Use of a Vertical Vorticity Equation in Variational Dual-Doppler Wind Analysis

2009 ◽  
Vol 26 (10) ◽  
pp. 2089-2106 ◽  
Author(s):  
Alan Shapiro ◽  
Corey K. Potvin ◽  
Jidong Gao
Keyword(s):  
Stokes Equations ◽  
Value Added ◽  
Mass Conservation ◽  
Conservation Equation ◽  
Analysis Procedure ◽  
Vorticity Equation ◽  
Vertical Vorticity ◽  
Beltrami Flow ◽  
Wind Analysis ◽  
Equation Constraint

Abstract The utility of the anelastic vertical vorticity equation in a weak-constraint (least squares error) variational dual-Doppler wind analysis procedure is explored. The analysis winds are obtained by minimizing a cost function accounting for the discrepancies between observed and analyzed radial winds, errors in the mass conservation equation, errors in the anelastic vertical vorticity equation, and spatial smoothness constraints. By using Taylor’s frozen-turbulence hypothesis to shift analysis winds to observation points, discrepancies between radially projected analysis winds and radial wind observations can be calculated at the actual times and locations the data are acquired. The frozen-turbulence hypothesis is also used to evaluate the local derivative term in the vorticity equation. Tests of the analysis procedure are performed with analytical pseudo-observations of an array of translating and temporally decaying counterrotating updrafts and downdrafts generated from a Beltrami flow solution of the Navier–Stokes equations. The experiments explore the value added to the analysis by the vorticity equation constraint in the common scenario of substantial missing low-level data (radial wind observations at heights beneath 1.5 km are withheld from the analysis). Experiments focus on the sensitivity of the most sensitive analysis variable—the vertical velocity component—to values of the weighting coefficients, volume scan period, number of volume scans, and errors in the estimated frozen-turbulence pattern-translation components. Although the vorticity equation constraint is found to add value to many of these analyses, the analysis can become significantly degraded if estimates of the pattern-translation components are largely in error or if the frozen-turbulence hypothesis itself breaks down. However, tests also suggest that these negative impacts can be mitigated if data are available in a rapid-scan mode.

Mathematical Modelling of Thermo-Hydro-Mechanical Behaviour for Concrete under Elevated Temperature

2014 ◽  
Vol 670-671 ◽  
pp. 355-364
Author(s):  
Shao Bo Zhang ◽  
Xiao Chun Wang ◽  
Xin Pu Shen
Keyword(s):  
Elevated Temperature ◽  
Stokes Equations ◽  
Constitutive Relations ◽  
Gaseous Mixture ◽  
Mass Conservation ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Energy Conservation Equation

A hydro-thermo-mechanical model was presented for concrete at elevated temperature. Three phases of continuum were adopted in this model: gaseous mixture of water vapor and dry air, liquid water, and solid skeleton of concrete. Mass conservation equations, linear momentum conservation equation, and energy conservation equation were derived on the basis of the macroscopic Navier-Stokes equations for a general continuum, along with assumptions made for the purpose of simplification. Mathematical relationships between selected primary variables and secondary variables were given with existing data from references. Specifications of the constitutive relations were made for the kinetic variables and their conjugate forces.

Numerical Modeling of Local Scour Below a Piggyback Pipeline in Currents

2006 ◽  
Author(s):  
Ming Zhao ◽  
Liang Cheng
Keyword(s):  
Stokes Equations ◽  
Large Diameter ◽  
Mass Conservation ◽  
Sediment Concentration ◽  
Conservation Equation ◽  
Diameter Ratio ◽  
Local Scour ◽  
Navier Stokes ◽  
Bed Scour ◽  
Different Diameters

Local scour under two pipelines of different diameters in steady currents is investigated numerically. The two pipelines are arranged in the so-called piggyback configuration where the small pipeline is located directly above the large pipeline (as shown in Fig. 1). The Reynolds-averaged Navier-Stokes equations and the transport equation of the suspended sediment concentration are solved using a finite element method. The sediment mass conservation equation is solved for predicting the bed scour profile. The numerical model is firstly validated against the scour below a single pipeline where the experimental data are available. Then the model is employed to simulate the scour below two pipelines in steady currents. Computations are carried out for the diameter ratio (the small pipe diameter (d) to the larger one (D)) of 0.2 and the gap (G, between the two pipelines) to the large diameter ratio G/D ranging from 0.0 to 0.5. It is found that the flow and the scour profiles are influenced significantly by the gap ratio.

