Dimensionless Curves Research Articles

Experimental and numerical investigation of a hybrid PCM–air heat sink

The present work deals with a combined device in which the heat may be both absorbed by a phase-change material (PCM) and dissipated to the ambient air. Accordingly, the heat sink, made of aluminum 6061, has compartments where the PCM (eicosane C20H42) is stored and fins exposed to the air. The experiments are performed in both room- and elevated-temperature environment. A simplified thermal model, based on a two-dimensional enthalpy formulation for the PCM, is developed for a conservative estimation of temperature evolution. The results, presented in terms of base temperature (experimental and numerical) and PCM melt fraction (predicted), show a fairly good agreement between the experiments and simulations. Also shown are some findings obtained using a more complex model, which accounts for convection in the melt. A dimensional analysis yields the melt fraction and Nusselt number as functions of the Fourier and modified Stefan numbers. It also addresses the relative contributions of latent/sensible accumulation and heat transfer to the air. The dimensionless curves for latent-heat-based accumulation rate are rather similar in various cases. On the other hand, it is found that the share of sensible-heat-based accumulation rate tends to increase when the heat input increases.

Band gap design for one-dimensional periodic structure with three oscillators

Dimensionless dispersion curve equation of one-dimensional periodic structure with three oscillators is deduced. It is proved by singularity theory that the topology of the dispersion curves does not change with mass and stiffness parameter. Then the equations of initial and final frequencies of the bands are presented. The method of band gap design is gained consequently. Two examples i.e., the system with the same stiffness and the system with the same mass, are given to verify it. The method may provide the reference for designing the band gap of the photonic and phononic crystals.

The Research of Liquid Producing Capacity Variation Law in Water Controlled Reservoir

Through relative permeability, we can calculate core water cut ratio, dimensionless fluid productivity index and production index curve. And according to the data provided by the site, we can calculate actual water-cut, dimensionless fluid productivity index and production index curve in demonstration zone. Then we compare with the theoretical curves. By using combination reservoir engineering theory and dynamic production data method, we study the variation law of reservoir liquid producing capacity.

Water Lubricated Mechanism Based on Multilevel Method

This paper presents the multilevel method basic theory and its material progress which is used in water lubricated plastic alloy bearing’s elastohydrodynamic lubrication(EHL) numerical calculation. On base of liner contact theory, the results of water lubricated plastic alloy bearing’s EHL numerical calculation model are gained to describe dimensionless pressure and water thickness curves. It discloses the lubrication mechanism of the water lubricated plastic alloy bearing’s EHL. The cuneiform water film of frictional surface between bearing and spindle is come into being because the plastic alloy has high elasticity and lower Young’s modulus which lead the water lubricated bearing is easy to be distorted

Similarity solution of dam-break flow on horizontal frictionless channel

Compared with the Blasius similarity approach for the boundary layer theory, a similarity solution for dam-break flow on a horizontal channel with zero friction is considered by the theory of scale transformation. Time and space coordinates as the two independent variables are substituted by one independent dimensionless similarity variable, so that the governing partial differential equations can be transformed into a system of ordinary differential equations. The analytical similarity dam-break solution on a dry bed and the multinomial algebraic equation of shock wave on a wet bed are proposed for a prismatic channel of triangular cross-section. Basing on the similarity characteristic of dam-break flow, the flood propagation at any time and space can be described by a dimensionless curve. The dimensionless positions of strong and weak discontinuities for dam-break shock wave do not change with time, and the description of the dam-break hydrograph is therefore simplified.

Steady flow rate to a partially penetrating well with seepage face in an unconfined aquifer

The flow rate to fully screened, partially penetrating wells in an unconfined aquifer is numerically simulated using MODFLOW 2000, taking into account the flow from the seepage face and decrease in saturated thickness of the aquifer towards the well. A simple three-step method is developed to find the top of the seepage face and hence the seepage-face length. The method is verified by comparing it with the results of previous predictive methods. The results show that the component of flow through the seepage face can supply a major portion of the total pumping rate. Variations in flow rate as a function of the penetration degree, elevation of the water level in the well and the distance to the far constant head boundary are investigated and expressed in terms of dimensionless curves and equations. These curves and equations can be used to design the degree of penetration for which the allowable steady pumping rate is attained for a given elevation of water level in the well. The designed degree of penetration or flow rate will assure the sustainability of the aquifer storage, and can be used as a management criterion for issuing drilling well permits by groundwater protection authorities.

