Quasi-steady Manner Research Articles

Transient surface pressure of a rectangular cylinder subjected to downburst-like winds

Thunderstorm downbursts are transient in nature and have been responsible for a variety of structural damages in recent years. Currently, the researchers have done several works on the characteristics of downburst wind speed. Nonetheless, rare attention has been placed on the structural aerodynamics characteristics subjected to downburst winds. Based on this, an experimental investigation is performed to reproduce downburst-like winds physically and to study the transient surface pressures (SPs) on a 5:1 rectangular cylinder (RC). The experiment is conducted within a multiple-fan active control wind tunnel (MFACWT) and mainly focuses on simulating the transient characteristics of downburst-like flow, including time-varying mean (TVM) wind speed and nonstationary wind fluctuation. The resulting SPs are measured to understand the influence of transient wind on the aerodynamic behavior of bluff bodies. The spatiotemporal characteristics of the SPs are analyzed using wavelet transform and Priestley's classic spectral theory. The results indicate that the transient nature of the downburst-like flow can be physically reproduced by a MFACWT. The instantaneous pressures of a RC are illustrated by both the turbulence parameters of the transient flow and the flow-separation characteristics. The pressure coefficients normalized by the TVM of the downburst-like winds remain constant, which provides a more appropriate way to estimate the transient gust loading in a quasi-steady manner. Interestingly, the phenomenon of the time-varying phase shift and time-varying correlation of chordwise SPs is observed when the turbulent velocity changes dramatically. In addition, the normalized surface pressure can be regarded as a stationary stochastic process, which provides a significant basis for further establishing the theoretical model of nonstationary gust-loading.

Transient heat transfer and temperatures in closed compressor rotors

During transient gas turbine operating cycles, the radial clearance between the rotating blades and the stationary casing is governed by the thermal stresses and radial growth of the compressor discs. Robust and accurate prediction of the temperature and heat transfer inside compressor cavities is critical to controlling these clearances and the design of reliable and efficient engines. This paper presents a fully predictive model to determine disc temperatures and shroud heat fluxes for a closed disc cavity (rotating cylindrical annulus), simulating an engine compressor. This is the first published reduced-order modelling of compressor cavities during engine transients in literature and the most detailed publication of transient experimental data in this context. Due to the conjugate nature of the heat transfer, a conduction model of the compressor disc and a model of the flow and heat transfer in the cavity between the co-rotating discs are included. The conduction was computed using a two-dimensional finite element solver, and the disc heat transfer was calculated assuming conductive laminar Ekman layers on the disc surfaces. Correlations for free convection on flat plates are used to model the heat transfer on the inner and outer radii of the rotating cavity. The transient core temperatures were calculated in a quasi-steady manner, with the heat transfer at every time step predicted assuming zero net heat flow. The model was validated using new transient data collected from the Compressor Cavity Rig at the University of Bath. The model shows consistent agreement with all experimental cases, providing insight into the conjugate relationship between the disc and shroud heat transfer, revealing that disc heat transfer is sustained long after there is no convective heat transfer from the shroud. This approach has direct application to practical thermo-mechanical codes, contributing to the design of next-generation, net-zero aerospace architectures.

Numerical investigations of electric field-mediated active droplet transfer in a ternary phase system

A method of active transport of a droplet from a carrier liquid to a target liquid is proposed with the aid of an electric field. Numerical investigations shed light on the dynamics associated with the active migration of a water droplet across the interface of two weakly conducting oils via application of an electric field. With the aid of two model ternary liquid systems, two modes of droplet transfer are identified—(i) the film drainage mode and (ii) the tailing mode. In the film drainage mode obtained for the model system of silicone oil–water–oleic acid, at low electric fields, the water droplets undergo negligible distortions in shape and the film drainage and rupture occur in a quasi-steady manner. At higher fields, the droplet distorts into a prolate with unsteady drainage and the film rupture. The rate of film drainage increases with the strength of the applied electric field. The tailing mode of droplet transport is achieved for very low interfacial tension between the carrier and the target liquids. For the model system of silicone oil–water–soybean oil, in the tailing mode, the droplet entrains carrier liquid approximately equal to 4.5 times its own volume into the target liquid with the length of the tail as high as eight times the drop radius. The interfacial tensions of the liquid pairs, densities, viscosities, and dielectric constants of the liquids comprising the ternary system are the key parameters influencing the dynamics of migrations. The phenomena may find applications in liquid–liquid extraction, micro-reactions, and ultra-low tensiometry.

