Hydrodynamic Forces on a Pipeline With Uneven Embedment

2012 ◽  
Author(s):  
Hongwei An ◽  
Liang Cheng ◽  
Ming Zhao
Keyword(s):  
Flow Structure ◽  
Oscillatory Flow ◽  
Stokes Equations ◽  
Seepage Flow ◽  
Maximum Error ◽  
Hydrodynamic Forces ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
The Difference ◽  
Two Sides

Hydrodynamic forces on a pipeline with uneven embedment on either side, subject to oscillatory flow, are investigated numerically. Two-dimensional Reynolds-Averaged Navier-Stokes equations with a k-ω turbulent model are solved to simulate the flow in the fluid. It is assumed the seepage flow in the seabed is governed by Darcy’s law and Laplace equation is solved to calculate the pore pressure under the assumption of isotropic and homogenous seabed. The effects of embedment depths and KC numbers on the hydrodynamic force are investigated. The flow structure and pressure distribution around the pipeline are discussed. The inline force and lift exerting on the pipeline are presented in the form of peak values and Fourier coefficients. It is found that flow structures around the pipeline are asymmetric due to the difference of seabed levels on the two sides of the pipeline. The degree of asymmetry increases with the increase of |e1-e2|/D. Obvious difference exists between the hydrodynamic forces experienced by the pipeline in two succeeding halves of a period due to the asymmetric flow structure around the pipeline. The peak values of inline force and lift reduce as e2/D increase for all values of e1 examined in this study. The maximum error of the inline force and lift predicted by using sixth order Fourier series is about 4%.

The inlet flow structure of a conceptual open-nose supersonic drone

2021 ◽  
pp. 095441002098304
Author(s):  
Eiman B Saheby ◽  
Xing Shen ◽  
Anthony P Hays ◽  
Zhang Jun
Keyword(s):  
Flow Structure ◽  
Stokes Equations ◽  
Fluid Dynamic ◽  
Three Dimensional ◽  
Computational Fluid Dynamic Simulation ◽  
Navier Stokes ◽  
Ansys Fluent ◽  
Navier Stokes Equations ◽  
Aerodynamic Efficiency ◽  
Performance Effects

This study describes the aerodynamic efficiency of a forebody–inlet configuration and computational investigation of a drone system, capable of sustainable supersonic cruising at Mach 1.60. Because the whole drone configuration is formed around the induction system and the design is highly interrelated to the flow structure of forebody and inlet efficiency, analysis of this section and understanding its flow pattern is necessary before any progress in design phases. The compression surface is designed analytically using oblique shock patterns, which results in a low drag forebody. To study the concept, two inlet–forebody geometries are considered for Computational Fluid Dynamic simulation using ANSYS Fluent code. The supersonic and subsonic performance, effects of angle of attack, sideslip, and duct geometries on the propulsive efficiency of the concept are studied by solving the three-dimensional Navier–Stokes equations in structured cell domains. Comparing the results with the available data from other sources indicates that the aerodynamic efficiency of the concept is acceptable at supersonic and transonic regimes.

scholarly journals Numerical Investigation on the Water Entry of Several Different Bow-Flared Sections

2020 ◽  
Vol 10 (22) ◽  
pp. 7952
Author(s):  
Qiang Wang ◽  
Boran Zhang ◽  
Pengyao Yu ◽  
Guangzhao Li ◽  
Zhijiang Yuan
Keyword(s):  
Stokes Equations ◽  
Water Entry ◽  
Navier Stokes ◽  
Hydrodynamic Characteristics ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Surface Evolution ◽  
Mesh Method ◽  
The Difference ◽  
Dynamics Method

The bow-flared section may be simplified in the prediction of slamming loads and whipping responses of ships. However, the difference of hydrodynamic characteristics between the water entry of the simplified sections and that of the original section has not been well documented. In this study, the water entry of several different bow-flared sections was numerically investigated using the computational fluid dynamics method based on Reynolds-averaged Navier–Stokes equations. The motion of the grid around the section was realized using the overset mesh method. Reasonable grid size and time step were determined through convergence studies. The application of the numerical method in the water entry of bow-flared sections was validated by comparing the present predictions with previous numerical and experimental results. Through a comparative study on the water entry of one original section and three simplified sections, the influences of simplification of the bow-flared section on hydrodynamic characteristics, free surface evolution, pressure field, and impact force were investigated and are discussed here.

