Initial Transients Research Articles

Computational and analytical study on the stability and utility aspects of single-phase natural circulation loop in parabolic trough collector

The use of passive heat transport devices in solar thermal energy devices is critical to make the systems more reliable and sustainable. Hence, linking single phase natural circulation loop to parabolic trough collector is the apt solution. In this regard, a 3-D computational model is built and validated for steady state and transient results. To acquire realistic results, solar irradiance pattern over the receiver is explored from SolTrace® and applied to the loop. The upper threshold of the horizontal heater horizontal cooler loop is found and validated using linear stability analysis. Since the loop is unstable at lower loads, instability restraining techniques viz. loop inclination (θ = 4°) and orifice insertion (β = 0.7) are employed. Although loop inclination gave desired results, the orifice couldn't improve the behavior due to loop geometry. The type of heat flux pattern does affect the initial transients of the loop, but it does not affect the steady state results in any manner. The loop was also tested with Therminol VP 1 and compared the stability aspects with water. In the end, intending NCL application in PTC, transient analysis was undertaken considering whole day solar flux distribution, which gave convincing results.

Simply solvable model capturing the approach to statistical self-similarity for the diffusive coarsening of bubbles, droplets, and grains.

Aqueous foams and a wide range of related systems are believed to coarsen by diffusion between neighboring domains into a statistically self-similar scaling state, after the decay of initial transients, such that dimensionless domain size and shape distributions become time independent and the average grows as a power law. Partial integrodifferential equationsfor the time evolution of the size distribution for such phase separating systems can be formulated for arbitrary initial conditions, but these are cumbersome for analyzing data on nonscaling state preparations. Here we show that essential features of the approach to the scaling state are captured by an exactly-solvable ordinary differential equationfor the evolution of the average bubble size. The key ingredient is to characterize the bubble size distribution approximately, using the average size of all bubbles and the average size of the critical bubbles, which instantaneously neither grow nor shrink. The difference between these two averages serves as a proxy for the width of the size distribution. Solution of our model shows that behavior is controlled by a signed length δ that is proportional to the width of the initial distribution relative to that in the scaling state. In particular, δ is negative if the initial preparation is too monodisperse, and is positive if it is too polydisperse. To test our approach, we compare with data for quasi-two dimensional dry foams created with three different initial amounts of polydispersity. This allows us to readily identify the critical radius from the average area of six-sided bubbles, whose growth rate is zero by the von Neumann law. The growth of the average and critical radii agree quite well with exact solution, though the most monodisperse sample crosses over to the scaling state faster than expected. A simpler approximate solution of our model performs equally well. Our approach is applicable to 3d foams, which we demonstrate by re-analyzing prior data, as well as to froths of dilute droplets and to phase separation kinetics for more general systems such as emulsions, binary mixtures, and alloys.

Accumulated dose implications from systematic dose-rate transients in gated treatments with Viewray MRIdian accelerators

The combination of magnetic resonance (MR) imaging and linear accelerators (linacs) into MR-Linacs enables continuous MR imaging and advanced gated treatments of patients. Previously, a dose-rate transient (∼8% reduced dose rate during the initial 0.5 s of each beam) was identified for a Viewray MRIdian MR-Linac (Klavsen et al 2022 Radiation Measurement 106759). Here, the dose-rate transient is studied in more detail at four linacs of the same type at different hospitals. The implications of dose-rate transients were examined for gated treatments. The dose-rate transients were investigated using dose-per pulse measurements with organic plastic scintillators in three experiments: (i) A gated treatment with the scintillator placed in a moving target in a dynamic phantom, (ii) a gated treatment with the same dynamic conditions but with the scintillator placed in a stationary target, and (iii) measurements in a water-equivalent material to examine beam quality deviations at a dose-per-pulse basis. Gated treatments (i) compared with non-gated treatments with a static target in the same setup showed a broadening of accumulated dose profiles due to motion (dose smearing). The linac with the largest dose-rate transient had a reduced accumulated dose of up to (3.1 ± 0.65) % in the center of the PTV due to the combined dose smearing and dose-rate transient effect. Dose-rate transients were found to vary between different machines. Two MR-Linacs showed initial dose-rate transients that could not be identified from conventional linearity tests. The source of the transients includes an initial change in photon fluence rate and an initial change in x-ray beam quality. For gated treatments, this caused a reduction of more than 1% dose delivered at the central part of the beam for the studied, cyclic-motion treatment plan. Quality assurance of this effect should be considered when gated treatment with the Viewray MRIdian is implemented clinically.

