scholarly journals The Homogeneous Cooling State as a Verification Test for Kinetic Theory-Based Continuum Models of Gas–Solid Flows

2017 ◽  
Vol 2 (4) ◽  
Author(s):  
William D. Fullmer ◽  
Christine M. Hrenya
Keyword(s):  
Analytical Solution ◽  
Kinetic Theory ◽  
Stokes Equations ◽  
Fluid Dynamic ◽  
Time Integration ◽  
Continuum Models ◽  
Integration Scheme ◽  
Backward Euler ◽  
Verification Test ◽  
Homogeneous Cooling State

Granular and multiphase (gas–solids) kinetic theory-based models have emerged a leading modeling strategy for the simulation of particle flows. Similar to the Navier–Stokes equations of single-phase flow, although substantially more complex, kinetic theory-based continuum models are typically solved with computational fluid dynamic (CFD) codes. Under the assumptions of the so-called homogeneous cooling state (HCS), the governing equations simplify to an analytical solution describing the “cooling” of fluctuating particle velocity, or granular temperature. The HCS is used here to verify the implementation of a recent multiphase kinetic theory-based model in the open source mfix code. Results from the partial verification test show that the available implicit (backward) Euler time integration scheme converges to the analytical solution with the expected first-order rate. A second-order accurate backward differentiation formula (BDF) is also implemented and observed to converge at a rate consistent with its formal accuracy.

scholarly journals Investigation of Air Pocket Behavior in Pipelines Using Rigid Column Model and Contributions of Time Integration Schemes

Water ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 785
Author(s):  
Arman Rokhzadi ◽  
Musandji Fuamba
Keyword(s):  
Transient Flow ◽  
Time Integration ◽  
Driving Pressure ◽  
Implicit Time ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Time Step ◽  
Column Model ◽  
Integration Schemes ◽  
Backward Euler

This paper studies the air pressurization problem caused by a partially pressurized transient flow in a reservoir-pipe system. The purpose of this study is to analyze the performance of the rigid column model in predicting the attenuation of the air pressure distribution. In this regard, an analytic formula for the amplitude and frequency will be derived, in which the influential parameters, particularly, the driving pressure and the air and water lengths, on the damping can be seen. The direct effect of the driving pressure and inverse effect of the product of the air and water lengths on the damping will be numerically examined. In addition, these numerical observations will be examined by solving different test cases and by comparing to available experimental data to show that the rigid column model is able to predict the damping. However, due to simplified assumptions associated with the rigid column model, the energy dissipation, as well as the damping, is underestimated. In this regard, using the backward Euler implicit time integration scheme, instead of the classical fourth order explicit Runge–Kutta scheme, will be proposed so that the numerical dissipation of the backward Euler implicit scheme represents the physical dissipation. In addition, a formula will be derived to calculate the appropriate time step size, by which the dissipation of the heat transfer can be compensated.

Computational Analysis of Characteristics and Mach Number Effects on Noise Emission From Ideally Expanded Highly Supersonic Free-Jet

2007 ◽  
Author(s):  
Taku Nonomura ◽  
Kozo Fujii
Keyword(s):  
Mach Number ◽  
Stokes Equations ◽  
Acoustic Noise ◽  
Time Integration ◽  
Three Dimensional ◽  
Integration Scheme ◽  
Noise Emission ◽  
Sonic Jet ◽  
Time Integration Scheme ◽  
Seventh Order

In this study, aero-acoustic noise from super-sonic jet plume is computationally investigated. Three-dimensional Navier-Stokes equations are solved with seventh order weighted compact non-linear scheme and total validation diminishing Runge-Kutta time integration scheme. At first, the noise from Mach 2.0 ideally expanded super-sonic jet is computed and validated with the past experimental study. Then the noises from various Mach number (2.0–3.5) ideally expanded jet plumes are computed. Noise source positions, directivity and convective Mach numbers are discussed.

Numerical simulation of parafoil inflation via a Robin–Neumann transmission-based approach

2017 ◽  
Vol 232 (4) ◽  
pp. 797-810 ◽  
Author(s):  
Shuai Nie ◽  
Yihua Cao ◽  
Zhenlong Wu
Keyword(s):  
Stokes Equations ◽  
Fluid Structure Interaction ◽  
Time Integration ◽  
Three Dimensional ◽  
Structural Deformation ◽  
Dimensional Case ◽  
Integration Scheme ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Highly Nonlinear

