Application of a Navier–Stokes Analysis to Flows Through Plane Cascades

1986 ◽  
Vol 108 (1) ◽  
pp. 103-111 ◽  
Author(s):  
O. Scha¨fer ◽  
H.-H. Fru¨hauf ◽  
B. Bauer ◽  
M. Guggolz
Keyword(s):  
Thin Layer ◽  
Stokes Equations ◽  
Density Ratio ◽  
Separated Flows ◽  
Stability And Convergence ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Fully Implicit ◽  
First Results ◽  
Viscous Solutions

A newly developed method is used to compute a variety of laminar/turbulent, attached/separated flows through plane turbine or compressor cascades. The thin-layer or full Navier–Stokes equations are solved in a 2-D or quasi-2-D/quasi-3-D form taking into account variable axial velocity density ratio/cascade aspect ratio. The turbulence is modeled by the Baldwin–Lomax algebraic two-layer eddy viscosity approach. Improved mesh generation and discretization techniques are introduced. A fully implicit formulation of the flow problem is developed which ensures high stability and convergence. Numerous quantitative comparisons of viscous solutions with experiments and other existing solutions are performed to validate the method. First results on the applicability of the thin-layer assumption are included.

NUMERICAL SIMULATION OF ISOTHERMAL AND THERMAL TWO-PHASE FLOWS USING PHASE-FIELD MODELING

2007 ◽  
Vol 18 (04) ◽  
pp. 536-545 ◽  
Author(s):  
NAOKI TAKADA ◽  
AKIO TOMIYAMA
Keyword(s):  
Phase Field ◽  
Stokes Equations ◽  
Density Ratio ◽  
Navier Stokes ◽  
Phase Field Modeling ◽  
Two Phase Flows ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Field Modeling ◽  
High Density Ratio

For interface-tracking simulation of two-phase flows in various micro-fluidics devices, we examined the applicability of two versions of computational fluid dynamics method, NS-PFM, combining Navier-Stokes equations with phase-field modeling for interface based on the van der Waals-Cahn-Hilliard free-energy theory. Through the numerical simulations, the following major findings were obtained: (1) The first version of NS-PFM gives good predictions of interfacial shapes and motions in an incompressible, isothermal two-phase fluid with high density ratio on solid surface with heterogeneous wettability. (2) The second version successfully captures liquid-vapor motions with heat and mass transfer across interfaces in phase change of a non-ideal fluid around the critical point.

Studies on Aerodynamic Characteristics of Dump Diffusers for Modern Aircraft Engines

2012 ◽  
Vol 232 ◽  
pp. 246-251 ◽  
Author(s):  
P. Sathyan ◽  
S. Srikanth ◽  
I. Dheepan ◽  
M. Arun ◽  
C. Aswin ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Dynamic ◽  
Aerodynamic Characteristics ◽  
Navier Stokes ◽  
Finite Volume Scheme ◽  
Aircraft Engines ◽  
Navier Stokes Equations ◽  
Dynamic Constraints ◽  
Fully Implicit

The geometrical optimization of dump diffusers are extremely demanding as the flow fields and stress fields are very complex and must be well understood to achieve the required design efficiencies. In this paper parametric analytical studies have been carried out for examining the aerodynamics characteristics of different dump diffusers for modern aircraft engines. Numerical studies have been carried out using SST K- ω turbulence model. This code solves SST k- ω turbulence equations using the coupled second order implicit unsteady formulation. In the numerical study, a fully implicit finite volume scheme of the compressible, Reynolds-Averaged, Navier-Stokes equations is employed. We concluded that in addition to the dump gap ratio, the aerodynamic shape of the flame tube case and the other geometric variables are also need to be optimized judiciously after considering the fluid dynamic constraints for controlling the pressure recovery and the losses.

scholarly journals A novel difference schemes for analyzing the fractional Navier-Stokes equations

2017 ◽  
Vol 25 (1) ◽  
pp. 195-206
Author(s):  
Khosro Sayevand ◽  
Dumitru Baleanu ◽  
Fatemeh Sahsavand
Keyword(s):  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Discrete Analogue ◽  
Stability And Convergence ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Suggested Approach ◽  
Stokes Problems ◽  
Picard Theorem ◽  
Dimensional Domain

Abstract In this report, a novel difference scheme is used to analyzing the Navier - Stokes problems of fractional order. Existence and uniqueness of the suggested approach with a Lipschitz condition and Picard theorem are proved. Furthermore, we find a discrete analogue of the derivative and then stability and convergence of our strategy in multi dimensional domain are proved.

scholarly journals Dynamics of a contracting fluid compound filament with a variable density ratio

2021 ◽  
Vol 24 (2) ◽  
pp. first
Author(s):  
Truong V. Vu ◽  
Vinh T. Nguyen ◽  
Phan H. Nguyen ◽  
Nang X. Ho ◽  
Binh D. Pham ◽  
...  
Keyword(s):  
Interfacial Tension ◽  
Stokes Equations ◽  
Weighting Function ◽  
Density Ratio ◽  
Variable Density ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Front Tracking Method ◽  
Fixed Grid ◽  
Eulerian Grid

Introduction: Compound fluid filaments appear in many applications, e.g., drug delivery and processing or microfluidic systems. This paper focuses on the numerical simulation of an incompressible, immiscible, and Newtonian fluid for the contraction process of a fluid compound filament by solving the Navier-Stokes equations. The front-tracking method is used to solve this problem, which uses connected segments (Lagrangian grid) that move on a fixed grid (Eulerian grid) to represent the interface between the liquids. Methods: The interface points are advected by the velocity interpolated from those of the fixed grid using the area weighting function. The coordinates of the interface points are used to construct the indicators specifying the different fluids and compute the interfacial tension force. Results: The simulation results show that under the effects of the interfacial tension, the capsuleshaped filament can transform into a spherical compound droplet (i.e., non-breakup) or can break up into smaller spherical compound and simple droplets (i.e., breakup). When the density ratio of the outer to middle fluids increases, the filament changes from non-breakup to breakup upon contraction. Conclusion: Increasing the density ratio enhances the breakup of the compound filament during contraction. The breakup is also promoted by increasing the initial length of the filament.

