Vibrations of Circular Cylindrical Shells With Nonuniform Constraints, Elastic Bed and Added Mass Coupled to Internal, External and Annular Flow

2002 ◽  
Author(s):  
M. Amabili ◽  
R. Garziera
Keyword(s):  
Annular Flow ◽  
Stokes Equations ◽  
Computer Code ◽  
Inviscid Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Viscous Forces ◽  
Added Masses ◽  
Circular Cylindrical Shells ◽  
Lumped Masses

The effect of steady viscous forces on vibrations of shell with internal and annular flow has been considered by using the time-mean Navier-Stokes equations. The model developed by Amabili & Garziera (2000), capable of simulating shells with non-uniform boundary conditions, added masses and partial elastic bed, has been extended to include non-uniform prestress. The effect of steady viscous forces has been added to the inviscid flow formulation considered by Amabili & Garziera (2002). The computer code DIVA has been developed by using the model developed in the present study. It has been validated by comparison with available results for shells with uniform constraints and has been used to study shells with non-uniform constraints and added lumped masses.

Dynamic and Stability Response of a Cylindrical Shell Subjected to Viscous Annular Flow and Thermal Load

2016 ◽  
Vol 16 (10) ◽  
pp. 1550072 ◽  
Author(s):  
W.-B. Ning ◽  
D.-Z. Wang
Keyword(s):  
Cylindrical Shell ◽  
Thermal Load ◽  
Annular Flow ◽  
Stokes Equations ◽  
Contour Method ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Critical Flow Velocity ◽  
Fluid Forces ◽  
Viscous Forces

This paper presents an analytical approach for investigating the dynamics and stability of an outer cylindrical shell conveying viscous fluid (i.e. water) in the annulus between the inner shell-type body and the outer shell with thermal load. The steady viscous forces that induce prestress on the shells are determined based on the time–mean Navier–Stokes equations. The shell motions are described by Flügge’s shell equations incorporating the prestress arising from the viscous effect. The shell-vibration-induced fluid forces are described by means of the potential flow theory, and the thermal loads are determined by the thermoelastic theory. The analytical model is conducted by the zero-level contour method with the aid of the weighted residual technology. The present study shows that the effect of viscosity in the annular flow renders the system more unstable. Moreover, the thermal load tends to reduce the critical flow velocity pronouncedly, for which there exists a critical temperature rise.

On the Dynamics and Stability of Cylindrical Shells Conveying Inviscid or Viscous Fluid in Internal or Annular Flow

1991 ◽  
Vol 113 (3) ◽  
pp. 409-417 ◽  
Author(s):  
A. El Chebair ◽  
A. K. Misra
Keyword(s):  
Annular Flow ◽  
Stokes Equations ◽  
Dynamical Behavior ◽  
Internal Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Fluid Forces ◽  
Viscous Forces ◽  
The Fourier Transform ◽  
The Stability

This paper investigates theoretically for the first time the dynamical behavior and stability of a simply supported shell located coaxially in a rigid cylindrical conduit. The fluid flow is incompressible and the fluid forces consist of two parts: (i) steady viscous forces which represent the effects of upstream pressurization of the flow; (ii) unsteady forces which could be inviscid or viscous. The inviscid forces were derived by linearized potential flow theory, while the viscous ones were derived by means of the Navier-Stokes equations. Shell motion is described by the modified Flu¨gge’s shell equations. The Fourier transform technique is employed to formulate the problem. First, the system is subjected only to the unsteady inviscid forces. It is found that increasing either the internal or the annular flow velocity induces buckling, followed by coupled mode flutter. When both steady viscous and unsteady inviscid forces are applied, for internal flow, the system becomes stabilized; while for annular flow, the system loses stability at much lower velocities. Second, the system is only subjected to the unsteady viscous forces. Calculations are only performed for the internal flow case. The results are compared to those of inviscid theory. It is found that the effects of unsteady viscous forces on the stability of the system are very close to those of unsteady inviscid forces.

scholarly journals Application of Through-Flow Calculation to Design and Performance Prediction of Centrifugal Compressor

1999 ◽  
Vol 5 (1) ◽  
pp. 17-33 ◽  
Author(s):  
Y. S. Choi ◽  
S. H. Kang
Keyword(s):  
Centrifugal Compressor ◽  
Performance Prediction ◽  
Stokes Equations ◽  
Control Volume ◽  
Computer Code ◽  
Secondary Flows ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Simpler Algorithm ◽  
And Performance

A computer code predicting the flows through the centrifugal compressor with the radial vaneless diffuser was developed and applied to investigate the detailed flowfields, i.e., secondary flows and jet-wake type flow pattern in design and off-design conditions. Various parameters such as slip factors, aerodynamic blockages, entropy generation and two-zone modeling which are widely used in design and performance prediction, were discussed.A control volume method based on a general curvilinear coordinate system was used to solve the time-averaged Navier–Stokes equations and SIMPLER algorithm was used to solve the pressure linked continuity equation. The standardk-εturbulence model was used to obtain the eddy viscosity. Performance of the code was verified using the measured data for the Eckardt impeller.

