Stagnation inlet pressure

Hence the ratio of the throat pressure to the stagnation inlet pressure at critical conditions is ... 

Finally, we realize that for an isentropic expansion, must equal Fq, the inlet pressure to the nozzle, which is essentially at stagnation. Applying this equality to Eq. (60), substituting E. (58) into Eq. (60), and dividing Eq. (60) by the... 

Equation (15.3) was developed for plenum flow with negligible inlet velocity. If the inlet velocity may not be neglected, a (fictitious) stagnation pressure - the actual inlet pressure increased by the pressure difference computed by an isentropic deceleration of flow to the velocity of zero - must be introduced in Eq. (15.3). This equation is not valid if gases condense or chemical reactions occur. 

Figure IS.S Isentropic exponent for ethylene accordingto EN-ISO 4126-7 and a cubic equation of state (SRK) as a function of reduced pressure and reduced temperature at stagnation inlet conditions.

Inlet and diseharge pressures are defined as the stagnation pressures at the inlet and diseharge, whieh are the sum of statie and veloeity pressures at the eorresponding points. Statie pressures should be measured at four stations in the same plane of the pipe as shown in the piping arrangements. Veloeity pressure, when less than 5% of the pressure rise, ean be eomputed by the formula... 

Figure 26.4 Surface temperature and surface fuel mole fraction (a), and NO (6) as functions of inlet composition, along the adiabatic curve, for the stagnation reactor (solid curves) and the PSR (dashed curves). The fuel-lean and fuel-rich regions are indicated. The conditions are pressure of 1 atm, inlet temperature of 25 °C, a strain rate of 1000 s (stagnation reactor), and a residence time of 1 ms (PSR)...

Figure 26.6 Wall conductive flux and surface fuel mole fraction (a) and NOa, near the surface (6) vs. the inverse of the strain rate for a stagnation reactor with the surface at temperatures of 500 K (dashed curves) and 1000 K (solid curves). The conditions of pressure and inlet temperature are the same as in Fig. 26.4...

Fig. 6.6 Comparison of two alternative stagnation-flow configurations. The upper illustration shows the streamlines that result from a semi-infinite potential flow and the lower illustration shows streamlines that result from a uniform inlet velocity issuing through a manifold that is parallel to the stagnation plane. Both cases are for isothermal air flow at atmospheric pressure and T = 300 K. In both cases the axial inlet velocity is u = —5 cm/s. The separation between the manifold and the substrate is 3 cm. For the outer-potential-flow case, the streamlines are plotted over the same domain, but the flow itself varies in the entire half plane above the stagnation surface. The stagnation plane is illustrated as a 10 cm radius, but the solutions are for an infinite radius.

Fig. 6.13 Comparison of streamlines from rotating-disk solutions at two rotation rates. Both cases are for air flow at atmospheric pressure and T = 300 K. The induced inlet velocity is greater for the higher rotation rate. In both cases the streamlines axe separated by 27tA4< = 1.0 x 10-6 kg/s. The solutions are illustrated for a 2 cm interval above the stagnation plane and a 3 cm radius rotation plane. The similarity solutions themselves apply for the semi-infinite half plane above the surface.

The pressure-gradient term Ar requires either a further boundary condition or a determination of the domain size. In the semi-infinite cases, Ar is a constant that is specified in terms of the outer potential-flow characteristics. However, the extent of the domain end must be determined in such a way that the viscous boundary layer is entirely contained within the domain. In the finite-gap cases, the inlet velocity n(zend) is specified at a specified inlet position. Since the continuity equation is first order, another degree of freedom must be introduced to accommodate the two boundary conditions on u, namely u — 0 at the stagnation surface and u specified at the inlet manifold. The value of the constant Ar is taken as a variable (an eigenvalue) that must be determined in such a way that the two velocity boundary conditions for u are satisfied. 

A further consequence of the upstream diffusion to the burner face could be heterogeneous reaction at the burner. Such reaction is likely on metal faces that may have catalytic activity. In this case the mass balance as stated in Eq. 16.99 must be altered by the incorporation of the surface reaction rate. In addition to the burner face in a flame configuration, an analogous situation is encountered in a stagnation-flow chemical-vapor-deposition reactor (as illustrated in Fig. 17.1). Here again, as flow rates are decreased or pressure is lowered, the enhanced diffusion tends to promote species to diffuse upstream toward the inlet manifold. 

