Flow Of Compressible Viscous Fluid Research Articles

Inverse of Divergence and Homogenization of Compressible Navier–Stokes Equations in Randomly Perforated Domains

We analyze the behavior of weak solutions to compressible viscous fluid flows in a bounded domain in {{,mathrm{{mathbb {R}}},}}^3, randomly perforated by tiny balls with random size. Assuming the radii of the balls scale like varepsilon ^alpha , alpha > 3, with varepsilon denoting the average distance between the balls, the problem homogenize to the same limiting equation. Our main contribution is a construction of the Bogovskiĭ operator, uniformly in varepsilon , without any assumptions on the minimal distance between the balls.

Symmetry actions and brackets for adjoint-symmetries. II: Physical examples

AbstractSymmetries and adjoint-symmetries are two fundamental (coordinate-free) structures of PDE systems. Recent work has developed several new algebraic aspects of adjoint-symmetries: three fundamental actions of symmetries on adjoint-symmetries; a Lie bracket on the set of adjoint-symmetries given by the range of a symmetry action; a generalised Noether (pre-symplectic) operator constructed from any non-variational adjoint-symmetry. These results are illustrated here by considering five examples of physically interesting nonlinear PDE systems – nonlinear reaction-diffusion equations, Navier-Stokes equations for compressible viscous fluid flow, surface-gravity water wave equations, coupled solitary wave equations and a nonlinear acoustic equation.

New Thought on Matsumura–Nishida Theory in the L_p–L_q Maximal Regularity Framework

This paper is devoted to proving the global well-posedness of initial-boundary value problem for Navier–Stokes equations describing the motion of viscous, compressible, barotropic fluid flows in a three dimensional exterior domain with non-slip boundary conditions. This was first proved by an excellent paper due to Matsumura and Nishida (Commun Math Phys 89:445–464, 1983). In [10], they used energy method and their requirement was that space derivatives of the mass density up to third order and space derivatives of the velocity fields up to fourth order belong to L_2 in space-time, detailed statement of Matsumura and Nishida theorem is given in Theorem 1 of Sect. 1 of context. This requirement is essentially used to estimate the L_infty norm of necessary order of derivatives in order to enclose the iteration scheme with the help of Sobolev inequalities and also to treat the material derivatives of the mass density. On the other hand, this paper gives the global wellposedness of the same problem as in [10] in L_p (1 <p le 2) in time and L_2cap L_6 in space maximal regularity class, which is an improvement of the Matsumura and Nishida theory in [10] from the point of view of the minimal requirement of the regularity of solutions. In fact, after changing the material derivatives to time derivatives by Lagrange transformation, enough estimates obtained by combination of the maximal L_p (1 <p le 2) in time and L_2cap L_6 in space regularity and L_p–L_q decay estimate of the Stokes equations with non-slip conditions in the compressible viscous fluid flow case enable us to use the standard Banach’s fixed point argument. Moreover, one of the purposes of this paper is to present a framework to prove the L_p–L_q maximal regularity for parabolic-hyperbolic type equations with non-homogeneous boundary conditions and how to combine the maximal L_p–L_q regularity and L_p–L_q decay estimates of linearized equations to prove the global well-posedness of quasilinear problems in unbounded domains, which gives a new thought of proving the global well-posedness of initial-boundary value problems for systems of parabolic or parabolic-hyperbolic equations appearing in mathematical physics.

Numerical simulation of the gas flow with radiation and heat transfer

In this article we focus on the heating of the solid body placed in the vicinity of the intense heat source. We simulate the heat transfer caused by the direct contact with surrounding heated gas. Furthermore it is necessary to take into account the heat transfer caused by the radiation, which radically affects the resulting heat flux. We work with the non-stationary viscous compressible fluid flow with additional heat sources, described by the RANS equations. The heat radiation is simulated using other supplemented equations. The heat transfer equations are solved inside the considered body.

Solution Formula of the Compressible Fluid Motion in Three Dimension Euclidean Space using Fourier Transform

We derive a detailed determination of the solution formula for the compressible viscous fluid flow in three dimensional Euclidean space using Fourier transform. For the further research, we can not only generalized the model problem to the N-dimensional Euclidean space (N>3) but also we can estimate the solution operator families of the model problem.

Numerical study of two models for viscous compressible fluid flows

Our aim is to evaluate the modelling capability of a recently proposed (Eulerian) model for viscous and heat conducting compressible fluids. The new model differs from the Navier-Stokes in the structure of the diffusive terms. Most notably, it includes a mass diffusive mechanism. Despite the lack of well-posedness theory, one has to recognize that the standard Navier-Stokes equations are known to give reasonably accurate results for numerous standard problems. Hence, the new model can not deviate too much from the Navier-Stokes equations for such cases, is it to be an accurate model. The purpose of the paper is to compare the new model with Navier-Stokes and determine an unknown model parameter (α) in the new model such that the best matches are obtained. Using a high-order discontinuous Galerkin scheme, with careful implementations of the boundary conditions, we perform accurate simulations of the two models for a suite of test cases. For the grid converged results, we have, for each problem, compared the two models with respect to a number of measures such as cL, cD, cM, skin friction coefficients, pressure coefficients and Mach number or pressure isolines. The numerical results reveal a remarkable sameness (the differences are typically 1%) of both models when α=1.

