Numerical study of a transitional synthetic jet in quiescent external flow

2007 ◽  
Vol 581 ◽  
pp. 287-321 ◽  
Author(s):  
RUPESH B. KOTAPATI ◽  
RAJAT MITTAL ◽  
LOUIS N. CATTAFESTA III
Keyword(s):  
Numerical Study ◽  
Time Integration ◽  
Three Dimensional ◽  
Internal Flow ◽  
External Flow ◽  
Second Order ◽  
Synthetic Jet ◽  
Transition To Turbulence ◽  
Step Method ◽  
Fractional Step Method

The flow associated with a synthetic jet transitioning to turbulence in an otherwise quiescent external flow is examined using time-accurate three-dimensional numerical simulations. The incompressible Navier–Stokes solver uses a second-order accurate scheme for spatial discretization and a second-order semi-implicit fractional step method for time integration. The simulations are designed to model the experiments of C. S. Yao et al. (Proc. NASA LaRC Workshop, 2004) which have examined, in detail, the external evolution of a transitional synthetic jet in quiescent flow. Although the jet Reynolds and Stokes numbers in the simulations match with the experiment, a number of simplifications have been made in the synthetic jet actuator model adopted in the current simulations. These include a simpler representation of the cavity and slot geometry and diaphragm placement. Despite this, a reasonably good match with the experiments is obtained in the core of the jet and this indicates that for these jets, matching of these key non-dimensional parameters is sufficient to capture the critical features of the external jet flow. The computed results are analysed further to gain insight into the dynamics of the external as well as internal flow. The results indicate that near the jet exit plane, the flow field is dominated by the formation of counter-rotating spanwise vortex pairs that break down owing to the rapid growth of spanwise instabilities and transition to turbulence a short distance from the slot. Detailed analyses of the unsteady characteristics of the flow inside the jet cavity and slot provide insights that to date have not been available from experiments.

Simulations of Complex Flows and Fluid-Structure Interaction Problems on Fixed Cartesian Grids

2003 ◽  
Author(s):  
Fady M. Najjar ◽  
Rajat Mittal
Keyword(s):  
Krylov Subspace ◽  
Time Integration ◽  
Three Dimensional ◽  
Synthetic Jet ◽  
Complex Flows ◽  
Step Method ◽  
Fractional Step Method ◽  
Central Difference ◽  
Pressure Poisson Equation ◽  
Structured Grid

A finite-difference based approach for computing flows with complex moving solid three-dimensional boundaries on fixed Cartesian grid has been developed. Internal solid boundaries are represented by “blocking off” the grid cells inside the boundary. This results in considerably increased computing efficiency over conventional body-conformal structured grid methods. A mixed explicit-implicit fractional step method is employed for time integration while the spatial discretization scheme is based on a second-order accurate central-difference scheme. The pressure Poisson equation is solved using algebraic multigrid as well as Krylov subspace based methods. The current simulation methodology is validated by simulating various canonical flows. Further, we compute the flow generated by a moving body as well as the flow generated by a synthetic jet in order to demonstrate the capabilities of this solver.

Second order accurate particle-based formulations

2016 ◽  
Vol 26 (3/4) ◽  
pp. 897-915 ◽  
Author(s):  
Masao Shimada ◽  
David Tae ◽  
Tao Xue ◽  
Rohit Deokar ◽  
K K Tamma
Keyword(s):  
Time Integration ◽  
Second Order ◽  
Particle Simulation ◽  
Step Method ◽  
Fractional Step Method ◽  
Content Type ◽  
Explicit Formulation ◽  
Mps Method ◽  
Algorithmic Framework ◽  
Time Accuracy

Purpose – The purpose of this paper is to present new implementation aspects of unified explicit time integration algorithms, called the explicit GS4-II family of algorithms, of a second-order time accuracy in all the unknowns (e.g. positions, velocities, and accelerations) with particular attention to the moving-particle simulation (MPS) method for solving the incompressible fluids with free surfaces. Design/methodology/approach – In the present paper, the explicit GS4-II family of algorithms is implemented in the MPS method in the following two different approaches: a direct explicit formulation with the use of the weak incompressibility equation involving the (modified) speed of sound; and a predictor-corrector explicit formulation. The first approach basically follows the concept of the explicit MPS method, presented in the literature, and the latter approach employs a similar concept used in, for example, a fractional-step method in computational fluid dynamics. Findings – Illustrative numerical examples demonstrate that any scheme within the proposed algorithmic framework captures the physics with the necessary second-order time accuracy and stability. Originality/value – The new algorithmic framework extended with the GS4-II family encompasses a multitude of pastand new schemes and offers a general purpose and unified implementation.

