Parameter Identification by Inverse Analysis Coupled with a Finite Pointset Method for Polyurethane Foam Expansion

2014 ◽  
Vol 611-612 ◽  
pp. 868-875 ◽  
Author(s):  
Hichem Abdessalam ◽  
Boussad Abbès ◽  
Yu Ming Li ◽  
Ying Qiao Guo ◽  
Elvis Kwassi ◽  
...  
Keyword(s):  
Parameter Identification ◽  
Reaction Temperature ◽  
Inverse Analysis ◽  
Stokes Equations ◽  
Foam Height ◽  
Test Tube ◽  
Navier Stokes ◽  
Foam Expansion ◽  
Mesh Free ◽  
Mesh Free Method

This paper deals with the parameter identification for polyurethane foaming process simulation by using an inverse analysis coupled with a Finite Pointset Method. Simultaneous measurements of the foam height rise, the reaction temperature and the viscosity on a cylindrical cardboard test tube are obtained by using the foam measurement system (FOAMAT). The simulation of the foam expansion is obtained by solving unsteady Navier-Stokes equations coupled with the energy equation, the curing reaction (reaction of isocyanate with polyol) and the foaming reaction (reaction of isocyanate with water to emit the CO2 gas) by using a mesh-free method. The inverse identification method consists in determining the parameters by comparing the computed quantities (height rise, reaction temperature and viscosity) computed by the finite pointset method to those measured experimentally.

Fully Lagrangian Modeling of Two-Phase Impulse Microjets

2013 ◽  
Author(s):  
Natalia Lebedeva ◽  
Alexander Osiptsov ◽  
Sergei Sazhin
Keyword(s):  
Carrier Phase ◽  
Stokes Equations ◽  
Order System ◽  
Navier Stokes ◽  
Time Step ◽  
Particle Trajectories ◽  
Two Phase ◽  
Novel Approach ◽  
Mesh Free ◽  
Lagrangian Modeling

A new fully Lagrangian approach to numerical simulation of 2D transient flows of viscous gas with inertial microparticles is proposed. The method is applicable to simulation of unsteady viscous flows with a dilute admixture of non-colliding particles which do not affect the carrier phase. The novel approach is based on a modification and combination of the full Lagrangian method for the dispersed phase, proposed by Osiptsov [1], and a Lagrangian mesh-free vortex-blob method for Navier-Stokes equations describing the carrier phase in the format suggested by Dynnikova [2]. In the combined numerical algorithm, both these approaches have been implemented and used at each time step. In the first stage, the vortex-blob approach is used to calculate the fields of velocity and spatial derivatives of the carrier-phase flow. In the second stage, using Osiptsov’s approach, particle velocities and number density are calculated along chosen particle trajectories. In this case, the problem of calculation of all parameters of both phases (including particle concentration) is reduced to the solution of a high-order system of ordinary differential equations, describing transient processes in both carrier and dispersed phases. The combined method is applied to simulate the development of vortex ring-like structures in an impulse two-phase microjet. This flow involves the formation of local zones of particle accumulation, regions of multiple intersections of particle trajectories, and multi-valued particle velocity and concentration fields. The proposed mesh-free approach enables one to reproduce with controlled accuracy these flow features without excessive computational costs.

A compact RBF-FD based meshless method for the incompressible Navier—Stokes equations

2009 ◽  
Vol 223 (3) ◽  
pp. 275-290 ◽  
Author(s):  
P P Chinchapatnam ◽  
K Djidjeli ◽  
P B Nair ◽  
M Tan
Keyword(s):  
Stokes Equations ◽  
Computational Method ◽  
Navier Stokes ◽  
Benchmark Problems ◽  
Navier Stokes Equations ◽  
Promising Alternative ◽  
Fluid Structure ◽  
Slip Boundary ◽  
Mesh Free ◽  
Model Fluid

Meshless methods for solving fluid and fluid-structure problems have become a promising alternative to the finite volume and finite element methods. In this paper, a mesh-free computational method based on radial basis functions in a finite difference mode (RBF-FD) has been developed for the incompressible Navier—Stokes (NS) equations in stream function vorticity form. This compact RBF-FD formulation generates sparse coefficient matrices, and hence advancing solutions will in time be of comparatively lower cost. The spatial discretization of the incompressible NS equations is done using the RBF-FD method and the temporal discretization is achieved by explicit Euler time-stepping and the Crank—Nicholson method. A novel ghost node strategy is used to incorporate the no-slip boundary conditions. The performance of the RBF-FD scheme with the ghost node strategy is validated against a variety of benchmark problems, including a model fluid—structure interaction problem, and is found to be in a good agreement with the existing results. In addition, a higher-order RBF-FD scheme (which uses ideas from Hermite interpolation) is then proposed for solving the NS equations.

