the stationary cyclic state, the constitutive equation need only predict the creep strain over a discrete number of cycles and need not predict the strains during a cycle. This observation should considerably simplify creep analysis.The solution of a simple example demonstrates the similarity between the predicting of the various constitutive relationships for isothermal problems. In fact they provide virtually identical solutions when expressed in terms of reference stress histories. The finite element solution of a plate containing a hole and subjected to variable edge loading is also presented for a viscous material. The solutions show behaviour which is similar to that of the two bar structure.     

Periodic cavitation shedding in a cylindrical orifice

Cavitation structures in a large-scale (D = 8.25 mm), plain orifice style nozzle within a unique experimental rig are investigated using high-speed visualisation and digital image processing techniques. Refractive index matching with an acrylic nozzle is achieved using aqueous sodium iodide for the test fluid. Cavitation collapse length, unsteady shedding frequency and spray angles are measured for cavitation conditions from incipient to supercavitation for a range of Reynolds numbers, for a fixed L/D ratio of 4.85. Periodic cavitation shedding was shown to occur with frequencies between 500 and 2,000 Hz for conditions in which cavitation occupied less than 30% of the nozzle length. A discontinuity in collapse length was shown to occur once the cavitation exceeded this length, coinciding with a loss of periodic shedding. A mechanism for this behaviour is discussed. Peak spray angles of approximately θ ≈ 14° were recorded for supercavitation conditions indicating the positive influence of cavitation bubble collapse on the jet atomisation process.     

Stress Independence of Poisson's Ratio and Divergence-Free Body Forces

In simply connected bodies, the compatibility conditions in 2D elasticity are independent of Poisson's ratio (and hence there is a reduction in the number of constants) for divergence-free body forces for the boundary-value problem of traction. It is shown that that for divergence-free body forces in two fields with different compliances and the same stress (hence, inducing a reduction in constants and independence of Poisson's ratio) the displacements differ by a field that is a solution for λ + 2μ = 0, where λ and μ are the Lamé constants for the elastic material, which is a constant rotation. Seen from another aspect, in a Cosserat spectral orthogonal and complete decomposition of the stress [12], the terms associated with Poisson's ratio in the stress representation have as coefficient the inner product of the body force with a displacement which is an eigenfunction at λ + 2μ = 0. This displacement is orthogonal to a divergence- free body force vector, which results in the vanishing of the coefficient of the Poisson's ratio dependence term in the orthogonal decomposition. Due to the completeness and orthogonality of the eigenfunctions, divergence-free body force is a necessary and sufficient condition for stress independence of Poisson's ratio in simply connected 2D bodies, while for multiply connected ones, the Michell generalized conditions also have to be satisfied, as shown here as well. Thus, both approaches, the CLM [1] theorem, which deals with reduction of constants, and the Cosserat spectral decomposition, which shows explicitly the material dependence of the solution, lead to the same conditions for stress independence of Poisson's ratio both for simply connected and multiply connected 2D bodies.     

The influence of oil on nucleate pool boiling heat transfer

The influence of various oil contents in R134a is investigated for nucleate pool boiling on copper tubes either sandblasted or with enhanced heating surfaces (GEWA-B tube). Polyolester oils (POE) (Reniso Triton) with medium viscosity 55 cSt (SE55) and high viscosity 170 cSt (SE170) were used. Heat transfer coefficients were obtained for boiling temperatures between −28.6 and +20.1°C. The oil content varied from 0 to 5% mass fraction. For the sandblasted tube and the SE55 oil the heat transfer coefficients for the refrigerant/oil-mixture can be higher or lower than those for the pure refrigerant, depending on oil mass fraction, boiling temperature and heat flux. In some cases the highest heat transfer coefficients were obtained at a mass fraction of 3%. For the 170 cSt oil there is a clear decrease in heat transfer for all variations except for a heat flux 4,000 W/m² and −10.1°C at 0.5% oil content. The heat transfer coefficients are compared to those in the literature for a smooth stainless steel tube and a platinum wire. For the enhanced tube and 55 cSt oil the heat transfer coefficients are clearly below those for pure refrigerant in all cases. The experimental results for the sandblasted tube are compared with the correlation by Jensen and Jackman. The calculated values are within +20 and −40% for the medium viscosity oil and between +50% and −40% for the high viscosity oil. A correlation for predicting oil-degradation effects on enhanced surfaces does not exist.     

