Small Pressure Perturbations Research Articles

A WENO SPH scheme with improved transport velocity and consistent divergence operator

The Arbitrary Lagrangian–Eulerian Smoothed Particle Hydrodynamics (ALE-SPH) formulation can guarantee stable solutions preventing the adoption of empirical parameters such as artificial viscosity. However, the convergence rate of the ALE-SPH formulation is still limited by the inaccuracy of the SPH spatial operators. In this work, a Weighted Essentially Non-Oscillatory (WENO) spatial reconstruction is then adopted to minimise the numerical diffusion introduced by the approximate Riemann solver (which ensures stability), in combination with two alternative approaches to restore the consistency of the scheme: corrected divergence SPH operators and the particle regularisation guaranteed by the correction of the transport velocity. The present work has been developed in the framework of the DualSPHysics open-source code. The beneficial effect of the WENO reconstruction to reduce numerical diffusion in ALE-SPH schemes is first confirmed by analysing the propagation of a small pressure perturbation in a fluid initially at rest. With the aid of a 2-D vortex test case, it is then demonstrated that the two aforementioned techniques to restore consistency effectively reduce saturation in the convergence to the analytical solution. Moreover, high-order (above second) convergence is achieved. Yet, the presented scheme is tested by means of a circular blast wave problem to demonstrate that the restoration of consistency is a key feature to guarantee accuracy even in the presence of a discontinuous pressure field. Finally, a standing wave has been reproduced with the aim of assessing the capability of the proposed approach to simulate free-surface flows.

Turbulence-induced bubble nucleation in hydrothermal fluids beneath Yellowstone Lake

Volcanic systems generate large amounts of gas, and understanding gas fluxes is a fundamental aspect of volcanology and hazard mitigation. Volcanic gases can be challenging to measure, but acoustic methods hold promise in underwater environments because gas bubbles are powerful sound sources. We deployed an acoustic system to study the nature of gas discharge at a large (~30 MW) thermal field on the floor of Yellowstone Lake, which has experienced numerous hydrothermal explosions since the last glaciation (~13.4 ka). We find that small (<10 Pa) turbulent flow instabilities trigger the nucleation of CO2 bubbles in the saturated fluids. The observation of CO2 bubbles nucleating in hydrothermal fluids due to small pressure perturbations informs our understanding of hydrothermal explosions in Yellowstone Lake, and demonstrates that acoustic data in underwater environments can provide insight into the stability of gas-rich systems, as well as gas fluxes.

A hybrid pseudo-incompressible–hydrostatic model

The pseudo-incompressible approximation, which assumes small pressure perturbations from a one-dimensional reference state, has long been used to model large-scale dynamics in stellar and planetary atmospheres. However, existing implementations do not conserve energy when the reference state is time-dependent. We use a variational formulation to derive an energy-conserving pseudo-incompressible model in which the reference state evolves while remaining hydrostatic. We present an algorithm for solving these equations in the case of closed boundaries, for which the pseudo-incompressible velocity constraint is degenerate. We implement the model within the low-Mach-number code MAESTROeX, and validate it against a fully compressible model in several test cases, finding that our hybrid pseudo-incompressible–hydrostatic model generally shows better agreement with the compressible results than the existing MAESTROeX implementation.

Effects of back pressure perturbation on shock train oscillations in a rectangular duct

The nature of flow field inside the scramjet engine consists of shock-shock interaction and the shock boundary layer interaction. For a sustained combustion, a device called isolator plays a critical role in providing adequate pressure to the combustion chamber by a series of bifurcated shock waves called “shock train”. A small downstream pressure perturbation can cause upstream movement of this shock train and results in engine unstart condition. The propagation speed of downstream disturbance can influence the shock train oscillation. In the present study, computational fluid dynamics analysis is conducted to understand the oscillatory characteristic of shock train in a rectangular duct at M =1.75. The impact of downstream perturbation frequency (fb = 10 – 50 Hz) and the amplitude (A = 0.01 – 0.1) are simulated and discussed. The presence of low-frequency oscillation is observed without back pressure perturbation. The downstream pressure perturbation has a noticeable effect on the shock train excursion length i.e., the maximum upstream to downstream distance moved by shock train. The increase in perturbation frequency leads to decrease in disturbance propagation speed. Similarly, the propagation speed increases with the increase in the perturbation amplitude.

