Flow Pathlines Research Articles

Scaling up a horizontal HVPE reactor

We have constructed a hydride vapor phase epitaxy (HVPE) reactor capable of producing four inch Gallium Nitride wafers. The design is based on a previously built and successfully operated two inch wafer system [Dam C.E.C., Grzegorczyk A.P., Hageman P.R., Dorsman R., Kleijn C.R., Larsen P.K., The effect of HVPE reactor geometry on GaN growth rate—experiments versus simulations , J. Cryst. Growth 271 (2004) 192; Dam C.E.C., Hageman P.R., Larsen P.K., Carrier gas and position effects on GaN growth in a horizontal HVPE reactor: an experimental and numerical study, J. Cryst. Growth 285 (2005) 31; Dam C.E.C., Grzegorczyk A.P., Hageman P.R., Larsen P.K., Method for HVPE growth of thick crack-free GaN layers, J. Cryst. Growth 290 (2006) 473 [1−3]], essentially by geometrically scaling up all dimensions by a factor λ = 2. To obtain identical processes in both reactors, we applied a scaling analysis based on the dimensionless numbers describing the processes in the system, i.e. the Reynolds, Grashof, and surface Damköhler numbers. When scaling up the reactor dimensions by a factor λ, these dimensionless numbers can be kept constant by adjusting the pressure and the inlet velocities of the gasses as p ∝ λ − 3 / 2 and ν∝ λ 1 / 2 respectively, and the inlet mole fraction of the rate limiting precursor GaCl as f in∝ λ. With the applied scaling rules, identical flow and deposition profiles are obtained in the scaled-up reactor. To verify our scale-up theory, we simulated both systems using computational fluid dynamics (CFD). The calculated flow path lines, concentration and depositions contours of the smaller and larger systems, when correctly scaled, agree very well with each other.

Water movement in the zone of interaction between groundwater and the Columbia River, Hanford Site, Washington

A two-dimensional model that simulates flow pathlines in a vertical cross section oriented perpendicular to the Columbia River has been developed for a location at the Hanford Site. Hydraulic head data from wells and the adjacent river were used to calculate flow direction and velocity in hourly increments for an entire seasonal cycle. River stage cycles extend through a range of several meters, thus exerting a strong influence on water movement in the zone of interaction. By including a fluctuating river stage at the river boundary (center of channel), the model showed that landward of and beneath the shoreline, flow pathlines within the aquifer are deflected downward. The region immediately beneath the shoreline is strongly influenced by river water that infiltrates during high river stage. On the river side of the shoreline, groundwater discharges upward into the river channel, with pathlines converging in the riverbed relatively close to shore. If the model is run assuming a constant, average river stage, these movement features are not represented, thus demonstrating the need to include transient boundary conditions when a fluctuating river stage influences the zone of interaction between groundwater and surface water. The model provides information that supports a variety of applications, including monitoring strategies. contaminant transport models, risk assessments, remedial action design, and compliance requirements for remedial actions.

Application of shape factor to determine the permeability of perfusive particles

A modified graphical–statistical method for shape factor estimation has been developed and used to estimate the permeability of a perfusive particle as an example. The shape factor was evaluated by calculating the average cross-sectional area for diffusion and the average flow path line length separately. According to this method, a perfusive particle with a sealing surface length ratio, L s, of 0.04, i.e. a contact length of the perfusive particle on the walls of the test cell tube to the perfusive particle diameter of 0.04, would have a shape factor of 1.25 πa. Then, the graphical–statistical method and the geometrical method were used to propose an expression to evaluate the shape factor of any perfusive particle with a sealing surface length ratio of L s and a radius of a. Finally, the shape factor approach was compared with the CFD numerical simulation approach of Pfeiffer et al. [AIChE J. 42 (1996) 932], and excellent agreement between the two approaches has been demonstrated.

Method of Predicting the Spray Cone Angle and the Flow Rate Distribution of a Liquid Injector.

Liquid injectors are found in many kinds of applications. In this work, we focus on the fuel injector of an automobile engine. It is important to predict the properties of the spray in order to improve the fuel spray pattern of the injector. We selected the spray cone angle and the flow rate distribution among the properties of the spray, and predicted them by numerically simulating the internal flow in the fuel injector. The finite volume method with an unstructured mesh was used in this numerical simulation. The spray cone angle was predicted by extrapolating the velocity vectors at the nozzle outlet. The flow rate distribution was predicted by numerically detecting the number of the flow path lines at the nozzle outlet. Moreover, the numerically simulated spray cone angle and the flow rate distribution agree well with experimentally measured ones.

