scholarly journals Global analysis of Navier–Stokes and Boussinesq stochastic flows using dynamical orthogonality

2013 ◽  
Vol 734 ◽  
pp. 83-113 ◽  
Author(s):  
T. P. Sapsis ◽  
M. P. Ueckermann ◽  
P. F. J. Lermusiaux
Keyword(s):  
Global Analysis ◽  
Computational Cost ◽  
Fluid Flows ◽  
Projection Methods ◽  
Navier Stokes ◽  
Mean Flow ◽  
Field Equations ◽  
Stochastic Fluctuations ◽  
Low Dimensionality ◽  
Orthogonal Field

AbstractWe provide a new framework for the study of fluid flows presenting complex uncertain behaviour. Our approach is based on the stochastic reduction and analysis of the governing equations using the dynamically orthogonal field equations. By numerically solving these equations, we evolve in a fully coupled way the mean flow and the statistical and spatial characteristics of the stochastic fluctuations. This set of equations is formulated for the general case of stochastic boundary conditions and allows for the application of projection methods that considerably reduce the computational cost. We analyse the transformation of energy from stochastic modes to mean dynamics, and vice versa, by deriving exact expressions that quantify the interaction among different components of the flow. The developed framework is illustrated through specific flows in unstable regimes. In particular, we consider the flow behind a disk and the Rayleigh–Bénard convection, for which we construct bifurcation diagrams that describe the variation of the response as well as the energy transfers for different parameters associated with the considered flows. We reveal the low dimensionality of the underlying stochastic attractor.

Numerical Investigation of Flow Over an Airfoil by the Lattice Boltzmann Method

2013 ◽  
Author(s):  
Felipe A. Valenzuela ◽  
Amador M. Guzmán ◽  
Andrés J. Díaz
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Preliminary Investigation ◽  
Computational Cost ◽  
Fluid Flows ◽  
Laminar Flows ◽  
Navier Stokes ◽  
Laminar Separation ◽  
Refinement Method ◽  
Boltzmann Method

During the last years the aerodynamics characteristics of airfoils have been studied solving numerically the Navier-Stokes (NS) equations. These calculations require a significant computational cost due to both the second order and the nonlinear characteristics of the NS partial differential equations. Therefore, efforts have been devoted to reduce this cost and increase the accuracy of the numerical methods. The Lattice-Boltzmann Method (LBM) has become a great alternative to simulate this problem and a variety of fluid flows. In this method, the convective operator is linear and the pressure is calculated directly by the equation of state without implementing iterative methods. This work represents a preliminary investigation of a laminar flow over airfoils under low Reynolds number conditions (Re = 500). Solutions are obtained using a Multi-Block mesh refinement method. In order to validate the computational code, calculations are performed on a SD7003 airfoil at an angle of attack of 4° and 30°, which corresponds to the available numerical and experimental results. The results of this study agree well with previous experimental and numerical studies demonstrating the capabilities of the LBM to simulate accurately laminar flows over airfoils as well as capturing and predicting the laminar separation bubbles.

Favre-Averaged Fourier-Based Methods for Gas Turbine Flows

2019 ◽  
Author(s):  
Feng Wang ◽  
Luca di Mare ◽  
Paolo Adami
Keyword(s):  
Gas Turbine ◽  
Linear Time ◽  
Computational Cost ◽  
Navier Stokes ◽  
Design Stage ◽  
Mean Flow ◽  
Non Linear ◽  
Time Marching ◽  
Turbine Design ◽  
Turbomachinery Design

