Laminar Incompressible Viscous Flow in Curved Ducts of Regular Cross-Sections

1977 ◽  
Vol 99 (4) ◽  
pp. 640-648 ◽  
Author(s):  
K. N. Ghia ◽  
J. S. Sokhey
Keyword(s):  
Cross Sections ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Dean Number ◽  
Navier Stokes Equations ◽  
Flow Parameters ◽  
Incompressible Viscous Flow ◽  
Square Ducts ◽  
Curved Ducts

The laminar three-dimensional flow in curved ducts has been analyzed for an incompressible viscous fluid. The mathematical model is formulated using three-dimensional parabolized Navier-Stokes equations. The equations are generalized using two indices which permit the choice of Cartesian or cylindrical coordinate systems and straight or curved ducts. The solutions are obtained numerically using an ADI method for a number of duct geometries and flow parameters. The study presents detailed results for developing laminar flow in rectangular curved ducts; also, the effect of longitudinal curvature on secondary flow is fully analyzed. An investigation is made of the occurrence of Dean’s instability and, for curved square ducts, it is found to first appear at Dean number ≃ 143.

Numerical Solution of Incompressible Unsteady Flows in Turbomachinery

2000 ◽  
Vol 123 (3) ◽  
pp. 680-685 ◽  
Author(s):  
L. He ◽  
K. Sato
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Time Stepping ◽  
Incompressible Viscous Flow ◽  
Dual Time Stepping

A three-dimensional incompressible viscous flow solver of the thin-layer Navier-Stokes equations was developed for the unsteady turbomachinery flow computations. The solution algorithm for the unsteady flows combines the dual time stepping technique with the artificial compressibility approach for solving the incompressible unsteady flow governing equations. For time accurate calculations, subiterations are introduced by marching the equations in the pseudo-time to fully recover the incompressible continuity equation at each real time step, accelerated with a multi-grid technique. Computations of test cases show satisfactory agreements with corresponding theoretical and experimental results, demonstrating the validity and applicability of the present method to unsteady incompressible turbomachinery flows.

Modeling of Three-Dimensional Flow in Turning Channels

1984 ◽  
Vol 106 (3) ◽  
pp. 682-691 ◽  
Author(s):  
I. M. Khalil ◽  
H. G. Weber
Keyword(s):  
Stokes Equations ◽  
Reverse Flow ◽  
Three Dimensional ◽  
Solution Procedure ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Pressure Gradients ◽  
Dean Number ◽  
Navier Stokes Equations ◽  
Curved Channels

The structure of developing flows inside curved channels has been investigated numerically using the time-averaged Navier Stokes equations in three dimensions. The equations are solved in primitive variables using finite difference techniques. The solution procedure involves a combination of repeated space-marching integration of the governing equations and correction for elliptic effects between two marching sweeps. Type-dependent differencing is used to permit downstream marching even in the reverse-flow regions. The procedure is shown to allow efficient calculations of turbulent flow inside strongly curved channels as well as laminar flow inside a moderately curved passage. Results obtained in both cases indicate that the flow structure is strongly controlled by local imbalance between centrifugal forces and pressure gradients. Furthermore, distortion of primary flow due to migration of low momentum fluid caused by secondary flow is found to be largely dependent on the Reynolds number and Dean number. Comparison with experimental data is also included.

Bifurcation in steady laminar flow through curved tubes

1982 ◽  
Vol 119 ◽  
pp. 475-490 ◽  
Author(s):  
K. Nandakumar ◽  
Jacob H. Masliyah
Keyword(s):  
Stokes Equations ◽  
Outer Wall ◽  
Dual Solutions ◽  
Navier Stokes ◽  
Dean Number ◽  
Navier Stokes Equations ◽  
Vortex Solution ◽  
Duct Geometry ◽  
Flow Through ◽  
Curved Ducts

The occurrence of dual solutions in curved ducts is investigated through a numerical solution of the Navier-Stokes equations in a bipolar-toroidal co-ordinate system. With the shape of duct being the region formed by the natural co-ordinate surfaces, it was possible to alter the duct geometry gradually and preserve the prevailing form of the velocity field, in a manner suggested by Benjamin (1978).In addition to the Dean number Dn = Re/Rc½, a geometrical parameter that defines the shape of the duct was also varied systematically to study the bifurcation of a two-vortex solution into a two- and four-vortex solution. Dual solutions have been found for all geometrical shapes investigated here. Of particular interest are the shapes of a full circle and a semicircle with a curved outer wall.

Study of Fully Developed Incompressible Flow in Curved Ducts, Using a Multi-Grid Technique

1987 ◽  
Vol 109 (3) ◽  
pp. 226-236 ◽  
Author(s):  
K. N. Ghia ◽  
U. Ghia ◽  
C. T. Shin
Keyword(s):  
Cross Sections ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Cross Flow ◽  
Internal Flow ◽  
Navier Stokes ◽  
Dean Number ◽  
Similarity Parameter ◽  
Fine Grid ◽  
Curved Ducts

Fully developed flows inside curved ducts of rectangular as well as polar cross sections have been analyzed using the Navier-Stokes equations in terms of the axial velocity and vorticity and the cross-flow stream function. Numerical solutions of the three second-order coupled elliptic partial differential equations governing this flow have been obtained using efficient numerical schemes. For curved-duct flows, the similarity parameter of significance is the Dean number K, rather than the Reynolds number Re. Results have been obtained for curved ducts with square cross sections for K up to 900 which, in the present study, corresponds to Re = 9,000 for this internal flow configuration. The fine-grid calculations show that, for square cross-section ducts, Dean’s instability occurs at K ≈ 125 and, further, that this phenomenon does not disappear even for K = 900. In ducts of polar cross sections, which are geometrically more representative of turbomachinery cascade passages, the phenomenon of Dean’s instability is not seen to occur for K up to 600.