Effects of curvature on triple flame propagation in fuel-oxidizer counterflow

In this study, we analyze the propagation of an expanding triple flame in an axisymmetric counterflow of a fuel against an oxidizer. The problem is formulated as a thermo-diffusive model with one-step global reaction. An asymptotic analysis in the limit of large activation energy and weak strain rate is conducted. The study is supported and complemented by numerical simulations carried out for arbitrary values of the strain rate. In addition to the flame front curvature 1/Rt associated with the variation in the reactants concentrations transverse to the mixing layer, the propagation of the expanding triple flame also depends on the azimuthal curvature 1/Rf where Rf is the front leading edge radial distance. As the triple flame expands to large radial distances, its propagation becomes quasi-steady. Under a quasi-steady state assumption, an explicit expression is derived for the displacement speed of the triple flame, which is found to be linearly proportional to the total curvature 1/Rf+1/Rt. Two-dimensional axisymmetric simulations are conducted to validate in particular the quasi-steady assumption. These include transient simulations of the expanding triple flame which are compared to the numerical solution of the steady eigenvalue problem obtained in a frame attached to the propagating front under a quasi-steady assumption. Following a transient ignition phase, the triple flame is found to propagate in a quasi-steady manner when Rf (measured with the stoichiometric planar flame thickness) exceeds 5, approximately. Although the theoretical analysis is performed in the weak strain limit, the linear dependence of the triple flame speed on the curvature 1/Rfis found to be applicable over a wide range of strain rates. Besides, the analysis is extended for inwardly propagating triple flames (flame holes) and similar expressions describing the relationship between displacement speed of the triple flame and curvatures are obtained.

Kinematics and hydrodynamics analyses of swimming penguins: wing bending improves propulsion performance.

Penguins are adapted to underwater life and have excellent swimming abilities. Although previous motion analyses revealed their basic swimming characteristics, the details of the 3D wing kinematics, wing deformation and thrust generation mechanism of penguins are still largely unknown. In this study, we recorded the forward and horizontal swimming of gentoo penguins (Pygoscelis papua) at an aquarium with multiple underwater action cameras and then performed a 3D motion analysis. We also conducted a series of water tunnel experiments with a 3D printed rigid wing to obtain lift and drag coefficients in the gliding configuration. Using these coefficients, the thrust force during flapping was calculated in a quasi-steady manner, where the following two wing models were considered: (1) an 'original' wing model reconstructed from 3D motion analysis including bending deformation and (2) a 'flat' wing model obtained by flattening the original wing model. The resultant body trajectory showed that the penguin accelerated forward during both upstroke and downstroke. The motion analysis of the two wing models revealed that considerable bending occurred in the original wing, which reduced its angle of attack during the upstroke in particular. Consequently, the calculated stroke-averaged thrust was larger for the original wing than for the flat wing during the upstroke. In addition, the propulsive efficiency for the original wing was estimated to be 1.8 times higher than that for the flat wing. Our results unveil a detailed mechanism of lift-based propulsion in penguins and underscore the importance of wing bending.

