Search Results (10)

The minimalist approach in the study of perturbations in fluid dynamics and magnetohydrodynamics involves describing their evolution in the linear regime using a single first-order ordinary differential equation, dubbed the principal equation.The dispersion relation is determined by requiring that the solution of the principal equation be continuous and satisfy specific boundary conditions for each problem. The formalism is presented for flows in Cartesian geometry and applied to classical cases such as the magnetosonic and gravity waves, the Rayleigh–Taylor instability, and the Kelvin–Helmholtz instability. For the latter, we discuss the influence of compressibility and the magnetic field, and also derive analytical expressions for the growth rates and the range of instability in the case of two fluids with the same characteristics. Full article

The density of a fluid or gas, which depends on the temperature, pressure and concentration of dissolved substances or suspended particles, changes under the influence of a large number of physical factors. We assume that an undisturbed liquid is heterogeneous. The propagation of periodic flows in viscous, uniformly stratified fluids is considered. The analysis is based on a system of fundamental equations for the transfer of energy, momentum and matter in periodic flows. Taking into account the compatibility condition, dispersion relations are constructed for two-dimensional internal, acoustic and surface linear periodic flows with a positive definite frequency and complex wave number in a compressible viscous fluid exponentially stratified by density. The temperature conductivity and diffusion effects are neglected. The obtained regularly perturbed solutions of the dispersion equations describe the conventional weakly damped waves. The families of singular solutions, specific for every kind of periodic flow, characterize the before unknown thin ligaments that accompany each type of wave. In limited cases, the constructed regular solutions transform into well-known expressions for a viscous homogeneous and an ideal fluid. Singular solutions are degenerated in a viscous homogeneous fluid or disappear in an ideal fluid. The developing method of the fundamental equation system analysis is directed to describe the dynamics and spatial structure of periodic flows in heterogeneous fluids in linear and non-linear approximations. Full article

In this investigation, the compressibility effects are visualized on the flow of non-Newtonian fluid, which obeys the stress–strain relationship of an upper convected Maxwell model in a microchannel. The fundamental laws of momentum and mass conservation are used to formulate the problem. The governing nonlinear partial differential equations are reduced to a set of ordinary differential equations and solved with the help of the regular perturbation method assuming the amplitude ratio (wave amplitude/half width of channel) as a flow parameter. The axial component of velocity and flow rate is computed through numerical integration. Graphical results for the mean velocity perturbation function, net flow and axial velocity have been presented and discussed. It is concluded that the net flow rate and $D_{wall}$ increase in case of the linear Maxwell model, while they decrease in case of the convected Maxwell model. The compressibility parameter shows the opposite results for linear and upper convected Maxwell fluid. Full article

The present study numerically investigated a cylinder under oscillating motions at a low Reynolds number. The effects of two oscillation frequencies and amplitudes on the lift drag coefficient, near-field surface pressure fluctuation, and far-field noise were studied. The models were examined at a Mach number of 0.05, corresponding to a Reynolds number of 1.0 × 10⁵. In this paper, the incompressible Navier–Stokes equations (INSE) and linearized perturbed compressible equations (LPCE) were coupled to form a hybrid noise prediction method, which was used to solve the flow field and acoustic radiation field. Based on the simulation results of the acoustic radiation field, the frequency characteristics of the acoustic waves were analyzed by the dynamic modal decomposition (DMD) method. It was observed that when the oscillation amplitude was the same, the variation amplitude and mean value of the lift-drag coefficient increased with the increase in the oscillation frequency. Under the same small oscillation frequency, the oscillation amplitude had little effect on the lift-drag coefficient. However, for the same large oscillation frequency, the variation amplitude of the lift-drag coefficient increased as the oscillation amplitude increased. In addition, both the amplitude and frequency had a significant effect on the directionality of the noise and the intensity of the sound waves. The main energy of the sound field was mainly concentrated on the first and second narrowband frequencies by using the DMD method to analyze the sound pressure level spectrum. Full article

A turbo compressor was investigated to ensure the operational reliability of the charging of fuel cell systems. This study investigated air-lubricated herringbone bearings to support the high-speed rotating shaft. For reliable operation of the rotor bearing system, stable operation in the whole speed range (up to 120 krpm), as well as low lift-off speed, is an important issue. Some publications containing guidelines for an optimized design in terms of stability and lift-off behavior date back to the 1970s, with some simplifying assumptions (such as narrow groove theory and small eccentricity analysis). Many publications have addressed the calculations, as well as the optimization of herringbone-grooved bearings; however, general design guidelines are still missing in the view of the authors. Although the investigations related to bearings for the support of a lightweight rotor for a special compressor of a fuel cell unit, this study could also indicate favorable bearing designs for other high-speed applications. Here, the compressible Reynolds equation was solved in the whole solution domain using a conservative finite difference scheme, and the corresponding bearing characteristics were determined. In a perturbation analysis, the linearized dynamic coefficients of the herringbone bearing are calculated. To compare the suitability and performance of the various herringbone-grooved bearing designs, especially at high speed, the simple model of a Jeffcott rotor airborne with two identical herringbone-grooved journal bearings (HGJBs) was used. The geometrical parameters of the HGJBs were varied, and their effects on bearing characteristics and stability were evaluated. Recommendations concerning favorable geometrical bearing parameters for a sufficiently high stability threshold speed and reasonable low lift-off speed were the result of the parameter study. Full article

