Large Density Gradients Research Articles

Study of natural convection in supercritical CO 2 cold wall reactors: Simulations and experiments

Fluid flow patterns and temperature profiles within cold wall, high pressure supercritical fluid (SCF) reactors were investigated by simulation and experiment at conditions relevant to the deposition of copper and other metals for applications in microelectronics. Steep thermal gradients between the heated platen, the bulk fluid, and the reactor walls produce large density gradients in the supercritical fluid. Rayleigh numbers are in excess of 1 × 10 10 and the flow is highly turbulent. Natural convection and buoyancy forces dominate the flow within the reactor in both the batch (closed domain) and continuous flow (open domain) configurations. The situation is unlike that in low pressure chemical vapor deposition reactors in which thermal gradients do not give rise to significant density gradients, flow is laminar, and forced convection dominates natural convection. Temperature distributions and flow patterns within cylindrical cold wall reactors containing supercritical carbon dioxide were simulated by computational fluid dynamics (CFD) and conjugate heat transfer calculations. Good agreement with experiment was achieved. The implications of the results for reactor design are discussed.

An adaptive grid method for two-dimensional viscous flows

This paper extends the gas-kinetic BGK-NS scheme to an adaptive grid for the viscous flow simulations. The grid movement and adaptation is controlled by a monitor function which may depend on velocity gradient or other flow variables, such as density or pressure. For the viscous flow computation, the use of adaptive mesh much improves the efficiency and accuracy of the method in comparison with the methods with static mesh points. The current method is an accurate and efficient method for the viscous flow computation, where the grid points can be easily moved and concentrated on the regions with large velocity and density gradients, such as the boundary layer and multi-material interface. Many numerical examples validate the current approach for the viscous flow simulations.

Design and fabrication of holographic variable line-spacing gratings for position sensor

Variable line-spacing gratings are widely used in spacial spectroscopic and synchrotron radiation devices, but their design and fabrication are difficult. In this paper, the geometrical theory of aspheric wave-front recording optics is briefly reviewed. The genetic algorithm is introduced to optimize parameters of holographic variable line-spacing gratings. In order to improve the efficiency of calculation. the integral expression of the objective function is also derived. Design example of holographic variable line-spacing gratings for position sensor is given to demonstrate the capability of this method. Holographic variable line-spacing gratings with large density gradient are fabricated successfully.

Information preservation method for micro-scale flow with temperature variation

Based on the information preservation(IP) method, a simple effective temperature model is presented. The IP method with new temperature model can simulate the flow which has temperature variation. Moreover, studies show that when the local density gradient of the simulated flow is large, it will cause numerical divergence if the second order central difference scheme of the mass conservation equation is used to update the information density. So the first order upwind scheme is recommended to update the information density for the flow with large density gradient.

Morphology of the equatorial anomaly and equatorial plasma bubbles using image subspace analysis of Global Ultraviolet Imager data

The equatorial anomaly (EA) is host to the highest ionospheric densities on Earth. Disturbances within the EA result in plasma density depletions and large density gradients. This paper presents observations of global quiet time morphology of the EA as measured by images of nighttime ionospheric 135.6 nm radiation taken by the Global Ultraviolet Imager (GUVI) on NASA's Thermosphere, Ionosphere, and Mesosphere, Energetics and Dynamics (TIMED) spacecraft. It also presents equatorial plasma bubble (EPB) morphology as determined by detection of intensity depletions in GUVI images. The technique used for analysis is unique in that it allows for simultaneous characterization of the EA and detection of EPBs. This paper also presents extensive observations of EA and EPB morphology and shows that EA morphology can be well characterized by data taken from the 2030–2130 MLT range. Further, this paper identifies crest symmetry in intensity and latitude as an indicator of both EA and EPB morphology. For all longitudes, the crest‐to‐trough ratio (CTR) is shown to be well correlated with the EPB rate. While the CTR may drop with solar flux, EPB levels do not. Thus the absolute CTR is less an indicator than the change in the CTR as a function of longitude for a given season and solar flux. One significant exception to this correlation is observed in the Pacific sector during the June solstice. In this case the EPB rate is high despite a low CTR.

