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Supersonic propeller noise in a uniform flow
The sound field produced by a supersonic propeller operating in a uniform flow is investigated. The main interest is the effect of the finite forward flight speed on the directivity of the sound field as seen by an observer on the aircraft. It is found that there are cones of silence on the axis of the propeller. The semiapex angles on these cones are equal fore and aft of the propeller plane, and depend on the tip Mach number only. The Fourier coefficients of the acoustic pressure contain the Doppler amplification factor. The sound field weakens in the upstream direction and strengthen downstream. Kinematic considerations of the emitted Mach waves not only confirm these results, but also provide physical insight into the sound generation mechanism. The predicted zone of silence and the Doppler amplification factor are compared to the theoretical prediction of shock wave formation and the flight test of the SR3 propeller.
F-111 natural laminar flow glove flight test data analysis and boundary layer stability analysis
An analysis of 34 selected flight test data cases from a NASA flight program incorporating a natural laminar flow airfoil into partial wing gloves on the F-111 TACT airplane is given. This analysis determined the measured location of transition from laminar to turbulent flow. The report also contains the results of a boundary layer stability analysis of 25 of the selected cases in which the crossflow (C-F) and Tollmien-Schlichting (T-S) disturbance amplification factors are correlated with the measured transition location. The chord Reynolds numbers for these cases ranges from about 23 million to 29 million, the Mach numbers ranged from 0.80 to 0.85, and the glove leading-edge sweep angles ranged from 9 deg to 25 deg. Results indicate that the maximum extent of laminar flow varies from 56% chord to 9-deg sweep on the upper surface, and from 51% chord at 16-deg sweep to 6% chord at 25-deg sweep on the lower. The results of the boundary layer stability analysis indicate that when both C-F and T-S disturbances are amplified, an interaction takes place which reduces the maximum amplification factor of either type of disturbance that can be tolerated without causing transition.
Generalized echo squeezing protocol with near-Heisenberg-limit sensitivity and strong robustness against detection noise and variation in squeezing parameter
We present a generalized echo squeezing protocol (GESP) as a generalization of the Schrödinger cat state protocol with the value of the squeezing parameter being an arbitrary number rather than π / 2 . We show analytically that over a very broad range of the squeezing parameter the sensitivity of the GESP reaches the Heisenberg limit within a factor of 2 . For a large number of atoms, N , this plateau interval is almost the whole range from zero to π / 2 , and the sensitivity is independent of the parity of N . Therefore, it is possible to operate a sensor over a wide interval of the squeezing parameter without changing the sensitivity. This is to be contrasted with the conventional echo squeezing protocol (CESP) which only works for a very small interval of the squeezing parameter. We also show that, in contrast to the CESP, the sensitivity of the GESP is close to the quantum Cramér-Rao bound over the whole range of the squeezing parameter, indicating that the phase-shift information contained in the quantum state is near-optimally extracted. We find that the enhancement in sensitivity in the case of the GESP is due to a combination of two parameters: the phase magnification factor (PMF) and the noise amplification factor (NAF). As the value of the squeezing parameter increases, both PMF and NAF increase, while keeping the ratio of the PMF to the NAF essentially constant, yielding a net enhancement of sensitivity at the Heisenberg limit within a factor of 2 over the whole plateau interval. An important consequence of this behavior is that the robustness of the GESP against detection noise easily exceeds that of the CESP for a broad range of values of the squeezing parameter. As such, in the context of an experimental study, it should be possible to achieve a net enhancement in sensitivity higher than that for the CESP, under typical conditions where detection noise exceeds the quantum projection noise of an unsqueezed state with the same number of atoms. Finally, we consider the fragility of the GESP against decoherence mechanisms, and show how a balance between the fragility against the decoherence mechanisms and the robustness against detection noise would in practice determine the optimal choice of parameters for the GESP.
Ground shock due to Rayleigh waves from sonic booms.
Steady state vertical displacements at surface of elastic half-space due to Rayleigh waves from sonic boom, obtaining shock amplification factors
Forecasting generative amplification
Generative networks are perfect tools to enhance the speed and precision of LHC simulations. Especially when generating events beyond the size of the training dataset, it is important to understand their statistical precision. We present two complementary methods to estimate the amplification factor without large holdout datasets. Averaging amplification uses Bayesian networks or ensembling to estimate amplification from the precision of integrals over given phase-space volumes. Differential amplification uses hypothesis testing to quantify amplification without any resolution loss. Applied to state-of-the-art event generators, both methods indicate that amplification is already possible in specific regions of phase space.