Resonance phenomena in a channel with oscillating walls

In the article we consider the flow of viscous compressible fluid in a channel with oscillating walls. The obtained solutions of linearized Navier–Stokes equations suggest that resonance phenomena are possible under certain conditions, namely, under the particular relation between the frequency of wall vibration, the geometrical characteristics of a channel and speed of sound in the fluid. Resonance phenomena result in the periodical changes of flow parameters with maximum amplitude. The numerical simulations based on full Navier–Stokes equations show that great increase in the mass rate of the flow can occur even if fluid is pumped at constant pressure gradient.

Characterization of temperature-dependent fluid properties in compressible viscous fluid flow induced by oscillation of disk

Abstract Time-dependent compressible flow of viscous fluid with temperature dependent density, thermal conductivity and viscosity is considered. The motion in fluid is generated due to periodic oscillations of rotating disk. The normalized system of partial differential equations is achieved by adopting similarity transformations. The obtained system is then solved numerically using Successive over Relaxation (SOR) method and finite difference schemes. The local similar solutions are presented. One-dimensional graphs, two-dimensional contours and three-dimensional flow phenomenon are drawn graphically. Tabular description of various physical parameters is also presented.

A Compressible Fluid Flow with Double-Deck Structure Inside an Axially Symmetric Wavy-Wall Pipe

The problem of viscous compressible fluid flow in an axially symmetric pipe with small periodic irregularities on the wall is considered for large Reynolds numbers. An asymptotic solution with double-deck structure of the boundary layer and unperturbed core flow is obtained. Numerical investigations of the influence of the density of the core flow on the flow behavior in the near-wall region are presented.

Transient boundary layer flow of viscous compressible fluid past a heated sphere with the effect of Mach number

Abstract A two-dimensional transient boundary layer flow of an unsteady, viscous, compressible fluid past a heated sphere with the effect of Mach number is considered. The governing boundary layer equations are reduced to nonsimilar form, and these are solved numerically by three methods, namely, the finite difference method for all time regime, perturbation solutions for small time regime, and the asymptotic solutions for large time regime. Comparisons of the results show a good agreement between the above mentioned methods. Effects of various practical values of the surface temperature parameter, α and the Mach number, M 0 on the local shear stress, the rate of heat transfer, streamlines and isoenthalpies are shown graphically. Further, it is observed that increase in the value of Mach number, M 0 , leads to an increase in the local shear stress and the rate of heat transfer; whereas opposite effect is found in case of local shear stress once the point of separation occured. On the other hand size of the vortex found to be decreased with an increase in Mach number.

The simulation of the gas flow through the porous media and fences

The paper is focused on the numerical simulation of the compressible gas flow through the porous media and fences. We work with the the non-stationary viscous compressible fluid flow, described by the RANS equations. The flow through the porous media is characterized by the loss of momentum. It is possible to use various methods for the simulation of such flow. Here we present the approach with the modification of the source term, and other possibilities using the modification of the face flux. The original approach was presented recently by the authors analysing the modification of the Riemann problem with one-side initial condition, complemented with the Darcy’s law and added inertial loss. Another aim of this paper is the evaluation and estimate of the forces acting on the diffusible barrier (fence) with given parameters. The presented examples were obtained with the own-developed code for the solution of the compressible gas flow.

An efficient runtime mesh smoothing technique for 3D explicit Lagrangian free‐surface fluid flow simulations

SummaryA fast runtime mesh smoothing algorithm for explicit Lagrangian simulations of 3D weakly compressible viscous fluid flows, implemented in conjunction with the particle finite element method (PFEM), is proposed. The formulation for weakly compressible fluids allows for the use of an explicit time integration scheme. Explicit solvers are appealing for large‐scale engineering problems characterized by fast dynamics and/or a high degree of nonlinearity. However, the conditional stability of these schemes requires the use of small time increments, proportional to the size of the element in the mesh with the worst geometrical quality. The Lagrangian description of the PFEM requires an efficient and robust runtime mesh generator algorithm, such as the Delaunay tessellation, to create new meshes during the analysis, whenever the current ones get too distorted because of the motion of the mesh nodes. When 3D problems are considered, a computationally effective mesh‐improving algorithm is also required because, in 3D, the Delaunay tessellation loses some of its optimality properties holding in 2D so that badly shaped tetrahedra are frequently included in the triangulation, leading to unacceptably small stable time step sizes for the explicit solver. To this purpose, a novel and efficient mesh smoothing technique is here proposed, exploiting an elastic analogy that allows for the use of the same explicit and parallelizable architecture of the fluid solver. This smoothing algorithm has been specifically designed to ensure reasonably large critical time step sizes at an acceptable computational cost. This is particularly appealing for the application of explicit Lagrangian PFEM in large‐scale 3D engineering problems, but it could be conveniently applied also to regularize the mesh and improve the solution of implicit solvers.

