Non-dimensional Distance Research Articles

PSEUDO-LAMINARIZATION OF MICRO-BUBBLE CONTAINING MILKY BUBBLY FLOW IN A PIPE

Micro bubble technology has become to attract people's concerns due to its wide potential in practical applications to a variety of advanced and conventional science and technologies. However, our knowledge of micro bubbles containing bubbly two-phase flow is almost nothing. We developed a specially designed nozzle which generates micro air bubbles with high bubble number density (mean diameter ≈ 40microns, number density higher than 2×105/cc). Using this micro-bubble generator, we carried out a measurement of two-phase frictional pressure drop, cross-sectional average void fraction, local void fraction profiles and liquid velocity profiles. The range of cross-sectional average void fraction covered was up to 0.6 % which is high enough to realize milky bubbly flow. The most exciting result we found is that the two-phase flow becomes pseudo-laminarized by injecting such ultra small bubbles into the water flow. For 0.3 ≈ 0.5% void fractions, pseudo-laminar-to-turbulent transition occurred at Re= 10,000 ≈ 20,000, showing a significant reduction in wall friction. The radial liquid velocity profiles show typical turbulent 1/7 th power law profile. However, the liquid velocity profiles in milky bubbly flow obviously shifted from von Karman's universal velocity profile towards lower values of the non-dimensional distance from the wall. The cross sectional averaged void fraction correlates well with a homogeneous flow model, which is verified by uniform profiles of the local void fraction distribution over the whole channel cross section. The mechanisms of pseudo-laminarization and flow structures have been discussed.

PSEUDO-LAMINARIZATION OF MICRO-BUBBLE CONTAINING MILKY BUBBLY FLOW IN A PIPE

Micro bubble technology has become to attract people's concerns due to its wide potential in practical applications to a variety of advanced and conventional science and technologies. However, our knowledge of micro bubbles containing bubbly two-phase flow is almost nothing. We developed a specially designed nozzle which generates micro air bubbles with high bubble number density (mean diameter ≈ 40microns, number density higher than 2×105/cc). Using this micro-bubble generator, we carried out a measurement of two-phase frictional pressure drop, cross-sectional average void fraction, local void fraction profiles and liquid velocity profiles. The range of cross-sectional average void fraction covered was up to 0.6 % which is high enough to realize milky bubbly flow. The most exciting result we found is that the two-phase flow becomes pseudo-laminarized by injecting such ultra small bubbles into the water flow. For 0.3 ≈ 0.5% void fractions, pseudo-laminar-to-turbulent transition occurred at Re= 10,000 ≈ 20,000, showing a significant reduction in wall friction. The radial liquid velocity profiles show typical turbulent 1/7 th power law profile. However, the liquid velocity profiles in milky bubbly flow obviously shifted from von Karman's universal velocity profile towards lower values of the non-dimensional distance from the wall. The cross sectional averaged void fraction correlates well with a homogeneous flow model, which is verified by uniform profiles of the local void fraction distribution over the whole channel cross section. The mechanisms of pseudo-laminarization and flow structures have been discussed.

Swelling pressures of compacted bentonites from diffuse double layer theory

The swelling pressures of several compacted bentonites (MX80, Febex, and Montigel) proposed for use as barrier materials in storing high-level radioactive waste in many countries were determined from the Gouy–Chapman diffuse double layer theory. The swelling pressures thus determined were compared with the reported experimental swelling pressures. The study revealed that, in general, at low compaction dry densities of the bentonites, the experimental swelling pressures are less than their theoretical counterparts, with the reverse trend at high compaction dry densities. Based on the reported experimental results for the three bentonites, relationships between the nondimensional midplane potential function, u, and the nondimensional distance function, Kd, were established. New equations for the swelling pressure were proposed on the basis of the diffuse double layer theory and the reported experimental data to compute swelling pressures of compacted bentonites. The suitability of the new equations was also verified with additionally reported experimental swelling pressures from three other bentonites (Kunigel V1, Kunigel, and bentonite S-2) that have been also proposed for use as barrier materials. Very good agreement was found in all the cases between the experimental swelling pressures and the swelling pressures obtained using the proposed equations. The use of the proposed equations is based on the weighted average valency of the cations present in bentonites, since the valency of the cations present has a significant influence on the swelling pressure.Key words: clays, compressibility, swelling pressure, expansive soils, chemical properties, radioactive waste disposal.

