Dimensionless Correction Research Articles

Equivalent Analogy Research on Filtration Resistance of Wet Fiber Layer for Mine Particles

The hypothesis of the flushing fluid that is evenly distributed and flowing on the surface of the wet filtering layer fiber was first introduced in the paper, on which the concept of equivalent diameter of the composite trap was given to build the theoretical model of filtration resistance of wet fiber layer for aerosol particles, therefore the theoretical formula of wet filtration resistance has been derived, making possible the theoretical research on the filtration and purification resistance of wet fiber layer for dust particles. Based on the theoretical analysis, a semi-theoretical and semi-empirical formula that can be applied to the practical use has been eventually obtained by means of the necessary dimensionless correction of the theoretical results through simulation experiments, the formula and the methods of research questions are of guiding significance and conductive to the filtration and purification of wet fiber layer for aerosol particles.

Characterization and mitigation of water vapor effects in the measurement of ozone by chemiluminescence with nitric oxide

Abstract. Laboratory experiments were conducted to investigate the effects of water vapor on the reaction of nitric oxide with ozone in a gas-phase chemiluminescence instrument used for fast response and high sensitivity detection of atmospheric ozone. Water vapor was introduced into a constant level ozone standard and both ozone and water vapor signals were recorded at 10 Hz. The presence of water vapor was found to reduce, i.e. quench, the ozone signal. A dimensionless correction factor was determined to be 4.15 ± 0.14 × 10−3, which corresponds to a 4.15% increase in the corrected ozone signal per 10 mmol mol−1 of co-sampled water vapor. An ozone-inert water vapor permeable membrane (a Nafion dryer with a counterflow of dry air from a compressed gas cylinder) was installed in the sampling line and was shown to remove the bulk of the water vapor in the sample air. At water vapor mole fractions above 25 mmol mol−1, the Nafion dryer removed over 75% of the water vapor in the sample. This reduced the required ozone signal correction from over 11% to less than 2.5%. The Nafion dryer was highly effective at reducing the fast fluctuations of the water vapor signal (more than 97%) while leaving the ozone signal unaffected, which is a crucial improvement for minimizing the quenching interference of water vapor fluxes and required density correction in the determination of ozone fluxes by the eddy covariance technique.

Spoiled FLASH MRI with slice selective excitation: Signal equation with a correction term

ABSTRACTSpoiled fast low‐angle shot (FLASH) magnetic resonance imaging (MRI) provides a simple contrast, largely independent of the spin‐spin relaxation time. Three‐dimensional FLASH imaging (3D FLASH) has gained importance due to its simplicity and its ability to produce isotropic, high‐resolution images. Nevertheless, 2D FLASH imaging can be more suited than 3D FLASH imaging in various specific applications requiring long repetition time, such as imaging of the proton density (PD), as it allows interleaved slice acquisition rather than consecutive slice acquisition. In practice, however, a slice‐selective excitation produces a nonuniform excitation profile, which needs to be taken into account to allow reliable quantitative data analysis. In this work, the influence of the nonuniform excitation profile on the detected signal is modeled as a dimensionless multiplicative correction, function of the flip angle, and the ratio of the repetition time to the spin‐lattice relaxation time T1. This model is validated experimentally by measuring the PD and T1 MR parameters in a phantom experiment on a 3T clinical scanner. A good accuracy in the estimation of T1 and in the reconstruction of the PD (weighted by the receiver sensitivity profile) is obtained, for example, a relative error of 3% in T1 within the range [500, 2000] ms and a precision of 1% in PD. It is also shown how the proposed theory can be extended to magnetization‐prepared 2D‐spoiled FLASH as well as other variations of the 2D‐spoiled FLASH sequence. © 2013 Wiley Periodicals, Inc. Concepts Magn Reson Part A 42A: 89–100, 2013.

Influence of polydispersity on micromechanics of granular materials

We study the effect of polydispersity on the macroscopic physical properties of granular packings in two and three dimensions. A mean-field approach is developed to approximate the macroscale quantities as functions of the microscopic ones. We show that the trace of the fabric and stress tensors are proportional to the mean packing properties (e.g., packing fraction, average coordination number, and average normal force) and dimensionless correction factors, which depend only on the moments of the particle-size distribution. Similar results are obtained for the elements of the stiffness tensor of isotropic packings in the linear affine response regime. Our theoretical predictions are in good agreement with the simulation results.