Initiation and propagation of one-dimensional planar flames in mixtures with variable reaction progress

In light of the recent high temperature flame experiment conducted in a shock tube, the main objective of the present study is to understand flame initiation regimes and propagation features with various ignition energy and various extents of unburnt mixture reaction progress. Flame initiation and propagation are numerically investigated for a partially reactive, near stoichiometric n-heptane/air/He mixtures under elevated temperature 700 K in a one-dimensional planar domain under nearly isobaric condition. Emphasis on flame initiation is placed on the effects of ignition energy and initial reaction progress. For ignition timing at tig = 0 s, while regular hot flames are directly initiated with higher ignition energy as expected, a class of autoignition-assisted cool flames can be directly triggered with relatively low ignition energy. By postponing ignition at later times, more pronounced chemical reaction progress is associated with the unburnt mixture such that autoignition-assisted hot flame can be achieved. For such flames, a notable flame speed increment is observed after the first-stage ignition occurs in the upstream unburnt mixture. It is found that both autoignition-assisted cool and hot flames prior to the first-stage ignition strongly depend on the ignition energy and ignition timing, and hence are case-sensitive. Extra caution needs to be taken to evaluate and compare these data. Hot flames in the post first-stage ignition mixture nevertheless exhibit much less variation to the ignition energy and initial reaction progress. For steady-state simulation, it is emphasized that a sufficiently short upstream and sufficiently long downstream domain are needed to obtain desired flame solution in the classical diffusion-reaction limit. A good agreement between the steady and unsteady simulations demonstrates the unsteady flame propagates in a quasi-steady manner with the classical flame structure, as long as τchem/τflame>>1. Sensitivity analysis and reaction network analysis have further suggested the similar key reactions on flame speed compared with regular conditions and demonstrated indirect effects from the low temperature ignition chemistry. This work provides useful insights into flame initiation regimes and propagation features under elevated temperature.

Fully Decentralized Reinforcement Learning-Based Control of Photovoltaics in Distribution Grids for Joint Provision of Real and Reactive Power

In this paper, we introduce a new framework to address the problem of voltage regulation in unbalanced distribution grids with deep photovoltaic penetration. In this framework, both real and reactive power setpoints are explicitly controlled at each solar panel smart inverter, and the objective is to simultaneously minimize system-wide voltage deviation and maximize solar power output. We formulate the problem as a Markov decision process with continuous action spaces and use proximal policy optimization, a reinforcement learning-based approach, to solve it, without the need for any forecast or explicit knowledge of network topology or line parameters. By representing the system in a quasi-steady state manner, and by carefully formulating the Markov decision process, we reduce the complexity of the problem and allow for fully decentralized (communication-free) policies, all of which make the trained policies much more practical and interpretable. Numerical simulations on a 240-node unbalanced distribution grid, based on a real network in Midwest U.S., are used to validate the proposed framework and reinforcement learning approach.

Operational mode transition in a rotating detonation engine

The relationship between the number of detonation waves and the evolution process of the flow field in a rotating detonation engine was investigated through a numerical analysis. The simulations were based on the Euler equation and a detailed chemical reaction model. In the given engine model, the flow-field evolution became unstable when a single detonation wave was released. New detonation waves formed spontaneously, changing the operational mode from single-wave to four-wave. However, when two or three detonation waves were released, the flow field evolved in a quasi-steady manner. Further study revealed that the newly formed detonation wave resulted from an accelerated chemical reaction on the contact surface between the detonation products and the reactive mixture. To satisfy the stable propagation requirements of detonation waves, we proposed a parameter called NL, which can be compared with the number of detonation waves in the combustor to predict the evolution (quasi-stable or unstable) of the flow field. Finally, we verified the effectiveness of NL in a redesigned engine. This study may assist the operational mode control in rotating detonation engine experiments.

Dynamic Stall Under Combined Pitching and Surging

Dynamic stall often occurs under conditions of simultaneous unsteady pitching and surging (e.g., rotorcraft and wind turbines), but many models employ a dimensionless time base that implicitly assumes that surging is superimposed, in a quasi-steady manner, on dynamic pitching. An unsteady wind tunnel was used to examine this assumption, where a technique was developed to quantify the unsteady effects of surging on a pitching NACA 0018 airfoil. The technique involved performing multiple harmonic pitching experiments under nominally steady freestream conditions that bracketed a corresponding 50% surging amplitude (). By interpolating these data, unsteady-pitching/quasi-steady-surging data sets were constructed and compared with de facto synchronous pitch and surging experiments, thereby isolating the unsteady effects of surging on a pitching airfoil. Both large and small poststall maximum angles of attack ( and ) were considered at multiple pitch-surge phase differences. During deep dynamic stall (), with large-scale separation, surging was seen to have a secondary effect on the unsteady aerodynamics. However, at small poststall maximum angles of attack (), either light or deep dynamic stall behavior was observed depending upon the pitch-surge phase difference. This was attributed to Reynolds number history effects, exemplified by boundary-layer transition, and thus it can be referred to as “transitional” dynamic stall.

