Numerical Simulation of an Annular Combustor

1993 ◽  
Author(s):  
P. Di Martino ◽  
G. Cinque
Keyword(s):  
Stokes Equations ◽  
Turbulent Transport ◽  
Three Dimensional ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Turbulent Reactive Flows ◽  
Interpolation Technique ◽  
Annular Combustor ◽  
Grid Points

A numerical model to solve three-dimensional turbulent reactive flows in arbitrary shapes is presented. The conservative form of the primitive-variable formulation of steady density-weighted Navier Stokes equations written for a general curvilinear system is adopted. Turbulent transport is described by the k-ε model. The reactions associated with heat release are assumed sufficiently fast for chemical equilibrium to prevail on an instantaneous basis and the influence of local turbulent fluctuations in mixture strenght accounted for by a β-probability density function. The numerical scheme is based on a non-staggered grid (cartesian velocity components and pressure located at the same grid-points) and a special interpolation technique is used to avoid checkerboard oscillations. The present model was used to simulate an annular combustion chamber for which experimental results were available. The agreement between calculation and experiments ranges from fair to good.

A Semi-Staggered Numerical Procedure for the Incompressible Navier-Stokes Equations on Curvilinear Grids

2011 ◽  
Author(s):  
Hessam Babaee ◽  
Sumanta Acharya
Keyword(s):  
Finite Difference ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Second Order ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Benchmark Problems ◽  
Navier Stokes Equations ◽  
Curvilinear Grids

An accurate and efficient finite difference method for solving the three dimensional incompressible Navier-Stokes equations on curvilinear grids is developed. The semi-staggered grid layout has been used in which all three components of velocity are stored on the corner vertices of the cell facilitating a consistent discretization of the momentum equations as the boundaries are approached. Pressure is stored at the cell-center, resulting in the exact satisfaction the discrete continuity. The diffusive terms are discretized using a second-order central finite difference. A third-order biased upwind scheme is used to discretize the convective terms. The momentum equations are integrated in time using a semi-implicit fractional step methodology. The convective and diffusive terms are advanced in time using the second-order Adams-Bashforth method and Crank-Nicolson method respectively. The Pressure-Poisson is discretized in a similar approach to the staggered gird layout and thus leading to the elimination of the spurious pressure eigen-modes. The validity of the method is demonstrated by two standard benchmark problems. The flow in driven cavity is used to show the second-order spatial convergence on an intentionally distorted grid. Finally, the results for flow past a cylinder for several Reynolds numbers in the range of 50–150 are compared with the existing experimental data in the literature.

Segmented Domain Decomposition Multigrid Solutions for Two and Three-Dimensional Viscous Flows

1993 ◽  
Vol 115 (4) ◽  
pp. 608-613
Author(s):  
Kumar Srinivasan ◽  
Stanley G. Rubin
Keyword(s):  
Domain Decomposition ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Flow ◽  
Mass Conservation ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Recirculation ◽  
Flux Vector Splitting

Several viscous incompressible two and three-dimensional flows with strong inviscid interaction and/or axial flow reversal are considered with a segmented domain decomposition multigrid (SDDMG) procedure. Specific examples include the laminar flow recirculation in a trough geometry and in a three-dimensional step channel. For the latter case, there are multiple and three-dimensional recirculation zones. A pressure-based form of flux-vector splitting is applied to the Navier-Stokes equations, which are represented by an implicit, lowest-order reduced Navier-Stokes (RNS) system and a purely diffusive, higher-order, deferred-corrector. A trapezoidal or box-like form of discretization insures that all mass conservation properties are satisfied at interfacial and outflow boundaries, even for this primitive-variable non-staggered grid formulation. The segmented domain strategy is adapted herein for three-dimensional flows and is extended to allow for disjoint subdomains that do not share a common boundary.

A HYBRID FINITE-ANALYTIC ALGORITHM FOR SOLVING THREE-DIMENSIONAL ADVECTION-DIFFUSION EQUATIONS

2004 ◽  
Vol 01 (03) ◽  
pp. 407-430 ◽  
Author(s):  
H. M. HU ◽  
K.-H. WANG
Keyword(s):  
Convergence Rates ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Diffusion Equations ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
The Stability

The hybrid finite-analytic (HFA) method for discretization of a three-dimensional advection-diffusion equation is developed using the superposition of the HFA solutions of locally linearized one-dimensional advection-diffusion equations. An example calculation of a system of three-dimensional nonlinear equations is conducted to test the convergence and accuracy of the 7-point numerical scheme. Good agreements between calculated and analytical solutions are obtained. An algorithm based on the HFA method with multigrid technique and Gauss-Seidel iteration is also developed to solve the three-dimensional Navier-Stokes equations in a staggered grid system. The stability and efficiency of the method are demonstrated by performing calculations of the fluid flow in a three-dimensional cubic cavity with a moving top wall. The proposed procedure is observed to exhibit good rates of smoothing and almost grid-independent convergence rates in comparison with a single-grid iteration method. The results are in excellent agreement with other published computational results.

Steady and Unsteady Three-Dimensional Flows in Confined Configurations With Constant and Variable Inflow Velocity

2012 ◽  
Author(s):  
Araz Panahi ◽  
Dan Mateescu
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Engineering Systems ◽  
Flow Induced Vibration ◽  
Navier Stokes Equations ◽  
Inflow Velocity ◽  
Operation Cycle ◽  
Tridiagonal Systems

This paper presents a three-dimensional analysis of the unsteady confined viscous flows generated by the variations in time of the inflow velocities (fluctuations) which often are present during the operation cycle of various engineering systems, and have to be taken into account in the study of flow-induced vibration and instability of these systems. Time-accurate solutions of the Navier-Stokes equations for these unsteady flows are obtained with a numerical method developed by the authors, which is second-order accurate in space and time and is based on a finite difference formulation on a stretched staggered grid and uses artificial compressibility. A factored alternate direction implicit (ADI) scheme and a special decoupling procedure, based on the utilization of the continuity equation, are used to substantially enhance the computational efficiency of the method by reducing the problem to the solution of scalar tridiagonal systems of equations. This method is applied to obtain solutions for the benchmark unsteady confined flow past a downstream-facing step, generated by the harmonic variations in time of the inflow velocity. The formation of the flow separation regions is thoroughly analyzed in the paper, including the influence on the flow separations of the Reynolds number, and of the oscillation frequency and amplitude of the inflow velocity variations.

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.

scholarly journals A Code for Simulating Heat Transfer in Turbulent Channel Flow

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 756
Author(s):  
Federico Lluesma-Rodríguez ◽  
Francisco Álcantara-Ávila ◽  
María Jezabel Pérez-Quiles ◽  
Sergio Hoyas
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulent Channel Flow ◽  
Passive Scalar ◽  
Direct Numerical Simulations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Thermal Flow ◽  
Navier Stokes Equations

One numerical method was designed to solve the time-dependent, three-dimensional, incompressible Navier–Stokes equations in turbulent thermal channel flows. Its originality lies in the use of several well-known methods to discretize the problem and its parallel nature. Vorticy-Laplacian of velocity formulation has been used, so pressure has been removed from the system. Heat is modeled as a passive scalar. Any other quantity modeled as passive scalar can be very easily studied, including several of them at the same time. These methods have been successfully used for extensive direct numerical simulations of passive thermal flow for several boundary conditions.

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