Empirical Correction Factors Research Articles

3-D microscale simulation of dust-loading in thin flat-sheet filters: A comparison with 1-D macroscale simulations

In this work, a microscale approach is undertaken to simulate the instantaneous pressure drop and collection efficiency of fibrous media exposed to particle loading, i.e., filter aging. The air flow field through 3-D disordered geometries representing the internal microstructure of a fibrous filter is obtained by numerically solving Stokes' equations. A Lagrangian approach is used to track the trajectory of particles through our virtual filter media and determine the filter's collection efficiency under different dust-load conditions. The calculations were conducted using the ANSYS CFD code enhanced with a series of in-house C++ subroutines. To better illustrate the value of such CPU-intensive 3-D microscale modeling, we compared the results of our simulations with those obtained from a 1-D macroscale model developed based on some of the pioneering studies reported in the literature. It was found that while the 1-D macroscale models can provide fast predictions for the pressure drop and collection efficiency of a given filter, they require a series of empirical correction factors or case-specific assumptions that limit their usage for design and development of new filter media. The 3-D microscale simulation methods, in contrast, are self-sufficient as they are developed based on first principles. With the current rate of progress in developing high-speed computers, it is expected that 3-D microscale simulations will be the preferred method of filter design in the near future.

Measurements of heat transport by turbulent Rayleigh-Bénard convection in rectangular cells of widely varying aspect ratios

High-precision measurements of the Nusselt number Nu for Rayleigh-Benard (RB) convection have been made in rectangular cells of water (Prandtl number Pr ≈ 5 and 7) with aspect ratios (Γ x ,Γ y ) varying between (1, 0.3) and (20.8, 6.3). For each cell the data cover a range of a little over a decade of Rayleigh number Ra and for all cells they jointly span the range 6×105 < Ra<1011. The two implicit equations of the Grossmann-Lohse (GL) model together with the empirical finite conductivity correction factor f(X) were fitted to obtain estimates of Nu ∞ in the presence of perfectly conducting plates, and the obtained Nu ∞ is independent of the cells’ aspect ratios. A combination of two-power-law, Nu ∞ = 0.025Ra 0.357+0.525Ra 0.168, can be used to describe Nu ∞(Ra). The fitted exponents 0.357 and 0.168 are respectively close to the predictions 1/3 and 1/5 of the II u and IV u regimes of the GL model. Furthermore, a clear transition from the II u regime to the IV u regime with increasing Ra is revealed.

Solution phase thermodynamics of strong electrolytes based on ionic concentrations, hydration numbers and volumes of dissolved entities

This article summarizes the successful restoration of Arrhenius’ theory of electrolytic dissociation founded 130 years ago. His idea of using the conductivity ratio for the degree of dissociation was a breakthrough in interpreting the properties of dilute solutions. For higher concentrations, as it was not satisfactory, attempts were being made to improve the methods of obtaining the degrees of dissociation. However, the latter was prematurely replaced by the empirical activity coefficient correction factors. Subsequently, the success of the Debye–Huckel (D–H) theory of inter-ionic interaction between free ions in explaining the properties of dilute solutions was taken to mean complete dissociation at all concentrations and interpretation of solution properties amounted to extending the D–H equations by the gradual addition of more parameters. At the end of six decades the equations became so complex that they failed to provide a unified interpretation of the causes of non-ideality at all concentrations and a molecular insight into the observed phenomena. Therefore, the present author abandoned them and started investigating the available experimental data as such. Using the degrees of dissociation and surface and bulk hydration numbers evaluated from solution vapour pressures, the author was able to interpret solution properties based on the idea due to Arrhenius a century earlier. Presented here is a comparison of the complicated equations based on complete dissociation with the simple equations obtained based on partial dissociation, hydration and volumes of entities in the solution. All the main equations are summarized in the table.

