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1
Fu, Jian-Ming, Hai-Min Tang, and Hong-Quan Chen. "Rapid computation of rotary derivatives for subsonic and low transonic flows." Engineering Computations 36, no. 9 (November 11, 2019): 3108–21. http://dx.doi.org/10.1108/ec-09-2018-0399.
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Purpose The purpose of this paper is to develop a new approach for rapid computation of subsonic and low-transonic rotary derivatives with the available steady solutions obtained by Euler computational fluid dynamics (CFD) codes. Design/methodology/approach The approach is achieved by the perturbation on the steady-state pressure of Euler CFD codes. The resulting perturbation relation is established at a reference Mach number between rotary derivatives and normal velocity on surface due to angular velocity. The solution of the reference Mach number is generated technically by Prandtl–Glauert compressibility correction based on any Mach number of interest under the assumption of simple strip theory. Rotary derivatives of any Mach number of interest are then inversely predicted by the Prandtl–Glauert rule based on the reference Mach number aforementioned. Findings The resulting method has been verified for three typical different cases of the Basic Finner Reference Projectile, the Standard Dynamics Model Aircraft and the Orion Crew Module. In comparison with the original perturbation method, the performance at subsonic and low-transonic Mach numbers has significantly improved with satisfactory accuracy for most design efforts. Originality/value The approach presented is verified to be an efficient way for computation of subsonic and low-transonic rotary derivatives, which are performed almost at the same time as an accounting solution of steady Euler equations.
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Zhang, Zhicheng, Yuhong Li, Étienne Spieser, Peng Zhou, and Xin Zhang. "An improved artificial compressibility method for aeroacoustics at low Mach numbers." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 268, no. 5 (November 30, 2023): 3025–33. http://dx.doi.org/10.3397/in_2023_0437.
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This work presents an improved artificial compressibility method that enables correct sound propagation behaviour in low Mach number flows. As an extension of incompressible approaches, it offers the advantage of low computational costs since compressible flow equations are simplified under the isentropic assumption, and the coupling of flow and sound is preserved. The non-uniform speed of sound is considered in this method, and eigenvalue analysis of the modified governing equations reveals that the propagation speed of pseudo waves restores to that of physical acoustic waves. The effect of Mach number on the dissipation and dispersion error is then studied using a two-dimentional monopole example with uniform background flow. The results suggest that the proposed method can provide a satisfactory prediction of sound propagation when the Mach number is below 0.3. Lastly, a direct noise computation of the aerofoil trailing-edge noise problem is performed to assess its capability to deal with the interaction between flow and sound. It shows that the present method can well capture the multiple-tone phenomenon.
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HULSHOFF, S. J., A. HIRSCHBERG, and G. C. J. HOFMANS. "Sound production of vortex–nozzle interactions." Journal of Fluid Mechanics 439 (July 23, 2001): 335–52. http://dx.doi.org/10.1017/s0022112001004554.
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The factors which affect the sound production of a vortex as it passes through a nozzle are investigated at both low and high Mach numbers using time-accurate inviscid-flow computations. Vortex circulation, initial position, and mean-flow Mach number are shown to be the primary factors which influence the amplitude and phase of the sound produced. Nozzle geometry and distribution of vorticity are also shown to play significant roles in determining the detailed form of the signal. Additionally, it is shown that solution bifurcations are possible at sufficiently large values of vortex circulation. Comparisons are made between sound signals computed directly using a numerical method for the Euler equations and predictions obtained using a compressible vortex-sound analogy coupled with a compact-source assumption for the computation of vorticity dynamics. The results confirm that the latter approach is accurate for a range of problems with low mean-flow Mach numbers. At higher Mach numbers, however, the non-compactness of the source becomes apparent, resulting in significant changes to the character of the signal which cannot be predicted using the analogy-based approach. Implications for the construction of simplified models of vortex sound in solid-rocket nozzles are discussed.
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Donzis, Diego A., and Shriram Jagannathan. "Fluctuations of thermodynamic variables in stationary compressible turbulence." Journal of Fluid Mechanics 733 (September 23, 2013): 221–44. http://dx.doi.org/10.1017/jfm.2013.445.
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AbstractA large database of new direct numerical simulations of forced compressible turbulence on up to $204{8}^{3} $ grids, and a range of Reynolds (${R}_{\lambda } $) and turbulent Mach (${M}_{t} $) numbers, is analysed to study the scaling of pressure, density and temperature fluctuations. Small-perturbation analysis is used to study the scaling of variances, and different cross-correlations as well as spectra. Qualitative differences are observed between low and high ${M}_{t} $. The probability density functions (p.d.f.s) of pressure and density are negatively skewed at low ${M}_{t} $ (consistent with incompressible results) but become positively skewed at high ${M}_{t} $. The positive tails are found to follow a log-normal distribution. A new variable is introduced to quantify departures from isentropic fluctuations (an assumption commonly used in the literature) and is found to increase as ${ M}_{t}^{2} $. However, positive fluctuations of pressure and density tend to be more isentropic than negative fluctuations. In general, Reynolds number effects on single-point statistics are observed to be weak. The spectral behaviour of pressure, density and temperature is also investigated. While at low ${M}_{t} $, pressure appears to scale as ${k}^{- 7/ 3} $ ($k$ is the wavenumber) in the inertial range as in incompressible flows, a ${k}^{- 5/ 3} $ scaling also appears to be consistent with the data at a range of Mach numbers. Density and temperature spectra are found to scale as ${k}^{- 5/ 3} $ for a range of Mach numbers.
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Freitas Rachid, Felipe B., and Heraldo S. Costa Mattos. "On the Suitability of the Low Mach Number Assumption in the Modeling of the Damage Induced by Pressure Transients in Piping Systems." Journal of Fluids Engineering 121, no. 1 (March 1, 1999): 112–17. http://dx.doi.org/10.1115/1.2821990.
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One-dimensional models for predicting the damage induced by pressure transients in piping systems conveying liquids have been proposed and analysed recently. However, such works have been concerned mainly with the adequacy of the constitutive equations adopted for different pipe materials and with the numerical techniques used for approximating the solution of the resulting mathematical problems. In the present paper the suitability of the simplifying low Mach number assumption adopted in the modeling is investigated. The analysis is carried out based on the eigenvalue problem associated to the governing equations, without appealing to any specific mechanical behavior of the pipe material. Numerical results obtained for the most used pipe materials show that this simplifying assumption is adequate for metallic tubes, but may fail when plastic tubes are considered.
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FREUND, JONATHAN B. "Noise sources in a low-Reynolds-number turbulent jet at Mach 0.9." Journal of Fluid Mechanics 438 (July 5, 2001): 277–305. http://dx.doi.org/10.1017/s0022112001004414.
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The mechanisms of sound generation in a Mach 0.9, Reynolds number 3600 turbulent jet are investigated by direct numerical simulation. Details of the numerical method are briefly outlined and results are validated against an experiment at the same flow conditions (Stromberg, McLaughlin & Troutt 1980). Lighthill's theory is used to define a nominal acoustic source in the jet, and a numerical solution of Lighthill's equation is compared to the simulation to verify the computational procedures. The acoustic source is Fourier transformed in the axial coordinate and time and then filtered in order to identify and separate components capable of radiating to the far field. This procedure indicates that the peak radiating component of the source is coincident with neither the peak of the full unfiltered source nor that of the turbulent kinetic energy. The phase velocities of significant components range from approximately 5% to 50% of the ambient sound speed which calls into question the commonly made assumption that the noise sources convect at a single velocity. Space–time correlations demonstrate that the sources are not acoustically compact in the streamwise direction and that the portion of the source that radiates at angles greater than 45° is stationary. Filtering non-radiating wavenumber components of the source at single frequencies reveals that a simple modulated wave forms for the source, as might be predicted by linear stability analysis. At small angles from the jet axis the noise from these modes is highly directional, better described by an exponential than a standard Doppler factor.
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Skalidis, R., J. Sternberg, J. R. Beattie, V. Pavlidou, and K. Tassis. "Why take the square root? An assessment of interstellar magnetic field strength estimation methods." Astronomy & Astrophysics 656 (December 2021): A118. http://dx.doi.org/10.1051/0004-6361/202142045.
