Optimal energy growth in pulsatile channel and pipe flows

Pulsatile channel and pipe flows constitute a fundamental flow configuration with significant bearing on many applications in the engineering and medical sciences. Rotating machinery, hydraulic pumps or cardiovascular systems are dominated by time-periodic flows, and their stability characteristics play an important role in their efficient and proper operation. While previous work has mainly concentrated on the modal, harmonic response to an oscillatory or pulsatile base flow, this study employs a direct–adjoint optimisation technique to assess short-term instabilities, identify transient energy-amplification mechanisms and determine their prevalence within a wide parameter space. At low pulsation amplitudes, the transient dynamics is found to be similar to that resulting from the equivalent steady parabolic flow profile, and the oscillating flow component appears to have only a weak effect. After a critical pulsation amplitude is surpassed, linear transient growth is shown to increase exponentially with the pulsation amplitude and to occur mainly during the slow part of the pulsation cycle. In this latter regime, a detailed analysis of the energy transfer mechanisms demonstrates that the huge linear transient growth factors are the result of an optimal combination of Orr mechanism and intracyclic normal-mode growth during half a pulsation cycle. Two-dimensional sinuous perturbations are favoured in channel flow, while pipe flow is dominated by helical perturbations. An extensive parameter study is presented that tracks these flow features across variations in the pulsation amplitude, Reynolds and Womersley numbers, perturbation wavenumbers and imposed time horizon.

Experimental studies of profile joints of machine parts under cyclic loading conditions

The increasing demands on the quality of machines, in particular multipurpose CNC machines, determine the tasks aimed at improving the designs of their critical components. The aim of the work is to ensure the accuracy, contact rigidity and durability of torquetransmitting connections of spindle assemblies during reusable replacements of auxiliary tools based on the use of conical profile connections with an equiaxed contour. The paper presents the results of experimental studies of these compounds on models that are made of optically active materials, which allows us to visually study the processes of contact interaction of profile parts under cyclic loading conditions. The method of static photoelasticity in the study of flat profile joints with an equiaxed contour made it possible to establish based on the analysis of isochrome patterns, that the change in the values of maximum tangential stresses per revolution of the profile joint is subject to a pulsation cycle.

Pulsating chromosphere of classical Cepheids

Context. It has recently been shown that the infrared (IR) emission of Cepheids, constant over the pulsation cycle, might be due to a pulsating shell of ionized gas with a radius of about 15% of that of the star radius, which could be attributed to the chromospheric activity of Cepheids. Aims. The aim of this paper is to investigate the dynamical structure of the chromosphere of Cepheids along the pulsation cycle and to quantify its size. Methods. We present Hα and calcium near-infrared triplet (Ca IR) profile variations using high-resolution spectroscopy with the UVES spectrograph of a sample of 24 Cepheids with a good period coverage from ≈3 to 60 days. After a qualitative analysis of the spectral line profiles, we quantified the Van Hoof effect (velocity gradient between the Hα and Ca IR) as a function of the period of the Cepheids. We then used the Schwarzschild mechanism (a line doubling due to a shock wave) to quantify the size of the chromosphere. Results. We find a significant Van Hoof effect for Cepheids with a period larger than P = 10 days. In particular, Hα lines are delayed with a velocity gradient up to Δv ≈ 30 km s−1 compared to Ca IR. By studying the shocks, we find that the size of the chromosphere of long-period Cepheids is of at least ≈50% of the stellar radius, which is consistent at first order with the size of the shell made of ionized gas previously found from the analysis of IR excess. Last, for most of the long-period Cepheids in the sample, we report a motionless absorption feature in the Hα line that we attribute to a circumstellar envelope that surrounds the chromosphere. Conclusions. Analyzing the Ca IR lines of Cepheids is of importance to potentially unbias the period–luminosity relation from their IR excess, particularly in the context of forthcoming observations of radial velocity measurements from the Radial Velocity Spectrometer on board Gaia, which could be sensitive to their chromosphere.

