Isothermal Compressible Flow Research Articles

Rigorous justification of the hydrostatic approximation limit of viscous compressible flows

This paper considers the asymptotic limit of small aspect ratio between vertical and horizontal spatial scales for viscous isothermal compressible flows. In particular, it is observed that fast vertical acoustic waves arise and induce an averaging mechanism of the density in the vertical variable, which at the limit leads to the hydrostatic approximation of compressible flows, i.e., the compressible primitive equations of atmospheric dynamics. We justify the hydrostatic approximation for general as well as “well-prepared” initial data. The initial data is called well-prepared when it is close to the hydrostatic balance in a strong topology. Moreover, the convergence rate is calculated in the well-prepared initial data case in terms of the aspect ratio, as the latter goes to zero.

General Exact Law of Compressible Isentropic Magnetohydrodynamic Flows: Theory and Spacecraft Observations in the Solar Wind

Abstract Various forms of exact laws governing magnetohydrodynamic (MHD) turbulence have been derived either in the incompressibility limit, or for isothermal compressible flows. Here we propose a more general method that allows us to obtain such laws for any turbulent isentropic flow (i.e., constant entropy). We demonstrate that the known MHD exact laws (incompressible and isothermal) and the new (polytropic) one can be obtained as specific cases of the general law when the corresponding closure equation is stated. We also recover all known exact laws of hydrodynamic (HD) turbulence (incompressible, isothermal, and polytropic) from this law in the limit B = 0. We furthermore show that the difference between the two forms (isothermal and polytropic) of the MHD exact laws of interest in this work resides in some of the source terms and in the explicit form of the flux term that depends on internal energy. Finally, we apply these two forms to Parker Solar Probe data taken in the inner heliosphere to highlight how the different closure equations affect the energy cascade rate estimates.

Numerical method for 3D two-component isothermal compressible flows with application to digital rock physics

Abstract We propose a numerical algorithm for simulations of two-component viscous compressible isothermal flows with surface effects in 3D domains of complex shape with voxel representation of geometry. The basic mathematical model is the regularized system of Navier–Stokes–Cahn–Hilliard equations. Simulations of droplet spreading over a flat base and displacement of one liquid by another one in a pore space of real rock sample are carried out. The simulation results demonstrate the applicability and good efficiency of the used system of equations, the corresponding difference scheme, and its implementation algorithms for numerical solution of the considered class of problems.

Isothermal compressible flow solver for prediction of cavitation erosion

Cavitation erosion can be observed on hydraulic mechanical devices and has long been studied as a challenging research topic. In this paper, a practical method to predict cavitation erosion was developed. To simulate cavitating flows using computational fluid dynamics (CFD), an isothermal compressible cavitating flow solver was developed using the OpenFOAM toolkit. A cavitation erosion coefficient was proposed as a function of the cavitation and Reynolds numbers. From the simulations, the cavitation erosion coefficients were calculated using metamodeling methods. Finally, the developed practical method of cavitation erosion was applied to a marine propeller. As observed in experiments, cavitation erosion was predicted near the propeller tip.

Comparative study of incompressible and isothermal compressible flow solvers for cavitating flow dynamics

Incompressible flow solvers are generally used for numerical analysis of cavitating flows, but with limitations in handling compressibility effects on vapor phase. To study compressibility effects on vapor phase and cavity interface, pressure-based incompressible and isothermal compressible flow solvers based on a cell-centered finite volume method were developed using the OpenFOAM libraries. To validate the solvers, cavitating flow around a hemispherical head-form body was simulated and validated against the experimental data. The cavity shedding behavior, length of a re-entrant jet, drag history, and the Strouhal number were compared between the two solvers. The results confirmed that computations of the cavitating flow including compressibility effects improved the reproduction of cavitation dynamics.

Leak Before Break: Studies in Support of New R6 Guidance on Leak Rate Evaluation

The concept of leak-before-break (LBB) is often used in safety cases for pressure systems, particularly, in the nuclear industry. An important factor in making a LBB case is in the prediction of the leak rate of fluid through a crack. This paper presents a summary of a program of work, which had the aim of improving guidance on leak rate evaluation for the LBB procedures in the R6 defect assessment methodology. Methods of calculating leak rates have been reviewed, and this has led to a crack morphology model being proposed, which represents single-phase isothermal compressible flow through a crack. In the crack morphology model, the flow is assumed by default to be fully rough turbulent, and the effective roughness to vary between a local roughness value for narrow cracks and a global value (i.e., the overall crack contours) for wide cracks. The effect of pressure drops due to changes in the flow direction at crack turns has also been included. Calculations using the model show that the friction factor relation due to Spence et al. (1991, “Leakage Flow Through Small Cracks—Report of Second Stage of Experimental Work,” unpublished) gives better agreement with measured flow rates than that due to Button et al. (1978, “Gas Flow Through Cracks,” ASME J. Fluids Eng., 100, pp. 453–458), which tends to overestimate the flow rate for the examples studied. The inclusion of an inertial pressure term arising from changes in overall flow direction appears to be justified.