Effect of longitudinal pitch on convective heat transfer in crossflow over in-line tube banks

An analytical study using a CFD (Computational Fluid Dynamics) code has been performed to investigate the effect of the longitudinal pitch on the single-phase heat transfer characteristics in crossflow over in-line tube banks. A simplified geometry with periodic and symmetric boundary conditions is employed for the analysis. A sensitivity analysis using various two-equation turbulence models has been conducted to examine the impact of the turbulence model on the heat transfer characteristics and to determine a turbulence model that can describe the physical phenomena of interest appropriately. The result indicates that the heat transfer coefficient might be reduced by 37.1% from the prediction by a well-known correlation by Zukauskas (Adv. Heat Trans., 2007, 8, 93) as the longitudinal pitch decreases. By analyzing the result, it is found that the heat transfer degradation can be estimated by using an empirical correction factor and the Zukauskas’ correlation can predict existing experimental data when the correlation is combined with the empirical correction factor developed in this study.

Production of medical radioisotope 153Sm in the Tehran Research Reactor (TRR) through theoretical calculations and practical tests

The feasibility of producing 2000–3000mCi 153Sm by irradiation of 152Sm in 5MW TRR was studied via TRR core simulation. In this study the cross-section of 152Sm (n,γ) 153Sm reaction from ENDF/B library was used. The effective activation cross section for production of 153Sm is obtained using the neutron spectra in different irradiation channel of the core. The activity of the simulated samples is calculated using the obtained fluxes and cross sections. Then samples were prepared and irradiated under different conditions and fluxes. The final production’s specific activity was measured by the standard dose calibrator ISOMED 1010. By comparison of the theoretical calculations and actual measurements, an empirical correction factor (Kf) was obtained, which is helpful in production procedure of the 153Sm radioisotope. The optimal weight of the samples and irradiation time was studied according to the flux calculations based on the location of the sample and saturated activity calculation. In order to test the proposed conditions, samples were prepared and were irradiated under the proposed conditions. According to the compared results with the initial irradiation condition, the new proposed sample which weighed 4mg of Sm2O3 is acceptable for the labeling, therefore this study led to nearly 60% decrease in the amount of material used in the production process.

A computationally efficient hybrid leakage model for positive displacement compressors and expanders

An empirical frictional correction factor to the isentropic nozzle model has been developed for application to refrigerant leakage modeling in scroll, rotary and other similar compressors and expanders. This correction factor is derived by calculating the leakage mass flow rate with a compressible, variable area, real gas properties model and referencing the results to an isentropic nozzle model. The ratio of flows is correlated to the Reynolds number, a characteristic length and the leakage gap width. A representative selection of fluids and geometries are employed. For all the correlations, at least 93% of the points are predicted within an absolute error band of 20%.

Application of Empirical Scale Correction Factors with Regional Flood Prediction Equations: A Case Study for Eastern Australia

Regional flood prediction equations are generally developed based on the recorded streamflow data in medium- to large-sized catchments, but these equations are often applied in practice to very small catchments. Since there is little/no recorded streamflow data available for very small catchments, the applicability of the developed regional flood prediction equations to these catchments cannot be verif ed directly. The empirical observations reveal that smaller catchments produce “steeper flood frequency curves” than larger catchments given all the flood generation factors remaining the same. This paper uses data from 429 catchments from the states of Victoria, New South Wales and Queensland to examine the effects of catchment size on flood quantile estimates. An empirical scale correction factor is proposed that can partially account for the effects of decreasing catchment size on flood quantile estimates. Independent testing using 32 catchments shows that the proposed method provides reasonable results for the catchments as small as 2.3 km2, but its applicability to very small catchments (ie. smaller than 2.3 km2) cannot be verif ed due to the unavailability of recorded streamflow data.

Experimental and theoretical studies of CO2 spectra for planetary atmosphere modelling: region 600–9650 cm−1 and pressures up to 60 atm

Extensive experimental studies of room-temperature carbon dioxide absorption coefficients are reported for a wide range of wavenumbers and pressures requested in atmospheric spectra modelling. The quality of measurements is optimised by the use of two complementary setups with long- and short-path optical cells for low and high gas densities, respectively. The recorded spectra provide a representative picture of band-shape evolutions from gaseous to nearly liquid phases of CO2 and enable a theoretical analysis of line-mixing effects. Various kinds of vibrational bands (Σ←Σ, Π←Σ as well as Π←Π transitions) are modelled using a specific, non-Markovian in the general case, approach of Energy-Corrected Sudden type which is based on the symmetric relaxation matrix and, in contrast to the standard ECS model used for infrared absorption calculations, ensures automatically the fundamental relations of detailed balance and double-sided sum rules. Moreover, this method properly accounts for the vibrational angular momenta of the initial and final molecular states and allows including Coriolis resonances via the usual Herman-Wallis factors in the dipole transition moments. With a set of ECS parameters previously obtained for isotropic and anisotropic Raman spectra modelling, completely neglected imaginary part of the relaxation operator and a simple change in the tensorial rank to get the dipole absorption case in the working formulae, the computed spectra reproduce quite correctly the vibrotational band shapes up to 20 amagat without any additional parameter. An empirical correction factor tentatively introduced to account globally for the Coriolis effects on the relaxation matrix leads to better matches with high-density band shapes but its role merits further studies with an accurately modelled imaginary part of the relaxation matrix.