Simulation of Acoustic Streaming in a Resonator

2004 ◽  
Author(s):  
Bakhtier Farouk ◽  
Murat K. Aktas
Keyword(s):  
Flow Field ◽  
Standing Wave ◽  
Oscillatory Flow ◽  
Stokes Equations ◽  
Acoustic Streaming ◽  
Flow Patterns ◽  
Vortical Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Streaming Flow

Formation of vortical flow structures in a rectangular enclosure due to acoustic streaming is investigated numerically. The oscillatory flow field in the enclosure is created by the vibration of a vertical side wall of the enclosure. The frequency of the wall vibration is chosen such that a standing wave forms in the enclosure. The interaction of this standing wave with the horizontal solid walls leads to the production of Rayleigh type acoustic streaming flow patterns in the enclosure. All four walls of the enclosure considered are thermally insulated. The fully compressible form of the Navier-Stokes equations is considered and an explicit time-marching algorithm is used to explicitly track the acoustic waves. Numerical solutions are obtained by employing a highly accurate flux corrected transport (FCT) algorithm for the convection terms. A time-splitting technique is used to couple the viscous and diffusion terms of the full Navier-Stokes equations. Non-uniform grid structure is employed in the computations. The simulation of the primary oscillatory flow and the secondary (steady) streaming flows in the enclosure is performed. Streaming flow patterns are obtained by time averaging the primary oscillatory flow velocity distributions. The effect of the amount of wall displacement on the formation of the oscillatory flow field and the streaming structures are studied. Computations indicate that the nonlinearity of the acoustic field increases with increasing amount of the vibration amplitude. The form and the strength of the secondary flow associated with the oscillatory flow field and viscous effects are found to be strongly correlated to the maximum displacement of the vibrating wall. Total number of acoustic streaming cells per wavelength is also determined by the strength and the level of the nonlinearity of the sound field in the resonator.

Numerical solution of the early stage of the unsteady viscous flow around a circular cylinder: a comparison with experimental visualization and measurements

1985 ◽  
Vol 160 ◽  
pp. 93-117 ◽  
Author(s):  
Ta Phuoc Loc ◽  
R. Bouard
Keyword(s):  
Circular Cylinder ◽  
Flow Structure ◽  
Stokes Equations ◽  
Early Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Grid Systems ◽  
Unsteady Viscous Flow ◽  
Vorticity Transport ◽  
New Phenomena

Early stages of unsteady viscous flows around a circular cylinder at Reynolds numbers of 3 × 103 and 9.5 × 103 are analysed numerically by direct integration of the Navier–Stokes equations – a fourth-order finite-difference scheme is used for the resolution of the stream-function equation and a second-order one for the vorticity-transport equation. Evolution with time of the flow structure is studied in detail. Some new phenomena are revealed and confirmed by experiments.The influence of the grid systems and the downstream boundary conditions on the flow structure and the velocity profiles is reported. The computed results are compared qualitatively and quantitatively with experimental visualization and measurements. The comparison is found to be satisfactory.

Numerical Simulation of the Cooling Process of Cubic Shells

2011 ◽  
Author(s):  
Manabu Okura ◽  
Kiyoaki Ono
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Temperature Fields ◽  
Numerical Code ◽  
Navier Stokes ◽  
Cooling Process ◽  
Air Velocity ◽  
Navier Stokes Equations ◽  
The Difference ◽  
The Heat Transfer Coefficient

In order to keep the environment in an air-conditioned room comfortable, it is important to anticipate the air velocity and temperature fields precisely. The numerical code, solving simultaneously the Navier-Stokes equations governing flow field inside and outside the room and the heat conduction equation applying to walls, are developed. The assumption that the heat transfer coefficient between the fluid and the surface of solids is not used. This code is applied to investigate the cooling process of a cubic shell. The computational results agree with the experimental results. We also investigated the same process of the cubic shells whose walls are internally or externally insulated. The difference of the amount of heat transfer will be discussed.

Numerical Study of Oscillatory Flow Past Four Cylinders in Square Arrangement for Pitch Ratio Equal to 4

2011 ◽  
Author(s):  
P. Anagnostopoulos ◽  
Ch. Dikarou ◽  
S. A. Seitanis
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Central Line ◽  
Circular Cylinders ◽  
Navier Stokes ◽  
Constant Frequency ◽  
Navier Stokes Equations ◽  
Symmetry Of The Solution ◽  
Pitch Ratio ◽  
Two Sides

