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At least 289 records · Page 16

Investigation of grid-based vorticity-velocity large eddy simulation off-body solvers for application to overset CFD

Accurately predicting unsteady wakes and vortex-dominated flows is essential to a wide range of engineering applications, including aircraft, rotorcraft, shipboard operations, bio-inspired unsteady flight and propulsion, wind turbines, and urban flows. While current CFD software can model the complete flow field and wake system, the computational costs incurred in high Reynolds number unsteady turbulent flow simulations often remain prohibitive for routine engineering use, particularly for applications involving moving components. Prior work has demonstrated that by adopting a vorticity-velocity formulation in a grid-based off-body flow solver (VorTran-M and VorTran-M2) one can lower these costs by several orders of magnitude when compared to conventional approaches. This paper describes the extensions made to VorTran-M2 to support turbulent flows, and associated benchmarking activity to assess its performance for problems involving strong stretching and diffusion processes, whose competing contributions to the vorticity field are core drivers of turbulent flow evolution. Predictions are presented for: (i) the Kida-Pelz problem whose inviscid form is of mathematical interest due to its apparent formation of singular flow in finite time; and (ii) the Taylor Green vortex arrangement, which has been extensively studied as a fundamental simulation challenge in the turbulent modeling community. Here, the results are used to evaluate the overall predictive ability and performance of two sub-grid scale models incorporated into VorTran-M2. Results indicate that the computational cost savings seen previously for inviscid and convection dominated problems extend to turbulent flow simulations supporting the viability of VorTran-M2 as a low cost means for accurately modeling the far-field and background flow, particularly when long duration vorticity evolution is of interest.

42 ENGINEERING↗

Development and Demonstration of a Fuel-Efficient, Class 8 Tractor & Trailer Engine System (SuperTruck II)

Navistar presents the SuperTruck II (ST II) Final Report to the Unites States Department of Energy (US DOE), which covers the five Budget Periods (BPs) from 10-1-2016 through 6-30-2022. For ST II, Navistar built on the achievements of the SuperTruck I (ST I) Program as a catalyst to continue critical research, design and development, testing, and operations to reach the ambitious goals of the ST II project. This approach allowed Navistar to continue contributing to the essential needs of our nation for safe, efficient, and cost-effective delivery of goods and services, as we reduced negative environmental effects and improved operational productivity. This document contains information specified in DOE F 4600.2, Final Scientific/Technical Report DOE F 241.3, B. SCIENTIFIC/TECHNICAL REPORTS, explaining how we met and exceeded program requirements. Throughout this Final Report, Navistar extracted information from documents prepared during the project that represent our management, design and development, building, and testing efforts to meet and exceed SuperTruck II project goals. Navistar followed Plan requirements to achieve / exceed Project Objectives: a) >100% improvement in vehicle freight efficiency (FE) (on ton-MPG basis) relative to 2009 baseline with stretch goal of 140% improvement [actual: 170%); b) >55% engine brake thermal efficiency (BTE) demonstrated in operational engine at a 65-mph cruise point on a dynamometer – ≥31% increase from 2009 baseline [actual: 55.20% of combined BTE) ; and c) development and implementation of commercially cost effective technologies (in terms of a simple payback). Technology selection / development path focused on developing technologies applicable for production within 3-year approach, while ensuring technology readiness and cost of ownership for end users. The Program was organized into five budget periods: Requirements / Technology Assessment and Initial Hardware Testing; Technology Development and Concept Readiness Demonstration; Technology Finalization and Validation Tractor / Trailer Fabrication, Integration and Commissioning Demonstration; and Fuel Economy (FE) and Brake Thermal Efficiency (BTE) and Program Completion. Leadership was provided by DOE, with tasks performed by laboratories (Argonne National Laboratory, Lawrence Livermore National Laboratory); partners at Bosch, TPI, Dana, and J.B. Hunt; , and support from University of Michigan and Clemson University. Navistar lead this team with Principal Investigator / Contracting Officer; Project Manager (PM); Vehicle, Engine, and Aftertreatment Engineers; Finance Manager, Technical Program Leads, and Legal/IP; and other key personnel. Work also included personnel in risk management; funding / budget / finance. Work involved analysis, development, testing, and down selection of individual/system engine, aftertreatment, and vehicle technologies, with integration of selected technologies into a prototype vehicle for demonstration of fuel-efficiency gain. Work also included component/integrated system level development of truck and trailer aerodynamics, base engine efficiency, advanced aftertreatment, combustion efficiency, waste heat recovery, hybrid powertrain, reduced rolling resistance, weight reduction, idle reduction, and driver feedback. As ST II progressed, Navistar performed computer-based modeling / simulations of technologies focused on the primary operational areas: Engine, Aftertreatment, and Vehicle. During the ST II Program, the COVID Virus outbreak unexpectedly challenged by the effects of, which affected staffing, scheduling, design, supplies, availability of materials, production procedures, and testing. The DOE responded by extending the program by three quarters to ensure that project tasks were completed for this vital project. Focus continued on analyzing, developing, testing, and down selecting individual-/system-level engine and vehicle technologies for integration of the final selected technologies into a prototype vehicle that would demonstrate fuel-efficiency gains made possible through these technologies. This included component/integrated system-level development of truck and trailer aerodynamics, base engine efficiency, advanced aftertreatment, combustion efficiency, waste heat recovery, solar power, distributed and intelligent vehicle power, hybrid powertrain, reduced rolling resistance, weight reduction, idle reduction, and driver feedback. Throughout the program, function, reliability, and performance at all levels were ensured through testing. Proof of this approach was demonstrated in multiple, on-road demonstrations: Scenario A (Flatland) Fuel Economy, Scenario B (Hilly) Fuel Economy, and City Cycle Tests. Other benefits derived from ST II included new/improved products, publications, patents, and next-step capabilities related to electric/hydrogen vehicles and autonomous driving.

