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Eigenvalue and eigenvector sensitivity and approximate analysis for repeated eigenvalue problems

A set of computationally efficient equations for eigenvalue and eigenvector sensitivity analysis are derived, and a method for eigenvalue and eigenvector approximate analysis in the presence of repeated eigenvalues is presented. The method developed for approximate analysis involves a reparamaterization of the multivariable structural eigenvalue problem in terms of a single positive-valued parameter. The resulting equations yield first-order approximations of changes in both the eigenvalues and eigenvectors associated with the repeated eigenvalue problem. Examples are given to demonstrate the application of such equations for sensitivity and approximate analysis.

Hou, Gene J. W.↗

Study of Multimission Modular Spacecraft (MMS) propulsion requirements

The cost effectiveness of various propulsion technologies for shuttle-launched multimission modular spacecraft (MMS) missions was determined with special attention to the potential role of ion propulsion. The primary criterion chosen for comparison for the different types of propulsion technologies was the total propulsion related cost, including the Shuttle charges, propulsion module costs, upper stage costs, and propulsion module development. In addition to the cost comparison, other criteria such as reliability, risk, and STS compatibility are examined. Topics covered include MMS mission models, propulsion technology definition, trajectory/performance analysis, cost assessment, program evaluation, sensitivity analysis, and conclusions and recommendations.

Fischer, N. H.↗

Discrete shape sensitivity equations for aerodynamic problems

Intensive research and development in Computational Fluid Dynamics (CFD) has recently produced many powerful CFD codes to simulate complex aerodynamic phenomena. However, in order to enhance the usefulness of these CFD codes for design practice, development of design sensitivity equations compatible to these codes becomes very important. This paper represents a part of such an effort to develop a sensitivity analysis methodology that enables the sensitivity equations to be implemented into existing CFD codes with minimal code modification. The methodology is based upon a preelimination procedure which accounts for consistently linearized boundary conditions. Formulations of both the direct differentiation and the adjoint variable methods will be presented in the paper.

Hou, Gene J.-W.↗

Three-dimensional aerodynamic shape optimization of supersonic delta wings

A recently developed three-dimensional aerodynamic shape optimization procedure AeSOP(sub 3D) is described. This procedure incorporates some of the most promising concepts from the area of computational aerodynamic analysis and design, specifically, discrete sensitivity analysis, a fully implicit 3D Computational Fluid Dynamics (CFD) methodology, and 3D Bezier-Bernstein surface parameterizations. The new procedure is demonstrated in the preliminary design of supersonic delta wings. Starting from a symmetric clipped delta wing geometry, a Mach 1.62 asymmetric delta wing and two Mach 1. 5 cranked delta wings were designed subject to various aerodynamic and geometric constraints.

Burgreen, Greg W.↗

Probabilistic Structural Evaluation of Uncertainties in Radiator Sandwich Panel Design

The Jupiter Icy Moons Orbiter (JIMO) Space System is part of the NASA's Prometheus Program. As part of the JIMO engineering team at NASA Glenn Research Center, the structural design of the JIMO Heat Rejection Subsystem (HRS) is evaluated. An initial goal of this study was to perform sensitivity analyses to determine the relative importance of the input variables on the structural responses of the radiator panel. The desire was to let the sensitivity analysis information identify the important parameters. The probabilistic analysis methods illustrated here support this objective. The probabilistic structural performance evaluation of a HRS radiator sandwich panel was performed. The radiator panel structural performance was assessed in the presence of uncertainties in the loading, fabrication process variables, and material properties. The stress and displacement contours of the deterministic structural analysis at mean probability was performed and results presented. It is followed by a probabilistic evaluation to determine the effect of the primitive variables on the radiator panel structural performance. Based on uncertainties in material properties, structural geometry and loading, the results of the displacement and stress analysis are used as an input file for the probabilistic analysis of the panel. The sensitivity of the structural responses, such as maximum displacement and maximum tensile and compressive stresses of the facesheet in x and y directions and maximum VonMises stresses of the tube, to the loading and design variables is determined under the boundary condition where all edges of the radiator panel are pinned. Based on this study, design critical material and geometric parameters of the considered sandwich panel are identified.

