scholarly journals Singularity formation in the shape of a vortex sheet in three dimensions-numerical simulation

1996 ◽  
Vol 1 ◽  
pp. 463-479
Author(s):  
Takashi Ishihara ◽  
Yukio Kaneda
Keyword(s):  
Numerical Simulation ◽  
Vortex Sheet ◽  
Three Dimensions ◽  
Singularity Formation

Singularity formation in three-dimensional motion of a vortex sheet

1995 ◽  
Vol 300 ◽  
pp. 339-366 ◽  
Author(s):  
Takashi Ishihara ◽  
Yukio Kaneda
Keyword(s):  
Asymptotic Analysis ◽  
Numerical Integration ◽  
Finite Time ◽  
Fourier Coefficients ◽  
Evolution Equations ◽  
Three Dimensional ◽  
Vortex Sheet ◽  
Three Dimensions ◽  
Leading Order ◽  
Singularity Formation

The evolution of a small but finite three-dimensional disturbance on a flat uniform vortex sheet is analysed on the basis of a Lagrangian representation of the motion. The sheet at time t is expanded in a double periodic Fourier series: R(λ1, λ2, t) = (λ1, λ2, 0) + Σn,mAn,m exp[i(nλ1 + δmλ2)], where λ1 and λ2 are Lagrangian parameters in the streamwise and spanwise directions, respectively, and δ is the aspect ratio of the periodic domain of the disturbance. By generalizing Moore's analysis for two-dimensional motion to three dimensions, we derive evolution equations for the Fourier coefficients An,m. The behaviour of An,m is investigated by both numerical integration of a set of truncated equations and a leading-order asymptotic analysis valid at large t. Both the numerical integration and the asymptotic analysis show that a singularity appears at a finite time tc = O(lnε−1) where ε is the amplitude of the initial disturbance. The singularity is such that An,0 = O(tc−1) behaves like n−5/2, while An,±1 = O(εtc) behaves like n−3/2 for large n. The evolution of A0,m(spanwise mode) is also studied by an asymptotic analysis valid at large t. The analysis shows that a singularity appears at a finite time t = O(ε−1) and the singularity is characterized by A0,2k ∝ k−5/2 for large k.

Hydraulic Characteristics of the New Type Bulb Turbine With Micro-Head

2013 ◽  
Author(s):  
Lingyu Li ◽  
Yuan Zheng ◽  
Daqing Zhou ◽  
Zihao Mi
Keyword(s):  
Numerical Simulation ◽  
Cfd Simulation ◽  
Guide Vane ◽  
Three Dimensional ◽  
Flow Distribution ◽  
Three Dimensions ◽  
Guide Vanes ◽  
Runner Blade ◽  
Cfd Method ◽  
Bulb Turbine

The head of low-head hydropower stations is generally higher than 2.5m in the world, while micro-head hydropower resources which head is less than 2.5m are also very rich. In the paper, three-dimensional CFD method has been used to simulate flow passage of the micro-head bulb turbine. The design head and unit flow of the turbine was 1m and 3m3/s respectively. With the numerical simulation, the bulb turbine is researched by analyzing external characteristics of the bulb turbine, flow distribution before the runner, pressure distribution of the runner blade surface, and flow distribution of the outlet conduit under three different schemes. The turbine in second scheme was test by manufactured into a physical model. According to the results of numerical simulation and model test, bulb turbine with no guide vane in second scheme has simpler structure, lower cost, and better flow capacity than first scheme, which has traditional multi-guide vanes. Meanwhile, efficiency of second scheme has just little decrease. The results of three dimensions CFD simulation and test results agree well in second scheme, and higher efficiency is up to 77% which has a wider area with the head of 1m. The curved supports in third scheme are combined guide vanes to the fixed supports based on 2nd scheme. By the water circulations flowing along the curved supports which improve energy transformation ability of the runner, the efficiency of the turbine in third scheme is up to 82.6%. Third scheme, which has simpler structure and best performance, is appropriate for the development and utilization of micro-head hydropower resources in plains and oceans.

scholarly journals Global ionospheric models in three dimensions from GPS measurements: Numerical simulation