Zukouski, Russ↗

A Phenomenological Thermal Spray Wall Interaction Modeling Framework Applied to a High Temperature Ignition Assistant Device

Airborne compression ignition engines must operate with reliable ignition systems to achieve proper ignition at every cycle, particularly at high altitudes. Glow-plug-based ignition-assistant (IA) devices can provide the necessary energy to preheat the fuel and ensure ignitability of the fuel-air mixture. Ignitability of liquid sprays can be facilitated via direct impingement onto the hot IA surface, however this comes with adverse effects on the IA durability. Therefore, optimizing an IA’s design requires detailed understanding of the physics of fuel spray impingement of superheated surfaces. While spray impingement on relatively low wall temperatures has been extensively studied and appropriate numerical models have been proposed through the years, fundamental understanding of high-speed liquid spray impingement on superheated walls is still elusive. This work aims to formulate a phenomenological thermal spray-wall interaction framework for modeling the film-boiling-induced heat transfer, atomization, and dispersion of fuel spray droplets impinging onto a superheated IA device. A qualitative comparison of the new phenomenological model is performed against optical experiments from the literature of an F-24 fuel spray injected onto an IA device located 12 mm away from the injector tip. The temperature of the IA was set at 1400 K. The fuel injection pressure was 400 bar, while the ambient gas pressure and temperature were 30 bar and 800 K, respectively. The performance of the phenomenological model is evaluated in comparison with two other state-of-art models from the literature. A qualitative analysis of the different spray and fuel-air mixture characteristics is performed to outline the differences in the predictions offered by the new phenomenological model and the two state-of-art spray-wall interaction models.

droplet dispersion↗

Pyomo.GDP: an ecosystem for logic based modeling and optimization development

We present three core principles for engineering-oriented integrated modeling and optimization tool sets—intuitive modeling contexts, systematic computer-aided reformulations, and flexible solution strategies—and describe how new developments in Pyomo.GDP for Generalized Disjunctive Programming (GDP) advance this vision. We describe a new logical expression system implementation for Pyomo.GDP allowing for a more intuitive description of logical propositions. The logical expression system supports automated reformulation of these logical constraints to linear constraints. We also describe two new logic-based global optimization solver implementations built on Pyomo.GDP that exploit logical structure to avoid “zero-flow” numerical difficulties that arise in nonlinear network design problems when nodes or streams disappear. These new solvers also demonstrate the capability to link to external libraries for expanded functionality within an integrated implementation. We present these new solvers in the context of a flexible array of solution paths available to GDP models. Finally, we present results on a new library of GDP models demonstrating the value of multiple solution approaches.