Abstract Steady Reynolds-Averaged Navier-Stokes (RANS) simulations are the workhorse of turbomachinery design. Recent trends in gas turbine design require full consideration of flow unsteadiness at the design stage to address issues of performance as well as integrity. Unsteady calculations using non-linear time marching methods are too computationally expensive to be used at the design stage. An alternative way is needed to reduce computational cost whilst retaining control on the accuracy of the simulations. To address this need, this paper presents a framework of Fourier-based methods for turbomachinery flows. The method is based on the non-linear harmonic (NLH) method. The method uses the favourable properties of Favre-averaging to obtain a simpler and more flexible formulation of the time-averaged system for NLH. This is ideal for implementing NLH in a CFD code where minimum modifications are desired. The approach allows the fidelity of the simulations to be tuned by switching on or off the coupling between the flow perturbations and the mean flow or the cross-coupling among the harmonics. This leads to a range of modelling fidelity for unsteady flows. For example, if the unsteady flow is linear, a linear harmonic method is sufficient for the design instead of using a harmonic balance simulation which has extra computational cost and slower convergence. The method has been tested on compressors and turbines which covers gas turbine flows in a range of flow regimes. Good agreement with data from non-linear time marching simulations are observed for all cases.

scholarly journals Attractor local dimensionality, nonlinear energy transfers and finite-time instabilities in unstable dynamical systems with applications to two-dimensional fluid flows

2013 ◽  
Vol 469 (2153) ◽  
pp. 20120550 ◽  
Author(s):  
Themistoklis P. Sapsis
Keyword(s):  
Finite Time ◽  
Stokes Equations ◽  
Fractal Dimensionality ◽  
Fluid Flows ◽  
Synergistic Activity ◽  
Energy Transfer Mechanism ◽  
Mean Flow ◽  
Low Dimensionality ◽  
The Mean ◽  
Nonlinear Energy

We examine the geometry of the finite-dimensional attractor associated with fluid flows described by Navier–Stokes equations and relate its nonlinear dimensionality to energy exchanges between dynamical components (modes) of the flow. Specifically, we use a stochastic framework based on the dynamically orthogonal equations to perform efficient order-reduction and describe the stochastic attractor in the reduced-order phase space in terms of the associated probability measure. We introduce the notion of local fractal dimensionality to describe the geometry of the attractor and we establish a connection with the number of positive finite-time Lyapunov exponents. Subsequently, we illustrate in specific fluid flows that the low dimensionality of the stochastic attractor is caused by the synergistic activity of linearly unstable and stable modes as well as the action of the quadratic terms. In particular, we illustrate the connection of the low-dimensionality of the attractor with the circulation of energy: (i) from the mean flow to the unstable modes (due to their linearly unstable character), (ii) from the unstable modes to the stable ones (due to a nonlinear energy transfer mechanism) and (iii) from the stable modes back to the mean (due to the linearly stable character of these modes).

scholarly journals Numerical simulation and experimental validation of cavitating flow in a multi-hole diesel fuel injector

2021 ◽  
pp. 146808742199863
Author(s):  
Aishvarya Kumar ◽  
Ali Ghobadian ◽  
Jamshid Nouri
Keyword(s):  
Computational Cost ◽  
Cavitating Flow ◽  
Field Analysis ◽  
Navier Stokes ◽  
Fuel Injector ◽  
Fluid Behavior ◽  
Flow Field Analysis ◽  
Charged Couple Device ◽  
Biodiesel Fuels ◽  
High Level

This study assesses the predictive capability of the ZGB (Zwart-Gerber-Belamri) cavitation model with the RANS (Reynolds Averaged Navier-Stokes), the realizable k-epsilon turbulence model, and compressibility of gas/liquid models for cavitation simulation in a multi-hole fuel injector at different cavitation numbers (CN) for diesel and biodiesel fuels. The prediction results were assessed quantitatively by comparison of predicted velocity profiles with those of measured LDV (Laser Doppler Velocimetry) data. Subsequently, predictions were assessed qualitatively by visual comparison of the predicted void fraction with experimental CCD (Charged Couple Device) recorded images. Both comparisons showed that the model could predict fluid behavior in such a condition with a high level of confidence. Additionally, flow field analysis of numerical results showed the formation of vortices in the injector sac volume. The analysis showed two main types of vortex structures formed. The first kind appeared connecting two adjacent holes and is known as “hole-to-hole” connecting vortices. The second type structure appeared as double “counter-rotating” vortices emerging from the needle wall and entering the injector hole facing it. The use of RANS proved to save significant computational cost and time in predicting the cavitating flow with good accuracy.