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Context. The magnetic field strength in interstellar clouds can be estimated indirectly from measurements of dust polarization by assuming that turbulent kinetic energy is comparable to the fluctuating magnetic energy, and using the spread of polarization angles to estimate the latter. The method developed by Davis (1951, Phys. Rev., 81, 890) and by Chandrasekhar and Fermi (1953, ApJ, 118, 1137) (DCF) assumes that incompressible magnetohydrodynamic (MHD) fluctuations induce the observed dispersion of polarization angles, deriving B ∝ 1∕δθ (or, equivalently, δθ ∝ MA, in terms of the Alfvénic Mach number). However, observations show that the interstellar medium is highly compressible. Recently, two of us (ST) relaxed the incompressibility assumption and derived instead B ∝ 1/√δθ (equivalently, δθ ∝ MA2). Aims. We explored what the correct scaling is in compressible and magnetized turbulence through theoretical arguments, and tested the assumptions and the accuracy of the two methods with numerical simulations. Methods. We used 26 magnetized, isothermal, ideal-MHD numerical simulations without self-gravity and with different types of forcing. The range of MA and sonic Mach numbers Ms explored are 0.1 ≤ MA ≤ 2.0 and 0.5 ≤ Ms ≤ 20. We created synthetic polarization maps and tested the assumptions and accuracy of the two methods. Results. The synthetic data have a remarkable consistency with the δθ ∝ MA2 scaling, which is inferred by ST, while the DCF scaling failed to follow the data. Similarly, the assumption of ST that the turbulent kinetic energy is comparable to the root-mean-square (rms) of the coupling term of the magnetic energy between the mean and fluctuating magnetic field is valid within a factor of two for all MA (with the exception of solenoidally driven simulations at high MA, where the assumption fails by a factor of 10). In contrast, the assumption of DCF that the turbulent kinetic energy is comparable to the rms of the second-order fluctuating magnetic field term fails by factors of several to hundreds for sub-Alfvénic simulations. The ST method shows an accuracy better than 50% over the entire range of MA explored; DCF performs adequately only in the range of MA for which it has been optimized through the use of a “fudge factor”. For low MA, it is inaccurate by factors of tens, since it omits the magnetic energy coupling term, which is of first order and corresponds to compressible modes. We found no dependence of the accuracy of the two methods on Ms. Conclusions. The assumptions of the ST method reflect better the physical reality in clouds with compressible and magnetized turbulence, and for this reason the method provides a much better estimate of the magnetic field strength over the DCF method. Even in super-Alfvénic cases where DCF might outperform ST, the ST method still provides an adequate estimate of the magnetic field strength, while the reverse is not true.
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Lee, Incheol, and Duck Joo Lee. "Investigation on the Source Locations of Axisymmetric Screech Tones Utilizing Data from Numerical Simulation." Journal of Theoretical and Computational Acoustics 27, no. 04 (January 21, 2019): 1850058. http://dx.doi.org/10.1142/s2591728518500585.
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The source locations of axisymmetric modes of screech tones are numerically investigated. Fourth-order optimized compact scheme and fourth-order Runge–Kutta method are used to solve the 2-D axisymmetric Euler equations. The screech tone is successfully reproduced, and the change in wavelength with respect to jet Mach number shows good agreement with the experimental data. At various low supersonic jet Mach numbers, the time-averaged contours of Mach number and root-mean-square pressure are investigated to identify the location of maximum interaction between shock cell structures and vortices. The source locations of two axisymmetric modes, A1 and A2 modes, are distinctly visualized and identified; the screech tones of A1 mode are generated at the apex of fifth shock cell, and the screech tones of A2 mode are generated at the apex of fourth shock cell. Based on the observation, a simple formula for the prediction of axisymmetric modes of screech tones is proposed. The formula is derived based on a form of Rossiter equation, with the assumption of different convection speeds along the jet mixing layer. The proposed formula successfully estimates the frequency of two axisymmetric modes of screech tones, which verifies that the identified source locations of the axisymmetric screech tones are reasonable.
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Ouajdi, Sanae, Fayçal Moufekkir, Ahmed Mezrhab, and Jean Pierre Fontaine. "Numerical Method of Weakly Compressible Poiseuille Flow Using Lattice Boltzmann Method." Defect and Diffusion Forum 384 (May 2018): 99–116. http://dx.doi.org/10.4028/www.scientific.net/ddf.384.99.
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The present work focuses on the numerical simulation of isothermal and weakly compressible Poiseuille flow in a planar channel using the Lattice Boltzmann method with multiple times of relaxation (MRT-LBE) coupled to the Finite Difference method (FDM). The active fluid considered is the air under low Mach number assumption. The flow is two-dimensional, laminar and all the physical properties are constants except the density which varies in the sense of the Boussinesq approximation. The effects of the compressibility, the inclination angle and the Reynolds number on the dynamical and thermal fields are studied numerically. The results are presented in terms of streamlines, isotherms and transverse velocity.
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Almagro, Antonio, Manuel García-Villalba, and Oscar Flores. "A numerical study of a variable-density low-speed turbulent mixing layer." Journal of Fluid Mechanics 830 (October 2, 2017): 569–601. http://dx.doi.org/10.1017/jfm.2017.583.
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Direct numerical simulations of a temporally developing, low-speed, variable-density, turbulent, plane mixing layer are performed. The Navier–Stokes equations in the low-Mach-number approximation are solved using a novel algorithm based on an extended version of the velocity–vorticity formulation used by Kim et al. (J. Fluid Mech., vol 177, 1987, 133–166) for incompressible flows. Four cases with density ratios $s=1,2,4$ and 8 are considered. The simulations are run with a Prandtl number of 0.7, and achieve a $Re_{\unicode[STIX]{x1D706}}$ up to 150 during the self-similar evolution of the mixing layer. It is found that the growth rate of the mixing layer decreases with increasing density ratio, in agreement with theoretical models of this phenomenon. Comparison with high-speed data shows that the reduction of the growth rates with increasing density ratio has a weak dependence with the Mach number. In addition, the shifting of the mixing layer to the low-density stream has been characterized by analysing one-point statistics within the self-similar interval. This shifting has been quantified, and related to the growth rate of the mixing layer under the assumption that the shape of the mean velocity and density profiles do not change with the density ratio. This leads to a predictive model for the reduction of the growth rate of the momentum thickness, which agrees reasonably well with the available data. Finally, the effect of the density ratio on the turbulent structure has been analysed using flow visualizations and spectra. It is found that with increasing density ratio the longest scales in the high-density side are gradually inhibited. A gradual reduction of the energy in small scales with increasing density ratio is also observed.
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Blair, Dane. "Seismic radiation from an explosive column." GEOPHYSICS 75, no. 1 (January 2010): E55—E65. http://dx.doi.org/10.1190/1.3294860.
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A scale-independent analytic model of seismic radiation from a column of explosive is derived in terms of the blast hole radius [Formula: see text], charge length, explosive velocity of detonation (VoD), and distance [Formula: see text] to a monitoring station. The treatment is based on linear viscoelasticity in which the nonlinear response of rock close to the blast hole is modeled as a sufficiently low-[Formula: see text] material having an exponential increase in [Formula: see text] with distance from the source. Although limited by this assumption, the present analytic model avoids the more serious discretization problems associated with numerical models when driven by the high-frequency pressure load. Furthermore, numerical models are not useful in displaying scale independence. Exploration and mining geophysics typically require short explosive charges characterized by a length/radius of approximately 10. The model shows that for such charges ata small [Formula: see text], the seismic displacement increases with the VoD; however, as the [Formula: see text] increases, the displacement becomes insensitive to the VoD. Field measurements of seismic-wave transmission resulting from short charges show that a plot of rise time against traveltime is approximately linear, with an intercept that traditionally is assumed to be the rise time of the explosive source itself. However, the present model shows that this assumption is incorrect and suggests that if measurements could be made very close to the blast hole, then the rise-time plot would be nonlinear and well might correspond to the region of nonlinear rock response. The extractive mining industry typically requires long explosive columns characterized by a length/radius [Formula: see text], for which [Formula: see text] typifies the near-field. The model predicts that seismic transmission in this region is dominated completely by P-Mach and S-Mach wave propagation, dependent on the VoD.
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Sommer, T. P., R. M. C. So, and H. S. Zhang. "Supersonic Flow Calculations Using a Reynolds-Stress and a Thermal Eddy Diffusivity Turbulence Model." Journal of Fluids Engineering 116, no. 3 (September 1, 1994): 469–76. http://dx.doi.org/10.1115/1.2910300.
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A second-order model for the velocity field and a two-equation model for the temperature field are used to calculate supersonic boundary layers assuming negligible real gas effects. The modeled equations are formulated on the basis of an incompressible assumption and then extended to supersonic flows by invoking Morkovin’s hypothesis, which proposes that compressibility effects are completely accounted for by mean density variations alone. In order to calculate the near-wall flow accurately, correcting functions are proposed to render the modeled equations asymptotically consistent with the behavior of the exact equations near the wall and, at the same time, display the proper dependence on the molecular Prandtl number. Thus formulated, the near-wall second-order turbulence model for heat transfer is applicable to supersonic flows with different Prandtl numbers. The model is validated against supersonic flows with free-stream Mach numbers as high as 10 and wall temperature ratios as low as 0.3. Among the flow cases considered, the momentum thickness Reynolds number varies from ~4000 to ~21,000. Good correlation with measurements of mean velocity and temperature is obtained. Discernible improvements in the law-of-the-wall are observed, especially in the range where the log-law applies.