42 ENGINEERING↗

Constructs and systems and methods for engineering a CO2 fixing photorespiratory by-pass pathway

Methods and compositions to introduce a synthetic pathway based on the 3-hydroxypropionate bicycle into an organism such as the model cyanobacterium, Synechococcus elongatus sp. PCC 7942. The heterologously expressed pathway acts as a photorespiratory bypass as well as an additional carbon fixation cycle orthogonal to the endogenous Calvin-Benson cycle. We demonstrate the function of all six introduced enzymes, which not only has implications on increasing net-photosynthetic productivity, but also key enzymes in the pathway are involved in high-value products that are of biotechnological interest, such as 3-hydroxypropionate.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

New Educational Modules Using a Cyber-Distribution System Testbed

At Washington State University (WSU), a modern cyber-physical system testbed has been implemented based on an industry grade distribution management system (DMS) that is integrated with remote terminal units (RTUs), smart meters, and a solar photovoltaic (PV). In addition, the real model from the Avista Utilities distribution system in Pullman, WA, is modeled in DMS. The proposed testbed environment allows students and instructors to utilize these facilities for innovations in learning and teaching. For power engineering education, this testbed helps students understand the interaction between a cyber system and a physical distribution system through industrial level visualization. The testbed provides a distribution system monitoring and control environment for students. Compared with a simulation based approach, the testbed brings the students' learning environment a step closer to the real world. The educational modules allow students to learn the concepts of a cyber-physical system and an electricity market through an integrated testbed. Furthermore, the testbed provides a platform in the study mode for students to practice working on a real distribution system model. Here, this paper describes the new educational modules based on the testbed environment. Three modules are described together with the underlying educational principles and associated projects.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DEVELOPMENT OF A SOFTWARE DESIGN TOOL FOR HYBRID SOLAR-GEOTHERMAL HEAT PUMP SYSTEMS IN HEATING- AND COOLING-DOMINATED BUILDINGS

This project provides an easy-to-use, menu-driven, software tool for designing hybrid solar-geothermal heat pump systems (GHP) for both heating- and cooling-dominated buildings. No such design tool currently exists. In heating-dominated buildings, the design approach takes advantage of glazed solar collectors to effectively balance the annual thermal loads on the ground with renewable solar energy. In cooling-dominated climates, the design approach takes advantage of relatively low-cost, unglazed solar collectors as the heat rejecting component. The primary benefit of hybrid GHPs is the reduced initial cost of the ground heat exchanger (GHX). Furthermore, solar thermal collectors can be used to balance the ground loads over the annual cycle, thus making the GHX fully sustainable; in heating-dominated buildings, the hybrid energy source (i.e., solar) is renewable, in contrast to a typical fossil fuel boiler or electric resistance as the hybrid component; in cooling-dominated buildings, use of unglazed solar collectors as a heat rejecter allows for passive heat rejection, in contrast to a cooling tower that consumes a significant amount of energy to operate, and hybrid GHPs can expand the market by allowing reduced GHX footprint in both heating- and cooling-dominated climates. The design tool allows for the straight-forward design of innovative GHP systems that currently pose a significant design challenge. The project lays the foundations for proper and reliable design of hybrid GHP systems, overcoming a series of difficult and cumbersome steps without the use of a system simulation approach, and without an automated optimization scheme. As new technologies and design concepts emerge, sophisticated design tools and methodologies must accompany them and be made usable for practitioners. Lack of reliable design tools results in reluctance of practitioners to implement more complex systems. A menu-driven software tool for the design of hybrid solar GHP systems is provided that is based on mathematically robust, validated models. An automated optimization tool is used to balance ground loads and incorporated into the simulation engine. With knowledge of the building loads, thermal properties of the ground, the borehole heat exchanger configuration, the heat pump peak hourly and seasonal COP for heating and cooling, the critical heat pump design entering fluid temperature, and the thermal performance of a solar collector, the total GHX length can be calculated along with the area of a supplemental solar collector array and the corresponding reduced GHX length. An economic analysis module allows for the calculation of the lowest capital cost combination of solar collector area and GHX length. ACKNOWLEDGMENTS This project was funded by the United States Department of Energy DOE-DE-FOA-0000116, Recovery Act Geothermal Technologies Program: Ground Source Heat Pumps. The lead contractor, The University of Hartford, was supported by The University of Dayton, and the Oak Ridge National Laboratories. All funding and support for this project as well as contributions of graduate and undergraduate students from the contributing institutions are gratefully acknowledged.

