Monitoring of cooling tower performance in a nuclear reactor facility is necessary to ensure safe operation; however, instrumentation for measuring performance characteristics can be difficult to install and may malfunction or break down over long duration experiments. This paper describes employing a thermodynamic approach to quantify cooling tower performance, the Merkel model, which requires only five parameters, namely, inlet water temperature, outlet water temperature, liquid mass flowrate, gas mass flowrate, and wet bulb temperature. Using this model, a general method to determine cooling tower operation for a nuclear reactor was developed in situations when neither the outlet water temperature nor gas mass flowrate are available, the former being a critical piece of information to bound the Merkel integral. Furthermore, when multiple cooling tower cells are used in parallel (as would be in the case of large-scale cooling operations), only the average outlet temperature of the cooling system is used as feedback for fan speed control, increasing the difficulty of obtaining the outlet water temperature for each cell. To address these shortcomings, this paper describes a method to obtain individual cell outlet water temperatures for mechanical forced-air cooling towers via parametric analysis and optimization. In this method, the outlet water temperature for an individual cooling tower cell is acquired as a function of the liquid-to-gas ratio (L/G). Leveraging the tight tolerance on the average outlet water temperature, an error function is generated to describe the deviation of the parameterized L/G to the highly controlled average outlet temperature. The method was able to determine the gas flowrate at rated conditions to be within 3.9% from that obtained from the manufacturer’s specification, while the average error for the four individual cooling cell outlet water temperatures were 1.6 °C, -0.5 °C, -1.0 °C, and 0.3 °C.
Bayesian inference is used to calibrate a bottom-up home PLC network model with unknown loads and wires at frequencies up to 30 MHz. A network topology with over 50 parameters is calibrated using global sensitivity analysis and transitional Markov Chain Monte Carlo (TMCMC). The sensitivity-informed Bayesian inference computes Sobol indices for each network parameter and applies TMCMC to calibrate the most sensitive parameters for a given network topology. A greedy random search with TMCMC is used to refine the discrete random variables of the network. This results in a model that can accurately compute the transfer function despite noisy training data and a high dimensional parameter space. The model is able to infer some parameters of the network used to produce the training data, and accurately computes the transfer function under extrapolative scenarios.
Reichardt, Thomas A.; Eaton, Samuel W.; Kulp, Thomas J.; DeJong, Stephanie D.; Ray, Will R.; Karnowski, Tom K.; Wetherington, Randall W.; Willis, Michael W.; Marcillo, Omar M.; Maceira, Monica M.; Chai, Chengping C.; Cardenas, Edna C.; Watson, Scott W.; Chichester, David C.; Gammans, Christine G.; Krebs, John K.; d'Entremont, Brian d.
Remote detection of a surface-bound chemical relies on the recognition of a pattern, or "signature," that is distinct from the background. Such signatures are a function of a chemical's fundamental optical properties, but also depend upon its specific morphology. Importantly, the same chemical can exhibit vastly different signatures depending on the size of particles composing the deposit. We present a parameterized model to account for such morphological effects on surface-deposited chemical signatures. This model leverages computational tools developed within the planetary and atmospheric science communities, beginning with T-matrix and ray-tracing approaches for evaluating the scattering and extinction properties of individual particles based on their size and shape, and the complex refractive index of the material itself. These individual-particle properties then serve as input to the Ambartsumian invariant imbedding solution for the reflectance of a particulate surface composed of these particles. The inputs to the model include parameters associated with a functionalized form of the particle size distribution (PSD) as well as parameters associated with the particle packing density and surface roughness. The model is numerically inverted via Sandia's Dakota package, optimizing agreement between modeled and measured reflectance spectra, which we demonstrate on data acquired on five size-selected silica powders over the 4-16 μm wavelength range. Agreements between modeled and measured reflectance spectra are assessed, while the optimized PSDs resulting from the spectral fitting are then compared to PSD data acquired from independent particle size measurements.
Validating predictive models and quantifying uncertainties inherent in the modeling process is a critical component of the HARD Solids Venture program [1]. Our current research focuses on validating physics-based models predicting the optical properties of solid materials for arbitrary surface morphologies and characterizing the uncertainties in these models. We employ a systematic and hierarchical approach by designing physical experiments and comparing the experimental results with the outputs of computational predictive models. We illustrate this approach through an example comparing a micro-scale forward model to an idealized solid-material system and then propagating the results through a system model to the sensor level. Our efforts should enhance detection reliability of the hyper-spectral imaging technique and the confidence in model utilization and model outputs by users and stakeholders.
This paper describes measurements being made on a series of material systems for the purpose of developing a radiative-transfer model that describes the reflectance of light by granular solids. It is well recognized that the reflectance spectra of granular materials depend on their intrinsic (n(λ) and k(λ)) and extrinsic (morphological) properties. There is, however, a lack of robust and proven models to relate spectra to these parameters. The described work is being conducted in parallel with a modeling effort1 to address this need. Each follows a common developmental spiral in which material properties are varied and the ability of the model to calculate the effects of the changes are tested. The parameters being varied include particle size/shape, packing density, material birefringence, optical thickness, and spectral contribution of a substrate. It is expected that the outcome of this work will be useful in interpreting reflectance data for hyperspectral imaging (HSI), and for a variety of other areas that rely on it.
We assess the measurement of hyperspectral reflectance for the outdoor monitoring of green algae and cyanobacteria cultures with a multi-channel, fiber-coupled spectroradiometer. Reflectance data acquired over a four-week period are interpreted via numerical inversion of a reflectance model, in which the above-water reflectance is expressed as a quadratic function of the single backscattering albedo, dependent on the absorption and backscatter coefficients. The absorption coefficient is treated as the sum of component spectra consisting of the cultured species (green algae or cyanobacteria), dissolved organic matter, and water (including the temperature dependence of the water absorption spectrum). The backscatter coefficient is approximated as the scaled Hilbert transform of the culture absorption spectrum with a wavelength-independent vertical offset. Additional terms in the reflectance model account for the pigment fluorescence features and the water surface reflection of sunlight and skylight. For both the green algae and cyanobacteria, the wavelength-independent vertical offset of the backscatter coefficient is found to scale linearly with daily dry weight measurements, providing the capability for a non-sampling measurement of biomass in outdoor ponds. Other fitting parameters in the reflectance model are compared to auxiliary measurements and physics-based calculations. The magnitudes of the sunlight and skylight water-surface contributions derived from the reflectance model compare favorably with Fresnel reflectance calculations, while the reflectance-derived quantum efficiency of Chl-a fluorescence is found to be in agreement with literature values. To conlclude, the water temperature derived from the reflectance model exhibits excellent agreement with thermocouple measurements during the morning hours and highlights significantly elevated temperatures in the afternoon hours.