Search

The velocity and temperature fields in an idealized thermoacoustic refrigerator are analyzed computationally. The numerical model simulates the unsteady mass, momentum, and energy equations in the thin-plate, low-Mach-number limits. Two-dimensional unsteady calculations of the flow field in the neighborhood of the stack and heat exchangers are performed using a vorticity-based scheme for stratified flow. The computations are applied to analyze the effects of heat-exchanger length and position on the performance of the device. The results indicate that the cooling load peaks at a well-defined heat-exchanger length, stack gap, and distance between the heat exchangers and the stack plates. [ABSTRACT FROM AUTHOR]

A two-dimensional, low-Mach-number computational model is used to analyze the unsteady flow and temperature fields in the neighborhood of an idealized stack heat exchanger configuration. The model relies on a vorticity-based formulation of the mass, momentum, and energy equations in the low-Mach-number, short-stack limit. The stack and heat exchangers are assumed to consist of flat plates of equal thickness. The heat exchanger plates are assumed isothermal and in perfect thermal contact with the stack plates. The simulations are used to study the effect of heat exchanger size and operating conditions on the heat transfer and stack performance. Computed results show that optimum stack performance is achieved when the length of the heat exchanger is nearly equal to the peak-to-peak particle displacement. Numerical estimates of the mean enthalpy flux within the channel are in good agreement with the predictions of linear theory. However, the results reveal that a portion of the heat exchangers is ineffective due to reverse heat transfer. Details of the energy flux density around the heat exchangers are visualized, and implications regarding heat exchanger design and model extension are discussed. [ABSTRACT FROM AUTHOR]

Analyzes the collapse of an axisymmetric mixed region in a continuously stratified pycnocline using direct simulation of the Navier-Stokes equations in the Boussinesq limit. Cylindrical mixed regions of size comparable to the thickness of the pycnocline; Formation of a cylindrical internal gravity wave; Gradual decay of the wave and vortex; Particle distributions.

Nanoscale layers of nickel and aluminum can mix rapidly to produce runaway reactions. While self-propagating high temperature synthesis reactions have been observed for decades, the solid-state ignition of these reactions has been challenging to study. Particularly elusive is characterization of the low-temperature chemical mixing that occurs just prior to the ignition of the runaway reaction. Characterization can be challenging due to inhomogeneous microstructures, uncontrollable heat losses, and the nonuniform distribution of heat throughout the material prior to ignition. To reduce the impact of these variables, we heat multilayered Ni/Al foils in a highly uniform manner and report ignition temperatures as low as 245 °C for heating rates ranging from 2000 °C/s to 50 000 °C/s. Igniting in this way reveals that there are four stages before the reaction is complete: heating to an ignition temperature, low temperature solid-state mixing, a separate high temperature solid-state mixing, and liquid-state mixing. Multiple bilayer spacings, heating rates, and heating times are compared to show that the ignition temperature is a function of the bilayer spacing. A symmetric numerical diffusion model is used to show that there is very little chemical mixing in the first 10 ms of heating but significant mixing after 50 ms. These predictions suggest that ignition temperatures should increase for the slowest heating rates but this trend could not be identified clearly. The modeling was also used to examine the kinetic parameters governing the early stages of solid-state diffusion and suggest that grain boundary diffusion is dominant. [ABSTRACT FROM AUTHOR]

We study the variability in the ignition delay time, τ ign , of n-butanol due to uncertainty in the enthalpies and entropies of the fuel and fuel radicals. A stoichiometric mixture reacting adiabatically at constant volume is considered, over a range of initial temperatures (700–1000 K) and pressures (10–80 bar). We develop a thermodynamic class approach to account for the variability in the thermodynamic properties of species of interest, and to define associated uncertainty ranges. To gain insight into the impact of the variability of the thermodynamic properties of individual species, a brute force sensitivity analysis is first performed. The results show that large variations in τ ign are mainly due to perturbations in the enthalpies of six species belonging to two thermodynamic classes. A refined 1D analysis is then conducted of the uncertain enthalpies and entropies of these six species. In particular, a complex, nonmonotonic dependence of τ ign on species enthalpies is observed, highlighting potential limitations in extrapolating local sensitivity results. The 1D analysis also shows that uncertainties in species entropies have a weaker impact on the variability in τ ign than the species enthalpies. A global sensitivity analysis of the impact of thermodynamic class uncertainties is then performed, namely using surrogates constructed using an adaptive pseudo-spectral method. The results indicate that the variability of τ ign is dominated by uncertainties in the classes associated with peroxy and hydroperoxide radicals. Lastly, we perform a combined sensitivity analysis of uncertainty in kinetic rates and thermodynamic properties. In particular, the results indicate that uncertainties in thermodynamic properties can induce variabilities in ignition delay time that are as large as those associated with kinetic rate uncertainties. [ABSTRACT FROM AUTHOR]