The results of a numerical study of the viscous oscillating flow around four circular cylinders are presented herein, for a constant frequency parameter, β, equal to 50, and Keulegan-Carpenter numbers, KC, ranging between 0.2 and 10. The cylinders were placed on the vertices of a square, whose two sides were perpendicular and two parallel to the oncoming flow, for a pitch ratio, P/D, equal to 4. The finite-element method was employed for the solution of the Navier-Stokes equations, in the formulation where the stream function and the vorticity are the field variables. The streamlines and the vorticity contours generated from the solution were used for the flow visualization. When the Keulegan-Carpenter number is lower than 4, the flow remains symmetrical with respect to the horizontal axis of symmetry of the solution domain and periodic at consecutive cycles. As KC increases to 4 the flow becomes aperiodic in different cycles, although symmetry with respect to the horizontal central line of the domain is preserved. For KC equal to 5 asymmetries appear intermittently in the flow, which are eventually amplified as KC increases still further. These asymmetries, in association with the aperiodicity at different cycles, lead to an almost chaotic configuration, as KC grows larger. For characteristic cases the flow pattern and the traces of the hydrodynamic forces are presented. In addition, the mean and r.m.s. values of the in-line and transverse forces and the hydrodynamic coefficients of the inline force were evaluated for the entire range of Keulegan-Carpenter numbers examined.

scholarly journals Direct numerical simulation of the oscillatory flow around a sphere resting on a rough bottom

2017 ◽  
Vol 822 ◽  
pp. 235-266 ◽  
Author(s):  
Marco Mazzuoli ◽  
Paolo Blondeaux ◽  
Julian Simeonov ◽  
Joseph Calantoni
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Oscillatory Flow ◽  
Stokes Equations ◽  
Coarse Sand ◽  
Spherical Particles ◽  
Navier Stokes ◽  
Sea Waves ◽  
Spherical Object ◽  
Navier Stokes Equations

The oscillatory flow around a spherical object lying on a rough bottom is investigated by means of direct numerical simulations of the continuity and Navier–Stokes equations. The rough bottom is simulated by a layer/multiple layers of spherical particles, the size of which is much smaller that the size of the object. The period and amplitude of the velocity oscillations of the free stream are chosen to mimic the flow at the bottom of sea waves and the size of the small spherical particles falls in the range of coarse sand/very fine gravel. Even though the computational costs allow only the simulation of moderate values of the Reynolds number characterizing the bottom boundary layer, the results show that the coherent vortex structures, shed by the spherical object, can break up and generate turbulence, if the Reynolds number of the object is sufficiently large. The knowledge of the velocity field allows the dynamics of the large-scale coherent vortices shed by the object to be determined and turbulence characteristics to be evaluated. Moreover, the forces and torques acting on both the large spherical object and the small particles, simulating sediment grains, can be determined and analysed, thus laying the groundwork for the investigation of sediment dynamics and scour developments.

Numerical Simulation Study on the Concentration Field in an Oscillatory Flow Reactor with Conic Ring Baffles

2013 ◽  
Vol 378 ◽  
pp. 418-423
Author(s):  
Gang Liu ◽  
Jia Wu ◽  
Wei Li
Keyword(s):  
Numerical Simulation ◽  
Oscillatory Flow ◽  
Flow Reactor ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Concentration Field ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Turbulent Diffusion Coefficient ◽  
Simulation Results

The three-dimensional construct of concentration field in an oscillatory flow reactor (OFR) containing periodically spaced conic ring baffles was investigated by numerical simulation employing Reynolds-averaged Navier-Stokes equations. The computation covered a range of Oscillatory Reynolds number (Reo) from 623.32 to 3116.58 at Strouhal number (St) 0.995 and 1.99. The contour of concentration field showed that the concentration in the most part of the channel is relative uniform and a small retention area is found below the conic ring baffles, which means a region of relative poor mixing. In addition, the turbulent diffusion coefficient calculated from the simulation results implied the greater oscillatory amplitude and oscillatory frequency superimposed to the fluid, the stronger is the turbulence intensity.

Non-parallel stability of a flat-plate boundary layer using the complete Navier-Stokes equations

1990 ◽  
Vol 221 ◽  
pp. 311-347 ◽  
Author(s):  
H. Fasel ◽  
U. Konzelmann
Keyword(s):  
Boundary Layer ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Plate Boundary ◽  
Detailed Comparison ◽  
Problem Formulation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
The Difference ◽  
Direct Numerical Integration

Non-parallel effects which are due to the growing boundary layer are investigated by direct numerical integration of the complete Navier-Stokes equations for incompressible flows. The problem formulation is spatial, i.e. disturbances may grow or decay in the downstream direction as in the physical experiments. In the past various non-parallel theories were published that differ considerably from each other in both approach and interpretation of the results. In this paper a detailed comparison of the Navier-Stokes calculation with the various non-parallel theories is provided. It is shown, that the good agreement of some of the theories with experiments is fortuitous and that the difference between experiments and theories concerning the branch I neutral location cannot be explained by non-parallel effects.

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