Theory of the positive column of a gas discharge

An attempt is made to provide a theoretical explanation of the effect of the positive column on the voltage-current characteristic of a glow or an arc discharge. Such theories have been developed before, and all are based on balancing the production and loss of charged particles and accounting for the energy supplied to the plasma by the applied electric field. Differences among the theories arise from the approximations and omissions made in selecting processes that affect the particle and energy balances. This work is primarily concerned with the deviation from the ambipolar description of the positive column caused by space charge, electron-ion volume recombination, and temperature inhomogeneities.

The presentation is divided into three parts, the first of which involved the derivation of the final macroscopic equations from kinetic theory. The final equations are obtained by taking the first three moments of the Boltzmann equation for each of the three species in the plasma. Although the method used and the equations obtained are not novel, the derivation is carried out in detail in order to appraise the validity of numerous approximations and to justify the use of data from other sources. The equations are applied to a molecular hydrogen discharge contained between parallel walls. The applied electric field is parallel to the walls, and the dependent variables—electron and ion flux to the walls, electron and ion densities, transverse electric field, and gas temperature—vary only in the direction perpendicular to the walls. The mathematical description is given by a sixth-order nonlinear two-point boundary value problem which contains the applied field as a parameter. The amount of neutral gas and its temperature at the walls are held fixed, and the relation between the applied field and the electron density at the center of the discharge is obtained in the process of solving the problem. This relation corresponds to that between current and voltage and is used to interpret the effect of space charge, recombination, and temperature inhomogeneities on the voltage-current characteristic of the discharge.

The complete solution of the equations is impractical both numerically and analytically, and in Part II the gas temperature is assumed uniform so as to focus on the combined effects of space charge and recombination. The terms representing these effects are treated as perturbations to equations that would otherwise describe the ambipolar situation. However, the term representing space charge is not negligible in a thin boundary layer or sheath near the walls, and consequently the perturbation problem is singular. Separate solutions must be obtained in the sheath and in the main region of the discharge, and the relation between the electron density and the applied field is not determined until these solutions are matched.

In Part III the electron and ion densities are assumed equal, and the complicated space-charge calculation is thereby replaced by the ambipolar description. Recombination and temperature inhomogeneities are both important at high values of the electron density. However, the formulation of the problem permits a comparison of the relative effects, and temperature inhomogeneities are shown to be important at lower values of the electron density than recombination. The equations are solved by a direct numerical integration and by treating the term representing temperature inhomogeneities as a perturbation.

The conclusions reached in the study are primarily concerned with the association of the relation between electron density and axial field with the voltage-current characteristic. It is known that the effect of space charge can account for the subnormal glow discharge and that the normal glow corresponds to a close approach to an ambipolar situation. The effect of temperature inhomogeneities helps explain the decreasing characteristic of the arc, and the effect of recombination is not expected to appear except at very high electron densities.

Solubility and Diffusivity of Water in Lunar Basalt, and Chemical Zonation in Olivine-Hosted Melt Inclusions

I report the solubility and diffusivity of water in lunar basalt and an iron-free basaltic analogue at 1 atm and 1350 °C. Such parameters are critical for understanding the degassing histories of lunar pyroclastic glasses. Solubility experiments have been conducted over a range of fO₂ conditions from three log units below to five log units above the iron-wüstite buffer (IW) and over a range of pH₂/pH₂O from 0.03 to 24. Quenched experimental glasses were analyzed by Fourier transform infrared spectroscopy (FTIR) and secondary ionization mass spectrometry (SIMS) and were found to contain up to ~420 ppm water. Results demonstrate that, under the conditions of our experiments: (1) hydroxyl is the only H-bearing species detected by FTIR; (2) the solubility of water is proportional to the square root of pH₂O in the furnace atmosphere and is independent of fO₂ and pH₂/pH₂O; (3) the solubility of water is very similar in both melt compositions; (4) the concentration of H₂ in our iron-free experiments is <3 ppm, even at oxygen fugacities as low as IW-2.3 and pH₂/pH₂O as high as 24; and (5) SIMS analyses of water in iron-rich glasses equilibrated under variable fO₂ conditions can be strongly influenced by matrix effects, even when the concentrations of water in the glasses are low. Our results can be used to constrain the entrapment pressure of the lunar melt inclusions of Hauri et al. (2011).

