Stochastic Modeling of Flow-Structure Interactions Using Generalized Polynomial Chaos

2001 ◽  
Vol 124 (1) ◽  
pp. 51-59 ◽  
Author(s):  
Dongbin Xiu ◽  
Didier Lucor ◽  
C.-H. Su ◽  
George Em Karniadakis
Keyword(s):  
Flow Structure ◽  
Polynomial Chaos ◽  
Stokes Equations ◽  
Hermite Polynomials ◽  
Weak Form ◽  
Galerkin Projection ◽  
Navier Stokes ◽  
Generalized Polynomial Chaos ◽  
Navier Stokes Equations ◽  
Generalized Polynomial

We present a generalized polynomial chaos algorithm to model the input uncertainty and its propagation in flow-structure interactions. The stochastic input is represented spectrally by employing orthogonal polynomial functionals from the Askey scheme as the trial basis in the random space. A standard Galerkin projection is applied in the random dimension to obtain the equations in the weak form. The resulting system of deterministic equations is then solved with standard methods to obtain the solution for each random mode. This approach is a generalization of the original polynomial chaos expansion, which was first introduced by N. Wiener (1938) and employs the Hermite polynomials (a subset of the Askey scheme) as the basis in random space. The algorithm is first applied to second-order oscillators to demonstrate convergence, and subsequently is coupled to incompressible Navier-Stokes equations. Error bars are obtained, similar to laboratory experiments, for the pressure distribution on the surface of a cylinder subject to vortex-induced vibrations.

Stochastic Modeling of Flow-Structure Interactions using Generalized Polynomial Chaos

2001 ◽  
Author(s):  
Dongbin Xiu ◽  
Didier Lucor ◽  
C. Su ◽  
George E. Karniadakis
Keyword(s):  
Flow Structure ◽  
Stochastic Modeling ◽  
Polynomial Chaos ◽  
Generalized Polynomial Chaos ◽  
Generalized Polynomial

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.

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.

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%.

Flow Structure in the Wake of an Oscillating Cylinder

1989 ◽  
Vol 111 (2) ◽  
pp. 139-148 ◽  
Author(s):  
Y. Lecointe ◽  
J. Piquet
Keyword(s):  
Circular Cylinder ◽  
Numerical Solution ◽  
Flow Structure ◽  
Vortex Shedding ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Oscillating Cylinder ◽  
Navier Stokes Equations ◽  
Uniform Stream

The numerical solution of the unsteady two-dimensional Navier-Stokes equations is used to investigate the vortex-shedding characteristics behind a circular cylinder immersed in a uniform stream and performing superimposed in-line or transversed oscillations of a given reduced amplitude.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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