Galerkin Boundary Elements for a Computation of the Surface Tractions in Exterior Stokes Flows

2014 ◽  
Vol 136 (11) ◽  
Author(s):  
Jorge D'Elía ◽  
Laura Battaglia ◽  
Alberto Cardona ◽  
Mario Storti ◽  
Gustavo Ríos Rodríguez
Keyword(s):  
Body Force ◽  
Three Dimensional ◽  
Boundary Integral ◽  
The Body ◽  
Creeping Flow ◽  
Viscous Drag ◽  
Singular Behavior ◽  
Fredholm Type ◽  
Total Body ◽  
Weighting Procedures

In the computation of a three–dimensional steady creeping flow around a rigid body, the total body force and torque are well predicted using a boundary integral equation (BIE) with a single concentrated pair Stokeslet- Rotlet located at an interior point of the body. However, the distribution of surface tractions are seldom considered. Then, a completed indirect velocity BIE of Fredholm type and second-kind is employed for the computation of the pointwise tractions, and it is numerically solved by using either collocation or Galerkin weighting procedures over flat triangles. In the Galerkin case, a full numerical quadrature is proposed in order to handle the weak singularity of the tensor kernels, which is an extension for fluid engineering of a general framework (Taylor, 2003, “Accurate and Efficient Numerical Integration of Weakly Singulars Integrals in Galerkin EFIE Solutions,” IEEE Trans. on Antennas and Propag., 51(7), pp. 1630–1637). Several numerical simulations of steady creeping flow around closed bodies are presented, where results compare well with semianalytical and finite-element solutions, showing the ability of the method for obtaining the viscous drag and capturing the singular behavior of the surface tractions close to edges and corners. Also, deliberately intricate geometries are considered.

Numerical simulations of nonlinear axisymmetric flows with a free surface

1987 ◽  
Vol 178 ◽  
pp. 195-219 ◽  
Author(s):  
Douglas G. Dommermuth ◽  
Dick K. P. Yue
Keyword(s):  
Free Surface ◽  
Numerical Simulations ◽  
Three Dimensional ◽  
Vertical Cylinder ◽  
Free Surface Flows ◽  
Boundary Integral ◽  
The Body ◽  
Special Treatment ◽  
Computational Domain ◽  
Vortex Sheets

A numerical method is developed for nonlinear three-dimensional but axisymmetric free-surface problems using a mixed Eulerian-Lagrangian scheme under the assumption of potential flow. Taking advantage of axisymmetry, Rankine ring sources are used in a Green's theorem boundary-integral formulation to solve the field equation; and the free surface is then updated in time following Lagrangian points. A special treatment of the free surface and body intersection points is generalized to this case which avoids the difficulties associated with the singularity there. To allow for long-time simulations, the nonlinear computational domain is matched to a transient linear wavefield outside. When the matching boundary is placed at a suitable distance (depending on wave amplitude), numerical simulations can, in principle, be continued indefinitely in time. Based on a simple stability argument, a regriding algorithm similar to that of Fink & Soh (1974) for vortex sheets is generalized to free-surface flows, which removes the instabilities experienced by earlier investigators and eliminates the need for artificial smoothing. The resulting scheme is very robust and stable.For illustration, three computational examples are presented: (i) the growth and collapse of a vapour cavity near the free surface; (ii) the heaving of a floating vertical cylinder starting from rest; and (iii) the heaving of an inverted vertical cone. For the cavity problem, there is excellent agreement with available experiments. For the wave-body interaction calculations, we are able to obtain and analyse steady-state (limit-cycle) results for the force and flow field in the vicinity of the body.