2000 ◽  
Vol 39 (1) ◽  
pp. 21-27
Author(s):  
Amali Meza ◽  
Claudio Brunini ◽  
Alfred Kleusberg
Keyword(s):  
Numerical Simulation ◽  
Three Dimensions ◽  
Gps Measurements ◽  
Atmospheric Research ◽  
Ionospheric Models

Gracias a las observaciones GPS en doble - frecuencia de receptores distribuidos uniformemente sobre la superficie terrestre es posible hacer un análisis de la ionosfera como puede verse en los trabajos de Mannucci A. et al., 1993; Beutler G., 1995 y Brunini C. et al., 1997 entre otros. Este análisis consiste básicamente en el modelado de las variaciones del contenido total de electrones en función de 2 coordenadas que bien pueden ser la latitud y la longitud en un sistema sol fijo. Estos modelos asumen que la ionosfera puede representarse por una capa esférica de espesor despreciable, situada a una determinada altura (entre los 300 y 400 km), donde se concentra la totalidad de los electrones libres. Para modelar la distribución espacial de la concentración total de electrones en la delgada capa, se han utilizado series de Taylor en dos dimensiones o armónicos esféricos entre otros. En abril de 1995, gracias al lanzamiento de la misión GPS-MET, se pudo hacer realidad la obtención de observaciones GPS desde un receptor en el espacio. GPS-MET es un experimento dirigido por el UCAR (University Corporation of Atmospheric Research), cuyo objetivo es el sondeo de la atmósfera terrestre mediante observaciones GPS colectadas por un receptor de alto rendimiento situado a bordo del satélite MicroLab I (MLI). Este satélite describe una órbita circular a 730 km de altura (LEO=Low Elevation Orbit), con una inclinación de 60°. Las observaciones colectadas por este receptor están disponibles vía ftp en una base de datos administrada por el UCAR. Este satélite de baja altura con receptor GPS de doble frecuencia nos brinda la posibilidad de contar con señales GPS que atraviesan la ionosfera a diferentes alturas. Este trabajo no apunta a discutir un modelo ionosférico en sí mismo, sino más bien a analizar las posibilidades de utilizar mediciones GPS para extraer información sobre el comportamiento vertical de la densidad electrónica, basadas en un modelo medio y global. En este trabajo emplearemos simulaciones numéricas con el objetivo de analizar si las observaciones del Microlab I son suficientemente sensibles a las variaciones en altura de la ionosfera. Afortunadamente y pese a la limitación en la geometría del problema, ya que sólo contamos con un satélite de órbita fija, se concluye que el receptor espacial nos brinda información fundamental para el modelado en altura de la densidad de electrones.

Numerical Simulation of Multibody Systems With Time Dependant Structure

1993 ◽  
Author(s):  
Pierre Joli ◽  
Madeleine Pascal ◽  
René Gibert
Keyword(s):  
Numerical Simulation ◽  
Multibody Systems ◽  
Computational Algorithm ◽  
Rigid Bodies ◽  
Three Dimensions ◽  
Integration Step ◽  
General Systems ◽  
Articulated Systems ◽  
Jump Velocity ◽  
Assembly Tasks

Abstract Current dynamic simulation programs are able to calculate the continuous motions of articulated systems or more general systems of rigid bodies in the absence of contact between members of the system or between the system and its environment. Some are able to simulate the effects of isolated contacts and impacts but none are able to simulate the motion with unrestricted multiple concurrent contacts. However, in special robotic programs such as robots performing assembly tasks or walking, it would be very interesting to simulate appropriate commands before implementing them on the robots. This paper develops intrinsic problems of collision to produce an efficient computational algorithm. This algorithm handles the detection of collision in three dimensions, the reduction of the integration step in order to avoid interpenetration between the bodies before impact, the jump velocity caused by a new collision and indicator magnitudes which determine the addition or deletion of constraints.