Nonlinear Dynamics of Motivational Flow

Motivational flow is the experience of intrinsic motivation, which is in turn the result of the levels of challenge and skill involvement for a particular task. The level of flow is predictive of the amount of time a person will spend in that task, and it is thought to form a basis for an individual's time allocation between occupational and leisure activities. In this study, 28 university students, many of whom were employed, completed a 7-day log of their daily activities, their duration, and provided ratings of the level of skills and challenges inherent in the task. The logs provided a time series of several hundred points for each participant, which were each subjected to nonlinear dynamical analysis through nonlinear regression. Principal results were: (1) Flow was chaotic for all subjects. (2) The average R ² for the nonlinear models was .22, compared to .02 for the linear counterpart. (3) R ² was higher for people who spent more time at paying jobs. Evidence for individual differences in dynamical character were uncovered.     

Innovative iteration technique for nonlinear ordinary differential equations of large deflection problem of circular plates

The large deflection problem of a bending circular plate is reduced to a nonlinear ordinary differential equation, and a type of pseudo-linearization is used to obtain the final solution. An innovative iteration technique is suggested. The initial iteration values of some functions for a given loading are adopted from the previous solution for a lower loading. This will significantly extend the range of solution for the non-dimensional loading. Previously, the solution for the non-dimensional loading Q = 100 was obtained. However, in this paper the solution for the non-dimensional loading Q = 1000 is achieved.     

T-stress evaluation for slightly curved crack using perturbation method

A general formulation for evaluating the T-stress at crack tips in a curved crack is introduced. In the formulation, a singular integral equation with the distribution of dislocation along the curve is suggested. For a slightly curved crack, a small parameter is generally assumed for the crack configuration. By using the assumption for the small parameter, the perturbation method is suggested and it reduces the singular integral equation into many successive singular integral equations. If the cracked plate has a remote loading and the curve configuration is a quadratic function, the mentioned successive singular integral equations can be solved in a closed form. Therefore, the solution for the T-stress in a closed form is obtained. The obtained results for T-stress are shown by figures. It is found that if the involved parameter is not too small, the influence of the curve configuration is significant. Comparison for T-stresses obtained from a quadratic-shaped curved crack and an arc crack is presented.     

A review of mobility metrics for next generation vehicle mobility models

In the United States, the NATO Reference Mobility Model (NRMM) has been used for evaluating military ground vehicle mobility and the Vehicle Cone Index (VCI) has been selected as a mobility metric. VCI represents the minimum soil strength required for a vehicle to consistently make a specific number of passes, usually one or fifty passes. In the United Kingdom, the Mean Maximum Pressure (MMP) has been adopted as a metric for assessing military vehicle cross-country mobility. MMP is the mean value of the maxima occurring under all the wheel stations of a vehicle. Both VCI and MMP are empirically based. This paper presents a review of the basis upon which VCI and MMP were developed, as well as their applications to evaluating vehicle mobility in practice. With the progress in terramechanics and in modelling and simulation techniques in recent years, there is a growing desire to develop physics-based mobility metrics for next generation vehicle mobility models. Based on the review, criteria for selecting physics-based mobility metrics are proposed. Following these criteria, metrics for characterizing military vehicle traction limits and traversability on a given operating area are recommended.     

The Falkner–Skan Wedge Flows of Power-Law Fluids Embedded in a Porous Medium

The non-Darcy flow characteristics of power-law non-Newtonian fluids past a wedge embedded in a porous medium have been studied. The governing equations are converted to a system of first-order ordinary differential equations by means of a local similarity transformation and have been solved numerically, for a number of parameter combinations of wedge angle parameter m, power-law index of the non-Newtonian fluids n, first-order resistance A and second-order resistance B, using a fourth-order Runge–Kutta integration scheme with the Newton–Raphson shooting method. Velocity and shear stress at the body surface are presented for a range of the above parameters. These results are also compared with the corresponding flow problems for a Newtonian fluid. Numerical results show that for the case of the constant wedge angle and material parameter A, the local skin friction coefficient is lower for a dilatant fluid as compared with the pseudo-plastic or Newtonian fluids.     