Towards maximal heat transfer rate densities for small-scale high effectiveness parallel-plate heat exchangers

This paper addresses the question to what extent parallel-plate heat exchangers can be downsized without loss of thermal-hydraulic performance. It is shown that when the characteristic length scales of the channels are reduced at a constant pressure drop, the effectiveness exhibits a maximum due to axial heat conduction. The point of maximal effectiveness is found to correspond to a maximal thermal power density and thus to the minimal volume required for obtaining that effectiveness. Based on asymptotic relations for the effectiveness in the small and large channel limit, closed-form expressions are derived for the optimum geometric parameters that maximize power density in the limit of design effectiveness approaching unity. These relations are extended to a broader effectiveness range by means of dimensionless correction functions that are calculated numerically. The resulting expressions define optimal elemental units that can be used to construct parallel-plate counter-flow heat exchangers with the lowest possible core volume for effectiveness values between 0.53 and 1.

Sound reflection at the open end of axisymmetric ducts issuing a subsonic mean flow: A numerical study

This paper investigates the reflection of sound waves as they propagate toward the open end of ducts issuing a cold subsonic mean flow in a stagnant fluid. The investigations are conducted by using a relatively new one-step numerical technique known as the lattice Boltzmann method. The results obtained in terms of end correction, l, and magnitude of the pressure reflection coefficient, | R | , for an unflanged pipe model are in very good agreement with theoretical predictions and experimental data for the range of Mach numbers M ≤ 0.15 and Helmholtz numbers ka ≤ 1.5 . Simulations carried out for a similar pipe terminated by circular horns of different curvature radii show that | R | is independent of the horn geometry for Strouhal numbers Sr 0 < 4 , Sr 0 = ka / M . For situations in which M > 0 , the amplification of the reflection coefficient magnitude, that is | R | > 1 , is normally ∼ 20 percent higher than that observed for an unflanged pipe issuing an equal Mach number flow. Furthermore, the amplification maxima is found to occur always at Sr 0 = π / 2 , regardless of whether the pipe is unflanged or terminated by different circular horns. Conversely, the results for the end correction are strongly dependent on the horn curvature. For the low Strouhal number limit, the dimensionless end correction measured at the junction between the horn and the pipe with radius a becomes l / a = 0.31 for a horn whose curvature radius is 2 a , and l / a = 0.62 for a horn with curvature radius equal to 4 a .

A generalized viscoelastic Biot/squirt model for clay-bearing sandstones in a wide range of permeabilities

To simultaneously take into account the Biot-flow mechanism, the squirt-flow mechanism, and the frame-viscoelasticity mechanism, a generalized viscoelastic BISQ (Biot/squirt) model is developed for wave propagation in clay-bearing sandstones based on Dvorkin’s elastic BISQ model. The present model is extended to a wide range of permeabilities (k > 0.05 mD) by introducing a dimensionless correction factor for viscoelastic parameters, defined as a function of the permeability and the clay content. We describe the frame’s stress-strain relationship of the clay-bearing sandstones by the differential constitutive equations of generalized viscoelasticity and then derive the viscoelastic-wave dynamic equations. With the assumption of a plane-wave solution, we finally yield the phase velocities and the attenuation coefficients by solving the dynamic wave equations in the frequency and wave number domain. The comparison of numerical results and experimental data shows that the generalized viscoelastic BISQ model is applicable for modeling the wave propagation in most of the sandstones mainly bearing kaolinite clay.

High pressure differential scanning calorimetry: Aspects of calibration

A high pressure differential scanning calorimeter (HP-DSC) based on an original design of Höhne and co-workers has been constructed at the University of Aberdeen to allow the characterisation of the thermal behaviour of materials under pressure in both fundamental and technological research areas, for example, in the offshore and pharmaceutical industries. The HP-DSC is equipped with an autoclave using silicone oil as the pressurising medium and may be operated in a temperature range from 20 °C to 300 °C at pressures from 0.1 MPa to 500 MPa and with various heating and cooling rates (from 0.5 K min −1 to 20 K min −1). For calibration purposes, the pressure dependence of the melting temperatures and associated enthalpy changes of both indium and tin have been investigated and compared to the data obtained by Höhne and co-workers for indium and from other published data in the literature for tin. From the heat flow calibration, a dimensionless enthalpy correction factor R corr( p) has been determined which may be used to correct the measured enthalpy values over the whole temperature range and for any given pressure value. Likewise a calibration diagram has been constructed from the temperature calibration over the full range of pressure up to 500 MPa to allow the corrected temperature to be determined from the measured temperature for a thermal event occurring at any pressure.