Kuguoglu, Latife↗

Assessing Seismic Risk for CO2 Geologic Storage: Comparative Analysis of the Delaware Basin and Basin and Range Province Projects

ABSTRACT: Effective management of induced seismicity is critical for safe and sustainable CO2 storage. This study evaluates fault slippage risks in the Delaware Basin (Texas) and Basin and Range Province (Utah), integrating geological, operational, and geomechanical parameters to assess fault stability and seismic hazard mitigation. In the Delaware Basin, two sites were analyzed under an injection rate of 20,000 bbl/day over 25 years. One site showed low fault slip risk, while the other exhibited higher reactivation potential due to proximity to critically stressed faults. Sensitivity analysis revealed that increased pore pressure significantly heightened slip potential, highlighting the necessity of precise pressure control and real-time monitoring. In the Basin and Range Province, fault stability was evaluated at Neck of the Desert, Escalante Desert, Parowan, and Beaver sites under injection rates of 8,750 bbl/day per site over 30 years. Minimal fault slip risk was observed at Neck of the Desert and Escalante Desert sites, whereas Parowan and Beaver sites exhibited elevated slip potential due to semi-critically stressed faults sensitive to modest pore pressure increases. The findings demonstrate that fault slippage analysis, combined with sensitivity analysis of pore pressure and friction coefficients, is essential for understanding seismic risks. Continuous monitoring, adaptive injection management, and rigorous geomechanical analysis are key strategies for minimizing induced seismicity in CO2 sequestration projects.

58 GEOSCIENCES↗

Bayesian Inference and the Effects of Varying Uncertainty Models in Charring Ablator Calibration and Uncertainty Quantification Problems

The Mars Science Laboratory (MSL) vehicle utilized a heat shield constructed from NASA’s Phenolic-Impregnated Carbon Ablator (PICA) material to protect the main structure from the high enthalpy environment encountered during hypersonic atmospheric entry. During the vehicle’s descent through Martian atmosphere, multiple thermocouples embedded within the heat shield captured in-depth material temperature data that allow for studies to be conducted on current material response reconstruction tools. In the present work, material temperature data obtained from thermocouples within the MISP-4 plug (MEDLI (Mars Science Laboratory Entry, Descent, and Landing Instrument) Integrated Sensor Plug) are utilized in the calibration of Theoretical Ablative Composite for Open Testing (TACOT) model parameters in conjunction with NASA’s Porous material Analysis Toolbox (PATO) through Bayesian inference where uncertainty due to parametric, modeling, and experimental sources is simultaneously quantified. Prior to the study, a sensitivity analysis is performed through computation of the robust Sobol indices in an effort to study the relationship between input space and model response and to reduce the dimensionality of the statistical inverse problem. The Bayesian inference methodology necessitates an a-priori choice to be made for the uncertainty model for which numerous possibilities are available. Across most works, however, only basic additive or multiplicative models are utilized with pre-defined magnitudes of uncertainty based on a-priori knowledge or to-be-calibrated multipliers of static covariance matrix structures. The present effort explores the effects of informed uncertainty models, ones with temporal dependence that are simultaneously calibrated through Bayesian inference, on calibrated results for parameters that make up the uncertain input space.

Sensitivity Analysis↗

Skeletal reaction models for methane combustion

A local-sensitivity-analysis technique is employed to generate new skeletal reaction models for methane combustion from the foundational fuel chemistry model (FFCM-1). Here, the sensitivities of the thermo-chemical variables with respect to the reaction rates are computed via the forced-optimally time dependent (f-OTD) methodology. In this methodology, the large sensitivity matrix containing all local sensitivities is modeled as a product of two low-rank time-dependent matrices. The evolution equations of these matrices are derived from the governing equations of the system. The modeled sensitivities are computed for the auto-ignition of methane at atmospheric and high pressures with different sets of initial temperatures, and equivalence ratios. These sensitivities are then analyzed to rank the most important (sensitive) species. A series of skeletal models with different number of species and levels of accuracy in reproducing the FFCM-1 results are suggested. The performances of the generated models are compared against FFCM-1 in predicting the ignition delay, the laminar flame speed, and the flame extinction. The results of this comparative assessment suggest the skeletal models with 24 and more species generate the FFCM-1 results with an excellent accuracy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Finite Element Model Calibration Approach for Area I-X