Eastward-moving equatorial modons in moist-convective shallow-water models

It is shown that steady large-scale slowly eastward-moving twin-cyclone coherent structures, the equatorial modons, exist in both one- and two layer versions of the rotating shallow water model on the equatorial beta plane. They arise via the process of “ageostrophic adjustment” from the analytic asymptotic modon solutions of the vorticity equation obtained in the limit of small pressure perturbations. Evolution of these structures in adiabatic and moist-convective environments, and also in the presence of topography is analysed, showing their robustness in the one-layer model. It is demonstrated that moist convection enhances and helps maintain the modons. In the two-layer model the barotropic and quasi-barotropic modons display similar to one-layer modon features, while increasing baroclinicity leads to eventual loss of coherence and arrest of the eastward propagation. Some features of equatorial modons resemble those observed in the Madden-Julian Oscillation events in tropical atmosphere, which hints at their possible relevance to the dynamics of this phenomenon.

Diffusion and dissipation in acoustic propagation simulation by convection-pressure split algorithms in all Mach number form

The topic of the paper is accuracy analysis of acoustic propagation simulation in low Mach number flows, by finite volume co-located discretisation methods of the time-dependent compressible fluid Euler equations that use the concept of convection-pressure splitting (CPS). These are algorithms that split the flux vectors into a part associated to the convection by the fluid particles, and a part associated to the propagation of the pressure waves. For the convection part, the appropriate space discretisation is the upwind one. For the pressure part, there are alternatives. We discern five types of algorithms that all are adapted for use in low Mach number flows, and thus are considered as all Mach number algorithms. We study the behaviour of the different types for the propagation of small pressure perturbations, of discontinuous or smooth shape, in low Mach number flows. We demonstrate that four of the proposed algorithms of convection-pressure split type are dissipative for such applications, although they are designed for low Mach number flows. The objective of the paper is to analyse why some algorithms are appropriate for acoustic propagation simulation and why some are not appropriate.

Sensitivity of Acoustic Emission Triggering to Small Pore Pressure Cycling Perturbations During Brittle Creep

AbstractFluid‐induced stress perturbations in the crust at seismogenic depths caused by sources such as tidal or seasonal loading may trigger earthquakes. We investigate the role of small periodic pore pressure (Pp) perturbation in rupture nucleation by performing laboratory triaxial creep experiments on Fontainebleau sandstone, saturated in water, under sinusoidal Pp variations. Results show that recorded acoustic emissions (AEs) correlate with Pp as the rock approaches failure. More interestingly, AEs occur significantly more when Pp is decreasing, that is, when strain rate is maximum with a progressive increase of Pp‐AEs correlation in time as the rock approaches failure. This suggests that the correlation of small stress perturbations and AEs not only depends on Pp amplitude but also on the criticality of the rock. Observations at the laboratory scale support field observations where tidal loading may have modulated seismic rates during the nucleation phase of the 2004 Sumatra‐Andaman and 2011 Tohoku‐Oki earthquakes.