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Fulat, Karol, Artem Bohdan, Gabriel Torralba Paz, and Martin Pohl. "Kinetic Simulations of Nonrelativistic High-mach-number Perpendicular Shocks Propagating in a Turbulent Medium." Astrophysical Journal 959, no. 2 (December 1, 2023): 119. http://dx.doi.org/10.3847/1538-4357/ad04dc.
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Abstract Strong nonrelativistic shocks are known to accelerate particles up to relativistic energies. However, for diffusive shock acceleration, electrons must have a highly suprathermal energy, implying the need for very efficient preacceleration. Most published studies consider shocks propagating through homogeneous plasma, which is an unrealistic assumption for astrophysical environments. Using 2D3V particle-in-cell simulations, we investigate electron acceleration and heating processes at nonrelativistic high-Mach-number shocks in electron-ion plasma with a turbulent upstream medium. For this purpose, slabs of plasma with compressive turbulence are simulated separately and then inserted into shock simulations, which require matching of the plasma slabs at the interface. Using a novel procedure of matching electromagnetic fields and currents, we perform simulations of perpendicular shocks setting different intensities of density fluctuations (≲10%) in the upstream region. The new simulation technique provides a framework for studying shocks propagating in turbulent media. We explore the impact of the fluctuations on electron heating, the dynamics of upstream electrons, and the driving of plasma instabilities. Our results indicate that while the presence of turbulence enhances variations in the upstream magnetic field, their levels remain too low to significantly influence the behavior of electrons at perpendicular shocks.
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Tabrizi, Amir Bashirzadeh, and Binxin Wu. "The role of compressibility in computing noise generated at a cavitating orifice." International Journal of Aeroacoustics 18, no. 1 (November 27, 2018): 73–91. http://dx.doi.org/10.1177/1475472x18812801.
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The computational fluid dynamics calculation can be accomplished by solving either compressible or incompressible Navier–Stokes equations to determine the flow-field variables of the noise source. The proper assumption depends on both the physical situation and the Mach number. Although in cavitating devices usually we are dealing with low Mach number flow, cavitation is an acoustic phenomenon that can be affected by compressibility. Cavitation behaves acoustically as a monopole and it is mentioned by some researchers that incompressible solution is sufficient to study the dipole sources. However, in order to study the monopole (and quadrupole) sources a compressible solution may be required. In this study, the role of compressibility in computing noise generated at a cavitating single-hole orifice was investigated using large eddy simulation and Ffowcs Williams–Hawkings formulation. The fluid zone downstream of the orifice where the cavitation occurs was evaluated as the acoustic source which generates sound. Time-accurate solutions of the flow-field variables on source surfaces were obtained from both compressible and incompressible flow simulations. Three cases of cavitation were studied and the sound pressure signals far downstream of the orifice were computed by the Ffowcs Williams–Hawkings formulation. For a developed cavitation regime at low frequencies, there is a big discrepancy between the computed values of sound pressure level from compressible and incompressible simulations, and at higher frequencies greater than 6 kHz, both simulation methods provide almost the same values for sound pressure levels. For a super cavitation regime, both compressible and incompressible simulations provide similar values for sound pressure levels at frequencies greater than 2 kHz. The results of this work demonstrate that the compressibility has a significant role in terms of computing noise generated at a cavitating orifice and cannot be ignored, especially when the noise generated by developed cavitation regimes at low frequencies is investigated.
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Josserand, M. A., and G. C. Lauchle. "Modeling the Wavevector-Frequency Spectrum of Boundary-Layer Wall Pressure During Transition on a Flat Plate." Journal of Vibration and Acoustics 112, no. 4 (October 1, 1990): 523–34. http://dx.doi.org/10.1115/1.2930138.
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A spectral model for the wall-pressure fluctuations induced on a zero pressure gradient, flat, rigid surface by a transitioning boundary layer at low Mach number is developed in this paper. The central assumption used in this modeling is that the space-time statistics associated with the formation, convection, and interaction of turbulent spots in a naturally occurring boundary-layer transition are independent of the space-time statistics of the wall-pressure fluctuations that are induced by the turbulence in the individual spots. Space-time correlations for the spots were determined experimentally and semi-empirical formulae are developed to predict these correlations. Previously published statistical descriptions of turbulence-induced wall-pressure fluctuations are coupled with the spot statistics to arrive at the model for the wavevector-frequency spectrum of the transition region. The basic result suggests that the wall-pressure wavevector-frequency spectrum of a transitioning boundary layer is approximately that produced by a fully-turbulent layer weighted by the intermittency factor.
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Sundermeier, Stephan, Maximilian Passmann, Stefan aus der aus der Wiesche, and Eugeny Y. Kenig. "Flow in Pillow-Plate Channels for High-Speed Turbomachinery Heat Exchangers." International Journal of Turbomachinery, Propulsion and Power 7, no. 2 (March 22, 2022): 12. http://dx.doi.org/10.3390/ijtpp7020012.
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In numerous turbomachinery applications, e.g., in aero-engines with regenerators for improving specific fuel consumption (SFC), heat exchangers with low-pressure loss are required. Pil low-plate heat exchangers (PPHE) are a novel exchanger type and promising candidates for high-speed flow applications due to their smooth profiles avoiding blunt obstacles in the flow path. This work deals with the overall system behavior and gas dynamics of pillow-plate channels. A pillow-plate channel was placed in the test section of a blow-down wind tunnel working with dry air, and compressible flow phenomena were investigated utilizing conventional and focusing schlieren optics; furthermore, static and total pressure measurements were performed. The experiments supported the assumption that the system behavior can be described through a Fanno–Rayleigh flow model. Since only wavy walls with smooth profiles were involved, linearized gas dynamics was able to cover important flow features within the channel. The effects of the wavy wall structures on pressure drop and Mach number distribution within the flow path were investigated, and a good qualitative agreement with theoretical and numerical predictions was found. The present analysis demonstrates that pressure losses in pillow-plate heat exchangers are rather low, although their strong turbulent mixing enables high convective heat transfer coefficients.
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Wu, Zhaoyu, Mingsong Ding, Weizhong Dong, Tiesuo Gao, and Tao Jiang. "Effect of MHD Control on Turbulent Boundary Layer Separation Flow in Scramjet Inlet." Journal of Physics: Conference Series 2381, no. 1 (December 1, 2022): 012015. http://dx.doi.org/10.1088/1742-6596/2381/1/012015.
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Abstract In order to study the effect of MHD control on the separation flow of turbulent boundary layer in the scramjet inlet based on the assumption of low magnetic Reynolds number, considering the source term of turbulent electromagnetic dissipation, the numerical simulation method is developed for electromagnetic field coupled with flow field. A Mach 4 plate is adopted as the basic configuration to assess the accuracy of the solver’s source term of turbulent electromagnetic dissipation. On this basis, numerical simulation of MHD control on the separation flow of boundary layer in scramjet inlet is carried out to study the influence of different electric field strengths and magnetic induction intensity on it. The results show that applying MHD local control alleviates the boundary layer separation in the scramjet inlet. Under different electric field strengths and magnetic induction intensity, the separation vortex’s scale significantly changes. The scale of the separation zone continues to decrease when the electric field strength or magnetic induction intensity increases, and the effect of MHD control is more significant.
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Barrios-Piña, Hector, Stéphane Viazzo, and Claude Rey. "Total energy balance in a natural convection flow." International Journal of Numerical Methods for Heat & Fluid Flow 27, no. 8 (August 7, 2017): 1735–47. http://dx.doi.org/10.1108/hff-03-2016-0093.
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Purpose The purpose of this paper is to show a thermodynamic analysis to determine the contribution of each term of the total energy balance. Design/methodology/approach The thermodynamic analysis comprises a number of numerical simulations where some terms, typically ignored by the commonly used approximations, are removed from the total energy equation to quantify the effects in the flow and heat transfer fields. The case study is the differentially heated square cavity flow, in which the effects of work done by the pressure forces contribute significantly to the energy balance. Because local magnitudes are computed here for discussion, the dimensional form of the governing equations is preferred and a numerical model without any restrictive approximation about the role of the pressure is used. Findings The results show that the work of gravity forces term is in perfect balance with the work of pressure forces term, and thus, ignoring the contribution of one of them yields an incorrect solution. In addition, it is shown that the assumption of zero divergence of the Boussinesq approximation can be erroneous, even for a natural convection flow case where the temperature difference is very small. Research limitations/implications As the flow and heat transfer governing equations are complex, simplifying assumptions are generally used; that is, the Boussinesq and low Mach number approximations. These assumptions are systematically adopted without any validation process and without considering that they modify the physical meaning of one or more of the thermodynamic quantities, particularly the pressure. This fact results in inconsistencies of the different forms of energy. Originality/value This is the first time that the terms of the total energy balance are quantified in such a way, in a differentially heated square cavity flow, which is a case study addressed by several authors.
