Low-order Model Research Articles

Stochastic low-order modelling of hydrogen autoignition in a turbulent non-premixed flow

Autoignition risk in initially non-premixed flowing systems, such as premixing ducts, must be assessed to help the development of low-NOx systems and hydrogen combustors. Such situations may involve randomly fluctuating inlet conditions that are challenging to model in conventional mixture-fraction-based approaches. A Computational Fluid Dynamics (CFD)-based surrogate modelling strategy is presented here for fast and accurate predictions of the stochastic autoignition behaviour of a hydrogen flow in a hot air turbulent co-flow. The variability of three input parameters, i.e., inlet fuel and air temperatures and average wall temperature, is first sampled via a space-filling design. For each sampled set of conditions, the CFD modelling of the flame is performed via the Incompletely Stirred Reactor Network (ISRN) approach, which solves the reacting flow governing equations in post-processing on top of a Large Eddy Simulation (LES) of the inert hydrogen plume. An accurate surrogate model, namely a Gaussian Process, is then trained on the ISRN simulations of the burner, and the final quantification of the variability of autoignition locations is achieved by querying the surrogate model via Monte Carlo sampling of the random input quantities. The results are in agreement with the observed statistics of the autoignition locations. The methodology adopted in this work can be used effectively to quantify the impact of fluctuations and assist the design of practical combustion systems.

An Investigation of Left Ventricular Valve Disorders and the Mechano-Electric Feedback Using a Synergistic Lumped Parameter Cardiovascular Numerical Model.

Cardiac diseases and failure make up one of largest contributions to global mortality and significantly detriment the quality of life for millions of others. Disorders in the valves of the left ventricle are a prominent example of heart disease, with prolapse, regurgitation, and stenoses—the three main valve disorders. It is widely known that mitral valve prolapse increases the susceptibility to cardiac arrhythmia. Here, we investigate stenoses and regurgitation of the mitral and aortic valves in the left ventricle using a synergistic low-order numerical model. The model synergy derives from the incorporation of the mechanical, chemical, and electrical elements. As an alternative framework to the time-varying elastance (TVE) method, it allows feedback mechanisms at work in the heart to be considered. The TVE model imposes the ventricular pressure–volume relationship using a periodic function rather than calculating it consistently. Using our synergistic approach, the effects of valve disorders on the mechano-electric-feedback (MEF) are investigated. The MEF is the influence of cellular mechanics on the electrical activity, and significantly contributes to the generation of arrhythmia. We further investigate stenoses and regurgitation of the mitral and aortic valves and their relationship with the MEF and generation of arrhythmia. Mitral valve stenosis is found to increase the sensitivity to arrhythmia-stimulating systolic stretch, and reduces the sensitivity to diastolic stretch. Aortic valve stenosis does not change the sensitivity to arrhythmia-stimulating stretch, and regurgitation reduces it. A key result is found when valve regurgitation is accompanied by diastolic stretch. In the presence of MEF disorder, ectopic beats become far more frequent when accompanied by valve regurgitation. Therefore, arrhythmia resulting from a disorder in the MEF will be more severe when valve regurgitation is present.

Low-Order Modeling of Dynamic Stall on Airfoils in Incompressible Flow

Airfoil dynamic stall in incompressible flow is characterized by two interacting viscous flow phenomena: time-varying trailing-edge separation and the shedding of intermittent leading-edge-vortex structures. In the current work, a physics based low-order method capable of modeling the interactions between the two flow phenomena is developed with the aim of predicting dynamic stall with only a few empirical tuning parameters. Large computational datasets are used to understand the flow physics of unsteady airfoils so as to augment an inviscid, unsteady airfoil theory to model the time-dependent viscous effects. The resulting model requires only three empirical coefficients for a given airfoil and Reynolds number, which could be obtained from a single moderate-pitch-rate unsteady motion for that airfoil/Reynolds number combination. Results from the low-order model are shown to compare excellently with computational and experimental solutions, in terms of both aerodynamic loads and flow-pattern predictions. In addition to formulating a method with limited empirical dependencies, the current research provides valuable insights into the flow physics of unsteady airfoils and their connection to rapidly predictable theoretical parameters.