Identifying Non-Stationarity in Non-Linear Harmonics of EIS Measurements of Li Batteries

Non-linear Harmonic Analysis is a technique used to investigate the distortions in Electrochemical Impedance Spectroscopy (EIS) measurements. The distortions are in both non-linear and non-stationary nature that appear as high order harmonics in the frequency domain. Differentiating the origin of the harmonics is important in understanding their nature and relating them to electrochemical phenomena. Here, we will show how the harmonics are in direct relation to the initial non-stationary response (initial transient) of the excited system [1]. We will show by both experimental measurements and simulations of dummy cell circuits, representing the electrochemical interface, that the initial transient exhibits high order harmonics that show the highest value at the characteristic frequency of the process [1]. We also extend the analysis to include more complex systems of primary Lithium batteries [2]. It is observed that the same non-stationary initial transient behavior is persistent in the time constants of the electrochemical processes. It is concluded that the capacitive components of the electrochemical processes are responsible for such non-stationary behavior in electrochemical systems [2].[1] G. Katırcı, M. A. Zabara, and B. Ülgüt, “Methods—Unexpected Effects in Galvanostatic EIS of Randles’ Cells: Initial Transients and Harmonics Generated,” J Electrochem Soc, vol. 169, no. 3, p. 030527, Mar. 2022, doi: 10.1149/1945-7111/ac5ad7.[2] M. A. Zabara, G. Katırcı, and B. Ülgüt, “Non-linear harmonics in EIS of batteries with lithium anodes: Proper controls and analysis,” Electrochim Acta, vol. 429, Oct. 2022, doi: 10.1016/j.electacta.2022.140969.

On a Robust Descriptor of the Flue Organ Pipe Transient

The initial transient of an organ pipe is known to be of great influence to the perceived sound quality. At the same time, the unsteady process of the tone onset is essentially nonlinear and lacks exact repeatability, so the search for a robust descriptor is in place. Initial transients were recorded using an adjustable flue organ pipe. The blowing pressure and cut-up height were varied. Prony’s method was employed to analyze the results. Utilizing the Principal Component Analysis (PCA) on the standardized exponential model coefficients, it was shown that the transients are well described by just one scalar parameter. Its value is predominantly dependent on the number of important Prony’s components taking part in the transient process (i.e., the overall complexity of the transient signal). A strong correlation was found between the PCA component and the Strouhal number inverse.

Novel barrier Lyapunov function-based backstepping fault tolerant control system for an ROV with thruster constraints

This paper proposes a novel Barrier Lyapunov Function (BLF)-based fault tolerant control system for a work-class Remotely-Operated Vehicle (ROV) with thruster saturation and rate limits. The proposed control system is composed of a fixed-time state and fault observer, and a novel BLF-based backstepping controller. The novel BLF-based controller is introduced to eliminate the sensitivity of conventional BLF-based algorithms to rate limitations of the thrusters. In addition, it helps to improve the performance during initial transients and provides faster response to fault and failures. The observer combines the dynamics of the ROV with the dynamics of the thruster system. This combination facilitates estimation of thruster faults and failures independently of the system uncertainties, so highly improved performance is expected compared to conventional extended-state observers. To account for thruster constraints and provide fault tolerance, control allocation is utilized. Stability analysis is performed for the observer and controller, and it is shown that the state estimation error is fixed-time convergent, the fault estimation unit is bounded-input bounded-output stable, and the controller is exponentially stable. Simulations are carried out and comparisons are made with several asymptotic and finite-time BLF-based control systems. The simulations confirm the superior performance of the proposed control system.

