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Supersonic flow

Fig. 9. Compressible flow in a converging—diverging no22le where A represents no flow, C subsonic flow, and F through H supersonic flow. See text. Fig. 9. Compressible flow in a converging—diverging no22le where A represents no flow, C subsonic flow, and F through H supersonic flow. See text.
Further reductions in reservoir pressure move the shock front downstream until it reaches the outlet of the no22le E. If the reservoir pressure is reduced further, the shock front is displaced to the end of the tube, and is replaced by an obflque shock, F, no pressure change, G, or an expansion fan, H, at the tube exit. Flow is now thermodynamically reversible all the way to the tube exit and is supersonic in the tube. In practice, frictional losses limit the length of the tube in which supersonic flow can be obtained to no more than 100 pipe diameters. [Pg.95]

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. [Pg.648]

There are certain limitations on the range of usefulness of pitot tubes. With gases, the differential is very small at low velocities e.g., at 4.6 m/s (15.1 ft/s) the differential is only about 1.30 mm (0.051 in) of water (20°C) for air at 1 atm (20°C), which represents a lower hmit for 1 percent error even when one uses a micromanometer with a precision of 0.0254 mm (0.001 in) of water. Equation does not apply for Mach numbers greater than 0.7 because of the interference of shock waves. For supersonic flow, local Mac-h numbers can be calculated from a knowledge of the dynamic and true static pressures. The free stream Mach number (MJ) is defined as the ratio of the speed of the stream (V ) to the speed of sound in the free stream ... [Pg.887]

R. Courant and K.O. Friedrichs, Supersonic Flow and Shock Waves Interscience, New York, 1948. [Pg.42]

A nozzle is correctly designed for any outlet pressure between P[ and PE in Figure 4.5. Under these conditions the velocity will not exceed the sonic velocity at any point, and the flowrate will be independent of the exit pressure PE = Pb- It is also correctly designed for supersonic flow in the diverging cone for an exit pressure of PEj. [Pg.157]

Unlike the orifice or nozzle, the pipeline maintains the area of flow constant and equal to its cross-sectional area. There is no possibility therefore of the gas expanding laterally. Supersonic flow conditions can be reached in pipeline installations in a manner similar to that encountered in flow through a nozzle, but not within the pipe itself unless the gas enters the pipe at a supersonic velocity. If a pipe connects two reservoirs and the upstream reservoir is maintained at constant pressure P, the following pattern will occur as the pressure P2 in the downstream reservoir is reduced. [Pg.158]

It will now be shown from purely thermodynamic considerations that for, adiabatic conditions, supersonic flow cannot develop in a pipe of constant cross-sectional area because the fluid is in a condition of maximum entropy when flowing at the sonic velocity. The condition of the gas at any point in the pipe where the pressure is P is given by the equations ... [Pg.172]

Fanno lines are also useful in presenting conditions in nozzles, turbines, and other units where supersonic flow arises.(5)... [Pg.172]

The several industrial applications reported in the hterature prove that the energy of supersonic flow can be successfully used as a tool to enhance the interfacial contacting and intensify mass transfer processes in multiphase reactor systems. However, more interest from academia and more generic research activities are needed in this fleld, in order to gain a deeper understanding of the interface creation under the supersonic wave conditions, to create rehable mathematical models of this phenomenon and to develop scale-up methodology for industrial devices. [Pg.300]

For adiabatic flow in a constant area duct, the governing equations can be formulated in a more generalized dimensionless form that is useful for the solution of both subsonic and supersonic flows. We will present the resulting expressions and illustrate how to apply them here, but we will not show the derivation of all of them. For this, the reader is referred to publications such as that of Shapiro (1953) and Hall (1951). [Pg.279]

Courant, R. und Friedrich K. O. Supersonic Flow and Shock Waves, Interscience Publ. Inc., New York 1948... [Pg.92]

Subsonic flow corresponds to Ma< 1 and supersonic flow to Ma> 1. The conditions of incompressible flow are approached as Ma—>0. [Pg.203]