Overview of the Alcator C-Mod program

Research on the Alcator C-Mod tokamak has emphasized RF heating, self-generated flows, momentum transport, scrape-off layer (SOL) turbulence and transport and the physics of transport barrier transitions, stability and control. The machine operates with PRF up to 6 MW corresponding to power densities on the antenna of 10 MW m−2. Analysis of rotation profile evolution, produced in the absence of external drive, allows transport of angular momentum in the plasma core to be computed and compared between various operating regimes. Momentum is clearly seen diffusing and convecting from the plasma edge on time scales similar to the energy confinement time and much faster than neo-classical transport. SOL turbulence and transport have been studied with fast scanning electrostatic probes situated at several poloidal locations and with gas puff imaging. Strong poloidal asymmetries are found in profiles and fluctuations, confirming the essential ballooning character of the turbulence and transport. Plasma topology has a dominant effect on the magnitude and direction of both core rotation and SOL flows. The correlation of self-generated plasma flows and topology has led to a novel explanation for the dependence of the H-mode power threshold on the ∇B drift direction. Research into internal transport barriers has focused on control of the barrier strength and location. The foot of the barrier could be moved to larger minor radius by lowering q or BT. The barriers, which are produced in C-Mod by off-axis RF heating, can be weakened by the application of on-axis power. Gyro-kinetic simulations suggest that the control mechanism is due to the temperature dependence of trapped electron modes which are destabilized by the large density gradients. A set of non-axisymmetric coils was installed allowing intrinsic error fields to be measured and compensated. These also enabled the determination of the mode locking threshold and, by comparison with data from other machines, provided the first direct measurement of size scaling for the threshold. The installation of a new inboard limiter resulted in the reduction of halo currents following disruptions. This effect can be understood in terms of the change in plasma contact with the altered geometry during vertical displacement of the plasma column. Unstable Alfven eigenmodes (AE) were observed in low-density, high-power ICRF heated plasmas. The damping rate of stable AEs was investigated with a pair of active MHD antennae.

Residence time of a freshwater embayment connected to a large lake

The average length of time water remains within the boundaries of an aquatic system is a key parameter controlling the system's biogeochemical behavior. This timescale, generally referred to as the hydraulic residence time, provides a first-order description of multiple and complex processes that drive transport. The procedures to estimate these transport timescales are reviewed and, through the analysis of numerical simulations, the links between residence timescales and the underlying hydrodynamic processes in a canonical freshwater embayment, Little Sodus Bay (LSB), are explored. LSB has negligible through-flow and is connected permanently to Lake Ontario (LO) through a narrow and shallow channel. Exchange in the channel is the result of a multiple balance where spatial thermal variations (baroclinic forcing), oscillations in water level (barotropic forcing), frictional mixing, wind, and the effects of unsteadiness are all important. The simulations indicate that baroclinic processes are the dominant exchange and mixing mechanisms in embayments like LSB. The largest density gradients across the channel are caused by episodic upwelling events in LO during the stratified season, when exchange rates increase by at least an order of magnitude. The mean residence timescales undergo dramatic variations in time and space and, in general, are comparable to the timescales of the systems' variability itself. The simulations reveal that temporal variations of mean residence timescales occur at interannual, seasonal, and down to synoptic timescales, and are closely related to the occurrence and frequency of upwelling events.

The shape of the inner rim in proto-planetary disks

This paper discusses the properties of the inner puffed-up rim which forms in circumstellar disks when dust evaporates. We argue that the rim shape is controlled by a fundamental property of circumstellar disks, namely their very large vertical density gradient, through the dependence of grain evaporation temperature on gas density. As a result, the bright side of the rim is curved, rather than vertical, as expected when a constant evaporation temperature is assumed. We have computed a number of rim models, which take into account this effect in a self-consistent way. The results show that the curved rim (as the vertical rim) emits most of its radiation in the near and mid-IR, and provides a simple explanation to the observed values of the near-IR excess (the 3 micron bump of Herbig Ae stars). Contrary to the vertical rim, for curved rims the near-IR excess does not depend much on the inclination, being maximum for face-on objects. We have then computed synthetic images of the curved rim seen under different inclinations; face-on rims are seen as bright, centrally symmetric rings on the sky; increasing the inclination, the rim takes an elliptical shape, with one side brighter than the other.

