Numerical simulation of a single fluid particle rising in non-Newtonian fluids

In this work, a level set method is developed for simulating the motion of a fluid particle rising in non-Newtonian fluids described by generalized Newtonian as well as viscoelastic model fluids. As the shear-thinning model we use a Carreau-Yasuda model, and the viscoelastic effect can be modeled with Oldroyd-B constitutive equations. The control volume formulation with the SIMPLEC algorithm incorporated is used to solve the governing equations on a staggered Eulerian grid. The level set method is implemented to compute the motion of a bubble in a Newtonian fluid as one of typical examples for validation, and the computational results are in good agreement with the reported experimental data．The level set method is also applied for simulating a Newtonian drop rising in Carreau-Yasuda and Oldroyd-B fluids．Numerical results including noticeably negative wake behind the drop and viscosity field are obtained, and compare satisfactorily with the known literature data.

Monte Carlo Simulation Of Thermal Fluctuations Below The Onset Of Rayleigh-Benard Convection

The density fluctuations below the onset of convection in the Rayleigh-Benard problem are studied with the direct simulation Monte Carlo method. The particle simulation results clearly show the connection between the static correlation functions of fluctuations below the critical Rayleigh number and the flow patterns above the onset of convection for small Knudsen number flows (Kn=0.01 and Kn=0.005). Furthermore, the physical nature for no convection in the Rayleigh-Benard problem under large Knudsen number conditions (Kn>0.028) is explained based on the dynamics of fluctuations.

Improved sampling techniques for the direct simulation Monte Carlo method

The direct simulation Monte Carlo (DSMC) method is a widely used approach for flow simulations having rarefied or nonequilibrium effects. It involves heavily to sample instantaneous values from prescribed distributions using random numbers. In this note, we briefly review the sampling techniques typically employed in the DSMC method and present two techniques to speedup related sampling processes. One technique is very efficient for sampling geometric locations of new particles and the other is useful for the Larsen-Borgnakke energy distribution.

Direct numerical simulation of hypersonic boundary layer transition over a blunt cone with a small angle of attack

The direct numerical simulation of boundary layer transition over a 5° half-cone-angle blunt cone is performed. The free-stream Mach number is 6 and the angle of attack is 1°. Random wall blow-and-suction perturbations are used to trigger the transition. Different from the authors’ previous work [Li et al., AIAA J. 46, 2899(2008)], the whole boundary layer flow over the cone is simulated (while in the author’s previous work, only two 45° regions around the leeward and the windward sections are simulated). The transition location on the cone surface is determined through the rapid increase in skin fraction coefficient (Cf). The transition line on the cone surface shows a nonmonotonic curve and the transition is delayed in the range of 0° ≤ θ ≤ 30° (θ = 0° is the leeward section). The mechanism of the delayed transition is studied by using joint frequency spectrum analysis and linear stability theory (LST). It is shown that the growth rates of unstable waves of the second mode are suppressed in the range of 20° ≤ θ ≤ 30°, which leads to the delayed transition location. Very low frequency waves VLFWs� are found in the time series recorded just before the transition location, and the periodic times of VLFWs are about one order larger than those of ordinary Mack second mode waves. Band-pass filter is used to analyze the low frequency waves, and they are deemed as the effect of large scale nonlinear perturbations triggered by LST waves when they are strong enough.The direct numerical simulation of boundary layer transition over a 5° half-cone-angle blunt cone is performed. The free-stream Mach number is 6 and the angle of attack is 1°. Random wall blow-and-suction perturbations are used to trigger the transition. Different from the authors’ previous work [ Li et al., AIAA J. 46, 2899 (2008) ], the whole boundary layer flow over the cone is simulated (while in the author’s previous work, only two 45° regions around the leeward and the windward sections are simulated). The transition location on the cone surface is determined through the rapid increase in skin fraction coefficient (Cf). The transition line on the cone surface shows a nonmonotonic curve and the transition is delayed in the range of 20° ≤ θ ≤ 30° (θ = 0° is the leeward section). The mechanism of the delayed transition is studied by using joint frequency spectrum analysis and linear stability theory (LST). It is shown that the growth rates of unstable waves of the second mode are suppressed in the range of 20° ≤ θ ≤ 30°, which leads to the delayed transition location. Very low frequency waves (VLFWs) are found in the time series recorded just before the transition location, and the periodic times of VLFWs are about one order larger than those of ordinary Mack second mode waves. Band-pass filter is used to analyze the low frequency waves, and they are deemed as the effect of large scale nonlinear perturbations triggered by LST waves when they are strong enough.

An Improved CE/SE Scheme for Numerical Simulation of Gaseous and Two-Phase Detonations

A new structure of solution elements and conservation elements based on rectangular mesh was pro- posed and an improved space-time conservation element and solution element (CE/SE) scheme with sec- ond-order accuracy was constructed. Furthermore, the application of improved CE/SE scheme was extended to detonation simulation. Three models were used for chemical reaction in gaseous detonation. And a two-fluid model was used for two-phase (gas–droplet) detonation. Shock reflections were simu- lated by the improved CE/SE scheme and the numerical results were compared with those obtained by other different numerical schemes. Gaseous and gas–droplet planar detonations were simulated and the numerical results were carefully compared with the experimental data and theoretical results based on C–J theory. Mach reflection of a cellular detonation was also simulated, and the numerical cellular pat- terns were compared with experimental ones. Comparisons show that the improved CE/SE scheme is clear in physical concept, easy to be implemented and high accurate for above-mentioned problems.