Tube-Based Adaptive Model Predictive Control for Deviation Correction in Vertical Drilling Process

The build-up rate of bottom hole assembly (BHA) fluctuates violently during deviation correction in vertical drilling process due to the mutation of stratum, low operation accuracy of BHA, etc. As a result, the uncertainty of the build-up rate of BHA has great influence on the performance of correction control and the quality of drilling trajectory. To deal with this control problem, a tube-based adaptive model predictive control (MPC) method is developed in this paper. By dividing the trajectory extension model into two lower-order models, the calculability of the disturbance invariant set of the tube-based MPC controller is ensured. Meanwhile, the bootstrap sampling method with a sliding window is used to estimate the range of the uncertainty online to reduce the conservativeness of the controller based on practical drilling data. Moreover, rules and a small interim deviation are introduced to adjust the parameters adaptively to decrease the curvature of the drilling trajectory and the calculation time. Simulations and hardware-in-the-loop experiment tests are carried out to illustrate the effectiveness of the control method. The results show that the proposed method completes the drilling task with higher quality of trajectory and needs less time for calculation.

Optimizing steady and dynamic hydroelastic performance of composite foils with low-order models

Predicting and controlling the steady and dynamic hydroelastic performance is a crucial challenge in marine composite lifting surface design. Excessive flow-induced vibrations and accelerated fatigue can be severe issues if not considered in the initial design. Most design optimizations only consider steady performance and neglect critical dynamic aspects of the marine environment, such as lower resonance frequencies and different band gaps between modal frequencies in water compared to in air. This work uses lower-order models to capture the steady and dynamic fluid–structure interaction behavior and optimize the design of composite hydrofoils. We formulate new objectives and constraints that consider the natural frequencies, damping, and frequency response spectra in addition to steady hydroelasticity to achieve the design intent. The optimization method is heuristic, which is appropriate for this level of model fidelity where holistic parameter trends are more of interest. Results for a 1/3 length-scale hydrofoil model showed a significant improvement in the optimized performance over the baseline. By tailoring geometric and material variables of the composite hydrofoil, we produced an optimal design. This design meets the steady design condition requirements and avoids excessive vibrations and dynamic load amplifications due to lock-in, resonance, flutter, and modal coalescence.

Impact of Flame-Generated Turbulent Intensity and Flame Speed on the Low-Order Modelling of Light-Round

A previously-developed low-order Lagrangian stochastic model for ignition of premixed and non-premixed flames is modified in this paper to improve the numerical prediction of the light-round process in premixed annular combustors. The model refinements take into account Flame-Generated Turbulent Intensity (FGTI) and impose a turbulent flame speed correlation to the flame particles using expressions from the literature. For this, using RANS CFD results as an input, the model was applied to simulate the ignition transient in a premixed, swirled bluff body stabilised annular combustor to characterise the light-round time, both in stable conditions and close to the stability limits. Several cases were analysed, where flame speed and fuel were varied and light-round times were compared to experimental results. The proposed modifications improved the accuracy of the light-round time predictions, suggesting that FGTI may be an important phenomenon to be modelled. This modified model coupled with dilatation and the Peter’s assumption for the turbulent flame speed resulted in considerable improvement for the light-round time calculation for the explored range of parameters. This is an attractive feature considering the low computational cost of these simulations, which can be run in a single core of a local workstation. The improved model can help gas turbine engineers assess the ignition behaviour of annular combustors early in the design process.