14 SOLAR ENERGY↗

Anomaly Detection and Identification Using a Leave-One-Variable-Out Method

At nuclear power plants (NPPs), anomaly detection and identification (i.e., determining the causes of anomalies) are important tasks for ensuring the safe and efficient operation of NPPs. These tasks are currently labor-intensive and costly, and are made more difficult by the size and complexity of NPP systems. An alternative approach to conducting these tasks is to automate them, such as via the reconstruction-based contribution method, which is a well-researched unsupervised machine learning method that uses a data-driven model of anomaly-free behavior to detect events and then identify each variable’s contributions to those events. The present effort developed a novel contribution approach that utilized a leave-one-variable-out (LOVO) model, with which each variable is predicted using all the other variables. The novelty lay in transforming this model into a reconstruction model and modifying the identification algorithm to work with the new reconstruction model. To evaluate this method in a controlled environment, a synthetic dataset based on spring-mass-damper (SMD) systems (commonly found in mechanical engineering references) was used, with known anomalies introduced into the system. The proposed method successfully detected the anomalies and afforded insights into their causes, thus enabling the appropriate identifications to be made.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Biconjugate Impedance Matching Control of the HERO WEC: Preprint

Effective control strategies are essential for maximizing the power output of wave energy converters (WECs). In this study, we explore the methodology of port-based modelling which can be used for bi-conjugate impedance matching, a type of reactive control that involves maximizing power transfer by setting the load (PTO) impedance to be the complex conjugate of the source impedance (WEC). Despite its foundational role in electrical engineering, this method has seen limited application in wave energy and has not yet been demonstrated in wave-powered desalination systems. We represent our complex multidisciplinary system as an equivalent circuit to explore frequency-based relations. The HERO WEC, a small-scale, modular point absorber (PA) designed for reverse osmosis desalination is used as a case study to demonstrate port-based modelling for control applications. Improving the performance of wave-powered water desalination systems could play a critical role in addressing freshwater scarcity for coastal communities, especially those in remote or disaster-prone regions.

16 TIDAL AND WAVE POWER↗

Engineering steady states using jump-based feedback for multipartite entanglement generation

We investigate the use of quantum-jump-based feedback to manipulate the stability of multipartite entangled dark states in an open quantum system. Using the model proposed in Phys. Rev. A 76, 010301(R) (2007) for a pair of atoms, we show a general strategy to produce many-body singlet stationary entangled states for larger number of atoms. In the case of four qubits, we propose a simple local feedback control that, although not optimal, is realistic and stabilizes a highly entangled state. We discuss the limitations and analyze alternative strategies within the framework of direct jump feedback schemes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

TH-AB-BRA-07: PENELOPE-Based GPU-Accelerated Dose Calculation System Applied to MRI-Guided Radiation Therapy

Purpose: The clinical commissioning of IMRT subject to a magnetic field is challenging. The purpose of this work is to develop a GPU-accelerated Monte Carlo dose calculation platform based on PENELOPE and then use the platform to validate a vendor-provided MRIdian head model toward quality assurance of clinical IMRT treatment plans subject to a 0.35 T magnetic field. Methods: We first translated PENELOPE from FORTRAN to C++ and validated that the translation produced equivalent results. Then we adapted the C++ code to CUDA in a workflow optimized for GPU architecture. We expanded upon the original code to include voxelized transport boosted by Woodcock tracking, faster electron/positron propagation in a magnetic field, and several features that make gPENELOPE highly user-friendly. Moreover, we incorporated the vendor-provided MRIdian head model into the code. We performed a set of experimental measurements on MRIdian to examine the accuracy of both the head model and gPENELOPE, and then applied gPENELOPE toward independent validation of patient doses calculated by MRIdian’s KMC. Results: We achieve an average acceleration factor of 152 compared to the original single-thread FORTRAN implementation with the original accuracy preserved. For 16 treatment plans including stomach (4), lung (2), liver (3), adrenal gland (2), pancreas (2), spleen (1), mediastinum (1) and breast (1), the MRIdian dose calculation engine agrees with gPENELOPE with a mean gamma passing rate of 99.1% ± 0.6% (2%/2 mm). Conclusions: We developed a Monte Carlo simulation platform based on a GPU-accelerated version of PENELOPE. We validated that both the vendor provided head model and fast Monte Carlo engine used by the MRIdian system are accurate in modeling radiation transport in a patient using 2%/2 mm gamma criteria. Future applications of this platform will include dose validation and accumulation, IMRT optimization, and dosimetry system modeling for next generation MR-IGRT systems.

