scholarly journals Development and verification of meshless diffuse approximate method for simulation of compressible flow between parallel plates

2021 ◽  
Vol 2116 (1) ◽  
pp. 012021
Author(s):  
K B Rana ◽  
R Zahoor ◽  
B Mavrič ◽  
B Šarler
Keyword(s):  
Numerical Model ◽  
Approximate Method ◽  
Compressible Flow ◽  
Weighted Least Squares ◽  
Mass Conservation ◽  
Momentum Conservation ◽  
Ideal Gas ◽  
Implicit Time ◽  
Parallel Plates ◽  
Gaussian Weight

Abstract A meshless numerical model is developed to simulate single-phase, Newtonian, compressible flow in the Cartesian coordinate system. The coupled set of partial differential equations, i.e., mass conservation, momentum conservation, energy conservation, and equation of state is solved by using Diffuse Approximate Method (DAM) and Pressure Implicit with Splitting of Operators (PISO) pressure correction algorithm on an irregular node arrangement. DAM is structured by using the second-order polynomial basis functions and the Gaussian weight function, leading to the weighted least squares approximation on overlapping sub-domains. Implicit time discretization is performed for the predictor step of PISO, while in the corrector steps the equations are discretized explicitly. The numerical model is validated for flow between parallel plates with helium obeying ideal gas law. The solver’s accuracy is assessed by investigating the shape of the Gaussian weight and the number of the nodes in the local subdomains. The calculated velocity, temperature and pressure fields are compared with the Finite Volume Method (FVM) results obtained by OpenFOAM software and show a reasonably good agreement.

A Numerical Model of In-Channel Pebble Bed Thermal Storage for a Solar Chimney

2012 ◽  
Author(s):  
Brandon Schulte ◽  
O. A. Plumb
Keyword(s):  
Numerical Model ◽  
Present Model ◽  
Thermal Storage ◽  
Implicit Time ◽  
Heat Transfer Characteristics ◽  
Solar Chimney ◽  
Pebble Bed ◽  
One Dimensional ◽  
Time Stepping ◽  
Daily Energy

In this study, solar chimney performance is numerically modeled. Previously published models have considered water bags and natural earth as means to store daytime thermal energy for nighttime operation of the system. The present model considers in-channel pebble bed thermal storage. A one-dimensional, implicit time stepping numerical model is developed to predict solar chimney performance throughout a 24 hour period. The model is partially verified with available experimental data. The daily energy, daily efficiency and heat transfer characteristics of the solar chimney with pebble bed thermal storage are summarized. The numerical simulation showed that by introducing a pebble bed, nightly exit velocities reach 40% of the peak daytime velocity. However, the daily kinetic energy delivered by a solar chimney with pebble bed thermal storage is much less than a traditional solar chimney, suggesting pebble bed thermal storage is more practicable in building heating applications as opposed to power generation.

scholarly journals Detailed description of the evolution mechanism for singularities in the system of pressureless gas dynamics

2019 ◽  
Vol 484 (6) ◽  
pp. 655-658 ◽  
Author(s):  
A. I. Aptekarev ◽  
Yu. G. Rykov
Keyword(s):  
Gas Dynamics ◽  
Variational Approach ◽  
Large Scale ◽  
Burgers Equation ◽  
Mass Conservation ◽  
Momentum Conservation ◽  
Material Objects ◽  
Vector Equation ◽  
Basic Principles ◽  
The Universe

The system of pressureless gas dynamics is a hydrodynamically justified generalization of the system consisting of the Burgers vector equation in the limit of vanishing viscosity and the mass conservation law. The latter system of equations was intensively used, in particular, in astrophysics to describe the large scale structure of the Universe. The solutions of the vector Burgers equation involve interesting dynamics of singularities, which can describe concentration processes. However, this dynamics does not satisfy the law of momentum conservation, which prevents us from treating it as dynamics of material objects. In this paper, momentum-conserving dynamics of singularities is investigated on the basis of the pressureless gas dynamics system. Such dynamics turns out to be more diverse and complex, but it is also possible to formulate a variational approach, for which the basic principles and relations are obtained in the work.