The influence of hydrogen on the stability of a perfectly premixed combustor

In this paper we investigate the effects of increasing the amount of hydrogen in the fuel mixture on the stability of a perfectly premixed combustor. Experiments are carried out on a single flame burner where the thermal power and equivalence ratio are kept constant while the amount of hydrogen is progressively increased from pure methane towards higher fractions of CH4−H2 blends. As hydrogen content is increased, the flame first experiences a series of topological changes until the system becomes unstable and a limit cycle is established. The changes experienced by the flame occur due to the increased burning speed of the mixture which shortens the flame. The flame changes from a lifted flame attached to the combustor wall, to a bluff body anchored flame also attached to the wall, to a bluff body anchored flame detached from the wall. For some CH4−H2 mixture fractions, there exists a bi-stable region where the last two flame shapes can be observed at the same operating conditions. As for the observed limit cycle, first a low amplitude limit cycle is established and a further increase in hydrogen content leads to a much higher amplitude one.The linear stability limit is predicted using a low-order network model where the flame response is modeled by a scaled distributed time lag model which provides good agreement with the experimental observations. The flame model only requires a measurement of the flame length and bulk velocities which significantly simplify the analysis when considering operating conditions where the flame transfer function has not been measured. In the region where the flame is bi-stable, the linear stability analysis shows that the flame attached to the combustor wall becomes unstable at lower hydrogen content when compared to the flame detached from the combustor wall. Therefore, from a linear stability perspective and in line with experimental observations, the flame changes shape in order to keep the system stable. Furthermore, a nonlinear model using the flame describing function approach is also implemented to analyze the transition between the two limit-cycles. The analysis shows that the system has a low amplitude stable limit cycle and a neighbouring unstable limit cycle with a slightly higher amplitude. This shows that the system is triggering until full saturation occurs at the much higher amplitude limit cycle, consistent with the experimental observations. The analysis presented in this paper demonstrates that the effect of premixed hydrogen on thermoacoustic instabilities can be predicted using well established methods.

A low-order dynamical model for fire-vegetation-climate interactions

Climate conditions play a key role in determining the occurrence and severity of wildfires. Despite the impacts of wildfires on ecosystems, human livelihoods, and air quality, little is known conceptually about how natural or anthropogenic shifts in climate may influence the fire activity on a regional or global scale. Here, we introduce a new low order dynamical model that describes the nonlinear interactions between climate, vegetation (fire fuel) and fire probabilities. This 1-dimensional model describes the influence of precipitation and temperature on burned area and fuel availability. Estimating key parameters from observations, the model successfully reproduces the spatio-temporal variability of wildfire occurrences, particularly, in semi-arid regions in Africa, South America, and northern Australia. The fidelity of the model translates into a high degree of longer-term predictability of fire conditions in these vulnerable regions. Our new low-order modeling framework may provide guidance to forestry managers to assess fire risks under present and future climate conditions.

Stress gradient plasticity theory development for cyclic and monotonic loading of thin-walled structures: Back-stress, size effect, passivation effect

Small scale plasticity behaviour is modelled by strain or stress gradient plasticity models. The stress gradient plasticity theory, proposed by Chakravarthy and Curtin, is a constitutive consideration of the stress gradient that affects the initial flow as well as strain hardening rate. We apply the lower-order stress gradient plasticity model to different monotonic problems and cyclic torsion, under small strain and rotation assumption. The stress gradient can be due to the problem geometry and loading and/or due to passivation. Passivation is considered in different monotonic loadings of classical problems. To use the stress gradient plasticity model in cyclic loading problems, a back-stress model is used and the kinematic hardening is considered. The developed model in microscale plasticity considers dislocation pile-ups, grain size, and dislocation density. The Bauschinger effect is also considered during reverse loading by the consideration of the kinematic hardening. The cyclic torsion of thin copper wires of different diameters is modelled by the developed model. Comparisons with the experimental results and distortion strain gradient plasticity model are also performed. It is shown that the simple developed model can capture the essential microscale plasticity behaviour of metals, with only one length scale parameter.

Using surrogate models and mechanics to predict pressure from strain data

Many marine structures rely upon hull monitoring systems that utilize strain information to make inferences about structural integrity. One of the most significant factors affecting structural integrity are wave loads, specifically the resultant pressures. While direct measurement is not often available, this study explores how to translate strain information into localized pressure estimates through two different low-order modeling paradigms, physics-based and surrogate modeling. Strain data was collected via strain gauges mounted on a scaled ship model that was tested in towing tank under a variety of regular and irregular wave conditions. Using a set of strain calibration data, two different models are developed, one using principal stress and strain relations and the other using a machine learning approach (Gaussian process model), for predicting pressure time histories for different wave conditions. The two modeling approaches are compared in terms of both a variety of error metrics as well as their ability to handle measurement noise and disturbances commonly encountered during marine structures testing and operations.