REDIM reduced chemistry for the simulation of counterflow diffusion flames with oscillating strain rates

The dynamic behaviour and structures of laminar counterflow diffusion methane flames under oscillatory strain rates are investigated based on both detailed and reduced chemistry. It is known both from experiment and numerical studies that flame can deviate from its quasi-steady manner for high frequencies, which makes the well-known steady laminar flamelet model questionable. In this work, the Reaction-diffusion manifolds (REDIM) concept for simplified chemistry is applied to study the laminar counterflow diffusion flames with oscillating strain rates. In the construction of REDIM, one needs little knowledge of the studied system, and the REDIM reduced chemistry can cover both stable and unstable (extinction) regimes of the studied system. It is shown that the REDIM can capture both the steady and unsteady behaviours of the flame structures even for high frequencies, where the standard laminar steady flamelet approach is not appropriate.

Interplay between random fluctuations and rate dependent phenomena at slow passage to limit-cycle oscillations in a bistable thermoacoustic system.

We study the impact of noise on the rate dependent transitions in a noisy bistable oscillator using a thermoacoustic system as an example. As the parameter-the heater power-is increased in a quasi-steady manner, beyond a critical value, the thermoacoustic system undergoes a subcritical Hopf bifurcation and exhibits periodic oscillations. We observe that the transition to this oscillatory state is often delayed when the control parameter is varied as a function of time. However, the presence of inherent noise in the system introduces high variability in the characteristics of this critical transition. As a result, if the value of the system variable-the acoustic pressure-approaches the noise floor before the system crosses the unstable manifold, the effect of rate on the critical transition becomes irrelevant in determining the transition characteristics, and the system undergoes a noise-induced tipping to limit-cycle oscillations. The presence of noise-induced tipping makes it difficult to identify the stability regimes in such systems by using stability maps for the corresponding deterministic system.

Relativistic shock breakout from a stellar wind

We construct an analytic model for the breakout of a relativistic radiation mediated shock from a stellar wind, and exploit it to calculate the observational diagnostics of the breakout signal. The model accounts for photon escape through the finite optical depth wind, and treats the fraction of downstream photons escaping to infinity as an adiabatic parameter that evolves in a quasi-steady manner. It is shown that the shock is mediated by radiation even when a large fraction of the downstream photons escape, owing to self-generation and adjustment of opacity through accelerated pair creation. Relativistic breakout occurs at radii at which the total optical depth of the wind ahead of the shock is $\sim (m_e/m_p)\Gamma_{sh}$, provided that the local shock Lorentz factor $\Gamma_{sh}$ exceeds unity at this location. Otherwise the breakout occurs in the Newtonian regime. A relativistic breakout is expected in a highly energetic spherical explosion ($10^{52}-10^{53}$ erg) of a Wolf-Rayet star, or in cases where a smaller amount of energy ($\sim 10^{51}$ erg) is deposited by a jet in the outer layers of the star. The properties of the emission observed in such explosions during the relativistic breakout are derived. We find that for typical parameters about $10^{48}$ ergs are radiated in the form of MeV gamma-rays over a duration that can range from a fraction of a second to an hour. Such a signal may be detectable out to 10-100 Mpc by current gamma-ray satellites.

Experiments and modelling of rate-dependent transition delay in a stochastic subcritical bifurcation.