Diffusion experiments were conducted over a range of fO₂ conditions from IW-2.2 to IW+6.7 and over a range of pH₂/pH₂O from nominally zero to ~10. The water concentrations measured in our quenched experimental glasses by SIMS and FTIR vary from a few ppm to ~430 ppm. Water concentration gradients are well described by models in which the diffusivity of water (D^*_water) is assumed to be constant. The relationship between D^*_water and water concentration is well described by a modified speciation model (Ni et al. 2012) in which both molecular water and hydroxyl are allowed to diffuse. The success of this modified speciation model for describing our results suggests that we have resolved the diffusivity of hydroxyl in basaltic melt for the first time. Best-fit values of D^*_water for our experiments on lunar basalt vary within a factor of ~2 over a range of pH₂/pH₂O from 0.007 to 9.7, a range of fO₂ from IW-2.2 to IW+4.9, and a water concentration range from ~80 ppm to ~280 ppm. The relative insensitivity of our best-fit values of D^*_water to variations in pH₂ suggests that H₂ diffusion was not significant during degassing of the lunar glasses of Saal et al. (2008). D^*_water during dehydration and hydration in H₂/CO₂ gas mixtures are approximately the same, which supports an equilibrium boundary condition for these experiments. However, dehydration experiments into CO₂ and CO/CO₂ gas mixtures leave some scope for the importance of kinetics during dehydration into H-free environments. The value of D^*_water chosen by Saal et al. (2008) for modeling the diffusive degassing of the lunar volcanic glasses is within a factor of three of our measured value in our lunar basaltic melt at 1350 °C.

In Chapter 4 of this thesis, I document significant zonation in major, minor, trace, and volatile elements in naturally glassy olivine-hosted melt inclusions from the Siqueiros Fracture Zone and the Galapagos Islands. Components with a higher concentration in the host olivine than in the melt (MgO, FeO, Cr₂O₃, and MnO) are depleted at the edges of the zoned melt inclusions relative to their centers, whereas except for CaO, H₂O, and F, components with a lower concentration in the host olivine than in the melt (Al₂O₃, SiO₂, Na₂O, K₂O, TiO₂, S, and Cl) are enriched near the melt inclusion edges. This zonation is due to formation of an olivine-depleted boundary layer in the adjacent melt in response to cooling and crystallization of olivine on the walls of the melt inclusions concurrent with diffusive propagation of the boundary layer toward the inclusion center.

Concentration profiles of some components in the melt inclusions exhibit multicomponent diffusion effects such as uphill diffusion (CaO, FeO) or slowing of the diffusion of typically rapidly diffusing components (Na₂O, K₂O) by coupling to slow diffusing components such as SiO₂ and Al₂O₃. Concentrations of H2O and F decrease towards the edges of some of the Siqueiros melt inclusions, suggesting either that these components have been lost from the inclusions into the host olivine late in their cooling histories and/or that these components are exhibiting multicomponent diffusion effects.

A model has been developed of the time-dependent evolution of MgO concentration profiles in melt inclusions due to simultaneous depletion of MgO at the inclusion walls due to olivine growth and diffusion of MgO in the melt inclusions in response to this depletion. Observed concentration profiles were fit to this model to constrain their thermal histories. Cooling rates determined by a single-stage linear cooling model are 150–13,000 °C hr^-1 from the liquidus down to ~1000 °C, consistent with previously determined cooling rates for basaltic glasses; compositional trends with melt inclusion size observed in the Siqueiros melt inclusions are described well by this simple single-stage linear cooling model. Despite the overall success of the modeling of MgO concentration profiles using a single-stage cooling history, MgO concentration profiles in some melt inclusions are better fit by a two-stage cooling history with a slower-cooling first stage followed by a faster-cooling second stage; the inferred total duration of cooling from the liquidus down to ~1000 °C is 40 s to just over one hour.