Ion-Exchange Affinity of Organic Cations to Natural Organic Matter: Influence of Amine Type and Nonionic Interactions at Two Different pHs

Sorption to standard soil organic matter (SOM) has been studied for a wide variety of organic cations using a flow through method with fully aqueous medium as eluent. SOM sorption for weak bases (pK(a) 4.5-7) was stronger at pH 4.5 than at pH 7, indicating that the ion-exchange affinity of the cationic species to SOM was higher than the bulk partition coefficient of corresponding neutral species to SOM. In the range of pH 4.5-7, the effect of pH on the sorption coefficients for strong bases with pK(a) > 7 was small, within 0.3 log units. For cations with the molecular formula C(x)H(y)N, sorption was accurately predicted by a model accounting for size (increase with alkyl chain length) and type of charged group (1° amine >4° ammonium of equal size). In addition to the C(x)H(y)N-model, several empirical correction factors were derived from the data for organic cations with polar functional groups. Models based on K(OW) or pK(a) fail to explain differences in sorption affinity of the ionic species. Our data on ion-exchange affinities for 80 organic cations show many examples where specific chemical moieties, for example, CH(2)-units, aromatic rings or hydroxyl groups, contribute differently to the sorption coefficient as compared to bulk partitioning data of neutral compounds. Other sorption models that were evaluated to explain variation between compounds suffered from outliers of more than one log unit and did not reduce relative log mean standard errors below 0.5. A wider range of sorption coefficients and more sorption data in general are required to improve modeling efforts further.

Boundary Shear Stress in a Trapezoidal Channel

This paper focuses on a hydraulic radius separation approach used to calculate the boundary shear stress in terms of bed and wall shear stress proposed in a trapezoidal channel. The average bed and sidewall shear stress in smooth trapezoidal open channels are derived after using Guo & Julien (2005) early equations taking a part of an investigation to cover both rectangular and trapezoidal channels. On the basis of the conformal mapping procedure, a numerical solution is obtained for a case of constant eddy viscosity without concerning secondary currents effect. In comparison with laboratory measurements data, the first approximation for a rectangular channel overestimates the average bed shear stress measurement by about 4.8% and by decreasing a sidewall slope, overestimation increases. It, however; underestimates the average sidewall shear stress by about 6.88%; in this case, underestimation increases while sidewall slope is decreasing. A second approximation is then presented by introducing two lumped empirical correction factors for taking into account the effects of secondary currents, variable eddy viscosity and else. Using experimental data, in terms of average bed shear stress, the second approximation agrees very well (at least R2>0.99, and an average relative error at most less than 5.35%) over a wide range of width to depth ratios. In terms of average wall shear stress, the second approximation returns acceptable results despite the scatter of the data with an average relative error less than 5.95% and by R2>0.93 where it seems to be reasonable, herein.

