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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Universality (beyond leading log) of soft radiative corrections to $\hat q$ in $p_\perp$ broadening and energy loss

It has been known for many years that soft radiation can give potentially large double-logarithm corrections to $p_\perp$ broadening of a high-energy particle traveling through QCD matter, but that this soft radiation correction can be absorbed into an effective value $\hat q_{eff}$ for the medium $p_\perp$-broadening parameter $\hat q$. Here ``soft'' means high energy compared to medium scales but soft compared to the original high-energy particle traveling through the medium. A similar situation arises in the case of soft corrections to hard splitting of a high-energy particle, such as hard g → gg, where double logarithms can also be absorbed using the same effective $\hat q_{eff}$. In this paper, I study whether the same holds true for potentially large, subleading, {\it single}-logarthim corrections. The correspondence is more indirect for single logarithms, but I show (in the large-$N_c$ limit) that single logarithms from soft radiation in the case of $p_\perp$ broadening also determine the single logarithms from soft radiative corrections to hard g → gg splitting. Along the way, there is an interesting variation of the original BDMPS-Z calculation of splitting rates in the q(hat) approximation. I also discuss how, for soft-radiative corrections to hard splitting processes, there are two different types of ''$\hat q_{eff}$'' that come into play, which differ by ''$i\pi$'' terms that multiply single logarithms.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1992

An off-center point explosion in a radially stratified medium - Kompaneets approximation

The Kompaneets (1960) approximation is applied to a blast in a medium that is radially stratified according to a power law. The basic equation is derived that gives the location of the shock front as a function of time. This equation is transformed by means of a conformal coordinate transformation into an equation in which the density variation of the medium does not appear. In the new coordinates, and the problem is reduced to that of a blast in a uniform medium, the solution of which is a set of concentric circles about the initial explosion point; in the transformed coordinates, the paths followed by points on the shock front are radial, making it possible to find the paths in the original coordinates. Using the new solution, the effect of the explosion is considered for a solid core embedded at the origin, and the extent of the core's surface that is affected by the blast is calculated.

Korycansky, D. G.↗
DOE OSTI2021

Development and Field Testing Novel Natural Gas Surface Process Equipment for Replacement of Water as Primary Hydraulic Fracturing Fluid (Final Report)

Southwest Research Institute® (SwRI ® ), Schlumberger Technology Corporation (SLB), and Chevron Corporation ® (Chevron) developed a novel, optimized, and lightweight process for natural gas (NG) to replace water as a low-cost fracturing medium with a low environmental impact. Hydraulic fracturing is used to increase oil and NG production by injecting high-pressure fluid, primarily water, into a rock formation, which fractures the rock and releases trapped oil and NG. This method was developed to increase yield and make feasible production areas that would not otherwise be viable for large-scale oil and NG extraction using traditional drilling technologies. Since the fracturing fluid is composed of approximately 90% water, one of the principal drawbacks to hydraulic fracturing is its excessive water use and associated large environmental footprint. According to recent data collected at fracture sites within the United States, fracturing applications in North America can consume as much as 9 million gallons of water per well. During the fracturing process, some of the fracturing fluid is permanently lost and the portion that is recovered is contaminated by both fracturing chemicals and dissolved solids from the formation. The recovered water or flow-back represents a significant environmental challenge, as it must be treated before it can be reintroduced into the natural water system. Although there is some recycling for future fracturing, the majority of the flow-back water is hauled from the well site to a treatment facility or to an injection well for permanent underground disposal. To mitigate these issues, an optimized, lightweight and modular surface process using NG to replace a majority of the water was developed as a cost-effective and environmentally clean fracturing fluid. Using NG will result in significantly less consumption since the gas that is injected as a fracturing fluid will be mixed with the formation gas and extracted as if it were from the formation itself. This process will minimize the collection, waste, and treatment of large amounts of water and will reduce the environmental impact of transporting and storing the fracturing fluid. There are two major steps involved in utilizing NG as the primary fracturing medium: (1) increasing the supply pressure of NG to wellhead pressures suitable for fracturing and (2) mixing the required chemicals and proppant needed for the fracturing process at these elevated pressures. The second step (NG-proppant mixing at elevated pressures) still requires demonstration; but very similar processes have been demonstrated in the field with other gases such as nitrogen (N 2 ) and carbon dioxide (CO 2 ). However, the first step (a compact, on-site unit for generating high-pressure NG at costs feasible for fracturing) has not been developed and is currently not commercially available. Due to the inherent compressibility of NG, more energy is required to compress the gas than what is required to pump water (or other incompressible liquids) to the very high pressure required for downhole injection. This project aimed to develop a novel, hybrid method to overcome this challenge. The project accomplishments and findings are discussed in this report. Ultimately, the research and development efforts described herein demonstrate that fracturing with NG foam is a feasible alternative to using water.