Based on our observations and models, compositions of zoned melt inclusions (even if measured at the centers of the inclusions) will typically have been diffusively fractionated relative to the initially trapped melt; for such inclusions, the initial composition cannot be simply reconstructed based on olivine-addition calculations, so caution should be exercised in application of such reconstructions to correct for post-entrapment crystallization of olivine on inclusion walls. Off-center analyses of a melt inclusion can also give results significantly fractionated relative to simple olivine crystallization.

All melt inclusions from the Siqueiros and Galapagos sample suites exhibit zoning profiles, and this feature may be nearly universal in glassy, olivine-hosted inclusions. If so, zoning profiles in melt inclusions could be widely useful to constrain late-stage syneruptive processes and as natural diffusion experiments.

Computational study of the vortex path variation with the VG height

An extensive range of conventional, vane-type, passive vortex generators (VGs) are in use for successful applications of flow separation control. In most cases, the VG height is designed with the same thickness as the local boundary layer at the VG position. However, in some applications, these conventional VGs may produce excess residual drag. The so-called low-profile VGs can reduce the parasitic drag associated to this kind of passive control devices. As suggested by many authors, low-profile VGs can provide enough momentum transfer over a region several times their own height for effective flow-separation control with much lower drag. The main objective of this work is to study the variation of the path and the development of the primary vortex generated by a rectangular VG mounted on a flat plate with five different device heights h = delta, h(1) = 0.8 delta, h(2) = 0.6 delta, h(3) = 0.4 delta and h(4) = 0.2 delta, where delta is the local boundary layer thickness. For this purpose, computational simulations have been carried out at Reynolds number Re = 1350 based on the height of the conventional VG h = 0.25m with the angle of attack of the vane to the oncoming flow beta = 18.5 degrees. The results show that the VG scaling significantly affects the vortex trajectory and the peak vorticity generated by the primary vortex.

Aspects of quality control of wind profiler measurements in complex topography

It is well known in the scientific community that some remote sensing instruments assume that sample volumes present homogeneous conditions within a defined meteorological profile. At complex topographic sites and under extreme meteorological conditions, this assumption may be fallible depending on the site, and it is more likely to fail in the lower layers of the atmosphere. This piece of work tests the homogeneity of the wind field over a boundary layer wind profiler radar located in complex terrain on the coast under different meteorological conditions. The results reveal the qualitative importance of being aware of deviations in this homogeneity assumption and evaluate its effect on the final product. Patterns of behavior in data have been identified in order to simplify the analysis of the complex signal registered. The quality information obtained from the homogeneity study under different meteorological conditions provides useful indicators for the best alternatives the system can offer to build wind profiles. Finally, the results are also to be considered in order to integrate them in a quality algorithm implemented at the product level.

Modeling of unsteady transitional boundary layers

In turbomachinery, a considerable proportion of the blade surface area can be covered by transitional boundary layers. This means that accurate prediction of the profile loss and boundary layer behavior in general depends on the accurate modeling of the transitional boundary layers, especially at low Reynolds numbers. This paper presents a model for determining the intermittency resulting from the unsteady transition caused by the passage of wakes over a blade surface. The model is founded on work by Emmons (1951) who showed that the intermittency could be calculated from a knowledge of the behavior of randomly formed turbulent spots. The model is used to calculate the development of the boundary layer on the rotor of a low Reynolds number single-stage turbine. The predictions are compared with experimental results obtained using surface-mounted hot-film anemometers and hot-wire traverses of the rotor midspan boundary layer at two different rotor-stator gaps. The validity and limitations of the model are discussed.

The contact of rough surfaces carrying pressure sensitive boundary layers

When two rough surfaces are loaded together it is well known that the area of true contact is very much smaller then the geometric area and that, consequently, local contact pressures are very much greater than the nominal value. If the asperities on each surface can be thought of as possessing smooth summits and each of the solids is elastically isotropic then the pressure distribution will consist of a series of small, but severe, Hertzian patches. However, if one of both of the surfaces in question is protected by a boundary layer then both the number and dimensions of these patches, and the form of the pressure distribution within them, will be modified. Recent experimental evidence from studies using both Atomic Force Microscopy and micro-tribometry suggests that boundary films produced by the action of commercial anti-wear additives, such as ZDTP, exhibit mechanical properties, which are affected by local values of pressure. These changes bring about further modifications to local conditions. These effects have been explored in a numerical model of rough surface contact and the implications for the mechanisms of surface distress and wear are discussed. © 2000 Elsevier Science B.V. All rights reserved.