Ares I-X is a pathfinder vehicle concept under development by NASA to demonstrate a new class of launch vehicles. Although this vehicle is essentially a shell of what the Ares I vehicle will be, efforts are underway to model and calibrate the analytical models before its maiden flight. Work reported in this document will summarize the model calibration approach used including uncertainty quantification of vehicle responses and the use of non-conventional boundary conditions during component testing. Since finite element modeling is the primary modeling tool, the calibration process uses these models, often developed by different groups, to assess model deficiencies and to update parameters to reconcile test with predictions. Data for two major component tests and the flight vehicle are presented along with the calibration results. For calibration, sensitivity analysis is conducted using Analysis of Variance (ANOVA). To reduce the computational burden associated with ANOVA calculations, response surface models are used in lieu of computationally intensive finite element solutions. From the sensitivity studies, parameter importance is assessed as a function of frequency. In addition, the work presents an approach to evaluate the probability that a parameter set exists to reconcile test with analysis. Comparisons of pretest predictions of frequency response uncertainty bounds with measured data, results from the variance-based sensitivity analysis, and results from component test models with calibrated boundary stiffness models are all presented.

Horta, Lucas G.↗

Comparative Evaluation of Spectral Methods for Robust Reactor Noise Estimation

Reactor noise analysis provides a noninvasive means to determine neutron kinetic parameters from stochastic fluctuations in detector signals. However, standard cross-power spectral density (CPSD) analyses can be sensitive to numerical processing choices, which may introduce processing-dependent systematic shifts in estimates of the prompt neutron decay constant (α) and limit reproducibility. This study uses a hybrid multitaper–Welch spectral estimator to analyze subcritical noise measurements from a fast-spectrum critical assembly. The decay constant α was extracted using three frequency-domain methods: the CPSD, the magnitude-squared coherence (MSC), and the generalized magnitude-squared coherence (GMSC). These coherence-based estimators normalize detector auto-spectral structure and are expected to reduce the sensitivity of fitted α values to processing parameters. A Sobol global sensitivity analysis identified which numerical inputs most strongly influence the fitted values of α. All estimators produced a linear dependence of α on inverse count rate, with delayed-critical extrapolations near 1.7 × 10 4 s −1 , in agreement within 8% of MCNP6.3 KOPTS benchmark calculations. Sensitivity results show that while the CPSD depends on both time-bin width and taper selection, the MSC and GMSC are dominated by time-bin width alone, indicating reduced parameter coupling and greater robustness to processing variability. These findings demonstrate the feasibility and practical value of coherence-based spectral estimators for extracting α from reactor noise and support their broader application to multi-detector and irregular datasets in subcritical system characterization.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Finite Element Model Calibration Approach for Ares I-X

Ares I-X is a pathfinder vehicle concept under development by NASA to demonstrate a new class of launch vehicles. Although this vehicle is essentially a shell of what the Ares I vehicle will be, efforts are underway to model and calibrate the analytical models before its maiden flight. Work reported in this document will summarize the model calibration approach used including uncertainty quantification of vehicle responses and the use of nonconventional boundary conditions during component testing. Since finite element modeling is the primary modeling tool, the calibration process uses these models, often developed by different groups, to assess model deficiencies and to update parameters to reconcile test with predictions. Data for two major component tests and the flight vehicle are presented along with the calibration results. For calibration, sensitivity analysis is conducted using Analysis of Variance (ANOVA). To reduce the computational burden associated with ANOVA calculations, response surface models are used in lieu of computationally intensive finite element solutions. From the sensitivity studies, parameter importance is assessed as a function of frequency. In addition, the work presents an approach to evaluate the probability that a parameter set exists to reconcile test with analysis. Comparisons of pre-test predictions of frequency response uncertainty bounds with measured data, results from the variance-based sensitivity analysis, and results from component test models with calibrated boundary stiffness models are all presented.

Horta, Lucas G.↗

Minimum weight design of rectangular and tapered helicopter rotor blades with frequency constraints

The minimum weight design of a helicopter rotor blade subject to constraints on coupled flap-lag natural frequencies has been studied. A constraint has also been imposed on the minimum value of the autorotational inertia of the blade in order to ensure that it has sufficient inertia to autorotate in the case of engine failure. The program CAMRAD is used for the blade modal analysis and CONMIN is used for the optimization. In addition, a linear approximation analysis involving Taylor series expansion has been used to reduce the analysis effort. The procedure contains a sensitivity analysis which consists of analytical derivatives of the objective function and the autorotational inertia constraint and central finite difference derivatives of the frequency constraints. Optimum designs have been obtained for both rectangular and tapered blades. Design variables include taper ratio, segment weights, and box beam dimensions. It is shown that even when starting with an acceptable baseline design, a significant amount of weight reduction is possible while satisfying all the constraints for both rectangular and tapered blades.