Stall Inception in a High-Speed Centrifugal Compressor During Speed Transients

The inception and evolution of rotating stall in a high-speed centrifugal compressor are characterized during speed transients. Experiments were performed in the single stage centrifugal compressor (SSCC) facility at Purdue University and include speed transients from subidle to full speed at different throttle settings while collecting transient performance data. Results show a substantial difference in the compressor transient performance for accelerations versus decelerations. This difference is associated with the heat transfer between the flow and the hardware. The heat transfer from the hardware to the flow during the decelerations locates the compressor operating condition closer to the surge line and results in a significant reduction in surge margin during decelerations. Additionally, data were acquired from fast-response pressure transducers along the impeller shroud, in the vaneless space, and along the diffuser passages. Two different patterns of flow instabilities, including mild surge and short-length-scale rotating stall, are observed during the decelerations. The instability starts with a small pressure perturbation at the impeller leading edge (LE) and quickly develops into a single-lobe rotating stall burst. The stall cell propagates in the direction opposite of impeller rotation at approximately one-third of the rotor speed. The rotating stall bursts are observed in both the impeller and diffuser, with the largest magnitudes near the diffuser throat. Furthermore, the flow instability develops into a continuous high frequency stall and remains in the fully developed stall condition.

An analysis of fast-response pressure probes dynamics for ORC power systems

The dynamic response of line-cavity systems in ideal and non-ideal compressible-fluid conditions is investigated numerically using the SU2 open-source suite for multi-physics simulations. The response of the system is studied for small but finite pressure perturbations, to predict the behaviour of fast-response pressure probes in turbomachinery for gas and ORC power systems. The probe step-response is found to present significant damping due to non-linear wave propagation. Non-idealities in the close proximity of the liquid-vapour curve increase the signal damping due to non-monotone variations of the speed of sound. A simplified approach is proposed to predict the probe dynamic characteristics in ideal regime. The estimation of the probe dynamics in non-ideal regime is found to be very critical and to strongly depend on the thermodynamic state of the fluid. The present results provides a guideline for the design of fast-response pressure probes to be used e.g. past the rotor stage of ORC turbine vanes.

Subsidence Warming as an Underappreciated Ingredient in Tropical Cyclogenesis. Part I: Aircraft Observations

Abstract The development of a compact warm core extending from the mid-upper levels to the lower troposphere and related surface pressure falls leading to tropical cyclogenesis (TC genesis) is not well understood. This study documents the evolution of the three-dimensional thermal structure during the early developing stages of Typhoons Fanapi and Megi using aircraft dropsonde observations from the Impact of Typhoons on the Ocean in the Pacific (ITOP) field campaign in 2010. Prior to TC genesis, the precursor disturbances were characterized by warm (cool) anomalies above (below) the melting level (~550 hPa) with small surface pressure perturbations. Onion-shaped skew T–logp profiles, which are a known signature of mesoscale subsidence warming induced by organized mesoscale convective systems (MCSs), are ubiquitous throughout the ITOP aircraft missions from the precursor disturbance to the tropical storm stages. The warming partially erodes the lower-troposphere (850–600 hPa) cool anomalies. This warming results in increased surface pressure falls when superposed with the upper-troposphere warm anomalies associated with the long-lasting MCSs/cloud clusters. Hydrostatic pressure analysis suggests the upper-level warming alone would not result in the initial sea level pressure drop associated with the transformation from a disturbance to a TC. As Fanapi and Megi intensify into strong tropical storms, aircraft flight-level (700 hPa) and dropsonde data reveal that the warm core extends down to 850–600 hPa and has some characteristics of subsidence warming similar to the eyes of mature TCs.