Condition (g) is that condition for which the exit pressure is equal to the back pressure and no shock wave occurs. This is called the design condition for supersonic flow. [Pg.212]

Equation 6.100 shows that in a diverging section (d5/5 > 0) the velocity must decrease for subsonic flow (Ma< 1) and increase for supersonic flow... [Pg.213]

A shock wave from subsonic to supersonic flow would require a decrease in the entropy so what would be an alarming phenomenon is thermodynamically impossible. [Pg.218]

Drag coefficient Q/l. .Re) is the drag coefficient calculated using the correlation for subsonic flow with Ma=l. f V/1.75, Re ) is the drag coefficient calculated using the correlation for supersonic flow with Ma00=1.75 Mach number based on relative velocity between gas and sphere ... [Pg.337]

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 ... [Pg.355]

Strong detonation since (supersonic flow to subsonic)... [Pg.274]

At points above J, P2 > thus, u2 < n2 ). Since the temperature increases somewhat at higher pressures, c2 > c2 i [c = ( jRT)1/2]. More exactly, it is shown in the next section that above J, c2 > u2. Thus, M2 above J must be less than 1. Similar arguments for points between J and K reveal M2 > M2 ) and hence supersonic flow behind the wave. At points past Y, l/p2 > 1/pi, or the velocities are greater than m2 Y. Also past Y, the sound speed is about equal to the value at Y. Thus, past Y, M2 > 1. A similar argument shows that M2< 1 between X and Y. Thus, past Y, the density decreases therefore, the heat addition prescribes that there be supersonic outflow. But, in a constant area duct, it is not possible to have heat addition and proceed past the sonic condition. Thus, region IV is not a physically possible region of solutions and is ruled out. [Pg.274]

Numerical studies of combustion control in simple combustors with flame holders have been made. The criterion of flame stabilization, based on the unambiguously defined characteristic residence and reaction times, is suggested and validated against numerous computational examples. The results of calculations were compared with available experimental findings. A good qualitative and reasonable quantitative agreement between the predictions and observations were attained. Futher studies are planned to include mixing between fuel jets with oxidizer and to extend the analysis to transonic and supersonic flow conditions. [Pg.205]

Supersonic combustion depends considerably (along with the kinetics) on the intensity of turbulent mixing. The significant factors in supersonic mixing enhancement are (1) the decrease in mixing intensity in supersonic flows, and... [Pg.373]

Haimovitch, Y., E. Gartenberg, A. S. Roberts, Jr., and G. B. Northam. 1997. Effects of internal nozzle geometry on compression-ramp mixing in supersonic flow. AIAA J. 35(4) 663-70. [Pg.383]

The solution expressed by Eq. (1.36) indicates that there is no discontinuous flow between the upstream 1 and the downstream 2. However, the solution given by Eq. (1.37) indicates the existence of a discontinuity of pressure, density, and temperature between 1 and 2. This discontinuity is called a normal shock wave , which is set-up in a flow field perpendicular to the flow direction. Discussions on the structures of normal shock waves and supersonic flow fields can be found in the relevant monographs. [Pg.10]

Equation (1.54) indicates that A/A becomes minimal at M = 1. The flow Mach number increases as A/A decreases when M < 1, and also increases as A/A increases when M > 1. When M = 1, the relationship A = A is obtained and is independent of Y- It is evident that A is the minimum cross-sectional area of the nozzle flow, the so-called nozzle throat", in which the flow velocity becomes the sonic velocity, furthermore, it is evident that the velocity increases in the subsonic flow of a convergent part and also increases in the supersonic flow of a divergent part. [Pg.13]


See other pages where Supersonic flow is mentioned: [Pg.94]    [Pg.15]    [Pg.651]    [Pg.889]    [Pg.934]    [Pg.486]    [Pg.486]    [Pg.353]    [Pg.158]    [Pg.299]    [Pg.159]    [Pg.281]    [Pg.7]    [Pg.203]    [Pg.213]    [Pg.337]    [Pg.337]    [Pg.357]    [Pg.33]    [Pg.34]    [Pg.36]    [Pg.157]    [Pg.157]    [Pg.484]   
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