Simulation of gas flow over a micro cylinder

Gas flow over a micro cylinder is simulated using both a compressible Navier-Stokes solver and a hybrid continuum /particle approach. The micro cylinder flow has low Reynolds number because of the small length scale and the low speed, which also indicates that the rarefied gas effect exists in the flow. A cylinder having a diameter of 20 microns is simulated under several flow conditions where the Reynolds number ranges from 2 to 50 and the Mach number varies from 0.1 to 0.8. It is found that the low Reynolds number flow can be compressible even when the Mach number is less than 0.3, and the drag coefficient of the cylinder increases when the Reynolds number decreases. The compressible effect will increase the pressure drag coefficient although the friction coefficient remains nearly unchanged. The rarefied gas effect will reduce both the friction and pressure drag coefficients, and the vortex in the flow may be shrunk or even disappear.

Catches per unit of effort of bigeye tuna: a new analysis with regression trees and simulated annealing

ENGLISH: We analyzed catches per unit of effort (CPUE) from the Japanese longline fishery for bigeye tuna (Thunnus obesus) in the central and eastern Pacific Ocean (EPO) with regression tree methods. Regression trees have not previously been used to estimate time series of abundance indices fronl CPUE data. The "optimally sized" tree had 139 parameters; year, month, latitude, and longitude interacted to affect bigeye CPUE. The trend in tree-based abundance indices for the EPO was similar to trends estimated from a generalized linear model and fronl an empirical model that combines oceanographic data with information on the distribution of fish relative to environmental conditions. The regression tree was more parsimonious and would be easier to implement than the other two nl0dels, but the tree provided no information about the nlechanisms that caused bigeye CPUEs to vary in time and space. Bigeye CPUEs increased sharply during the mid-1980's and were more variable at the northern and southern edges of the fishing grounds. Both of these results can be explained by changes in actual abundance and changes in catchability. Results from a regression tree that was fitted to a subset of the data indicated that, in the EPO, bigeye are about equally catchable with regular and deep longlines. This is not consistent with observations that bigeye are more abundant at depth and indicates that classification by gear type (regular or deep longline) may not provide a good measure of capture depth. Asimulated annealing algorithm was used to summarize the tree-based results by partitioning the fishing grounds into regions where trends in bigeye CPUE were similar. Simulated annealing can be useful for designing spatial strata in future sampling programs. SPANISH: Analizamos la captura por unidad de esfuerzo (CPUE) de la pesquería palangrera japonesa de atún patudo (Thunnus obesus) en el Océano Pacifico oriental (OPO) y central con métodos de árbol de regresión. Hasta ahora no se han usado árboles de regresión para estimar series de tiempo de índices de abundancia a partir de datos de CPUE. EI árbol de "tamaño optimo" tuvo 139 parámetros; ano, mes, latitud, y longitud interactuaron para afectar la CPUE de patudo. La tendencia en los índices de abundancia basados en árboles para el OPO fue similar a las tendencias estimadas con un modelo lineal generalizado y con un modelo empírico que combina datos oceanográficos con información sobre la distribución de los peces en relación con las condiciones ambientales. EI árbol de regresión fue mas parsimonioso y seria mas fácil de utilizar que los dos otros modelos, pero no proporciono información sobre los mecanismos que causaron que las CPUE de patudo valiaran en el tiempo y en el espacio. Las CPUE de patudo aumentaron notablemente a mediados de los anos 80 y fueron mas variables en los extremos norte y sur de la zona de pesca. Estos dos resultados pueden ser explicados por cambios en la abundancia real y cambios en la capturabilidad. Los resultados de un arbal de regresión ajustado a un subconjunto de los datos indican que, en el OPO, el patudo es igualmente capturable con palangres regulares y profundos. Esto no es consistente con observaciones de que el patudo abunda mas a profundidad e indica que clasificación por tipo de arte (palangre regular 0 profundo) podría no ser una buena medida de la profundidad de captura. Se uso un algoritmo de templado simulado para resumir los resultados basados en el árbol clasificando las zonas de pesca en zonas con tendencias similares en la CPUE de patudo. El templado simulado podría ser útil para diseñar estratos espaciales en programas futuros de muestreo. (PDF contains 45 pages.)

Numerical simulation of condensation of bubbles under microgravity conditions by moving mesh method in the double-staggered grid

A numerical 2D method for simulation of two-phase flows including phase change under microgravity conditions is presented in this paper, with a level set method being coupled with the moving mesh method in the double-staggered grid systems. When the grid lines bend very much in a curvilinear grid, great errors may be generated by using the collocated grid or the staggered grid. So the double-staggered grid was adopted in this paper. The level set method is used to track the liquid-vapor interface. The numerical analysis is fulfilled by solving the Navier-Stokes equations using the SIMPLER method, and the surface tension force is modeled by a continuum surface force approximation. A comparison of the numerical results obtained with different numerical strategies shows that the double-staggered grid moving-mesh method presented in this paper is more accurate than that used previously in the collocated grid system. Based on the method presented in this paper, the condensation of a single bubble in the cold water under different level of gravity is simulated. The results show that the condensation process under the normal gravity condition is different from the condensation process under microgravity conditions. The whole condensation time is much longer under the normal gravity than under the microgravity conditions.