02 PETROLEUM↗
NASA NTRS1961

A General Computer Program for Ionospheric Ray-Tracing

The study of the ionosphere using the Faraday rotation effect has been undertaken recently by means of rocket, satellite, and moon echo experiments. Different approximations have been used by different authors, resulting in methods with different degrees of complexity, and it is possible to say that the more accurate a method is, the more difficult its application becomes. However, the use of modern high-speed digital computers offers the possibility of using more complex methods in the solution of this problem, The program described in this report was written for the ILLIAC, the digital computer of the University of Illinois. Only the general features common to most digital computers will be mentioned. This program was prepared having in mind the analysis of the Faraday rotation effect, as recorded from artificial satellites. It is intended to be as general as possible in the conditions imposed on the assumed propagating medium: specifically there are no restrictions on the models of the electron density distribution and the earth's magnetic fields. long as the ray theory Ls valid. The program will trace separately the ordinary and the extraordinary mode, and it will find the virtual phase path length of a ray of each mode between the transmitter (satellite) and a receiver (station). The difference between respective phase path-lengths is related to the Faraday rotation through a constant which depends on the frequency.

Gonzales, Victor H.↗
DOE OSTI2022

Spatiotemporally resolved measurements of electric field around a piezoelectric transformer using electric-field induced second harmonic (E-FISH) generation

When a piezoelectric transformer (PT) is actuated at its second harmonic frequency by a low input voltage, the generated electric field at the distal end can be sufficient to breakdown the surrounding gas, making them attractive power sources for non-equilibrium plasma generation. Understanding the potential and electric fields produced in the surrounding medium by the PT is important for effectively designing and using PT plasma devices. In this work, the spatiotemporally resolved characteristics of the electric field generated by a PT operating in open air have been investigated using the femtosecond electric field-induced second harmonic generation (E-FISH) method. Here, electric field components were determined by simultaneously conducting E-FISH measurements with the incident laser polarized in two orthogonal directions relative to the PT crystal. Results of this work demonstrate the spatial distribution of electric field around the PT’s output distal end and how it evolves as a function of time. Notably, the strongest electric field appears on the face of the PT’s distal surface, near the top and bottom edges and decreases by approximately 70% over 3 mm. The time delay between the PT’s input voltage and measured electric field indicates that there is an about 0.45 phase difference between the PT’s input voltage and output signal.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1993

Turbulent mixing layers in the interstellar medium of galaxies

We propose that turbulent mixing layers are common in the interstellar medium (ISM). Injection of kinetic energy into the ISM by supernovae and stellar winds, in combination with density and temperature inhomogeneities, results in shear flows. Such flows will become turbulent due to the high Reynolds number (low viscosity) of the ISM plasma. These turbulent boundary layers will be particularly interesting where the shear flow occurs at boundaries of hot (approximately 10(exp 6) K) and cold or warm (10(exp 2) - 10(exp 4) K) gas. Mixing will occur in such layers producing intermediate-temperature gas at T is approximately equal to 10(exp 5.0) - 10(exp 5.5) that radiates strongly in the optical, ultraviolet, and EUV. We have modeled these layers under the assumptions of rapid mixing down to the atomic level and steady flow. By including the effects of non-equilibrium ionization and self-photoionization of the gas as it cools after mixing, we predict the intensities of numerous optical, infrared, and ultraviolet emission lines, as well as absorption column densities of C 4, N 5, Si 4, and O 6.