Abstract We investigate the sensitivity of the ignition delay time, τ ign , of n-butanol to uncertainties in the rate-rule kinetic rate parameters, at various initial temperatures (600–1000 K), pressures (10–80 bar) and equivalence ratios (0.5–2.0). We start by considering a 30-dimensional stochastic germ in which each random variable is associated with one reaction class, and build a surrogate model for the ignition delay time using polynomial chaos expansions. The adaptive pseudo-spectral projection technique is used for this purpose. The surrogate model is used to estimate first-order and total-order sensitivity indices characterizing the dependence of the ignition delay time on the uncertain inputs. Results indicate that τ ign is mostly sensitive to variations in four dominant reaction classes, namely, H–atom abstraction from the fuel (reaction class 2), addition of O 2 to the fuel radicals (reaction class 11), fuel radical isomerization including Waddington type reactions (reaction class 15), and concerted elimination reactions (reaction class 16). We consequently focus our attention on these four reaction classes, and consider variations within corresponding subrules. We explore two approaches to define the subrules of reaction class 2, one based on the radical abstracting from the fuel resulting in eleven subrules and another based on the abstraction site resulting in five subrules. Hence, we investigate the sensitivity of τ ign due to variability in the rate parameters of 26 and 20 subrules of the resulting models. In particular, the simulations indicate that in reaction class 2 H–atom abstraction by HO 2 dominates the variability in τ ign at all initial conditions considered. Analysis of this finding reveals that correlations inherent in the rate rule construction plays an important role in the resulting sensitivity predictions, and suggests a hierarchical approach to the calibration of elementary reaction rates. [ABSTRACT FROM AUTHOR]

This paper addresses model dimensionality reduction for Bayesian inference based on prior Gaussian fields with uncertainty in the covariance function hyper-parameters. The dimensionality reduction is traditionally achieved using the Karhunen–Loève expansion of a prior Gaussian process assuming covariance function with fixed hyper-parameters, despite the fact that these are uncertain in nature. The posterior distribution of the Karhunen–Loève coordinates is then inferred using available observations. The resulting inferred field is therefore dependent on the assumed hyper-parameters. Here, we seek to efficiently estimate both the field and covariance hyper-parameters using Bayesian inference. To this end, a generalized Karhunen–Loève expansion is derived using a coordinate transformation to account for the dependence with respect to the covariance hyper-parameters. Polynomial Chaos expansions are employed for the acceleration of the Bayesian inference using similar coordinate transformations, enabling us to avoid expanding explicitly the solution dependence on the uncertain hyper-parameters. We demonstrate the feasibility of the proposed method on a transient diffusion equation by inferring spatially-varying log-diffusivity fields from noisy data. The inferred profiles were found closer to the true profiles when including the hyper-parameters’ uncertainty in the inference formulation. [ABSTRACT FROM AUTHOR]

A computational model is developed to describe the oxidation of nanolaminates comprising Zr/Al bilayers. The model is developed in light of recent experimental observations of reactive multilayers ignited in air. These suggest that at early stages following the completion of the formation reaction, the oxidation process is more closely described using a surface-reaction controlled growth regime; however, as the oxide layer thickens, transition to the diffusion controlled growth occurs. A simplified computational model is consequently developed that incorporates both regimes of oxide growth. The evolution of the foil temperature is described using an energy balance equation that takes into account the oxidation heat, oxygen intake and radiative heat loss. The computations are implemented to estimate the oxidation heat release rates and the temperature of the oxidizing foil, and to analyze the impact of radiative heat losses. The temperature measurements are then exploited to characterize the transition from the surface-reaction controlled growth regime to the diffusion-limited growth regime. [ABSTRACT FROM AUTHOR]

Tsunami computational models are employed to explore multiple flooding scenarios and to predict water elevations. However, accurate estimation of water elevations requires accurate estimation of many model parameters including the Manning’s n friction parameterization. Our objective is to develop an efficient approach for the uncertainty quantification and inference of the Manning’s n coefficient which we characterize here by three different parameters set to be constant in the on-shore, near-shore and deep-water regions as defined using iso-baths. We use Polynomial Chaos (PC) to build an inexpensive surrogate for the G eo C law model and employ Bayesian inference to estimate and quantify uncertainties related to relevant parameters using the DART buoy data collected during the Tōhoku tsunami. The surrogate model significantly reduces the computational burden of the Markov Chain Monte-Carlo (MCMC) sampling of the Bayesian inference. The PC surrogate is also used to perform a sensitivity analysis. [ABSTRACT FROM AUTHOR]