scholarly journals Obtaining Expressions for Time-Dependent Functions That Describe the Unsteady Properties of Swirling Jets of Viscous Fluid

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1860
Author(s):  
Eugene Talygin ◽  
Alexander Gorodkov
Keyword(s):  
Blood Flow ◽  
Viscous Fluid ◽  
Swirling Flow ◽  
Fluid Flows ◽  
Theoretical Method ◽  
Flow Channel ◽  
Navier Stokes ◽  
Swirling Jets ◽  
Continuity Equations ◽  
Dynamic Velocity

Previously, it has been shown that the dynamic geometric configuration of the flow channel of the left heart and aorta corresponds to the direction of the streamlines of swirling flow, which can be described using the exact solution of the Navier–Stokes and continuity equations for the class of centripetal swirling viscous fluid flows. In this paper, analytical expressions were obtained. They describe the functions C0t and Г0t, included in the solutions, for the velocity components of such a flow. These expressions make it possible to relate the values of these functions to dynamic changes in the geometry of the flow channel in which the swirling flow evolves. The obtained expressions allow the reconstruction of the dynamic velocity field of an unsteady potential swirling flow in a flow channel of arbitrary geometry. The proposed approach can be used as a theoretical method for correct numerical modeling of the blood flow in the heart chambers and large arteries, as well as for developing a mathematical model of blood circulation, considering the swirling structure of the blood flow.

Hybrid LES Approach for Practical Turbomachinery Flows—Part I: Hierarchy and Example Simulations

2011 ◽  
Vol 134 (2) ◽  
Author(s):  
Paul Tucker ◽  
Simon Eastwood ◽  
Christian Klostermeier ◽  
Richard Jefferson-Loveday ◽  
James Tyacke ◽  
...  
Keyword(s):  
Convex Surface ◽  
Computational Cost ◽  
Companion Paper ◽  
Navier Stokes ◽  
Computationally Efficient ◽  
Turbulent Structures ◽  
Hybrid Strategy ◽  
Eddy Simulation ◽  
Related Approach ◽  
Les Model

Unlike Reynolds-averaged Navier–Stokes (RANS) models that need calibration for different flow classes, LES (where larger turbulent structures are resolved by the grid and smaller modeled in a fashion reminiscent of RANS) offers the opportunity to resolve geometry dependent turbulence as found in complex internal flows—albeit at substantially higher computational cost. Based on the results for a broad range of studies involving different numerical schemes, large eddy simulation (LES) models and grid topologies, an LES hierarchy and hybrid LES related approach is proposed. With the latter, away from walls, no LES model is used, giving what can be termed numerical LES (NLES). This is relatively computationally efficient and makes use of the dissipation present in practical industrial computational fluid dynamics (CFD) programs. Near walls, RANS modeling is used to cover over numerous small structures, the LES resolution of which is generally intractable with current computational power. The linking of the RANS and NLES zones through a Hamilton–Jacobi equation is advocated. The RANS-NLES hybridization makes further sense for compressible flow solvers, where, as the Mach number tends to zero at walls, excessive dissipation can occur. The hybrid strategy is used to predict flow over a rib roughened surface and a jet impinging on a convex surface. These cases are important for blade cooling and show encouraging results. Further results are presented in a companion paper.

