Improved numerical methods for turbulent viscous flows aerothermal modeling program, phase 2

The details of a study to develop accurate and efficient numerical schemes to predict complex flows are described. In this program, several discretization schemes were evaluated using simple test cases. This assessment led to the selection of three schemes for an in-depth evaluation based on two-dimensional flows. The scheme with the superior overall performance was incorporated in a computer program for three-dimensional flows. To improve the computational efficiency, the selected discretization scheme was combined with a direct solution approach in which the fluid flow equations are solved simultaneously rather than sequentially

Aerothermal modeling program. Phase 2, element A: Improved numerical methods for turbulent viscous recirculating flows

The objective of this effort is to develop improved numerical schemes for predicting combustor flow fields. Various candidate numerical schemes were evaluated, and promising schemes were selected for detailed assessment. The criteria for evaluation included accuracy, computational efficiency, stability, and ease of extension to multidimensions. The candidate schemes were assessed against a variety of simple one- and two-dimensional problems. These results led to the selection of the following schemes for further evaluation: flux spline schemes (linear and cubic) and controlled numerical diffusion with internal feedback (CONDIF). The incorporation of the flux spline scheme and direct solution strategy in a computer program for three-dimensional flows is in progress

Aerothermal modeling program, phase 2

The main objective of the NASA sponsored Aerothermal Modeling Program, Phase 2--Element A, is to develop an improved numerical scheme for predicting combustor flow fields. This effort consists of the following three technical tasks. Task 1 involves the selection and evaluation of various candidate numerical techniques. Task 2 involves an in-depth evaluation of the selected numerical schemes. Task 3 involves the convection-diffusion scheme and the direct solver that will be incorporated in the NASA 3-D elliptic code (COM3S)

Natural Convection Heat Transfer in Enclosures With Multiple Vertical Partitions

of air or vacuum, N 2 = n + IK is the complex refractive index of the lamina material, and 9 2 is the (complex) angle of refraction, which is related to 9 t by Snell's law: N, sin #, = N 2 sin 9 2 . Since r 2l = -r i2 , the reflectance at both interfaces is equal to p = r n rf 2 , where * denotes the complex conjugate. The internal transmittance T is related to the (complex) phase change 6 by r = exp . After carefully examining the transmittance formulae of a lamina, this work shows that the geometric-optics formula may result in a significant error for a highly absorbing medium even in the incoherent limit (when interference effects are negligible). Introduction Consider the transmission of electromagnetic radiation through a lamina with smooth and parallel surfaces. In the incoherent limit when radiation coherence length is much smaller than the thickness of the lamina, the transmittance (or reflectance) may be obtained either by tracing the multiply reflected radiant power fluxes (ray-tracing method) or by separating the power flux at each interface into an outgoing component and an incoming component (net-radiation method), viz. ( where p is the reflectance at the interface and r is the internal transmittance. This formula is also called the geometric-optics formula since it is obtained without considering interference effects. For a plane wave, p equals the square of the absolute value of the complex Fresnel reflection coefficient (i.e., the ratio of the reflected electric field to the incident electric field at the interface). The Fresnel reflection coefficient is (Heavens, 1965) r\ 2 = { cos 9 2 -N 2 cos f?i JVi cos (2) N, cos 0, -N 2 cos 6*2 , . , for s -polarization ,7V, cos 9 t + N 2 cos 9 2 where 9 l is the angle of incidence, /V, = 1 is the refractive index where d is the lamina thickness and X is the wavelength in vacuum. In the coherent limit, the transmittance of a lamina may be obtained from thin-film optics (i.e., wave optics) either by tracing the reflected and transmitted waves (Airy's method) or by separating the electric fields into a forward-propagating component (forward wave) and a backward-propagating component (backward wave), viz. (Heavens, 1965; Analysis and Discussion The power transmittance at the interface between the air (or vacuum) and the medium (lamina) is where (1 + r !2 ) is the Fresnel transmission coefficient. The power transmittance at the second interface between the medium and the air can be obtained by exchanging the subscripts 1 and 2 in Eq. (6). At normal incidence, r 12 = (1 -n -('K)/(1 If both K and Im(r 21 ) are nonzero, T 2 \ =t= 1 -p. As discussed by Journal of Heat Transfer AUGUST 1997, Vol. 119/645 Copyright © 1997 by ASME Zhang The above equation is identical to Eq. (5). However, it is not a simple replacement of (1 -p) 2 in Eq. As an example, suppose the lamina is a LaA10 3 wafer of thickness d = 100 p,m. The optical constants are calculated from the Lorentian dielectric function determined by (1) and the transmittance for a LaA10 3 lamina at wavelengths from 9 to 14 p,m at normal incidence are shown in The difference between the wave-optics formula and the incoherent formula is shown in For a highly absorbing lamina (i.e., r < § 1), multiple reflections may be neglected. The transmittance obtained from Eq. (1), when multiple reflections are negligible, is (1 -pfr. The transmittance calculated from Eq. (8) for T < 1 is where the last expression is for normal incidence only. Eq. Concluding Remarks By inspecting the energy balance at the second interface, this work reveals an implicit assumption associated with Eq. Certain important applications require the determination of transmittance below 10~4. Examples are in the characterization of attenuation filters, bandpass filters, and materials with strong absorption bands Acknowledgments This work has been supported by the University of Florida through a start-up fund and an Interdisciplinary Research Initiative award. / Vol. 119, AUGUST 1997 Transactions of the ASME A. A., 1994, "Modelling of the Reflectance of Silicon," Infrared Physics and Technology, Vol. 35, pp. 701 -708. Frenkel, A" and Zhang, Z. M" 1994, "Broadband High Optical Density Filters in the Infrared," Optics Letters, Vol. 19, pp. 1495-1497 Gentile, T. R., Frenkel, A" Migdall, A. L., and Zhang, Z. M" 1995, "Neutral Density Filter Measurements at the National Institute of Standards and Technology," Spectrophotometry, Luminescence and Colour; Science and Compliance, C. Burgess and D. G. Jones, eds., Elsevier, Amsterdam, The Netherlands, pp. 129-139. Grossman, E. N" and McDonald, D. G" 1995, "Partially Coherent Transmittance of Dielectric Lamellae," Optical Engineering, Vol. 34, pp. 1289-1295. Heavens, O. S., 1965, Optical Properties of Thin Solid Films, Dover Publications, Inc., New York, chap. 4, pp. 46-95. Knittl, Z" 1976, Optical of Thin Films, John Wiley & Sons, Inc., NY, pp. 203-204. Salzberg, B., 1948, "A Note on the Significance of Power Reflection," American Journal of Physics, Vol. 16, pp. 444-446. Siegel, R" and Howell, J. R., 1992, Thermal Radiation Heat Transfer, 3rd ed" Hemisphere Publishing Corp., Washington D.C., chap. 4, p. 120, and chap. 18, pp. 928-930. Yeh, P., 1988, Optical Waves in Layered Media, John Wiley & Sons, Inc., New York, chap. 4, pp. 83-101. Zhang, Z. M., 199