This paper compares risk-averse optimization methods to address the self-scheduling and market involvement of a virtual power plant (VPP). The decision-making problem of the VPP involves uncertainty in the wind speed and electricity price forecast. We focus on two methods: risk-averse two-stage stochastic programming (SP) and two-stage adaptive robust optimization (ARO). We investigate both methods concerning formulations, uncertainty and risk, decomposition algorithms, and their computational performance. To quantify the risk in SP, we use the conditional value at risk (CVaR) because it can resemble a worst-case measure, which naturally links to ARO. We use two efficient implementations of the decomposition algorithms for SP and ARO; we assess (1) the operational results regarding first-stage decision variables, estimate of expected profit, and estimate of the CVaR of the profit and (2) their performance taking into consideration different sample sizes and risk management parameters. The results show that similar first-stage solutions are obtained depending on the risk parameterizations used in each formulation. Computationally, we identified three cases: (1) SP with a sample of 500 elements is competitive with ARO; (2) SP performance degrades comparing to the first case and ARO fails to converge in four out of five risk parameters; (3) SP fails to converge, whereas ARO converges in three out of five risk parameters. Overall, these performance cases depend on the combined effect of deterministic and uncertain data and risk parameters. Summary of Contribution: The work presented in this manuscript is at the intersection of operations research and computer science, which are intrinsically related with the scope and mission of IJOC. From the operations research perspective, two methodologies for optimization under uncertainty are studied: risk-averse stochastic programming and adaptive robust optimization. These methodologies are illustrated using an energy scheduling problem. The study includes a comparison from the point of view of uncertainty modeling, formulations, decomposition methods, and analysis of solutions. From the computer science perspective, a careful implementation of decomposition methods using parallelization techniques and a sample average approximation methodology was done. A detailed comparison of the computational performance of both methods is performed. Finally, the conclusions allow establishing links between two alternative methodologies in operations research: stochastic programming and robust optimization. [ABSTRACT FROM AUTHOR]

We investigate the behavior of the time derivatives of the solution to a linear time-fractional, advection–diffusion–reaction equation, allowing space- and time-dependent coefficients as well as initial data that may have low regularity. Our focus is on proving estimates that are needed for the error analysis of numerical methods. The nonlocal nature of the fractional derivative creates substantial difficulties compared with the case of a classical parabolic PDE. In our analysis, we rely on novel energy methods in combination with a fractional Gronwall inequality and certain properties of fractional integrals. [ABSTRACT FROM AUTHOR]

This work tackles the problem of calibrating the unknown parameters of a debris flow model with the drawback that the information regarding the experimental data treatment and processing is not available. In particular, we focus on the evolution over time of the flow thickness of the debris with dam-break initial conditions. The proposed methodology consists of establishing an approximation of the numerical model using a polynomial chaos expansion that is used in place of the original model, saving computational burden. The values of the parameters are then inferred through a Bayesian approach with a particular focus on inference discrepancies that some of the important features predicted by the model exhibit. We build the model approximation using a preconditioned non-intrusive method and show that a suitable prior parameter distribution is critical to the construction of an accurate surrogate model. The results of the Bayesian inference suggest that utilizing directly the available experimental data could lead to incorrect conclusions, including the over-determination of parameters. To avoid such drawbacks, we propose to base the inference on few significant features extracted from the original data. Our experiments confirm the validity of this approach, and show that it does not lead to significant loss of information. It is further computationally more efficient than the direct approach, and can avoid the construction of an elaborate error model. [ABSTRACT FROM AUTHOR]

Highlights • Polynomial Chaos methods are used to quantify uncertainties in ocean forecasting. • The EOF-based perturbations lead to realistic uncertainty representation. • Two EOFs for initial condition perturbations captures Loop Current uncertainty. • The analysis of the SSH PDFs shows a strong non-Gaussian signal. Abstract We present an analysis of two recent efforts aimed at quantifying the uncertainties in a 30-day HYbrid Coordinate Ocean Model forecast of the circulation in the Gulf of Mexico, with particular emphasis on the separation of Loop Current Eddy Franklin, using Polynomial Chaos methods. The analysis herein explores whether the model perturbations lead to realistic representation of the uncertainty in the Gulf Circulation. Comparisons of model output with Sea Surface Height and current mooring data show that the observational data generally falls within the envelope of the ensemble and that the modal decomposition delivers "realistic" perturbations in the Loop Current region. We use information theory metrics to quantify the information gain and the computational trade-offs between different wind and initial conditions perturbation modes. The relative entropy measures indicate that two modes for initial condition perturbations are enough, in our model configuration, to represent the uncertainty in the Loop Current region; while two modes for wind forcing perturbations are necessary in order to estimate the uncertainty in the coastal zone. The ensemble statistics are then explored using the Polynomial Chaos surrogate and the newly developed contour boxplot methods. [ABSTRACT FROM AUTHOR]