Chattopadhyay, Aditi↗

Minimum weight design of rotorcraft blades with multiple frequency and stress constraints

Minimum weight designs of helicopter rotor blades with constraints on multiple coupled flap-lag natural frequencies are studied. Constraints are imposed on the minimum value of the blade autorotational inertia to ensure sufficient rotary inertia to autorotate in case of engine failure and on stresses to guard against structural failure due to blade centrifugal forces. Design variables include blade taper ratio, dimensions of the box beam located inside the airfoil and magnitudes of nonstructural weights. The program CAMRAD is used for the blade modal analysis; the program CONMIN is used for the optimization. A linear approximation involving Taylor series expansion is used to reduce the analysis effort. The procedure contains a sensitivity analysis consisting of analytical derivatives for objective function and constraints on autorotational inertia and stresses. Central finite difference derivatives are used for frequency constraints. Optimal designs are obtained for both rectangular and tapered blades. Using this method, it is possible to design a rotor blade with reduced weight, when compared to a baseline blade, while satisfying all the imposed design requirements.

Chattopadhyay, Aditi↗

Minimum weight design of rectangular and tapered helicopter rotor blades with frequency constraints

The minimum weight design of a helicopter rotor blade subject to constraints on coupled flap-lag natural frequencies has been studied. A constraint has also been imposed on the minimum value of the autorotational inertia of the blade in order to ensure that it has sufficient inertia to aurorotate in the case of engine failure. The program CAMRAD is used for the blade modal analysis and CONMIN is used for the optimization. In addition, a linear approximation analysis involving Taylor series expansion has been used to reduce the analysis effort. The procedure contains a sensitivity analysis which consists of analytical derivatives of the objective function and the autorotational inertia constraint and central finite difference derivatives of the frequency constraints. Optimum designs have been obtained for both rectangular and tapered blades. Design variables include taper ratio, segment weights, and box beam dimensions. It is shown that even when starting with an acceptable baseline design, a significant amount of weight reduction is possible while satisfying all the constraints for both rectangular and tapered blades.

Chattopadhyay, Aditi↗

Minimum weight design of helicopter rotor blades with frequency constraints

The minimum weight design of helicopter rotor blades subject to constraints on fundamental coupled flap-lag natural frequencies has been studied in this paper. A constraint has also been imposed on the minimum value of the blade autorotational inertia to ensure that the blade has sufficient inertia to autorotate in case of an engine failure. The program CAMRAD has been used for the blade modal analysis and the program CONMIN has been used for the optimization. In addition, a linear approximation analysis involving Taylor series expansion has been used to reduce the analysis effort. The procedure contains a sensitivity analysis which consists of analytical derivatives of the objective function and the autorotational inertia constraint and central finite difference derivatives of the frequency constraints. Optimum designs have been obtained for blades in vacuum with both rectangular and tapered box beam structures. Design variables include taper ratio, nonstructural segment weights and box beam dimensions. The paper shows that even when starting with an acceptable baseline design, a significant amount of weight reduction is possible while satisfying all the constraints for blades with rectangular and tapered box beams.

Chattopadhyay, Aditi↗

Potential Impact of Land Use Change on Future Regional Climate in the Southeastern U.S.: Reforestation and Crop Land Conversion

The impact of future land use and land cover changes (LULCC) on regional and global climate is one of the most challenging aspects of understanding anthropogenic climate change. We study the impacts of LULCC on regional climate in the southeastern U.S. by downscaling the NASA Goddard Institute for Space Studies global climate model E to the regional scale using a spectral nudging technique with the Weather Research and Forecasting Model. Climate-relevant meteorological fields are compared for two southeastern U.S. LULCC scenarios to the current land use/cover for four seasons of the year 2050. In this work it is shown that reforestation of cropland in the southeastern U.S. tends to warm surface air by up to 0.5 K, while replacing forested land with cropland tends to cool the surface air by 0.5 K. Processes leading to this response are investigated and sensitivity analyses conducted. The sensitivity analysis shows that results are most sensitive to changes in albedo and the stomatal resistance. Evaporative cooling of croplands also plays an important role in regional climate. Implications of LULCC on air quality are discussed. Summertime warming associated with reforestation of croplands could increase the production of some secondary pollutants, while a higher boundary layer will decrease pollutant concentrations; wintertime warming may decrease emissions from biomass burning from wood stoves