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Chen, Kang Ping, and Di Shen. "Drainage flow of a viscous compressible fluid from a small capillary with a sealed end." Journal of Fluid Mechanics 839 (February 2, 2018): 621–43. http://dx.doi.org/10.1017/jfm.2018.56.
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Volumetric expansion driven drainage flow of a viscous compressible fluid from a small capillary with a sealed end is studied in the low Mach number limit using the linearized compressible Navier–Stokes equations with no-slip condition. Density relaxation, oscillation and decay as well as the velocity field are investigated in detail. It is shown that fluid drainage is controlled by the slow decay of the standing acoustic wave inside the capillary; and the acoustic wave retards the density diffusion by reducing the diffusion coefficient of the density envelope equation by one half. Remarkably the no-slip flow exhibits a slip-like mass flow rate. The period-averaged mass flow rate at the exit (drainage rate) is found proportional to the fluid’s kinematic viscosity via the density diffusion coefficient and the average drainage speed is independent of the capillary radius. These findings are valid for arbitrarily small capillaries as long as the continuum assumption holds and they are in stark contrast to the classical lubrication based theory. Generalization to a capillary with a sound absorbing end is achieved by a simple model. The reported results offer new insights to the nature of slow viscous compressible flows in very small capillaries.
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Polifke, W., A. Fischer, and T. Sattelmayer. "Instability of a Premix Burner With Nonmonotonic Pressure Drop Characteristic." Journal of Engineering for Gas Turbines and Power 125, no. 1 (December 27, 2002): 20–27. http://dx.doi.org/10.1115/1.1519267.
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Instabilities in combustion systems have frequently been reported to occur when slight changes in operating conditions lead to significant and abrupt changes in flame shape or flame position, i.e., changes in the mode of flame stabilization. The present paper offers an explanation and mathematical model of this observation. The analysis rests on the assumption that changes in the mode of flame stabilization are accompanied by a significant variation of the pressure drop across burner and flame, such that the pressure drop-flow rate characteristic locally displays a negative slope. In the limit of low frequencies (Helmholtz mode), it is then straightforward to show that an oscillatory instability can result from such behavior. An analytical stability criterion is derived, relating the nondimensionalized gradient of the pressure drop characteristic to the Helmholtz number of the burner. The physical mechanism of the instability is explained, and it is observed that the Rayleigh criterion need not be satisfied for this kind of instability to occur. In order to extend the stability analysis to higher frequencies, the transfer matrix for a burner with nonmonotonic pressure drop is derived in the limit of low Mach number and negligible fluctuations of the rate of heat release. The transfer matrix is employed in stability analysis based on a linear acoustic model of a combustion system. Experimental results obtained with an externally premixed swirl burner are presented. The pressure drop characteristic, the observed onset of instability and the instability frequency match the model predictions very well.
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Guicking, L., K. H. Glassmeier, H. U. Auster, M. Delva, U. Motschmann, Y. Narita, and T. L. Zhang. "Low-frequency magnetic field fluctuations in Venus' solar wind interaction region: Venus Express observations." Annales Geophysicae 28, no. 4 (April 15, 2010): 951–67. http://dx.doi.org/10.5194/angeo-28-951-2010.
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Abstract. We investigate wave properties of low-frequency magnetic field fluctuations in Venus' solar wind interaction region based on the measurements made on board the Venus Express spacecraft. The orbit geometry is very suitable to investigate the fluctuations in Venus' low-altitude magnetosheath and mid-magnetotail and provides an opportunity for a comparative study of low-frequency waves at Venus and Mars. The spatial distributions of the wave properties, in particular in the dayside and nightside magnetosheath as well as in the tail and mantle region, are similar to observations at Mars. As both planets do not have a global magnetic field, the interaction process of the solar wind with both planets is similar and leads to similar instabilities and wave structures. We focus on the spatial distribution of the wave intensity of the fluctuating magnetic field and detect an enhancement of the intensity in the dayside magnetosheath and a strong decrease towards the terminator. For a detailed investigation of the intensity distribution we adopt an analytical streamline model to describe the plasma flow around Venus. This allows displaying the evolution of the intensity along different streamlines. It is assumed that the waves are generated in the vicinity of the bow shock and are convected downstream with the turbulent magnetosheath flow. However, neither the different Mach numbers upstream and downstream of the bow shock, nor the variation of the cross sectional area and the flow velocity along the streamlines play probably an important role in order to explain the observed concentration of wave intensity in the dayside magnetosheath and the decay towards the nightside magnetosheath. But, the concept of freely evolving or decaying turbulence is in good qualitative agreement with the observations, as we observe a power law decay of the intensity along the streamlines. The observations support the assumption of wave convection through the magnetosheath, but reveal at the same time that wave sources may not only exist at the bow shock, but also in the magnetosheath.
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Oliveira, T. F., R. B. Miserda, and F. R. Cunha. "Dynamical Simulation and Statistical Analysis of Velocity Fluctuations of a Turbulent Flow behind a Cube." Mathematical Problems in Engineering 2007 (2007): 1–28. http://dx.doi.org/10.1155/2007/24627.
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A statistical approach for the treatment of turbulence data generated by computer simulations is presented. A model for compressible flows at large Reynolds numbers and low Mach numbers is used for simulating a backward-facing step airflow. A scaling analysis has justified the commonly used assumption that the internal energy transport due to turbulent velocity fluctuations and the work done by the pressure field are the only relevant mechanisms needed to model subgrid-scale flows. From the numerical simulations, the temporal series of velocities are collected for ten different positions in the flow domain, and are statistically treated. The statistical approach is based on probability averages of the flow quantities evaluated over several realizations of the simulated flow. We look at how long of a time average is necessary to obtain well-converged statistical results. For this end, we evaluate the mean-square difference between the time average and an ensemble average as the measure of convergence. This is an interesting question since the validity of the ergodic hypothesis is implicitly assumed in every turbulent flow simulation and its analysis. The ergodicity deviations from the numerical simulations are compared with theoretical predictions given by scaling arguments. A very good agreement is observed. Results for velocity fluctuations, normalized autocorrelation functions, power spectra, probability density distributions, as well as skewness and flatness coefficients are also presented.
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Gao, Yuan, Liuming Yang, Yang Yu, Guoxiang Hou, and Zhongbao Hou. "Improved simplified and highly stable lattice Boltzmann methods for incompressible flows." International Journal of Modern Physics C 32, no. 06 (February 28, 2021): 2150077. http://dx.doi.org/10.1142/s0129183121500777.
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In this work, improved simplified and highly stable lattice Boltzmann methods (SHSLBMs) are developed for incompressible flows. The SHSLBM is a newly developed scheme within the lattice Boltzmann method (LBM) framework, which utilizes the fractional step technology to resolve the governing equations recovered from lattice Boltzmann equation (LBE) and reconstructs the equations in the Lattice Boltzmann frame. By this treatment, the SHSLBM directly tracks the macroscopic variables in the evolution process rather than the distribution functions of each grid node, which greatly saves virtual memories and simplifies the implementation of physical boundary conditions. However, the Chapman–Enskog expansion analysis reveals that the SHSLBM recover the weakly compressible Navier–Stokes equations with the low Mach number assumption. Therefore, the original SHSLBM can be regarded as an artificial compressible method and may cause some undesired errors. By modifying the evolution equation for the density distribution function, the improved SHSLBMs can eliminate the compressible effects. The incompressible SHSLBMs are compared with the original SHSLBM in terms of accuracy and stability by simulating several two-dimensional steady and unsteady incompressible flow problems, and the results demonstrate that the present SHSLBMs ensure the second order of accuracy and can reduce the compressible effects efficiently, especially for the incompressible flows with large pressure gradients. We then extended the present SHSLBMs to study the more complicated two-dimensional lid-driven flow and found that the present results are in good agreement with available benchmark results.
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Bra¨unling, W., and F. Lehthaus. "Investigations of the Effect of Annulus Taper on Transonic Turbine Cascade Flow." Journal of Engineering for Gas Turbines and Power 108, no. 2 (April 1, 1986): 285–92. http://dx.doi.org/10.1115/1.3239901.
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In a test facility for rotating annular cascades with three conical test sections of different taper angles (0, 30, 45 deg), experiments are conducted for two geometrically different turbine cascade configurations, a hub section cascade with high deflection and a tip section cascade with low deflection. The evaluation of time-averaged data derived from conventional probe measurements upstream and downstream of the test wheel in the machine-fixed absolute system is based on the assumption of axisymmetric stream surfaces. The cascade characteristics, i.e., mass flow, deflection, and losses, for a wide range of inlet flow angles and outlet Mach numbers are provided in the blade-fixed relative system with respect to the influence of annulus taper. Some of the results are compared with simple theoretical calculations. To obtain some information about the spatial structure of the flow within the cascade passages, surface pressure distributions on the profiles of the rotating test wheels are measured at three different radial blade sections. For some examples those distributions are compared with numerical results on plane cascades of the same sweep and dihedral angles and the same aspect ratios. The computer code used is based on a three-dimensional time-marching finite-volume method solving the Euler equations. Both experimental and numerical results show a fairly good qualitative agreement in the three-dimensional blade surface pressure distributions. This work will be continued with detailed investigations on the spatial flow structure.