Are PAHs precursors of small hydrocarbons in photo-dissociation regions? The Horsehead case

We present maps at high spatial and spectral resolution in emission lines of CCH, c-C3H2, C4H, 12CO and C18O of the edge of the Horsehead nebula obtained with the IRAM Plateau de Bure Interferometer (PdBI). The edge of the Horsehead nebula is a one-dimensional Photo-Dissociation Region (PDR) viewed almost edge-on. All hydrocarbons are detected at high signal-to-noise ratio in the PDR where intense emission is seen both in the H2 ro-vibrational lines and in the PAH mid-infrared bands. C18O peaks farther away from the cloud edge. Our observations demonstrate that CCH, c-C3H2 and C4H are present in UV-irradiated molecular gas, with abundances nearly as high as in dense, well-shielded molecular cores. PDR models i) need a large density gradient at the PDR edge to correctly reproduce the offset between the hydrocarbons and H2 peaks; and ii) fail to reproduce the hydrocarbon abundances. We propose that a new formation path of carbon chains, in addition to gas phase chemistry, should be considered in PDRs: because of intense UV-irradiation, large aromatic molecules and small carbon grains may fragment and feed the interstellar medium with small carbon clusters and molecules in significant amounts.

Ionospheric irregularity characteristics from quasiperiodic structure in the radio wave scintillation

Quasiperiodic (QP) diffraction pattern in scintillation patches has been known to highly correlate with the edge structures of a plasma bubble (Franke et al., 1984). A new time‐frequency analysis method of Hilbert‐Huang transform (HHT) has been applied to analyze the scintillation data taken at Ascension Island to understand the characteristics of corresponding ionosphere irregularities. The HHT method enables us to extract the quasiperiodic diffraction signals embedded inside the scintillation data and to obtain the characteristics of such diffraction signals. The cross correlation of the two sets of diffraction signals received by two stations at each end of Ascension Island indicates that the density irregularity pattern that causes the diffraction pattern should have an eastward drift velocity of ∼130 m/s. The HHT analysis of the instantaneous frequency in the QP diffraction patterns also reveals some frequency shifts in their peak frequencies. For the QP diffraction pattern caused by the leading edge of the large density gradient at the east wall of a structured bubble, an ascending note in the peak frequency is observed, and for the trailing edge a descending note is observed. The linear change in the transient of the peak frequency in the QP diffraction pattern is consistent with the theory and the simulation result of Franke et al. Estimate of the slope in the transient frequency provides us the information that allows us to identify the locations of plasma walls, and the east‐west scale of the irregularity can be estimated. In our case we obtain about 24 km in the east‐west scale. Furthermore, the height location of density irregularities that cause the diffraction pattern is estimated to be between 310 and 330 km, that is, around the F peak during observation.

The stability analysis of two layers in a supercritical pure fluid: Rayleigh–Taylor-like instabilities

We numerically investigate the linear stability of two superposed near critical isobar fluid layers of variable thickness initially at two different temperatures. The very large compressibility and the very low heat diffusivity of near critical pure fluids induce very large density gradients which lead to a Rayleigh–Taylor-like (RTL) gravitational instability of the heat diffusion layer when the top layer temperature is some mK cooler than the bottom one. This instability in a one-phase fluid seems to be similar to that which occurs in between two miscible liquids where the species diffusion is replaced by the heat diffusion coefficient. We find that this RTL configuration becomes stable when the heat diffusion length on the time scale of the faster unstable mode becomes larger than the bottom hot layer thickness.

Investigation of mass transport phenomena in an upflow cold-wall CVD reactor by gas phase Raman spectroscopy and modeling

Steady and transient mass transport phenomena within an inverted, stagnation-flow, cold-wall CVD reactor were investigated by observing the concentration of a tracer species (CH 4) with in situ Raman spectroscopy. The transient studies revealed that the use of matched reactor inlet velocities is crucial to minimize recirculating flow patterns and that the magnitude of the gas velocity is also important in gas switching. In the steady-state studies, it was observed that the existence of a sufficiently large density gradient in the reactor initiates natural convection and under some conditions introduces a flow instability and thus three-dimensional (3-D) flows. The onset of instability was characterized by solutal density difference, gas velocity, and distance traveled by the gas. A steady-state, 2-D axisymmetric reactor model validated with experimental data was used to analyze the measured tracer concentration profiles.