Modeling coherent structures in the atmosphere and assessing their impact on aircraft

2021 ◽  
Author(s):  
V.V. Vyshinsky ◽  
K.T. Zoan
Keyword(s):  
Stokes Equations ◽  
Grid Method ◽  
Computer Code ◽  
Light Transport ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Large Structures ◽  
Glide Path ◽  
Coherent Vortex ◽  
Coherent Vortex Structure

The paper introduces an engineering method for assessing the aerodynamic effect of disturbed atmosphere on an aircraft. As a source of vortex structures, we can consider vortex wind wakes that arise when the atmospheric wind flows around the landscape, large structures, moving or stationary aircraft-carrying platforms, vortex wakes behind aircraft, etc. In this study, we consider the situation when a light transport aircraft and an aircraft of the MC-21 type get into the vortex wake behind the super-heavy aircraft A-380 when flying along the glide path. A coherent vortex structure behind the A-380 is formed by the grid method within the framework of the boundary value problem for the Reynolds-averaged Navier —Stokes equations. The evolution and stochastics of the far wake are carried out using the author’s computer code written in the MATLAB system, within the framework of discrete vortices with a Rankine core. The assessment of the increment of forces and moments from the effect of the vortex system on the aircraft was carried out using the panel method.

Magnetic field effects on the slip velocity and temperature jump of nanofluid forced convection in a microchannel

2015 ◽  
Vol 230 (11) ◽  
pp. 1921-1936 ◽  
Author(s):  
Arash Karimipour ◽  
Masoud Afrand
Keyword(s):  
Magnetic Field ◽  
Forced Convection ◽  
Slip Velocity ◽  
Temperature Jump ◽  
Stokes Equations ◽  
Volume Fraction ◽  
Computer Code ◽  
Navier Stokes ◽  
Magnetic Field Effects ◽  
Navier Stokes Equations

Forced convection of water–Cu nanofluid in a two-dimensional microchannel is studied numerically. The microchannel wall is divided into three parts. The entry and exit ones are kept insulated while the middle one has more temperature than the inlet fluid. The whole of microchannel is under the influence of a magnetic field with uniform strength of B0. Slip velocity and temperature jump are involved along the microchannel walls for different values of slip coefficient such as B = 0.001, B = 0.01, and B = 0.1 for Re = 10, Re = 50, and Re = 100. Navier–Stokes equations are discretized and numerically solved by a developed computer code in FORTRAN. Results are presented as the velocity, temperature, and Nusselt number profiles. Moreover, the effect of magnetic field on slip velocity and temperature jump is investigated for the first time in the present work. Larger Hartmann number, Reynolds number, and volume fraction correspond to more heat transfer rate; however, the effects of Ha and ϕ are more significant at higher Re.

Some numerical experiments on developing laminar flow in circular-sectioned bends

1985 ◽  
Vol 154 ◽  
pp. 357-375 ◽  
Author(s):  
J. A. C. Humphrey ◽  
H. Iacovides ◽  
B. E. Launder
Keyword(s):  
Shear Stress ◽  
Laminar Flow ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Inviscid Flow ◽  
Streamwise Velocity ◽  
Navier Stokes ◽  
Dean Number ◽  
Navier Stokes Equations ◽  
Numerical Predictions

The paper reports numerical solutions to a semi-elliptic truncation of the Navier–Stokes equations for the case of developing laminar flow in circular-sectioned bends over a range of Dean numbers. The ratios of bend radius to pipe radius are 7:1 and 20:1, corresponding with the configurations examined experimentally by Talbot and his co-workers in recent years. The semi-elliptic treatment facilitates a much finer grid than has been possible in earlier studies. Numerical accuracy has been further improved by assuming radial equilibrium over a thin sublayer immediately adjacent to the wall and by re-formulating the boundary conditions at the pipe centre.Streamwise velocity profiles at Dean numbers of 183 and 565 are in excellent agreement with laser-Doppler measurements by Agrawal, Talbot & Gong (1978). Good, albeit less complete, accord is found with the secondary velocities, though the differences that exist may be mainly due to the difficulty of making these measurements. The paper provides new information on the behaviour of the streamwise shear stress around the inner line of symmetry. Upstream of the point of minimum shear stress, our numerical predictions display a progressive shift towards the result of Stewartson, Cebici & Chang (1980) as the Dean number is successively raised. Downstream of the minimum, however, in contrast with the monotonic approach to an asymptotic level reported by Stewartson, the numerical solutions display a damped oscillatory behaviour reminiscent of those from Hawthorne's (1951) inviscid-flow calculations. The amplitude of the oscillation grows as the Dean number is raised.