Rotational and Quasiviscous Cold Flow Models for Axisymmetric Hybrid Propellant Chambers

2010 ◽  
Vol 132 (10) ◽  
Author(s):  
Joseph Majdalani ◽  
Michel Akiki
Keyword(s):  
Rocket Engine ◽  
Navier Stokes ◽  
Mathematical Treatment ◽  
Hybrid Rocket ◽  
Mean Flow ◽  
Viscous Effects ◽  
Navier Stokes Equation ◽  
Flow Models ◽  
Hybrid Rocket Engine ◽  
Wall Injection

In this work, we present two simple mean flow solutions that mimic the bulk gas motion inside a full-length, cylindrical hybrid rocket engine. Two distinct methods are used. The first is based on steady, axisymmetric, rotational, and incompressible flow conditions. It leads to an Eulerian solution that observes the normal sidewall mass injection condition while assuming a sinusoidal injection profile at the head end wall. The second approach constitutes a slight improvement over the first in its inclusion of viscous effects. At the outset, a first order viscous approximation is constructed using regular perturbations in the reciprocal of the wall injection Reynolds number. The asymptotic approximation is derived from a general similarity reduced Navier–Stokes equation for a viscous tube with regressing porous walls. It is then compared and shown to agree remarkably well with two existing solutions. The resulting formulations enable us to model the streamtubes observed in conventional hybrid engines in which the parallel motion of gaseous oxidizer is coupled with the cross-streamwise (i.e., sidewall) addition of solid fuel. Furthermore, estimates for pressure, velocity, and vorticity distributions in the simulated engine are provided in closed form. Our idealized hybrid engine is modeled as a porous circular-port chamber with head end injection. The mathematical treatment is based on a standard similarity approach that is tailored to permit sinusoidal injection at the head end.

Lattice-Boltzmann Simulation of Two-Phase Fluid Flows

1998 ◽  
Vol 09 (08) ◽  
pp. 1383-1391 ◽  
Author(s):  
Yu Chen ◽  
Shulong Teng ◽  
Takauki Shukuwa ◽  
Hirotada Ohashi
Keyword(s):  
Lattice Boltzmann ◽  
Fluid Flows ◽  
Navier Stokes ◽  
Interface Model ◽  
Two Phase ◽  
Navier Stokes Equation ◽  
Lattice Boltzmann Simulation ◽  
Dam Breaking ◽  
Volumetric Stress ◽  
Phase Fluid

A model with a volumetric stress tensor added to the Navier–Stokes Equation is used to study two-phase fluid flows. The implementation of such an interface model into the lattice-Boltzmann equation is derived from the continuous Boltzmann BGK equation with an external force term, by using the discrete coordinate method. Numerical simulations are carried out for phase separation and "dam breaking" phenomena.

Two Algorithms for Solving Coupled Particle Dynamics and Flow Field Equations in Two-Phase Flows

2010 ◽  
Author(s):  
R. Kamali ◽  
S. A. Shekoohi
Keyword(s):  
Flow Field ◽  
Particle Dynamics ◽  
Fluid Particle ◽  
Navier Stokes ◽  
Test Cases ◽  
Particle Interactions ◽  
Field Equations ◽  
Two Phase ◽  
Coupled Equations ◽  
Solution Accuracy

Two methods for solving coupled particle dynamics and flow field equations simultaneously by considering fluid-particle interactions to simulate two-phase flow are presented and compared. In many conditions, such as magnetic micro mixers and shooting high velocity particles in fluid, the fluid-particle interactions can not be neglected. In these cases it is necessary to consider fluid-particle interactions and solve the related coupled equations simultaneously. To solve these equations, suitable algorithms should be used to improve convergence speed and solution accuracy. In this paper two algorithms for solving coupled incompressible Navier-Stokes and particle dynamics equations are proposed and their efficiencies are compared by using them in a computer program. The main criterion that is used for comparison is the time they need to converge for a specific accuracy. In the first algorithm the particle dynamics and flow field equations are solved simultaneously but separately. In the second algorithm in each iteration for solving flow field equations, the particle dynamics equation is also solved. Results for some test cases are presented and compared. According to the results the second algorithm is faster than the first one especially when there is a strong coupling between phases.

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