Quasi-steady Hypothesis Research Articles

Unsteady gasdynamic modeling of double-entry turbine integrated with engine exhaust manifolds

Pulsating turbocharging system with a dual-entry turbine is always applied for the utilization of pulsating energy and improvement of low-speed torque for the internal combustion engine. With the enhancement of pulsating energy via the pulsating turbocharging system and dual-entry turbine, the interaction between exhaust manifolds and dual-entry turbine cannot be disregarded by either side when confronted by pulsating inflows. This paper proposes a gasdynamic model of double-entry turbine coupling with exhaust manifolds to examine the interaction effect between turbine and exhaust manifolds. This gasdynamic model can predict the propagation of pressure and mass flow rate from exhaust manifolds to the double-entry turbine as well as transient turbine performance. Predictions of this gasdynamic model are validated against detailed 3-D simulation and show good consistency with 3-D results. The performance and energy distribution of the double-entry turbine coupled to exhaust manifolds under various pulsating conditions are thoroughly discussed via this reduced-order model. Results show that with increasing frequency or amplitude of pulsating inflows imposed on inlets of the exhaust manifolds, the performance of the entire system deviates from the quasi-steady hypothesis, particularly the swallowing capacity. This phenomenon indicates that the matched operating point between the turbine and engine deviates from the quasi-steady conditions. In addition, exhaust manifolds geometries have a notable impact on turbine performance and energy distributions in exhaust systems. It is found that with an increase in the volume or length of the exhaust manifolds, the pulse at the turbine inlet is amplified, and available energy at the turbine inlet is increased, even though the inlet conditions of exhaust manifolds remain unchanged. This study may provide a guiding effect for the optimization of the turbo-engine matching process and the development of high-performance turbocharged engines.

Nonlinear dynamical and harvesting characteristics of bistable energy harvester under hybrid base vibration and galloping

To harvest wind energy and vibration energy simultaneously, the nonlinear dynamical and harvesting characteristics of a bistable piezoelectric energy harvester (BPEH) under hybrid excitations are studied in this manuscript. A distributed model of BPEH is established by the generalized Hamilton’s principle, Kirchhoff’s law, and the quasi-steady hypothesis. The influences of wind speed, base excitation level, magnetic distance and resistance are studied by the harmonic balance method (HBM). The results show that the structure can be optimized to reach the best harvesting performance for wind energy and vibration energy. The analytical prediction and simulation results are verified by the experiments. The coexisting solutions appear while the BPEH is under a hybrid excitation of wind galloping and base vibration. The dynamical response will approach different branches for different initial conditions, by which the system can be intentionally designed to attain the high energy orbit. The experimental results show that the BPEH could reach the highest output efficiency while it undergoes the motion of inter-well period-1. Thus, a high energy output can be realized by controlling the initial conditions to the desired range. This study could provide a comprehensive insight into the promotion of harvesting performance for hybrid ambient excitations.

Developments in analytical wall shear stress modelling for water hammer phenomena

New developments in analytical modelling of wall shear stresses during water hammer events are presented and discussed in this paper. These include further development of models based on the quasi-steady and unsteady hypothesis of hydraulic resistances. All the analyzed solutions have been improved so that they have extended ranges of applicability and the simplest possible mathematical form. Exemplary comparative studies were carried out, which showed their advantages and disadvantages. Explicit analytical formulas of wall shear stress were derived for the first time. They will be particularly useful at the stage of design and modernization of the pressurized piping systems (water supply, oil-hydraulics etc.) and enable effective analysis of leakages and other damages (ruptures, fatigue related failures) occurring in industrial pipeline systems. With their help, it will be easier to prevent the increased pulsating pressures occurring during water hammer events (protect against failures), and to verify numerical models used for years in simulations of transient pipe flows.

Auto-encoder-assisted analysis of amplitude and wavelength modulation of near-wall turbulence by outer large-scale structures in channel flow at friction Reynolds number of 5200

This paper reports a novel methodology that allows the intensity of, and the underlying mechanism for, the amplitude and length-scale modulation (amplification or attenuation) of turbulent stresses in the inner layer of a channel flow at Reτ≈5200 to be clarified. A unique aspect of the present framework is the use of an auto-encoder algorithm to separate full-volume extremely large direct numerical simulation (DNS) fields into large-scale and small-scale motions. This approach is adopted in preference to the empirical mode decomposition (EMD) previously used by the present authors at the lower Reynolds number, Reτ≈1000, because resource requirements posed by the EMD quickly become untenable due to the extremely large DNS dataset and the large solution box needed to capture the wide spectrum of scales at the present Reynolds number. A second original element is a formalism that derived the modulation, conditional on large-scale fluctuations, from continuous statistical quantities represented as multivariable-joint probability-density functions, thus obviating the need for any discrete representation or binning beyond that imposed by the discrete DNS solution. A third novel aspect is the use of the length-scale-wise derivative of the second-order structure function to quantify the modulation (increase or decrease) in the length scale, again conditional on large-scale structures. Apart from illuminating the modulation itself, the study examined the validity of the quasi-steady hypothesis that proposes that the near-wall turbulence is universal when scaled by the spatially and temporally varying large-scale wall shear stress rather than its time average.

