Subsonic gas flow

The dimensionless parameter % or xm is a function of Mach number and can be determined from a universal curve for the atomization of various liquid metals, i.e., a plot of % or xm vs- Mach number, as presented by Bradley in Ref. 329 for subsonic gas flow, and in... 

Derived from an analytical model for flat, infinitely thick liquid layer Effects of gas compressibility included Effects of gas/liquid ratio, liquid viscosity, and nozzle geometry not included X and Xm can be determined from the universal curves for metals in P29] for subsonic gas flow and in [330] for sonic/supersonic gas flow ... 

Mathematical models for steady state subsonic gas flow in a straight pipe. 

Additional droplet size work under flow conditions was not undertaken. The empirical expressions provided by Ingebo and Foster (10) were developed under conditions sufficiently similar to those present in the ACR to justify their use as a first approximation. Their data were derived from the injection of sprays into a transverse subsonic gas flow. They obtained the following correlation in Equations 5 and 6 between drop size parameters and force ratios by using dimensional analysis. 

Darbandi M, Roohi E (2011) Study of supersonic-subsonic gas flows through micro-nano scale nozzles using unstructured DSMC solver. Microfluids Nanofluids 10(2) 321-335... 

B. Hiller, J.C. McDaniel, E.C. Rea, Jr., R.K. Hanson Laser-induced fluorescence technique for velocity field measurements in subsonic gas flows. Opt. Lett. 8, 474 (1983)... 

For the delivery of atomization gas, different types of nozzles have been employed, such as straight, converging, and converging-diverging nozzles. Two major types of atomizers, i.e., free-fall and close-coupled atomizers, have been used, in which gas flows may be subsonic, sonic, or supersonic, depending on process parameters and gas nozzle designs. In sonic or supersonic flows, the mass flow rate of atomization gas can be calculated with the following equation based on the compressible fluid dynamics ... 

In a supersonic gas flow, the convective heat transfer coefficient is not only a function of the Reynolds and Prandtl numbers, but also depends on the droplet surface temperature and the Mach number (compressibility of gas). 154 156 However, the effects of the surface temperature and the Mach number may be substantially eliminated if all properties are evaluated at a film temperature defined in Ref. 623. Thus, the convective heat transfer coefficient may still be estimated using the experimental correlation proposed by Ranz and Marshall 505 with appropriate modifications to account for various effects such as turbulence,[587] droplet oscillation and distortion,[5851 and droplet vaporization and mass transfer. 555 It has been demonstrated 1561 that using the modified Newton s law of cooling and evaluating the heat transfer coefficient at the film temperature allow numerical calculations of droplet cooling and solidification histories in both subsonic and supersonic gas flows in the spray. 

A nozzle used for a rocket is composed of a convergent section and a divergent section. The connected part of these two nozzle sections is the minimum cross-sectional area termed the throat The convergent part is used to increase the flow velocity from subsonic to sonic velocity by reducing the pressure and temperature along the flow direction. The flow velocity reaches the sonic level at the throat and continues to increase to supersonic levels in the divergent part. Both the pressure and temperature of the combustion gas flow decrease along the flow direction. This nozzle flow occurs as an isentropic process. 

The supersonic air induced into the air-intake is converted into a pressurized subsonic airflow through the shock wave in the air-intake. The fuel-rich gas produced in the gas generator pressurizes the combustion chamber and flows into the ramburner through a gas flow control system. The pressurized air and the fuel-rich gas produce a premixed and/or a diffusional flame in the ramburner. The combustion gas flows out through the convergent-divergent nozzle and is accelerated to supersonic flow. 

Let the rear boundary of reaction wave move with.a specific velocity Up along the line P in the x,t-plane as in Fig 9 of Ref 2 (our Fig 1). Then initial data are prescribed along two lines. One is the x-axis, which is spacelike with. respect to the material behind it and carries the quantity u = 0 (if. the material is initially at rest), and p=p0. The other line is P, which is timelike, or subsonic to the gas flow, since it is identical with the path of the adjacent gas particles it carries velocity Up. The discontinuity of the reaction wave is represented by the line W. The deductions on uniqueness which. can be Used for non-reactive flow (See Ref 2, pp 136-37) cannot be applied here directly because of the interference of the unknown discontinuity W. 

