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Base pressures and convective heat transfer coefficients for clustered sonic nozzles with emphasis on choked exhaust backflow
Two theoretical procedures are developed for designing asymmetric supersonic nozzles for which the calculated exit flow is nearly uniform over a range of Mach numbers. One procedure is applicable at Mach numbers less than approximately 3. This approach yields, without iteration, a nozzle for which the calculated exit flow is uniform at two Mach numbers and, with proper design, is nearly uniform at Mach numbers between, slightly above, and slightly below these two. The use of an inclined and curved sonic line is an essential feature of this approach, The second procedure requires iteration and is used far designs at Mach numbers exceeding 3. Although it is not a necessary feature, an inclined and curved sonic line is also used in this procedure. In both approaches the flow field dawn stream of the sonic line is determined using the method of characteristics.
Sonic discharge coefficients are presented for two different geometry flow nozzles using nitrogen gas at high pressures where real-gas corrections are significant. Throat Reynolds number range extended up to 8,000,000. Experimentally obtained coefficients for a nozzle with a continuous and finite radius of curvature agreed with those obtained analytically to within 0.2 per cent. Experimental coefficients for a long-radius ASME nozzle agreed to within 0.25 per cent to an empirical equation representing the most probable subsonic discharge coefficient.
Sonic discharge coefficients are obtained for two different geometry flow nozzles using high-pressure nitrogen gas (100 atm) with significant real-gas flow corrections. Throat Reynolds number range extended up to 8 million. Discharge coefficients for both nozzles monotonically increase in value at the high throat Reynolds numbers. The 95-percent confidence band for each nozzle is shown. Analytical discharge coefficients for the continuous and finite radius of curvature nozzle are presented. These analytical results for the laminar and turbulent boundary-layer cases are compared to experimental values for sonic flow. Experimental values are also compared to values calculated from the best empirical curve fit equation for subsonic flow.
Sonic discharge coefficients are presented for two different geometry flow nozzles using nitrogen gas at high pressures where real gas corrections are significant. Throat Reynolds number range extended up to 8 million. Experimentally obtained coefficients for a nozzle with a continuous and finite radius of curvature agreed with those obtained analytically to within 0.2 percent. Experimental coefficients for a long radius ASME nozzle agreed to within 1/4 percent to an empirical equation representing the most probable subsonic discharge coefficient.
Pressure distributions and erosion patterns on simulated lunar surfaces (hard and soft) and interference effects between the surface and two representative lunar vehicles (cylindrical and spherical) were obtained with cold-air jets at various descent heights and nozzle total-pressure ratios up to 288,000. Surface pressure distributions were dependent on both nozzle area ratio and, nozzle contour. Peak pressures obtained with a sonic nozzle agreed closely with those predicted theoretically for a near-sonic jet expanding into a vacuum. Short bell-shaped nozzles gave annular pressure distributions; the low center pressure resulted from the coalescence of shocks that originated within the nozzle. The high surface pressures were contained within a circle whose diameter was about 16 throat diameters, regardless of nozzle area ratio or contour. The peak pressure increased rapidly as the vehicle approached the surface; for example, at a descent height of 40 throat diameters the peak pressure was 0.4 percent of the chamber pressure, but increased to 6 percent at 13 throat diameters. The exhaust jet eroded a circular concave hole in white sand at descent heights from about 200 to 600 throat diameters. The hole diameter was about 225 throat diameters, while the depth was approximately 60 throat diameters. The sand particles, which formed a conical sheet at a semivertex angle of 50 deg, appeared to follow a ballistic trajectory and at no time struck the vehicle. An increase in pressure was measured on the base of the cylindrical lunar vehicle when it approached to within 14 throat diameters of the hard, flat surface. No interference effects were noted between the spherical model and the surface to descent heights as low as 8 throat diameters.
Jet effects on cylindrical afterbodies housing sonic and supersonic nozzles
Nearfield pressure data are presented for an unheated jet issuing from an underexpanded sonic nozzle for two exit lip thicknesses of 0.200 and 0.625 nozzle diameters. Fluctuating measurements were obtained on the nozzle exit surface as well as in the acoustic nearfield. Narrowband spectra are presented for numerous operating conditions expressed in terms of the fully expanded Mach number based on nozzle pressure ratio.
Reducing or eliminating the operational restrictions of supersonic aircraft over populated areas has led to extensive research at NASA. Restrictions were due to the disturbance of the sonic boom, caused by the coalescence of shock waves formed off the aircraft. Recent work has been performed to reduce the magnitude of the sonic boom N-wave generated by airplane components with a focus on shock waves caused by the exhaust nozzle plume. Previous Computational Fluid Dynamics (CFD) analysis showed how the shock wave formed at the nozzle lip interacts with the nozzle boat-tail expansion wave. An experiment was conducted in the 1- by 1-foot Supersonic Wind Tunnel (SWT) at the NASA Glenn Research Center. Results show how the shock generated at the nozzle lip affects the near field pressure signature, and thereby the potential sonic boom contribution for a nozzle at vector angles from 3 to 8 . The experiment was based on the NASA F-15 nozzle used in the Lift and Nozzle Change Effects on Tail Shock experiment, which possessed a large external boat-tail angle. In this case, the large boat-tail angle caused a dramatic expansion, which dominated the near field pressure signature. The impact of nozzle vector angle and nozzle pressure ratio are summarized.