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Fossi, Alain, and Alain DeChamplain. "Large eddy simulation of spark ignition of a bluff-body stabilized burner using a subgrid-ignition model coupled with FGM-based combustion models." International Journal of Numerical Methods for Heat & Fluid Flow 27, no. 2 (February 6, 2017): 400–427. http://dx.doi.org/10.1108/hff-07-2015-0299.
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Purpose Safety improvement and pollutant reduction in many practical combustion systems and especially in aero-gas turbine engines require an adequate understanding of flame ignition and stabilization mechanisms. Improved software and hardware have opened up greater possibilities for translating basic knowledge and the results of experiments into better designs. The present study deals with the large eddy simulation (LES) of an ignition sequence in a conical shaped bluff-body stabilized burner involving a turbulent non-premixed flame. The purpose of this paper is to investigate the impact of spark location on ignition success. Particular attention is paid to the ease of handling of the numerical tool, the computational cost and the accuracy of the results. Design/methodology/approach The discrete particle ignition kernel (DPIK) model is used to capture the ignition kernel dynamics in its early stage of growth after the breakdown period. The ignition model is coupled with two combustion models based on the mixture fraction-progress variable formulation. An infinitely fast chemistry assumption is first done, and the turbulent fluctuations of the progress variable are captured with a bimodal probability density function (PDF) in the line of the Bray–Moss–Libby (BML) model. Thereafter, a finite rate chemistry assumption is considered through the flamelet-generated manifold (FGM) method. In these two assumptions, the classical beta-PDF is used to model the temporal fluctuations of the mixture fraction in the turbulent flow. To model subgrid scale stresses and residual scalars fluxes, the wall-adapting local eddy (WALE) and the eddy diffusivity models are, respectively, used under the low-Mach number assumption. Findings Numerical results of velocity and mixing fields, as well as the ignition sequences, are validated through a comparison with their experimental counterparts. It is found that by coupling the DPIK model with each of the two combustion models implemented in a LES-based solver, the ignition event is reasonably predicted with further improvements provided by the finite rate chemistry assumption. Finally, the spark locations most likely to lead to a complete ignition of the burner are found to be around the shear layer delimiting the central recirculation zone, owing to the presence of a mixture within flammability limits. Research limitations/implications Some discrepancies are found in the radial profiles of the radial velocity and consequently in those of the mixture fraction, owing to a mismatch of the radial velocity at the inlet section of the computational domain. Also, unlike FGM methods, the BML model predicts the overall ignition earlier than suggested by the experiment; this may be related to the overestimation of the reaction rate, especially in the zones such as flame holder wakes which feature high strain rate due to fuel-air mixing. Practical implications This work is adding a contribution for ignition modeling, which is a crucial issue in various combustion systems and especially in aircraft engines. The exclusive use of a commercial computational fluid dynamics (CFD) code widely used by combustion system manufacturers allows a direct application of this simulation approach to other configurations while keeping computing costs at an affordable level. Originality/value This study provides a robust and simple way to address some ignition issues in various spark ignition-based engines, namely, the optimization of engines ignition with affordable computational costs. Based on the promising results obtained in the current work, it would be relevant to extend this simulation approach to spray combustion that is required for aircraft engines because of storage volume constraints. From this standpoint, the simulation approach formulated in the present work is useful to engineers interested in optimizing the engines ignition at the design stage.
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van Limbeek, Michiel A. J., Martin H. Klein Schaarsberg, Benjamin Sobac, Alexey Rednikov, Chao Sun, Pierre Colinet, and Detlef Lohse. "Leidenfrost drops cooling surfaces: theory and interferometric measurement." Journal of Fluid Mechanics 827 (August 29, 2017): 614–39. http://dx.doi.org/10.1017/jfm.2017.425.
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When a liquid drop is placed on a highly superheated surface, it can be levitated by its own vapour. This remarkable phenomenon is referred to as the Leidenfrost effect. The thermally insulating vapour film results in a severe reduction of the heat transfer rate compared to experiments at lower surface temperatures, where the drop is in direct contact with the solid surface. A commonly made assumption is that this solid surface is isothermal, which is at least questionable for materials of low thermal conductivity, resulting in an overestimation of the surface temperature and heat transfer for such systems. Here we aim to obtain more quantitative insight into how surface cooling affects the Leidenfrost effect. We develop a technique based on Mach–Zehnder interferometry to investigate the surface cooling of a quartz plate by a Leidenfrost drop. The three-dimensional plate temperature field is reconstructed from interferometric data by an Abel inversion method using a basis function expansion of the underlying temperature field. By this method we are able to quantitatively measure the local cooling inside the plate, which can be as strong as 80 K. We develop a numerical model which shows good agreement with experiments and enables extending the analysis beyond the experimental parameter space. Based on the numerical and experimental results we quantify the effect of surface cooling on the Leidenfrost phenomenon. By focusing on the role of the solid surface we provide new insights into the Leidenfrost effect and demonstrate how to adjust current models to account for non-isothermal solids and use previously obtained isothermal scaling laws for the neck thickness and evaporation rate.
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Stevens, Robin, Andrei Ryjkov, Mahtab Majdzadeh, and Ashu Dastoor. "An improved representation of aerosol mixing state for air quality–weather interactions." Atmospheric Chemistry and Physics 22, no. 20 (October 19, 2022): 13527–49. http://dx.doi.org/10.5194/acp-22-13527-2022.
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Abstract. We implement a detailed representation of aerosol mixing state in the Global Environmental Multiscale – Modelling Air quality and CHemistry (GEM-MACH) air quality and weather forecast model. Our mixing-state representation includes three categories: one for more hygroscopic aerosol, one for less hygroscopic aerosol with a high black carbon (BC) mass fraction, and one for less hygroscopic aerosol with a low BC mass fraction. The more detailed representation allows us to better resolve two different aspects of aerosol mixing state: differences in hygroscopicity due to aerosol composition and the amount of absorption enhancement of BC due to non-absorbing coatings. Notably, this three-category representation allows us to account for BC thickly coated with primary organic matter, which enhances the absorption of the BC but has a low hygroscopicity. We compare the results of the three-category representation (1L2B, (one hydrophilic, two hydrophobic)) with a simulation that uses two categories, split by hygroscopicity (HYGRO), and a simulation using the original size-resolved internally mixed assumption (SRIM). We perform a case study that is focused on North America during July 2016, when there were intense wildfires over northwestern North America. We find that the more detailed representation of the aerosol hygroscopicity in both 1L2B and HYGRO decreases wet deposition, which increases aerosol concentrations, particularly of less hygroscopic species. The concentration of PM2.5 increases by 23 % on average. We show that these increased aerosol concentrations increase cloud droplet number concentrations and cloud reflectivity in the model, decreasing surface temperatures. Using two categories based on hygroscopicity yields only a modest benefit in resolving the coating thickness on black carbon, however. The 1L2B representation resolves BC with thinner coatings than the HYGRO simulation, resulting in absorption aerosol optical depths that are 3 % less on average, with greater differences over strong anthropogenic source regions. We did not find strong subsequent effects of this decreased absorption on meteorology.
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Bradley, M. T., and K. I. Klohn. "Machiavellianism, the Control Question Test and the Detection of Deception." Perceptual and Motor Skills 64, no. 3 (June 1987): 747–57. http://dx.doi.org/10.2466/pms.1987.64.3.747.
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Individuals, differing in levels of Machiavellianism, were involved in a mock crime psychophysiological detection of deception study. It was hypothesized that those scoring high on Machiavellianism would perceive detection results as more accurately reflecting their actual guilt or innocence, especially under conditions of high arousal, than those with low scores. The hypothesis was based on assumptions that subjects must appropriately discriminate amongst crime-relevant and irrelevant questions, that this discrimination is moderately difficult with Control Question Tests, and that high-Mach scorers under arousing conditions will make this discrimination more readily than low-Mach scorers. Partial support for the hypothesis was found in that guilty high-Mach scorers were more accurately detected than guilty low-Mach scorers. This result did not hold for innocent Mach scorers, and there was no augmentation of the effect in conditions designed to increase emotional arousal.
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GEDALIN, M., and M. BALIKHIN. "Rankine–Hugoniot relations for shocks with demagnetized ions." Journal of Plasma Physics 74, no. 2 (April 2008): 207–14. http://dx.doi.org/10.1017/s0022377807006708.
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AbstractThe width of a quasi-perpendicular collisionless shock front is smaller than the convective ion gyroradius so that ions become demagnetized in the ramp. An approach is proposed for derivation of approximate expressions for the magnetic compression ratio and cross-shock potential from the analysis of the ion motion across the ramp and pressure balance condition, without making assumptions about the ion equation of state. The cross-shock potential and magnetic compression ratio are found as functions of the Mach number for low-Mach-number perpendicular shocks.
