Modeling of Particulate Pressure in the Frame of Mesoscopic Eulerian Formalism for Compressible Reactive Dispersed Two-Phase Flows

2006 ◽  
Author(s):  
M. Simoes ◽  
O. Simonin
Keyword(s):  
Stokes Equations ◽  
Flow Region ◽  
Navier Stokes ◽  
Two Phase Flows ◽  
Two Phase ◽  
Specific Flow ◽  
Navier Stokes Equations ◽  
Rocket Motors ◽  
Eulerian Approach ◽  
Liquid Rocket

In space propulsion, compressible reactive dispersed two-phase flows are investigated in order to predict the behavior of solid or liquid rocket motors. In the frame of full Eulerian approach, physical modeling of aerodynamic flows in such motors is performed resolving unsteady compressible Navier-Stokes equations for both phases. However, numerical simulations performed on a simple axisymmetric motor have pointed out a flaw of this basic Eulerian approach. Indeed, the variance of the particle velocity distribution is not accounted for, leading to unrealistic accumulations of particles in some specific flow region. To correct this shortcoming, we have developed an advanced Eulerian model based on a statistical approach in the framework of the Mesoscopic Eulerian Formalism (MEF).

Modeling of Particulate Pressure in the Frame of Eulerian Approach for Compressible Reactive Dispersed Two-Phase Flows

2005 ◽  
Author(s):  
Marine Simoes ◽  
Patrick Della Pieta ◽  
Franck Godfroy ◽  
Olivier Simonin
Keyword(s):  
Stokes Equations ◽  
Specific Impulse ◽  
Flow Region ◽  
Navier Stokes ◽  
Two Phase ◽  
Specific Flow ◽  
Navier Stokes Equations ◽  
Rocket Motors ◽  
Eulerian Approach ◽  
Solid Rocket

In solid rocket motors (SRM) used for space propulsion, such as Ariane 5, aluminum is frequently used as a propellant additive to increase specific impulse. However, its combustion produces aluminum oxide residues that are carried away by the flow field. Thus, physical modeling of aerodynamic flows in SRM should account for this condensed phase. In the frame of full Eulerian approach, unsteady compressible Navier-Stokes equations are solved for both phases. However, numerical simulations performed on a simple axisymmetric motor have pointed out a flaw of the basic Eulerian approach. Indeed, the variance of the particle velocity distribution is not accounted for, leading to unrealistic accumulations of particles in some specific flow region. Hence, we have developed an advanced Eulerian model to correct this shortcoming, which is presented in this paper.

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.

scholarly journals Simulating two-phase flows with thermodynamically consistent energy stable Cahn-Hilliard Navier-Stokes equations on parallel adaptive octree based meshes

2020 ◽  
Vol 419 ◽  
pp. 109674
Author(s):  
Makrand A. Khanwale ◽  
Alec D. Lofquist ◽  
Hari Sundar ◽  
James A. Rossmanith ◽  
Baskar Ganapathysubramanian
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Two Phase Flows ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Energy Stable

A HYBRID SCHEME FOR THREE-DIMENSIONAL INCOMPRESSIBLE TWO-PHASE FLOWS

2010 ◽  
Vol 02 (04) ◽  
pp. 889-905 ◽  
Author(s):  
LI CAI ◽  
JUN ZHOU ◽  
FENG-QI ZHOU ◽  
WEN-XIAN XIE
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Heaviside Function ◽  
Hybrid Scheme ◽  
Two Phase Flows ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Two Fluids ◽  
Marker And Cell Method

We present a hybrid scheme for computations of three-dimensional incompressible two-phase flows. A Poisson-like pressure equation is deduced from the incompressible constraint, i.e., the divergence-free condition of the velocity field, via an extended marker and cell method, and the moment equations in the 3D incompressible Navier–Stokes equations are solved by our 3D semi-discrete Hermite central-upwind scheme. The interface between the two fluids is considered to be the 0.5 level set of a smooth function being a smeared out Heaviside function. Numerical results are offered to verify the desired efficiency and accuracy of our 3D hybrid scheme.