Impact of a Vertical Vorticity Constraint in Variational Dual-Doppler Wind Analysis: Tests with Real and Simulated Supercell Data

2012 ◽  
Vol 29 (1) ◽  
pp. 32-49 ◽  
Author(s):  
Corey K. Potvin ◽  
Alan Shapiro ◽  
Ming Xue
Keyword(s):  
Vertical Velocity ◽  
Three Dimensional ◽  
Mass Conservation ◽  
Vorticity Equation ◽  
Vertical Vorticity ◽  
Advanced Regional Prediction System ◽  
Supercell Storm ◽  
Radar Networks ◽  
Regional Prediction ◽  
The Impact

Abstract One of the greatest challenges to dual-Doppler retrieval of the vertical wind is the lack of low-level divergence information available to the mass conservation constraint. This study examines the impact of a vertical vorticity equation constraint on vertical velocity retrievals when radar observations are lacking near the ground. The analysis proceeds in a three-dimensional variational data assimilation (3DVAR) framework with the anelastic form of the vertical vorticity equation imposed along with traditional data, mass conservation, and smoothness constraints. The technique is tested using emulated radial wind observations of a supercell storm simulated by the Advanced Regional Prediction System (ARPS), as well as real dual-Doppler observations of a supercell storm that occurred in Oklahoma on 8 May 2003. Special attention is given to procedures to evaluate the vorticity tendency term, including spatially variable advection correction and estimation of the intrinsic evolution. Volume scan times ranging from 5 min, typical of operational radar networks, down to 30 s, achievable by rapid-scan mobile radars, are considered. The vorticity constraint substantially improves the vertical velocity retrievals in our experiments, particularly for volume scan times smaller than 2 min.

Transport of Microorganisms in the Underground – Processes, Experiments and Simulation Models

1991 ◽  
Vol 24 (2) ◽  
pp. 309-314 ◽  
Author(s):  
G. Teutsch ◽  
K. Herbold-Paschke ◽  
D. Tougianidou ◽  
T. Hahn ◽  
K. Botzenhart
Keyword(s):  
Simulation Models ◽  
Mass Conservation ◽  
Breakthrough Curves ◽  
Conservation Equation ◽  
Retardation Factor ◽  
Natural Systems ◽  
Laboratory Setup ◽  
Preliminary Model ◽  
Sand And Gravel ◽  
Mass Conservation Equation

In this paper the major processes governing the persistence and underground transport of viruses and bacteria are reviewed in respect to their importance under naturally occurring conditions. In general, the simulation of the governing processes is based on the macroscopic mass-conservation equation with the addition of some filter and/or retardation factor and a decay coefficient, representing the natural “die-off” of the microorganisms. More advanced concepts try to incorporate growth and decay coefficients together with deposition and declogging factors. At present, none of the reported concepts has been seriously validated. Due to the complexity of natural systems and the pathogenic properties of some of the microorganisms, experiments under controlled laboratory conditions are required. A laboratory setup is presented in which a great variety of natural conditions can be simulated. This comprises a set of 1 metre columns and an 8 metre stainless-steel flume with 24 sampling ports. The columns are easily filled and conditioned and therefore used to study the effects of different soil-microorganism combinations under various environmental conditions. In the artificial flume natural underground conditions are simulated using sand and gravel aquifer material from the river Neckar alluvium. A first set of results from the laboratory experiments is presented together with preliminary model simulations. The large variety of observed breakthrough curves and recovery for the bacteria and viruses under investigation demonstrates the great uncertainty encountered in microbiological risk assessment.

scholarly journals Thermochemical Nonequilibrium in Rapidly Expanding Flows of High-Temperature Air