Reducing or eliminating the operational restrictions of supersonic aircraft over populated areas has led to extensive research at NASA. Restrictions were due to the disturbance of the sonic boom, caused by the coalescence of shock waves formed off the aircraft. Recent work has been performed to reduce the magnitude of the sonic boom N-wave generated by airplane components with focus on shock waves caused by the exhaust nozzle plume. Previous Computational Fluid Dynamics (CFD) analysis showed how the shock wave formed at the nozzle lip interacts with the nozzle boat-tail expansion wave. An experiment was conducted in the 1- by 1-ft Supersonic Wind Tunnel at the NASA Glenn Research Center to validate the computational study. Results demonstrated how the nozzle lip shock moved with increasing nozzle pressure ratio (NPR) and reduced the nozzle boat-tail expansion, causing a favorable change in the observed pressure signature. Experimental results were presented for comparison to the CFD results. The strong nozzle lip shock at high values of NPR intersected the nozzle boat-tail expansion and suppressed the expansion wave. Based on these results, it may be feasible to reduce the boat-tail expansion for a future supersonic aircraft with under-expanded nozzle exhaust flow by modifying nozzle pressure or nozzle divergent section geometry.
The acoustic emission and initial shear layer of a cold jet issuing from an underexpanded sonic nozzle were measured where the lip thickness of the nozzle exit varied from 0.015 to 0.625 nozzle diameters. Because the amplitude of plume resonance (or screech) has been shown to be very sensitive to the initial conditions of the plume, the effects of nozzle lip thickness on this sound component in particular was investigated (although it will be shown that other noise components are also affected). Nearfield acoustic measurements have revealed the amplitude and frequency of certain modes of screech to be dependent on nozzle lip thickness. Fluctuating pressure measurements made on the nozzle exit surface have acoustic amplitudes in excess of near field microphone measurements. The dominant mode of instability that exists in the shear layer is also related to this geometric parameter. Detailed shear layer measurements were performed in an attempt to quantify any associated changes in the momentum thickness caused by altering the nozzle exit.
Equation for sonic line in nonequilibrium nozzle flows of gas and application in supersonic flow computations
An investigation was made at free-stream Mach numbers of 1.62, 1.93, and 2.41 to determine the effects of a primary jet and secondary air flow on the base pressure and pressures acting over the boattailsurface of a body of revolution for two secondary discharge areas. The Mach numbers of the primary nozzles were 1 and 3.23 with the secondary mass flow being varied from 0 to 10 percent of the primary mass flow. The ratio of jet stagnation temperature to tunnel stagnation temperature was about 0.96. The Reynolds number range of the investigation was from 2.1 x 10(6) to 2.9 x 10(6)based on body length. All testing was conducted with a turbulent boundary layer along the model. This report presents results obtained with zero-length ejector and covers jet static-pressure ratios from the jet-off condition to a maximum of about 128 for the sonic nozzle and to a maximum of about 9 for the supersonic nozzle.
We report pure-rotational N 2 –N 2 , N 2 –air, and O 2 –air S-branch linewidths for temperatures of 80–200 K by measuring the time-dependent decay of rotational Raman coherences in an isentropic free-jet expansion from a sonic nozzle. We recorded pure-rotational hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering (fs/ps CARS) spectra along the axial centerline of the underexpanded jet, within the barrel shock region upstream of the Mach disk. The dephasing of the pure-rotational Raman coherence was monitored using probe-time-delay scans at different axial positions in the jet, corresponding to varying local temperatures and pressures. The local temperature was obtained by fitting CARS spectra acquired at zero probe time delay, where the impact of collisions was minimal. The measured decay of each available Raman transition was fit to a dephasing constant and corrected for the local pressure, which was obtained from the CARS-measured static temperature and thermodynamic relationships for isentropic expansion from the known stagnation state. Nitrogen self-broadened transitions decayed more rapidly than those broadened in air for all temperatures, corresponding to higher Raman linewidths. In general, the measured S-branch linewidths deviated significantly in absolute and relative magnitudes from those predicted by extrapolating the modified exponential gap model to low temperatures. The temperature dependence of the Raman linewidth for each measured rotational state of nitrogen (J ≤ 10) and oxygen (N ≤ 11) was fit to a temperature-dependent power law over the measurable temperature domain (80–200 K) and extrapolated to both higher rotational states and room temperature. Furthermore, the measured and modeled low-temperature linewidth data provided here will aid low temperature gas-phase pressure measurements with fs/ps CARS.
Three dimensional steady radial expansion of viscous Newtonian gas from sonic nozzle into vacuum analyzed using Navier-Stokes equation
Real gas corrections to gas flow computations for sonic nozzles
Real gas mass flow rate computation through sonic nozzle
A procedure was described for calibrating air velocity sensors in the exhaust flow of a gas flow calibrator. The average velocity in the test section located at the calibrator exhaust was verified from the mass flow rate accurately measured by the calibrator's precision sonic nozzles. Air at elevated pressures flowed through a series of screens, diameter changes, and flow straighteners, resulting in a smooth flow through the open test section. The modified system generated air velocities of 2 to 90 meters per second with an uncertainty of about two percent for speeds below 15 meters per second and four percent for the higher speeds. Wind tunnel data correlated well with that taken in the flow calibrator.