Complex systems exhibiting critical transitions when one of their governing parameters varies are ubiquitous in nature and in engineering applications. Despite a vast literature focusing on this topic, there are few studies dealing with the effect of the rate of change of the bifurcation parameter on the tipping points. In this work, we consider a subcritical stochastic Hopf bifurcation under two scenarios: the bifurcation parameter is first changed in a quasi-steady manner and then, with a finite ramping rate. In the latter case, a rate-dependent bifurcation delay is observed and exemplified experimentally using a thermoacoustic instability in a combustion chamber. This delay increases with the rate of change. This leads to a state transition of larger amplitude compared with the one that would be experienced by the system with a quasi-steady change of the parameter. We also bring experimental evidence of a dynamic hysteresis caused by the bifurcation delay when the parameter is ramped back. A surrogate model is derived in order to predict the statistic of these delays and to scrutinize the underlying stochastic dynamics. Our study highlights the dramatic influence of a finite rate of change of bifurcation parameters upon tipping points, and it pinpoints the crucial need of considering this effect when investigating critical transitions.

Transient growth of optimal perturbation in a decaying channel flow

Stability of an unsteady channel flow is investigated by incorporating the effect of the base flow change with time and comparing with the optimal growth of the normal mode analysis. The existing literature shows that the modal analysis can be done on the velocity profiles in a quasi-steady manner to study the stability characteristics of unsteady internal flows. But, in the current study, it is shown that the mode obtained from the optimal growth analysis provides higher growth and estimates the structures observed in experiments. Initially, the optimal mode is obtained using Farrell’s analysis, and its energy growth is compared with that of the most unstable eigenmode. Later, to incorporate the base flow change, the optimal mode for maximum growth is obtained by solving the problem with a variational approach. The results are compared to provide justification of Farrell’s analysis, which is quasi-steady, against the requirement of complete study considering the time dependent base flow.

A self-consistent model for the saturation dynamics of the vortex shedding around the mean flow in the unstable cylinder wake

The supercritical instability leading to the Bénard-von Karman vortex street in a cylinder wake is a well known example of supercritical Hopf bifurcation: the steady solution becomes linearly unstable and saturates into a periodic limit cycle. Nonetheless, a simplified physical formulation accurately predicting the transition dynamics of the saturation process is lacking. Building upon our previous work, we present here a simple self-consistent model that provides a clear description of the saturation mechanism in a quasi-steady manner by means of coupling the instantaneous mean flow with its most unstable eigenmode and its instantaneous amplitude through the Reynolds stress. The system is coupled for different oscillation amplitudes, providing an instantaneous mean flow as function of an equivalent time. A transient physical picture is described, wherein a harmonic perturbation grows and changes in amplitude, frequency, and structure due to the modification of the mean flow by the Reynolds stress forcing, saturating when the flow is marginally stable. Comparisons with direct numerical simulations show an accurate prediction of the instantaneous amplitude, frequency, and growth rate, as well as the saturated mean flow, the oscillation amplitude, frequency, and the resulting mean Reynolds stresses.

Analysis of Multimode Coupled Buffeting Response of Long-Span Bridges to Nonstationary Winds with Force Parameters from Stationary Wind

AbstractThis paper presents a general frequency domain framework for predicting multimode coupled buffeting response of long-span bridges to nonstationary winds. Within this framework, the wind speed field, aerodynamic forces, and bridge response are separated into deterministic time-varying mean and evolutionary random fluctuating components. Under the assumption of low variation rate of mean wind speed, the time-varying mean and self-excited and buffeting forces are modeled in static force coefficients, flutter derivatives, and admittance functions, determined in a wind tunnel under stationary wind, but with consideration of nonstationary wind characteristics in a quasi-steady manner. The time-varying mean bridge response is calculated through static analysis at each time instant. The random buffeting response is expressed in generalized modal displacements governed by the equations of a frequency-dependent linear time-variant (LTV) system. An equivalent frequency-independent LTV system is introduced, w...