Nonlinear hydrodynamic instability and turbulence in pulsatile flow

Pulsating flows through tubular geometries are laminar provided that velocities are moderate. This in particular is also believed to apply to cardiovascular flows where inertial forces are typically too low to sustain turbulence. On the other hand, flow instabilities and fluctuating shear stresses are held responsible for a variety of cardiovascular diseases. Here we report a nonlinear instability mechanism for pulsating pipe flow that gives rise to bursts of turbulence at low flow rates. Geometrical distortions of small, yet finite, amplitude are found to excite a state consisting of helical vortices during flow deceleration. The resulting flow pattern grows rapidly in magnitude, breaks down into turbulence, and eventually returns to laminar when the flow accelerates. This scenario causes shear stress fluctuations and flow reversal during each pulsation cycle. Such unsteady conditions can adversely affect blood vessels and have been shown to promote inflammation and dysfunction of the shear stress-sensitive endothelial cell layer.

Analysis of Retinal Vessel Pulsation with Electrographic Gating – Pulsation Amplitude and the Influence of Hyperoxia

Purpose To analyse the amplitude of vessel pulsation in the retina and to determine whether constriction of the vessels by oxygen would decrease their pulsation amplitude and could thus be used to quantify the rigidity of the retinal vessels. Patients and Methods The study included 20 healthy young subjects. With the RVA (retinal vessel analyser), we aimed to quantify vessel pulsations under normal and hyperoxic conditions. Electrocardiographic (ECG)-gated RVA was used for this purpose, with change in vessel pulsation as the primary endpoint and shift in vessel pulsation during the heart cycle as the secondary endpoint. Furthermore, we assessed the correlation between the amplitude of retinal vessel wall pulsation and blood pressure. Descriptive statistics, paired t-tests, and correlation analysis were applied. Results Retinal veins in proximity to the optic disc demonstrated the highest pulsation amplitude under all conditions. All retinal vessels significantly constricted under hyperoxic conditions. There was no significant change in the amplitude of vessel pulsation nor a significant shift in the pulsation cycle under hyperoxic conditions in the examined cohort. No correlation was found between systemic blood pressure parameters and amplitude of retinal vessel wall pulsation or any change in this. Conclusion ECG-gated RVA recording is not able to detect any relevant change in vessel pulsation behaviour under oxygen, despite clearly observed vasoconstriction in retinal vessels. New approaches are necessary to reliably quantify the rigidity of the retinal vessels.

Dynamical structure of the pulsating atmosphere of RR Lyrae

Context. RRab stars are large amplitude pulsating stars in which the pulsation wave is a progressive wave. Consequently, strong shocks, stratification effects, and phase lag may exist between the variations associated with line profiles formed in different parts of the atmosphere, including the shock wake. The pulsation is associated with a large extension of the expanding atmosphere, and strong infalling motions are expected. Aims. The objective of this study is to provide a general overview of the dynamical structure of the atmosphere occurring over a typical pulsation cycle. Methods. We report new high-resolution observations with high time resolution of Hα and sodium lines in the brightest RR Lyrae star of the sky: RR Lyr (HD 182989). A detailed analysis of line profile variations over the whole pulsation cycle is performed to understand the dynamical structure of the atmosphere. Results. The main shock wave appears when it exits from the photosphere at φ ≃ 0.89, i.e., when the main Hα emission is observed. Whereas the acceleration phase of the shock is not observed, a significant deceleration of the shock front velocity is clearly present. The radiative stage of the shock wave is short: 4% of the pulsation period (0.892 < φ < 0.929). A Mach number M > 10 is required to get such a radiative shock. The sodium layer reaches its maximum expansion well before that of Hα (Δφ = 0.135). Thus, a rarefaction wave is induced between the Hα and sodium layers. A strong atmospheric compression occurring around φ = 0.36, which produces the third Hα emission, takes place in the highest part of the atmosphere. The region located lower in the atmosphere where the sodium line is formed is not involved. The amplification of gas turbulence seems mainly due to strong shock waves propagating in the atmosphere rather than to the global compression of the atmosphere caused by the pulsation. It has not yet been clearly established whether the microturbulence velocity increases or decreases with height in the atmosphere. Furthermore, it seems very probable that an interstellar component is visible within the sodium profile.