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Hientzsch, Lars Eric. "On the low Mach number limit for 2D Navier–Stokes–Korteweg systems." Mathematics in Engineering 5, no. 2 (2022): 1–26. http://dx.doi.org/10.3934/mine.2023023.
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<abstract><p>This paper addresses the low Mach number limit for two-dimensional Navier–Stokes–Korteweg systems. The primary purpose is to investigate the relevance of the capillarity tensor for the analysis. For the sake of a concise exposition, our considerations focus on the case of the quantum Navier-Stokes (QNS) equations. An outline for a subsequent generalization to general viscosity and capillarity tensors is provided. Our main result proves the convergence of finite energy weak solutions of QNS to the unique Leray-Hopf weak solutions of the incompressible Navier-Stokes equations, for general initial data without additional smallness or regularity assumptions. We rely on the compactness properties stemming from energy and BD-entropy estimates. Strong convergence of acoustic waves is proven by means of refined Strichartz estimates that take into account the alteration of the dispersion relation due to the capillarity tensor. For both steps, the presence of a suitable capillarity tensor is pivotal.</p></abstract>
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Farhad, Abu Baker Mohammad, and Abul Kalam Azad. "Power law inflation with a varying condstant of gravitation and Brans-Dicke cosmology." GANIT: Journal of Bangladesh Mathematical Society 31 (April 9, 2012): 23–32. http://dx.doi.org/10.3329/ganit.v31i0.10305.
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The homogeneous and isotropic Brans-Dicke cosmological solutions satisfying Whitrow Randalls[18] relation which have been discussed recently by Berman and Som[2] are re-examined. We extend their results and present the most general solution by solving a differential equation completely. We show that Machs assumption leads to power-law solutions in the Euclidean case.DOI: http://dx.doi.org/10.3329/ganit.v31i0.10305GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 31 (2011) 23-32
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Luo, Zhengyan, Lintao Ma, and Yinghui Zhang. "Optimal decay rates of higher–order derivatives of solutions for the compressible nematic liquid crystal flows in $ \mathbb R^3 $." AIMS Mathematics 7, no. 4 (2022): 6234–58. http://dx.doi.org/10.3934/math.2022347.
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<abstract><p>In this paper, we are concerned with optimal decay rates of higher–order derivatives of the smooth solutions to the $ 3D $ compressible nematic liquid crystal flows. The main novelty of this paper is three–fold: First, under the assumptions that the initial perturbation is small in $ H^N $–norm $ (N\geq3) $ and bounded in $ L^1 $–norm, we show that the highest–order spatial derivatives of density and velocity converge to zero at the $ L^2 $–rates is $ (1+t)^{-\frac{3}{4}-\frac{N }{2 }} $, which are the same as ones of the heat equation, and particularly faster than the $ L^2 $–rate $ (1+t)^{-\frac{1}{4}-\frac{N }{2 }} $ in [J.C. Gao, et al., J. Differential Equations, 261: 2334-2383, 2016]. Second, if the initial data satisfies some additional low frequency assumption, we also establish the lower optimal decay rates of solution as well as its all–order spatial derivatives. Therefore, our decay rates are optimal in this sense. Third, we prove that the lower bound of the time derivatives of density, velocity and macroscopic average converge to zero at the $ L^2 $–rate is $ (1+t)^{-\frac{5}{4}} $. Our method is based on low-frequency and high-frequency decomposition and energy methods.</p></abstract>
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GRAZIOSI, PAOLO, and GARRY L. BROWN. "Experiments on stability and transition at Mach 3." Journal of Fluid Mechanics 472 (November 30, 2002): 83–124. http://dx.doi.org/10.1017/s0022112002002094.
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The results of an experimental study of stability, receptivity and transition of the flat-plate laminar boundary layer at Mach 3 are discussed. With a relatively low free-stream disturbance level (∼0.1%), spectra, growth rates and amplitude distributions of naturally occurring boundary layer waves were measured using hot wires. Physical (mass-flux) amplitudes in the boundary layer and free stream are reported and provide stability and receptivity results against which predictions can be directly compared. Comparisons are made between measurements of growth rates of unstable high-frequency waves and theoretical predictions based on a non-parallel, mode-averaging stability theory and receptivity assumptions; good agreement is found. In contrast, it was found that linear stability theory does not account for the measured growth of low-frequency disturbances. A detailed investigation of the disturbance fields in the free stream and on the nozzle walls provides the basis for a discussion of the source and the development of the measured boundary layer waves. Attention is drawn to the close matching in streamwise wavelengths for instability waves and the free-stream acoustic disturbances. It was also found that a calibration of the hot wire in the free stream yields a double-peak boundary layer disturbance amplitude distribution, as has been found by previous investigators, which is not consistent with the predictions of linear stability theory. This double peak was found to be an experimental anomaly which resulted from assumptions that are frequently made in the free-stream calibration procedure. A single-peak amplitude distribution across the boundary layer was established only when the hot-wire voltage was calibrated against the mean boundary layer profile. Finally, the late stages of transition, at a higher Reynolds number with a higher free-stream disturbance level, were explored. Calibrated amplitude levels are provided at locations where nonlinearities are first detected and where the mean boundary layer profile is first observed to depart from the laminar similarity solution. A qualitative discussion of the character of ensuing nonlinearities is also included.
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Chirinko, Robert S., and Debdulal Mallick. "The Substitution Elasticity, Factor Shares, and the Low-Frequency Panel Model." American Economic Journal: Macroeconomics 9, no. 4 (October 1, 2017): 225–53. http://dx.doi.org/10.1257/mac.20140302.
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The value of the elasticity of substitution between labor and capital (σ) is a crucial assumption in understanding the secular decline in the labor share of income. This paper develops and implements a new strategy for estimating this crucial parameter by combining a low-pass filter with panel data to identify the low-frequency/long-run relations appropriate to production function estimation. Standard estimation methods, which do not filter out transitory variation, generate downwardly biased estimates of 40 percent to 70 percent relative to the benchmark value. Despite correcting for this bias, our preferred estimate of 0.40 is substantially below the Cobb-Douglas assumption of σ = 1. (JEL C51, E22, E24, E25, O41)
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HALLERÖD, BJÖRN. "Sour Grapes: Relative Deprivation, Adaptive Preferences and the Measurement of Poverty." Journal of Social Policy 35, no. 3 (June 26, 2006): 371–90. http://dx.doi.org/10.1017/s0047279406009834.
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One frequently used direct measure of deprivation and poverty is the objective relative deprivation index (O-RDindex), developed by Mack and Lansley (1985). One assumption underlying the O-RDindex is that respondents can distinguish between what that they cannot afford and what they do not want. This assumption contradicts the subjective usage of the concept relative deprivation (S-RD), which suggests a connection between economic circumstances, choice of reference group and consumption preferences.The present analysis supports the S-RD assumptions. People with limited access to economic resources are more likely to say they ‘do not want’ various consumable items. The results indicate a subjective bias that leads to underestimation of the incidence of O-RD among those suffering from the greatest economic hardship. However, it is also concluded that asking people to differentiate between choice and economic constraint improves our measurement of O-RD and decreases the risk that relatively well-off individuals will score high on the O-RDindex due to peculiar prioritising of consumption. Yet it is still the case that the social mechanisms related to S-RD most probably lead to underestimation of O-RD.
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Sansica, A., J. Ch Robinet, F. Alizard, and E. Goncalves. "Three-dimensional instability of a flow past a sphere: Mach evolution of the regular and Hopf bifurcations." Journal of Fluid Mechanics 855 (September 24, 2018): 1088–115. http://dx.doi.org/10.1017/jfm.2018.664.
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A fully three-dimensional linear stability analysis is carried out to investigate the unstable bifurcations of a compressible viscous fluid past a sphere. A time-stepper technique is used to compute both equilibrium states and leading eigenmodes. In agreement with previous studies, the numerical results reveal a regular bifurcation under the action of a steady mode and a supercritical Hopf bifurcation that causes the onset of unsteadiness but also illustrate the limitations of previous linear approaches, based on parallel and axisymmetric base flow assumptions, or weakly nonlinear theories. The evolution of the unstable bifurcations is investigated up to low-supersonic speeds. For increasing Mach numbers, the thresholds move towards higher Reynolds numbers. The unsteady fluctuations are weakened and an axisymmetrization of the base flow occurs. For a sufficiently high Reynolds number, the regular bifurcation disappears and the flow directly passes from an unsteady planar-symmetric solution to a stationary axisymmetric stable one when the Mach number is increased. A stability map is drawn by tracking the bifurcation boundaries for different Reynolds and Mach numbers. When supersonic conditions are reached, the flow becomes globally stable and switches to a noise-amplifier system. A continuous Gaussian white noise forcing is applied in front of the shock to examine the convective nature of the flow. A Fourier analysis and a dynamic mode decomposition show a modal response that recalls that of the incompressible unsteady cases. Although transition in the wake does not occur for the chosen Reynolds number and forcing amplitude, this suggests a link between subsonic and supersonic dynamics.