Exact solutions of nonlinear differential equations arising in third grade fluid flows

Exact solutions for a class of non-linear second-order differential equations arising in a third grade fluid flow, at a rotating cylinder (unbounded domain case) and between rotating cylinders (bounded domain case), are obtained. Furthermore, the exact solutions are compared with the numerical ones. It is observed that the difference between the exact and the numerical solutions is about 1% for small R (the non-dimensional distance between the cylinders) and is about 3% when R=100. This difference increases with an increasing R. Moreover, for large R it is not easy to obtain meaningful results numerically. Hence, these exact solutions for various values of the parameters R and ω (rotation parameter) are useful for experimental and numerical studies, and warrant further study.

A Relationship Between the 2-body Energy of Kaxiras–Pandey and Pearson–Takai–Halicioglu–Tiller Potential Functions

A parametric relationship between the Pearson–Takai–Halicioglu–Tiller (PTHT) and the Kaxiras–Pandey (KP) empirical potential energy functions is developed for the case of 2-body interaction. The need for such relationship arises when preferred parametric data and adopted software correspond to different potential functions. The analytical relationship was obtained by equating the potential functions' derivatives at zeroth, first and second order with respect to the interatomic distance at the equilibrium bond length, followed by comparison of coefficients in the repulsive and attractive terms. Plots of non-dimensional 2-body energy versus the nondimensional interatomic distance verified the analytical relationships developed herein. The discrepancy revealed in theoretical plots suggests that the 2-body PTHT and KP potentials are more suitable for curve-fitting "softer" and "harder" bonds respectively.

The effect of damköhler number on the stand-off distance of cross-flow flames

Cross-flow flames, formed between two reactants approaching at 90°, have many similarities to edge flames formed between parallel-flowing reactants. Two types can be distinguished: one whose inlet velocity profiles have a uniform strain rate and another whose inlet velocity profile is flat. Dimensional analysis suggests that the distance between the flame head and the confluence point, L c , is affected by a Damköhler number. A simplified solution for the relationship between the non-dimensional stand-off distance Π and the Damköhler number is determined here by correlating the results of several hundred numerical simulations. For a cross-flow flame that is controlled by the strain rate, it is found that L c ∝A𝒟1/2τc 1/2, where A is the strain rate, 𝒟 is the diffusivity and τ c is the chemical time. For a convection-controlled flame, the expression is: L c ∝U 3 τ c 2𝒟−1, where U is the entry velocity.

Experimental and numerical study of twin underexpanded impinging jets

In this paper, the dual underexpanded impinging jets are experimentally and numerically studied. The experiments were performed by measuring the unsteady and averaged wall static pressures and by visualizing density fields using schlieren method. Numerical calculations were also conducted by solving unsteady three dimensional compressible Navier-Stokes equations with Baldwin-Lomax turbulence model. The main parameters for the dual jets are the non-dimensional distance between the two nozzle centers H/D covering 1.5, 2.0, the nozzle to plate separation L/D 2.0, 3.0,4.0 and 5.0 and the pressure ratio defined by p o /p b 1.0–6.0, where D is the diameter of each nozzle exit, p o the stagnation pressure and p o the back pressure. It is found that the agreement between the experiments and the calculations is good. The fountain flow at the middle of the two jets is observed both in the experiments and the calculation. According to FFT analysis of the experiments for the twin jets, relatively low frequency (up to 5 kHz) is dominant for H/D=1.5, L/D=2.0 and pressure ratio p o /p b =3.0 and 5.0, which is confirmed by the experiments.

Finite Element Investigation of Friction Condition in a Backward Extrusion of Aluminum Alloy

Finite element simulations are being widely used to increase the efficiency and effectiveness of design of bulk metal forming processes. In such simulations, proper consideration of friction condition is important in obtaining reliable results. For this purpose, the shear friction factor is widely used for bulk deformation analyses. In the earlier work, it was found that a radial tip was formed on the extruded end of the workpiece and that the radial tip distance had a linear relationship with the forming load in the tip test. In order to characterize the global average shear friction factor, a linear relationship between the nondimensionalized radial tip distance and shear friction factor was numerically determined in this study for AL6061-O for various lubrication conditions. The global average friction condition at the bottom die interface was determined to be about 60 percent of the one at the punch in the backward extrusion under the present conditions.