scholarly journals Resonance Vibration of Mistuned Bladed Discs in Stationary Operations

1997 ◽  
Author(s):  
Romuald Rządkowski
Keyword(s):  
Numerical Model ◽  
Compressible Flow ◽  
Two Dimensional ◽  
Rotating System ◽  
Response Level ◽  
Stationary Response ◽  
The Real ◽  
Disc Model ◽  
Real Geometry ◽  
Airfoil Blades

A numerical model for the calculation of resonance stationary response of mistuned bladed disc is presented. The bladed disc model includes all important effects on a rotating system of the real geometry. The excitation forces were calculated by a code on the basis of two-dimensional compressible flow (to M < 0.8) for thin airfoil blades. The calculations presented in this paper show that centrifugal stress, and the values of excitation forces, play an important role in considering the influence of mistuning on the response level.

Mathematical Modelling of Thermo-Hydro-Mechanical Behaviour for Concrete under Elevated Temperature

2014 ◽  
Vol 670-671 ◽  
pp. 355-364
Author(s):  
Shao Bo Zhang ◽  
Xiao Chun Wang ◽  
Xin Pu Shen
Keyword(s):  
Elevated Temperature ◽  
Stokes Equations ◽  
Constitutive Relations ◽  
Gaseous Mixture ◽  
Mass Conservation ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Energy Conservation Equation

A hydro-thermo-mechanical model was presented for concrete at elevated temperature. Three phases of continuum were adopted in this model: gaseous mixture of water vapor and dry air, liquid water, and solid skeleton of concrete. Mass conservation equations, linear momentum conservation equation, and energy conservation equation were derived on the basis of the macroscopic Navier-Stokes equations for a general continuum, along with assumptions made for the purpose of simplification. Mathematical relationships between selected primary variables and secondary variables were given with existing data from references. Specifications of the constitutive relations were made for the kinetic variables and their conjugate forces.

A PRIORI PRESSURE FIELD CONSTRUCTION ITERATIVE METHOD FOR THE SOLUTION OF THE STEADY-STATE NAVIER–STOKES EQUATIONS USING GENERAL FINITE-VOLUME CO-LOCATED GRIDS

2007 ◽  
Vol 04 (04) ◽  
pp. 567-601
Author(s):  
JOSE A. LAMAS
Keyword(s):  
Iterative Method ◽  
Pressure Field ◽  
Stokes Equations ◽  
A Priori ◽  
Mass Conservation ◽  
Momentum Conservation ◽  
Navier Stokes ◽  
Pressure Equation ◽  
Navier Stokes Equations ◽  
Correction Equations

An iterative method has been developed for the solution of the Navier–Stokes equations and implemented using finite volumes with co-located variable arrangement. A pressure equation is obtained combining algebraic momentum and mass conservation equations resulting in a self-consistent set of equations. An iterative procedure solves the pressure equation consistently with mass conservation and then updates velocities based on momentum equations without introducing velocity or pressure correction equations. The process is repeated until velocities satisfy both mass and momentum conservation. Tests demonstrate a priori pressure field solution consistent with mass conservation, and solution of hydrostatic problems in one iteration.

Numerical Research on 3-D Flow Field in 5×5 Rod Bundles With Spacer Grids

2010 ◽  
Author(s):  
Rui-feng Tian ◽  
Xiao-hui Mao ◽  
Pu-zhen Gao ◽  
Xiao-jun Wang
Keyword(s):  
Flow Field ◽  
Single Phase ◽  
Mass Conservation ◽  
Momentum Conservation ◽  
Rod Bundles ◽  
Experiment Data ◽  
Spacer Grids ◽  
Simplec Algorithm ◽  
Numerical Research ◽  
Hybrid Grids

3-D single-phase flow field in 5×5 rod bundles with spacer grids was studied by numerical method. Using hybrid grids technique, SST k-ω model and SIMPLEC algorithm, the Reynolds averaged mass conservation and momentum conservation equations were solved, and the pressure and velocity field were obtained. The simulation results show that the spacer grids leads to intense lateral flow in rod bundles channel, and it submitted parabola distributing raw; axial velocities were distributed uniformly in the channel; drag coefficient decreased as inlet Reynolds number increased. Calculated results agreed with experiment data well, it shows that numerical methods employed in this paper is suitable to study flow field in 5×5 rod bundles.