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Zhou, Zhiteng, Yi Liu, Hongping Wang, and Shizhao Wang. "Mass-Conserved Solution to the Ffowcs-Williams and Hawkings Equation for Compact Source Regions." Aerospace 10, no. 2 (February 6, 2023): 148. http://dx.doi.org/10.3390/aerospace10020148.
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A mass-conserved formulation for the Ffowcs-Williams–Hawkings (FW–H) integral is proposed to suppress contributions of spurious mass flux to the far-field sound at very low Mach numbers. The far-field condition and compact-source region assumptions are employed. By using higher-order derivatives of Green’s function, an expansion of the integrand in the monopole term is performed. This expansion transforms the mass-flux like monopole term into a series including different orders of velocity moment. At very low Mach numbers, the zero-order term is exactly the contribution from the spurious mass flux. The proposed mass-conserved formulation is confirmed by using an unsteady dipole, a two-dimensional (2D) incompressible convecting vortex, a circular-cylinder flow, and a co-rotating vortex pair. Additional spurious mass flux is added to the unsteady dipole, 2D incompressible convecting vortex, and flows over a circular cylinder; and the spurious mass flux of the co-rotating vortex pair comes from the residual of an incompressible-flow simulation. The far-field sound is found to be sensitive to spurious mass flux in the unsteady dipole and 2D incompressible convecting vortex cases. Then, the computation of the monopole-term expansion with the flow over a circular cylinder is presented. Fast convergence performance was observed, suggesting that the expansion requires little extra computational resources. Finally, FW–H boundary dependence is observed in the co-rotating vortex-pair case and eliminated by using the proposed mass-conserved formulation.
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Ganguli, Swetava, and Sanjiva K. Lele. "Drag of a heated sphere at low Reynolds numbers in the absence of buoyancy." Journal of Fluid Mechanics 869 (April 23, 2019): 264–91. http://dx.doi.org/10.1017/jfm.2019.187.
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Fully resolved simulations are used to quantify the effects of heat transfer in the absence of buoyancy on the drag of a spatially fixed heated spherical particle at low Reynolds numbers ($Re$) in the range $10^{-3}\leqslant Re\leqslant 10$ in a variable-property fluid. The case where buoyancy is present is analysed in a subsequent paper. This analysis is carried out without making any assumptions on the amount of heat addition from the sphere and thus encompasses both the heating regime where the Boussinesq approximation holds and the regime where it breaks down. The particle is assumed to have a low Biot number, which means that the particle is uniformly at the same temperature and has no internal temperature gradients. Large deviations in the value of the drag coefficient as the temperature of the sphere increases are observed. When $Re<O(10^{-2})$, these deviations are explained using a low-Mach-number perturbation analysis as irrotational corrections to a Stokes–Oseen base flow. Correlations for the drag and Nusselt number of a heated sphere are proposed for the range of Reynolds numbers $10^{-3}\leqslant Re\leqslant 10$ which fit the computationally obtained values with less than 1 % and 3 % errors, respectively. These correlations can be used in simulations of gas–solid flows where the accuracy of the drag law affects the prediction of the overall flow behaviour. Finally, an analogy to incompressible flow over a modified sphere is demonstrated.
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Peña Balderrama, Jenny, Thomas Alfstad, Constantinos Taliotis, Mohammad Hesamzadeh, and Mark Howells. "A Sketch of Bolivia’s Potential Low-Carbon Power System Configurations. The Case of Applying Carbon Taxation and Lowering Financing Costs." Energies 11, no. 10 (October 12, 2018): 2738. http://dx.doi.org/10.3390/en11102738.
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This paper considers hypothetical options for the transformation of the Bolivian power generation system to one that emits less carbon dioxide. Specifically, it evaluates the influence of the weighted average cost of capital (WACC) on marginal abatement cost curves (MACC) when applying carbon taxation to the power sector. The study is illustrated with a bottom-up least-cost optimization model. Projections of key parameters influence the shape of MACCs and the underlying technology configurations. These are reported. Results from our study (and the set of assumptions on which they are based) are country-specific. Nonetheless, the methodology can be replicated to other case studies to provide insights into the role carbon taxes and lowering finance costs might play in reducing emissions.
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Steinke, Robert. "Walther, Reinmar, and Biographism in the Second Degree: A Text-Centered Interpretation of Walther von der Vogelweide's Obituary of Reinmar Walther, Reinmar und der Biographismus auf zweiter Stufe: Eine textfokussierte Interpretation des Reinmar-Nachrufs Walthers von der Vogelweide." Zeitschrift fuer deutsches Altertum und Literatur 149, no. 1 (January 1, 2020): 22–42. http://dx.doi.org/10.3813/zfda-2020-0002.
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Most critics have seen the remarks of Walther von der Vogelweide on the death of his colleague Reinmar as an expression of a private quarrel between both singers. The contrast between the obituary's emphatic praise of Reinmar's singing on the one hand and apparent personal disparagement on the other is usually regarded either as a result of interpersonal conflicts or, alternatively, as a rhetorical means to even intensify the praise of Reinmar's art. This article wants to demonstrate that the assumption of a personal struggle between Walther and Reinmar is based on a biographistic circular argument. A reading that refrains from biographical assumptions proves the obituary's supposed personal aspect to be mere speculation. Instead, a purely text-centered reading points out the text's poetological and auto-reflexive functions. In der Forschung sind die Aussagen Walthers von der Vogelweide zum Tod seines Sängerkollegen Reinmar zumeist als Ausdruck tiefgreifender persönlicher Differenzen zwischen beiden Sängern verstanden worden. Der Kontrast zwischen ausdrücklichem Lob der Sangeskunst einerseits und scheinbarer persönlicher Abwertung andererseits wurde entweder als Nachwirkung persönlicher Konflikte interpretiert oder aber als rhetorisches Mittel Walthers, das Lob der Kunst Reinmars noch zu verstärken. Die vorliegende Untersuchung zeigt auf, dass der Nachruf nur dann als Beleg für eine nicht-literarische, persönliche Dimension der Auseinandersetzung Walthers mit Reinmar aufgeführt werden kann, wenn man mittlerweile widerlegte oder fragwürdige außerliterarische Axiome an den Text heranträgt und einen biographistischen Zirkelschluss zur Basis der Lektüre macht. Eine Lesart hingegen, die auf jegliche biographische Präsuppositionen verzichtet, erweist den vermeintlichen privaten Aspekt des Nachrufs als spekulativ und verdeutlicht stattdessen die poetologischen und autoreflexiven Funktionen des Textes.
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Xu, Mingzhou. "Complete convergence and complete moment convergence for maximal weighted sums of extended negatively dependent random variables under sub-linear expectations." AIMS Mathematics 8, no. 8 (2023): 19442–60. http://dx.doi.org/10.3934/math.2023992.
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<abstract><p>In this article, we study the complete convergence and complete moment convergence for maximal weighted sums of extended negatively dependent random variables under sub-linear expectations. We also give some sufficient assumptions for the convergence. Moreover, we get the Marcinkiewicz-Zygmund type strong law of large numbers for weighted sums of extended negatively dependent random variables. The results obtained in this paper generalize the relevant ones in probability space.</p></abstract>
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Huang, Haiwu, Yuan Yuan, and Hongguo Zeng. "An extension on the rate of complete moment convergence for weighted sums of weakly dependent random variables." AIMS Mathematics 8, no. 1 (2022): 622–32. http://dx.doi.org/10.3934/math.2023029.
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<abstract><p>The authors study the convergence rate of complete moment convergence for weighted sums of weakly dependent random variables without assumptions of identical distribution. Under the moment condition of $ E{{{\left| X \right|}^{\alpha }}}/{{{\left(\log \left(1+\left| X \right| \right) \right)}^{\alpha /\gamma -1}}}\; < \infty $ for $ 0 < \gamma < \alpha $ with $ 1 < \alpha \le 2 $, we establish the complete $ \alpha $-th moment convergence theorem for weighted sums of weakly dependent cases, which improves and extends the related known results in the literature.</p></abstract>
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Tang, Shuqi, and Chunhua Li. "Decay estimates for Schrödinger systems with time-dependent potentials in 2D." AIMS Mathematics 8, no. 8 (2023): 19656–76. http://dx.doi.org/10.3934/math.20231002.
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<abstract><p>We consider the Cauchy problem for systems of nonlinear Schrödinger equations with time-dependent potentials in 2D. Under assumptions about mass resonances and potentials, we prove the global existence of the nonlinear Schrödinger systems with small initial data. In particular, by analyzing the operator $ \Delta $ and time-dependent potentials $ {V_{j}} $ separately, we show that the small global solutions satisfy time decay estimates of order $ O((t\log{t})^{-1}) $ when $ p = 2 $, and the small global solutions satisfy time decay estimates of order $ O({t}^{-1}) $ when $ p > 2 $.</p></abstract>
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Amiet, R. K. "Airfoil leading-edge suction and energy conservation for compressible flow." Journal of Fluid Mechanics 289 (April 25, 1995): 227–42. http://dx.doi.org/10.1017/s0022112095001315.