Polyurethane Foaming Process Modelling by Finite Point Method

2014 ◽  
Vol 881-883 ◽  
pp. 841-845 ◽  
Author(s):  
Hichem Abdessalam ◽  
Boussad Abbès ◽  
Yu Ming Li ◽  
Ying Qiao Guo ◽  
Elvis Kwassi ◽  
...  
Keyword(s):  
Numerical Modelling ◽  
Stokes Equations ◽  
Point Method ◽  
Navier Stokes ◽  
Finite Point ◽  
Navier Stokes Equations ◽  
Foaming Process ◽  
Finite Point Method ◽  
Mesh Free ◽  
Polyurethane Foaming

Polyurethane foaming process is under fluid mechanics with complex geometries, its numerical modelling by using the classical grid methods such as the finite element method and the finite volume method can cause problems related to the mesh deformation. In order to avoid these problems a mesh free Lagrangian method developed by Kuhnert called Finite Point Method (FPM) is used in this study. The FPM consists in representing the fluid domain by a set of particles. It is proved efficient in the numerical modelling of polyurethane foaming. In this model, the chemical kinetics contribution and the rheological coupling are adopted and the expansion of the mixture is governed by the front velocity which is calculated by solving the Navier-Stokes equations. The numerical results for polyurethane foaming process in a conical beaker using the FPM are compared with the experimental results.

Approximate Analytical Solution for Laminar Flow Over a Backward Step

2015 ◽  
Author(s):  
P. Venkataraman
Keyword(s):  
Analytical Solution ◽  
Stokes Equations ◽  
Approximate Analytical Solution ◽  
Continuous Functions ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Mesh Free ◽  
Numeric Calculation ◽  
Domain Discretization

Analytical solution of Navier-Stokes equations are extremely difficult and rare. It is one of the unsolved Clay Millennium problems in mathematics. Many solutions that exist are examples of degenerate cases where the nonlinearity is controlled. In this paper we explore the application of Bézier functions to solve the two-dimensional laminar fluid flow over a backward step. The Bézier functions provide a mesh free alternative to domain discretization methods that are currently used to solve such problems. The Navier-Stokes equation are handled directly without transformation and the setup is direct, simple, and involves minimizing the error in the residuals of the differential equations along with the error on the boundary conditions over the domain. The solutions for the velocity and pressure are available in polynomial form. They are single continuous functions over the entire domain. The procedure employs a combination of symbolic and numeric calculation in MATLAB. Two problems are explored. The first is the flow in a 2D channel to illustrate the technique. The second is the flow over the backward step. The solutions are compared to the corresponding finite element solutions from COMSOL Multiphysics software.

scholarly journals Lagrangian Differencing Dynamics for Time-Independent Non-Newtonian Materials

Materials ◽  
2021 ◽  
Vol 14 (20) ◽  
pp. 6210
Author(s):  
Martina Bašić ◽  
Branko Blagojević ◽  
Chong Peng ◽  
Josip Bašić
Keyword(s):  
Power Law ◽  
Stokes Equations ◽  
Computing Time ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Driven Cavity ◽  
Newtonian Flows ◽  
Fully Implicit ◽  
Mesh Free ◽  
The Matrix

This paper introduces a novel meshless and Lagrangian approach for simulating non-Newtonian flows, named Lagrangian Differencing Dynamics (LDD). Second-order-consistent spatial operators are used to directly discretize and solve generalized Navier–Stokes equations in a strong formulation. The solution is obtained using a split-step scheme, i.e., by decoupling the solutions of the pressure and velocity. The pressure is obtained by solving a Poisson equation, and the velocity is solved in a semi-implicit formulation. The matrix-free solution to the equations, and Lagrangian advection of mesh-free nodes allowed for a fully parallelized implementation on the CPU and GPU, which ensured an affordable computing time and large time steps. A set of four benchmarks are presented to demonstrate the robustness and accuracy of the proposed formulation. The tested two- and three-dimensional simulations used Power Law, Casson and Bingham models. An Abram slump test and a dam break test were performed using the Bingham model, yielding visual and numerical results in accordance with the experimental data. A square lid-driven cavity was tested using the Casson model, while the Power Law model was used for a skewed lid-driven cavity test. The simulation results of the lid-driven cavity tests are in good agreement with velocity profiles and stream lines of published reports. A fully implicit scheme will be introduced in future work. As the method precisely reproduces the pressure field, non-Newtonian models that strongly depend on the pressure will be validated.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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