In this paper, a partitioned coupled iterative approach based on the Robin–Neumann transmission condition is proposed for the fluid–structure interaction simulation of the inflation process of a parafoil. The Reynold-averaged Navier–Stokes equations and the versatile finite element method are employed to solve the fluid flow field and the structural deformation, respectively. The generalized-α time integration scheme for the structure and the second order back Euler scheme for the fluid are incorporated in the Robin-Neumann method. A modified spring-transfinite interpolation hybrid method is exploited to detect the deformation of the grid and regenerate the grid for the fluid architecture. Both a two-dimensional case and a three-dimensional case are studied to examine the feasibility of the present approach. The simulation results reveal the evolution of the flow regime during the inflation process when the air pours into the parafoil. The whole inflation process can be concluded as two stages: the span-wise deployment and the longitudinal expansion. The numerical aerodynamic performance agrees well with that obtained by wind-tunnel experiment, suggesting the effectiveness of this method in handling such a highly nonlinear fluid–structure interaction in parachute inflation.

scholarly journals A low—storage Runge—Kutta OpenFOAM solver for compressible low—Mach number flows: aeroacoustic and thermo—fluid dynamic applications

2019 ◽  
Vol 128 ◽  
pp. 10001
Author(s):  
Valerio D’Alessandro ◽  
Matteo Falone ◽  
Luca Giammichele ◽  
Sergio Montelpare
Keyword(s):  
Sound Propagation ◽  
Stokes Equations ◽  
Fluid Dynamic ◽  
Time Integration ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Central Schemes ◽  
Thermal Boundary Conditions ◽  
Finite Volume Approach ◽  
The Impact

A solver for compressible Navier–Stokes equations is presented in this paper. Low-storage RungeKutta schemes were adopted for time integration; on the other hand the finite volume approach available within OpenFOAM library has been adopted for space discretization. Kurganov-Noelle-Petrova approach was used for convective terms, while central schemes for diffusive ones. The aforementioned techniques were selected and tested in order to allow the possibility of solving a broad range of physical phenomena with particular emphasis to aeroacoustic and thermo-fluid dynamic problems. Indeed, that standard OpenFOAM solution techniques produce an unacceptable dissipation for acoustic phenomena computations. Non–reflective boundary treatment was also considered to avoid spurious numerical reflections. The reliability and the robustness of the solver is proved by computing several benchmarks. Lastly, the impact of the thermal boundary conditions on the sound propagation was analyzed.

scholarly journals Load balancing method for heterogeneous CFD algorithms

2021 ◽  
Vol 23 (2) ◽  
pp. 193-206
Author(s):  
Sergey A. Soukov
Keyword(s):  
Load Balancing ◽  
Performance Test ◽  
Stokes Equations ◽  
Domain Decomposition Method ◽  
Time Integration ◽  
Dual Graph ◽  
Numerical Algorithms ◽  
Integration Scheme ◽  
Distribution Method ◽  
Time Integration Scheme

Abstract. The problem of load balancing for unstructured heterogeneous numerical algorithms for simulation of physical processes is considered. A computational distribution method for hybrid supercomputers with multicore CPUs and massively parallel accelerators is described. The load balancing procedure includes determination of dual graph vertices and edges weights, devices’ performance test and two-level decomposition of the computational mesh based on domain decomposition method. First level decomposition involves the graph partitioning between supercomputer nodes. On the second level node subdomains are partitioned between the MPI- processes running on the nodes. The details of the proposed approach are considered on the example of an unstructured finite-volume algorithm for modeling the Navier-Stokes equations with polynomial reconstruction of variables and explicit time integration scheme. The parallel version of the algorithm is developed using the MPI, OpenMP and CUDA programming models. The parameters of performance, parallel efficiency and scalability of the heterogeneous program are given. The results mentioned are obtained during the simulation of a supersonic flow around a sphere on a mixed mesh consisting of tetrahedrons, triangular prisms, quadrangular pyramids and hexagons.

Semi-Lagrangian exponential time-integration method for the shallow water equations on the cubed sphere grid

2020 ◽  
Vol 35 (6) ◽  
pp. 355-366
Author(s):  
Vladimir V. Shashkin ◽  
Gordey S. Goyman
Keyword(s):  
Shallow Water ◽  
Gravity Waves ◽  
Shallow Water Equations ◽  
Time Integration ◽  
Standard Test ◽  
Integration Scheme ◽  
Test Problems ◽  
Cubed Sphere ◽  
Lagrangian Scheme ◽  
Inertia Gravity Waves

AbstractThis paper proposes the combination of matrix exponential method with the semi-Lagrangian approach for the time integration of shallow water equations on the sphere. The second order accuracy of the developed scheme is shown. Exponential semi-Lagrangian scheme in the combination with spatial approximation on the cubed-sphere grid is verified using the standard test problems for shallow water models. The developed scheme is as good as the conventional semi-implicit semi-Lagrangian scheme in accuracy of slowly varying flow component reproduction and significantly better in the reproduction of the fast inertia-gravity waves. The accuracy of inertia-gravity waves reproduction is close to that of the explicit time-integration scheme. The computational efficiency of the proposed exponential semi-Lagrangian scheme is somewhat lower than the efficiency of semi-implicit semi-Lagrangian scheme, but significantly higher than the efficiency of explicit, semi-implicit, and exponential Eulerian schemes.

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.

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