MAGNETOHYDRODYNAMIC SLOW MODE WITH DRIFTING He++: IMPLICATIONS FOR CORONAL SEISMOLOGY AND THE SOLAR WIND

The MHD slow mode wave has application to coronal seismology, MHD turbulence, and the solar wind where it can be produced by parametric instabilities. We consider analytically how a drifting ion species (e.g. He$^{++}$) affects the linear slow mode wave in a mainly electron-proton plasma, with potential consequences for the aforementioned applications. Our main conclusions are: 1. For wavevectors highly oblique to the magnetic field, we find solutions that are characterized by very small perturbations of total pressure. Thus, our results may help to distinguish the MHD slow mode from kinetic Alfv\'en waves and non-propagating pressure-balanced structures, which can also have very small total pressure perturbations. 2. For small ion concentrations, there are solutions that are similar to the usual slow mode in an electron-proton plasma, and solutions that are dominated by the drifting ions, but for small drifts the wave modes cannot be simply characterized. 3. Even with zero ion drift, the standard dispersion relation for the highly oblique slow mode cannot be used with the Alfv\'en speed computed using the summed proton and ion densities, and with the sound speed computed from the summed pressures and densities of all species. 4. The ions can drive a non-resonant instability under certain circumstances. For low plasma beta, the threshold drift can be less than that required to destabilize electromagnetic modes, but damping from the Landau resonance can eliminate this instability altogether, unless $T_{\mathrm e}/T_{\mathrm p}\gg1$.

Deflagration-to-detonation transition by amplification of acoustic waves in type Ia supernovae

We study a new mechanism for deflagration to detonation transition in thermonuclear supernovae (SNe Ia), based on the formation of shocks by amplification of sound waves in the steep density gradients of white dwarfs envelopes. Given a large enough jump in density a small pressure and velocity perturbation, produced by the turbulent deflagration, turns into a shock down of the gradient, where it will dissipate and heat up the media. With the right frequency and amplitude the heating can be enough to initiate a detonation, which can propagate backward and up the density gradient. We studied planar and spherical geometry. In the planar case we made a parametric study of the frequency and amplitude. We found it possible to obtain a detonation for perturbations down to Mach number M=0.003. In the spherical case, geometrical damping makes it harder to initiate a detonation, but considering a small He atmosphere (<0.01 Msol) makes it possible again to obtain a detonation down to small perturbation (M=0.002). In the context of thermonuclear supernovae, this could be a mean to turn a turbulent flame producing sound waves to a detonation.

Instability of black hole formation under small pressure perturbations

We investigate here the spectrum of gravitational collapse endstates when arbitrarily small perfect fluid pressures are introduced in the classic black hole formation scenario as described by Oppenheimer, Snyder and Datt (OSD) (Oppenheimer and Snyder in Phys Rev 56:455, 1939; Datt in Zs f Phys 108:314, 1938). This extends a previous result on tangential pressures (Joshi and Malafarina Phys Rev D 83:024009, 2011) to the physically more realistic scenario of perfect fluid collapse. The existence of classes of pressure perturbations is shown explicitly, which has the property that injecting any smallest pressure changes the final fate of the dynamical collapse from a black hole to a naked singularity. It is therefore seen that any smallest neighborhood of the OSD model, in the space of initial data, contains collapse evolutions that go to a naked singularity outcome. This gives an intriguing insight on the nature of naked singularity formation in gravitational collapse.

GENERICITY ASPECTS IN GRAVITATIONAL COLLAPSE TO BLACK HOLES AND NAKED SINGULARITIES

Here we investigate the genericity and stability aspects for naked singularities and black holes that arise as the final states for a complete gravitational collapse of a spherical massive matter cloud. The form of the matter considered is a general Type I matter field, which includes most of the physically reasonable matter fields such as dust, perfect fluids and such other physically interesting forms of matter widely used in gravitation theory. Here, we first study in some detail the effects of small pressure perturbations in an otherwise pressure-free collapse scenario, and examine how a collapse evolution that was going to the black hole endstate would be modified and go to a naked singularity, once small pressures are introduced in the initial data. This allows us to understand the distribution of black holes and naked singularities in the initial data space. Collapse is examined in terms of the evolutions allowed by Einstein equations, under suitable physical conditions and as evolving from a regular initial data. We then show that both black holes and naked singularities are generic outcomes of a complete collapse, when genericity is defined in a suitable sense in an appropriate space.

