scholarly journals The Sensitivity Analysis for the Flow Past Obstacles Problem with Respect to the Reynolds Number

2012 ◽  
Vol 4 (1) ◽  
pp. 21-35 ◽  
Author(s):  
Kazufumi Ito ◽  
Zhilin Li ◽  
Zhonghua Qiao
Keyword(s):  
Sensitivity Analysis ◽  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Irregular Domains ◽  
Time Step ◽  
Immersed Interface Method ◽  
Navier Stokes Equations ◽  
Flow Past

AbstractIn this paper, numerical sensitivity analysis with respect to the Reynolds number for the flow past obstacle problem is presented. To carry out such analysis, at each time step, we need to solve the incompressible Navier-Stokes equations on irregular domains twice, one for the primary variables; the other is for the sensitivity variables with homogeneous boundary conditions. The Navier-Stokes solver is the augmented immersed interface method for Navier-Stokes equations on irregular domains. One of the most important contribution of this paper is that our analysis can predict the critical Reynolds number at which the vortex shading begins to develop in the wake of the obstacle. Some interesting experiments are shown to illustrate how the critical Reynolds number varies with different geometric settings.

Unsteady flow past a rotating circular cylinder at Reynolds numbers 103 and 104

1990 ◽  
Vol 220 ◽  
pp. 459-484 ◽  
Author(s):  
H. M. Badr ◽  
M. Coutanceau ◽  
S. C. R. Dennis ◽  
C. Ménard
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Unsteady Flow ◽  
Rotation Rate ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Number Range ◽  
Flow Past

The unsteady flow past a circular cylinder which starts translating and rotating impulsively from rest in a viscous fluid is investigated both theoretically and experimentally in the Reynolds number range 103 [les ] R [les ] 104 and for rotational to translational surface speed ratios between 0.5 and 3. The theoretical study is based on numerical solutions of the two-dimensional unsteady Navier–Stokes equations while the experimental investigation is based on visualization of the flow using very fine suspended particles. The object of the study is to examine the effect of increase of rotation on the flow structure. There is excellent agreement between the numerical and experimental results for all speed ratios considered, except in the case of the highest rotation rate. Here three-dimensional effects become more pronounced in the experiments and the laminar flow breaks down, while the calculated flow starts to approach a steady state. For lower rotation rates a periodic structure of vortex evolution and shedding develops in the calculations which is repeated exactly as time advances. Another feature of the calculations is the discrepancy in the lift and drag forces at high Reynolds numbers resulting from solving the boundary-layer limit of the equations of motion rather than the full Navier–Stokes equations. Typical results are given for selected values of the Reynolds number and rotation rate.

HIGH-ORDER CURVILINEAR SIMULATIONS OF FLOWS AROUND NON-CARTESIAN BODIES

2005 ◽  
Vol 13 (04) ◽  
pp. 731-748 ◽  
Author(s):  
OLIVIER MARSDEN ◽  
CHRISTOPHE BOGEY ◽  
CHRISTOPHE BAILLY
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Stokes Equations ◽  
Acoustic Scattering ◽  
High Order ◽  
Navier Stokes ◽  
Numerical Techniques ◽  
Navier Stokes Equations ◽  
Flow Around A Cylinder ◽  
Naca 0012

The current work describes the application of high-order numerical techniques to single or multiple overset curvilinear body-fitted grids, demonstrating the feasibility of direct computations of noise radiated by flows around complex non-Cartesian bodies. Flows of both physical and industrial interest can be investigated with this approach. We first rapidly describe the numerical techniques implemented in our curvilinear simulations. The explicit high-order differencing and filtering schemes are presented, as well as their application to the curvilinear Navier–Stokes equations. We then present brief results of various 2-D acoustic simulations. First the flow around a cylinder, and the associated acoustic field, are described. The diameter-based Reynolds number Re D = 150 is under the critical Reynolds number of the onset of 3-D phenomena in the vortex-shedding. Simulation results can thus be meaningfully compared to experimental measurements. A case of acoustic scattering is then examined. A non-compact monopolar source is placed half way between two differently sized cylinders. A complex diffraction pattern is created, and resulting RMS pressure data are compared to the analytical solution. Finally the noise generated by a low Reynolds number laminar flow around a NACA 0012 airfoil is presented.

scholarly journals An immersed interface method for the Navier-Stokes equations on irregular domains

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 1025401-1025402
Author(s):  
Zhilin Li ◽  
Ming-Chih Lai ◽  
Kazufumi Ito
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Irregular Domains ◽  
Immersed Interface Method ◽  
Immersed Interface ◽  
Navier Stokes Equations

scholarly journals Using a non-conforming meshes method to simulate an interaction be-tween incompressible flow and rigid and elastic boundaries