Slavin, J. D.↗
NASA NTRS1979

Charge equilibrium and radiation of low-energy cosmic rays passing through interstellar medium

The charge equilibrium and radiation of an oxygen and an iron beam in the MeV per nucleon energy range, representing a typical beam of low-energy cosmic rays passing through the interstellar medium, are considered. Electron loss of the beam has been taken into account by means of the first Born approximation, allowing for the target atom to remain unexcited or to be excited to all possible states. Electron-capture cross sections have been calculated by means of the scaled Oppenheimer-Brinkman-Kramers approximation, taking into account all atomic shells of the target atoms and capture into all excited states of the projectile. The capture and loss cross sections are found to be within 20%-30% of the existing experimental values for most of the cases considered. Radiation of the beam due to electron capture into the excited states of the ion, collisional excitation, and collisional inner-shell ionization, taking into account the fluorescence yield of the ions, has been considered. Effective X-ray production cross sections and multiplicities for the most energetic X-ray lines emitted by the Fe and O beams have been calculated, and error estimates made for the results.

Rule, D. W.↗
NASA NTRS1992

Venus: The case for a wet origin and a runaway greenhouse

To one interested in atmospheric evolution, the most intriguing aspect of our neighboring planet Venus is its lack of water. Measurements made by Pioneer Venus and by Several Venera spacecraft indicate that the present water abundance in Venus' lower atmosphere is of the order of 20 to 200 ppmv, or 3 x 10( exp -6) to 3 x 10 (exp -5) of the amount of water in Earth's oceans. The exact depletion factor is uncertain, in part because of an unexplained vertical gradient in H2O concentration in the lowest 10 km of the venusian atmosphere, but the general scarcity of water is well established. The interesting question, then, is: Was venus deficient in water when it formed and, if not, where did its water go? The conclusion that Venus was originally wet is consistent with its large endowment of other volatiles and with the enhanced D/H ratio in the present atmosphere. The most likely mechanism by which Venus could have lost its water is by the development of a runaway or moist greenhouse atmosphere followed by photodissociation of water vapor and escape of hydrogen to space. Climate model calculations that neglect cloud albedo feedback predict the existence of two critical transitions in atmospheric behavior at high solar fluxes: (1) at a solar flux of approximately 1.1 times the value at Earth's orbit, S(o), the abundance of stratospheric water vapor increases dramatically, permitting rapid escape of hydrogen to space (termed a moist greenhouse) and (2) at a solar flux of approximately 1.4 S(o), the oceans vaporize entirely, creating a true runaway greenhouse. If cloudiness increases at high surface temperatures, as seems likely, and if the dominant effect of clouds is to cool the planet by reflecting incident solar radiation, the actual solar flux required to create moist or runaway conditions would be higher than the values quoted above. Early in solar system history, solar luminosity was about 25 percent to 30 percent less than today, putting the flux at Venus' orbit in the range of 1.34 S(o) to 1.43 S(o). Thus, it is possible that Venus had liquid water on its surface for several hundred million years following its formation. Paradoxically, this might have facilitated water loss by sequestering atmospheric CO2 in carbonate rocks and by providing an effective medium for surface oxidation.

Kasting, J. F.↗
NASA NTRS2000

Star Formation in the Galaxy and the Fluctuating UV Radiation Field

We examine the formation of massive stars in the Galaxy, the resultant fluctuating UV radiation field, and the effect of this Field on the star-forming interstellar medium. Following previous researchers such as Habing (1968), we calculate the average interstellar radiation field at the Solar Circle of the Galaxy. However, our new calculations follow more closely the time dependence of the field at any point. We show that there is a significant difference between the mean field and the median field, and that there are substantial fluctuations of the field (on timescales of order 100 million years) at a given point. Far Ultraviolet Radiation (FUV, photon energies of 6 eV - 13.6 eV) has been recognized as the main source of heating of the neutral interstellar gas. Given the pressure of the interstellar medium (ISM) the FUV field determines whether the thermal balance of the neutral gas results in cold (T approximately 50 - 100 K) clouds (CNM), warm (T about 10,000 K) (WNM), for a combination of the two (the two phase ISM) We present results for the time history of the FUV field for points in the local ISM of the Milky Way Galaxy. The presence of this fluctuating heating rate converts CNM to WNM and vice versa. We show how to calculate the average fractions of the gas in the CNM and WNM when the interstellar gas is subject to this fluctuating FUV field. The knowledge of how these fractions depend on the gas properties (i.e. mean density and composition) and on the FUV-sources (i.e. the star formation rate, or the IMF, or the size distribution of associations) is a basic step in building any detailed model of the large scale behavior of the ISM and the mutual relation between the ISM and the SFR.