Empirical STORM-E model: I. Theoretical and observational basis

Auroral nighttime infrared emission observed by the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) instrument onboard the Thermosphere–Ionosphere–Mesosphere Energetics and Dynamics (TIMED) satellite is used to develop an empirical model of geomagnetic storm enhancements to E-region peak electron densities. The empirical model is called STORM-E and will be incorporated into the 2012 release of the International Reference Ionosphere (IRI). The proxy for characterizing the E-region response to geomagnetic forcing is NO+(v) volume emission rates (VER) derived from the TIMED/SABER 4.3μm channel limb radiance measurements. The storm-time response of the NO+(v) 4.3μm VER is sensitive to auroral particle precipitation. A statistical database of storm-time to climatological quiet-time ratios of SABER-observed NO+(v) 4.3μm VER are fit to widely available geomagnetic indices using the theoretical framework of linear impulse-response theory. The STORM-E model provides a dynamic storm-time correction factor to adjust a known quiescent E-region electron density peak concentration for geomagnetic enhancements due to auroral particle precipitation. Part II of this series describes the explicit development of the empirical storm-time correction factor for E-region peak electron densities, and shows comparisons of E-region electron densities between STORM-E predictions and incoherent scatter radar measurements. In this paper, Part I of the series, the efficacy of using SABER-derived NO+(v) VER as a proxy for the E-region response to solar-geomagnetic disturbances is presented. Furthermore, a detailed description of the algorithms and methodologies used to derive NO+(v) VER from SABER 4.3μm limb emission measurements is given. Finally, an assessment of key uncertainties in retrieving NO+(v) VER is presented.

On the influence of site conditions and earthquake magnitude on ground-motion within-earthquake correlation: analysis of PGA data from TSMIP (Taiwan) network

We analysed the within-earthquake correlation of ground motion using the strong-motion records accumulated by the TSMIP (Taiwan Strong Motion Instrumentation Program) network in Taiwan during 1993–2009. Two ground-motion prediction equations, which were recently developed for peak ground acceleration (PGA) in the region and based on moment and local magnitude and hypocentral distance, were used for the calculation and analysis of ground-motion residuals. We also used the database containing shear-wave velocity data averaged for the top 30 m of the soil column (Vs30) for the TSMIP stations. We showed that the within-earthquake correlation may vary significantly depending on site classes, gross geological features of the area, and magnitude of earthquakes, records of which dominate the analysed dataset. On the one hand, there is a prominent correspondence between the within-earthquake correlation of PGA residuals and spatial correlation of Vs30 values, which was estimated for particular geological structures (e.g., sedimentary filled basins and large plain areas). On the other hand, the high level of ground-motion correlation (or significant non-random component of residuals) may be caused by the joint influence of soft surface soil and thick sediments and by the path or azimuthal effects. The point-source approximation of extended fault and neglected hanging- and foot-wall effects may also result in non-random residuals. The application of empirical correction factors, which consider the magnitude of earthquakes, source-to-site distance and Vs30 value for given stations, allows for the effective reduction in the level of within-earthquake correlation, as well as the within-earthquake standard deviation. The results of the analysis may be used in practical estimates of seismic hazard, damage and loss for spatially distributed structures (portfolios, lifelines) in Taiwan, as well in other regions with similar geological characteristics.

Practical use of the regression offset approach for the prediction of in vivo intrinsic clearance from hepatocytes

Systematic under-prediction of clearance is frequently associated with in vitro kinetic data when extrapolated using physiological scaling factors, appropriate binding parameters and the well-stirred model. The present study describes a method of removing this systematic bias through application of empirical correction factors derived from regression analyses applied to the in vitro and in vivo data for a defined set of reference compounds.Linear regression lines were established with in vivo intrinsic clearance (CLint), derived from in vivo clearance data and scaled in vitro intrinsic clearance from isolated hepatocyte incubations. The scaled CLint was empirically corrected to a predicted in vivo CLint using the slope and intercept from a uniform weighted linear regression applied to the in vitro to in vivo extrapolation.Cross validation of human data demonstrated that 66% of the reference compounds had a predicted in vivo CLint within two-fold of the observed value. The average absolute fold error (AAFE) for the in vivo CLint predictions was 1.90. For rat, 54% of the compounds had a predicted value within two-fold of the observed and the AAFE was 1.98.Three AstraZeneca projects are used to exemplify how a two-sided prediction interval, applied to the rat regression corrected reference data, can form the basis for assessing the likelihood that, for a given chemical series, the in vitro kinetic data is predictive of in vivo clearance and is therefore appropriate to guide optimisation of compound metabolic stability.