On the reduction of nonlinear electromechanical systems

The present work revisits the reduction of the nonlinear dynamics of an electromechanical system through a quasi-steady state hypothesis, discussing the fundamental aspects of this type of approach and clarifying some confusing points found in the literature. Expressions for the characteristic time scales of dynamics are deduced from a physical analysis that establishes an analogy between electromechanical dynamics and the kinetics of a chemical reaction. It provides a physical justification, supplemented by non-dimensionalization and scaling of the equations, to reduce the dynamics of interest by assuming a quasi-steady state for the electrical subsystem, eliminating the inductive term from the electrical equation. Numerical experiments help to illustrate the typical behavior of the electromechanical system, a boundary layer phenomenon near the initial dynamic state, and the validity limits of the electromechanical quasi-steady-state assumption discussed here.

Galloping of circular cylinder induced by downstream strip-plate in cruciform arrangement

It has been reported that two longitudinal vortices are periodically shed from a cruciform two-cylinder system in a uniform flow. These depend on the gap, s, between the two cylinders and can induce a vibration called the “longitudinal vortex-induced vibration”. In previous studies, the authors showed that stationary longitudinal vortices are formed by a cruciform circular-cylinder/strip-plate (CC/SP) system when the upstream cylinder is moving along the downstream strip plate, and that one of these longitudinal vortices, the necklace vortex (NV), generates a lift force that acts on the cylinder in the direction of the motion. The “stationary” position of the NV is believed to make the system unstable, leading to fluid-elastic instability vibration. This study measured the fluid force acting on the rotating upstream circular cylinder blade in a wind turbine-type CC/SP system, and the vibration behavior of a pendulum-type CC/SP system was investigated through wind-tunnel experiments. The lift force coefficient, together with the ranges for the gap ratio (s/d) and velocity ratio (λ=V/U) needed to achieve stationary positions, were obtained (d: diameter of the upstream circular cylinder, U: flow velocity, V: rotational velocity of cylinder). It was confirmed that a cross-flow vibration of the cylinder in the pendulum-type CC/SP system was induced, and an analytical method to predict the vibration amplitude was proposed based on the quasi-steady hypothesis. The vibration amplitude of the pendulum device was well predicted by the method using the lift coefficient, obtained through the wind turbine-type CC/SP experiment. In conclusion it was verified that the vibration was caused by the stationary formation of the NV. It was classified as galloping, although it did not occur for an isolated circular cylinder because of its axisymmetric cross-sectional geometry.

Metabolic flux simulation of microbial systems based on optimal planning algorithms

The genomic scale metabolic networks of the microorganisms can be constructed based on their genome sequences, functional annotations, and biochemical reactions, reflecting almost all of the metabolic functions. Mathematical simulations of metabolic fluxes could make these functions be visualized, thereby providing guidance for rational engineering design and experimental operations. This review summarized recently developed flux simulation algorithms of microbial systems. For the single microbial systems, the optimal planning algorithm has low complexity because there is no interaction between microorganisms, and it can quickly simulate the stable metabolic states through the pseudo-steady hypothesis. Besides, the experimental conditions of single microbial systems are easier to reach or close to the optimal states of simulation, compared with polymicrobial systems. The polymicrobial culture systems could outcompete the single microbial systems as they could relieve metabolic pressure through metabolic division, resource exchange, and complex substrate co-utilization. Besides, they provide varieties of intracellular production environments, which render them the potential to achieve efficient bioproduct synthesis. However, due to the quasi-steady hypothesis that restricts the simulation of the dynamic processes of microbial interactions and the algorithm complexity, there are few researches on simulation algorithms of polymicrobial metabolic fluxes. Therefore, this review also analyzed and combed the microbial interactions based on the commonly used hypothesis of maximizing growth rates, and studied the strategies of coupling interactions with optimal planning simulations for metabolism. Finally, this review provided new insights into the genomic scale metabolic flux simulations of polymicrobial systems.