FROM THE BOLTZMANN TO THE LATTICE-BOLTZMANN EQUATION: BEYOND BGK COLLISION MODELS

In this work, we present a derivation for the lattice-Boltzmann equation directly from the linearized Boltzmann equation, combining the following main features: multiple relaxation times and thermodynamic consistency in the description of non isothermal compressible flows. The method presented here is based on the discretization of increasingly order kinetic models of the Boltzmann equation. Following a Gross-Jackson procedure, the linearized collision term is developed in Hermite polynomial tensors and the resulting infinite series is diagonalized after a chosen integer N, establishing the order of approximation of the collision term. The velocity space is discretized, in accordance with a quadrature method based on prescribed abscissas (Philippi et al., Phys. Rev E 73, 056702, 2006). The problem of describing the energy transfer is discussed, in relation with the order of approximation of a two relaxation-times lattice Boltzmann model. The velocity-step, temperature-step and the shock tube problems are investigated, adopting lattices with 37, 53 and 81 velocities.

A segregated method for compressible flow computation Part I: isothermal compressible flows

AbstractTraditionally, coupled methods have been employed for the computation of compressible flows, whereas segregated methods have been preferred for the computation of incompressible flows. Compared to coupled methods, segregated solvers present the advantage of reduced computer memory and CPU time requirements, although at the cost of an inferior robustness. Therefore, in a series of papers we present unified computational techniques to compute compressible and incompressible flows with segregated stabilized methods. The proposed algorithms have an increased robustness compared to existing techniques, while possessing additional benefits such as employing standard pressure boundary conditions. In this first part, the thermodynamics of isothermal, thermally perfect compressible flows is set up in the framework of symmetric systems and the corresponding segregated algorithms are introduced. Copyright © 2005 John Wiley & Sons, Ltd.

Adhesion and Removal of Particles from Surfaces Under Humidity Controlled Air Stream

The adhesion and the removal of individual micrometer-sized particles on a plane substrate are studied using an air shear flow cell. Laminar isothermal compressible flow characterization enables us to analyze the effect of various parameters such as particle size, air humidity, surface nature and surface charge on the aerodynamic forces required to remove the particles from the substrate. The results show that the increase of humidity (up to a critical value) favors particle removal when particles adhere under strong electrostatic forces on a non-conductive charged substrate. On the contrary, the existence of a capillary force disfavors particle removal beyond this critical humidity. The increase of the humidity disfavors the removal of particles in contact with an uncharged substrate. The results are interpreted in terms of a global adhesion force using a force and torque balance on a single particle in contact with a plane substrate. Moreover, the use of a high-speed video recording system enables us to determine the particle removal mechanisms as a function of the particle Reynolds number.

Laminar Compressible Flow Over a Stationary Disk in a Rotating Cylinder

The laminar isothermal compressible flow in a rotating cylinder with a stationary bottom is treated both numerically and by boundary layer matching. The numerical solution of the Navier-Stokes equations is based on a modified Cheng-Allen finite difference scheme. An approximate solution is obtained by matching boundary layers to an interior core. For sufficiently low Ekman numbers, the approximate and numerical solutions are in close agreement. The compressibility is shown to increase the angular velocity in the core and to decrease the meridional circulation. When the aspect ratio of the cylinder is increased, both the angular velocity in the core and the meridional circulation increase.

An Extended Variational Formulation for Isothermal Gas-Dynamic Lubrication

Abstract An extended variational formulation is derived which can be applied to problems in isothermal compressible flow where the medium obeys the perfect gas law. The Reynold’s approximations for fluid film lubrication have been applied to this variational formulation to obtain an expression that is applicable to the field of gas-dynamic lubrication. This variational formulation for gas-dynamic lubrication has as its Euler-Lagrange equation, the Reynolds’ equation of lubrication for a perfect gas. The extended variational formulation is shown to differ from the classical Lagrangian expression with respect to its form and to its applicability to nonlinear problems.