For convective processes involving high-velocity gas flows (high subsonic or supersonic flows), a more meaningful and useful definition of the heat transfer coefficient is given by... 

But, as shown previously, RkT IM is the square of the speed of sound at state 1, or Cl, so the left side is (1/,/c,). The ratio V/c is called the Mach number M in honor of the Austrian physicist Ernst Mach. This ratio plays a crucial role in the study of high-velocity gas flows (and is widely reported in the press describing the speed of supersonic aircraft). It is the ratio of the local flow velocity to the local speed of sound. For subsonic flows M is less than 1 for sonic flows it equals 1 for supersonic flows it is greater than 1. Making this definition, we can rearrange Eq. 8.15 to... 

Here we can explain the fact, merely stated in Sec. 5.5, that when a fluid, liquid, or gas flows as a jet into another fluid, the pressure of the jet will be the same as that of the surrounding fluid, if the flow is subsonic, but not if the flow is sonic or supersonic. If the flow is subsonic and the pressure of the surrounding fluid is less than that of the jet, that information will propagate back along the flow, causing the flow to speed up until the pressures match. If the flow is sonic or supersonic, that information cannot propagate upstream, and the jet can have a pressure different from the surrounding pressure. 

The term on the left-hand side of Eq. (14.40) changes sign at the transition through the velocity of sound. Therefore, the influence of various effects on gas flow under subsonic and supersonic conditions is reversed. At subsonic flow (M < 1), flow acceleration (dU > 0) may be caused by a narrowing of the channel dS < 0), by supply of an additional mass of gas (dG > 0), as a result of work done by the gas (dL > 0), or by the supply of heat (dQs > 0). The same effects in... 

If dL > 0, which corresponds to a case whereby the gas flow does work, for example, on a turbine wheel in a turbo-expander, then in subsonic flow (M < 1) the gas is accelerated, but in supersonic flow (M > 1) it is slowed down. If energy is supplied to the gas dL < 0), as for example in a compressor, then in subsonic flow the gas is decelerated, whereas in supersonic flow it is accelerated. The basic property of a mechanical nozzle (turbine compressor) is that upon passage of a gas through it, the gas flow velocity is increased, and the pressure, density, and temperature are decreased according to the expressions ... 

Natural gas leak rate gap in long-distance transportation pipeline is closely related to its flow state. Determine the state of the gas flow and then calculate the leak. Its flow state is divided into sonic and subsonic flow. According to formula (7) and (8), when formula (7) is established, it belongs to sonic flow when formula (8) is founded, it belongs to subsonic flow. 

Melt atomization processes can be classified into various categories, according to the physical properties and flow characteristics of the atomization fluid water atomization, oil atomization, and gas atomization. Gas atomization can be further classified into subsonic gas atomization, supersonic gas atomization, and ultrasonic gas atomization. The considerations in selecting a particular melt atomization method include economic factors, production scale, the physical and chemical properties of fluid to be atomized and powder to be produced, and the morphology of the powder desired [3, 5]. 

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... 

Sun Q, Boyd ID (2002) A direct simulation method for subsonic microscale gas flows. J Comput Phys 179 400 25... 

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. 

Another key metastable energy carrier is NCl(a A), which is isovalent with NF(a A) and 02(0 A). The discoveiy of the efficient energy transfer from NCl(a A) to atomic iodine opened the door to an all-gas-phase, chemically pumped atomic iodine laser operating at the same wavelength as COIL. Indeed, a subsonic transverse flow device... 

When the line pressure drop in gas or vapor flow exceeds roughly 40 percent of the absolute upstream pressure, density variations must be considered. The NASA charts can be used to solve compressible flow problems. Adiabatic, subsonic, compressible flow for two common cases are given ... 

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