scholarly journals Viscous Analysis of Three-Dimensional Turbomachinery Flows on Body Conforming Grids Using an Implicit Solver

1991 ◽  
Author(s):  
K. F. Weber ◽  
R. A. Delaney
Keyword(s):  
Coordinate System ◽  
Stokes Equations ◽  
Three Dimensional ◽  
The Body ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Turbulence Effects ◽  
Implicit Solver ◽  
Cartesian Coordinate ◽  
Solution Accuracy

A 3-D Navier-Stokes analysis for turbomachinery flows on C- or O-type grids is presented. The analysis is based on the Beam and Warming implicit algorithm for solution of the unsteady Navier-Stokes equations and is derived from an early version of the ARC3D flow code developed at NASA Ames Research Center. The Navier-Stokes equations are written in a Cartesian coordinate system rotating about the z-axis, and then mapped to a general body-fitted coordinate system. All viscous terms are calculated and the turbulence effects are modelled using the Baldwin-Lomax turbulence model. The equations are discretized using finite differences on stacked body-conforming grids. Modifications made to convert ARC3D from external flow to internal turbomachinery flows and to improve solution accuracy are given in detail. The body-conforming grid construction procedure is also presented. Calculations for several rotor flows have been made, and results of code experimental verification studies are presented. Comparisons of the solutions obtained on the C- and O-type grids are also presented, with particular attention to shock resolution.

A Quasi-Generalized-Coordinate Approach for Numerical Simulation of Complex Flows

2006 ◽  
Vol 128 (6) ◽  
pp. 1394-1399 ◽  
Author(s):  
Donghyun You ◽  
Meng Wang ◽  
Rajat Mittal ◽  
Parviz Moin
Keyword(s):  
Coordinate System ◽  
Stokes Equations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Cost Effective ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Curvilinear Coordinate ◽  
Generalized Coordinate

A novel structured grid approach which provides an efficient way of treating a class of complex geometries is proposed. The incompressible Navier-Stokes equations are formulated in a two-dimensional, generalized curvilinear coordinate system complemented by a third quasi-curvilinear coordinate. By keeping all two-dimensional planes defined by constant third coordinate values parallel to one another, the proposed approach significantly reduces the memory requirement in fully three-dimensional geometries, and makes the computation more cost effective. The formulation can be easily adapted to an existing flow solver based on a two-dimensional generalized coordinate system coupled with a Cartesian third direction, with only a small increase in computational cost. The feasibility and efficiency of the present method have been assessed in a simulation of flow over a tapered cylinder.

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.

Numerical and Experimental Study on Oblique Collision of Water Droplet With a Solid Substrate

2005 ◽  
Author(s):  
Hitoshi Fujimoto ◽  
Yu Shiotani ◽  
Albert Y. Tong ◽  
Hirohiko Takuda
Keyword(s):  
Liquid Surface ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Solid Substrate ◽  
Free Liquid Surface ◽  
Numerical Results ◽  
Navier Stokes ◽  
Oblique Collision ◽  
Navier Stokes Equations ◽  
Cartesian Coordinate

This study is concerned with the collision behavior of water droplets impacting onto a solid. Three-dimensional computer simulations are performed to understand the physics of phenomena. The Navier-Stokes equations for unsteady, incompressible, viscous fluid in a three-dimensional Cartesian coordinate system are approximated and solved by a finite difference method. The VOF (Volume-of-Fluid) technique is used to track free liquid surface. The effects of liquid viscosity, surface tension, gravity, and wettability between liquid and solid are taken into account. Normal and oblique collisions of droplets with the substrate are simulated at relatively low impact inertia of droplets. Experiments are also carried out in order to validate the numerical results. The numerical results agree reasonably well with experiments. The physics of phenomena is discussed in detail from theoretical aspects.

scholarly journals An Accurate Cartesian Method for Incompressible Flows with Moving Boundaries

2014 ◽  
Vol 15 (5) ◽  
pp. 1266-1290 ◽  
Author(s):  
M. Bergmann ◽  
J. Hovnanian ◽  
A. Iollo
Keyword(s):  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Viscous Flows ◽  
The Body ◽  
Navier Stokes ◽  
Ghost Cell ◽  
Order Accuracy ◽  
Navier Stokes Equations ◽  
Moving Body

AbstractAn accurate cartesian method is devised to simulate incompressible viscous flows past an arbitrary moving body. The Navier-Stokes equations are spatially discretized onto a fixed Cartesian mesh. The body is taken into account via the ghost-cell method and the so-called penalty method, resulting in second-order accuracy in velocity. The accuracy and the efficiency of the solver are tested through two-dimensional reference simulations. To show the versatility of this scheme we simulate a three-dimensional self propelled jellyfish prototype.

scholarly journals On a Modified Form of Navier-Stokes Equations for Three-Dimensional Flows

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
J. Venetis
Keyword(s):  
Stokes Equations ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Vector Form ◽  
Navier Stokes Equations ◽  
First Order ◽  
Modified Equations ◽  
Cartesian Coordinate ◽  
Fundamental Equations

A rephrased form of Navier-Stokes equations is performed for incompressible, three-dimensional, unsteady flows according to Eulerian formalism for the fluid motion. In particular, we propose a geometrical method for the elimination of the nonlinear terms of these fundamental equations, which are expressed in true vector form, and finally arrive at an equivalent system of three semilinear first order PDEs, which hold for a three-dimensional rectangular Cartesian coordinate system. Next, we present the related variational formulation of these modified equations as well as a general type of weak solutions which mainly concern Sobolev spaces.

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.

scholarly journals Dynamics of Single Droplet Splashing on Liquid Film by Coupling FVM with VOF

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 841
Author(s):  
Yuzhen Jin ◽  
Huang Zhou ◽  
Linhang Zhu ◽  
Zeqing Li
Keyword(s):  
Liquid Film ◽  
Weber Number ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Single Droplet ◽  
Navier Stokes Equations ◽  
Volume Method ◽  
The Relationship

A three-dimensional numerical study of a single droplet splashing vertically on a liquid film is presented. The numerical method is based on the finite volume method (FVM) of Navier–Stokes equations coupled with the volume of fluid (VOF) method, and the adaptive local mesh refinement technology is adopted. It enables the liquid–gas interface to be tracked more accurately, and to be less computationally expensive. The relationship between the diameter of the free rim, the height of the crown with different numbers of collision Weber, and the thickness of the liquid film is explored. The results indicate that the crown height increases as the Weber number increases, and the diameter of the crown rim is inversely proportional to the collision Weber number. It can also be concluded that the dimensionless height of the crown decreases with the increase in the thickness of the dimensionless liquid film, which has little effect on the diameter of the crown rim during its growth.

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.

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