Pascal Bruel

Pressure-velocity coupling allowing acoustic calculation in low Mach number flow

Low Mach number flow computation in co-located grid arrangement requires pressure-velocity coupling in order to prevent the checkerboard phenomenon. Two broad categories of pressure-velocity coupling methods for unsteady flows can be distinguished based on the time-step dependency of the coupling coefficient in the definition of the transporting velocity on a face of a control volume. As an example of the time-step independent category, the AUSM^+-up scheme is studied. As an example of the second category, Rhie-Chow momentum interpolation methods are studied. Within the momentum interpolation techniques, again two broad categories can be distinguished based on the time-step dependency of the coupling coefficient used for unsteady flow computations, but when a steady state is reached. Variants of Rhie-Chow interpolation methods in each subcategory are studied on critical test cases. The result of the study is that for a good representation of unsteady flows containing acoustic information, the pressure-velocity coupling coefficient must explicitly depend on the time-step, but that the transporting velocity must become independent of the time-step when a steady state is reached.

Asymptotic Behavior of a Storage Unit Undergoing Cyclic Melting and Solidification Processes

In this paper, the asymptotic behavior of a thermal latent-energy storage system undergoing periodic charge/ discharge cycles is numerically investigated. The system consists of a cylindrical tank, which is randomly packed with spheres having uniform sizes and encapsulating paraffin as phase change material. The working fluid flowing through the bed is pure air. In the main part of this study, the entrance air temperature is supposed to vary in a sinusoidal way with a one-day period. The related governing equations are solved by a control-volume-based finite difference method. First- and second-law-based efficiency indicators are used to characterize the performances of the system. The effects of the phase change material melting point temperature on the energy efficiency and the irreversibility of the system are investigated. It is shown that in all situations, an asymptotic regime of charge/ discharge cycles is reached. For a zero-cycle-average Stefan number, the bed proves to behave like a quasi-perfect reject band filter (i.e., it yields a quasi-constant outlet temperature signal). In such a case, the energy efficiency reaches its maximum value, which also corresponds to a maximum of irreversibility. Thus, this indicates that because of such opposite trends, the design of practical systems should be based on a sound compromise, on a case-by-case basis, and between energy and exergy efficiencies on one side and utilization requirements on the other side. Finally, the predictive capability of such a model is assessed in the situation in which a realistic inlet temperature of the working fluid is considered. The predicted time evolution of the outlet temperature of the working fluid proves to be in good agreement with that reported in the selected reference

Pressure-velocity coupling for unsteady low Mach number flow simulations: An improvement of the AUSM+-up scheme

The proper scaling of the pressure-velocity coupling that arises from the momentum interpolation approach for unsteady calculation in low Mach number flow is first identified. Then, it is used to suggest a modification of the AUSM^+-up scheme that allows acoustic simulations in low Mach number flow.

Godunov-type schemes with an inertia term for unsteady full Mach number range flow calculations

An inertia term is introduced in the AUSM+-up scheme. The resulting scheme, called AUSM-IT (IT for Inertia Term), is designed as an extension of the AUSM+-up scheme allowing for full Mach number range calculations of unsteady flows including acoustic features. In line with the continuous asymptotic analysis, the AUSM-IT scheme satisfies the conservation of the discrete linear acoustic energy at first order in the low Mach number limit. Its capability to properly handle low Mach number unsteady flows, that may include acoustic waves or discontinuities, is numerically illustrated. The approach for building the AUSM-IT scheme from the AUSM+-up scheme is applicable to any other Godunov-type scheme.

Solving low Mach number Riemann problems by a momentum interpolation method

A momentum interpolation based scheme is proposed, giving satisfactory acoustic solutions in low Mach number regime.

Semi-implicit characteristic-based boundary treatment for acoustics in low Mach number flows

For low Mach number flow calculation, when acoustic waves have to be captured, semi-implicit methods allow to avoid the time-step limitation that arises when explicit schemes are used. A method is suggested to solve the boundary equations so that the semi-implicitness of the algorithm is maintained, as well as its pressure-velocity coupling. This method is studied theoretically and numerically, in the low Mach number regime. Partially non-reflective characteristic-based boundary conditions, with the linear relaxation form suggested by Rudy and Strikwerda, J. Comput. Phys. 36 (1980) 55-70], are considered. It is shown that their properties, well known in the framework of explicit schemes, are recovered with the proposed semi-implicit treatment and an acoustic CFL number significantly larger than unity.

EXPERIMENTAL INVESTIGATIONS OF PLANAR WATER SHEETS FLOWING UNDER GRAVITY

In this work, the main physical characteristics of plane water sheets flowing under gravity and surrounded by free air are experimentally investigated. By varying the mean flow rate through a 0.8 mm × 100 mm nozzle, water sheets are produced over a range of Reynolds and Weber numbers between 210 to 1240 and 0.37 to 13.52, respectively. First, the sensitivity of the sheets shapes to a mass flow rate variation is evidenced. For a sufficiently high flow rate, a liquid sheet forms with two rims bordering it. These rims join after a certain length Lc resulting in a triangle-like shape of the sheet. This characteristic length is compared with a theoretical prediction given by a model valid for Re 1. Furthermore, some capillary waves forming a striped pattern are present at the sheet interface near the rims and are propagating towards the central axis as the sheet falls. These waves are interpreted as the consequence of the displacement of a high curvature gradient zone at the rim-sheet interface as suggested by their stationary shape. The critical mass flow rate at which the sheet destabilization is systematically observed is Qc = 0.056kg.s−1. It corresponds to a Weber number We 2.7, a value in line with the theoretical one Weth = O(1) which usually indicates a sufficient condition to maintain a stable sheet. Such ruptures are characterized by the appearance of expanding hole(s), predominantly in the lower half of the sheet. The experimentally determined mean expansion velocity proved to be within ±20% of that provided by the well-known Culick expression. As expected, when considering mass flow rates below the above mentioned critical one, an intermittent regime of rupture is obtained characterized by the presence of sheets, threadlines, jets or drops.