Understanding climatic controls on sea-ice transport pathways in the Arctic Ocean

AbstractThe primary goal of this paper is to demonstrate the dependence of Arctic Ocean sea-ice transport pathways on climate variations. We build our analysis on the results of Proshutinsky and Johnson (1997), Johnson and others (1999), Polyakov and others (1999) and Proshutinsky and others (1999), where we have shown that wind-driven ice motion and upper ocean circulation alternate between anticyclonic and cyclonic states. Shifts between regimes occur at 5−7 year intervals, resulting in a 10−15 year period. The anticyclonic circulation regime has been observed in our model results for 1946−52,1958−62,1972−79,1984−88 and 1998−present. The cyclonic circulation regime prevailed during 1953−57,1963−71,1980−83 and 1989−97. The regime shifts are fundamentally important to understanding the Arctic’s general circulation and particularly useful for estimating pollution transport by sea ice and surface waters. It is important to pollution studies to understand which circulation regime prevails. Initially, we simulate trajectories of a non-reactive, conservative soluble tracer. Results from this research demonstrate realistic potential flow pathlines and we describe how those pathlines change in response to climate forcing. These results can be used to aid current and future scenario risk assessments and may provide management agencies with the tools to determine where risks from contaminants might exist.

3. Surface flow pathlines between groins visualized by the DMS method

3. Surface flow pathlines between groins visualized by the DMS method

Hydrogeologic and Water Quality Issues Along the El Paso/Juarez Corridor: An International Case Study

The twin cities of El Paso, Texas, and Juarez, in Chihuahua, Mexico, depend heavily upon well water from the Hueco Bolson aquifer for municipal and industrial water needs. Over-pumping of the Hueco Bolson aquifer has resulted in drawdown of the water table (as much as 150 ft [45.7 m]) and salinization by brackish water encroachment. Predevelopment ground-water flow pathlines ran from recharge areas along mountains to discharge areas at the Rio Grande. Pumping cones of depression beneath El Paso and Juarez have reoriented the hydraulic gradient, capturing the natural discharge of the aquifer. The deeper cone of depression is beneath Juarez. At one location in the aquifer, ground water now flows under the international border from the United States into Mexico. Chloride and other dissolved solids have increased over time in many municipal wells of El Paso and Juarez. Salinization of water wells is associated with extensive ground-water development and arid climate. A freshwater zone beneath El Paso and Juarez is underlain and in some places overlain by inferior-quality ground water. Mixing due to pumping, leakage from mud interbeds and artesian confining beds, cascading waters along well casings and screens, lateral saltwater encroachment, and potential upconing have degraded the freshwater zone. Other contaminants of concern in the aquifer include fecal coliform bacteria, and nitrate. Of particular concern are fecal coliform bacteria because many residents in Mexico use untreated well water.

Response of the dynamic LES model to heat release induced effects

The response of the dynamic large eddy simulation (LES) subgrid model to heat release effects is investigated. Nonpremixed turbulent flames are considered in the case of large Damköhler number combustion in homogeneous and isotropic flows. The subgrid fluctuations of mixture fraction are accounted for through a presumed probability density function approach. In this work, dynamic LES includes a procedure minimizing, over flow path lines, the error in the determination of the parameters entering the turbulence model [Meneveau, Lund, and Cabot, Proceedings of the 1994 Summer Program (CTR, Stanford, CA, 1994), pp. 271–299]. Both direct numerical simulation (DNS) and LES are performed. It is found that the flux of turbulent kinetic energy toward the subgrid is correctly represented by the dynamic LES model in the presence of heat release.

A Lagrangian dynamic subgrid-scale model of turbulence

The dynamic model for large-eddy simulation of turbulence samples information from the resolved velocity field in order to optimize subgrid-scale model coefficients. When the method is used in conjunction with the Smagorinsky eddy-viscosity model, and the sampling process is formulated in a spatially local fashion, the resulting coefficient field is highly variable and contains a significant fraction of negative values. Negative eddy viscosity leads to computational instability and as a result the model is always augmented with a stabilization mechanism. In most applications the model is stabilized by averaging the relevant equations over directions of statistical homogeneity. While this approach is effective, and is consistent with the statistical basis underlying the eddy-viscosity model, it is not applicable to complex-geometry inhomogeneous flows. Existing local formulations, intended for inhomogeneous flows, are most commonly stabilized by artificially constraining the coefficient to be positive. In this paper we introduce a new dynamic model formulation, that combines advantages of the statistical and local approaches. We propose to accumulate the required averages over flow pathlines rather than over directions of statistical homogeneity. This procedure allows the application of the dynamic model with averaging to in-homogeneous flows in complex geometries. We analyse direct numerical simulation data to document the effects of such averaging on the Smagorinsky coefficient. The characteristic Lagrangian time scale over which the averaging is performed is chosen based on measurements of the relevant Lagrangian autocorrelation functions, and on the requirement that the model be purely dissipative, guaranteeing numerical stability when coupled with the Smagorinsky model. The formulation is tested in forced and decaying isotropic turbulence and in fully developed and transitional channel flow. In homogeneous flows, the results are similar to those of the volume-averaged dynamic model, while in channel flow, the predictions are slightly superior to those of the spatially (planar) averaged dynamic model. The relationship between the model and vortical structures in isotropic turbulence, as well as ejection events in channel flow, is investigated. Computational overhead is kept small (about 10% above the CPU requirements of the spatially averaged dynamic model) by using an approximate scheme to advance the Lagrangian tracking through first-order Euler time integration and linear interpolation in space.