To illustrate the behavior of a stagnation flame impinging into a wall, consider the following example based on an atmospheric-pressure, stoichiometric, premixed, methane-air flame [271]. Geometrically the situation is similar to that shown in Fig. 17.1. The manifold-to-surface separation distance is one centimeter, the inlet mixture is at 300 K, and the surface temperature is maintained at Ts = 800 K. Figure 17.4 shows the flow field and flame structure for two inlet velocities. The flow is from right to left, with the inlet manifold on the right-hand side and the surface on the left. 

The remarks on sonic flow made at the beginning of Section 5.4.1 apply also to real nozzles, where there is a degree of friction present. The nozzle throat will pass flow at speeds up to and including sonic, but cannot support supersonic flow. Sonic flow will be reached when the ratio of throat pressure to inlet stagnation pressure has reached a critical value. 

Since there is no inlet velocity, the stagnation values of temperature, pressure etc. are unchanged from the basic values. Treating air as a perfect gas with a compressibility factor of unity, we may use the characteristic gas equation to calculate the specific volume at nozzle inlet as... 

Note that the nozzle inlet enthalpy, ho, is taken as the actual value, not the stagnation value in this definition. The expansion over the blades will, of course, be associated with a drop in pressure, and we may deduce its value by expressing the enthalpy drops in terms of temperature ratios and then pressure ratios as follows ... 

Estimate the stagnation values of pressure and specific volume at the inlet to the current stage using the methods outlined in Chapter 14, and hence determine the next stage mass flow and nozzle outlet velocity. 

The formulation above used stagnation values of inlet and outlet pressure and temperature, but since the section inlet and outlet velocities will be small, little will be lost by using the actual values po Par, P2 Pit, To Tor, Ti Tit. Given the inlet temperature and the speed, the speed parameter, N/,yR ToT, may be calculated. Add to this a knowledge of the section s inlet and outlet pressures, from which to calculate Pi/Po, and the flow parameter, (W,/R Tot)/Pot, may be read off the projection of the characteristic curve onto the horizontal axis, usually after interpolation for the speed parameter. Mass flow, W, may then be disentangled from the flow parameter. A knowledge of both the speed and the flow parameters allows the polytropic efficiency to be found from a map (assumed provided) of equation (17.101). 

In his paper Reaction tests of turbine nozzles for supersonic velocities , Keenan (1949) presented the results of experimental tests on five turbine nozzles one is convergent-only and four are convergent-divergent. He measured the outlet velocity using a force balance and then calculated the velocity coefficient as the ratio of measured velocity downstream of the nozzle, c, to the velocity, cu that would occur following an isentropic expansion from the stagnation state at nozzle inlet to the exhaust chamber pressure, pi ... 

Figure 16.13 Schlieren images of supersonic flow over various aspect-ratio cavities under off-design inlet conditions. Inlet flow stagnation pressure is 35 psi (a) and 120 psi (6).

Figure 5-40. Typical parameters of a nozzle system in supersonic plasma-chemical experiments. Subscripts 1 and 2 are related to inlet and exit of a discharge zone subscript 3 is related to exit from the nozzle system subscript 0 is related to stagnation pressure and temperature.

Typically, pulse combustors operate at frequencies from 20 to 250 Hz. Pressure oscillation in the combustion chamber of 10 kPa produces velocity oscillation in the tailpipe of about 100 m/s, so the instantaneous velocity of a gas jet at the tailpipe exit varies from 0 to 100 m/s (Keller et al., 1992). Although pulse combustors deliver flue gases at a higher pressure than the inlet air pressure, the resulting increase in stagnation pressure is relatively small. This restricts practical applications of pulse combustors to the systems where pressure drop is not critical. The amplitude of the pressure rise may vary from 10% (domestic heating applications) to 100% as for heavy-duty pulse combustors for industrial use (Kentfleld, 1993). The output power for commercially available pulse combustors ranges from 70 to 1000 kW. 

For a compressible flow, this is the thermodynamic state that would exist if a flow were brought to rest isentropically. In practice, this would correspond to the thermodynamic state of a veiy low-speed flow entering the nozzle inlet from an upstream combustion chamber or a pressurized reservoir. For this reason, stagnation cOTiditions are also sometimes referred to as chamber or reservoir conditions. 

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