Dynamics of vortices on a uniformly shelving beach

Laboratory experiments are described which investigate the dynamics of a vortex dipole moving in water towards a planar sloping beach inclined at an angle α to the horizontal. Results are compared with those of a vortex ring model first developed by Peregrine (1996). The vortices separate as they travel up the beach, eventually moving in opposite directions and nearly parallel to the shoreline. The ranges of conditions examined are 3°[les ]α[les ]45°, 1×103[les ]Re[les ]6×103 and 0.05[les ]Fr[les ]0.14, where Re and Fr are the on-slope Reynolds number and the Froude number of the vortices, respectively. The minimum distance from the shoreline reached by the vortices and their along-shore speed are in general agreement with the predictions when, respectively, R*i<3 (where R*i is the non-dimensional initial distance of the vortices from the shore-line) and Re[gsim ]1500. The vortex ring model is likely to have useful applications to the study of the dynamics of the near-shore zone.

Asymptotic determination of effective elastic properties of composite materials with fibrous square-shaped inclusions

Abstract We propose an asymptotic approach for evaluating effective elastic properties of two-components periodic composite materials with fibrous inclusions. We start with a nontrivial expansion of the input elastic boundary value problem by ratios of elastic constants. This allows to simplify the governing equations to forms analogous to the transport problem. Then we apply an asymptotic homogenization method, coming from the original problem on a multi-connected domain to a so called cell problem, defined on a characterizing unit cell of the composite. If the inclusions' volume fraction tends to zero, the cell problem is solved by means of a boundary perturbation approach. When on the contrary the inclusions tend to touch each other we use an asymptotic expansion by non-dimensional distance between two neighbouring inclusions. Finally, the obtained “limiting” solutions are matched via two-point Pade approximants. As the results, we derive uniform analytical representations for effective elastic properties. Also local distributions of physical fields may be calculated. In some partial cases the proposed approach gives a possibility to establish a direct analogy between evaluations of effective elastic moduli and transport coefficients. As illustrative examples we consider transversally-orthotropic composite materials with fibres of square cross section and with square checkerboard structure. The obtained results are in good agreement with data of other authors.

Double-sided onshore–offshore seismic imaging of a plate boundary: “super-gathers” across South Island, New Zealand

Onshore–offshore seismic refraction profiling allows for the determination of crustal and mantle structures in the transition between continental and oceanic environments. Islands and narrow landmasses have the unique geometry of allowing for double-sided onshore–offshore experiments that favor the construction of composite “super-gathers” using the acquisition of onshore–offshore and ocean-bottom seismometer receiver gathers, land explosion shot gathers, and near-vertical incidence multichannel seismic (MCS) profiling. A number of sites at plate boundaries are amenable to the application of double-sided onshore–offshore imaging, including the Indo-Australian/Pacific transform boundary on South Island, New Zealand. By comparing the ratio of island width to mantle refraction (Pn) “maximum” crossover distance, using nondimensional distances, we provide an indicator of raypath “coverage” for crustal illumination. Islands or narrow land masses whose widths are less than twice their maximum crossover distance are candidates for double-sided onshore–offshore experiments. The SIGHT (South Island GeopHysical invesTigation) experiment in New Zealand is located where the width of South Island is sufficiently narrow with respect to its crustal thickness that a double-sided onshore–offshore experiment allows for complete crustal imaging of the associated plate boundary.

Investigation of the flow field of a highly heated jet of air

Measurements of mean and fluctuating velocity and temperature and their self- and cross-products to the third-order are presented for a heated axisymmetric air jet. Froude numbers in the range of 3500–13,190, Reynolds numbers in the range of 3470–8500 and non-dimensional streamwise distances, X ∗ , from 0.27 to 1.98 are covered by the data. It was found that turbulence intensity decreases for the heated jet in the region between the inertia dominated and the buoyancy dominated regions which is contrary to findings with helium jets mixing with ambient air to produce density fluctuations. The effects of heating on the turbulent kinetic energy budget and the temperature variance budget show small differences for the inertia dominated region and the intermediate region which help to explain the transition process to the far field plume region. Constants are evaluated for the isotropic eddy diffusivity and generalised gradient hypothesis models as well as the scalar variance model. No significant effect of heating on the dissipation time-scale ratio was found. A novel wire array with an inclined cold wire was used. Measurements obtained with this probe are found to lead to asymmetries in some of the higher-order products. Further investigation suggested that the asymmetries are attributable to an as yet unreported interference effect produced by the leading prong of the inclined temperature wire. The effect may also have implications for inclined velocity wires which contain a temperature component when used in heated flows.

