Subsonic regime

Figure 13.1 Near-field entrainment measurements in noncircular jets based on experimental and computational studies [16]. Subsonic regimes. Experiments 1 — elliptic [37] 2 — square [16] 3 — round [38]. Simulations 4 — square [16]. A ...

Rowe and co-workers are developing a so-called diffusion technique to extend the temperature and pressure range. The technique will use the conversion of the initial kinetic energy (per unit volume) of the jet into a pressure increase downstream of the mass spectrometer, when the flow is brought from a supersonic to a subsonic regime through suitably shaped tubing. Also, it has been shown that the use of pulsed Laval nozzles reduces the appreciable amounts of gas that are consumed in the continuous flow CRESU apparatus [55]. 

It is shown in specialized texts on fluid dynamics that a convergent-diveigent nozzle is needed to accelerate a gas from subsonic to supersonic conditions, since gas acceleration in the subsonic regime requires the flow area to diminish with speed, while gas acceleration from sonic to supersonic speeds requires the flow area to expand with speed. The subsonic, convergent part of the nozzle is linked to the supersonic, divergent part of the nozzle by a duct of constant flow area, known as the throat, which is kept very short in practice in order to avoid frictional losses. The throat is the only section of the nozzle in which sonic flow can occur, and it is impossible for the throat to support any speed greater than sonic. The above remarks apply to all polytropic... 

This regime exists at very low values of the Reynolds number, usually below Re 10. In the true subdynamic regime, the character of the flow ceases to depend on the Reynolds number, and the flow field becomes self-similar. Microfluidic devices are rarely, if at all, employed in the subsonic regime— usually, the inertial effects remain noticeable in them. The regime, however, serves as a useful reference asymptotic state. 

There are two flow regimes corresponding to sonic (or choked) flow for liigher pressure drops and subsonic flow for lower pressure drops. The transition between the two flow regimes occurs at tlie dimensionless critical pressure ratio, Ter,I, which is related to tlie gas lieiit capacity ratio y via... 

The flow factor for equation 7.6.2, v , is dependant on the flow regime as follows For subsonic flows... 

According to the equations for supersonic pipe flow, pressure increases and velocity decreases in the direction of flow. However, this flow regime is unstable, and a supersonic stream entering a pipe of constant cross section undergoes a compression shock, the result of which is an abrupt and finite increase in pressure and decrease in velocity to a subsonic value. 

Unless otherwise stated, neutrino-driven winds refer to transonic as well as subsonic winds, the latter being referred to as a breeze regime (e.g. [24])... 

Several wind models of analytical nature exist. They differ in their level of physical sophistication and in their way to parametrize the wind characteristics. In all cases, the wind is assumed to be spherically symmetric, which appears to be a reasonable first approximation even in two-dimensional simulations, at least late enough after core bounce. In addition, the wind is generally treated as a stationary flow, meaning no explicit time dependence of any physical quantity at a given radial position. Newtonian and post-Newtonian descriptions of a spherically symmetric stationary neutrino-driven (supersonic) wind or (subsonic) breeze emerging from the surface of a PNS have been developed. The reader is referred to [24] for the presentation of a Newtonian, adiabatic and steady-state model for the wind and breeze regimes, and for a general-relativistic steady-state wind solution. 

VHIM is based on a simple transfer to the pipe-plus-valve case of the method outlined in Section 6.4 for calculating flow in a pipe. It will be less accurate than SVHIM in the subsonic-valve region because only the liquid valve coefficient, C , is used in this flow regime, rather than the more representative gas coefficient, Cg. This causes a small discontinuity to occur when sonic flow conditions are met in the valve, and the C characterization is superseded by a characterization based on Cg. The loss in accuracy compared with SVHIM is 3% or less, but VHIM retains the disadvantage that it requires an iterative solution. 

Rgure 14.8 Pressure profile downstream of throat when the throat pressure Is critical subsonic and supersonic regimes (nozzle outlet corresponds to a normalized downstream distance of unity). 

Fan J, Shen C (1999) Statistical simulations of low-speed unidirectional flows in transition regime. In Brun A et al (eds) Rarefied gas dynamics, vol 2. Cepadus-Editions, Toulouse, p 245 Sun Q, Boyd ID (2002) A direct simulation method for subsonic microscale gas flows. J Comput Phys 179 400-425... 

Usually, the regime of gas flow in a macrochannel refers to viscous and compressibility effects, respectively quantified by the Reynolds number Re and the Mach number Ma. For low Reynolds numbers (typically for Re < 2,000), the flow is laminar and it becomes turbulent for higher values of Re. For Ma < 1, the flow is subsonic and for Ma > 1, it is supersonic. Generally, if Ma > 0.3, compressibility effects should be taken into account. 

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