Microdamage Accumulation Changes According to Animal Mass: An Intraspecies Investigation

The fatigue life of a structure is also influenced by its size. Statistically, a bone from a large animal is expected to bear a higher risk of stress fracture if compared to the same bone from a small animal of the same species. This is not documented in the dog, where individuals can have a 40 times difference in body mass. We investigated the effect of body size on cortical bone microdamage accumulation, cortical microstructural organization (porosity, osteon area, and osteocyte lacunar density), and turnover in dogs with a wide body mass range. The aim was to understand and mathematically model how the bone tissue copes with the microdamage accumulation linked to body mass increase. Calcified transverse cortical sections of 18 canine radii of remarkably different size were examined by means of a standard bulk-staining technique and histomorphometric standard algorithms. Relationships between the investigated histomorphometric variables age, sex and mass were analyzed by general linear multivariate models and exponential equations. Type and location of microdamage and bone turnover were not influenced by body mass. Gender did not influence any parameter. Age influenced bone turnover and activation frequency. Microcrack density was influenced by bone mass. Bones had a similar microstructural organization within the same species regardless of the subject's dimension. Microdamage accumulation is inversely related to bone mass, whereas bone turnover is mass-invariant. We theorize a mass-related change in the bone fracture toughness targeted to reach an optimal unique dimensionless curve for fatigue life.

Two-dimensional study of lubrication mechanism of water-lubricated rubber alloy bearing

Because of the high elasticity and low elastic modulus of rubber alloy, the accurate calculation of Elastohydrodynamic Lubrication (EHL) of water-lubricated rubber alloy bearing is complex. In this paper, the numerical analysis of lubrication mechanism of water-lubricated rubber alloy bearings is carried out by using multi-grid method. Curves of dimensionless film thickness and dimensionless pressure are drawn. The results indicate that on the dimensionless pressure curve second pressure peak does not exist and on the dimensionless film thickness curve the minimum film thickness appears on symmetrical axis without 'earlobe'. It is good for forming of EHL and friction-wear property is enhanced.

Averaging effects of a strain gage

Choosing the right strain gage for a measurement application requires selecting gages with the right characteristics for the job. In general, the strain gage is to be used to measure the strain at the center of the gage, but it inherently underestimates the peak strain when it is mounted in high stress gradient areas. This paper concerns itself with the averaging effects of a strain gage along gage filaments. The approach is unconventional in dealing with the orientation and size of the gage. The results provide insight into the averaging effect and selecting gages for measuring strains in areas of steep strain gradients. Dimensionless curves which can be used to estimate errors as well as enhance hole-drilling method results are presented. Practical recommendations are made for selecting gages for high strain gradient measurements.

In silico screening for unmonitored, potentially problematic high production volume (HPV) chemicals prone to sequestration in biosolids

Thousands of high production volume (HPV) chemicals are used in the US at rates exceeding 450,000 kg (1 million pounds) per year, yet little is known about their fates during wastewater treatment and upon release into the environment. We utilized a recently introduced empirical model to predict the fraction of the mass loading (in raw sewage) that is expected to persist in digested sludge following conventional municipal treatment of chemical-laden sewage. The model requires only two readily available input parameters, a compound's log K(OW) value and a dimensionless curve fitting parameter (p(fit)). Following refinement of the fitting parameter and cross-validation of the model using the Jackknife method, we predicted the mass fractions of 207 hydrophobic HPV chemicals (log K(OW) of ≥ 4.0) that are expected to accumulate in digested municipal sludge during conventional wastewater treatment. Using this screening approach in conjunction with information from toxicity databases, we identified 11 HPV chemicals that are of potential concern due to (i) their propensity to accumulate and persist in sludge (>50% of mass loading), (ii) unfavorable ecotoxicity threshold values, and (iii) structural characteristics suggestive of environmental persistence following release of these HPV chemicals on land during biosolids recycling. The in silico screening approach taken in this study highlights existing environmental monitoring needs and may guide risk management strategies for biosolids disposal.