Regional climate change↗

Field Validation of Thermoelectric Generation System at Holcim Cement Plant in Alpena, Michigan

Executive Summary Project Background The Industrial Technology Validation (ITV) program aims to identify and demonstrate the performance of new, emerging, and underutilized energy-saving technologies in the industrial sector to help inform decisions to help accelerate their commercialization and deployment, as well as to help make industries more competitive. This ITV demonstration evaluated a thermoelectric generation (TEG) technology at a cement plant, aiming to reduce energy demand in the cement industry. A median cement plant consumes 5.73 million British thermal units per ton of clinker production (resulting in 0.838 metric tons of carbon dioxide [CO₂] emissions per ton of clinker) (Boyd and Zhang 2011, EPA 2021), equivalent to approximately 6.9 trillion British thermal units (TBtu) per year in energy consumption at a cement plant producing 3,300 tons of clinker per day.¹ Collaborating with Holcim, Advanced Thermovoltaic Systems (ATS) developed and deployed a pilot-scale thermoelectric power system to efficiently capture and convert waste heat to electricity. The system leverages the Seebeck effect to convert temperature differences on two sides of semiconductor cartridges into electrical power (ScienceDirect, n.d.). This generation is realized with minimal moving parts compared to existing waste-heat-to-generation solutions and allows capture from heat sources with temperatures as low as 150°C. This project aimed to validate a scalable solution applicable for capturing medium-temperature waste heat, including ambient losses from other high-temperature processes, and high-temperature sources less suitable for other waste-heat-to-power solutions. By recovering this otherwise wasted heat, this project intends to validate improvements to overall process efficiency through reduction in purchased electricity, thereby reducing operational costs while enhancing resiliency and competitiveness. Description and Scope This study evaluated the performance of a TEG system from ATS as a solution to convert waste heat into useful power at a Holcim cement plant in Alpena, Michigan. This plant is a fully integrated cement plant that has been operating since 1907. The facility operates continuously (24/7/365) with approximately 250 employees and five long dry kilns, yielding a total production capacity of 7,852 tons of cement per day (EPA 2023). Currently, the Alpena plant uses waste heat boilers to convert waste heat from the exhaust of each kiln into steam, which drives steam turbine generators. The ATS TEG is being evaluated for its potential to supplement the steam turbines by capturing the remaining lower grade heat. This technology is also being considered for other Holcim plants where steam turbines are not a viable option. ATS installed a pilot-scale TEG unit with an array of 582 individual thermoelectric semiconductor cartridges, of which 573 were operational. The cartridges are sandwiched between 48 hot plates and 49 cold plates. Each cartridge is designed to generate 20 watts (W) of gross power at a hot-side temperature of 240°C and cold-side temperature of 20°C. As such, the total gross generation capacity of the installed system is 11.5 kilowatts (kW) at design conditions. The system configuration for the evaluation was designed to prioritize convenience of installation and minimize disruption to production at the site, while ensuring that the heat required can be obtained for evaluating the TEG system at various operational conditions. To accomplish this, a portion of the steam supplied to Alpena’s steam turbine generation system was diverted to be used as the heat source for the TEG system, while water was supplied to the cold side of the system from nearby Lake Huron. This configuration was designed for the evaluation of the pilot-scale system to assess the performance at different conditions. A commercial-scale system will likely vary from the pilot system depending on typical configurations, including both scale and application. Future commercial applications of the ATS system would involve integrating the system into the exhaust from kiln preheaters, clinker coolers, or radiant heat capture from kiln shells for the heat source. For the cold source, a range of cooling solutions can be considered, including a mechanical cooling system, depending on the location and the application. To increase the generation capacity for commercial applications, the technology provider is working toward developing a commercial-scale TEG system, which would combine multiple TEG units (each similar in design to the pilot system) together. The scope of this evaluation includes the pilot-scale TEG system and all impacted equipment including pumps, controllers, and power handling equipment. Study Objectives The evaluation's goal was to assess the potential of the ATS TEG system to generate useful electrical power by capturing waste heat from cement production kilns. The objectives of this study are to evaluate and verify the following claims made by ATS regarding the pilot-scale system installed at the Holcim Alpena plant. The following design parameters and claims are also outlined in Table ES- 