Direct solar-pumped iodine laser amplifier
The optimum conditions of a solar pumped iodine laser are found in this research for the case of a continuous wave operation and a pulsed operation. The optimum product of the pressure(p) inside the laser tube and the tube diameter(d) was pd=40 approx. 50 torr-cm on the contrary to the case of a high intensity flashlamp pumped iodine laser where the optimum value of the product is known to be pd=150 torr-cm. The pressure-diameter product is less than 1/3 of that of the high power iodine laser. During the research period, various laser materials were also studied for solar pumping. Among the laser materials, Nd:YAG is found to have the lowest laser threshold pumping intensity of about 200 solar constant. The Rhodamine 6G was also tested as the solar pumped laser material. The threshold pumping power was measured to be about 20,000 solar constant. The amplification experiment for a continuously pumped iodine laser amplifier was performed using Vortek solar simulator and the amplification factors were measured for single pass amplification and triple pass amplification of the 15 cm long amplifier tube. The amplification of 5 was obtained for the triple pass amplification.
Two-frequency laser with distributed feedback formed by a space charge wave
The regimes of amplification and generation of optical TE waves arising on a grating formed by a space charge wave (SCW) in a plane optical waveguide based on an n-GaAs semiconductor are considered. For the perturbed n-GaAs waveguide, the reflectance and transmittance of TE modes with the same indices (m = n = 0) are calculated depending on the pump level and length of interaction between the optical and SCWs. It is shown that even with a relatively small depth of modulation of the dielectric constant (Δε≈10{sup −5}) under conditions of high optical pumping (with an amplification factor γ≈150 cm{sup −1}) and corresponding SCW-optical interaction length, there is a possibility of not only amplification, but also generation of forward and backward optical modes at a wavelength of 10.6 μm. The results can be used to create tunable semiconductor laser generators based on the SCW-optical interaction and operating in the near and mid-IR range.
Convolutional Neural Network for Transition Modeling Based on Linear Stability Theory
Transition prediction is an important aspect of aerodynamic design because of its impact on skin friction and potential coupling with flow separation characteristics. Traditionally, the modeling of transition has relied on correlation-based empirical formulas based on integral quantities such as the shape factor of the boundary layer. However, in many applications of computational fluid dynamics, the shape factor is not straightforwardly available or not well-defined. We propose using the complete velocity profile along with other quantities (e.g., frequency, Reynolds number) to predict the perturbation amplification factor. While this can be achieved with regression models based on a classical fully connected neural network, such a model can be computationally more demanding. We propose a novel convolutional neural network inspired by the underlying physics as described by the stability equations. Specifically, convolutional layers are first used to extract integral quantities from the velocity profiles, and then fully connected layers are used to map the extracted integral quantities, along with frequency and Reynolds number, to the output (amplification ratio). Numerical tests on classical boundary layers clearly demonstrate the merits of the proposed method. More importantly, we demonstrate that, for Tollmien-Schlichting instabilities in two-dimensional, low-speed boundary layers, the proposed network encodes information in the boundary layer profiles into an integral quantity that is strongly correlated to a well-known, physically defined parameter – the shape factor.
Effect of 3D Roughness Patch on Instability Amplification in a Supersonic Boundary Layer
Surface roughness is known to have a substantial impact on the aerothermodynamic loading of high-speed vehicles, particularly via its influence on the laminar-turbulent transition process within the boundary layer. Numerical simulations are performed to investigate the effects of a distributed region of densely packed, sinusoidal shape roughness elements on a Mach 3.5 flat plate boundary layer for flow conditions corresponding to the planned conditions of an upcoming experiment in the Mach 3.5 Supersonic Low Disturbance Tunnel at the NASA Langley Research Center. Analysis of convective instabilities in the wake of the roughness patch was reported in a previous paper and the current work extends that analysis to instability amplification across the length of the roughness patch. Quasi-parallel stability analysis of the modified boundary layer flow over the patch indicates two dominant families of unstable disturbances, namely, a group of high frequency modes that amplify in localized regions along the roughness patch and another group of low frequency modes that have smaller peak amplification rates but amplify steadily both above the roughness patch and in the wake region behind it. The results suggest that the amplification factors associated with the high-frequency modes are sufficiently low, at least for the roughness patches considered in this paper, so that these modes are unlikely to have a major influence on the transition process. The amplification of the low-frequency modes within the region of the roughness patch is further quantified via direct numerical simulations. Results confirm the strongly destabilizing influence of the roughness patch on the first mode instabilities, yielding an N-factor increment of ΔN ≈ 3.6 for a roughness patch length of eight wavelengths.