Tangential Flow Effects in Cross Flow Hydraulic Turbines

The crossflow turbine is now well established as a suitable machine for micro and small hydropower generation. An inherent feature of many of these machines is the phenomenon of tangential flow which leads to reduced efficiency. This paper presents a theoretical method, based on a flow path line approach, for estimating the amount of tangential flow and loss of efficiency and discusses the physical factors causing such effects, with some suggestions for improving performance.

Mathematical Modeling of Flow and Heat‐Transfer Phenomena in Glass Furnace Channels and Forehearths

A three‐dimensional mathematical model was developed to calculate fluid‐flow and heat‐transfer phenomena in a channel/forehearth system used for delivering glass from the melting end to the forming end of a continuous‐glass‐fiber furnace. The model allowed for a varying cross section of the delivery system and for the temperature‐dependent physical properties of the molten glass. Also, a formulation was presented to calculate heat transfer by radiation at the combustion gas/glass interface. The model was used to investigate the effects of natural convection, throughput, and radiation in the glass on velocity and temperature distribution in a glass delivery system. The results showed that, although the natural convection velocities were much lower than the average velocity due to throughput, the presence of natural convection significantly affected the flow path lines in the system. The results also illustrated the distribution of surface and bottom glass streams entering a channel into different forehearths.

Dissolution of Polydisperse Silica Grains in Glass Melts–Analysis

By combining population balance with mass‐transfer‐controlled dissolution, a formulation is developed to analyze the dissolution of polydisperse silica grains in glass furnaces. For an initial lognormal distriution of particle sizes, the change in the distribution with respect to a modified time scale is expressed analytically. This paper shows how the formulation can be combined with time‐temperature data along various flow path lines in a glass melter to calculate the extent of dissolution in the melter. Calculated results are presented on the dissolution of polydisperse silica grains in a glass melter for which the information on path lines was obtained by using a three‐dimensional mathematical model for flow and heat transfer. The effects of maximum particle size of a truncated distribution and the standard deviation on the extent of dissolution are examined.

原子炉建屋内運転階の新換気空調設備の開発

A heating, ventilating and air conditioning (HVAC) system is installed on the operation floor of a BWR reactor building for temperature control and dust protection in work areas. In the current HVAC system, it is necessary to ensure that its exhaust ducts do not interfere with other structures and pipes, since pipings are buried under the floor.In this study, air velocity and temperature distributions and heat removal rate were analytically and experimentally investigated, and duct arrangements without the buried exhaust ducts were evaluated. In the analysis, a three-dimensional thermal hydraulic analysis computer program for incompressible viscous fluid was applied, and a laminar flow model and slip condition on the wall surface were used, based on a comparison of calculated results with measured ones. In the experiments, a one-twentieth scale model was used, and the temperature distribution was measured by thermocouples. Furthermore an airflow distribution was visualized and three-dimensional flow path lines were obtained by computer-aided image processing. The proposed HVAC system uses a rising current of air on the hotter surface of the reactor refueling pool and spent fuel pool, and exhausts air through exhaust ducts on the ceiling. Consequently, it is confirmed that the new HVAC system can be realized, which increases the removal heat capability on condition of the same ventilation rate as the current system.

Flow visualization of a recirculating flow by rheoscopic liquid and liquid crystal techniques

Experiments were conducted in a three-dimensional lid-driven cavity flow to study the behavior of longitudinal Taylor-Gortler-like vortices. Flow visualization was accomplished by use of a rheoscopic liquid and of liquid crystals, together with laser-light and white-light sheets, respectively. Photographs of the lighted planes in the flow confirmed the existence of the vortices for a wide range of Reynolds numbers and for stable, neutrally-buoyant and buoyant global flow conditions. As usual the flow visualization revealed flow patterns not deducible by in situ measurements; the liquid crystal photographs give both flow pathlines and temperature distribution on any lighted plane.

Brownian diffusion of aerosols to the face of a nuclepore filter

An approximate solution of the transport equation is found for aerosols in the flow approaching a Nuclepore filter. Small aerosols are shown to be collected on the front face of the filter owing to Brownian diffusion relative to to the mean flow path lines. A formula is derived for the diffusive collection efficiency of the filter, and it is valid for filter porosities in the range 0.05–0.64.