A new and homogeneous metallicity scale for Galactic classical Cepheids

We gathered more than 1130 high-resolution optical spectra for more than 250 Galactic classical Cepheids. The spectra were collected with the optical spectrographs UVES at VLT, HARPS at 3.6 m, FEROS at 2.2 m MPG/ESO, and STELLA. To improve the effective temperature estimates, we present more than 150 new line depth ratio (LDR) calibrations that together with similar calibrations already available in the literature allowed us to cover a broad range in wavelength (5348 ≤ λ ≤ 8427 Å) and in effective temperature (3500 ≤ Teff ≤ 7700 K). This gives us the unique opportunity to cover both the hottest and coolest phases along the Cepheid pulsation cycle and to limit the intrinsic error on individual measurements at the level of ~100 K. As a consequence of the high signal-to-noise ratio of individual spectra, we identified and measured hundreds of neutral and ionized lines of heavy elements, and in turn, have the opportunity to trace the variation of both surface gravity and microturbulent velocity along the pulsation cycle. The accuracy of the physical parameters and the number of Fe I (more than one hundred) and Fe II (more than ten) lines measured allowed us to estimate mean iron abundances with a precision better than 0.1 dex. We focus on 14 calibrating Cepheids for which the current spectra cover either the entire or a significant portion of the pulsation cycle. The current estimates of the variation of the physical parameters along the pulsation cycle and of the iron abundances agree very well with similar estimates available in the literature. Independent homogeneous estimates of both physical parameters and metal abundances based on different approaches that can constrain possible systematics are highly encouraged.

Linear and nonlinear dynamics of pulsatile channel flow

The dynamics of small-amplitude perturbations, as well as the regime of fully developed nonlinear propagating waves, is investigated for pulsatile channel flows. The time-periodic base flows are known analytically and completely determined by the Reynolds number $Re$ (based on the mean flow rate), the Womersley number $Wo$ (a dimensionless expression of the frequency) and the flow-rate waveform. This paper considers pulsatile flows with a single oscillating component and hence only three non-dimensional control parameters are present. Linear stability characteristics are obtained both by Floquet analyses and by linearized direct numerical simulations. In particular, the long-term growth or decay rates and the intracyclic modulation amplitudes are systematically computed. At large frequencies (mainly $Wo\geqslant 14$), increasing the amplitude of the oscillating component is found to have a stabilizing effect, while it is destabilizing at lower frequencies; strongest destabilization is found for $Wo\simeq 7$. Whether stable or unstable, perturbations may undergo large-amplitude intracyclic modulations; these intracyclic modulation amplitudes reach huge values at low pulsation frequencies. For linearly unstable configurations, the resulting saturated fully developed finite-amplitude solutions are computed by direct numerical simulations of the complete Navier–Stokes equations. Essentially two types of nonlinear dynamics have been identified: ‘cruising’ regimes for which nonlinearities are sustained throughout the entire pulsation cycle and which may be interpreted as modulated Tollmien–Schlichting waves, and ‘ballistic’ regimes that are propelled into a nonlinear phase before subsiding again to small amplitudes within every pulsation cycle. Cruising regimes are found to prevail for weak base-flow pulsation amplitudes, while ballistic regimes are selected at larger pulsation amplitudes; at larger pulsation frequencies, however, the ballistic regime may be bypassed due to the stabilizing effect of the base-flow pulsating component. By investigating extended regions of a multi-dimensional parameter space and considering both two-dimensional and three-dimensional perturbations, the linear and nonlinear dynamics are systematically explored and characterized.