Modeling the damping properties of perforated screens traversed by a bias flow and backed by a cavity at low Strouhal number

Acoustic absorption properties of perforated screens traversed by a bias flow and backed by a resonant cavity are examined at a new absorption regime. The reflection coefficient of these dampers can be canceled at specific frequencies for low Strouhal numbers St ⪡ 1 and Helmholtz numbers of order unity He ∼ 1 . This regime differs from the classical one where resonance is sought at low Helmholtz numbers He ⪡ 1 and large Strouhal numbers St ⪢ 1 . A theoretical analysis is carried out and analytical expressions are derived to determine conditions for optimal absorption in this regime. It is shown that the optimal bias flow velocity and back cavity length can be fixed separately. The former is determined by the plate porosity and the latter controls the peak absorption frequency. This operating regime at low Strouhal numbers enables to increase sound absorption at low frequencies over a larger frequency bandwidth around the peak absorption frequency than the one obtained with a damping system working at high Strouhal numbers. This is confirmed by experiments carried out on a set of dampers in the frequency range 100–1000 Hz. Predictions of the reflection coefficient, including effects of bias flow velocity and cavity depth, show good agreement with experimental data for small pressure perturbation levels. These elements can contribute to the development of robust dampers to control low frequency thermoacoustic instabilities in gas turbines and jet engines.

On the explosivity of a molten drop submitted to a small pressure perturbation

Under some circumstances that we aim to determine, a hot molten fuel drop flowing into a volatile liquid coolant and submitted to a small pressure wave, can be destabilized and explode in a few milliseconds. We propose a new approach to address this problem: in contrast with previous studies, we do not try to model the complete phenomenon but concentrate on its initiation. This way, we can differentiate favourable and non-favourable conditions with applications to PWR/BWR safety. We do the hypothesis that the occurrence of contacts between the two fluids is the criterion of explosion and phenomena occurring up to the contacting event are modelled, including the vapour film oscillations and the amplification of Rayleigh–Taylor instabilities at its interface. The latter feature receives a particular attention with a transient modelling adapted for variable acceleration cases. The fragmentation process itself is not studied in details but we give arguments supporting the fact that contacts between both liquids should induce a strong destabilization of the drops and initiate fragmentation. In this way, we can characterize the explosivity, i.e. the ability for the drop to explode, as a function of the various physical properties (e.g. pressure, temperatures). The model so deduced is qualified by comparison with the explosivity maps provided by Nelson and Duda [Nelson, L.S., Duda, P.M., 1985. Steam explosion experiments with single drops of iron oxide: Part II: parametric studies, NUREG CR-2718, April 1985]. Results obtained with this model confirm the experimental trends regarding the role of ambient pressure and liquid temperature. The influence of other parameters as the drop and the trigger characteristics are also investigated. We conclude this paper with some consideration on the implications for nuclear safety.

Pressure perturbation calorimetry, heat capacity and the role of water in protein stability and interactions

It is widely acknowledged, and usually self-evident, that solvent water plays a crucial role in the overall thermodynamics of protein stabilization and biomolecular interactions. Yet we lack experimental techniques that can probe unambiguously the nature of protein-water or ligand-water interactions and how they might change during protein folding or ligand binding. PPC (pressure perturbation calorimetry) is a relatively new technique based on detection of the heat effects arising from application of relatively small pressure perturbations (+/-5 atm; 1 atm=101.325 kPa) to dilute aqueous solutions of proteins or other biomolecules. We show here how this can be related to changes in solvation/hydration during protein-protein and protein-ligand interactions. Measurements of 'anomalous' heat capacity effects in a wide variety of biomolecular interactions can also be related to solvation effects as part of a quite fundamental principle that is emerging, showing how the apparently unusual thermodynamics of interactions in water can be rationalized as an inevitable consequence of processes involving the co-operative interaction of multiple weak interactions. This leads to a generic picture of the thermodynamics of protein folding stabilization in which hydrogen-bonding plays a much more prominent role than has been hitherto supposed.