Convergence criteria analysis for thermal conductance measurements of building walls: A case study

The significance of on-site measurements for the thermal characterization of building components is widely recognized. Walls thermal performance can be identified through the widely used Heat-Flow Meter (HFM) method, which has been frequently applied in literature. However, only a few scientific works have examined the convergence criteria suggested by the ISO 9869–1. Starting from this, the aim of this work is evaluating the convergence criteria in a case study using the progressive average method. Thermal conductance (C-value) measurements were carried out in a small-scale building, placed in the external area of a building school site near Rome (Italy). The building is internally equipped with an electric heating system. Heat-flux sensor and surface temperature probes were applied to assess the C-value of the envelope. The different switching-on of the heater characterized by different power levels and the reaching of regular thermal conditions after initial transients were considered to evaluate the acquired data and their influence on the results. The known walls stratigraphy allowed to compute and compare theoretical and experimental C-values. Based on the examined data, it is possible to assert that the convergence conditions are very strict, mainly due to the third criterion.

Fault tolerant control system for an ROV based on a novel integral sliding mode control and a state and fault observer in the presence of thruster limitations

This paper presents a novel fault tolerant control system for remotely operated vehicles in the presence of unknown system dynamics and unknown thruster faults and failures while accounting for magnitude and rate limits of the thrusters. The proposed control system consists of a novel integral sliding mode control (ISMC) and a new state and fault observer. The proposed ISMC utilizes a novel asymptotic sliding surface to enhance the performance of the control system during both initial transients and steady-state conditions. The observer takes thrusters system dynamics into account and provides estimation of faults and failures. Control allocation is utilized for fault accommodation and to separate the high-level control system and the low-level thruster controllers. Stability analyses are carried out and it is shown that the state observer is guaranteed to be fixed-time convergent while the fault observation error is input-to-state stable. It is also shown that the ISMC-based closed-loop control system is uniformly-ultimately bounded with practically fixed-time reaching phase. Simulations are carried out and comparisons are made with several fixed-time and finite-time control systems. The results outline the superior performance of the proposed control system in terms of positioning accuracy and fault tolerance during initial transients and steady-state conditions.

Online learning compensation control of an electro-hydraulic shaking table using Echo State Networks

Electro-hydraulic shaking table (EHST) is widely used to simulate earthquake excitation in structural seismic tests. However, the nonlinear characteristics of the EHST, such as oil flow, friction, and dead zone, often lead to the distortion of seismic wave acceleration tracking and even cause the failure of the test. This paper describes the first application of Echo-State Networks (ESNs) to achieve high-precision seismic acceleration tracking of the EHST. The nonlinear control ability of the conventional three-variable control (TVC) algorithm in the EHST is discussed. An online learning compensation control framework using ESNs for “Transfer System” (The “Transfer System” denotes the nonlinear EHST controlled by TVC) is proposed. The least mean square (LMS) algorithm based on filtered-X is used to train the “ESN-Controller” online, and the initial transients of the “ESN-Controller” are reduced by using an estimation model of the actual “Transfer System” and a conditional switch. The offline iterative control (OIC) and nonlinear signal-based control (NSBC) are taken as the baseline algorithms of the proposed online learning compensation control. Simulation results show that the proposed online learning compensation control achieved excellent control with Pearson correlation coefficients of reference and responses above 99.6%, whereas the OIC and NSBC provided insufficient control. Moreover, the proposed online learning compensation control can also reduce the control error caused by the non-optimal TVC gains in the linear part of the EHST. This work throws new light on the study of the online learning control algorithm of the EHST.

Chaotic advection in a recirculating flow: Effect of a fluid multiple-flexible-solid interaction.