The onset of plasticity of a Zr-based bulk metallic glass

The deformation behaviors of a Zr41.2Ti13.8Cu12.5Ni10Be22.5 bulk metallic glassy alloy under step-controlled tensile loads have been studied in situ and systematically using scanning electron microscopy and synchrotron X-ray diffraction. A circular hole, as a stress concentrator, was introduced in the middle of the gauge length of the sample to facilitate the creation of shear bands in a controllable way at the edge of the hole in situ imaging and diffraction studies could be carried out at the identical loads in a quasi-steady state manner. Pair distribution function was used to calculate the strains of different atomic coordination shells and the relative change of the bond lengths of different atomic pairs. The combined imaging and diffraction studies revealed that (1) the extension of solvent–solvent (Zr–Zr) atomic pairs under tension causes the nucleation of shear bands, and (2) the compressive stress field around the shear band tip effectively slows down the fast propagation of shear bands.

Quasi-steady prediction of coupled bending–torsion flutter under rotating stall

A method is presented in this paper to predict cascade flutter under subsonic stalled flow condition in a quasi-steady manner. The ability to predict the occurrence of aeroelastic flutter is highly important from the compressor design point of view. In the present work, the well known Moore–Greitzer compression system model is used to evaluate the flow under rotating stall and the linearized aerodynamic theory of Whitehead is used to estimate the blade loading. The cascade stability is then predicted by solving the structural model, which is posed as a complex eigenvalue problem. The possibility of occurrence of flutter in both bending and torsional modes is considered and the latter is found to be the dominant one, under subsonic stalled flow, for a large range of frequency ratios examined. It is also shown that the design of compressor blades at frequency ratios close to unity may result in rapid initiation of torsional flutter in the presence of stalled flow. A frequency ratio of 0.9 is primarily emphasized for most part of the study as many interesting features are revealed and the results are physically interpreted. Roughly a pitchfork pattern of energy distribution appears to occur between bending mode and torsional mode which ensures that only one flutter mode is possible at any instant in time. A bifurcation from bending flutter to torsional flutter is shown to occur during which the frequency of the two vibrating modes appear to coalesce for a very short period of time.

Resonant responses in periodic turbulent flows: computations using a k–ε eddy viscosity model

Periodically-oscillated pipe flows in which the bulk velocity is varied about a non-zero mean level (Ub = Ub0[1 + γ cos ωt]) are computed using a low-Reynolds-number k–ε turbulence model. Comparison is made with data for periodic pipe flow and it is shown that model is capable of resolving the principal features of the highly non-universal turbulence profiles that occur under conditions of harmonic forcing. There follows an examination of the frequency response of the phase-averaged turbulent kinetic energy, k, which is analysed in terms of its first harmonic variation (k(r, ωt) = k 0 + k 1 cos(ωt + ψ); k 0, k 1,ψ = f(r)). In confirmation of the stress-transport model results of Cotton and Guy [J. Hydraul. Res. 42 (2004) 293], it is found that the modulation of the turbulent kinetic energy, k 1/γ k0 first responds in a quasi-steady manner and then, with increasing frequency, exhibits resonant behaviour, which is itself succeeded by a frozen response at higher frequencies. The resonant condition occurs when the time scale of large-scale turbulence is an order of magnitude less than the period of the imposed oscillation. The paper concludes with a discussion of the parallels that may be drawn between the present results and the experimental study of Mizushina et al. [J. Chem. Engng. Jpn. 6 (1973) 487] in which the effect of external pulsation on the turbulence “bursting” process was investigated

Investigation of turbulence behavior in pipe transient using a k–εmodel

Existing wall shear stress models and turbulence closure equations for water hammer problems are based on far-reaching assumptions in relation to the turbulence behavior during a transient event. It is often postulated that the turbulence behaves in a quasi-steady, frozen or quasi-laminar manner. Presently, the experimental or numerical data needed to investigate turbulence behavior during a transient, and to assess the often used assumptions regarding the turbulence behavior in water hammer flows, are lacking. The recent development of highly efficient numerical scheme makes it feasible to conduct numerical experiments using a k–εmodel suitable for time-dependent flows. As a result, this paper develops a k–εmodel for water hammer and applies it to transient pipe flows to investigate the turbulence behavior during a water hammer event and to assess the quasi-steady, frozen or quasi-laminar turbulence hypothesis