New low-order continuum models for the dynamics of a Timoshenko beam lattice with next-nearest interactions

In this paper, the dynamic behaviour of a novel Timoshenko beam lattice with long-range interactions, accounting for both bending and shear deformations, is investigated. Several new non-classical continuum models are developed with the aim of capturing its dispersive behaviour with a lower computational cost. For this, innovative continualization procedures are used, comparing them with techniques commonly used in lattices continualization, as well as with advanced ones. Moreover, low-order continuum governing equations are pursued, thus avoiding the need for extra boundary conditions, whose physical meaning is unclear. A comprehensive analysis of the transition frequency, which initiates the shear propagation spectrum, has been performed here for the first time for this lattice and the corresponding continuum models. The capability of these continuum models in capturing the behaviour of the lattice is assessed by conducting both dispersion and natural frequency analyses, for the latter providing an original method to treat the edges for the three possible boundary conditions in Timoshenko beam lattices. The influence of long-range interactions is analysed, and the way shear effect affects the shape vibration modes of the discrete model is interestingly illustrated, finally concluding that some of the new developed continuum models accurately capture the behaviour of the lattice.

Reduced order dynamical models for complex dynamics in manufacturing and natural systems using machine learning

Dynamical analysis of manufacturing and natural systems provides critical information about production of manufactured and natural resources, respectively. Current dynamic models for full industrial process plants exist as highly accurate first-principle relationships. However, their integration is computationally intensive and provides no simplified understanding of the underlying mechanisms driving the overall dynamics. Similarly, for natural systems, most dynamical models are first principle based, with high data requirements and low state accuracy. Consequently, lower-order models that may sacrifice accuracy for simplicity and ease of training can prove useful. Yet, there have been few attempts at finding low-order models of chemical manufacturing processes and natural systems, with work focusing on modeling individual mechanisms. We seek to fill this research gap by using a machine learning (ML) approach, SINDy, validated on a soybean-diesel process plant and watershed system. This ML method combines sparse, grey-box modeling with additional nonlinear optimization to identify governing dynamics as ODEs. We find a linear ODE model for the process plant that gives an accurate relation between input and output and selected internal molar flow rates reflective of underlying linear stoichiometric mechanisms and an internal mass balance. For the natural system, we modify the SINDy approach to include the effect of past dynamics on training the model, which gives a nonlinear model for streamflow dynamics. This improves dynamical transitions, but falls short of accurate state estimation. We conclude that the proposed ML approach works well for non-chaotic systems with minimal hysteresis, but is limited when this condition is not met.

An unsteady two-dimensional vortex method for the flow separation over a flapping wing

The flow separation over a very flexible or morphing aircraft, especially during flying or oscillation at a high angle of attack, is stronger than that for conventional aircraft. However, a low-order model for reliably predicting the dynamics of the LEV and its influence on the force is still not found. It is valuable to develop such aerodynamic approaches for optimizing the wing structure and kinematics and for designing a flight control strategy considering the flow separation problem. This paper presents a two-dimensional vortex method in which an artificial boundary is constructed for the velocity adjustment of the vortices near the control panels. This artificial boundary is established in accordance with the thickness of the actual wing. A sub-time step is introduced into the solution process of the vortex method to predict the vortex locations and perform velocity adjustments. Crossing vortices retain only their tangential velocity components relative to the artificial boundary in order to avoid entering the range of the airfoil represented by the artificial boundary. Moreover, the excessive induced velocities on the control panels caused by crossing vortices are decreased, and the nonphysical behaviors and discontinuous pressure are avoided. To demonstrate the advantages of the proposed artificial boundary method in modeling an airfoil during high-angle-of-attack flight, the proposed approach is applied to a flat-plate starting problem and a flapping problem. The simulation results are then compared with the results of several experiments and numerical data for both attached and separated test cases, verifying the capabilities of the proposed method.

