Circulation-based models for Boussinesq internal bores

2013 ◽  
Vol 726 ◽  
Author(s):  
Zachary Borden ◽  
Eckart Meiburg
Keyword(s):  
Energy Equation ◽  
Control Volume ◽  
Momentum Conservation ◽  
Pressure Jump ◽  
Conservation Of Mass ◽  
Volume Model ◽  
Internal Bores ◽  
Volume Models ◽  
Additional Equation ◽  
Internal Bore

AbstractExisting control-volume models for predicting the front velocity of internal bores enforce the conservation of mass and streamwise momentum, but not vertical momentum. Instead, they usually invoke an empirical assumption relating the up- and downstream energy fluxes to obtain an additional equation required for determining the pressure jump across a bore. The present investigation develops a control-volume model for internal bores on the basis of mass and momentum conservation alone, without the need for considering energy. This is accomplished by combining the streamwise and vertical momentum equations to obtain a vorticity relation that no longer involves pressure. Hence, this vorticity equation, in combination with the conservation of mass, is sufficient for evaluating the bore velocity. The energy loss across the bore can then be predicted by the streamwise energy equation and compared to the assumptions underlying earlier models. The flux of vorticity across the internal bore predicted by the new model is seen to be in close agreement with direct numerical simulation results. Any discrepancies with experimentally measured bore velocities are shown to be due to the effects of downstream mixing.

scholarly journals Real Color Model of a Cadaver for Deep Brain Stimulation of the Subthalamic Nucleus

2021 ◽  
Vol 11 (11) ◽  
pp. 4999
Author(s):  
Chung-Yoh Kim ◽  
Jin-Seo Park ◽  
Beom-Sun Chung
Keyword(s):  
Deep Brain Stimulation ◽  
Subthalamic Nucleus ◽  
Brain Stimulation ◽  
Magnetic Resonance Images ◽  
Target Point ◽  
Anatomical Structures ◽  
Volume Model ◽  
Segmented Images ◽  
Volume Models ◽  
Deep Brain

When performing deep brain stimulation (DBS) of the subthalamic nucleus, practitioners should interpret the magnetic resonance images (MRI) correctly so they can place the DBS electrode accurately at the target without damaging the other structures. The aim of this study is to provide a real color volume model of a cadaver head that would help medical students and practitioners to better understand the sectional anatomy of DBS surgery. Sectioned images of a cadaver head were reconstructed into a real color volume model with a voxel size of 0.5 mm × 0.5 mm × 0.5 mm. According to preoperative MRIs and postoperative computed tomographys (CT) of 31 patients, a virtual DBS electrode was rendered on the volume model of a cadaver. The volume model was sectioned at the classical and oblique planes to produce real color images. In addition, segmented images of a cadaver head were formed into volume models. On the classical and oblique planes, the anatomical structures around the course of the DBS electrode were identified. The entry point, waypoint, target point, and nearby structures where the DBS electrode could be misplaced were also elucidated. The oblique planes could be understood concretely by comparing the volume model of the sectioned images with that of the segmented images. The real color and high resolution of the volume model enabled observations of minute structures even on the oblique planes. The volume models can be downloaded by users to be correlated with other patients’ data for grasping the anatomical orientation.

A Complete Solution for Thermal-Elastohydrodynamic Lubrication of Line Contacts Using Circular Non-Newtonian Fluid Model

1992 ◽  
Vol 114 (3) ◽  
pp. 540-551 ◽  
Author(s):  
Hsing-Sen S. Hsiao ◽  
Bernard J. Hamrock
Keyword(s):  
Boundary Conditions ◽  
Newtonian Fluid ◽  
Energy Equation ◽  
Control Volume ◽  
Fluid Model ◽  
Complete Solution ◽  
Circular Model ◽  
Line Contacts ◽  
Stress Boundary Conditions ◽  
Stress Boundary

A complete solution is obtained for elastohydrodynamically lubricated conjunctions in line contacts considering the effects of temperature and the non-Newtonian characteristics of lubricants with limiting shear strength. The complete fast approach is used to solve the thermal Reynolds equation by using the complete circular non-Newtonian fluid model and considering both velocity and stress boundary conditions. The reason and the occasion to incorporate stress boundary conditions for the circular model are discussed. A conservative form of the energy equation is developed by using the finite control volume approach. Analytical solutions for solid surface temperatures that consider two-dimensional heat flow within the solids are used. A straightforward finite difference method, successive over-relaxation by lines, is employed to solve the energy equation. Results of thermal effects on film shape, pressure profile, streamlines, and friction coefficient are presented.

Measurements Versus Predictions for the Dynamic Impedance of Annular Gas Seals—Part II: Smooth and Honeycomb Geometries

2002 ◽  
Vol 124 (4) ◽  
pp. 963-970 ◽  
Author(s):  
M. P. Dawson ◽  
D. W. Childs
Keyword(s):  
Control Volume ◽  
Test Facility ◽  
Radial Clearance ◽  
Cell Width ◽  
Volume Model ◽  
Numerical Predictions ◽  
Dynamic Impedance ◽  
Honeycomb Seals ◽  
Gas Seals ◽  
Honeycomb Cell