Reexamination of Hagen-Poiseuille flow: Shape dependence of the hydraulic resistance in microchannels

We consider pressure-driven, steady-state Poiseuille flow in straight channels with various cross-sectional shapes: elliptic, rectangular, triangular, and harmonic-perturbed circles. A given shape is characterized by its perimeter P and area A which are combined into the dimensionless compactness number C= P2/A, while the hydraulic resistance is characterized by the well-known dimensionless geometrical correction factor alpha. We find that alpha depends linearly on C, which points out C as a single dimensionless measure characterizing flow properties as well as the strength and effectiveness of surface-related phenomena central to lab-on-a-chip applications. This measure also provides a simple way to evaluate the hydraulic resistance for the various shapes.

Modeling of a large-scale wastewater treatment plant for efficient operation

Environmental legislations in the Western world impose stringent effluent quality standards for ultimate protection of the environment. This is also observed in Turkey. The current paper presents efforts made to simulate an existing 0.77 million m3/day conventional activated sludge plant located at Ankara, AWTP. The ASM1 model was used for simulation in this study. The model contains numerous stoichiometric and kinetic parameters, some of which need to be determined on case by case bases. The easily degradable COD (S(S)) was determined by two methods, physical-chemical and respirometric methods, namely. The latter method was deemed unreliable and rejected in the further study. Dynamic simulation with SSSP program predicted effluent COD and MLSS values successfully while overestimating OUR. A complete fit could only be obtained by introducing a dimensionless correction factor (etaO2 = 0.58) to the oxygen term in ASM1.

Evaporation heat transfer of falling water film on a horizontal tube bundle

AbstractA numerical simulation and experimental study were carried out for evaporation heat transfer of a falling water film on a smooth horizontal tube bundle evaporator. A laminar model and a turbulence model were respectively adopted to calculate the heat transfer coefficients of falling water film on horizontal heated tubes. The calculation zone on the heated tube was divided into the top stagnation zone and the lateral free film zone. The initial boundary conditions for the free film zone were determined from the calculated results of the stagnation zone. The modified wall function method was used for the turbulent flow. Comparisons between the experimental data and the numerical solutions by use of two flow models show that the experimental data lie between the laminar model solutions and the latter turbulence model solutions and that they are closer to the latter solutions. Finally, a simple dimensionless correction based on the numerical simulations is proposed for predicting the evaporation heat transfer of falling water film for actual engineering applications. © 2001 Scripta Technica, Heat Trans Asian Res, 31(1): 42–55, 2002

Virtual origin correction for lazy turbulent plumes

The location of the asymptotic virtual origin of positively buoyant turbulent plumes with a deficit of initial momentum flux when compared with equivalent pure plumes is investigated. These lazy plumes are generated by continuous steady releases of momentum, buoyancy and volume into a quiescent uniform environment from horizontal sources (at z = 0) of finite area, and are shown to be equivalent to the far-field flow above point source pure plumes, of buoyancy only, rising from the asymptotic virtual source located below the actual source at z = −zavs.An analytical expression for the location of the asymptotic virtual source relative to the actual source of the lazy plume is developed. The plume conservation equations are solved for the volume flow rate, and the position of the asymptotic virtual origin is deduced from the scaling for the volume flow rate at large distances from the source.The displacement zavs of the asymptotic virtual origin from the actual origin scales on the source diameter and is a function of the source parameter Γ ∝ Qˆ20Fˆ0/Mˆ5/20 which is a measure of the relative importance of the initial fluxes of buoyancy Fˆ0, momentum Mˆ0, and volume Qˆ0 in the plume. The virtual origin correction developed is valid for Γ &gt; 1/2 and is therefore applicable to lazy plumes for which Γ &gt; 1, pure plumes for which Γ = 1, and forced plumes in the range 1/2 &lt; Γ &lt; 1. The dimensionless correction z*avs decreases as Γ increases, and for Γ [Gt ] 1, z*avs → 0.853Γ−1/5. Comparisons made between the predicted location of the asymptotic virtual origin and the location inferred from measurements of lazy saline plumes in the laboratory show close agreement.