Stethoscope acoustics

For over 200 years, stethoscopes have been used to diagnose disease by listening to the sounds from the human body. However, the physics of how stethoscopes work remains poorly understood, mainly because their performance depends not only on the stethoscopes themselves, but on the coupled system that forms when the hand of a clinician presses the device against the chest of a patient. We develop an experimental setup that allows us to characterise the effect of each constituent part on the behaviour of the coupled system. By using a suitably instrumented ‘chest phantom’ we are able to quantify the response of stethoscopes in a repeatable manner and account for the effect of the phantom on the response. We provide a theoretical framework for understanding the acoustics of the coupled stethoscope system and propose a low-order lumped-element model that captures the effects of the key design choices. For example, minimising the air cavity volume inside the stethoscope maximises the response, while a stethoscope’s tubing significantly attenuates the response and introduces distorting standing-wave resonances. Using a diaphragm attenuates the response and shifts the resonances to higher frequencies. However, it also allows the air cavity volume to be minimised, which can offset the attenuation. We dispel several misconceptions, such as that the stiffness of diaphragms leads to an amplification of higher frequencies or that the dimensions of the rim and the mass of the chestpiece play no role in stethoscope performance. We hope that this paper will help to optimise the design of stethoscopes.

Multi-fidelity uncertainty quantification of particle deposition in turbulent pipe flow

Particle deposition in fully-developed turbulent pipe flow is quantified taking into account uncertainty in electric charge, van der Waals strength, and temperature effects. A framework is presented for obtaining variance-based sensitivity in multiphase flow systems via a multi-fidelity Monte Carlo approach that optimally manages model evaluations for a given computational budget. The approach combines a high-fidelity model based on direct numerical simulation and a lower-order model based on a one-dimensional Eulerian description of the two-phase flow. Significant speedup is obtained compared to classical Monte Carlo estimation. Deposition is found to be most sensitive to electrostatic interactions and exhibits largest uncertainty for mid-sized (i.e., moderate Stokes number) particles.

Dynamical and chaotic behaviors of natural convection flow in semi-annular cylindrical domains using energy-conserving low-order spectral models

This paper presents a comprehensive theoretical study on the dynamical behavior of natural convection flow in the confined region between horizontal half-cylinders. For this purpose, a low-order spectral model with three modes will produce for the fluid flow system using the Galerkin technique. It proved that the generated model is physically meaningful, as it conserves energy in the dissipationless limit and has bounded solutions in the phase space. Analytical procedures indicate that the system has three stationary points and the onset of instability in the flow is when the Rayleigh number reaches a critical value. With an appropriate Lyapunov function is proved that for the Rayleigh numbers below the critical value, the flow is globally stable. As the Rayleigh number gets higher and reaches a fixed value, a Hopf bifurcation occurs, and chaotic motion appears in the system. The critical and Hopf Rayleigh numbers relation are derived parametrically based on dynamical system theories. Also, numerical simulations will carry on the presented low-order model. Different dynamical behaviors of this flow and its transition from regular to chaotic motion are explained, with phase portraits and velocity-temperature diagrams obtained by numerical solutions. This parametric study can pave the way for future researchers to determine at around values of critical parameters should an experiment or direct numerical simulation be performed to have more accurate data without resorting to tests at all operating conditions.

Consistency regularization-based deep polynomial chaos neural network method for reliability analysis

Polynomial chaos expansion (PCE) is a powerful method for building a surrogate model that can be applied to assist reliability analysis. Generally, a PCE model with a higher expansion order is required to obtain an accurate surrogate model for some complex non-linear stochastic systems. However, the high-order PCE increases the number of labeled data necessary for solving the expansion coefficients. To alleviate this problem, this paper proposes a consistency regularization-based deep polynomial chaos neural network (Deep PCNN) method, including the low-order adaptive PCE model (the auxiliary model) and the high-order polynomial chaos neural network (the main model). The expansion coefficients of the main model are parameterized into the learnable weights of the polynomial chaos neural network, realizing iterative learning of expansion coefficients to obtain more accurate high-order PCE models. By unlabeled data, the auxiliary model uses the proposed consistency regularization loss function to assist in training the main model. The consistency regularization-based Deep PCNN method can precisely solve the expansion coefficients with fewer labeled data without reducing the high-order PCE model accuracy compared to the existing PCE methods. Two numerical examples validate the effectiveness of the consistency regularization-based Deep PCNN method, which is then applied to satellite reliability analysis.

