Mach number effects

The incidence angle now must be corrected for the Mach number effect The effect of the Mach number on incidence angle is shown in Figure 7-26. The incidence angle is not affected until a Mach number of. 7 is reached. 

At a high Reynolds number, the drag coefficient shows an increase with Mach number reaching a maximum value for light supersonic flow. This increase is due to the formation of shock waves on the particle and the attendant wave drag (essentially form drag). Mach number effects become significant for a Mach number of 0.6, which is the critical Mach number, that is, when sonic flow first occurs on the sphere. 

Most often, the Mach number is calculated using the speed of sound evaluated at the local pressure and temperature. When M = 1, the flow is critical or sonic and the velocity equals the local speed of sound. For subsonic flowM < 1 while supersonic flows have M > 1. Compressibility effects are important when the Mach number exceeds 0.1 to 0.2. A common error is to assume that compressibihty effects are always negligible when the Mach number is small. The proper assessment of whether compressibihty is important should be based on relative density changes, not on Mach number. 

Isothermal Gas Flow in Pipes and Channels Isothermal compressible flow is often encountered in long transport lines, where there is sufficient heat transfer to maintain constant temperature. Velocities and Mach numbers are usually small, yet compressibihty effects are important when the total pressure drop is a large fraction of the absolute pressure. For an ideal gas with p = pM. JKT, integration of the differential form of the momentum or mechanical energy balance equations, assuming a constant fric tion factor/over a length L of a channel of constant cross section and hydraulic diameter D, yields,... 

The effect of compressibility is important in high mach number machines. Mach number is the ratio of velocity to the acoustic speed of a gas at a given temperature M = Vja. Acoustic speed is defined as the ratio change in pressure of the gas with respect to its density if the entropy is held constant ... 

Free-vortex prewhirl. This type is represented by r Ve = constant with respect to the inducer inlet radius. This prewhirl distribution is shown in Figure 6-13. Vg is at a minimum at the inducer inlet shroud radius. Therefore, it is not effective in decreasing the relative Mach number in this manner. 

Carter s rule, which shows that the deviation angle is directly a function of the camber angle and is inversely proportional to the solidity 8 = mQ Xja) has been modified to take into account the effect of stagger, solidity, Mach number, and blade shape as shown in the following relationship ... 

The up-rate looks feasible considering that none of the inlet nozzle guidelines have been exceeded, the Mach number is still a low value, and the pressure drop is not significant. If the pressure drop had been significant, the effect of the drop could have been evaluated with respect to the compressor head and possibly a usable compromise worked out. 

Any effect of Mach number is experienced by rotor and stator equally and thus neither (or both) are limiting, and this Mach number will be lower than for other degrees of reaction under the conditions stated. If equal lift and drag are assumed in both rotor and stator, then optimum efficiency is obtained with R = 0.5 and VJu = 0.5. Although the latter is not always true, it does provide a useful criterion. Furthermore, the blade angles are similar in rotor and stator, which may be an advantage in the... 

Mach number, 26, IHO, 42 effect on axials, 23 L rotor tip, 100 Magnetic bearings, 204-8 air gap, 207 auxiliary bearing, 207 electromagnets, 205 laminated sleeve. 2U load capacity, 206 sensors, 206... 

These equations can be used when the Mach number is small, and the acceleration effect is ignored. 

In addition to a near-shock and an acoustic region, Deshaies and Clavin (1979) distinguished a third—a near-piston region—where nonlinear effects play a role as well. As already pointed out by Taylor (1946), the near-piston flow regime may be well approximated by the assumption of incompressibility. For each of these regions, Deshaies and Clavin (1979) developed solutions in the form of asymptotic expansions in powers of small piston Mach number. These solutions are supposed to hold for piston Mach numbers lower than 0.35. 

The influence of compressibility was assessed by varying the Mach number in the range 0 < Ma < 0.38, while Kn and ks/H were kept low. Friction factor data were reported only with Ma < 1 at the exit, to ensure the flow rate was controlled by viscous forces alone. A mild increase in the friction factor (8%) was observed as Ma approached 0.38. This effect was verified independently by numerical analysis for the same conditions as in the experiment. The range of relative surface roughness tested was 0.001 < ka/H < 0.06, yet there was no significant influence on the friction factor for laminar gas flow. 

