Stagnation pressure ratio

It is obvious that the entropy change will be positive in the region Mi > 1 and negative in the region Mi < 1 for gases with 1 < y < 1-67. Thus, Eq. (1.46) is valid only when Ml is greater than unity. In other words, a discontinuous flow is formed only when Ml > 1. This discontinuous surface perpendicular to the flow direction is the normal shock wave. The downstream Mach number, Mj, is always < 1, i. e. subsonic flow, and the stagnation pressure ratio is obtained as a function of Mi by Eqs. (1.37) and (1.41). The ratios of temperature, pressure, and density across the shock wave are obtained as a function of Mi by the use of Eqs. (1.38)-(1.40) and Eqs. (1.25)-(1.27). The characteristics of a normal shock wave are summarized as follows ... 

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. 

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 ... 

We may estimate rjnoc for the purposes of these equations from the measured efficiency at low pressure ratios, and hence find ntoc- As discussed at the end of Section A6.1, the local and stagnation temperatures will be almost identical, so that TqtITo ... 

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).

The present experiments were conducted using a convergent axisymmetric nozzle operating at a nozzle pressure ratio of 3, which resulted in a jet Mach number of 1.38. The nozzle temperature ratio (stagnation temperature/ambient temperature) was kept nominally at 3. The microjet mass flow rate was kept at less than 2% of the main jet meiss flow rate. 

Experiments were conducted in the newly built High Temperature Supersonic Jet Facility at the Fluid Mechanics Research Laboratory of the Florida State University in Tallahassee. A schematic of the facility can be seen in Fig. 3.2. In the present experiments, a converging axisymmetric nozzle having an exit diameter of 50.8 mm Wcis used. The nozzle profile was designed using a fifth-order polynomial with a contraction ratio of approximately 2.25. The stagnation pressure and temperature were held constant to within 0.5% of its nominal value during the experiment. 

Fig.4 shows a comparison of two series of expansions obtained with the nozzles B1 and B2 at equal stagnation pressure and varied stagnation temperature. The expansions with 1 325 K show no condensation effect within the nozzle they were used for calibration of the effective nozzle profile. With decreasing stagnation temperature the Wilson-point moves upstream. Downstream of the Wilson-point the supersaturation is quickly reduced and the expansion obviously tends to a two-phase flow in which equilibrium between vapour and droplets is nearly attained. For equal values of the stagnation temperature, the Wilson points obtained in the faster expansion (nozzle B2) are found at a somewhat lower pressure ratio p/p j i.e. at a higher supersaturation than with nozzle B1. 

The critical mass flux is thus = G/hg, Pg, S). The Moody model (1965) is based on maximizing specific kinetic energy of the mixture with respect to the slip ratio whereas the Fauske model (1961, 1965) is based on the flow momentum with respect to the slip ratio. In Figure 22.18, the critical discharge rate of water at various stagnation pressure and enthalpy with Fauske slip model is shown. 

Stage Pressure Ratio Ratio of the stagnation pressure at the end of a single stage of a turbomachine to the stagnation pressure ahead of the stage. 

Another possible source of nonideal behavior and large pressure fluctuations would be boundary layer separation caused by the interaction with the reflected shock wave. Boundary layer separation and bifurcated reflected shock waves are observed under certain conditions in shock tubes with nonreactive flows. Mark formulated a simple model that predicts the occurrence of bifurcation shock bifurcation and boundary layer separation will occur when the pressure jump across the reflected shock exceeds the maximum stagnation pressure possible in the cold boundary layer fluid. Numerical calculation for the present situation reveals bifurcation would not be expected when the detonation first reflects. This is a situation peculiar to detonations and is due to the much lower reflected-shock pressure ratio relative to that which would be produced by reflecting a shock wave of comparable strength. Consideration of the reflected shock motion at later times indicates that bifurcation would not occur until after the shock had reflected from the far end of the tube. 

Here zu is the distance from the nozzle exit to the Mach disk, Ku is a constant that depends on y, and Pq is the stagnation pressure at the nozzle inlet conditions for a perfectly isentropic expansion. The dimensionless distance, zm/D2, was found by Ashkenas and Sherman (36) to be a function of the isentropic expansion pressure ratio ... 

A plot of P y/PA vs. the expansion pressure ratio, Po/Pa, is given as Figure 7 and shows that, for typical RESS conditions, the stagnation pressure on the downstream side of the Mach disk never exceeds 1 or 2. 

The mass flow rate is obtained by a progressive variation of the state conditions in the nozzle throat at a constant stagnation enthalpy - or approximately in the case of isentropic flow (no heat transfer, = 0) - until the back pressure or a maximum of the mass flow rate (critical pressure ratio) is reached. 

In combustion rockets, the combustion temperature is not directly available as a design parameter but rather is determined by the propellant selection, mixture ratio and combustion pressure. In heat transfer rockets however, the initial temperature of the propellant, that is, the stagnation temperature of the propellant, is available as a design parameter. It is probably sufficient to say that the propellant stagnation temperature should be maximized for maximum performance. 

Here the temperature ratio T/To has been replaced using equation (14.25), while we have also assumed that the pressure and specific volume in the stagnation state are related to temperature by ... 

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