Hollenbach, David↗
NASA NTRS1994

Low density of neutral hydrogen and helium in the local interstellar medium: Extreme Ultraviolet Explorer photometry of the Lyman continuum of the hot white dwarfs MCT 0501-2858, MCT 0455-2812, HZ 43, and GD 153

The first comprehensive sky survey of the extreme ultraviolet (EUV) spectral range performed by the Extreme Ultraviolet Explorer (EUVE) has uncovered a handful of very bright sources at wavelengths longer than the He I 504 A photoionization edge. Among these objects are four white dwarfs with exceptionally low interstellar medium (ISM) column densities along the line of sight. Analysis of EUV photometry of the He-rich DO white dwarf MCT 0501-2858 and the H-rich DA white dwarf MCT 0455-2812 along one line of sight and of the DA white dwarfs HZ 43 and GD 153 near the north Galactic pole indicates that the overall minimum column density of the neutral material centered on the Sun is N(H I) = 0.5-1.0 x 10(exp 18)/sq cm. In the case of MCT 0501-2858, EUV photometric measurements provide a clear constraint to the effective temperature (60,000-70,000 K). Given these neutral hydrogen columns, the actual contribution to the density of neutral species from the immediate solar environment (the 'local fluff') would only cover a distance of approximately equals 2-3 pc (assuming an average density n(H I) = 0.1/cu cm) leaving these lines of sight almost entirely within the hot phase of the ISM. A preliminary examination of the complete EUVE long-wavelength survey indicates that these lines of sight are exceptional and set a minimum column density in the solar environment.

Vennes, Stephane↗
DOE OSTI2024

Developing a Control Strategy for Minimum Airflow Setting Considering CO2 Level and Energy Consumption in a Variable Air Volume System

In an office building equipped with a Variable Air Volume (VAV) system, this paper introduces a novel method for controlling the minimum supply airflow fraction in each zone’s VAV box, having a capability to consider indoor CO2 level and energy consumption. The EnergyPlus simulation using the medium office prototype model was employed, which evaluated the performance of the energy and CO2 concentration for five VAV box airflow control strategies. The paper focuses on CO2 concentration-based airflow control method and compares it with other four methods including conventional single-max, reduced minimum single-max, demand-controlled ventilation(DCV), and dualmax control methods according to guidelines and common practices. The newly proposed control strategy directly correlates the minimum airflow fraction to CO2 concentration. A general trend emerged when comparing CO2 concentrations—lower minimum airflow fractions were associated with higher concentrations. The proposed control method effectively maintained low CO2 concentrations and enabled a lower airflow fraction contributing to energy consumption reduction. It was confirmed that heating energy consumption in climate zone 4A, 5B, and 6A showed a maximum saving of approximately 30% compared to the conventional single-max and dual max control strategies. It was found that cooling energy consumption in climate zone 4A and 6A can achieve a maximum saving of approximately 10% compared to the conventional control strategies. The proposed CO2 concentration-based control logic is promising as it not only improves the indoor air quality lowering the CO2 concentration in the occupied spaces, but also contributes to HVAC energy savings.

Lee, Jong Man↗
NASA NTRS2015

Physical Models of Layered Polar Firn Brightness Temperatures from 0.5 to 2 GHz

We investigate physical effects influencing 0.5-2 GHz brightness temperatures of layered polar firn to support the Ultra Wide Band Software Defined Radiometer (UWBRAD) experiment to be conducted in Greenland and in Antarctica. We find that because ice particle grain sizes are very small compared to the 0.5-2 GHz wavelengths, volume scattering effects are small. Variations in firn density over cm- to m-length scales, however, cause significant effects. Both incoherent and coherent models are used to examine these effects. Incoherent models include a 'cloud model' that neglects any reflections internal to the ice sheet, and the DMRT-ML and MEMLS radiative transfer codes that are publicly available. The coherent model is based on the layered medium implementation of the fluctuation dissipation theorem for thermal microwave radiation from a medium having a nonuniform temperature. Density profiles are modeled using a stochastic approach, and model predictions are averaged over a large number of realizations to take into account an averaging over the radiometer footprint. Density profiles are described by combining a smooth average density profile with a spatially correlated random process to model density fluctuations. It is shown that coherent model results after ensemble averaging depend on the correlation lengths of the vertical density fluctuations. If the correlation length is moderate or long compared with the wavelength (approximately 0.6x longer or greater for Gaussian correlation function without regard for layer thinning due to compaction), coherent and incoherent model results are similar (within approximately 1 K). However, when the correlation length is short compared to the wavelength, coherent model results are significantly different from the incoherent model by several tens of kelvins. For a 10-cm correlation length, the differences are significant between 0.5 and 1.1 GHz, and less for 1.1-2 GHz. Model results are shown to be able to match the v-pol SMOS data closely and predict the h-pol data for small observation angles.