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When a flat-plate airfoil at zero angle of attack encounters a vertical gust in an otherwise uniform flow, it experiences a force along the chord. This leading-edge suction force is examined for compressible flow with a time-dependent gust. A simple derivation of the thrust force is based on the fact that the leading edge is a singular point so that the flow here is dominated by the leading-edge dipole strength. From the viewpoint of a fluid-fixed observer the fluid does work on the airfoil, and this energy must come from the incident gust. Demonstrating energy conservation is not surprising, but it gives a better understanding of the relationship between the individual energy terms. The derivation shows that the acoustic energy can be calculated using compact assumptions at low frequency, but that it must be calculated non-compactly at high frequency. For a general gust the work done on the airfoil is shown to equal the energy taken from the fluid, the energy transfer occurring at the leading edge. For a sinusoidal gust the energy contained in the incident gust is shown to equal the sum of the energy remaining in the wake, the work done on the airfoil and the acoustic energy radiated away. The relative proportions of the incident energy going to these three energy types depends on the gust frequency, the acoustic radiation becoming more efficient as the frequency increases. For a fixed gust frequency, the thrust force goes to zero at a Mach number of one, and for an incident gust consisting of vorticity on the airfoil axis, the entire energy of the gust is radiated as acoustic energy at this Mach number.
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Commault, Jeanne. "Does Consumption Respond to Transitory Shocks? Reconciling Natural Experiments and Semistructural Methods." American Economic Journal: Macroeconomics 14, no. 2 (April 1, 2022): 96–122. http://dx.doi.org/10.1257/mac.20190296.
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Studies based on natural experiments find that consumption responds strongly and significantly to a transitory variation in income, while semistructural estimations find no pass-through of transitory shocks to consumption. I develop a more robust semistructural estimator that relaxes the assumption that log consumption is a random walk. The robust pass-through estimate is significant and large, implying a yearly marginal propensity to consume of 0.32, close to the natural experiment findings. The robust estimator performs well in numerical simulations of a life cycle model, while nonrobust estimators do not. The difference between the two in the simulations is similar to their difference in the survey data. (JEL D15, E21, J11)
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Nan, Jiaqi, Jingxuan Li, and Lijun Yang. "Three-Dimensional Analytical Solutions for Acoustic Transverse Modes in a Cylindrical Duct with Axial Temperature Gradient and Non-Zero Mach Number." Aerospace 9, no. 10 (October 10, 2022): 588. http://dx.doi.org/10.3390/aerospace9100588.
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Cylindrical ducts with axial mean temperature gradient and mean flows are typical elements in rocket engines, can combustors, and afterburners. Accurate analytical solutions for the acoustic waves of the longitudinal and transverse modes within these ducts can significantly improve the performance of low order acoustic network models for analyses of acoustic behaviours and combustion instabilities in these kinds of ducts. Here, we derive an acoustic wave equation as a function of pressure perturbation based on the linearised Euler equations (LEEs), and the modified WKB approximation method is applied to derive analytical solutions based on very few assumptions. The eigenvalue system is built based on the proposed solutions and applied to predict the resonant frequencies and growth rate for transverse modes. Validations of the proposed solutions are performed by comparing them to the numerical results directly calculated from the LEEs. Good agreements are found between analytical reconstruction and numerical results of three-dimensional transverse modes. The system with both mean temperature profile and mean flow presents a larger absolute value of the growth rate than the condition of either uniform mean temperature or no mean flow.
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Cheng, Yuanyuan, and Yuan Li. "A novel event-triggered constrained control for nonlinear discrete-time systems." AIMS Mathematics 8, no. 9 (2023): 20530–45. http://dx.doi.org/10.3934/math.20231046.
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<abstract><p>In this paper, a novel event-triggered optimal control method is developed for nonlinear discrete-time systems with constrained inputs. First, a non-quadratic utility function is constructed to overcome the challenge caused by saturating actuators. Second, a novel triggering condition is designed to reduce computational burden. Difference from other triggering conditions, fewer assumptions are required to guarantee asymptotic stability. Then, the optimal cost function and control law are obtained by constructing the action-critic network. Convergence analysis of the system is provided in the consideration of the system state and neural network weight estimation errors. Finally, the effectiveness and correctness of the proposed method are verified by two numerical examples.</p></abstract>
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Kafkas, Angelos, and George Lampeas. "Static Aeroelasticity Using High Fidelity Aerodynamics in a Staggered Coupled and ROM Scheme." Aerospace 7, no. 11 (November 17, 2020): 164. http://dx.doi.org/10.3390/aerospace7110164.
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Current technology in evaluating the aeroelastic behavior of aerospace structures is based on the staggered coupling between structural and low fidelity linearized aerodynamic solvers, which has inherent limitations, although tried and trusted outside the transonic region. These limitations arise from the assumptions in the formulation of linearized aerodynamics and the lower fidelity in the description of the flowfield surrounding the structure. The validity of low fidelity aerodynamics also degrades fast with the deviation from a typical aerodynamic shape due to the inclusion of various control devices, gaps, or discontinuities. As innovative wings tend to become more flexible and also include a variety of morphing devices, it is expected that using low fidelity linearized aerodynamics in aeroelastic analysis will tend to induce higher levels of uncertainty in the results. An obvious solution to these issues is to use high fidelity aerodynamics. However, using high fidelity aerodynamics incurs a very high computational cost. Various formulations of reduced order models have shown promising results in reducing the computational cost. In the present work, the static aeroelastic behavior of three characteristic aeroelastic problems is obtained using both a full three-dimensional staggered coupled scheme and a time domain Volterra series based reduced order model (ROM). The reduced order model’s ability to remain valid for a wide range of dynamic pressures around a specific Mach number (and Reynolds number regime if viscous flow is considered) and the capability to modify structural parameters such as damping ratios and natural frequencies are highlighted.
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Lu, Guanghui, and Shuangping Tao. "Commutators of Littlewood-Paley gκ∗ $g_{\kappa}^{*} $-functions on non-homogeneous metric measure spaces." Open Mathematics 15, no. 1 (November 13, 2017): 1283–99. http://dx.doi.org/10.1515/math-2017-0110.
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Abstract The main purpose of this paper is to prove that the boundedness of the commutator $\mathcal{M}_{\kappa,b}^{*} $ generated by the Littlewood-Paley operator $\mathcal{M}_{\kappa}^{*} $ and RBMO (μ) function on non-homogeneous metric measure spaces satisfying the upper doubling and the geometrically doubling conditions. Under the assumption that the kernel of $\mathcal{M}_{\kappa}^{*} $ satisfies a certain Hörmander-type condition, the authors prove that $\mathcal{M}_{\kappa,b}^{*} $ is bounded on Lebesgue spaces Lp(μ) for 1 < p < ∞, bounded from the space L log L(μ) to the weak Lebesgue space L1,∞(μ), and is bounded from the atomic Hardy spaces H1(μ) to the weak Lebesgue spaces L1,∞(μ).
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Grubin, S. E., and V. N. Trigub. "The asymptotic theory of hypersonic boundary-layer stability." Journal of Fluid Mechanics 246 (January 1993): 361–80. http://dx.doi.org/10.1017/s0022112093000175.
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In this paper the linear stability of the hypersonic boundary layer is considered in the local-parallel approximation. It is assumed that the Prandtl-number ½ < σ < 1 and the viscosity-temperature law is a power function: μ/μ∞ = (T/T∞)ω. The asymptotic theory in the limit M∞ → ∞ is developed.Smith & Brown found for the Blasius base flow and Balsa & Goldstein for the mixing layer that, in this limit, the disturbances of the vorticity mode are located in the thin region between the boundary layer and the external flow. The gas model with σ = 1, ω = 1 was exploited in these studies. Here it is demonstrated that the vorticity mode also exists for gas with ½ < σ 1, ω < 1, but its structure and characteristics are considerably different. The nomenclature is discussed, i.e. what an acoustic mode and a vorticity mode are. The numerical solution of the inviscid instability problem for the vorticity mode is obtained for helium and compared with the solution of the complete Rayleigh equation at finite Mach numbers.The limit M∞ → ∞ in the local-parallel approximation for the Blasius base flow is considered so as to understand the viscous structure of the vorticity mode. The viscous stability problem for the vorticity mode is formulated under these assumptions. The problem contains only a single similarity parameter which is a function of the Mach and Reynolds numbers, the temperature factor and wave inclination angle. This problem is numerically solved for helium. The universal upper branch of the neutral curve is obtained as a result. The asymptotic results are compared with the numerical solutions of the complete problem.