This paper analyses the stability of thin power-law fluid flowing down a moving plane in a vertical direction by using the long-wave perturbation method. Linear and nonlinear stability are discussed. The linear stable region increases as the downward speed increases and the power-law index increases. More accurate results are obtained on the coefficients of the nonlinear generalized kinematic equation in the power-law part. The regions of sub-critical instability and absolute stability are expanded when the downward movement of plane increases, or the power-law index increases, and meanwhile the parts of supercritical stability and explosive supercritical instability are compressed. By substituting the power-law index and moving speed into the generalized nonlinear kinematic equation of the power-law film on the free surface, the results can be applied to estimate the stability of the thin film flow in the field of engineering. Full article

Cherenkov radiation may occur whenever the source is moving faster than the waves it generates. In a radiation dominated universe, with equation-of-state $w=1/3$, we have recently shown that the Bardeen scalar-metric perturbations contribute to the linearized Weyl tensor in such a manner that its wavefront propagates at acoustic speed $\sqrt{w}=1/\sqrt{3}$. In this work, we explicitly compute the shape of the Bardeen Cherenkov cone and wedge generated respectively by a supersonic point mass (approximating a primordial black hole) and a straight Nambu-Goto wire (approximating a cosmic string) moving perpendicular to its length. When the black hole or cosmic string is moving at ultra-relativistic speeds, we also calculate explicitly the sudden surge of scalar-metric induced tidal forces on a pair of test particles due to the passing Cherenkov shock wave. These forces can stretch or compress, depending on the orientation of the masses relative to the shock front’s normal. Full article

Cerebrospinal fluid (CSF) is a symmetric flow transport that surrounds brain and central nervous system (CNS). Congenital hydrocephalusis is an asymmetric and unusual cerebrospinal fluid flow during fetal development. This dumping impact enhances the elasticity over the ventricle wall. Henceforth, compression change influences the force of brain tissues. This paper presents a mathematical model to establish the effects of ventricular elasticity through a porous channel. The current model is good enough for immediate use by a neurosurgeon. The mathematical model is likely to be a powerful tool for the better treatment of hydrocephalus and other brain biomechanics. The non-linear dimensionless governing equations are solved using a perturbation technique, and the outcome is portrayed graphically with the aid of MATLAB. Full article

An in-house 3D fluid–structure–acoustic interaction numerical solver was employed to investigate the effect of subglottic stenosis (SGS) on dynamics of glottal flow, vocal fold vibration and acoustics during voice production. The investigation focused on two SGS properties, including severity defined as the percentage of area reduction and location. The results show that SGS affects voice production only when its severity is beyond a threshold, which is at 75% for the glottal flow rate and acoustics, and at 90% for the vocal fold vibrations. Beyond the threshold, the flow rate, vocal fold vibration amplitude and vocal efficiency decrease rapidly with SGS severity, while the skewness quotient, vibration frequency, signal-to-noise ratio and vocal intensity decrease slightly, and the open quotient increases slightly. Changing the location of SGS shows no effect on the dynamics. Further analysis reveals that the effect of SGS on the dynamics is primarily due to its effect on the flow resistance in the entire airway, which is found to be related to the area ratio of glottis to SGS. Below the SGS severity of 75%, which corresponds to an area ratio of glottis to SGS of 0.1, changing the SGS severity only causes very small changes in the area ratio; therefore, its effect on the flow resistance and dynamics is very small. Beyond the SGS severity of 75%, increasing the SGS severity, leads to rapid increases of the area ratio, resulting in rapid changes in the flow resistance and dynamics. Full article

Harmonic drop surface area oscillations are performed at a fixed frequency (0.1 Hz) to measure the dilational visco-elasticity for three proteins: β-casein (BCS), β-lactoglobulin (BLG), and human serum albumin (HSA). The surface area oscillations were performed with different amplitudes in order to find the origin of non-linearity effects. The analysis of data shows that the non-linearity in the equation of state—i.e., the relation between surface pressure and surface concentration of adsorbed protein molecules—is the main source of the amplitude effects on the apparent visco-elasticity, while perturbations due to non-uniform expansions and compressions of the surface layer, inertia effects leading to deviations of the drop profile from the Laplacian shape, or convective transport in the drop bulk are of less importance. While for the globular proteins, HSA and BLG the amplitude effects on the apparent visco-elasticity are rather large, for the non-globular protein BCS this effect is negligible in the studied range of up to 10% area deformation. Full article