1 and Table ES- 2: • Gross Power: The thermoelectric system converts heat into power to create gross power, the total measured power generated by the system. The 573 active cartridge pilot-scale system is expected to generate 11.5 kW of gross power at the designed hot-side temperature of 240°C and cold-side temperature of 20°C. Power production is dependent on the temperature difference between the heat source (ultimately from the waste heat) and cold temperature supply source. • Net Power: The net power is the total usable power provided to the site by the TEG system after deducting parasitic power loads from the gross generated power. Supplementary equipment is required to operate the TEG system including pumps, controllers, and, in certain anticipated applications, mechanical cooling, which introduce parasitic loads to system operation. After deducting the parasitic loads from the gross power generation, ATS anticipates achieving a net power generation of 7.5 kW from the pilot-scale system. • Thermal Efficiency: The thermal efficiency is the percent of the total heat transferred to the TEG system that is converted to gross power. Historically, TEGs have a thermal efficiency of 2%–5% (DOE 2008). Prior industrial-scale TEG systems, such as the E1 TEG offered by Alphabet Energy, operated at an efficiency of 2.5% (Lamonica, 2014). ATS anticipates achieving an average efficiency of 4.8% or higher in converting heat energy to usable electricity. • Cartridge Performance: The TEG system comprises 573 active individual semiconductor cartridges, each of which generates a portion of the total power. Cartridge optimization and selection is an important design consideration for potential future TEG system design performance. Therefore, understanding the distribution of gross power and efficiency within the pilot system is vital to understanding what is achievable. At a design hot-side temperature of 240°C and cold-side temperature of 20°C, ATS anticipates a cartridge performance of 20 W of gross power per cartridge at an efficiency of 4.8% per cartridge. In addition to evaluating the claimed performance of the TEG pilot-scale unit, the study estimated the potential annual impacts of a scaled-up commercial system used to capture kiln waste heat over annual operations. The evaluation estimated the gross and net annual electric generation achievable by capturing heat from the two proposed tap-in points: the kiln exhaust and the clinker cooler exhaust; see Section 2.1 for details. Two use cases were examined: • Holcim Alpena: The Holcim Alpena site consists of long dry kilns with superheater boilers, which differs from the rest of Holcim’s cement plant portfolio and results in lower waste heat temperatures. The study estimates gross and net annual generation using the superheater boiler exhaust and clinker cooler exhaust, based on 2023 operational data. • Typical Installation: Common cement plants have preheater kilns with higher exhaust temperatures than Holcim Alpena across a range of production rates. The study estimates gross and net annual generation using the preheater exhaust and clinker cooler exhaust, with a sensitivity analysis to account for the typical range of preheater exhaust temperatures, clinker cooler exhaust temperatures, and clinker production rates. Methodology The evaluation methodology followed a measurement and verification (M&V) strategy based on the International Performance Measurement and Verification Protocol Option B through comprehensive measurements and analyses of the affected systems. Evaluation data was collected from March 9 to March 11, 2024, the test period of the pilot TEG system. During the test period, in coordination with the ITV team, the ATS team adjusted system operations to capture the range of variability expected for each of the variables pertinent to performance of the system. The methodology consisted of two parts: evaluating the performance of the pilot unit's TEG system and estimating the annual TEG impact in terms of gross and net power based on a given waste heat profile. First, the evaluation of the thermoelectric generation performance of the pilot unit relative to the claims was performed by analyzing the collected test data. Gross power of the pilot TEG system was directly measured. Net power was determined by deducting the measured parasitic power from the gross power. The gross power generation was compared to heat transferred to the system by the working fluid (which was heated by steam generated from the kiln waste heat) to calculate the thermal efficiency achieved by the system. Performance of individual semiconductor cartridges within the pilot array was also assessed in terms of measured gross cartridge power and calculated cartridge thermal efficiency. The second part of the evaluation estimated the annual TEG impacts in terms of gross power and net power (calculated from the difference between gross power and parasitic power). This analysis comprised development of mathematical regression models for gross power and parasitic power, with assessment of each model’s goodness-of-fit characteristics to ensure satisfaction of statistical requirements. The models predicted the gross power generation, the parasitic load based on the temperature difference