Mechanika ◽  
2019 ◽  
Vol 25 (4) ◽  
pp. 276-282
Author(s):  
Anas Abid Mattie ◽  
Asad Alizadeh
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Shape Change ◽  
Medical Engineering ◽  
Navier Stokes ◽  
Immersed Interface Method ◽  
Navier Stokes Equations ◽  
Bending Modulus ◽  
Elastic Boundary ◽  
Conforming Meshes

The interaction between incompressible fluids and elastic and rigid boundaries is seen in many medical, engineering and natural issues. The immersed interface method is used as a non-conforming meshes method to simulate such problems. In this method, the effect of the presence of a body immersed in a fluid is considered by adding a force term to the Navier-Stokes equations. An important advantage of this method is that there is no compulsion to adapt the fluid grids and the boundary grids. First, the flow around a circular cylinder was simulated. As the Reynolds number rises, the vortex dimensions become larger and, as a result, the separation angle of the flow increases. Also, with the Reynolds number increasing, the drag coefficient decreases and the Strouhal number increases and the flow separated from cylinder and two symmetrical vortices is generated behind the cylinder. Then, the behavior of an elastic boundary in shear flow was investigated. It was observed that by increasing bending modulus (increasing stiffness) of body the shape change of the boundary decreases. As well as the tank-treading motion is also observed that this type of movement has been confirmed in experiments.Also observed that the sick cell makes smaller defor-mation, while the normal cell is more deformed and easier passes  the stenosis. This results in reduction of the flow rate in stenosis.This behavior is caused by a type of dis-ease called sickle cell anemia.

Sensitivity analysis for Navier-Stokes equations on unstructured meshes using complex variables

AIAA Journal ◽  
2001 ◽  
Vol 39 ◽  
pp. 56-63
Author(s):  
W. Kyle Anderson ◽  
James C. Newman ◽  
David L. Whitfield ◽  
Eric J. Nielsen
Keyword(s):  
Sensitivity Analysis ◽  
Stokes Equations ◽  
Unstructured Meshes ◽  
Complex Variables ◽  
Navier Stokes ◽  
Navier Stokes Equations

A note on the solution of the Navier-Stokes equations for a spherically symmetric expansion into a very low pressure

1973 ◽  
Vol 59 (2) ◽  
pp. 391-396 ◽  
Author(s):  
N. C. Freeman ◽  
S. Kumar
Keyword(s):  
Shock Wave ◽  
Reynolds Number ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Low Pressure ◽  
Navier Stokes ◽  
Spherically Symmetric ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Type Flow

It is shown that, for a spherically symmetric expansion of a gas into a low pressure, the shock wave with area change region discussed earlier (Freeman & Kumar 1972) can be further divided into two parts. For the Navier–Stokes equation, these are a region in which the asymptotic zero-pressure behaviour predicted by Ladyzhenskii is achieved followed further downstream by a transition to subsonic-type flow. The distance of this final region downstream is of order (pressure)−2/3 × (Reynolds number)−1/3.

A finite element method for the Navier-Stokes equations in moving domain with application to hemodynamics of the left ventricle

2017 ◽  
Vol 32 (4) ◽  
Author(s):  
Alexander Danilov ◽  
Alexander Lozovskiy ◽  
Maxim Olshanskii ◽  
Yuri Vassilevski
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Left Ventricle ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Computed Tomography Images ◽  
Time Dependent Domain ◽  
Element Method

AbstractThe paper introduces a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method is based on a quasi-Lagrangian formulation of the problem and handling the geometry in a time-explicit way. We prove that numerical solution satisfies a discrete analogue of the fundamental energy estimate. This stability estimate does not require a CFL time-step restriction. The method is further applied to simulation of a flow in a model of the left ventricle of a human heart, where the ventricle wall dynamics is reconstructed from a sequence of contrast enhanced Computed Tomography images.

NUMERICAL SOLUTIONS OF 2D AND 3D SLAMMING PROBLEMS

2021 ◽  
Vol 153 (A2) ◽  
Author(s):  
Q Yang ◽  
W Qiu
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Type Equation ◽  
The Body ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Highly Nonlinear ◽  
2D And 3D

Slamming forces on 2D and 3D bodies have been computed based on a CIP method. The highly nonlinear water entry problem governed by the Navier-Stokes equations was solved by a CIP based finite difference method on a fixed Cartesian grid. In the computation, a compact upwind scheme was employed for the advection calculations and a pressure-based algorithm was applied to treat the multiple phases. The free surface and the body boundaries were captured using density functions. For the pressure calculation, a Poisson-type equation was solved at each time step by the conjugate gradient iterative method. Validation studies were carried out for 2D wedges with various deadrise angles ranging from 0 to 60 degrees at constant vertical velocity. In the cases of wedges with small deadrise angles, the compressibility of air between the bottom of the wedge and the free surface was modelled. Studies were also extended to 3D bodies, such as a sphere, a cylinder and a catamaran, entering calm water. Computed pressures, free surface elevations and hydrodynamic forces were compared with experimental data and the numerical solutions by other methods.

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