This paper deals with chaotic advection due to a two-way interaction between flexible elliptical-solids and a laminar lid-driven cavity flow in two dimensions. The present Fluid multiple-flexible-Solid Interaction study involves various number N(= 1-120) of equal-sized neutrally buoyant elliptical-solids (aspect ratio β = 0.5) such that they result in the total volume fraction Φ = 10 % as in our recent study on single solid, done for non-dimensional shear modulus G ∗ = 0.2 and Reynolds number R e = 100. Results are presented first for flow-induced motion and deformation of the solids and later for chaotic advection of the fluid. After the initial transients, the fluid as well as solid motion (and deformation) attain periodicity for smaller N ≤ 10 while they attain aperiodic states for larger N > 10. Adaptive material tracking (AMT) and Finite-Time Lyapunov Exponent (FTLE)-based Lagrangian dynamical analysis revealed that the chaotic advection increases up to N = 6 and decreases at larger N(= 6-10) for the periodic state. Similar analysis for the transient state revealed an asymptotic increase in the chaotic advection with increasing N ≤ 120. These findings are demonstrated with the help of two types of chaos signatures: exponential growth of material blob's interface and Lagrangian coherent structures, revealed by the AMT and FTLE, respectively. Our work, which is relevant to several applications, presents a novel technique based on the motion of multiple deformable-solids for enhancement of chaotic advection.

On the use of drift correction for electrochemical impedance spectroscopy measurements

The effectiveness of drift correction is explored for measurement of electrochemical impedance spectra. Numerical simulations and experimental data for batteries and capacitors are used to show that drift correction cannot generate Kramers–Kronig consistent data for nonstationary systems. Application of drift correction improves, but does not fully recover, the original spectrum that is not corrupted by the drift. Drift correction improved the quality of spectra obtained for stationary systems under galvanostatic modulation, where the change from one frequency to another caused initial transients that corrupted the measurement.

The role of the particle aspect ratio in the discharge of a narrow silo

The time evolution of silo discharge is investigated for different granular materials made of spherical or elongated grains in laboratory experiments and with discrete element model (DEM) calculations. For spherical grains, we confirm the widely known typical behavior with constant discharge rate (except for initial and final transients). For elongated particles with aspect ratios between 2 ⩽ L/d ⩽ 6.1, we find a peculiar flow rate increase for larger orifices before the end of the discharge process. While the flow field is practically homogeneous for spherical grains, it has strong gradients for elongated particles with a fast-flowing region in the middle of the silo surrounded by a stagnant zone. For large enough orifice sizes, the flow rate increase is connected with a suppression of the stagnant zone, resulting in an increase in both the packing fraction and flow velocity near the silo outlet within a certain parameter range.

Superdiffusive quantum work and adiabatic quantum evolution in finite temperature chaotic Fermi systems

We study the full distribution of quantum work in generic, noninteracting, disordered fermionic nanosystems at finite temperature. We derive an analytical determinant formula for the characteristic function of work statistics for quantum quenches starting from a thermal initial state. For work small compared to the thermal energy of the Fermi gas, work distribution is Gaussian, and the variance of work is proportional to the average work, while in the low-temperature or large-work limit, a non-Gaussian distribution with superdiffusive work fluctuations is observed. Similarly, the time dependence of the probability of adiabaticity crosses over from an exponential to a stretched exponential behavior. For large enough average work, the work distribution becomes universal, and depends only on the temperature and the mean work. Apart from initial low-temperature transients, work statistics are well captured by a Markovian energy-space diffusion process of hardcore particles, starting from a thermal initial state. Our findings can be verified by measurements on nanoscale circuits or via single qubit interferometry.

High impedance fault arc analysis on 11 kV distribution networks

This paper presents a study of high impedance fault (HIF) arc analysis on 6 km 11 kV distribution network from New Haven to New NNPC, Enugu State. These HIF currents have low fault current ratings and are not readily detected by the distribution sub-station relays and protective equipment. This was realized with the aid of MATLAB. Firstly, the HIF was modelled based on the electric arc theory method for single line-to-ground and double line-to-ground faults, when the 11 kV New-haven to New NNPC Enugu distribution line interfaces with a dry asphalt ground surface. The HIF was incident on the midpoint of the distribution line between the switching times of the circuit breaker from 0.02 to 0.05 seconds. The results showed that for single line-to-ground and double line-to-ground faults, a peak current magnitude of 12.4 A and 2280 A were seen respectively and initial spikes due to arcing in the system voltages at the initial switching times of 0.02 seconds. The corresponding residual currents Ib and Ic are very small with a peak spike of 0.3 A and 1.9 A for double line-to-ground fault (BC-G). These spikes are because of the impact of the initial transients caused by the arc flames as its quenches and re-ignites.