Optimal sizing of rain water tanks for domestic water conservation

Melbourne is facing a severe drought having its 12th consecutive below average rainfall year. Water authorities have been forced to impose rigorous water restrictions including voluntary per capita water use targets after more than 20 years of unrestricted water supply. The current severe drought and dwindling water resources have accelerated the use of alternative water sources including domestic rainwater. There is a large variation in average annual rainfall in the Greater Melbourne area ranging from 1050 mm in the east to 450 mm in the west. Hence, there is a significant difference in the tank size required in the west and the east of Melbourne to meet a similar demand and to provide the same supply reliability. The paper presents a novel methodology and a relationship for optimal sizing of rainwater tanks considering the annual rainfall at the geographic location, the demand for rainwater, the roof area (catchment area) and the desired supply reliability. The characteristic of the developed dimensionless curve reflects these variables and paves the way for developing a web based interactive tool for selecting the optimum rainwater tank size.

Modeling of Out-of-Plane Behavior of Masonry Walls

The flexural behavior of rectangular masonry sections is investigated by considering nonlinear stress-strain in compression and limited-tension material. A preliminary analysis shows that, with variation in the parameters specializing with the adopted conventional constitutive law, the experimentally observed behavior of different kinds of masonry materials can be approximated. Subsequently, moment-curvature dimensionless curves are derived numerically by satisfying the equilibrium equations of the section. In the case of negligible tensile strength these curves exhibit a typical shape that can be approximated by analytical expressions; consequently, suitable functions are proposed that are governed by only a few parameters which depend on the compression level of the section and the available ductility of the material. The reliability of the proposed modeling procedure is also verified by using the experimental results of a previous study, where masonry elements subjected to an increasing eccentric normal load were considered. Therefore, the analytically defined flexural behavior is transferred to the characteristic sections of a discrete model of slender masonry column, in order to reproduce the experimental results of full-scale tests on bearing masonry walls subjected to increasing lateral deflections for stability analyses. Comments on the results obtained with this model would be useful for further investigations.

Parameters affecting the occurrence of quicksand and the drying up of large diameter wells that gain water from the bottom: a case study from Iran

Large diameter fully cased wells that gain water from the bottom are often dug in sandy and collapsible aquifers. They have cylindrical vertical walls lined with brick or concrete. The well bottom is partially filled with aquifer material through which the flow is vertically upward. When the vertical hydraulic gradient reaches a critical value, quicksand occurs and the well structure can be destroyed. Another difficulty encountered is drawdown in the wellbore and the drying up of the well. To overcome these problems, the flow around and beneath these wells is numerically simulated. The simulation results are used to investigate the effect of well and aquifer parameters on quicksand and drawdown. For practical purposes, the dimensionless drawdown-time and dimensionless vertical gradient-time curves are developed. It was found that the ratio of filling material thickness to well radius affects the shape of these type curves. The type curves may be used to predict the time after pumping commences when quicksand occurs and the well dries up. They are also useful to design the safe pumping rate and duration as well as the optimum well radius. These are demonstrated by analyzing the pumping test data from a case study in the arid Chah Kutah region, southern Iran.

Computation of Normal and Critical Depths in Parabolic Cross Sections

With a suitable non-dimensionalization, the available charts for normal depth computation in parabolic sections are reduced to a single dimensionless curve when either Manning's or Chezy's resistance equation is used. Moreover, simple approximate solutions are presented to compute normal depth with a quite adequate degree of accuracy. Upon rearranging the critical-flow criterion equation, relevant explicit relationships are derived for this state of flow. The procedure of normal and critical depths calculation is clearly described through some examples.