Small field diode correction factors derived using an air core fibre optic scintillation dosimeter and EBT2 film

There is no commercially available real-time dosimeter that can accurately measure output factors for field sizes down to 4 mm without the use of correction factors. Silicon diode detectors are commonly used but are not dosimetrically water equivalent, resulting in energy dependence and fluence perturbation. In contrast, plastic scintillators are nearly dosimetrically water equivalent. A fibre optic dosimeter (FOD) with a 0.8 mm3 plastic scintillator coupled to an air core light guide was used to measure the output factors for Novalis/BrainLab stereotactic cones of diameter 4–30 mm and Novalis MLC fields of width 5–100 mm. The FOD data matched the output factors measured by a 0.125 cm3 Semiflex ion chamber for the MLC fields above 30 mm and those measured with the EBT2 radiochromic film for the cones and MLC fields below 30 mm. Relative detector readings were obtained with four diode types (IBA SFD, EFD, PFD, PTW 60012) for the same fields. Empirical diode correction factors were determined by taking the ratio of FOD output factors to diode relative detector readings. The diodes were found to over-respond by 3%–16% for the smallest field. There was good agreement between different diodes of the same model number.

Prediction of Effective Heat Storage Coefficient of Multi-Phase Materials

A theoretical model, to predict effective heat storage coefficient (HSC) from the values of HSCs of the constituent phases and their volume fractions for real two-phase systems is presented and is extended to three-phase moist materials, assuming an effective continuous medium (ECM) approach. Particles are assumed to be ellipsoidal in shape and arranged in three-dimensional cubic array. The arrangement has been divided into unit cells, each of which contains an ellipsoid. The HSC of the unit cell has been determined by applying resistor model. To take account of the non-linear flow of heat flux lines in real systems, incorporating an empirical correction factor in the place of physical porosity modifies an expression for HSC. An effort is made to correlate it in terms of the ratio of HSCs of the constituents and the physical porosity. To test the validity of the derived expression, the HSC of some building materials saturated with different liquids have been determined. The HSC of metal powders and metallic oxides at varying temperatures have also been determined. A good agreement has been found between the experimental and the predicted values reported in the literature.

Boundary Condition Effects on Maximum Groundwater Withdrawal in Coastal Aquifers

Prevention of sea water intrusion in coastal aquifers subject to groundwater withdrawal requires optimization of well pumping rates to maximize the water supply while avoiding sea water intrusion. Boundary conditions and the aquifer domain size have significant influences on simulating flow and concentration fields and estimating maximum pumping rates. In this study, an analytical solution is derived based on the potential-flow theory for evaluating maximum groundwater pumping rates in a domain with a constant hydraulic head landward boundary. An empirical correction factor, which was introduced by Pool and Carrera (2011) to account for mixing in the case with a constant recharge rate boundary condition, is found also applicable for the case with a constant hydraulic head boundary condition, and therefore greatly improves the usefulness of the sharp-interface analytical solution. Comparing with the solution for a constant recharge rate boundary, we find that a constant hydraulic head boundary often yields larger estimations of the maximum pumping rate and when the domain size is five times greater than the distance between the well and the coastline, the effect of setting different landward boundary conditions becomes insignificant with a relative difference between two solutions less than 2.5%. These findings can serve as a preliminary guidance for conducting numerical simulations and designing tank-scale laboratory experiments for studying groundwater withdrawal problems in coastal aquifers with minimized boundary condition effects.

Pressure drop and aerosol filtration efficiency of microfibrous entrapped catalyst and sorbent media: Semi-empirical models

A three dimensional network of 4–12μm sintered nickel fibers occupying 2.5–40% (vol.) was used to entrap 5–45% (vol.) aluminum oxide particles with diameters between 90–600μm. Pressure drop was measured at face velocities of ⩽100cm/s, and filtration efficiency was measured using polydispersed aerosols of potassium chloride particles from 0.09 to 5μm (dia.). Traditional models for pressure drop and filtration efficiency use mixing rules when combining two components of different diameters. However, these mixing rules gave large errors because of the significant difference between the diameters of the fibers and the entrapped particles. This study describes semi-empirical models for estimating aerosol filtration efficiency and pressure drop, taking into account the heterogeneity created due to wide diameter variations of the components. An empirical factor accounting for the filtration efficiency due to entrapped particles was added to the single fiber efficiency model by Payet et al. (1992) [15]. An empirical correction factor accounting for heterogeneity due to entrapped particles was needed to fit the data to the pressure drop model developed by Harris et al. (2001) [4]. The modeled filtration efficiency agreed with the experimental results with errors less than 8% for structures with fiber loading from 2.5% to 12% (vol.) and particle loading from 5% to 45% (vol.). Pressure drop model agreed with the experimental results with errors less than 10% for structures with fiber loading from 2.5% to 40% (vol.) and particle loading from 5% to 45% (vol.).