Trajectory Design and Maneuver Strategy for the MESSENGER Mission to Mercury

Destined to become the first spacecraft to orbit the planet Mercury, the MESSENGER spacecraft was launched on 3 August 2004. The 6.6-year ballistic trajectory to Mercury will utilize six gravity-assist flybys of Earth (one), Venus (two), and Mercury (three). With three trajectory correction maneuvers completed by mid-December 2005, many more maneuvers will be necessary during the journey to Mercury and the subsequent 1-year duration Mercury orbit phase. The spacecraft's design and operational capability will enable real-time monitoring of every course-correction maneuver. A complex mission plan will provide multiple opportunities to obtain observational data that will help fulfill the mission's scientific objectives. Soon after entering Mercury orbit in mid-March 2011, the initial primary science orbit will have an 80-deg orbit inclination relative to Mercury's equator, 200-km periapsis altitude, 60°N subspacecraft periapsis latitude, and a 12-h orbit period. With science goals requiring infrequent orbit-phase trajectory adjustments, pairs of orbit-correction maneuvers occur at about the same time every Mercury year, or every 88 days. For the first time, the spacecraft's orbit design at Mercury accounts for the best available Mercury gravity model, small solar pressure perturbations due to changes in the solar array tilt angle, and an improved strategy for performing orbit correction maneuvers.

Two-dimensional magnetohydrodynamic liner-on-plasma simulations for the compression phase of a magnetized target fusion system based on inverse Z pinch

This article reports, for the first time, two-dimensional magnetohydrodynamic liner-on-plasma simulations for the compression phase of a magnetized target fusion (MTF) system with an inverse Z-pinch target. These simulations evolve the complete liner-plasma system along with the driving pulsed-power source. First, it has been demonstrated that closely coupled liner-on-plasma simulations produce results that are significantly different from loosely coupled simulations that have been reported in the literature. Second, it has been found that an initially stable plasma, satisfying the Kadomtsev criteria, and with a small initial pressure perturbation in the axial direction, remains stable all through the compression phase, even though there are large changes in the pressure and magnetic field levels. Third, a plasma that violates the Kadomtsev criteria, even by a small amount, turns out to be unstable, as predicted by theory. In practical terms, this means that it is preferable to stay well away from the stability limit, even at the cost of some reduction of initial plasma pressure. Fourth, even during the burn phase, when there is a large and rapid increase in plasma pressure due to fusion energy deposition, an initially stable plasma generally tends to remain stable, and even improves its stability margin. This observation shows that the inverse Z pinch is fairly benign as a MTF target, as an initially stable plasma remains stable during both the compression and burn phases. Fifth, certain unusual features are observed in the temperature profile—these depend upon the time scale for implosion. This has implications for plasma-surface interactions at the liner and central conductor.

Local perturbation of thin film flow

The flow of a thin viscous film over a profiled substrate under the action of an external pressure profile along its free surface, in addition to gravity and capillarity, is considered. Specifically, the linear response of the film flow to localized small pressure perturbations is analyzed. The linear evolution equation of the response analysis is derived from the nonlinear flow equation of the film, which is formulated for the present purpose by reinterpreting the individual terms in the equation of film flow over flat substrates in terms of film thickness or surface curvature. This equation displays an equivalence, within the range of its validity, the lubrication approximation, between a particular, stationary persistent pressure action and the action of a (fixed) substrate topography on the film flow; the equivalence relation is formulated in the paper. The core of the paper is the derivation and analysis of the response of the film to an instantaneous pressure perturbation. For a point source of perturbation this response is the fundamental solution of the linear evolution equation. It is evaluated analytically, exactly or asymptotically, for the two extreme situations of either gravitational or capillary dominance of the flow (i.e. for large and small Bond numbers, respectively), and numerically in the intermediate situations. From the response signal to the instantaneous perturbation the film response to a (harmonically) persistent perturbation is then constructed by superposition. For a steadily acting point source this superposition is a ‘Green’s’ function. Its analytic evaluation for gravitational dominance provides, in addition to those of the fundamental solution, useful support of validation and interpretation for numerical signal evaluations. Such evaluations are given for steady persistent excitation. Finally, the signal analysis is discussed in a process-engineering perspective.