Magneto elastic stress subjected to uniform magnetic field over a thin infinite plate containing an elliptical hole with an edge crack

Two dimensional solutions of the magnetic field and magneto elastic stress are presented for a magnetic material of a thin infinite plate containing an elliptical hole with an edge crack subjected to uniform magnetic field. Using a rational mapping function, each solution is obtained as a closed form. The linear constitutive equation is used for these analyses. According to the electro-magneto theory, only Maxwell stress is caused as a body force in a plate. In the present paper, it raises a plane stress state for a thin plate, the deformation of the plate thickness and the shear deflection. Therefore the magneto elastic stress is analyzed using Maxwell stress. No further assumption of the plane stress state that the plate is thin is made for the stress analysis, though Maxwell stress components are expressed by nonlinear terms. The rigorous boundary condition expressed by Maxwell stress components is completely satisfied without any linear assumptions on the boundary. First, magnetic field and stress analyses for soft ferromagnetic material are carried out and then those analyses for paramagnetic and diamagnetic materials are carried out. It is stated that those plane stress components are expressed by the same expressions for those materials and the difference is only the magnitude of the permeability, though the magnetic fields H_x, H_y are different each other in the plates. If the analysis of magnetic field of paramagnetic material is easier than that of soft ferromagnetic material, the stress analysis may be carried out using the magnetic field for paramagnetic material to analyze the stress field, and the results may be applied for a soft ferromagnetic material. It is stated that the stress state for the magnetic field H_x, H_y is the same as the pure shear stress state. Solutions of the magneto elastic stress are nonlinear for the direction of uniform magnetic field. Stresses in the direction of the plate thickness and shear deflection are caused and the solutions are also obtained. Figures of the magnetic field and stress distribution are shown. Stress intensity factors are also derived and investigated for the crack length.     

A locally DIV‐free projection scheme for incompressible flows based on non‐conforming finite elements

We present a projection scheme whose end‐of‐step velocity is locally pointwise divergence free, using a continuous ?₁ approximation for the velocity in the momentum equation, a first‐order Crouzeix–Raviart approximation at the projection step, and a ?₀ approximation for the pressure in both steps. The analysis of the scheme is done only for grids that guarantee the existence of a divergence free conforming ?₁ interpolant for the velocity. Optimal estimates for the velocity error in L²‐ and H¹‐norms are deduced. The numerical results demonstrate that these estimates should also hold on grids on which the continuous ?₁ approximation for the velocity locks. Since the end‐of‐step velocity is locally solenoidal, the scheme is recommendable for problems requiring good mass conservation. Copyright © 2005 John Wiley & Sons, Ltd.     

Spectroscopic properties of a perfluorinated ketone for PLIF applications

This work identifies the fluorescence characteristics of a perfluorinated ketone, 2-trifluoromethyl-1,1,1,2,4,4,5,5,5-nonafluoro-3-pentanone, further referred to as fluoroketone. This compound is suitable for use with the third harmonic of an Nd:YAG laser for quantitative concentration measurements, as it exhibits strong emission even for relatively low excitation and has a near-linear response of fluorescence intensity with concentration. This makes it suitable for a broad range of fluorescence applications. The absorption cross-section of 3.81 × 10⁻¹⁹ cm² was found to be constant for a temperature range of 293–441 K and a pressure range of 1–18 atm. A calibration line has been generated that relates the concentration of gaseous and liquid fluoroketone with its absorption coefficient.     

A physical decomposition of the stress tensor for complex flows

Traditionally, the components of the stress with respect to a relevant coordinate system are used for the purpose of stress visualisation and interpretation. A case for using a flow dependent measure to interpret and visualise stress is made for two dimensional flow, together with a suggestion for extending the idea to three dimensions. The method is illustrated for Newtonian and Oldroyd B fluids in both the eccentrically rotating cylinder and flow past a cylinder benchmark problems. In the context of a generalised Newtonian fluid, the relation between the flow-dependent stress measure to other field variables under certain flow conditions, is examined and is indicative of its importance in complex flow.

Effects of temperature-dependence of viscosity and viscous dissipation on laminar flow heat transfer in circular tubes

Heat transfer effects of variable viscosity and viscous dissipation for heated developing laminar flows in circular tubes have been investigated. Three studies are reported covering a comprehensive range of input data for the case of constant wall heat flux. Initially the program was used to predict the effect on heat transfer of temperature-dependent viscosity via a general temperature power relation. In addition, predictions were made for nine particular fluids covering a range of Prandtl numbers from 0.025 to 12 500, and a range of Brinkman numbers from 1.8 × 10^?10 to 6.8 × 10³. A more detailed study was made for two particular oils covering a range of practical interest. For the liquids considered their viscosity temperature-dependence resulted in enhancement of heat transfer, whereas for fluids with a Prandtl number <200 the effect of viscous dissipation was negligible, and for fluids of a Brinkman number > × 10^?2 the outcome was a reduction of heat transfer. A numerical instability problem occurred for situations of very high viscous dissipation which limited the length of duct that could be examined.