Velocity profiles and frictional pressure drop for shear thinning materials in lid-driven cavities with fully developed axial flow

A finite element numerical study has been carried out on the isothermal flow of power law fluids in lid-driven cavities with axial throughflow. The effects of the tangential flow Reynolds number (Re-U), axial flow Reynolds number (Re-W), cavity aspect ratio and shear thinning property of the fluids on tangential and axial velocity distributions and the frictional pressure drop are studied. Where comparison is possible, very good agreement is found between current numerical results and published asymptotic and numerical results. For shear thinning materials in long thin cavities in the tangential flow dominated flow regime, the numerical results show that the frictional pressure drop lies between two extreme conditions, namely the results for duct flow and analytical results from lubrication theory. For shear thinning materials in a lid-driven cavity, the interaction between the tangential flow and axial flow is very complex because the flow is dependent on the flow Reynolds numbers and the ratio of the average axial velocity and the lid velocity. For both Newtonian and shear thinning fluids, the axial velocity peak is shifted and the frictional pressure drop is increased with increasing tangential flow Reynolds number. The results are highly relevant to industrial devices such as screw extruders and scraped surface heat exchangers. (c) 2006 Elsevier Ltd. All rights reserved.

Novel actuator design to overcome stiction and backlash for low-velocity applications

This paper presents a novel actuator design that ameliorates or eliminates the effects of non-linearities that are characteristically present in geared actuator systems and which are very problematic for low velocity applications. The design centres on the providing an internal rotational element within a single actuator to ensure operation of actuator away from the stiction region, whilst allowing zero velocity external output of the actuator. The construction has the added advantage of substantially reducing backlash. The prototype comprises two commercially available servo-actuators to test the principle of operation and results presented indicate that the concept is worth exploring further.

Vertical velocity variance and skewness in clear and cloud-topped boundary layers as revealed by Doppler lidar

In this paper, observations by a ground-based vertically pointing Doppler lidar and sonic anemometer are used to investigate the diurnal evolution of boundary-layer turbulence in cloudless, cumulus and stratocumulus conditions. When turbulence is driven primarily by surface heating, such as in cloudless and cumulus-topped boundary layers, both the vertical velocity variance and skewness follow similar profiles, on average, to previous observational studies of turbulence in convective conditions, with a peak skewness of around 0.8 in the upper third of the mixed layer. When the turbulence is driven primarily by cloud-top radiative cooling, such as in the presence of nocturnal stratocumulus, it is found that the skewness is inverted in both sign and height: its minimum value of around −0.9 occurs in the lower third of the mixed layer. The profile of variance is consistent with a cloud-top cooling rate of around 30Wm−2. This is also consistent with the evolution of the thermodynamic profile and the rate of growth of the mixed layer into the stable nocturnal boundary layer from above. In conditions where surface heating occurs simultaneously with cloud-top cooling, the skewness is found to be useful for diagnosing the source of the turbulence, suggesting that long-term Doppler lidar observations would be valuable for evaluating boundary-layer parametrization schemes. Copyright c 2009 Royal Meteorological Society

Velocity-based moving mesh methods for nonlinear partial differential equations

This article describes a number of velocity-based moving mesh numerical methods formultidimensional nonlinear time-dependent partial differential equations (PDEs). It consists of a short historical review followed by a detailed description of a recently developed multidimensional moving mesh finite element method based on conservation. Finite element algorithms are derived for both mass-conserving and non mass-conserving problems, and results shown for a number of multidimensional nonlinear test problems, including the second order porous medium equation and the fourth order thin film equation as well as a two-phase problem. Further applications and extensions are referenced.

Cloud-base vertical velocity statistics: a comparison between an atmospheric mesoscale model and remote sensing observations

The statistics of cloud-base vertical velocity simulated by the non-hydrostatic mesoscale model AROME are compared with Cloudnet remote sensing observations at two locations: the ARM SGP site in Central Oklahoma, and the DWD observatory at Lindenberg, Germany. The results show that, as expected, AROME significantly underestimates the variability of vertical velocity at cloud-base compared to observations at their nominal resolution; the standard deviation of vertical velocity in the model is typically 4-6 times smaller than observed, and even more during the winter at Lindenberg. Averaging the observations to the horizontal scale corresponding to the physical grid spacing of AROME (2.5 km) explains 70-80% of the underestimation by the model. Further averaging of the observations in the horizontal is required to match the model values for the standard deviation in vertical velocity. This indicates an effective horizontal resolution for the AROME model of at least 4 times the physically-defined grid spacing. The results illustrate the need for special treatment of sub-grid scale variability of vertical velocities in kilometer-scale atmospheric models, if processes such as aerosol-cloud interactions are to be included in the future.

Estimation of the friction velocity in stably stratified boundary-layer flows over hills

A method is suggested for the calculation of the friction velocity for stable turbulent boundary-layer flow over hills. The method is tested using a continuous upstream mean velocity profile compatible with the propagation of gravity waves, and is incorporated into the linear model of Hunt, Leibovich and Richards with the modification proposed by Hunt, Richards and Brighton to include the effects of stability, and the reformulated solution of Weng for the near-surface region. Those theoretical results are compared with results from simulations using a non-hydrostatic microscale-mesoscale two-dimensional numerical model, and with field observations for different values of stability. These comparisons show a considerable improvement in the behaviour of the theoretical model when the friction velocity is calculated using the method proposed here, leading to a consistent variation of the boundary-layer structure with stability, and better agreement with observational and numerical data.