Streaming potential in heterogeneous networks

It is well‐known that when in contact with an electrolyte, the surfaces of minerals like quartz become charged. In porous rocks, this causes coupling of fluid flow and electrical conduction. In this paper, the theory of electrokinetic coupling in a single capillary is first reviewed. The rest of the paper is concerned with the upscaling of the microscopic (i.e., pore scale) equations and parameters into their macroscopic counterparts. Upscaling was explicitly performed here in a large number of arbitrarily heterogeneous, two‐dimensional networks. As a result, the macroscopic equations were established in a new form using C, the macroscopic coupling coefficient, and δk, a dimensionless correction to permeability. In particular, it was shown that Onsager's [1931] reciprocity holds at macroscopic scales and that the scale invariant Helmholtz‐Smoluchowski formula is not always valid. Accordingly, the macroscopic coupling coefficient C may not always be independent of permeability. In the networks considered here, the coupling coefficient appeared to be controlled by Johnson and Schwartz's [1989] weighted average length scale Λ. Another goal of this paper was to examine the spatial and statistical distributions of electrical currents and potential gradients in networks with varying heterogeneity levels. Similar to local fluid fluxes and pressure gradients, local electrical currents and potential gradients become localized in highly heterogeneous networks. The current field can equivalently be described in terms of current loops, and their spatial distribution can be analyzed. It was found that the current loop field becomes increasingly structured as the level of heterogeneity augments. One important consequence of the spatial distribution of currents and current loops is that at high levels of heterogeneity, the possibility exists to generate a magnetic field of significant intensity over wide areas of the networks. It was also observed that the magnitude of the local electric field appears normally distributed at low variance of the pore radii distribution and becomes increasingly non‐Gaussian as the heterogeneity is increased. Owing to the fact that the total current is zero, the local currents have an unusual distribution, i.e., uniform with a high‐end, −1 power, tail.

Mechanical response of thickness-shear mode quartz-crystal resonators to linear viscoelastic fluids

A mechanically based description of the response of thickness-shear mode quartz-crystal resonators to contact with linear viscoelastic fluids is presented. The calculation describes the effect of viscoelasticity in terms of a dimensionless correction to the Newtonian result, χ which is primarily dependent on the product of the dominant relaxation time of the overlying medium and the oscillation frequency of the resonator. The results show that the effect of a finite relaxation time is a lower frequency shift compared to a viscous reservoir with identical density and a viscosity matching the low-frequency limit of the viscoelastic reservoir. This is due to reduced viscous dissipation in the boundary layer adjacent to the crystal surface and an effectively smaller inertial load on the resonator. The model is shown to reduce appropriately to previously published results in the low- and high-frequency limits, in addition to predicting correctly experimental results for polymeric fluids assuming Rouse-like behaviour.

Bending of thin flexible fibre reinforced sheets

It has been found that the bending moment to which a thin fibre reinforced cement slab is exposed may be calculated in most cases by applying the usual bending formulae, based on the assumption that small deflections are obtained during their testing. Some slabs, however, may exhibit in certain conditions, so large deflections just before failure, that the above mentioned assumption and the resulting simple bending formulae are no more applicable. A simple dimensionless correction factor is derived from the theory of bending with large deflections, which, when used for multiplying the maximum bending moment, calculated by the simple small deflection formula, results in values equal to those resulting from the exact method of calculation, in which the actual magnitude of the beam deflection is taken into consideration. In addition, simple formulae are derived for the calculation of the slope at the end of a simply supported beam loaded at its mid-span and of the secant modulus of elasticity of such a beam, both taking into account the non-linear theory of large deflections.

The effect of thermal diffusion in multicomponent gas absorption

The contribution of thermal diffusion to interfacial mass transfer rates is examined in multicomponent gas absorption systems. Each interfacial flux is expressed as the product of the isothermal expression corresponding to the bulk temperature of the liquid and a dimensionless correction factor that includes the pure heat effects in multicomponent absorption and the contributions of thermal diffusion. It is shown that when the influence of thermal diffusion is to increase the interfacial mass flux, it is opposite to the heat effect and that the two effects may cancel within a realistic range of values of the thermal diffusion coefficient. A monotonic trend to greater significance of thermal diffusion with the number of components being absorbed is illustrated. This trend is shown to be very rapid for the more dilute species in the mixture. Examples based on the absorption of propane, n-pentane, and n-hexane by paraffin oil are treated. The error induced in the correction factor for the flux of n-pentane by neglecting thermal diffusion when adding propane and n-hexane is less than 6·1 per cent, but the corresponding result for propane is 59·2 per cent for a thermal diffusion coefficient of 1· X 10 −7 g/(cm sec °K) for each species.