Academic literature on the topic 'Low Mach assumption'

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.