The Experts below are selected from a list of 14595 Experts worldwide ranked by ideXlab platform
Stephen Whitaker - One of the best experts on this subject based on the ideXlab platform.
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transport in ordered and disordered porous media volume averaged equations closure problems and comparison with experiment
Chemical Engineering Science, 1993Co-Authors: Michel Quintard, Stephen WhitakerAbstract:In this paper we consider transport in ordered and disordered rigid porous media. We define order and disorder in terms of geometrical integrals that arise naturally in the method of volume Averaging and we show that dependent variables for ordered media must generally be defined in terms of the cellular average. This leads to the use of weighting functions to produce a generalized Averaging Procedure that is valid for any porous medium. The method of volume Averaging leads to spatially smoothed transport equations and a closure problem that allows one to predict effective transport coefficients on basis of a geometrical model of the porous medium under consideration. In order to develop a local closure problem, a spatially periodic model is used for both ordered and disordered systems. Comparison between theory and experiment suggest that this is an acceptable approach for many systems.
Hector J Cantero - One of the best experts on this subject based on the ideXlab platform.
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a systematic time space and time space Averaging Procedure for bulk phase equations in systems with multiphase flow
Chemical Engineering Science, 1994Co-Authors: Ricardo Jose Antonio Grau, Hector J CanteroAbstract:Abstract The time-, space- and time—space-averaged bulk transport equations for multiphase flow systems are derived through a systematic Averaging Procedure based on a suitable definition for phase indicator functions with a single scalar argument. Then the local instantaneous field equations, used as a starting point, are integrated in the appropriate multidimensional fields, in a way analogous to the one used for a one-dimensional field. Also the time-, space- and time—space-averaged expressions for the main geometric parameters of the multiphase systems, holdup and specific interfacial area, are consistently developed for each Averaging type.
Johannes Schwider - One of the best experts on this subject based on the ideXlab platform.
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design considerations for the absolute testing approach of aspherics using combined diffractive optical elements
Applied Optics, 2007Co-Authors: Gufran S Khan, Norbert Lindlein, Klaus Mantel, Irina Harder, Johannes SchwiderAbstract:Aspheric optical surfaces are often tested using diffractive optics as null elements. For precise measurements, the errors caused by the diffractive optical element must be calibrated. Recently, we reported first experimental results of a three position quasi-absolute test for rotationally invariant aspherics by using combined-diffractive optical elements (combo-DOEs). Here we investigate the effects of the DOE substrate errors on the proposed calibration Procedure and present a set of criteria for designing an optimized combo-DOE. It is demonstrated that this optimized design enhances the overall consistency of the Procedure. Furthermore, the rotationally varying part of the surface deviations is compared with the rotationally varying deviations obtained by an N-position Averaging Procedure and is found to be in good agreement.
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Absolute calibration in grazing incidence interferometry via rotational Averaging
Applied optics, 2006Co-Authors: Klaus Mantel, Norbert Lindlein, Juergen Lamprecht, Johannes SchwiderAbstract:Interferometry in grazing incidence can be used to test cylindrical mantle surfaces. The absolute accuracy of the resulting surface profiles is limited by systematic wavefront aberrations caused in the interferometer, in particular due to an inversion of the test wavefront in an interferometer using diffractive beam splitters. For cylindrical specimens, a calibration method using four positions has therefore been investigated. This test is combined with another method of optical metrology: the rotational Averaging Procedure. The implementation for grazing incidence is described and measurement results for hollow cylinders are presented. The gain in accuracy is demonstrated.
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improved combined diffractive optical elements for quasi absolute testing of aspherics
2006Co-Authors: Gufran S Khan, Norbert Lindlein, Klaus Mantel, Johannes SchwiderAbstract:We present a three position quasi absolute test for aspherics by using Combined Diffractive Optical Elements (Combo-DOEs). We discuss the effects of DOE’s substrate quality on the accuracy of the proposed calibration Procedure and present an improved design of the Combo-DOE. Further, the non-rotational deviations extracted from this Procedure are compared with that of N-position rotational Averaging Procedure and are found in good agreement.
Michel Quintard - One of the best experts on this subject based on the ideXlab platform.
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transport in ordered and disordered porous media volume averaged equations closure problems and comparison with experiment
Chemical Engineering Science, 1993Co-Authors: Michel Quintard, Stephen WhitakerAbstract:In this paper we consider transport in ordered and disordered rigid porous media. We define order and disorder in terms of geometrical integrals that arise naturally in the method of volume Averaging and we show that dependent variables for ordered media must generally be defined in terms of the cellular average. This leads to the use of weighting functions to produce a generalized Averaging Procedure that is valid for any porous medium. The method of volume Averaging leads to spatially smoothed transport equations and a closure problem that allows one to predict effective transport coefficients on basis of a geometrical model of the porous medium under consideration. In order to develop a local closure problem, a spatially periodic model is used for both ordered and disordered systems. Comparison between theory and experiment suggest that this is an acceptable approach for many systems.
L.d. Tsendin - One of the best experts on this subject based on the ideXlab platform.
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the space time Averaging Procedure and modeling of the rf discharge ii model of collisional low pressure rf discharge
IEEE Transactions on Plasma Science, 1992Co-Authors: Igor Kaganovich, L.d. TsendinAbstract:For pt.I see ibid., vol.19, p.130-40 (1991). A self-consistent equations system for the low-pressure RF discharge is formulated and qualitatively analyzed. If the plasma and sheath dimensions exceed the electron-energy relaxation length, a simple spatially averaged kinetic equation can be derived that resembles the conventional one for the local case. Since the energy-diffusion coefficient for the slow electrons that are trapped by the average electric field in the discharge center is small, the distribution function slope decreases significantly with the energy growth. Analytic estimates are derived and reasonable agreement with the experiments of Godyak (1976, 1979, 1986, 1990) is obtained. >
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The space-time-Averaging Procedure and modeling of the RF discharge
IEEE Transactions on Plasma Science, 1991Co-Authors: A.s. Smirnov, L.d. TsendinAbstract:An approach to modeling RF discharges and the ensuing analysis of fast electron and ion motions for the case of electrode sheaths in the high-pressure RF discharge is discussed. Time-Averaging over fast electron motions with the applied voltage frequency gives analytic expressions for the average electric field and average ionization density. The resulting relatively simple equations for the ion density profile describe drift, diffusion, ionization, and recombination processes. The simple scaling rules, the approximate expressions for the density profile in various regions, the sheath length, the ion density at the plasma-sheath boundary, and the dimensionless criteria for various discharge regimes can be deduced. For the non-self-sustained discharge, it is demonstrated that the ion drag towards the electrode and the diffusion results in significant lowering of the ion density in the sheath compared with the positive column at not too high a pressure. The analytic transition criterion from alpha to gamma forms of the self-sustained discharge is obtained. The numerical solution of the averaged ion equations yields the results which nearly coincide with the results of full-scale modeling. >