Cloud optical thickness and liquid water path – does the &amp;lt;i&amp;gt;k&amp;lt;/i&amp;gt; coefficient vary with droplet concentration?

Abstract. Cloud radiative transfer calculations in general circulation models involve a link between cloud microphysical and optical properties. Indeed, the liquid water content expresses as a function of the mean volume droplet radius, while the light extinction is a function of their mean surface radius. There is a small difference between these two parameters because of the droplet spectrum width. This issue has been addressed by introducing an empirical multiplying correction factor to the droplet concentration. Analysis of in situ sampled data, however, revealed that the correction factor decreases when the concentration increases, hence partially mitigating the aerosol indirect effect. Five field experiments are reanalyzed here, in which standard and upgraded versions of the droplet spectrometer were used to document shallow cumulus and stratocumulus topped boundary layers. They suggest that the standard probe noticeably underestimates the correction factor compared to the upgraded versions. The analysis is further refined to demonstrate that the value of the correction factor derived by averaging values calculated locally along the flight path overestimates the value derived from liquid water path and optical thickness of a cloudy column, and that there is no detectable relationship between the correction factor and the droplet concentration. It is also shown that the droplet concentration dilution by entrainment-mixing after CCN activation is significantly stronger in shallow cumuli than in stratocumulus layers. These various effects are finally combined to produce the today best estimate of the correction factor to use in general circulation models.

Unbiased estimation of refractive state of aberrated eyes

We seek unbiased methods for estimating the target vergence required to maximize visual acuity based on wavefront aberration measurements. Experiments were designed to minimize the impact of confounding factors that have hampered previous research. Objective wavefront refractions and subjective acuity refractions were obtained for the same monochromatic wavelength. Accommodation and pupil fluctuations were eliminated by cycloplegia. Unbiased subjective refractions that maximize visual acuity for high contrast letters were performed with a computer controlled forced choice staircase procedure, using 0.125 diopter steps of defocus. All experiments were performed for two pupil diameters (3mm and 6mm). As reported in the literature, subjective refractive error does not change appreciably when the pupil dilates. For 3mm pupils most metrics yielded objective refractions that were about 0.1D more hyperopic than subjective acuity refractions. When pupil diameter increased to 6mm, this bias changed in the myopic direction and the variability between metrics also increased. These inaccuracies were small compared to the precision of the measurements, which implies that most metrics provided unbiased estimates of refractive state for medium and large pupils. Thus a variety of image quality metrics may be used to determine ocular refractive state for monochromatic (635nm) light, thereby achieving accurate results without the need for empirical correction factors.

Discrete-State Representation of Ion Permeation Coupled to Fast Gating in a Model of CLC-Chloride Channels: Analytic Estimation of the State-to-State Rate Constants

Analytical estimation of state-to-state rate constants is carried out for a recently developed discrete state model of chloride ion motion in a CLC chloride channel (Coalson and Cheng, J. Phys. Chem. B 2010, 114, 1424). In the original presentation of this model, the same rate constants were evaluated via three-dimensional Brownian dynamics simulations. The underlying dynamical theory is an appropriate single- or multiparticle three-dimensional Smoluchowski equation. Taking advantage of approximate geometric symmetries (based on the details of the model channel geometry), well-known formulas for state-to-state transition rates are appealed to herein and adapted as necessary to the problem at hand. Rates of ionic influx from a bulk electrolyte reservoir to the nearest binding site within the channel pore are particularly challenging to compute analytically because they reflect multi-ion interactions (as opposed to single-ion dynamics). A simple empirical correction factor is added to the single-ion rate constant formula in this case to account for the saturation of influx rate constants with increasing bulk Cl(-) concentration. Overall, the agreement between all analytically estimated rate constants is within a factor of 2 of those computed via three-dimensional Brownian dynamics simulations, and often better than this. Current-concentration curves obtained using rate constants derived from these two different computational approaches agree to within 25%.