On Space-Time Inversion Invariance and its Relation to Non-Dissipatedness of a CESE Core Scheme
The core motivating ideas of the space-time CESE method are clearly presented and critically analyzed. It is explained why these ideas result in all the simplifying and enabling features of the CESE method. A thorough discussion of the a scheme, a two-level non-dissipative CESE solver of a simple advection equation with two independent mesh variables and two equations per mesh point is also presented. It is shown that the scheme possesses some rather intriguing properties such as: (i) its two independent mesh variables separately satisfy two decoupled three-level leapfrog schemes and (ii) it shares with the leapfrog scheme the same amplification factors, even though the a scheme and the leapfrog scheme have completely different origins and structures. It is also explained why the leapfrog scheme is not as robust as the a scheme. The amplification factors/matrices of several non-dissipative schemes are carefully studied and the key properties that contribute to their non-dissipatedness are clearly spelled out. Finally we define and establish space-time inversion (STI) invariance for several non-dissipative schemes and show that their non-dissipatedness is a result of their STI invariance.
Far-Infrared Hydrogen Lasers in the Peculiar Star MWC 349A
Far-infrared hydrogen recombination lines H15(alpha)(169.4 micrometers), H12(alpha)(88.8 micrometers), and H10(alpha)(52.5 micrometers) were detected in the peculiar luminous star MWC 349A from the Kuiper Airborne Observatory. Here it is shown that at least H15(alpha) is strongly amplified, with the probable amplification factor being greater than or about equal to 10(exp 3) and a brightness temperature that is greater than or about equal to 10(exp 7) kelvin. The other two lines also show signs of amplification, although to a lesser degree. Beyond H10(alpha) the amplification apparently vanishes. The newly detected amplified lines fall into the laser wavelength domain. These lasers, as well as the previously detected hydrogen masers may originate in the photoionized circumstellar disk of MWC 349A and constrain the disk's physics and structure.
Instability Wave–Streak Interactions in a High Mach Number Boundary Layer at Flight Conditions
The interaction of stationary streaks undergoing nonmodal growth with modally unstable instability waves in a hypersonic boundary-layer flow is studied using numerical computations. The geometry and flow conditions are selected to match a relevant trajectory location from the ascent phase of the HIFiRE-1 flight experiment; namely, a 7 degree half-angle, circular cone with 2.5 mm nose radius, freestream Mach number equal to 5.30, unit Reynolds number equal to 13.42 m -1 , and wall-to-adiabatic temperature ratio of approximately 0.35 over most of the vehicle. This paper investigates the nonlinear evolution of initially linear optimal disturbances that evolve into finite-amplitude streaks, followed by an analysis of the modal instability characteristics of the perturbed, streaky boundary-layer flow. The investigation is performed with stationary direct numerical simulations (DNS) and plane-marching parabolized stability equations (PSE), in conjunction with partial-differential-equation-based planar eigenvalue analysis. The overall effect of streaks is to reduce the peak amplification factors of instability waves, indicating a possible downstream shift in the onset of laminar-turbulent transition. The present study confirms previous findings that the mean flow distortion of the nonlinear streak perturbation reduces the amplification rates of the Mack-mode instability. More importantly, however, the present results demonstrate that the spanwise varying component of the streak can produce a larger effect on the Mack-mode amplification. The study with selected azimuthal wavenumbers for the stationary streaks reveals that a wavenumber of approximately 1.4 times larger than the optimal wavenumber is more effective in stabilizing the planar Mack-mode instabilities. In the absence of unstable first-mode waves for the present cold-wall condition, transition onset is expected to be delayed until the peak streak amplitude increases to nearly 35 percent of the freestream velocity, when intrinsic instabilities of the boundary-layer streaks begin to dominate the transition process. For streak amplitudes below that limit a significant net stabilization is achieved, yielding a potential transition delay that can exceed 100 percent of the length of the laminar region in the uncontrolled case.