Results are presented from tests conducted using an experimental test facility to measure the leakage and dynamic impedance of smooth and honeycomb straight-bore annular gas seals. The test seals had a 114.3 mm (4.500 in.) bore with a length-to-diameter ratio of 0.75 and a nominal radial clearance of 0.19 mm (0.0075 in.). The honeycomb cell depth for both seals was 3.10 mm (0.122 in.), and the cell width was 0.79 mm (0.031 in.). Dynamic impedance and leakage measurements are reported using air at three supply pressures out to 1.72 Mpa (250 psi), three speeds out to 20,200 rpm, and exit-to-inlet pressure ratios of 40% and 50%. Comparisons to the predictions from the two-control-volume model of Kleynhans and Childs [1] are of particular interest. This model predicts that honeycomb seals do not fit the conventional frequency independent model for smooth annular gas seals. The experimental results verify this new theory. Numerical predictions from a computer program incorporating the new two-control-volume model of Kleynhans and Childs [1] correlate well with both measured seal leakage and dynamic impedances for the honeycomb seals.

scholarly journals ODREĐIVANJE TERMIČKIH VELIČINA KOD PRAVOLINIJSKOG KLIZNOG LEŽIŠTA NA BAZI DISIPACIONE FUNKCIJE

2021 ◽  
Author(s):  
Mirko Radic ◽  
◽  
Duško Kostic ◽  
Branko Pejovic ◽  
Srđan Jovic ◽  
...  
Keyword(s):  
Continuity Equation ◽  
Energy Equation ◽  
Control Volume ◽  
Mass Conservation ◽  
Dissipation Function ◽  
Second Law ◽  
Specific Calculation ◽  
Influence Of Temperature ◽  
Technical Practice ◽  
Two Dimensional Flow

In the first part of the paper, the continuity equation in the boundary layer for stationary two-dimensional flow is derived on the basis of the law of mass conservation. After that, using Newton's second law for control volume, the equation for the momentum was derived. Using the derived equations, the analysis was performed with respect to the influence of temperature. After that, on the basis of the energy balance, an energy equation was derived in which a viscous dissipation function was introduced, which enabled a wider application. At the end of the paper, the derived equations were applied to a specific calculation example from technical practice in the calculation of thermal quantities in a rectilinear sliding bearing, which was the aim of the work

scholarly journals Combination of Multi-Temporal Sentinel 2 Images and Aerial Image Based Canopy Height Models for Timber Volume Modelling

Forests ◽  
2019 ◽  
Vol 10 (9) ◽  
pp. 746 ◽  
Author(s):  
Johannes Schumacher ◽  
Margret Rattay ◽  
Melanie Kirchhöfer ◽  
Petra Adler ◽  
Gerald Kändler
Keyword(s):  
Forest Inventory ◽  
Point Clouds ◽  
Support Vector ◽  
Timber Volume ◽  
Volume Model ◽  
Broadleaf Tree ◽  
Multi Temporal ◽  
Conifer Trees ◽  
Volume Models ◽  
Sentinel 2

Multi-temporal Sentinel 2 optical images and 3D photogrammetric point clouds can be combined to enhance the accuracy of timber volume models on large spatial scale. Information on the proportion of broadleaf and conifer trees improves timber volume models obtained from 3D photogrammetric point clouds. However, the broadleaf-conifer information cannot be obtained from photogrammetric point clouds alone. Furthermore, spectral information of aerial images is too inconsistent to be used for automatic broadleaf-conifer classification over larger areas. In this study we combined multi-temporal Sentinel 2 optical satellite images, 3D photogrammetric point clouds from digital aerial stereo photographs, and forest inventory plots representing an area of 35,751 km2 in south-west Germany for (1) modelling the percentage of broadleaf tree volume (BL%) using Sentinel 2 time series and (2) modelling timber volume per hectare using 3D photogrammetric point clouds. Forest inventory plots were surveyed in the same years and regions as stereo photographs were acquired (2013–2017), resulting in 11,554 plots. Sentinel 2 images from 2016 and 2017 were corrected for topographic and atmospheric influences and combined with the same forest inventory plots. Spectral variables from corrected multi-temporal Sentinel 2 images were calculated, and Support Vector Machine (SVM) regressions were fitted for each Sentinel 2 scene estimating the BL% for corresponding inventory plots. Variables from the photogrammetric point clouds were calculated for each inventory plot and a non-linear regression model predicting timber volume per hectare was fitted. Each SVM regression and the timber volume model were evaluated using ten-fold cross-validation (CV). The SVM regression models estimating the BL% per Sentinel 2 scene achieved overall accuracies of 68%–75% and a Root Mean Squared Error (RMSE) of 21.5–26.1. The timber volume model showed a RMSE% of 31.7%, a mean bias of 0.2%, and a pseudo-R2 of 0.64. Application of the SVM regressions on Sentinel 2 scenes covering the state of Baden-Württemberg resulted in predictions of broadleaf tree percentages for the entire state. These predicted values were used as additional predictor in the timber volume model, allowing for predictions of timber volume for the same area. Spatially high-resolution information about growing stock is of great practical relevance for forest management planning, especially when the timber volume of a smaller unit is of interest, for example of a forest stand or a forest district where not enough terrestrial inventory plots are available to make reliable estimations. Here, predictions from remote-sensing based models can be used. Furthermore, information about broadleaf and conifer trees improves timber volume models and reduces model errors and, thereby, prediction uncertainties.

Accuracy in the context of a control‐volume model

1998 ◽  
Vol 36 (4) ◽  
pp. 355-384 ◽  
Author(s):  
Brian Sanderson ◽  
Gary Brassington
Keyword(s):  
Control Volume ◽  
Volume Model
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