between the hot working fluid and the cold-side fluid (cold water from Lake Huron) entering the system, the volumetric flow rate of the cold-side fluid at the inlet, and the volumetric flow rate of the hot working fluid at the inlet. The annual impact analysis considered a theoretical commercial-scale system sized to capture the available waste heat at a cement plant, consisting of linked pilot-scale units that receive heat from a theoretical gas-to-working-fluid heat exchanger. To estimate annual impacts at the Alpena plant, the gross power and parasitic power regression models were applied to the arrays in the theoretical commercial-scale system. The heat supplied to the unit was calculated based on the kiln run time, annual production, kiln exhaust waste heat, and clinker cooler waste heat derived from 2023 Holcim Alpena kiln operational data. Net power impacts were calculated by deducting the resulting parasitic power from the estimated gross power. Inputs for the model were generated from a combination of hourly data, assumed design considerations for TEG system scale-up from the pilot-scale unit, and assumptions regarding TEG system operations. This analysis was then used as the basis for estimating annual impacts of typical TEG installation at cement plants, by applying sensitivity analyses to key kiln operational characteristics including kiln preheater exhaust temperatures, cooler clinker exhaust temperatures, and plant daily production rates across a range of expected values. Project Results/Findings Table ES- 2 and Table ES- 2 provide a summary of the operating conditions and evaluation results compared to the stated claims from the technology provider. Key takeaways include: • Gross Power: The peak gross power achieved during the testing period was 10.0 kW, compared to the 11.5 kW expected for 573 active cartridges. The claimed gross power was associated with a target hot side of 240°C; however, the system only received a maximum hot-side mean plate temperature of 212°C during the testing period. • Net Power: The pilot-scale unit exceeded the claims for net power, achieving a peak of 7.7 kW net compared to a claim of 7.5 kW. One factor contributing to the higher achieved net power is the relatively high water pressure available through Lake Huron. The pilot TEG system did not require cold-side pumps during the test, whereas most installations would. This reduced the parasitic loads on the system, ultimately contributing to higher net power relative to the gross power. • Thermal Efficiency: The pilot-scale unit outperformed the claimed efficiency, achieving a peak system efficiency of 5.0% thermal efficiency compared to the stated 4.8%. • Cartridge Performance: To compare cartridge performance against claims, the study focused on the third day of testing, which aimed for conditions closest to the design specifications, with a hot side of 240°C and cold-side exit temperature of 6.4°–30°C. On this day, the mean gross power observed in the cartridges within the TEG array was 18.1 W/cartridge, and the peak performance was 34.7 W/cartridge. The estimated mean cartridge efficiency was 5.2%, and the estimated efficiency at peak gross cartridge power was 10%. The regression models developed for gross power generation and parasitic loads were used to estimate the generation impact for given heat input to the TEG from the working fluid (captured from the waste heat) and from the cold loop (Lake Huron) on an hourly basis for a year of operation. Based on this analysis, installation of a commercial-scale TEG system at the Holcim cement plant in Alpena, Michigan, with a waste heat exchanger of 0.85 effectiveness, would generate up to 391 kW of net power, translating to between 920,000 and 1,800,000 kilowatt-hours (kWh) in net electricity per year. Based on typical grid emissions for Alpena, this would avoid estimated net emissions by 752 metric tons of CO₂ annually.² The sensitivity analysis estimated that typical TEG system installations at cement plants could generate an average of 56–1,040 kW of net power, or between 488,000 and 9,110,000 kWh of net energy. This generation potential is most significantly affected by plant production rates and also influenced by preheater and clinker cooler exhaust temperatures. Applying the national average emission rate, typical commercial-scale installations at Holcim plants are projected to avoid between 182 and 3,401 metric tons of CO₂ annually per site. Table ES- 3 shows a summary of the estimated annual impacts.³ While parasitic loads are significant and vary by application, this analysis assumed the use of heating loop pumps and access to Lake Huron as a cold sink. This setup assumed no need for cooling loop pumps due to the available water pressure at the test site. Applications that require cooling towers or additional equipment are likely to experience higher parasitic loads. Therefore, the study’s estimates are most applicable to scenarios with similar parasitic load configurations—namely, access to a high-pressure cold sink. Applicability to other locations may be limited, as differing conditions could necessitate additional pumps and cooling systems, potentially impacting performance significantly.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