layered polar firn emission↗
DOE OSTI2022

Experimental driving performance evaluation of battery-powered medium and heavy duty all-electric vehicles

As the push to reduce air pollutants and carbon dioxide for global warming continues, there is increasing interest in the development and deployment of battery electric vehicles for heavy-duty applications as one of the critical and challenging steps of a broader effort to fully electrify the transportation sector. This study evaluated and quantified the energy consumption rates and energy regeneration rates for three heavy-duty battery electric vehicles (a step van, a yard tractor, and a class 8 truck) using driving cycle tests with a heavy-duty vehicle chassis dynamometer. Information in this area is currently very limited, and yet it is critical to understanding how effective heavy-duty battery electric vehicles will be for a wide range of applications as the electrification of the heavy-duty vehicle market continues to expand. Energy consumption rates ranged from 0.37 and 2.71 kWh/km for most vehicle/cycle combinations. On a diesel liter energy-equivalent basis, the heavy-duty vehicles had approximately 3 to 6 times better energy consumption rates compared to comparable diesel vehicles, with weight normalized energy consumption rates also comparing favorably to the current and future greenhouse gas/fuel economy standards for equivalent diesel vehicles. Based on battery capacities ranging from 80 to 215 kWh, the vehicle ranges varied from 38.18 km to 171.2 km, with ranges of 115.9 km to 171.2 km for most types of driving and lower ranges of 38.18 to 42.20 km for sustained grade cycles. Overall, the advantage of improved energy consumption rates coupled with improvements that can be expected for battery technology and vehicle range, provide promise for expanded use of heavy-duty vehicles going into the future.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2024

3D small-gain formula allowing strong focusing and harmonic lasing for a ring-based x-ray free electron laser oscillator

We present a detailed derivation of a formula for the small-gain calculation for an x-ray free electron laser oscillator (XFELO) based on a medium-energy (3–4 GeV) storage ring. We found harmonic lasing and strong focusing are essential for this beam energy range. Taking the small-signal low-gain formula developed by Kim and his colleagues, we modified it in such a way that the gain can be calculated without the “no focusing approximation,” and a strong focusing can be applied, as well as harmonic lasing. In this formula, the gain is represented as a product of two factors with one of them depending only on the harmonic number, undulator period, and gap. Using this factor, we show that it is favorable to use harmonic lasing to achieve hard x-ray FEL working in the small-signal low-gain regime with the medium-energy electron beam. Our formula also allows FEL optimization by varying the vertical gradient of the undulator, the vertical dispersion, and the horizontal and vertical focusing, independently. As an example, we applied this formula to study the feasibility of an XFELO option for the National Synchrotron Light Source II (NSLS-II) upgrade. Since a quite high peak current is required for the FEL, collective effects of beam dynamics in medium-energy synchrotrons significantly affect the electron beam parameters. We carried out a multiparameter optimization taking collective effects into account. Note, even though our example is for a ring-based XFELO at 3 to 4 GeV, the formula and, in particular, the approach developed here may be applied to other types of FELs. Published by the American Physical Society 2024

36 MATERIALS SCIENCE↗
NASA NTRS1975

Remarks on the theory of aerodynamic noise

The accuracy of approximations employed in the Lighthill theory in current aerodynamic noise research is critically evaluated. Based on the method of matched asymptotic expansions, the full Navier-Stokes equations are expanded for small Mach numbers. To the first order, the near-field is generally nonisentropic. The pressure field (pseudo-sound) is generated by the incompressible Reynolds stresses in the turbulent flow and the velocity, pressure perturbation, and their derivatives on the boundaries. In the far-field, the first-order pressure (acoustic) field satisfying a linear wave equation is obtained by matching with the pseudo-sound field. A uniformly valid solution for the pressure field in a stationary or uniformly moving medium is obtained. The solution shows that the generation of the first-order aerodynamic noise does not depend on the viscous, thermal, or entropy effects in the adiabatic flow nor on the shear stress on a smooth rigid boundary.