Superior mirage effect in supercritical CO 2: Experiment and model

At temperatures near T c, supercritical CO 2 is highly compressible and it follows that a small temperature gradient will create a large density gradient. We established stable density gradients by maintaining the bottom of a sc-CO 2-cell cooler than its other sides. That created a large refractive index gradient that bent a laser beam through an angle that is roughly proportional to the density gradient. Such light bending causes, for example, the mirage of water on a hot road. A He–Ne laser beam traversed a 7.62 cm long cell and was deflected downward as much as 5.9°. The magnitude of the beam deflections agreed within 3% with a model that used only fundamental geometrical optics and known PVT data, but that employed no adjustable parameters.

A new water column profiler for shallow aquatic systems

Coupled physical and biogeochemical processes in shallow (<2 m deep) productive systems must be observed on fine temporal and spatial scales with automated sampling and monitoring devices. We developed a pump profiler system that can sample six to eight depths at 10-cm resolution every 30 min. The system is economical, secure from vandalism, portable, and capable of integration with a real-time remote monitoring system. Solenoid valves select the suction depth, and a diaphragm pump delivers water to a flow cell where temperature, oxygen, pH, specific conductivity, turbidity, oxidation reduction potential, and fluorescence are measured with probes mounted on a water quality sonde. A microcontroller is used to direct the operation of the system. Water column disturbance and maintenance requirements are minimized by eliminating exposed moving parts. The data can be retrieved remotely and graphically displayed on the Internet in real time. The system has been deployed successfully in two freshwater ponds and a tidal saltwater system. The pump profiler is used to study coupled physical biogeochemical processes in shallow systems with strong diel cycles and large density and chemical gradients. Applications may include studies in aquaculture ponds, storm water retention ponds, shallow lakes, and small estuaries.

PROBES OF SUPERCRITICAL CO2 BY DEFLECTION OF MULTIPLE BEAMLETS

We describe the creation of sets of 633-nm beamlets and their bending by supercritical СО2. Small temperature gradients within a cell that contains the fluid resulted in large density gradients that, in turn, are almost proportional to gradients of the optical refractive index. The paths of such beamlets can be described quantitatively. Beamlets were made with a He−Ne laser-beam that impinged on an array of apertures. The transmitted light forms Fraunhofer diffraction patterns whose shapes depend upon the arrangement of the apertures. The beamlets traversed a 7.62-cm-long cell and were deflected downward to a degree that depended upon the spatial distribution of CO2 density. The deflection is as much as 0.25 m at a distance of 2 m.

Critical properties of thin films of polymer solutions

The critical properties of polymer solutions confined in thin-film environments is studied with simple scaling arguments and a molecular theory. For purely repulsive surfaces, the critical volume fraction is a universal function of x = N1/2/L, where N is the chain length and L is the film thickness. The critical volume fraction is nonmonotonic in x and shows a deep minimum at a film thickness several times larger than the chain's radius of gyration. This nonmonotonic behavior results from the interplay between the surface–polymer entropic repulsion and the tendency of the film to avoid large density gradients. The critical temperature is a monotonically increasing function of L, as L goes from the two-dimensional limit to the three-dimensional limit. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1849–1853, 2005

Statistical analysis of high-order moments in a turbulent boundary layer with large density gradients

An experimental study of the effects of large density variations on the turbulent transfers in a boundary layer is carried out in this paper. Density differences were generated by tangential injection of air or helium in a mixture of these two components. In order to study the fine structure of wall turbulence in the presence of significant density variations, a statistical analysis of the experimental data, obtained in a wind tunnel, is carried out. The results show that the relaxation of the skewness factor of u′(Su′) is carried out more quickly in the external layer than close to the wall, for the air injection as well as for the helium injection. Su′ grows close to the injection slot in an appreciable way, and this increase definitely is stronger for the air injection than for the helium injection. This growth of the skewness factor close to the injection slot can be explained by the increase in the longitudinal convective flux of turbulent energy in this zone. For the distributions of the flatness factor Fu′ the results show that there is no significant effect of the density gradient on the intermittent structure of the instantaneous longitudinal velocity in the developed zone, x/δ≥5, where δ is the boundary-layer thickness. Differences remain, of course, between the profiles of Fu′ for density gradients Open image in new window in the relaxation zone, where the longitudinal gradients are significant. It should, however, be noted that Open image in new window has a smaller effect on the flatness factor compared to the skewness factor. The statistical analysis carried out in this study shows that the helium injection in the boundary layer generates more violent ejections than the air injection. This result is confirmed by the significant contribution of the ejections to turbulent mass flux.