Lid-driven cavity flow-induced dynamics of a neutrally buoyant solid: Effect of Reynolds number, flexibility, and size

The present work is on Fluid flexible–Solid Interaction (FfSI), involving a recirculating flow-induced motion of a neutrally buoyant and deformable circular solid. For a Newtonian fluid flow and neo-Hookean flexible-solid deformation, a single FfSI solver—based on fully Eulerian and monolithic approaches—is used. The effect of Reynolds Number Re (20–500), volume fraction Φ (1%–12%) of the solid, and its non-dimensional shear modulus G*(0.02–1) on transient/periodic flow-induced solid-motion and the associated FfSI analysis is presented. The solid undergoes a transient spiraling motion before attaining a periodic orbit-based limit cycle. The flow also attains the periodic state after the initial transients. Time-averaged flow velocity-magnitude ⟨v*⟩ surrounding the limit cycle increases with increasing Re, increasing G*, and decreasing Φ. Equivalent radius req* of the limit cycle and time-averaged velocity-magnitude ⟨vc*⟩ of the centroid of the solid increase with increasing Re and decrease with decreasing G* (or increasing flexibility) and increasing volume fraction Φ (or size) of the solid. Also, frequency f* of the limit cycle decreases with increasing Re and remains almost constant with G* and Φ. With increasing Φ, the limit cycle undergoes a transition from the single loop to double loop beyond a critical volume fraction Φc=2%. A critical Reynolds number Rec, below which the periodic limit cycle collapses to a point, decreases with decreasing Φ. Our findings will help in the prediction and control of the motion of the solid in a bounded fluid flow involving solids of varying flexibility, which is relevant to a wide range of industrial and biological applications.

Non-intrusive balancing transformation of highly stiff systems with lightly damped impulse response

Balanced truncation (BT) is a model reduction method that uses a coordinate transformation to retain eigen-directions that are highly observable and reachable. To address realizability and scalability of BT applied to highly stiff and lightly damped systems, a non-intrusive data-driven method is developed for balancing discrete-time linear systems via the eigensystem realization algorithm (ERA). The advantage of ERA for balancing transformation makes full-state outputs tractable. Further, ERA enables balancing despite stiffness, by eliminating computation of balancing modes and adjoint simulations. As a demonstrative example, we create balanced reduced-order models (ROMs) for a one-dimensional reactive flow with pressure forcing, where the stiffness introduced by the chemical source term is extreme (condition number [Formula: see text]), preventing analytical implementation of BT. We investigate the performance of ROMs in prediction of dynamics with unseen forcing inputs and demonstrate stability and accuracy of balanced ROMs in truly predictive scenarios, whereas without ERA, proper orthogonal decomposition-Galerkin and least-squares Petrov-Galerkin projections fail to represent the true dynamics. We show that after the initial transients under unit impulse forcing, the system undergoes lightly damped oscillations, which magnifies the influence of sampling properties on predictive performance of the balanced ROMs. We propose an output domain decomposition approach and couple it with tangential interpolation to resolve sharp gradients at reduced computational costs. This article is part of the theme issue 'Data-driven prediction in dynamical systems'.