Numerical Modeling of Unidirectional Stratified Flow Between Parallel Plates

2004 ◽  
Author(s):  
Y. F. Yap ◽  
J. C. Chai ◽  
K. C. Toh ◽  
T. N. Wong ◽  
Y. C. Lam
Keyword(s):  
Exact Solutions ◽  
Cross Section ◽  
Correction Term ◽  
Stratified Flow ◽  
Mass Conservation ◽  
Parallel Plates ◽  
Two Fluids ◽  
Mass Correction ◽  
Developing Region ◽  
Mass Flowrate

Unidirectional stratified flow of two fluids between two parallel plates is modeled using the Level-Set method. A localized mass correction term is used to ensure mass conservation at every axial cross section. The mass correction term is based on the mass flowrates. Results for various combinations of density, viscosity and mass flowrate ratios are presented. Available fully-developed exact solutions for unidirectional stratified flow are used to validate the numerical simulations. The evolutions of the interface in the developing region are also captured and compared well with “exact” solutions.

Spatial Discretizations

2013 ◽  
Author(s):  
Gary A. Glatzmaier
Keyword(s):  
Finite Difference ◽  
Finite Difference Methods ◽  
Fourier Method ◽  
Mass Conservation ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Nonuniform Grids ◽  
Coordinate Mapping ◽  
Difference Methods ◽  
Basic Ideas

This chapter considers two ways of employing a spatial resolution that varies with position within a finite-difference method: using a nonuniform grid and mapping to a new coordinate variable. It first provides an overview of nonuniform grids before discussing coordinate mapping as an alternative way of achieving spatial discretization. It then describes an approach for treating both the vertical and horizontal directions with simple finite-difference methods: defining a streamfunction, which automatically satisfies mass conservation, and solving for vorticity via the curl of the momentum conservation equation. It also explains the use of the Chebyshev–Fourier method to simulate the convection or gravity wave problem by employing spectral methods in both the horizontal and vertical directions. Finally, it looks at the basic ideas and some issues that need to be addressed with respect to parallel processing as well as choices that need to be made when designing a parallel code.

scholarly journals Compressible flow at high pressure with linear equation of state

2018 ◽  
Vol 843 ◽  
pp. 244-292 ◽  
Author(s):  
William A. Sirignano
Keyword(s):  
Equation Of State ◽  
Compressible Flow ◽  
Sound Speed ◽  
Ideal Gas ◽  
Real Gas ◽  
Cubic Equation Of State ◽  
Cubic Equation ◽  
Wide Range ◽  
Real Gas Effects ◽  
Flow Configurations

Compressible flow varies from ideal-gas behaviour at high pressures where molecular interactions become important. It is widely accepted that density is well described through a cubic equation of state while enthalpy and sound speed are functions of both temperature and pressure, based on two parameters, $A$ and $B$, related to intermolecular attraction and repulsion, respectively. Assuming small variations from ideal-gas behaviour, a closed-form approximate solution is obtained that is valid over a wide range of conditions. An expansion in these molecular interaction parameters simplifies relations for flow variables, elucidating the role of molecular repulsion and attraction in variations from ideal-gas behaviour. Real-gas modifications in density, enthalpy and sound speed for a given pressure and temperature lead to variations in many basic compressible-flow configurations. Sometimes, the variations can be substantial in quantitative or qualitative terms. The new approach is applied to choked-nozzle flow, isentropic flow, nonlinear wave propagation and flow across a shock wave, all for a real gas. Modifications are obtained for allowable mass flow through a choked nozzle, nozzle thrust, sonic wave speed, Riemann invariants, Prandtl’s shock relation and the Rankine–Hugoniot relations. Forced acoustic oscillations can show substantial augmentation of pressure amplitudes when real-gas effects are taken into account. Shocks at higher temperatures and pressures can have larger pressure jumps with real-gas effects. Weak shocks decay to zero strength at sonic speed. The proposed framework can rely on any cubic equation of state and can be applied to multicomponent flows or to more complex flow configurations.

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