Predicting onset of high speed gas metal arc weld bead defects using dimensional analysis techniques

The onset of geometric defects such as humping or discontinuous weld beads during gas metal arc welding (GMAW) frequently limits the use of higher welding speeds and increased productivity. In the present study, a dimensional analysis of the GMAW process was performed in order to identify a number of dimensionless groups formulated based on various GMAW process parameters and material properties that could be used to predict when humping or discontinuous weld beads would occur. Experimental data from bead on plate GMA welds in plain carbon steel plate made using argon and two different reactive shielding gases, welding powers between 5 and 12 kW and a range of welding speeds were then used to create dimensionless process maps. These maps showed the limiting welding speed above which the high speed weld defects occurred as a function of all influential process parameters. It was shown that all experimental data for limiting welding speeds could be collapsed onto two collinear dimensionless curves. Also, the transition from spray to rotational metal transfer was found to occur at a well defined value of one of these dimensionless parameters. The effects of work piece preheat temperature on humping were correctly predicted and there was a good correlation between the dimensionless GMAW process map and experimental data from other independent studies. These results suggest that the occurrence of high speed weld bead defects such as humping and discontinuous weld beads as well as the transition from spray to rotational metal transfer can be predicted using these new dimensionless GMAW process maps.

Nuclear-magnetic-resonance diffusion simulations in two phases in porous media

Time-dependent diffusion simulations which can be measured by nuclear magnetic resonance (NMR) were numerically performed in consolidated reconstructed porous media saturated by two immobile fluids. The phase distributions were obtained by an immiscible lattice Boltzmann technique which incorporates interfacial tension and wetting. The apparent diffusion coefficient in each fluid was determined by a random walk algorithm. Permeability and conductivity tensors were calculated by finite-difference schemes. The major properties valid for a single phase could be generalized to two phases. First, the characteristic length Lambda introduced by Johnson et al.[Phys. Rev. Lett. 57, 2564 (1986)] is of the order of twice the phase volume to surface ratio. Second, the apparent diffusion coefficients for all porosities, saturations, and phases can be represented by a single dimensionless curve.

Thermal Stress and Deflection Analysis of a Glass Window (Circular Plate) Elastically Restrained Along its Edge in a Photonic Device

An exact analysis is presented for the stresses and deflections of circular plates (glass windows) elastically restrained along its edge in a photonic device’s housing subjected to the pressure and temperature loadings. Dimensionless curves and charts are also provided for engineering practice convenience. These charts show the interactions of the deflection, stress, temperature, pressure, linear spring constant, rotational spring constant, geometry of the glass windows, and the Young’s modulus, Poisson’s ratio, thermal coefficient of expansion, geometry, stress-optical coefficient, and birefringence of glass materials. The results presented herein should be useful for designing glass windows for shipping, storing, handling, functioning, and reliability.

Modeling analytical tests of supercritical fluid extraction from solids with langmuir kinetics

A model for the analytical supercritical fluid extraction (SFE) tests from solid samples in which desorption of the solute from the surface of the solid is the rate determining step is presented. The desorption process is described by the Langmuir kinetics. The two stages of the test (static and dynamic) are modeled, where each of the two phases (solid and supercritical fluid) are considered well mixed. The resulting ordinary differential equations are solved analytically for the static stage and numerically for the dynamic stage. Dimensionless curves of concentrations of the two phases and fractional recovery during the two stages of the tests are predicted. These curves are characterized by two dimensionless parameters for the static stage, the equilibrium constant and the fractional initial capacity, in addition to one parameter for the dynamic stage, the desorption coefficient. The model provides a good fit to experimental results for SFE from solids. The trends in the fitted parameters with respect to pressure and temperature are in agreement with theory.

Closure to “Dimensionless Curves for Normal-Depth Calculations in Canal Sections” by K. Babaeyan-Koopaei

Closure to “Dimensionless Curves for Normal-Depth Calculations in Canal Sections” by K. Babaeyan-Koopaei

Discussion of “Dimensionless Curves for Normal-Depth Calculations in Canal Sections” by K. Babaeyan-Koopaei

Discussion of “Dimensionless Curves for Normal-Depth Calculations in Canal Sections” by K. Babaeyan-Koopaei