Pan, Y. S.↗
NASA NTRS1975

Multifrequency techniques for studying interplanetary scintillations

Rytov's approximation, or the method of smooth perturbations, is utilized to derive the temporal frequency spectra of the amplitude and phase fluctuations of multifrequency plane and spherical waves propagating in the interplanetary medium and solar corona. It is shown that multifrequency observations of interplanetary scintillations using either compact radio stars of spacecraft radio signals are desirable because the correlation of the multifrequency waves yields additional independent measurements of the solar wind and turbulence. Measurements of phase fluctuations are also desirable because, unlike amplitude fluctuations, they provide information on the full range of scale sizes for the electron-density fluctuations. It is also shown that a coherent dual-frequency radio system is particularly useful in making such measurements. In addition to providing a means for interpreting observations of multifrequency interplanetary scintillations, the present analysis is essential for estimating the effects of solar corona turbulence on the communications and navigation of a spacecraft whose line-of-sight path passes close to the sun.

Woo, R.↗
NASA NTRS1996

Buoyancy-Driven Heat Transfer During Application of a Thermal Gradient for the Study of Vapor Deposition at Low Pressure Using and Ideal Gas

A mathematical model has been developed to determine heat transfer during vapor deposition of source materials under a variety of orientations relative to gravitational accelerations. The model demonstrates that convection can occur at total pressures as low as 10-2 mm Hg. Through numerical computation, using physical material parameters of air, a series of time steps demonstrates the development of flow and temperature profiles during the course of vapor deposition. These computations show that in unit gravity vapor deposition occurs by transport through a fairly complicated circulating flow pattern when applying heat to the bottom of the vessel with parallel orientation with respect to the gravity vector. The model material parameters for air predict the effect of kinematic viscosity to be of the same order as thermal diffusivity, which is the case for Prandtl number approx. 1 fluids. Qualitative agreement between experiment and the model indicates that 6-(2-methyl-4-nitroanilino)-2,4-hexadiyn-l-ol (DAMNA) at these pressures indeed approximates an ideal gas at the experiment temperatures, and may validate the use of air physical constants. It is apparent that complicated nonuniform temperature distribution in the vapor could dramatically affect the homogeneity, orientation, and quality of deposited films. The experimental test i's a qualitative comparison of film thickness using ultraviolet-visible spectroscopy on films generated in appropriately oriented vapor deposition cells. In the case where heating of the reaction vessel occurs from the top, deposition of vapor does not normally occur by convection due to a stable stratified medium. When vapor deposition occurs in vessels heated at the bottom, but oriented relative to the gravity vector between these two extremes, horizontal thermal gradients induce a complex flow pattern. In the plane parallel to the tilt axis, the flow pattern is symmetrical and opposite in direction from that where the vessel is positioned vertically. The ground-based experiments are sufficient preliminary tests of theory and should be of significant interest regarding vapor deposited films in microgravity.

Frazier, D. O.↗
NASA NTRS1987

Effects of afterbody boattail design and empennage arrangement on aeropropulsive characteristics of a twin-engine fighter model at transonic speeds

The effects of empennage arrangement and afterbody boattail design of nonaxisymmetric nozzles on the aeropropulsive characteristics of a twin-engine fighter-type model have been determined in an investigation conducted in the Langley 16-Foot Transonic Tunnel. Three nonaxisymmetric and one twin axisymmetric convergent-divergent nozzle configurations were tested with three different tail arrangements: a two-tail V-shaped arrangement; a staggered, conventional three-tail arrangement; and a four-tail arrangement similar to that on the F-18. Two of the nonaxisymmetric nozzles were also vectorable. Tests were conducted at Mach numbers from 0.60 to 1.20 over an angle-of-attack range from -3 deg to 9 deg. Nozzle pressure ratio was varied from 1 (jet off) to approximately 12, depending on Mach number. Results indicate that at design nozzle pressure ratio, the medium aspect ratio nozzle (with equal boattail angles on the nozzle sidewalls and upper and lower flaps) had the lowest zero angle of attack drag of the nonaxisymmetric nozzles for all tail configurations at subsonic Mach numbers. The drag levels of the twin axisymmetric nozzles were competitive with those of the medium-aspect-ratio nozzle at subsonic Mach number.

Bangert, Linda S.↗