Study of a Three-Dimensional Crack Terminating at an Interface

1986 ◽  
Vol 53 (2) ◽  
pp. 311-316 ◽  
Author(s):  
J. C. Lee ◽  
L. M. Keer
Keyword(s):  
Body Force ◽  
Crack Opening ◽  
Three Dimensional ◽  
Circular Crack ◽  
The Body ◽  
Solution Technique ◽  
Bimaterial Interface ◽  
Opening Displacement ◽  
Body Force Method ◽  
Method Of Solution

In this study the stress intensity factors for a three-dimensional crack perpendicular to and terminating at a bimaterial interface are calculated. It is assumed that the crack is pressurized by a uniform pressure. The method of solution used here is based upon the body-force method and requires the analytical results from the elasticity point-force solution for a bimaterial interface. The solution technique leads to the reduction of the problem to a two-dimensional singular integral equation, which can be solved numerically for the crack opening displacement. Numerical examples of a semi-circular, semi-elliptical crack and growth of circular crack are given.

scholarly journals TO THE THEORY OF n-DIMENSIONAL BRACHISTOCHRONE

2020 ◽  
pp. 53-60
Author(s):  
Gladkov S.O. ◽  
◽  
Bogdanova S.B. ◽  
Keyword(s):  
Three Dimensional ◽  
Plane Curve ◽  
Viscous Friction ◽  
Analytical Description ◽  
The Body ◽  
Viscous Drag ◽  
Friction Forces ◽  
Drag Forces ◽  
Moving Body ◽  
Plane Shape

In this paper, a solution to the problem of the motion of a brachistochrone in the ndimensional Euclidean space is firstly presented. The very first formulation of the problem in a two-dimensional case was proposed by J. Bernoulli in 1696. It represented an analytical description of the trajectory for the fastest rolling down under gravitational force only. Thereafter, a number of problems devoted to a brachistochrone were considered with account for gravitational forces, dry and viscous drag forces, and a possible variation in the mass of a moving body. Analytical solution to the formulated problem is presented in details by an example of the body moving along a brachistochrone in three-dimensional Cartesian coordinates. The obtained parametric solution is confirmed by a graphical interpretation of the calculated result. The formulated problem is solved for an ideal case when drag forces are neglected. If dry and viscous friction forces are taken into account, the plane shape of the brachistochrone remains the same,while the analysis of the solution becomes more complicated. When, for example, a side air flow is taken into account, the plane curve is replaced by a three-dimensional brachistochrone.

A Method of Stall and Surge Prediction in Axial Compressors Based On Three-Dimensional Body-Force Model

2021 ◽  
Author(s):  
Hanxuan Zeng ◽  
Xinqian Zheng ◽  
Mehdi Vahdati
Keyword(s):  
Body Force ◽  
Reverse Flow ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Rotating Stall ◽  
The Body ◽  
Force Model ◽  
Computational Domain ◽  
Forward Flow ◽  
Axial Compressors

Abstract The occurrence of stall and surge in axial compressors has a great impact on the performance and reliability of aero-engines. Accurate and efficient prediction of the key features during these events has long been the focus of engine design processes. In this paper, a new body-force model that can capture the three-dimensional and unsteady features of stall and surge in compressors at a fraction of time required for URANS computations is proposed. To predict the rotating stall characteristics, the deviation of local airflow angle from the blade surface is calculated locally during the simulation. According to this local deviation, the computational domain is divided into stalled and forward flow regions, and the body-force field is updated accordingly; to predict the surge characteristics, the local airflow direction is used to divide the computational domain into reverse flow regions and forward flow regions. A single-stage axial compressor and a three-stage axial compressor are used to verify the proposed model. The results show that the method is capable of capturing stall and surge characteristics correctly. Compared to the traditional fully three-dimensional URANS method (fRANS), the simulation time for multi-stage axial compressors is reduced by 1 to 2 orders of magnitude.

scholarly journals Cavity dynamics in water entry at low Froude numbers

2009 ◽  
Vol 641 ◽  
pp. 441-461 ◽  
Author(s):  
HONGMEI YAN ◽  
YUMING LIU ◽  
JAKUB KOMINIARCZUK ◽  
DICK K. P. YUE
Keyword(s):  
Free Surface ◽  
Asymptotic Theory ◽  
Numerical Study ◽  
Three Dimensional ◽  
Maximum Size ◽  
Water Entry ◽  
Boundary Integral ◽  
The Body ◽  
Gravitational Acceleration ◽  
Slender Body Theory