A156 2 つの不足膨張衝突噴流に関する研究

The temperature and pressure distributions on a plate in the dual underexpanded impinging jets are experimentally investigated. The static pressure fluctuations on the plate were also measured and compared with the case of the single jet. The main parameters for the experiments are the non-dimensional distance between the two nozzle centers H/D=1.5,2.0,the nozzle to plate separation L/D=2.0,and 5.0,and pressure ratio defined by p_o/p_b=1.0∿6.0. The results show that the temperature at the middle point between the jet axes is considerably affected by the pressure ratio p_o/p__b, where p_o is the stagnation pressure, p_b the back pressure. Moreover, FFT analyses of the static pressure fluctuations on the plate suggest that relatively low frequency range between 0 and 1.5kHz for the dual jets is dominant under the condition of H/D=1.5 and L/D=2.0,and at the pressure ratio of about 3.0 compare to the single jet.

Interacting droplet combustion under conditions of extinction

This paper presents the results of an experimental investigation into the extinction behavior of single droplets and binary droplet arrays of decane fuel in normal gravity and microgravity. The test ambients were air at reduced pressure for the normal gravity experiments and nitrogen/oxygen and helium/oxygen at reduced pressure for the microgravity experiments. The data show that interaction effects have a stronger influence on the extinction behavior of a binary array than the quasi-steady burning behavior. In normal gravity, the burning rate constant is only a very weak function of the interdroplet spacing at initial nondimensional separation distances greater than 5. The extinction droplet diameter, however, is much smaller (if it exists) for the droplet array at an instantaneous non-dimensional spacing of approximately 20. The microgravity experiments in nitrogen/oxygen (0.15 oxygen mole fraction) ambients exhibited different extinction behavior than the normal gravity tests. In this ambient condition, the flame surrounding the binary array always extinguished at a larger droplet diameter compared with single droplets. The microgravity experiments in the helium/oxygen (0.25 oxygen mole fraction) ambients exhibited behavior opposite of the nitrogen diluted tests with the binary array extinguishing at smaller droplet diameters than a single droplet. For the microgravity experiments, the observed difference between the two ambients is attributed to the importance of radiative loss. The nitrogen/oxygen tests had larger, weaker flames and smaller burning rates and consequently were affected more significantly by radiative loss from the flame zone compared to the helium/oxygen tests. A qualitative explanation of the different extinction behavior is detailed in the paper.

Adaptive Output Feedback Control of a Nonlinear Aeroelastic Structure

Based on a backstepping design technique, a new adaptive controller for the control of an aeroelastic system using output feedback is derived. The chosen dynamic model describes the nonlinear plunge and pitch motion of a wing. Theparameters of thesystem areassumed to becompletely unknown, and only the plunge displacement and the pitch angle measurements are used for thesynthesis of thecontroller. A canonical state variable representation of the system is derived, and e lters are designed to obtain the estimates of the derivatives of the pitch angle and the plunge displacement. Then adaptive control laws for the trajectory control of the pitch angle and the plunge displacement are derived. In the closed-loop system the state vector asymptotically converges to the origin. Simulation results are presented, which show that regulation of the state vector to the equilibrium state and trajectory following are accomplished using a single control surface in spite of the uncertainty in the aerodynamic and structural parameters. Nomenclature a = nondimensionalized distance from the midchord to the elastic axis bs = semichord of the wing ch = structural damping coefe cient in plunge caused by viscous damping ci, L, Li, = design parameters di, C ca = structural damping coefe cient in pitch caused by

Numerical Study of Wake Vortex Decay and Descent in Homogeneous Atmospheric Turbulence

Numerical simulations are performed to isolate the effect of ambient turbulence on the wake vortex decay rate within a neutrally stratified atmosphere. Simulations are conducted for a range of turbulence intensities by injecting wake vortex pairs into an approximately homogeneous and isotropic turbulence field. Consistent with field observations, the decay rate of the vortex circulation increases clearly with increasing levels of ambient turbulence. Based on the results from the numerical simulations, simple decay models for the vortex pair are proposed as functions of nondimensional ambient turbulence intensity, nondimensional radial distance, and nondimensional time. For strong atmospheric turbulence, the model predictions are in reasonable agreement with the observational data. For weak turbulence with stable stratification, the model, based on turbulence dissipation alone, underestimates circulation decay with consistent overestimation of vortex descent, unless stratification effects are included