Analysis of Circumferential Fluctuation in Compressor Cascades

2014 ◽  
Author(s):  
Ke Wan ◽  
Mingzhi Tang ◽  
Donghai Jin ◽  
Xingmin Gui
Keyword(s):  
Stokes Equations ◽  
Incidence Angle ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Parameters ◽  
Camber Angle ◽  
Definition Of ◽  
The Relationship ◽  
Peak Value

This paper presents the relation between circumferential fluctuation and the geometric and flow parameters. The governing equations are derived by circumferentially averaging the three-dimensional (3D) Navier-Stokes equations. Different types of compressor cascades are simulated and the circumferential fluctuation terms are extracted according to the definition of circumferential average. Three different blade profiles are chosen, including CDA, C4 and NACA65 profile, respectively. The peak value of circumferential fluctuation terms often occurs at the leading or the trailing edge and increases as the radius grows. Meanwhile, the circumferential fluctuation terms exist at the inlet of the blade which can be accurately calculated. 0°, 15° and 30° camber angles are chosen to study the influence of camber angle. When the camber angle is smaller, the flow is more uniform and therefore, the value of circumferential fluctuation is lower. Different incidence angles are compared to discuss the relationship between circumferential fluctuation and incidence angle. For specific term of circumferential fluctuations, the distribution curves are different.

Three Dimensional FSI Modelling of Sulcus Vocalis Disorders of Vocal Folds

2018 ◽  
Vol 34 (6) ◽  
pp. 791-800 ◽  
Author(s):  
A. Vazifehdoostsaleh ◽  
N. Fatouraee ◽  
M. Navidbakhsh ◽  
F. Izadi
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Vocal Folds ◽  
Element Model ◽  
Navier Stokes ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
Flow Parameters ◽  
Sulcus Vocalis ◽  
Underlying Mechanisms

AbstractThe effect of sulcus vocalis on vocal folds function is investigated. A type II sulcus vocalis is defined, parameterized and incorporated into a three-dimensional, fully coupled finite element model of vocal folds and laryngeal airway. The proposed Fluid-Structure Interaction (FSI) model is utilized in computational fluid dynamics, Arbitrary Lagrangian-Eulerian (ALE), incompressible continuity and Navier-Stokes equations and in a structure range of a three-layer elastic linear model. Flow parameters, vibration behavior and glottal jet aerodynamics of healthy and patient vocal folds models are compared with each other. Flow visualization is utilized to characterize Coanda effect and three dimensionality of flow patterns. The vibration frequency of vocal folds having sulcus vocalis decreases in comparison with that of healthy ones. Upon increasing the volume flux in the sulcus vocalis model, the non-periodic and disordered behavior of it is visible for patient vocal folds. Underlying mechanisms for the observed changes, possible implications for treatments of sulcus vocalis and human perfect voice production are also discussed.

Internal Three-Dimensional Viscous Flow Solution Using the Streamlike Function

1986 ◽  
Vol 108 (3) ◽  
pp. 348-353 ◽  
Author(s):  
A. Hamed ◽  
S. Abdallah
Keyword(s):  
Viscous Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Viscous Flows ◽  
Navier Stokes ◽  
Streamwise Vorticity ◽  
Elliptic Solution ◽  
Inviscid Flows ◽  
Navier Stokes Equations ◽  
Curved Ducts

This paper presents a new method for the three-dimensional elliptic solution of the Navier–Stokes equations. It is based on the streamlike-function vorticity formulation which was developed by the authors to study the development of secondary velocities and streamwise vorticity for inviscid flows in curved ducts. This formulation is generalized for viscous flows and used to predict the development of internal three dimensional flow fields. The computed results are presented and compared with experimental measurements for the three-dimensional viscous flow in a straight duct.

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.

Mathematical modeling of steady stratified flows

2003 ◽  
Vol 3 ◽  
pp. 195-207
Author(s):  
A.M. Ilyasov ◽  
V.N. Kireev ◽  
S.F. Urmancheev ◽  
I.Sh. Akhatov
Keyword(s):  
Stokes Equations ◽  
Approximate Model ◽  
Immiscible Liquid ◽  
Stratified Flows ◽  
Navier Stokes ◽  
Flat Channel ◽  
Navier Stokes Equations ◽  
Two Fluids ◽  
Flow Parameters ◽  
Direct Numerical Solution

The work is devoted to the analysis of the flow of immiscible liquid in a flat channel and the creation of calculation schemes for determining the flow parameters. A critical analysis of the well-known Two Fluids Model was carried out and a new scheme for the determination of wall and interfacial friction, called the hydraulic approximation in the theory of stratified flows, was proposed. Verification of the proposed approximate model was carried out on the basis of a direct numerical solution of the Navier–Stokes equations for each fluid by a finite-difference method with phase-boundary tracking by the VOF (Volume of Fluid) method. The graphical dependencies illustrating the change in the interfase boundaries of liquids and the averaged over the occupied area of the phase velocities along the flat channel are presented. The results of comparative calculations for two-fluid models are also given, according to the developed model in the hydraulic approximation and direct modeling. It is shown that the calculations in accordance with the hydraulic approximation are more consistent with the simulation results. Thus, the model of hydraulic approximation is the most preferred method for calculating stratified flows, especially in cases of variable volumetric content of liquids.

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