Investigation on the characteristics of a novel internal resonance galloping oscillator for concurrent aeroelastic and base vibratory energy harvesting

Harnessing energy from concurrent wind flow and base vibration is a prospective method to enable self-powered sensing in the circumstances where wind and base motion are coexisting, like aircrafts, bridges, railways and ocean buoys. This paper proposes a novel two-degree-of-freedom galloping energy harvester with 2:1 internal resonance for efficient dual-source energy harvesting. The harvester consists of a primary and a secondary beam with a square-sectioned bluff body attached to the free end and two pairs of magnets repulsively arranged at the beam joint. Careful tuning of the magnetic force with a quadratic nonlinear stiffness term triggers the internal resonance, leading to a remarkably superior performance compared to its linear counterpart. A fully coupled aero-electro-mechanical distributed parameter model is established based on Euler-Bernoulli beam theory and quasi-steady aerodynamic hypothesis. Explicit analytical solution for steady-stage mechanical and electrical responses is derived using harmonic balance method and validated by numerical simulation. At the wind speed of 3 m/s and base acceleration of 0.9 m/s2, the conceptual prototype achieves a 211.1% increase in the effective bandwidth and a 50% increase in the peak voltage around the first resonance. The results provide a theoretical guideline to improve the system capacity of dual-source energy harvesting.

Homoclinic bifurcation for a bi-stable piezoelectric energy harvester subjected to galloping and base excitations

In this paper, we studied the homoclinic bifurcation and nonlinear characteristics of a bistable piezoelectric energy harvester while it is concurrently excited by galloping and base excitation. Firstly, the electromechanical model of the energy harvester is established analytically by the energy approach, the Kirchhoff's law and quasi-steady hypothesis. Then, by the Melnikov method, the threshold for underlying snap-through in the system is derived, and the necessary conditions for homoclinic bifurcation and chaos are presented. The threshold is a determinant for the occurrence of high-energy oscillation. The analysis results reveal that the wind speed and the distance between magnets could affect the threshold for inter-well chaos and high energy oscillation. Finally, numerical simulation and experiments are carried out. Both results from numerical simulation and experiment support the theoretical prediction from Melnikov theory. The study could provide a guideline for the optimum design of the bi-stable piezoelectric energy harvester for wind and vibration in practice.

Large-to-small scale frequency modulation analysis in wall-bounded turbulence via visibility networks

Abstract

A near-wall predictive model for passive scalars using minimal flow unit

In the present study, direct numerical simulations (DNSs) are performed to the passive scalar transport in minimal flow units (MFUs) at Reτ=1000, 2000, and 4000 and in a full-sized channel at Reτ=1000 for comparison. The molecular Prandtl number ranges from 0.2 to 2.0. At each Prandtl number, the scalar intensities in MFUs at different Reynolds numbers agree well with each other, and with those at MFU-contained scales in the full-sized channel. This suggests that scalar transport in MFUs is Reynolds number independent and is able to represent that at small scales in the full-sized channel. A near-wall predictive model for passive scalars based on MFU data is proposed in the framework of superposition and modulation of the outer large-scale motions. The modulation coefficients at different Prandtl numbers are collapsed together under the presently proposed transforming. Both the scalar intensities and the joint probability density functions of the predicted results agree well with those of the DNS results. Furthermore, a predictive model for wall scalar-flux based on MFU data and the quasi-steady hypothesis is put forward and validated against the DNS results.

Energy harvesting from iced-conductor inspired wake galloping

Energy harvesting from wake galloping of crescent-shape and D-shape cross-section bluff bodies inspired by galloping of iced conductors is investigated. Analytical models are derived in the framework of electromechanical extension of the Hamilton’s principle, Euler–Bernoulli beam assumption and quasi-steady hypothesis. Experiments are performed in an open-circuit boundary layer wind tunnel to investigate the wake effects of the upstream fixed interference cylinder on the performance of the downstream energy harvester and validate the analytical model. The observations are explained with the wake characteristics and lift force as determined from Large Eddy Simulation. The results show that the wake effects of the upstream fixed interference cylinders can positively enhance the performance of the downstream energy harvester. The wake galloping energy harvesters with the iced D-shape and crescent-shape bluff bodies display remarkable enhancement in terms of the harvested power density for wide interference spacing range when compared to energy harvesters placed in the wake of a non-iced circular bluff body. The power density of the wake galloping energy harvester with the iced-conductor inspired bluff bodies at the optimal interference spacing is about 63 times that of the power density of the wake galloping energy harvester with the classic circular bluff body.