Numerical simulation of fluid flow through simplified blade cascade with prescribed harmonic motion using discontinuous Galerkin method

This paper deals with a numerical simulation of compressible viscous fluid flow around three flat plates with prescribed harmonic motion. This arrangement presents a simplified blade cascade with forward wave motion. The aim of this simulation is to determine the aerodynamic forces acting on the flat plates. The mathematical model describing this problem is formed by Favre-averaged system of Navier-Stokes equations in arbitrary Lagrangian-Eulerian (ALE) formulation completed by one-equation Spalart-Allmaras turbulence model. The simulation was performed using the developed in-house CFD software based on discontinuous Galerkin method, which offers high order of accuracy.

Numerical and experimental study of fluid flow in simplified blade cascade with prescribed harmonic motion

In this paper, a numerical simulation and experimental measurements of compressible viscous fluid flow in simplified blade cascade are compared. The cascade consists of five flat plates three of which perform prescribed harmonic motion. The computed unsteady velocity field is compared with experimental measurements at selected points. Moreover, the power spectral density corresponding to the frequency of harmonic motion is computed for both the numerical and experimental data and compared. The numerical simulation was performed using the developed in-house CFD software based on the discontinuous Galerkin method, which offers high order of accuracy.

Numerical simulation of fluid flow through simplified blade cascade with prescribed harmonic motion using discontinuous Galerkin method

This paper deals with a numerical simulation of compressible viscous fluid flow around three flat plates with prescribed harmonic motion. This arrangement presents a simplified blade cascade with forward wave motion. The aim of this simulation is to determine the aerodynamic forces acting on the flat plates. The mathematical model describing this problem is formed by Favre-averaged system of Navier-Stokes equations in arbitrary Lagrangian-Eulerian (ALE) formulation completed by one-equation Spalart-Allmaras turbulence model. The simulation was performed using the developed in-house CFD software based on discontinuous Galerkin method, which offers high order of accuracy.

Numerical and experimental study of fluid flow in simplified blade cascade with prescribed harmonic motion

In this paper, a numerical simulation and experimental measurements of compressible viscous fluid flow in simplified blade cascade are compared. The cascade consists of five flat plates three of which perform prescribed harmonic motion. The computed unsteady velocity field is compared with experimental measurements at selected points. Moreover, the power spectral density corresponding to the frequency of harmonic motion is computed for both the numerical and experimental data and compared. The numerical simulation was performed using the developed in-house CFD software based on the discontinuous Galerkin method, which offers high order of accuracy.

The simulation of the flow through the porous media and diffusible barriers

Here we work with the RANS equations describing the non-stationary viscous compressible fluid flow. We focus on the numerical simulation of the flow through the porous media, characterized by the loss of momentum. Further we simulate the flow through the set of diffusible barriers. Here we analyze the modification of the Riemann problem with one-side initial condition, complemented with the Darcy’s law and added inertial loss. We show the computational results obtained with the own-developed code for the solution of the compressible gas flow.

Numerical Solution of Unsteady Viscous Compressible Fluid Flow along a Porous Plate with Induced Magnetic Field

Numerical Solution of Unsteady Viscous Compressible Fluid Flow along a Porous Plate with Induced Magnetic Field

Numerical simulation of reactive polymer flow during rotational molding using smoothed particle hydrodynamics method and experimental verification

A numerical study of flow behavior and the heat transfer process of reactive polymer in reactive rotational molding systems is carried out using the Smoothed Particle Hydrodynamics method (SPH). The flow of reactive polymer during rotational molding inside a horizontal rotating cylinder is modeled as the slightly compressible viscous fluid flow and with free surface. These simulations show the influence of process parameters on the flow of polymer. Especially, the influence of the change of viscosity on the flow, due to the chemical reactions, is simulated by using an adapted viscosity expression. For a constant rotational speed, several flow regimes are observed as follows: the fluid remains at the bottom of the mold with the formation of a thin layer on the surface if the viscosity of reactive polymer is very low (less than 850 Pa.s), the presence of cascades is shown (after the point of maximum height) if the viscosity is higher (850 to 980 Pa.s), and the fluid moves at the same speed as the mold if the viscosity is sufficiently high (approximately 1230 Pa.s). The heat transfer between the mold and reactive polymer is also simulated. The results of SPH simulations are then compared to the experimental results conducted on polyurethane (TPU) system based on 1,6-hexamethylene diisocyanate (HDI, Sigma Aldrich, France), polyethylene glycol (PEG 1000) as macrodiol, 1,3-propanediol (PDO), and dibutyl tin dilaurate (DBTDL).

The boundary data immersion method for compressible flows with application to aeroacoustics

This paper introduces a virtual boundary method for compressible viscous fluid flow that is capable of accurately representing moving bodies in flow and aeroacoustic simulations. The method is the compressible extension of the boundary data immersion method (BDIM, Maertens & Weymouth (2015), [18]). The BDIM equations for the compressible Navier–Stokes equations are derived and the accuracy of the method for the hydrodynamic representation of solid bodies is demonstrated with challenging test cases, including a fully turbulent boundary layer flow and a supersonic instability wave. In addition we show that the compressible BDIM is able to accurately represent noise radiation from moving bodies and flow induced noise generation without any penalty in allowable time step.