Propeller Wake Sheet Roll-up Modeling in Three Dimensions

1997 ◽  
Vol 41 (01) ◽  
pp. 81-92
Author(s):  
Sangwoo Pyo ◽  
Spyros A. Kinnas
Keyword(s):  
Three Dimensional ◽  
Vortex Sheet ◽  
Experimental Information ◽  
Higher Order ◽  
Three Dimensions ◽  
Tip Vortex ◽  
Propeller Wake ◽  
Wake Interaction ◽  
Radial Circulation ◽  
Wake Sheet

An algorithm for predicting the complete three-dimensional vortex sheet roll-up is developed. A higher order panel method, which combines a hyperboloidal panel geometry with a bi-quadratic dipole distribution, is used in order to accurately model the highly rolled-up regions. For given radial circulation distributions, the predicted wake shapes are shown to be convergent and consistent with those predicted from other methods. Then, a previously developed flow-adapted grid and the three-dimensional wake sheet roll-up algorithm are combined in order to estimate the propeller loading/trailing wake interaction. The complete wake geometry is determined by the method without the need of any experimental information on the shape of the wake. Predicted forces and tip vortex trajectories are shown to agree well with those measured in experiments.

scholarly journals The vortex-entrainment sheet in an inviscid fluid: theory and separation at a sharp edge

2019 ◽  
Vol 866 ◽  
pp. 660-688 ◽  
Author(s):  
A. C. DeVoria ◽  
K. Mohseni
Keyword(s):  
Mass Density ◽  
Normal Component ◽  
Vortex Sheet ◽  
Three Dimensions ◽  
Sharp Edge ◽  
Pressure Jump ◽  
Inviscid Fluid ◽  
Fluid Theory ◽  
Viscous Boundary ◽  
Singularity Removal

In this paper a model for viscous boundary and shear layers in three dimensions is introduced and termed a vortex-entrainment sheet. The vorticity in the layer is accounted for by a conventional vortex sheet. The mass and momentum in the layer are represented by a two-dimensional surface having its own internal tangential flow. Namely, the sheet has a mass density per-unit-area making it dynamically distinct from the surrounding outer fluid and allowing the sheet to support a pressure jump. The mechanism of entrainment is represented by a discontinuity in the normal component of the velocity across the sheet. The velocity field induced by the vortex-entrainment sheet is given by a generalized Birkhoff–Rott equation with a complex sheet strength. The model was applied to the case of separation at a sharp edge. No supplementary Kutta condition in the form of a singularity removal is required as the flow remains bounded through an appropriate balance of normal momentum with the pressure jump across the sheet. A pressure jump at the edge results in the generation of new vorticity. The shedding angle is dictated by the normal impulse of the intrinsic flow inside the bound sheets as they merge to form the free sheet. When there is zero entrainment everywhere the model reduces to the conventional vortex sheet with no mass. Consequently, the pressure jump must be zero and the shedding angle must be tangential so that the sheet simply convects off the wedge face. Lastly, the vortex-entrainment sheet model is demonstrated on several example problems.

scholarly journals Modeling debris-flow runout patterns on two alpine fans with different dynamic simulation models

2015 ◽  
Vol 15 (7) ◽  
pp. 1483-1492 ◽  
Author(s):  
K. Schraml ◽  
B. Thomschitz ◽  
B. W. McArdell ◽  
C. Graf ◽  
R. Kaitna
Keyword(s):  
Numerical Simulation ◽  
Debris Flow ◽  
Mass Movement ◽  
Simulation Models ◽  
Realistic Model ◽  
Three Dimensions ◽  
Model Parameters ◽  
Alpine Regions ◽  
Digital Elevation ◽  
Higher Sensitivity

Abstract. Predicting potential deposition areas of future debris-flow events is important for engineering hazard assessment in alpine regions. To this end, numerical simulation models are commonly used tools. However, knowledge of appropriate model parameters is essential but often not available. In this study we use two numerical simulation models, RAMMS–DF (rapid mass movement system–debris-flow) and DAN3D (dynamic analysis of landslides in three dimensions), to back-calculate two well-documented debris-flow events in Austria and to compare the range and sensitivity of input parameters for the Voellmy flow model. All simulations are based on the same digital elevation models and similar boundary conditions. Our results show that observed deposition patterns are best matched with a parameter set of μ [–] and ξ [m s-2], ranging between 0.07 to 0.11 and 200 to 300 m s-2, respectively, for RAMMS–DF, and between 0.07 to 0.08 and 300 to 400 m s-2, respectively, for DAN3D. Sensitivity analysis shows a higher sensitivity of model parameters for the DAN3D model than for the RAMMS–DF model. This contributes to the evaluation of realistic model parameters for simulation of debris-flows in steep mountain catchments and highlights the sensitivity of the models.

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