60 APPLIED LIFE SCIENCES↗

FLYING SERVING: On-the-Fly Parallelism Switching for Large Language Model Serving

Production LLM serving must simultaneously deliver high throughput, low latency, and sufficient context capacity under non-stationary traffic and mixed request requirements. Data parallelism (DP) maximizes throughput by running independent replicas, while tensor parallelism (TP) reduces per-request latency and pools memory for long-context inference. However, existing serving stacks typically commit to a static parallelism configuration at deployment; adapting to bursts, priorities, or long-context requests is often disruptive and slow. We present Flying Serving, a vLLM-based system that enables online DP-TP switching without restarting engine workers. Flying Serving makes reconfiguration practical by virtualizing the state that would otherwise force data movement: (i) a zero-copy Model Weights Manager that exposes TP shard views on demand, (ii) a KV Cache Adaptor that preserves request KV state across DP/TP layouts, (iii) an eagerly initialized Communicator Pool to amortize collective setup, and (iv) a deadlock-free scheduler that coordinates safe transitions under execution skew. Across three popular LLMs and realistic serving scenarios, Flying Serving improves performance by up to 4.79 × under high load and 3.47 × under low load while supporting latency- and memory-driven requests.

Gao, Shouwei [ORNL]↗

Towards a predictive, physics-based friction model for the dynamics of jointed structures

Bolted connections are ubiquitous in mechanical designs and pose a significant challenge to understanding and predicting the vibration response of assembled structures. The present paper develops a physics-based rough contact model of the frictional interactions within a joint. This model sums over the probable interactions of asperities – defined as locally maximum surface features – to determine the contact forces. Here, the tangential contact forces vary smoothly between sticking and slipping and allow the model to better capture the qualitative trends of experimental amplitude dependent frequency and damping than previous studies. Furthermore, the novel model is generalized to allow for arbitrarily varying normal pressure including potential separation to better represent the interfacial dynamics. This includes developing a new, computationally tractable approximation to the analytical Mindlin partial slip solution for tangential loading of contacting spheres. Further, the results highlight the importance of accurately characterizing the as-built topology of the interface, the plastic behavior of the contacting asperities, the relevant length scale of asperities, and the eccentricity of asperities. A predictive friction coefficient based on plasticity provides a poor match to experiments, so fitting the friction coefficient is also considered. Numerical results are compared to experiments on the Brake-Reuß Beam to assess the predictive potential of the models. While blind predictions over-predict the slip limit, the current model presents a significant improvement in physics-based modeling and highlights areas for ongoing research.

42 ENGINEERING↗

Model predictive control for robust quantum state preparation

A critical engineering challenge in quantum technology is the accurate control of quantum dynamics. Model-based methods for optimal control have been shown to be highly effective when theory and experiment closely match. Consequently, realizing high-fidelity quantum processes with model-based control requires careful device characterization. In quantum processors based on cold atoms, the Hamiltonian can be well-characterized. For superconducting qubits operating at milli-Kelvin temperatures, the Hamiltonian is not as well-characterized. Unaccounted for physics (i.e., mode discrepancy), coherent disturbances, and increased noise compromise traditional model-based control. This work introduces model predictive control (MPC) for quantum control applications. MPC is a closed-loop optimization framework that (i) inherits a natural degree of disturbance rejection by incorporating measurement feedback, (ii) utilizes finite-horizon model-based optimizations to control complex multi-input, multi-output dynamical systems under state and input constraints, and (iii) is flexible enough to develop synergistically alongside other modern control strategies. We show how MPC can be used to generate practical optimized control sequences in representative examples of quantum state preparation. Specifically, we demonstrate for a qubit, a weakly-anharmonic qubit, and a system undergoing crosstalk, that MPC can realize successful model-based control even when the model is inadequate. These examples showcase why MPC is an important addition to the quantum engineering control suite.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

