Nombre de Mach

Résumé

Le nombre de Mach est un nombre sans dimension, noté Ma, qui exprime le rapport de la vitesse d'un objet dans un fluide à la vitesse du son dans ce même fluide. La vitesse du son dans un gaz variant avec sa nature et sa température, le nombre de Mach ne correspond pas à une vitesse fixe, il dépend des conditions locales. Il a été ainsi nommé en l'honneur du physicien et philosophe autrichien Ernst Mach par Jakob Ackeret. Définition du nombre de Mach Aux températures habituelles et dans l'air, la vitesse du son vaut environ ou . Le nombre de Mach mesure le rapport entre les forces liées au mouvement et la compressibilité du fluide. : \mathrm{Ma} = \frac V a où :

Ma est le nombre de Mach ;
V est la vitesse de l'objet (par rapport à son environnement) ;
a est la vitesse de propagation ou célérité du son dans l'environnement considéré. Elle représente la vitesse de propagation de tout ébranlement produit dans le milieu.

La vitesse du son dans l'air, l

Source officielle

https://fr.wikipedia.org/wiki/Nombre_de_Mach

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Chargement

The Role of Impeller Outflow Conditions on the Performance of Vaned Diffusers

Jürg Alexander Schiffmann

Highly loaded impellers, typically used in turbocharger and gas turbine applications, exhaust an unsteady, transonic flow that is nonuniform across the span and pitch and swirling at angles approaching tangential. With the exception of the flow angle, conflicting data exist regarding whether these attributes have substantial influence on the performance of the downstream diffuser. This paper quantifies the relative importance of the flow angle, Mach number, nonuniformity, and unsteadiness on diffuser performance, through diffuser experiments in a compressor stage and in a rotating swirling flow test rig. This is combined with steady and unsteady Reynolds-averaged Navier–Stokes (RANS) computations. The test article is a pressure ratio 5 turbocharger compressor with an airfoil vaned diffuser. The swirling flow rig is able to generate rotor outflow conditions representative of the compressor except for the periodic pitchwise unsteadiness and fits a 0.86 scale diffuser and volute. In both rigs, the time-mean impeller outflow is mapped across a diffuser pitch using miniaturized traversing probes developed for the purpose. Across approximately two-thirds of the stage operating range, diffuser performance is well correlated to the average impeller outflow angle when the metric used is effectiveness, which describes the pressure recovery obtained relative to the maximum possible given the average inflow angle and Mach number and the vane exit metal angle. Utilizing effectiveness captures density changes through the diffuser at higher Mach numbers; a 10% increase in pressure recovery is observed as the inlet Mach number is increased from 0.5 to 1. Further, effectiveness is shown to be largely independent of the time-averaged spanwise and unsteady pitchwise nonuniformity from the rotor; this independence is reflective of the strong mixing processes that occur in the diffuser inlet region. The observed exception is for operating points with high time-averaged vane incidence. Here, it is hypothesized that temporary excursions into high-loss flow regimes cause a nonlinear increase in loss as large unsteady angle variations pass by from the rotor. Given that straight-channel diffuser design charts typically used in preliminary radial vaned diffuser design capture neither streamtube area changes from impeller exit to the diffuser throat nor vane incidence effects, their utility is limited. An alternative approach, utilizing effectiveness and vane leading edge incidence, is proposed.

American Society of Mechanical Engineers2017

Chargement

Highly-loaded impellers, typically used in turbocharger and gas turbine applications, exhaust an unsteady, transonic flow that is non-uniform across the span and pitch and swirling at angles approaching tangential. With the exception of the flow angle, conflicting data exist regarding whether these attributes have substantial influence on the performance of the downstream diffuser. This paper quantifies the relative importance of the flow angle, Mach number, non-uniformity and unsteadiness on diffuser performance, through diffuser experiments in a compressor stage and in a rotating swirling flow test rig. This is combined with steady and unsteady Reynolds-Averaged Navier Stokes computations. The test article is a pressure ratio 5 turbocharger compressor with an airfoil vaned diffuser. The swirling flow rig is able to generate rotor outflow conditions representative of the compressor except for the periodic pitchwise unsteadiness, and fits a 0.86 scale diffuser and volute. In both rigs, the time-mean impeller outflow is mapped across a diffuser pitch using miniaturized traversing probes developed for the purpose. Across approximately two-thirds of the stage operating range, diffuser performance is well correlated to the average impeller outflow angle when the metric used is effectiveness, which describes the pressure recovery obtained relative to the maximum possible given the average inflow angle, Mach number and the vane exit metal angle. Utilizing effectiveness captures density changes through the diffuser at higher Mach numbers; a 10% increase in pressure recovery is observed as the inlet Mach number is increased from 0.5 to 1. Further, effectiveness is shown to be largely independent of the time-averaged spanwise and unsteady pitchwise non-uniformity from the rotor; this independence is reflective of the strong mixing processes that occur in the diffuser inlet region. The observed exception is for operating points with high time-averaged vane incidence. Here, it is hypothesized that temporary excursions into high-loss flow regimes cause a non-linear increase in loss as large unsteady angle variations pass by from the rotor. Given that straight-channel diffuser design charts typically used in preliminary radial vaned diffuser design capture neither streamtube area changes from impeller exit to the diffuser throat nor vane incidence effects, their utility is limited. An alternative approach, utilizing effectiveness and vane leading edge incidence, is proposed.

Amer Soc Mechanical Engineers2016

Chargement

An algorithm for unsteady viscous flows at all speeds

Michel Deville

An algorithm for the simulation of unsteady, viscous, stratified compressible flows, which remains valid at all speeds, is presented. The method is second-order accurate in both space and time and is independent of the Mach number. In order to remove the stiffness of the numerical problem due to the large disparity between the flow speed and the acoustic wave speed at low Mach number, an approximate Newton method, based on artificial compressibility, is proposed. Additionally, a modified advection upstream splitting method (AUSM +) scheme is used, which permits accurate computations of both compressible and incompressible flows. A detailed description of the method and an efficiency comparison with other approximate Newton methods described in the literature are given. Furthermore, it is shown that the accuracy of the algorithm is not dependent on the Mach number through the computations of various benchmark test cases. Copyright (C) 2000 John Wiley & Sons, Ltd.

1999

Chargement

The Role of Impeller Outflow Conditions on the Performance of Vaned Diffusers

Jürg Alexander Schiffmann

American Society of Mechanical Engineers2017

Amer Soc Mechanical Engineers2016