Reynolds number influence on turbulent blocking effects of a rigid plane boundary (2nd report, direct numerical simulation using townsend's eddy forcing)

The Reynolds number influence on turbulent blocking effects by a rigid plane boundary is studied using direct numerical simulation (DNS). A new forcing method using 'simple model eddies' (Townsend 1976) for DNS of stationary homogeneous isotropic turbulence is proposed. A force field is obtained in real space by sprinkling many space-filling 'simple model eddies' whose centers are randomly but uniformly distributed in space and whose axes of rotation are random. The method is applied to a shear-free turbulent boundary layer over a rigid plane boundary and the blocking effects are investigated. The results show that stationary homogeneous isotropic turbulence is generated in real space using the present method. By using different model eddies with different sizes and rotation speeds, we could change the turbulence properties such as the integral and micro scales, the turbulent Reynolds number and the isotropy of turbulence. Turbulence intensities near the wall showed good agreements with the previous measurement and the linear analysis based on a rapid distortion theory (RDT). The splat effect (i.e., turbulence intensities of the components parallel to the boundary are amplified) occurs near the boundary and the viscous effect prohibits the splat effect at the quasi steady state at low Reynolds number.

Reynolds number influence on turbulent blocking effects of a rigid plane boundary (3rd report, direct numerical simulation on wall blocking effects for anisotropic turbulence)

The Reynolds number influence on turbulent blocking effects by a rigid plane boundary is studied using direct numerical simulation (DNS). A new forcing method proposed in the second report using Townsend's "simple model eddies" for DNS was extended to generate axisymmetric anisotropic turbulence. A force field is obtained in real space by sprinkling many space-filling "simple model eddies" whose centers are randomly but uniformly distributed in space. The axes of rotation are controlled in this study to generate axisymmetric anisotropic turbulence. The method is applied to a shear-free turbulent boundary layer over a rigid plane boundary and the blocking effects for anisotropic turbulence are investigated. The results show that stationary axisymmetric anisotropic turbulence is generated using the present method. Turbulence intensities near the wall showed good agreements with the rapid distortion theory (RDT) for small t (t ≪ TL), where TL. is the eddy turnover time. The splat effect (i. e. turbulence intensities of the components parallel to the surface are amplified) occurs near the boundary and the viscous effect attenuates the splat effect at the quasi steady state at low Reynolds number as for Isotropic turbulence. Prandtl's secondary flow of the second kind does not occur for low Reynolds number flows, which qualitatively agrees with previous observetion in a mixing-box.

Corner effect and asymmetry in transonic channel flows

An experimental and numerical investigation into transonic shock/boundary-layer interactions in rectangular ducts has been performed. Experiments have shown that flow development in the corners of transonic shock/boundary-layer interactions in confined channels can have a significant impact on the entire flowfield. As shock strength is increased from M∞ = 1:3 to 1.5, the flowfield becomes very slightly asymmetrical. The interaction of corner flows with one another is thought to be a potential cause of this asymmetry. Thus, factors that govern the size of corner interactions (such as interaction strength) and their proximity to one another (such as tunnel aspect ratio) can affect flow symmetry. The results of the computational study show reasonable agreement with experiments, although simulations with particular turbulence models predict highly asymmetrical solutions for flows that were predominantly symmetrical in experiments. These discrepancies are attributed to the tendency of numerical schemes to overprediction corner-interaction size, and this also accounts for why computational fluid dynamics predicts the onset of asymmetry at lower shock strengths than in experiments. The findings of this study highlight the importance of making informed decisions about imposing artificial constraints on symmetry and boundary conditions for internal transonic flows. Future effort into modeling corner flows accurately is required. Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Study of the turbulence in the air-side and water-side boundary layers in experimental laboratory wind induced surface waves