We consider the problem of liquid and gas flow in micro-channels under the conditions of small Knudsen and Mach numbers that correspond to the continuum model. Data from the literature on pressure drop in micro-channels of circular, rectangular, triangular and trapezoidal cross-sections are analyzed, whereas the hydraulic diameter ranges from 1.01 to 4,010 pm. The Reynolds number at the transition from laminar to turbulent flow is considered. Attention is paid to a comparison between predictions of the conventional theory and experimental data, obtained during the last decade, as well as to a discussion of possible sources of unexpected effects which were revealed by a number of previous investigations. 

As will be outlined below, the computation of compressible flow is significantly more challenging than the corresponding problem for incompressible flow. In order to reduce the computational effort, within a CED model a fluid medium should be treated as incompressible whenever possible. A rule of thumb often found in the literature and used as a criterion for the incompressibility assumption to be valid is based on the Mach number of the flow. The Mach number is defined as the ratio of the local flow velocity and the speed of sound. The rule states that if the Mach number is below 0.3 in the whole flow domain, the flow may be treated as incompressible [84], In practice, this rule has to be supplemented by a few additional criteria [3], Especially for micro flows it is important to consider also the total pressure drop as a criterion for incompressibility. In a long micro channel the Mach number may be well below 0.3, but owing to the small hydraulic diameter of the channel a large pressure drop may be obtained. A pressure drop of a few atmospheres for a gas flow clearly indicates that compressibility effects should be taken into account. 

The procedure to determine the gas expansion factor is as follows. First, the upstream Mach number Maj is determined using Equation 4-67.2 Kf must be substituted for 4fLId to include the effects of pipes and fittings. The solution is obtained by trial and error, by guessing values of the upstream Mach number and determining whether the guessed value meets the equation objectives. This can be easily done using a spreadsheet. 

Henderson 575 presented a set of new correlations for drag coefficient of a single sphere in continuum and rarefied flows (Table 5.1). These correlations simplify in the limit to certain equations derived from theory and offer significantly improved agreement with experimental data. The flow regimes covered include continuum, slip, transition, and molecular flows at Mach numbers up to 6 and at Reynolds numbers up to the laminar-turbulent transition. The effect on drag of temperature difference between a sphere and gas is also incorporated. 

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. 

As the relative velocity difference is increased, however, coherent structure development is suppressed by compressibility effect [7, 8] and thus the effect on mixing by coherent structures diminishes. The compressibility effect can be quantified in terms of the convective Mach number, which is defined as the... 

Since plume-air mixing typically occurs at high convective Mach numbers, a special technique was needed to apply mixing control over the stabilizing influence of the compressibility effect. Thus, flow-induced cavity resonance was uti-... 

As discussed in the previous section, excited shear layers dispersed at a higher rate than the natural shear layer growth rate. The amount of increase depended on the excitation frequency and amplitude. It was difficult to assess the effect of amplitude due to the passive nature of the excitation technique, but the frequency effect was investigated by comparing the results obtained with various cavities [14]. The results will be discussed in this section along with two other issues. One deals with the compressibility effect such as extending the results to a higher convective Mach number and the other concerned with possible thrust penalty associated with the passive excitation method. 

As long as the Mach number is small—meaning the velocities are small compared to the sound speed—it is reasonable to assume that the incompressible continuity equation is a good approximation for isothermal, single-species flow. That is, velocity variations have little effect on density variations. As a result the simplifications associated with V-V 0 can be enjoyed. In practical terms, most consider that flows with Ma < 0.3 can be assumed to be gas-dynamically incompressible. 

Figure 6.13. Effect of Cp and Nup on the dynamic properties of phases over a plane shock in a gas-solid suspension with a Mach number of 1.5, 10 /tm glass beads, and mp = 0.2 (from Rudinger, 1969) (a) Temperature distributions (b) Pressure and particle velocity distributions.

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