1997 ◽  
Vol 52 (4) ◽  
pp. 358-368 ◽  
Author(s):  
Michio Nishida ◽  
Masashi Matsumotob
Keyword(s):  
High Temperature ◽  
Vibrational Energy ◽  
Stokes Equations ◽  
Computational Study ◽  
Mass Conservation ◽  
Navier Stokes ◽  
Tvd Scheme ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Free Jet

Abstract • This paper describes a computational study of the thermal and chemical nonequilibrium occuring in a rapidly expanding flow of high-temperature air transported as a free jet from an orifice into low-density stationary air. Translational, rotational, vibrational and electron temperatures are treated separately, and in particular the vibrational temperatures are individually treated; a multi-vibrational temperature model is adopted. The governing equations are axisymmetric Navier-Stokes equations coupled with species vibrational energy, electron energy and species mass conservation equations. These equations are numerically solved, using the second order upwind TVD scheme of the Harten-Yee type. The calculations were carried out for two different orifice temperatures and also two different orifice diameters to investigate the effects of such parameters on the structure of a nonequilibrium free jet.

The mechanism of vortex connection at a free surface

1999 ◽  
Vol 384 ◽  
pp. 207-241 ◽  
Author(s):  
CHIONG ZHANG ◽  
LIAN SHEN ◽  
DICK K. P. YUE
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Vortex Ring ◽  
Stokes Equations ◽  
Incidence Angle ◽  
Surface Boundary ◽  
Viscous Layer ◽  
Vertical Vorticity ◽  
Vorticity Component ◽  
Stress Boundary Conditions

Vortex connections at the surface are fundamental and prominent features in free-surface vortical flows. To understand the detailed mechanism of such connection, we consider, as a canonical problem, the laminar vortex connections at a free surface when an oblique vortex ring impinges upon that surface. We perform numerical simulations of the Navier–Stokes equations with viscous free-surface boundary conditions. It is found that the key to understanding the mechanism of vortex connection at a free surface is the surface layers: a viscous layer resulting from the dynamic zero-stress boundary conditions at the free surface, and a thicker blockage layer which is due to the kinematic boundary condition at the surface. In the blockage layer, the vertical vorticity component increases due to vortex stretching and vortex turning (from the transverse vorticity component). The vertical vorticity is then transported to the free surface through viscous diffusion and vortex stretching in the viscous layer leading to increased surface-normal vorticity. These mechanisms take place at the aft-shoulder regions of the vortex ring. Connection at the free surface is different from that at a free-slip wall owing to the generation of surface secondary vorticity. We study the components of this surface vorticity in detail and find that the presence of a free surface accelerates the connection process. We investigate the connection time scale and its dependence on initial incidence angle, Froude and Reynolds numbers. It is found that a criterion based on the streamline topology provides a precise definition for connection time, and may be preferred over existing definitions, e.g. those based on free-surface elevation or net circulation.

A New Model for the Simulation of CO2 Absorption in an Industrial-Scale Packed Column

2012 ◽  
Vol 557-559 ◽  
pp. 2208-2216 ◽  
Author(s):  
Wen Bin Li ◽  
Guo Cong Yu ◽  
Bo Tan Liu ◽  
Xi Gang Yuan
Keyword(s):  
Mass Transfer ◽  
Packed Column ◽  
Mass Conservation ◽  
Conservation Equation ◽  
Industrial Scale ◽  
Transfer Model ◽  
Turbulent Heat ◽  
Proposed Model ◽  
Heat Conservation ◽  
Phase Temperature

A new computational mass transfer model is proposed for simulating the chemical absorption process with heat effect by solving the average fluctuating mass flux in turbulent mass conservation equation and the average fluctuating heat flux in turbulent heat conservation equation, so that the concentration profile and the temperature profile of column can be obtained. The feather of the proposed model is to abandon the conventional way of introducing the unknown turbulent mass transfer diffusivity Dtand the turbulent thermal diffusivity αtin the mass and heat conservation equations. By using the proposed model, the simulated results of CO2absorption by aqueous monoethanolamine (MEA) solution in an industrial scale column is presented, including MEA concentration, CO2loading and liquid phase temperature. The simulations are in agreement with the published experiment data.