An Efficient Way of Specifying Profile Inflow Boundary Conditions

An efficient way to systematically reproduce inflow profiles across a compressible, turbulent boundary layer for the mean flow variables, as well as the turbulent quantities in one-equation and two-equation turbulence-models, from given external flow conditions and one boundary layer parameter, is described. The reproduced profiles are checked against both experimental results and numerical solution of boundary layer equations. Theoretical analysis shows that a new form of density-weighted velocity, rather the Van Driest density-weighted velocity, obeys the linear-law at the viscous sublayer in a compressible turbulent boundary layer. Especially for non-adiabatic wall at hypersonic Mach numbers, where there are large density gradients, these two kinds of density-weighted velocity could differ considerably. Therefore, the new form of density-weighted velocity proposed in this paper should be employed for the viscous sublayer. It is also shown that power-law fitting for the streamwise velocity gives an unacceptable profile in the viscous sublayer. An efficient way to specify the normal velocity profile is also proposed and tested. The reproduced normal velocity at the boundary layer edge is found to agree remarkably well with the numerical solution of boundary layer equations.

Modified kappa-epsilon Turbulence Model for Calculating Hot Jet Mean Flows and Noise

The κ-e model has no provision to include the effect of the presence of a large-density gradient when used to compute the mean flow and noise of very hot jets. As a result, the model is found to give good predictions only when the jet is cold or moderately hot. Stability consideration indicates that a large density difference across a shear layer would generate strong spatial Kelvin-Helmholtz instabilities. Such instabilities would, invariably, lead to intense mixing in the jet shear layer. This, in turn, gives rise to an increase in turbulence intensity and jet spreading rate. A modification to the κ-e model is proposed to mimic these effects

The influence of double-diffusive processes on the melting of ice in the Arctic Ocean: laboratory analogue experiments and their interpretation

This study has been motivated by two oceanographic observations: an increased rate of melting of sea ice in the Arctic Ocean, and the advance of an anomalously warm tongue of Atlantic water across the Arctic below the halocline over the last few decades. A series of laboratory experiments has been carried out in order to explore the physical principles underlying these phenomena, and the possibility that the extra heating at depth is responsible for the enhanced melting rate. A tank was filled with salt solution having various constant vertical density gradients. A block of ice one third of the length of the tank was floated on the surface at one end, and the rest of the surface and the walls of the tank were insulated. When no extra heat was supplied the melting rate (loss of weight of the ice in 1 h) systematically decreased as the stratification was changed from homogeneous fluid to increasingly large density gradients, while keeping the salinity of the solution in contact with the ice constant. An analogue of the intruding Atlantic water was produced by heating the lower portion of the vertical end wall at the end of the tank opposite to the ice end, keeping its temperature constant, and using the same range of salinity gradients as in the unheated experiments. Again the melting rate decreased as the density gradient was increased, but for low gradients it was larger than that in the unheated experiments. Above a certain intermediate gradient there was no significant difference in melting rate between the unheated and heated runs. The melting data were supplemented by photographs and vertical temperature and salinity profiles. The upward transfer of heat from the body of the fluid to melt the ice was clearly double-diffusive: overturning layers, separated by ‘diffusive’ interfaces, were visible on shadowgraphs, and the thickness of the layers decreased as the density gradient increased. The mean thickness of the layers through the depth of the tank also systematically decreased as the density gradient increased. With weak gradients an extra heat flux to the ice came from the intruding heated layer, but at large gradients this tongue of warm water at depth did not add to the flux near the surface. Though they were obtained in a simple, arbitrary and fixed geometry, we believe that the results of these experiments can be used as the basis for a better physical understanding of the melting rates of ice in the Arctic under various conditions.