A femtosecond time-resolved coherent anti-Stokes Raman spectroscopy thermometry for steady-state high-temperature flame

A simplified thermometry based on femtosecond coherent anti-Stokes Raman spectroscopy (fs-CARS) was proposed to measure the temperature of steady-state high-temperature flame. Nitrogen molecules were used as a temperature gage and the polarization beats appearing in the initial partial fs-CARS transients were used to access the temperature. As the contribution of all rotational levels to the CARS signal was summarized as the frequency-spread decay, the calculation complexity of extracting temperature from CARS transients can be significantly reduced with this method. In our experiments, the CARS transients of atmospheric N2 from room temperature to 1200 K were well fitted with this simplified principle, which proved the effectiveness of this method. The flame temperature of a butane Bunsen burner was practically measured using this fs-CARS thermometry, and the measured temperature was slightly higher than that given by a platinum-rhodium thermocouple. Since the intrusive thermocouple wire will influence the flame reacting flow, we suggest that the measurement result given by fs-CARS is more reliable. At present, this simplified thermometry is only suitable for the measurement of steady flow. Considering the practical diagnostic requirements of dynamic processes, the possibility of fast thermometry based on this method was also discussed.

Methods—Unexpected Effects in Galvanostatic EIS of Randles’ Cells: Initial Transients and Harmonics Generated

Non-linear EIS analysis is gaining wider attention and interest due to the deeper understanding that is provided especially when combined with linear EIS. The nonlinear part of the data can get corrupted due to a number of effects. One of these is the initial transient, which is the response right after excitation signal is applied before a steady-state is reached. In this study, we demonstrate this phenomenon through analyzing simplified Randles’ cells via Kirchoff’s laws. To get rid of the effects of the initial transient, instrument manufacturers typically discard some fraction of the response, the effectiveness of which, as demonstrated here has to be checked.

Weak branch and multimodal convection in rapidly rotating spheres at low Prandtl number

The focus of this study is to investigate primary and secondary bifurcations to weakly nonlinear flows (weak branch) in convective rotating spheres in a regime where only strongly nonlinear oscillatory sub- and super-critical flows (strong branch) were previously found in [E. J. Kaplan, N. Schaeffer, J. Vidal, and P. Cardin, Phys. Rev. Lett. 119, 094501 (2017)]. The relevant regime corresponds to low Prandtl and Ekman numbers, indicating a predominance of Coriolis forces and thermal diffusion in the system. We provide the bifurcation diagrams for rotating waves (RWs) computed by means of continuation methods and the corresponding stability analysis of these periodic flows to detect secondary bifurcations giving rise to quasiperiodic modulated rotating waves (MRWs). Additional direct numerical simulations (DNS) are performed for the analysis of these quasiperiodic flows for which Poincar\'e sections and kinetic energy spectra are presented. The diffusion time scales are investigated as well. Our study reveals very large initial transients (more than 30 diffusion time units) for the nonlinear saturation of solutions on the weak branch, either RWs or MRWs, when DNS are employed. In addition, we demonstrate that MRWs have multimodal nature involving resonant triads. The modes can be located in the bulk of the fluid or attached to the outer sphere and exhibit multicellular structures. The different resonant modes forming the nonlinear quasiperiodic flows can be predicted with the stability analysis of RWs, close to the Hopf bifurcation point, by analyzing the leading unstable Floquet eigenmode.

Predicting space-charge affected field emission current from curved tips

Field-emission studies incorporating the effect of space charge reveal that for planar emitters, the steady-state field EP, after initial transients, settles down to a value lower than the vacuum field EL. The ratio ϑ=EP/EL is a measure of the severity of space-charge effect, with ϑ=0 being the most severe and ϑ≃1 denoting the lack of significant effect. While EL can be determined from a single numerical evaluation of the Laplace equation, EP is largely an unknown quantity whose value can be approximately found using physical models or can be determined “exactly” by particle-in-cell or molecular dynamics codes. We propose here a simple model that applies to planar as well as curved emitters based on an application of Gauss’s law. The model is then refined using simple approximations for the magnitude of the anode field and the spread of the beam when it reaches the anode. The predictions are compared with existing molecular dynamics results for the planar case and particle-in-cell simulation results using PASUPAT for curved emitters. In both cases, the agreement is good. The method may also be applied to large area field emitters if the individual enhancement factors are known, for instance, using the hybrid model [D. Biswas, J. Vac. Sci. Technol. B 38, 063201 (2020)].