Experimental validation of a three-dimensional through-flow model for high-speed compressor surge

This paper describes the validation of surge simulations produced using the low-order code ACRoSS with experimental data from a 4. 5-stage high-speed rig, representative of the front stages of a modern high-pressure compressor (HPC). ACRoSS is an unsteady, 3D through-flow code developed at Cranfield University to predict compressor performance during stall events. The experimental data was derived during the Rig250 build 6B test campaign, carried out in 2016 by the DLR Institute of Propulsion Technology. To correctly represent the surge events, the ducting of the testbed upstream and downstream of the compressor is included in the simulation.The results from the low-order model are compared with measurements from unsteady probes for two surge events at design speed with different downstream plenum sizes. The surge frequency and pressure profiles in time are closely reproduced by the low-order model. Analysis of the unsteady pressure measurement and the acoustic waves modelled by ACRoSS indicates that the surge period is likely to be influenced by the reflection of the initial surge wave in the inlet duct.Using the ACRoSS model, surge can be accurately reproduced both in 3D and 2D. Two-dimensional, axisymmetric simulations are shown to be sufficient for the cases investigated, and surge can be simulated with a computational cost of less than one hour per event using just 40 CPUs. This represents over an order of magnitude improvement in computational power and time required to simulate surge, compared to traditional URANS 3D CFD.

Passive suppression of vortex-induced vibrations using a nonlinear energy sink—Numerical and analytical perspective

This study investigates the suppression mechanism of instabilities induced by fluid–structure interactions (FSI) using passive vibration absorption devices, such as nonlinear energy sink (NES). The present FSI framework comprises a low-order phenomenological model, wherein the wake effect is modeled using the classical Van der Pol oscillator. The structure is represented as a cylindrical bluff body with degree-of-freedom along the cross-flow direction. The response of the NES-augmented structure exhibits specific relaxation type oscillations, referred to as strongly modulated response (SMR), passively suppressing the high amplitude vortex-induced vibrations (VIV). The underlying mechanism of SMR is studied using an analytical approach based on the Complexification-Averaging (CXA) technique. Using the CXA technique, the slow flow for the coupled FSI system with the NES attachment is modeled effectively, revealing nonlinear beating regimes and initiation of the targeted energy transfer (TET) mechanism. Subsequently, a transient resonance capture, implying a significant energy transfer from the structure to the NES, results in effective VIV suppression. The occurrence of SMRs is explained by analyzing the global dynamics using the slow invariant manifold (SIM) derived from the slow flow of the coupled system. The resultant SIM topology reveals a jump phenomenon between the stable branches, wherein the flow jumps from a lower stable branch to a higher stable branch through SMR. The novelty of this study lies in identifying the occurrence of SMRs as the mechanism of energy transfer and uses the CXA technique to explain the global dynamics by modeling the SIM for the 3-DOF coupled FSI framework with the NES attachment. Furthermore, the optimal operational parameter ranges for an efficient NES design are identified through a parametric study using the slow-flow model.

Accuracy assessment of light detection and ranging system measurements for jointed concrete pavement surface geometry

ABSTRACT Stationary Light Detection and Ranging (LiDAR) systems provide detailed three-dimensional (3D) point clouds for pavement surface geometry measurements. Despite their long presence in the market, LiDAR systems are still relatively new to pavement engineers and there are only few studies verifying their accuracy. To bridge this gap, laboratory and field tests were performed to investigate the accuracy of LiDAR instrument. In the laboratory test, a wooden board was set up and a dial indicator was used to measure deflections when loads were applied. The magnitudes were compared with the deflections from LiDAR scans estimated by a low-order polynomial fit model and a thin-plate spline (TPS) fit model. In the field test, profiles were acquired for concrete pavement using a standard profilometer and the LiDAR system. Agreement among these profiles was investigated. Test results assured that this stationary LiDAR system could provide acceptable accuracy and precision for slab surface geometry measurements.