Two-Fluid Flow Between Rotating Annular Disks

1976 ◽  
Vol 98 (2) ◽  
pp. 214-222 ◽  
Author(s):  
J. E. Zweig ◽  
H. J. Sneck
Keyword(s):  
Annular Flow ◽  
Stokes Equations ◽  
Fluid Flows ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Two Fluids ◽  
Small Clearance ◽  
Annular Disks ◽  
Two Fluid

The general hydrodynamic behavior at small clearance Reynolds numbers of two fluids of different density and viscosity occupying the finite annular space between a rotating and stationary disk is explored using a simplified version of the Navier-Stokes equations which retains only the centrifugal force portion of the inertia terms. A criterion for selecting the annular flow fields that are compatible with physical reservoirs is established and then used to determine the conditions under which two-fluid flows in the annulus might be expected for specific fluid combinations.

Simulations of the formation of an axisymmetric vortex ring

1997 ◽  
Vol 339 ◽  
pp. 199-211 ◽  
Author(s):  
R. S. HEEG ◽  
N. RILEY
Keyword(s):  
Vortex Ring ◽  
Reasonable Agreement ◽  
Stokes Equations ◽  
Circular Tube ◽  
Inviscid Flow ◽  
High Rate ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Axisymmetric Vortex ◽  
High Reynolds

In this paper we present the results from numerical calculations, based upon the Navier–Stokes equations at relatively high Reynolds number, of the formation of a vortex ring when fluid is ejected from a circular tube. Our results are compared with the experiments of Didden (1979), and the inviscid flow calculations of Nitsche & Krasny (1994). Reasonable agreement is achieved except for the rate of shedding of circulation during the initial stages of ring formation. The theoretically predicted rate of shedding is substantially higher than that predicted by Didden. By contrast the inviscid theory predicts an anomalously high rate of initial shedding. We offer explanations for both of these apparent discrepancies.

Viscous oscillatory flow about a circular cylinder at small to moderate Strouhal number

1995 ◽  
Vol 303 ◽  
pp. 215-232 ◽  
Author(s):  
H. M. Badr ◽  
S. C. R. Dennis ◽  
S. Kocabiyik ◽  
P. Nguyen
Keyword(s):  
Circular Cylinder ◽  
Strouhal Number ◽  
Transient Flow ◽  
Stokes Equations ◽  
Inviscid Flow ◽  
Navier Stokes ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Method Of Solution ◽  
High Reynolds

The transient flow field caused by an infinitely long circular cylinder placed in an unbounded viscous fluid oscillating in a direction normal to the cylinder axis, which is at rest, is considered. The flow is assumed to be started suddenly from rest and to remain symmetrical about the direction of motion. The method of solution is based on an accurate procedure for integrating the unsteady Navier–Stokes equations numerically. The numerical method has been carried out for large values of time for both moderate and high Reynolds numbers. The effects of the Reynolds number and of the Strouhal number on the laminar symmetric wake evolution are studied and compared with previous numerical and experimental results. The time variation of the drag coefficients is also presented and compared with an inviscid flow solution for the same problem. The comparison between viscous and inviscid flow results shows a better agreement for higher values of Reynolds and a Strouhal numbers. The mean flow for large times is calculated and is found to be in good agreement with previous predictions based on boundary-layer theory.

Dynamic simulation of a coated microbubble in an unbounded flow: response to a step change in pressure

2017 ◽  
Vol 822 ◽  
pp. 717-761 ◽  
Author(s):  
M. Vlachomitrou ◽  
N. Pelekasis
Keyword(s):  
Stokes Equations ◽  
Step Change ◽  
Basis Functions ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Viscous Forces ◽  
Compressive Stresses ◽  
Post Buckling ◽  
Flow Domain

A numerical method is developed to study the dynamic behaviour of an encapsulated bubble when the viscous forces of the surrounding liquid are accounted for. The continuity and Navier–Stokes equations are solved for the liquid, whereas the coating is described as a viscoelastic shell with bending resistance. The Galerkin Finite Element Methodology is employed for the spatial discretization of the flow domain surrounding the bubble, with the standard staggered grid arrangement that uses biquadratic and bilinear Lagrangian basis functions for the velocity and pressure in the liquid, respectively, coupled with a superparametric scheme with $B$-cubic splines as basis functions pertaining to the location of the interface. The spine method and the elliptic mesh generation technique are used for updating the mesh points in the interior of the flow domain as the shape of the interface evolves with time, with the latter being distinctly superior in capturing severely distorted shapes. The stabilizing effect of the liquid viscosity is demonstrated, as it alters the amplitude of the disturbance for which a bubble deforms and/or collapses. For a step change in the far-field pressure the dynamic evolution of the microbubble is captured until a static equilibrium is achieved. Static shapes that are significantly compressed are captured in the post-buckling regime, leading to symmetric or asymmetric shapes, depending on the relative dilatation to bending stiffness ratio. As the external overpressure increases, shapes corresponding to all the solution families that were captured evolve to exhibit contact as the two poles approach each other. Shell viscosity prevents jet formation by relaxing compressive stresses and bending moments around the indentation generated at the poles due to shell buckling. This behaviour is conjectured to be the inception process leading to static shapes with contact regions.

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