Probability encoding of hydrologic parameters for basalt. Elicitation of expert opinions from a panel of three basalt waste isolation project staff hydrologists

The present study implemented a probability encoding method to estimate the probability distributions of selected hydrologic variables for the Cohassett basalt flow top and flow interior, and the anisotropy ratio of the interior of the Cohassett basalt flow beneath the Hanford Site. Site-speciic data for these hydrologic parameters are currently inadequate for the purpose of preliminary assessment of candidate repository performance. However, this information is required to complete preliminary performance assessment studies. Rockwell chose a probability encoding method developed by SRI International to generate credible and auditable estimates of the probability distributions of effective porosity and hydraulic conductivity anisotropy. The results indicate significant differences of opinion among the experts. This was especially true of the values of the effective porosity of the Cohassett basalt flow interior for which estimates differ by more than five orders of magnitude. The experts are in greater agreement about the values of effective porosity of the Cohassett basalt flow top; their estimates for this variable are generally within one to two orders of magnitiude of each other. For anisotropy ratio, the expert estimates are generally within two or three orders of magnitude of each other. Based on this study, the Rockwell hydrologists estimate the effective porosity of the Cohassett basalt flow top to be generally higher than do the independent experts. For the effective porosity of the Cohassett basalt flow top, the estimates of the Rockwell hydrologists indicate a smaller uncertainty than do the estimates of the independent experts. On the other hand, for the effective porosity and anisotropy ratio of the Cohassett basalt flow interior, the estimates of the Rockwell hydrologists indicate a larger uncertainty than do the estimates of the independent experts

Probability encoding of hydrologic parameters for basalt. Elicitation of expert opinions from a panel of five consulting hydrologists

The Columbia River basalts underlying the Hanford Site in Washington State are being considered as a possible location for a geologic repository for high-level nuclear waste. To investigate the feasibility of a repository at this site, the hydrologic parameters of the site must be evaluated. Among hydrologic parameters of particular interest are the effective porosity of the Cohassett basalt flow top and flow interior and the vertical-to-horizontal hydraulic conductivity, or anisotropy ratio, of the Cohassett basalt flow interior. The Cohassett basalt flow is the prime candidate horizon for repository studies. Site-specific data for these hydrologic parameters are currently inadequate for the purpose of preliminary assessment of candidate repository performance. To obtain credible, auditable, and independently derived estimates of the specified hydrologic parameters, a panel of five nationally recognized hydrologists was assembled. Their expert judgments were quantified during two rounds of Delphi process by means of a probability encoding method developed to estimate the probability distributions of the selected hydrologic variables. The results indicate significant differences of expert opinion for cumulative probabilities of less than 10% and greater than 90%, but relatively close agreement in the middle ranges of values. The principal causes of the diversity of opinion are believed to be the lack of site-specific data and the absence of a single, widely accepted, conceptual or theoretical basis for analyzing these variables