Energetics of two circular inclusions in anti-plane elastostatics

In this paper, we use the recently derived solution of two circular elastic inclusions under anti-plane shear deformation ( Honein et al., 1992a, b) to evaluate the material forces, as well as expanding and rotating moments ‘acting’ on inclusions. These may be defined as the energy changes (e.g. energy release rates) accompanying unit translation, self-similar expansion and rotation of inclusions, respectively. The bond between the inclusions and the matrix is assumed to be perfect and the calculation is performed using the concept of the J, M and L path-independent integrals, respectively. The results obtained are valid under arbitrary loading. An illustrative example shows that two circular holes under remote uniform shear stress attract each other and that the J and M integrals grow without bound as the two holes become infinitely close. A careful examination of the expression for these integrals yields the result that the J and M integrals tend to infinity proportionally to 1/ ε , where ε is a non-dimensional distance between the holes. It is also noticed that the J integral decays rapidly to zero as the two holes become four or five radii apart. Other examples of two circular holes and inclusions under various stress fields are also considered and discussed.

Buoyant low-stretch diffusion flames beneath cylindrical PMMA samples

To study flame structure and extinction characteristics in low-stretch environments, a normal gravity low-stretch diffusion flame was established beneath a cylindrical PMMA sample of varying large radii. Burning rates, visible flame thickness, visible flame standoff distance, temperature profiles in the solid and gas, and radiative loss from the system were measured. A transition from the blowoff side of the flammability map to the quenching side of the flammability map was observed at approximately 6–7 s −1, as determined by curvefits to the nonmonotonic trends in peak temperatures, solid and gas-phase temperature gradients, and nondimensional standoff distances. A surface energy balance reveals that the fraction of heat transfer from the flame that is lost to in-depth conduction and surface radiation increases with decreasing stretch until quenching extinction is observed. This is primarily due to decreased heat transfer from the flame, while the magnitude of the losses remains the same. A unique local extinction flamelet phenomenon and associated preextinction oscillations are observed at very low stretch. An ultimate quenching extinction limit is found at low stretch with sufficiently high induced heat losses.

Developing Laminar Flow and Heat Transfer in Annular-Sector Ducts

For annular-sector ducts, steady, laminar, and constant-property forced-convection flow and heat transfer in the entrance region have been analyzed numerically using a general, marching procedure. Two types of thermal boundary conditions have been considered: (1) uniform temperature both axially and peripherally (T boundary condition); (2) uniform axial heat flux with uniform peripherally temperature at any cross section (H1 boundary condition). Numerical analysis has been conducted in the following range of parameters: Di/Do = 0.00, 0.25, 0.50, apex angle of the sector 2 alpha = 18 degrees, 20 degrees, 24 degrees, 30 degrees, 40 degrees, and Pr = 0.707. The solutions of the developing Nusselt number and friction factor are presented as functions of nondimensional axial distance. Comparisons are made between the computed results and the analytical or numerical results available in the literature. For all cases compared, satisfactory agreement is obtained.

Status of the noble crayfish Astacus astacus (L.) in Germany : monitoring protocol and the use of RAPD markers to assess the genetic structure of populations

On the basis of a literature review and new studies in Brandenburg, northeast Germany, the status and the genetic structure of the noble crayfish Astacus astacus (L.) in Germany are described. The present situation is characterized by a patchy distribution comprising at least 719 stocks, documented after 1990. Stocks are mainly confined to the uppermost stretches of small streams or to small lakes without connection to other surface waters. As is typical of Europe, geographical isolation, inbreeding and genetic drift may play an important role in the population structure of the noble crayfish in Germany. By means of RAPD-PCR, stocks in Brandenburg (Brl, Br2 and Br3), Schleswig-Holstein (SH) and Bavaria (B1 and 62) were analysed for their genetic structure. RAPD markers show high ability to separate significantly all investigated stocks as single populations. Mean non-dimensional distances were 5.8, 5.6 and 4.2 for SH-B, SH-Br and B-Br between-region comparisons, respectively. Values for within-region comparisons were 3.1 and 1.3 for B-B and Br-Br, respectively. However, even the three different lakes located in Brandenburg, which are only about 20 km apart from each other, contained significantly distinguishable populations. So far it is not possible to judge whether the distinct populations result from isolation of stocks or indicate local adaptations to the specific environmental conditions. The answer to this question is important with respect to conservational management and the design of restocking programmes. A decision tree for the inventory and monitoring of noble crayfish stocks is suggested, since some areas in the northeast of Germany may still contain many unknown stocks, which are of considerable importance for conservation.