Numerical Modeling of Evolution of Boundary Between Incompressible Gas and Liquid in Two-Dimensional Region

2006 ◽  
Vol 4 ◽  
pp. 224-236
Author(s):  
A.S. Topolnikov
Keyword(s):  
Numerical Modeling ◽  
Interphase Boundary ◽  
Incompressible Liquid ◽  
Stokes Equations ◽  
Numerical Code ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Incompressible Media ◽  
Good Agreement

The paper is devoted to numerical modeling of Navier–Stokes equations for incompressible media in the case, when there exist gas and liquid inside the rectangular calculation region, which are separated by interphase boundary. The set of equations for incompressible liquid accounting for viscous, gravitational and surface (capillary) forces is solved by finite-difference scheme on the spaced grid, for description of interphase boundary the ideology of Level Set Method is used. By developed numerical code the set of hydrodynamic problems is solved, which describe the motion of two-phase incompressible media with interphase boundary. As a result of numerical simulation the solutions are obtained, which are in good agreement with existing analytical and experimental solutions.

Self-Excited Oscillation of Transonic Flow Around an Airfoil in Two-Dimensional Channel

1989 ◽  
Author(s):  
Kazuomi Yamamoto ◽  
Yoshimichi Tanida
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Transonic Flow ◽  
Stokes Equations ◽  
Flow Region ◽  
Boundary Layer Separation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Layer Separation ◽  
Excited Oscillation

A self-excited oscillation of transonic flow in a simplified cascade model was investigated experimentally, theoretically and numerically. The measurements of the shock wave and wake motions, and unsteady static pressure field predict a closed loop mechanism, in which the pressure disturbance, that is generated by the oscillation of boundary layer separation, propagates upstream in the main flow and forces the shock wave to oscillate, and then the shock oscillation disturbs the boundary layer separation again. A one-dimensional analysis confirms that the self-excited oscillation occurs in the proposed mechanism. Finally, a numerical simulation of the Navier-Stokes equations reveals the unsteady flow structure of the reversed flow region around the trailing edge, which induces the large flow separation to bring about the anti-phase oscillation.

scholarly journals Do the Volume-of-Fluid and the Two-Phase Euler Compete for Modeling a Spillway Aerator?

Water ◽  
2021 ◽  
Vol 13 (21) ◽  
pp. 3092
Author(s):  
Lourenço Sassetti Mendes ◽  
Javier L. Lara ◽  
Maria Teresa Viseu
Keyword(s):  
Stokes Equations ◽  
Cost Benefit ◽  
Volume Of Fluid ◽  
Navier Stokes ◽  
Type Model ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Entrained Air ◽  
Computational Resources ◽  
Mesh Convergence

Spillway design is key to the effective and safe operation of dams. Typically, the flow is characterized by high velocity, high levels of turbulence, and aeration. In the last two decades, advances in computational fluid dynamics (CFD) made available several numerical tools to aid hydraulic structures engineers. The most frequent approach is to solve the Reynolds-averaged Navier–Stokes equations using an Euler type model combined with the volume-of-fluid (VoF) method. Regardless of a few applications, the complete two-phase Euler is still considered to demand exorbitant computational resources. An assessment is performed in a spillway offset aerator, comparing the two-phase volume-of-fluid (TPVoF) with the complete two-phase Euler (CTPE). Both models are included in the OpenFOAM® toolbox. As expected, the TPVoF results depend highly on the mesh, not showing convergence in the maximum chute bottom pressure and the lower-nappe aeration, tending to null aeration as resolution increases. The CTPE combined with the k–ω SST Sato turbulence model exhibits the most accurate results and mesh convergence in the lower-nappe aeration. Surprisingly, intermediate mesh resolutions are sufficient to surpass the TPVoF performance with reasonable calculation efforts. Moreover, compressibility, flow bulking, and several entrained air effects in the flow are comprehended. Despite not reproducing all aspects of the flow with acceptable accuracy, the complete two-phase Euler demonstrated an efficient cost-benefit performance and high value in spillway aerated flows. Nonetheless, further developments are expected to enhance the efficiency and stability of this model.

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