Piezoelectromagnetic synergy design and performance analysis for wind galloping energy harvester

To improve the performance of the wind galloping energy harvester, the piezoelectromagnetic synergy design is proposed. Hamilton's principle and Euler–Bernoulli beam assumptions, quasi-steady hypothesis, Gauss law and Faraday's law are adopted to establish an electromechanical coupled distributed parameter model for the hybrid energy harvesting system. Using the harmonic balance method, the approximate analytical solutions of the dynamic response and electric output are derived. Wind tunnel experiments validate the nonlinear results of the proposed model including the Hopf bifurcation and unsteady response. The load resistances are optimized via finding the extreme of the power binary function. For the wind speed smaller than the critical wind speed, the piezoelectric module works with switched-off electromagnetic module. For the wind speed larger than the critical wind speed, piezoelectric and electromagnetic modules work concurrently to realize the synergistic effect. The piezoelectromagnetic galloping energy harvester is demonstrated to be superior than the piezoelectric galloping energy harvester and the electromagnetic energy harvester for higher harvested power from smaller galloping oscillations.

Enhanced low-velocity wind energy harvesting from transverse galloping with super capacitor

To improve the low-velocity wind energy extracting performance, a galloping piezoelectric energy harvester with an external super capacitor in addition to the small internal piezoelectric capacitor is designed. The electromechanical extension of the Hamilton's principle is adopted to establish the fluid-structure-electricity coupled distributed-parameter model with the Euler-Bernoulli beam assumption and quasi-steady hypothesis. Using the harmonic balance method, the approximate analytical solutions of the onset galloping speed, dynamic response and electric output of the nonlinear energy harvester are derived. Simulink simulations validate the nonlinear multiple solutions of the proposed model. The interface circuit is optimized via the electrical damping dependent of the external capacitance, inductance and resistance. The external super capacitor is chosen to satisfy the optimal electrical damping with the acceptable inductance for the power maximization. Wind tunnel experiments demonstrate that the harvested power is enhanced 450% by incorporating the super capacitor in the galloping system for low-velocity wind energy harvesting. The proposed energy harvester is able to be extended to meter scale or shrunk to millimeter scale for the field application needs.

Low velocity water flow energy harvesting using vortex induced vibration and galloping

The oceans, seas, rivers and channels store abundant renewable low velocity flow energy but without large-scale exploitation. For energy harvesting, the vortex induced vibration (VIV) and galloping convert flow energy to vibration energy. This paper studies the piezoelectric energy harvesting from low velocity water flow by VIV and galloping. A piecewise distributed parameter model for the piezoelectric cantilever beam with three types of bluff bodies is proposed. The modified Van der Pol model is established to simulate the VIV force for the cylinder bluff body, and the quasi-steady hypothesis is used to obtain the galloping hydrodynamic force for the tri-prism and semi-cylinder bluff bodies. The added-mass term of the hydrodynamic force is accounted in both the VIV and galloping forces. The approximate analytical solutions of the harvested power for the VIV and galloping models are derived. The circulating water channel experiments are performed and verify the theoretical models. The harvested maximum power density is 1.949 mW/cm3 for the VIV harvester at the flow velocity of 0.48 m/s. The harvested maximum power densities are 4.286 mW/cm3 and 7.582 mW/cm3, respectively for the tri-prism galloping harvester and semi-cylinder galloping harvester at the flow velocity of 0.54 m/s. The fluid fields for the three bluff bodies are simulated using the large eddy simulation turbulence model to present the vortex, pressure and velocity distributions. This study indicates that the galloping energy harvesting is superior to the VIV energy harvesting. The ratio of the linear to the cubic hydrodynamic coefficient is crucial in the galloping energy harvesting.

On the departure of near-wall turbulence from the quasi-steady state

An examination is undertaken of the validity and limitations of the quasi-steady hypothesis of near-wall turbulence. This hypothesis is based on the supposition that the statistics of the turbulent fluctuations are universal if scaled by the local, instantaneous, wall shear when its variations are determined from footprints of large-scale, energetic, structures that reside in the outer part of the logarithmic layer. The examination is performed with the aid of direct numerical simulation data for a single Reynolds number, which are processed in a manner that brings out the variability of locally scaled statistics when conditioned on the local value of the wall friction. The key question is to what extent this variability is insignificant, thus reflecting universality. It is shown that the validity of the quasi-steady hypothesis is confined, at best, to a thin layer above the viscous sublayer. Beyond this layer, substantial variations in the conditioned shear-induced production rate of large-scale turbulence cause substantial departures from the hypothesis. Even within the wall-proximate layer, moderate departures are provoked by large-scale distortions in the conditioned strain rate that result in variations in small-scale production of turbulence down to the viscous sublayer.