A Numerical Study on the Structure of Tip Clearance Flow in a Highly Forward-Swept Axial-Flow Fan

2002 ◽  
Author(s):  
Gong Hee Lee ◽  
Je Hyun Baek
Keyword(s):  
Numerical Study ◽  
Three Dimensional ◽  
Axial Flow ◽  
Streamwise Velocity ◽  
Tip Clearance ◽  
Wake Flow ◽  
Axial Flow Fan ◽  
Step Method ◽  
Fractional Step Method ◽  
Tip Clearance Flow

A three-dimensional Navier-Stokes analysis was performed to investigate the tip clearance flows in a highly forward-swept axial flow fan operating at design condition. The numerical solution was based on a fractional step method, and two-layer k-ε model was used to obtain the eddy viscosity. The tip leakage vortex decayed very quickly inside the blade passage and, thus, no distinct leakage vortex appeared behind trailing edge. The main reason was the severe decrease of the streamwise velocity of the vortex. Also the interaction of the vortex with the casing boundary layer and the through-flow were other possibilities of the fast decay of the vortex. Comparison between the numerical results and LDV measurements data indicated that the complex viscous flow patterns inside the tip region as well as the wake flow could be properly predicted, but more refinement in numerical aspects are needed.

A Numerical Study of Swirling Buoyant Laminar Jets at Low Reynolds Numbers

2009 ◽  
Author(s):  
Gordon N. Taub ◽  
Hyungoo Lee ◽  
S. Balachandar ◽  
S. A. Sherif
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Reynolds Numbers ◽  
Second Order ◽  
Step Method ◽  
Fractional Step Method ◽  
Central Difference ◽  
Buoyant Jets ◽  
Low Reynolds Numbers ◽  
Low Reynolds

The effect of swirl on laminar buoyant jets with low Reynolds numbers is explored. Three dimensional direct numerical simulations are performed to solve the time-dependent, incompressible Navier-Stokes equations. We use a body fitted grid system and employ the finite volume method to discretize the governing equations. A second-order central difference scheme is employed for all spatial derivative terms. The numerical simulation is advanced in time by a fractional step method with the second-order Adams-Bashforth scheme for explicit-convection terms and the Crank-Nicholson scheme for implicit-diffusion terms. The amount of swirl and buoyancy is varied from zero to very large values and the effect on the velocity field, jet width, entrainment and vortex are examined. Comparisons with analytical and experimental models are discussed.

Numerical study of multi-dimensional hyperbolic telegraph equations arising in nuclear material science via an efficient local meshless method

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Imtiaz Ahmad ◽  
Aly R. Seadawy ◽  
Hijaz Ahmad ◽  
Phatiphat Thounthong ◽  
Fuzhang Wang
Keyword(s):  
Meshless Method ◽  
Material Science ◽  
Numerical Study ◽  
Research Work ◽  
Time Integration ◽  
Three Dimensional ◽  
Nuclear Material ◽  
Telegraph Equations ◽  
Model Equations ◽  
Derivatives Of

Abstract This research work is to study the numerical solution of three-dimensional second-order hyperbolic telegraph equations using an efficient local meshless method based on radial basis function (RBF). The model equations are used in nuclear material science and in the modeling of vibrations of structures. The explicit time integration technique is utilized to semi-discretize the model in the time direction whereas the space derivatives of the model are discretized by the proposed local meshless procedure based on multiquadric RBF. Numerical experiments are performed with the proposed numerical scheme for rectangular and non-rectangular computational domains. The proposed method solutions are converging quickly in comparison with the different existing numerical methods in the recent literature.

Numerical Study of Density-Currents Using the Non-Staggered Grid Fractional-Step-Method

2000 ◽  
Author(s):  
J. Rafael Pacheco ◽  
Arturo Pacheco-Vega ◽  
Sigfrido Pacheco-Vega
Keyword(s):  
Numerical Study ◽  
Density Variation ◽  
Staggered Grid ◽  
Mapping Technique ◽  
Fractional Step ◽  
Density Currents ◽  
Step Method ◽  
Fractional Step Method ◽  
New Approach ◽  
Flow Equations

Abstract A new approach for the solution of time-dependent calculations of buoyancy driven currents is presented. This method employs the idea that density variation can be pursued by using markers distributed in the flow field. The analysis based on the finite difference technique with the non-staggered grid fractional step method is used to solve the flow equations written in terms of primitive variables. The physical domain is transformed to a rectangle by means of a numerical mapping technique. The problems analyzed include two-fluid flow in a tank with sloping bottom and colliding density currents. The numerical experiments performed show that this approach is efficient and robust.

scholarly journals Shear Wave Splitting and Polarization in Anisotropic Fluid-Infiltrating Porous Media: A Numerical Study

Materials ◽  
2020 ◽  
Vol 13 (21) ◽  
pp. 4988
Author(s):  
Nico De Marchi ◽  
WaiChing Sun ◽  
Valentina Salomoni
Keyword(s):  
Porous Media ◽  
Shear Wave ◽  
Numerical Study ◽  
Time Integration ◽  
Three Dimensional ◽  
Mixed Finite Elements ◽  
Shear Wave Splitting ◽  
Anisotropic Fluid ◽  
Structural Anisotropy ◽  
Wave Splitting