This study detailed the structure of turbulence in the air-side and water-side boundary layers in wind-induced surface waves. Inside the air boundary layer, the kurtosis is always greater than 3 (the value for normal distribution) for both horizontal and vertical velocity fluctuations. The skewness for the horizontal velocity is negative, but the skewness for the vertical velocity is always positive. On the water side, the kurtosis is always greater than 3, and the skewness is slightly negative for the horizontal velocity and slightly positive for the vertical velocity. The statistics of the angle between the instantaneous vertical fluctuation and the instantaneous horizontal velocity in the air is similar to those obtained over solid walls. Measurements in water show a large variance, and the peak is biased towards negative angles. In the quadrant analysis, the contribution of quadrants Q2 and Q4 is dominant on both the air side and the water side. The non-dimensional relative contributions and the concentration match fairly well near the interface. Sweeps in the air side (belonging to quadrant Q4) act directly on the interface and exert pressure fluctuations, which, in addition to the tangential stress and form drag, lead to the growth of the waves. The water drops detached from the crest and accelerated by the wind can play a major role in transferring momentum and in enhancing the turbulence level in the water side.On the air side, the Reynolds stress tensor's principal axes are not collinear with the strain rate tensor, and show an angle α σ≈=-20°to-25°. On the water side, the angle is α σ≈=-40°to-45°. The ratio between the maximum and the minimum principal stresses is σ a/σ b=3to4 on the air side, and σ a/σ b=1.5to3 on the water side. In this respect, the air-side flow behaves like a classical boundary layer on a solid wall, while the water-side flow resembles a wake. The frequency of bursting on the water side increases significantly along the flow, which can be attributed to micro-breaking effects - expected to be more frequent at larger fetches. © 2012 Elsevier B.V.

Comparison of bleed and micro-vortex generator effects on supersonic boundary-layers

An experimental study of bleed and vortex generators in supersonic ow has been conducted. Methods were developed to analyze and directly compare the two systems' effects on turbulent boundary layers to better understand their potential to mitigate ow separation. LDA was used to measure two components of velocity in the boundary-layer for three cases|baseline, with bleed, or with a VG|at Mach numbers of 1.3, 1.5 and 1.8. The bleed system was comprised of a series of 2mm diameter normal holes operated at different suction rates, removing up to 10% of the incoming boundary layer. Three VG shapes were tested only at Mach 1.5 and 1.8. Measurements of the evolution of Hi and Cf downstream of each device indicate that Hi is not an appropriate parameter to gauge the effectiveness of vortex generators due to boundary layer wake distortion. The skin friction coeficient Cf may be a more appropriate measure. Similar increases in Cf were generated by VGs and bleed. The recovery to baseline conditions downstream of bleed was sensitive to Mach number, and more investigation of that effect will be required. Copyright © 2012 by University of Cambridge.

Direct numerical simulation of turbulent flows over superhydrophobic surfaces with gas pockets using linearized boundary conditions

Superhydrophobic surfaces are shown to be effective for surface drag reduction under laminar regime by both experiments and simulations (see for example, Ou and Rothstein, Phys. Fluids 17:103606, 2005). However, such drag reduction for fully developed turbulent flow maintaining the Cassie-Baxter state remains an open problem due to high shear rates and flow unsteadiness of turbulent boundary layer. Our work aims to develop an understanding of mechanisms leading to interface breaking and loss of gas pockets due to interactions with turbulent boundary layers. We take advantage of direct numerical simulation of turbulence with slip and no-slip patterned boundary conditions mimicking the superhydrophobic surface. In addition, we capture the dynamics of gas-water interface, by deriving a proper linearized boundary condition taking into account the surface tension of the interface and kinematic matching of interface deformation and normal velocity conditions on the wall. We will show results from our simulations predicting the dynamical behavior of gas pocket interfaces over a wide range of dimensionless surface tensions.

Characteristics of low-frequency components of the near-bottom current in the Chinese Pioneer Area

Two deep-sea moorings were deployed respectively in the east area and the west area of Chinese Pioneer Area (CPA) in the tropic east Pacific to monitor the regional deep-sea dynamics below 600 meters above bottom (mab) from July 1997 to Oct. 1999. Results of statistics, spectral estimate and correlation analysis of the low-passed velocity data show that time scales of low-frequency components of the near-bottom currents are 25similar to120 days, in which 51-day period dominates the lower band of the frequency domain. Topographic features have obvious effect on low-frequency currents below 50 mab; modulations of the bottom-intensified sheared mean flow to the low-frequency currents are the dynamic mechanism of the frequency shift that occurs in both the east-area and the west-area.