The dynamics of the air cavity created by vertical water entry of a three-dimensional body is investigated theoretically, computationally and experimentally. The study is focused in the range of relatively low Froude numbers, Fr ≡ V(gD)−1/2 ≤ O(10) (where V is the dropping velocity of the body, D its characteristic dimension and g the gravitational acceleration), when the inertia and gravity effects are comparable. To understand the physical processes involved in the evolution of cavity, we conduct laboratory experiments of water entry of freely dropping spheres. A matched asymptotic theory for the description of the cavity dynamics is developed based on the slender-body theory in the context of potential flow. Direct comparisons with experimental data show that the asymptotic theory properly captures the key physical effects involved in the development of the cavity, and in particular gives a reasonable prediction of the maximum size of the cavity and the time of cavity closure. Due to the inherent assumption in the asymptotic theory, it is incapable of accurately predicting the flow details near the free surface and the body, where nonlinear free surface and body boundary effects are important. To complement the asymptotic theory, a fully nonlinear numerical study using an axisymmetric boundary integral equation is performed. The numerically obtained dependencies of the cavity height and closure time on Froude number and body geometry are in excellent agreement with available experiments.

Deterministic and Stochastic Prediction of the Hydrodynamics of a Three-Dimensional Body Falling Through Water

2008 ◽  
Author(s):  
Xuemei Zhu ◽  
Yuming Liu
Keyword(s):  
Deterministic Model ◽  
Three Dimensional ◽  
Field Measurements ◽  
The Body ◽  
Statistical Prediction ◽  
Viscous Drag ◽  
Physical Parameters ◽  
Practical Applications ◽  
Characteristic Features ◽  
Six Degree Of Freedom

We investigate the dynamics of a three-dimensional mine-shaped body falling through water deterministically and stochastically. A physics-based deterministic model, MINE6D, is developed for the prediction of the six degree-of-freedom motion of the body falling freely through water. In MINE6D, the hydrodynamic load due to the added inertia effect is obtained exactly by using a boundary-element method while the viscous drag associated with flow separation and vortex shedding is modeled using a quasi-steady approach. Since the mine motion is found to be highly sensitive to varying the physical parameters such as body geometry, mass distribution, and initial releasing conditions, we develop a stochastic model using Monte-Carlo MINE6D simulation for the statistical analysis of mine motions in practical applications. The statistical prediction is compared with available field measurements both qualitatively and quantitatively. The characteristic features and dependence on physical parameters of the statistical prediction of mine motions are investigated. The present study is of importance to the prediction of mine burial in seabed and the design of mines.

scholarly journals Long-time asymptotic expansions for Navier-Stokes equations with power-decaying forces

2019 ◽  
Vol 150 (2) ◽  
pp. 569-606 ◽  
Author(s):  
Dat Cao ◽  
Luan Hoang
Keyword(s):  
Asymptotic Expansion ◽  
Body Force ◽  
Stokes Equations ◽  
Three Dimensional ◽  
The Body ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Gevrey Space ◽  
Long Time ◽  
The Individual

AbstractThe Navier-Stokes equations for viscous, incompressible fluids are studied in the three-dimensional periodic domains, with the body force having an asymptotic expansion, when time goes to infinity, in terms of power-decaying functions in a Sobolev-Gevrey space. Any Leray-Hopf weak solution is proved to have an asymptotic expansion of the same type in the same space, which is uniquely determined by the force, and independent of the individual solutions. In case the expansion is convergent, we show that the next asymptotic approximation for the solution must be an exponential decay. Furthermore, the convergence of the expansion and the range of its coefficients, as the force varies are investigated.

scholarly journals Attenuation of cross-flow instability in three-dimensional boundary layer by means of multi-discharge actuator system

2019 ◽  
Vol 488 (2) ◽  
pp. 147-152
Author(s):  
S. A. Baranov ◽  
M. D. Gamirullin ◽  
A. Ph. Kiselev ◽  
A. P. Kuryachii ◽  
D. S. Sboev ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Body Force ◽  
Flow Instability ◽  
Three Dimensional ◽  
Cross Flow ◽  
The Body ◽  
Subsonic Wind Tunnel ◽  
Significant Area ◽  
Dimensional Boundary ◽  
Force Impact

Results of experiments in low-turbulence subsonic wind tunnel sustaining the possibility of significant attenuation of the cross-flow velocity and the intensity of stationary instability vortices due to the body force impact on three-dimensional boundary layer are presented. The unidirectional body force over a significant area of the streamlined surface has been created with the help of dielectric barrier discharge actuator.

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