Film Cooling of Compound Angle Upstream Sister Holes

2019 ◽  
Author(s):  
Sana Abd Alsalam ◽  
Bassam Jubran
Keyword(s):  
Film Cooling ◽  
Turbulence Modeling ◽  
Stokes Equations ◽  
Density Ratio ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Cooling Performance ◽  
Film Cooling Effectiveness ◽  
Simple Strategy ◽  
Compound Angle

Abstract This study introduces a novel and simple strategy; compound angle upstream sister holes (CAUSH) to increase film cooling performance of the cylindrical hole by combining two techniques: Sister holes; (two small round holes placed upstream the primary hole) and compound angle hole. Whereas the upstream sister holes were injected at several compound angles β = 0°, 45°, 75°, and 90°, while the main hole was injected to the streamwise direction at 35° on a flat plate. FLUENT-ANSYS code was used to perform the simulation by solving the 3D Reynolds Averaged Navier-Stokes Equations. The capability of three types of k-ε turbulence modeling combined with the enhanced wall treatment is investigated to predict the film cooling performance of sister holes. A detailed computational analysis of the cooling performance of the (CAUSH) and the flow field was done at a density ratio equal to two (D.R = 2) and four blowing ratios M = 0.25, 0.5, 1.0 and 1.5 to predict the centerline and laterally averaged film cooling performance. The centerline effectiveness results showed that the highest cooling performance from the examined (CAUSH) was obtained at β = 0°, 45°, and 90° for low and high blowing ratio, the highest laterally averaged film cooling performance was captured at β = 0° and 90° for all tested blowing ratios. Also, the results indicated that the upstream sister hole with 90° compound angle holes has the best overall film cooling effectiveness while the worst performance is attained at β = 75°.

scholarly journals Numerical Investigation of Water Entry of Half Hydrophilic and Half Hydrophobic Spheres

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Sun Zhao ◽  
Cao Wei ◽  
Wang Cong
Keyword(s):  
Stokes Equations ◽  
Density Ratio ◽  
Surface Force ◽  
Simulation Method ◽  
Numerical Approach ◽  
Water Entry ◽  
Numerical Results ◽  
Navier Stokes ◽  
Force Coefficient ◽  
Navier Stokes Equations

A numerical simulation to investigate the water entry of half-half sphere which is hydrophobic on one hemisphere and hydrophilic on the other is performed. Particular attention is given to the simulation method based on solving the Navier-Stokes equations coupled with VOF (volume of fluid) method and CSF (continuum surface force) method. Numerical results predicted experimental results, validating the suitability of the numerical approach to simulate the water entry problem of sphere under different wetting conditions. Numerical results show that the water entry of the half-half sphere creates an asymmetric cavity and “cardioid” splash, causing the sphere to travel laterally from the hydrophobic side to the hydrophilic side. Further investigations show that the density ratio and mismatch of asymmetric in wetting condition affect the trajectory, velocity, and acceleration of the half-half sphere during water entry. In addition, the total hydrodynamic force coefficient is investigated as a result of the forces acting on the sphere during water entry dictated by the cavity formation.

Three-Dimensional Time-Marching Inviscid and Viscous Solutions for Unsteady Flows Around Vibrating Blades

1994 ◽  
Vol 116 (3) ◽  
pp. 469-476 ◽  
Author(s):  
L. He ◽  
J. D. Denton
Keyword(s):  
Thin Layer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Correction Method ◽  
Navier Stokes ◽  
Finite Volume Scheme ◽  
Time Step ◽  
Blade Passage ◽  
Time Marching ◽  
Viscous Solutions

A three-dimensional nonlinear time-marching method of solving the thin-layer Navier–Stokes equations in a simplified form has been developed for blade flutter calculations. The discretization of the equations is made using the cell-vertex finite volume scheme in space and the four-stage Runge–Kutta scheme in time. Calculations are carried out in a single-blade-passage domain and the phase-shifted periodic condition is implemented by using the shape correction method. The three-dimensional unsteady Euler solution is obtained at conditions of zero viscosity, and is validated against a well-established three-dimensional semi-analytical method. For viscous solutions, the time-step limitation on the explicit temporal discretization scheme is effectively relaxed by using a time-consistent two-grid time-marching technique. A transonic rotor blade passage flow (with tip-leakage) is calculated using the present three-dimensional unsteady viscous solution method. Calculated steady flow results agree well with the corresponding experiment and with other calculations. Calculated unsteady loadings due to oscillations of the rotor blades reveal some notable three-dimensional viscous flow features. The feasibility of solving the simplified thin-layer Navier–Stokes solver for oscillating blade flows at practical conditions is demonstrated.

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