Transition Analysis for the CRM-NLF Wind Tunnel Configuration using Transport Equation Models and Linear Stability Correlations
Transition models based on auxiliary transport equations augmenting the Reynolds-averaged Navier-Stokes (RANS) framework rely upon transition correlations that were derived from a limited number of low-speed experiments. Furthermore, these models often account for only a subset of the relevant transition mechanisms and/or cannot accurately predict the sensitivity of those mechanisms to the changes in significant flow parameters. A preceding investigation had targeted the assessment of the transport-equation-based transition models in NASA's OVERFLOW 2.3b solver, namely, the amplification factor transport (AFT-2017b) equation model coupled with the Spalart-Allmaras RANS model and the Langtry-Menter transition models (LM2009 without crossflow effects and LM2015 including the modeling of crossflow transition) implemented with Menter’s shear-stress transport equation (SST2003) RANS model. Comparisons with recent measurements at transonic freestream conditions on the Common Research Model with Natural Laminar Flow (CRM-NLF) reinforced our earlier finding that all three of the above models significantly underpredict the reported extent of the laminar flow region over the entire span of the wing, regardless of the dominant instability mechanism(s) underlying the onset of the transition process. The underprediction of the laminar flow extent was attributed to the failure of the above models in accounting for the stabilizing effect of compressibility on the amplification of Tollmien-Schlichting instabilities. Based on previous linear stability studies related to compressibility effects, the present work proposes modifications to the two classes of transition models that reduce to the original form of each model at low subsonic speeds and do not require any nonlocal flow information or additional transport equation(s). The modifications are shown to significantly improve the predicted laminar extent of the flow and compare well against the data from the CRM-NLF experiment. Additionally, a previous assessment of transition prediction based on the dual, nonparallel N -factor method in conjunction with linear parabolized stability equations (PSE) is extended to additional angles of attack to provide the first comprehensive assessment of transition models based on nonparallel disturbance amplification over the CRM-NLF. In general, the transition criterion based on the dual, nonparallel N-factor method with N TS = N CF = 6 is reasonably successful at correlating with the measured transition fronts at R eMAC = 15 million for all angles of attack investigated herein and provides additional validation of the improved predictions from the compressibility-corrected transition models.
Transition Analysis for the CRM-NLF Wind Tunnel Configuration using Transport Equation Models and Linear Stability Correlations
Transition models based on auxiliary transport equations augmenting the Reynolds-averaged Navier-Stokes (RANS) framework rely upon transition correlations that were derived from a limited number of low-speed experiments. Furthermore, these models often account for only a subset of the relevant transition mechanisms and/or cannot accurately predict the sensitivity of those mechanisms to the changes in significant flow parameters. A preceding investigation had targeted the assessment of the transport-equation-based transition models in NASA's OVERFLOW 2.3b solver, namely, the amplification factor transport (AFT-2017b) equation model coupled with the Spalart-Allmaras RANS model and the Langtry-Menter transition models (LM2009 without crossflow effects and LM2015 including the modeling of crossflow transition) implemented with Menter’s shear-stress transport equation (SST2003) RANS model. Comparisons with recent measurements at transonic freestream conditions on the Common Research Model with Natural Laminar Flow (CRM-NLF) reinforced our earlier finding that all three of the above models significantly underpredict the reported extent of the laminar flow region over the entire span of the wing, regardless of the dominant instability mechanism(s) underlying the onset of the transition process. The underprediction of the laminar flow extent was attributed to the failure of the above models in accounting for the stabilizing effect of compressibility on the amplification of Tollmien-Schlichting instabilities. Based on previous linear stability studies related to compressibility effects, the present work proposes modifications to the two classes of transition models that reduce to the original form of each model at low subsonic speeds and do not require any nonlocal flow information or additional transport equation(s). The modifications are shown to significantly improve the predicted laminar extent of the flow and compare well against the data from the CRM-NLF experiment. Additionally, a previous assessment of transition prediction based on the dual, nonparallel N -factor method in conjunction with linear parabolized stability equations (PSE) is extended to additional angles of attack to provide the first comprehensive assessment of transition models based on nonparallel disturbance amplification over the CRM-NLF. In general, the transition criterion based on the dual, nonparallel N-factor method with N TS = N CF = 6 is reasonably successful at correlating with the measured transition fronts at R eMAC = 15 million for all angles of attack investigated herein and provides additional validation of the improved predictions from the compressibility-corrected transition models.