Tropospheric aerosol detection over Southern Ireland using a backscatter Raman lidar

Lidar is an optical remote sensing instrument that can measure atmospheric parameters. A Raman lidar instrument (UCLID) was established at University College Cork to contribute to the European lidar network, EARLINET. System performance tests were carried out to ensure strict data quality assurance for submission to the EARLINET database. Procedures include: overlap correction, telecover test, Rayleigh test and zero bin test. Raman backscatter coefficients, extinction coefficients and lidar ratio were measured from April 2010 to May 2011 and February 2012 to June 2012. Statistical analysis of the profiles over these periods provided new information about the typical atmospheric scenarios over Southern Ireland in terms of aerosol load in the lower troposphere, the planetary boundary layer (PBL) height, aerosol optical density (AOD) at 532 nm and lidar ratio values. The arithmetic average of the PBL height was found to be 608 ± 138 m with a median of 615 m, while average AOD at 532 nm for clean marine air masses was 0.119 ± 0.023 and for polluted air masses was 0.170 ± 0.036. The lidar ratio showed a seasonal dependence with lower values found in winter and autumn (20 ± 5 sr) and higher during spring and winter (30 ± 12 sr). Detection of volcanic particles from the eruption of the volcano Eyjafjallajökull in Iceland was measured between 21 April and 7 May 2010. The backscatter coefficient of the ash layer varied between 2.5 Mm-1sr-1 and 3.5 Mm-1sr-1, and estimation of the AOD at 532 nm was found to be between 0.090 and 0.215. Several aerosol loads due to Saharan dust particles were detected in Spring 2011 and 2012. Lidar ratio of the dust layers were determine to be between 45 and 77 sr and AOD at 532 nm during the dust events range between 0.84 to 0.494.

Contribution of the North Atlantic subtropical high to regional climate model (RCM) skill in simulating southeastern United States summer precipitation

© 2014, Springer-Verlag Berlin Heidelberg.This study assesses the skill of advanced regional climate models (RCMs) in simulating southeastern United States (SE US) summer precipitation and explores the physical mechanisms responsible for the simulation skill at a process level. Analysis of the RCM output for the North American Regional Climate Change Assessment Program indicates that the RCM simulations of summer precipitation show the largest biases and a remarkable spread over the SE US compared to other regions in the contiguous US. The causes of such a spread are investigated by performing simulations using the Weather Research and Forecasting (WRF) model, a next-generation RCM developed by the US National Center for Atmospheric Research. The results show that the simulated biases in SE US summer precipitation are due mainly to the misrepresentation of the modeled North Atlantic subtropical high (NASH) western ridge. In the WRF simulations, the NASH western ridge shifts 7° northwestward when compared to that in the reanalysis ensemble, leading to a dry bias in the simulated summer precipitation according to the relationship between the NASH western ridge and summer precipitation over the southeast. Experiments utilizing the four dimensional data assimilation technique further suggest that the improved representation of the circulation patterns (i.e., wind fields) associated with the NASH western ridge substantially reduces the bias in the simulated SE US summer precipitation. Our analysis of circulation dynamics indicates that the NASH western ridge in the WRF simulations is significantly influenced by the simulated planetary boundary layer (PBL) processes over the Gulf of Mexico. Specifically, a decrease (increase) in the simulated PBL height tends to stabilize (destabilize) the lower troposphere over the Gulf of Mexico, and thus inhibits (favors) the onset and/or development of convection. Such changes in tropical convection induce a tropical–extratropical teleconnection pattern, which modulates the circulation along the NASH western ridge in the WRF simulations and contributes to the modeled precipitation biases over the SE US. In conclusion, our study demonstrates that the NASH western ridge is an important factor responsible for the RCM skill in simulating SE US summer precipitation. Furthermore, the improvements in the PBL parameterizations for the Gulf of Mexico might help advance RCM skill in representing the NASH western ridge circulation and summer precipitation over the SE US.