Investigations on the presence of electrical frequency on the characteristics of energy harvesters under base and galloping excitations

The characteristics and performance of piezoelectric energy harvesters concurrently subjected to galloping and base excitations when using a complex electrical circuit are studied. The considered energy harvester is composed of a bilayered cantilever beam with a square cylindrical structure at its tip. Euler–Bernoulli beam theory, nonlinear quasi-steady hypothesis, and Galerkin method are used to develop a reduced order model of this system. The electrical circuitry of the harvester consists of a load resistance, a capacitance, and an inductance. The impacts of the electrical components of the harvester’s circuitry, the wind speed, and the base excitation frequency and acceleration on the broadband characteristics of the harvester, quenching phenomenon, and appearance of new nonlinear behaviors are deeply investigated and discussed. Different methods were used to characterize the new nonlinear phenomena that took place due to mechanical electrical interaction like the power spectrum and time history. When both coupled frequencies of electrical and mechanical types exist and are far from each other, it is shown that the quenching phenomenon is only related to the coupled frequency of mechanical type. It was also proven that this configuration results on high harvested power with low displacement near the electrical frequency. On the other hand, for a well-defined choice of the electrical components, the results show that a broadband configuration of the harvester can be designed. It is also indicated that the quenching phenomenon interacts with the appearance of hysteresis regions that depends on the value of the base acceleration and initial conditions. Moreover, it was shown that the presence of this inductance may result in broadband system harvesting more power from both galloping and base excitation.

Dry galloping in inclined cables: linear stability analysis

In the last decade, dry galloping has been frequently observed on real stay cables also in the case of circular cross section. It is an aeroelastic phenomenon which occurs when structures or structural elements are generically placed with respect to the wind, being both incidence and yaw angles different from zero. Here, after writing down the equations which describe the static reference configuration of an inclined cable under the self-weight, the equations of motion are obtained up to third order, where the forces related to the wind are evaluated coherently with an aerodynamic model, drawn under the quasi-steady hypothesis. A Galerkin projection is carried out and the critical conditions causing Hopf bifurcation on the trivial equilibium configuration are then evaluated.

Auto-thermal reforming (ATR) of natural gas: An automated derivation of optimised reduced chemical schemes

A fully automated strategy is discussed to construct reduced chemistry suitable for the numerical simulation of stationary combustion systems of large dimension, such as auto-thermal reforming (ATR) of natural gas for syngas production. Because of computing limitations in terms of space and time resolution, three-dimensional simulations of an ATR unit cannot be addressed with detailed chemistry. A procedure is proposed to automatically derive optimised and reduced chemical schemes under specific ATR operating conditions. A stochastic model problem is first designed to probe the dynamical response of a detailed chemical scheme, over a large range of chemical compositions of the mixture. Reference composition space trajectories are built, featuring turbulent micro-mixing and reactions. Following these trajectories, the chemical response is analysed using directed relation graphs with error propagation combined with quasi-steady state hypothesis, to reduce the number of species and elementary reactions. Then, the time evolution of the model problem is coupled with a genetic algorithm, to optimise on the fly the chemical rates of the reduced kinetics, according to the reference composition space trajectories. The accuracy of the reduced scheme is monitored with a fitness function and the results are tested against the reference detailed chemistry.

On the validity of the quasi-steady-turbulence hypothesis in representing the effects of large scales on small scales in boundary layers

The “quasi-steady hypothesis,” as understood in the context of large-scale/small-scale interactions in near-wall turbulence, rests on the assumption that the small scales near the wall react within very short time scales to changes imposed on them by energetic large scales whose length scales differ by at least one order of magnitude and whose energy reaches a maximum in the middle to the outer portion of the log-law layer. A key statistical manifestation of this assumption is that scaling the small-scale motions with the large-scale wall-friction-velocity footprints renders the small-scale statistics universal. This hypothesis is examined here by reference to direct numerical simulation (DNS) data for channel flow at Reτ ≈ 4200, subjected to a large-scale/small-scale separation by the empirical mode decomposition method. Flow properties examined include the mean velocity, second moments, joint probability density functions, and skewness. It is shown that the validity of the hypothesis depends on the particular property being considered and on the range of length scales of structures included within the large-scale spectrum. The quasi-steady hypothesis is found to be well justified for the mean velocity and streamwise energy of the small scales up to y+∼O(80), but only up to y+∼O(30) for other properties.