Aeroheating Predictions for the X-43 Cowl-Closed Configuration at Mach 7 and 10
A pre-flight analysis was conducted for the Mach 7 and Mach 10 X-43 cowl-closed configurations to evaluate three-dimensional flow-field effects on localized heating in the vicinity of the closed cowl flap and sidewall. First, engineering-level analyses based on documented laminar and turbulent surface heating database were used to estimate localized heating amplification factors to account for turbulent flow effects, corner flow effects and the presence of forebody boundary layer trip devices. These estimated factors were applied to 2-D computational predictions to develop surface heat loads. Second, thin-film gauge surface heating data were obtained for a Mach 10 cowl-closed configuration in a reflected shock tunnel at simulated flight conditions. Third, computational fluid dynamics (CFD) flow-field predictions were obtained at Mach 10 ground test conditions to provide comparisons with the engineering database predictions and experimental measurements. Similarly, a CFD solution was also obtained at Mach 7 flight conditions to provide qualitative comparisons with engineering predictions. The Mach 10 CFD predictions compare favorably with the experimental measurements and the engineering estimates for surface heating amplification on the closed cowl. However, experimental measurements were not of sufficient quantity on the sidewall surface to capture the highest localized heating rates, and also the Mach 10 CFD predictions suggest higher peak heating on the sidewall compared to the engineering estimates. Also, the Mach 7 CFD predictions indicate qualitative agreement with the database estimates in terms of flow-field structure and peak heating locations on the closed-cowl flap and sidewall surfaces.
Modeling the Effects of a Backward-Facing Step on Boundary-Layer Transition
We model transition to turbulence in a two-dimensional boundary layer downstream of a backward-facing step (BFS) along a flat plate. With the goal of evaluating the available engineering models for predicting the effects of step excrescences on the transition characteristics, two separate methodologies are used to monitor the streamwise shift in the transition onset location as the step height and the flow speed are varied across the range of a previously reported experiment involving step-height-to-local-displacement-thickness ratios of 0 < h/δ* < 1.6. Unlike the variable N -factor method from the previous literature, both of these methods are general in scope and do not involve any empirical correlations that are specific to step excrescences. The first of these techniques involves an N -factor method that directly accounts for the change in boundary-layer instability characteristics due to the step. Stability computations using the harmonic linearized Navier-Stokes equations (HLNSE), which fully account for the nonparallel-mean-flow effects close to the BFS, indicate that the measured transition locations at nearly all test conditions ( h/δ* < 1.3) correlate well with a computed N -factor of N tr = 7.6, demonstrating a successful stability-based transition criterion related to step excrescences. Linear stability theory, which does not account for nonparallel effects, demonstrates reasonable agreement with the HLNSE results, yielding good predictions for the overall trends, but predicts a somewhat earlier onset of transition than HLNSE. The other methodology used in this work involves transport-equation-based transition models. We first show that the Langtry-Menter y - Re θt transition model cannot accurately predict the location of transition onset for moderate BFS heights because it is unable to accurately account for the flow history effects. Along with the Langtry-Menter transition model, we also show the amplification factor transport model does not produce accurate transition locations for subsonic flow over steps even though it accounts for some flow history effects.
Modeling the Effects of a Backward-Facing Step on Boundary-Layer Transition
We model transition to turbulence in a two-dimensional boundary layer downstream of a backward-facing step (BFS) along a flat plate. With the goal of evaluating the available engineering models for predicting the effects of step excrescences on the transition characteristics, two separate methodologies are used to monitor the streamwise shift in the transition onset location as the step height and the flow speed are varied across the range of a previously reported experiment involving step-height-to-local-displacement-thickness ratios of 0 < h/δ* < 1.6. Unlike the variable N -factor method from the previous literature, both of these methods are general in scope and do not involve any empirical correlations that are specific to step excrescences. The first of these techniques involves an N -factor method that directly accounts for the change in boundary-layer instability characteristics due to the step. Stability computations using the harmonic linearized Navier-Stokes equations (HLNSE), which fully account for the nonparallel-mean-flow effects close to the BFS, indicate that the measured transition locations at nearly all test conditions ( h/δ* < 1.3) correlate well with a computed N -factor of N tr = 7.6, demonstrating a successful stability-based transition criterion related to step excrescences. Linear stability theory, which does not account for nonparallel effects, demonstrates reasonable agreement with the HLNSE results, yielding good predictions for the overall trends, but predicts a somewhat earlier onset of transition than HLNSE. The other methodology used in this work involves transport-equation-based transition models. We first show that the Langtry-Menter y - Re θt transition model cannot accurately predict the location of transition onset for moderate BFS heights because it is unable to accurately account for the flow history effects. Along with the Langtry-Menter transition model, we also show the amplification factor transport model does not produce accurate transition locations for subsonic flow over steps even though it accounts for some flow history effects.