Effects of Non-Linearity of the Momentum Conservation Equation During Electrokinetic Transport in Nano and Microchannels

2010 ◽  
Author(s):  
Subir Bhattacharjee ◽  
Noor Al Quddus
Keyword(s):  
Porous Media ◽  
Electric Fields ◽  
Stokes Equations ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Small Scale ◽  
Electrokinetic Transport ◽  
Electrokinetic Flow ◽  
Non Linear ◽  
Momentum Conservation Equation

Electrokinetic transport phenomena, such as electroosmosis, streaming potential, electrophoresis, and sedimentation potential, are central to many micro- and nano-channel flows. During continuum modeling of such phenomena, incorporation of the electrical body force term can make the fluid momentum conservation equation highly non-linear. This non-linearity is often ignored in small-scale electrokinetic flow modeling because of our implicit reliance on the linearity of the Stokes equations for low Reynolds number flows. In this paper, ramifications of this non-linear Stokes equation in electrokinetic flows will be described with examples of our recent studies on pressure driven flows through porous media for electrokinetic power generation, electroosmotic flow of charged entities in nanochannels, and flow of DNA through self-assembled porous media under pulsed electric fields.

scholarly journals High-Resolution, Rapid-Scan Dual-Doppler Retrievals of Vertical Velocity in a Simulated Supercell

2019 ◽  
Vol 36 (8) ◽  
pp. 1477-1500 ◽  
Author(s):  
Nathan A. Dahl ◽  
Alan Shapiro ◽  
Corey K. Potvin ◽  
Adam Theisen ◽  
Joshua G. Gebauer ◽  
...  
Keyword(s):  
Variational Method ◽  
Vertical Velocity ◽  
Traditional Method ◽  
Mass Conservation ◽  
Conservation Equation ◽  
Observation System ◽  
Near Surface ◽  
Rapid Scan ◽  
Close Range ◽  
The Impact

AbstractObservation system simulation experiments are used to evaluate different dual-Doppler analysis (DDA) methods for retrieving vertical velocity w at grid spacings on the order of 100 m within a simulated tornadic supercell. Variational approaches with and without a vertical vorticity equation constraint are tested, along with a typical (traditional) method involving vertical integration of the mass conservation equation. The analyses employ emulated radar data from dual-Doppler placements 15, 30, and 45 km east of the mesocyclone, with volume scan intervals ranging from 10 to 150 s. The effect of near-surface data loss is examined by denying observations below 1 km in some of the analyses. At the longer radar ranges and when no data denial is imposed, the “traditional” method produces results similar to those of the variational method and is much less expensive to implement. However, at close range and/or with data denial, the variational method is much more accurate, confirming results from previous studies. The vorticity constraint shows the potential to improve the variational analysis substantially, reducing errors in the w retrieval by up to 30% for rapid-scan observations (≤30 s) at close range when the local vorticity tendency is estimated using spatially variable advection correction. However, the vorticity constraint also degrades the analysis for longer scan intervals, and the impact diminishes with increased range. Furthermore, analyses using 30-s data also frequently outperform analyses using 10-s data, suggesting a limit to the benefit of increasing the radar scan rate for variational DDA employing the vorticity constraint.

Macroscopic Modeling of Pedestrian Flow Considering the Herd Behavior

2013 ◽  
Vol 444-445 ◽  
pp. 906-911
Author(s):  
Yan Qun Jiang
Keyword(s):  
Numerical Experiments ◽  
Mass Conservation ◽  
Conservation Equation ◽  
Behavioral Characteristics ◽  
Herd Behavior ◽  
Pedestrian Flow ◽  
Evacuation Time ◽  
Macroscopic Modeling ◽  
Pedestrian Simulation ◽  
Mass Conservation Equation

This paper aims to mimic the herd behavior of pedestrian flow, i.e., the tendency towards majority when a congestion occurs, by macroscopic modeling approach. The macroscopic pedestrian simulation model is composed of a mass-conservation equation and a simple model to reflect behavioral characteristics of pedestrians based on a specific traffic situation. Numerical experiments are designed to show some preliminary results, e.g. the beneficial effect of herding on evacuation time in some situations.

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