The triggering and spreading of volumetric waves in soils, namely pressure (P) and shear (S) waves, developing from a point source of a dynamic load, are analyzed. Wave polarization and shear wave splitting are innovatively reproduced via a three-dimensional Finite Element research code upgraded to account for fast dynamic regimes in fully saturated porous media. The mathematical–numerical model adopts a u-v-p formulation enhanced by introducing Taylor–Hood mixed finite elements and the stability features of the solution are considered by analyzing different implemented time integration strategies. Particularly, the phenomena have been studied and reconstructed by numerically generating different types of medium anisotropy accounting for (i) an anisotropic solid skeleton, (ii) an anisotropic permeability tensor, and (iii) a Biot’s effective stress coefficient tensor. Additionally, deviatoric-volumetric coupling effects have been emphasized by specifically modifying the structural anisotropy. A series of analyses are conducted to validate the model and prove the effectiveness of the results, from the directionality of polarized vibrations, the anisotropy-induced splitting, up to the spreading of surface waves.

scholarly journals Numerical Study of the Internal Flow Field of a Centrifugal Impeller

1994 ◽  
Author(s):  
Mou-jin Zhang ◽  
Chuan-gang Gu ◽  
Yong-miao Miao
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Simple Algorithm ◽  
Internal Flow ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Centrifugal Impeller ◽  
High Reynolds

The complex three-dimensional flow field in a centrifugal impeller with low speed is studied in this paper. Coupled with high–Reynolds–number k–ε turbulence model, the fully three–dimensional Reynolds averaged Navier–Stokes equations are solved. The Semi–Implicit Method for Pressure–Linked Equations (SIMPLE) algorithm is used. And the non–staggered grid arrangement is also used. The computed results are compared with the available experimental data. The comparison shows good agreement.

Fluid Flow and Lateral Fluid Dispersion in Bounded Granular Beds

2002 ◽  
Author(s):  
Azita Soleymani ◽  
Eveliina Takasuo ◽  
Piroz Zamankhan ◽  
William Polashenski
Keyword(s):  
Reynolds Number ◽  
Porous Media ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Numerical Results ◽  
Transition To Turbulence ◽  
Wide Range

Results are presented from a numerical study examining the flow of a viscous, incompressible fluid through random packing of nonoverlapping spheres at moderate Reynolds numbers (based on pore permeability and interstitial fluid velocity), spanning a wide range of flow conditions for porous media. By using a laminar model including inertial terms and assuming rough walls, numerical solutions of the Navier-Stokes equations in three-dimensional porous packed beds resulted in dimensionless pressure drops in excellent agreement with those reported in a previous study (Fand et al., 1987). This observation suggests that no transition to turbulence could occur in the range of Reynolds number studied. For flows in the Forchheimer regime, numerical results are presented of the lateral dispersivity of solute continuously injected into a three-dimensional bounded granular bed at moderate Peclet numbers. Lateral fluid dispersion coefficients are calculated by comparing the concentration profiles obtained from numerical and analytical methods. Comparing the present numerical results with data available in the literature, no evidence has been found to support the speculations by others for a transition from laminar to turbulent regimes in porous media at a critical Reynolds number.

Multi-Dimensional Two-Phase Flow Modeling Applied to Interior Ballistics

2011 ◽  
Vol 78 (5) ◽  
Author(s):  
Julien Nussbaum ◽  
Philippe Helluy ◽  
Jean-Marc Herard ◽  
Barbara Baschung
Keyword(s):  
Three Dimensional ◽  
Hyperbolic Model ◽  
Finite Volume Scheme ◽  
Step Method ◽  
Fractional Step Method ◽  
Two Phase ◽  
Decomposition Reactions ◽  
Solid Decomposition ◽  
The One ◽  
Complex Phenomena

Complex phenomena occur in a combustion chamber during a ballistic cycle. From the ignition of the black powder in the primer to the exit of the projectile through the muzzle, two-phase gas-powder mix undertakes various transfers in different forms. A detailed comprehension of these effects is fundamental to predict the behavior of the whole system, considering performances and safety. Although the ignition of the powder bed is three-dimensional due to the primer’s geometry, simulations generally only deal with one- or two-dimensional problem. In this study, we propose a method to simulate the two-phase flows in 1, 2 or 3 dimensions with the same system of partial differential equations. A one-pressure, conditionally hyperbolic model [1] was used and solved by a nonconservative finite volume scheme associated to a fractional step method, where each step is hyperbolic. We extend our study to a two-pressure, unconditionally hyperbolic model [2] in which a relaxation technique was applied in order to recover the one-pressure model by using the granular stress. The second goal of this study is also to propose an improved ignition model of the powder grains, by taking into account simplified chemical kinetics for decomposition reactions in the two phases. Here we consider a 0th-order solid decomposition and an unimolecular, 2nd-order gas reaction. Validation of the algorithm on several test cases is presented.

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