MOFA: Multi-objective Flux Analysis for the COBRA Toolbox

Environments of biological organisms are frequently nutrient and energy limited. This necessitates that systems exert tight regulation of trade-offs among key biological processes. Quantitative knowledge of these tradeoffs is essential for successful manipulation of biosystems (e.g., metabolic engineering projects). Using genome-scale constraint-based models of metabolism (GSMs), Multi-Objective Flux Analysis (MOFA) allows analyses of trade-offs among a system’s key biological tasks. The leading software for conducting a variety of constraint-based analyses using GSMs is the COBRA Toolbox for MATLAB. Results: We have developed a new add-on tool for COBRA that performs MOFA for a number of objectives only limited by computation power.

59 BASIC BIOLOGICAL SCIENCES↗

Development of Integrated Thermal Fluids Modeling Capability for MSRs

The DOE Nuclear Energy Advanced Modeling and Simulation (NEAMS) program supports a full range of computational thermal fluids analysis capabilities and code developments for a broad class of light-water and advanced reactor concepts. The research and development approach under thermal fluids technical area synergistically combines three length and time scales in a hierarchal multi-scale approach. To demonstrate the feasibility and capabilities of a multi-scale thermal fluids capability using these codes, a key joint effort has been pursued to develop an integrated system-and engineering-scale thermal fluids analysis capability with the MOOSE-based codes, through integration of SAM and Pronghorn, both based on the MOOSE framework. This report summarizes the progress in developing an integrated system- and engineering-scale thermal fluids analysis capability based on SAM and Pronghorn for molten salt reactors (MSRs), which gained significant interest in recently years. Two coupling approaches were studied, i.e. separate domain or domain-segregated coupling approach and the domain-overlapping approach. A series of coupled multi-physics models have been developed for a common reference molten salt fast reactor (MSFR) concept, ranging from standalone SAM system model to integrated SAM-Pronghorn-Griffin models. Both the steady state and the transient simulations are performed to the state-of-the-art simulation capabilities of NEAMS software suite in MSFR system applications. This report also covers further development and testing of the gas transport model in SAM for MSR modeling support. The presence of noncondensable gas in MSR systems would have strong impacts on fission gas removal and transport of noble metals throughout the system. Fission products removed through the off-gas system can also impact reactivity and can act as an additional point of heat removal. To ensure that the gas transport model is adequately tested, the supported modeling capabilities and features of SAM were identified, and a suite of tests were developed to test the model for each identified feature. Validation and UQ testing were also performed for the model and demonstrated that the buoyancy term, which was originally developed using non-salt/helium gas experimental data, can capture the experimental gas bubble velocity and diameter to within experimental and code uncertainty. An existing MSRE model was also modified in this work to include the gas transport model and to demonstrate the gas model behavior for realistic conditions of interest.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Reinforcement learning for adaptive maintenance policy optimization under imperfect knowledge of the system degradation model and partial observability of system states

Maintenance policy optimization usually is faced with challenges that arise from an imperfect knowledge of system degradation models and from the partial observability of system degradation states. Here, this paper proposes a reinforcement learning method to address these two challenges for a class of maintenance problems with Markov degradation processes. The reinforcement learning approach consists of a learning component and a planning component. Using sequentially collected observations, at each step of decision-making the learning component improves the knowledge of system degradation in terms of the probability distributions of the transition rates based on sequential Bayesian inference. Using the updated transition rates, at each step of decision-making the maintenance policy optimization problem is then formulated as a partially observable Markov decision problem, and the planning component computes the optimal maintenance policy that maximizes the expected cumulative reward. The proposed method is illustrated using a numerical example with repair and inspection maintenance actions. The result shows that as more observations are collected, the learning component progressively learns the true system degradation process, and the planning component adjusts the optimal maintenance policy accordingly as well, which leads to increased reward.

42 ENGINEERING↗

Asymptotic analysis of the fluid flow with a pressure-dependent viscosity in a system of thin pipes

We consider the incompressible fluid with a pressure-dependent viscosity flowing through a multiple pipe system. The viscosity–pressure relation is given by the Barus law commonly used in the engineering applications. Assuming that the ratio between pipes thickness and its length is small, we propose a rigorous asymptotic approach based on the concept of the transformed pressure. As a result, we obtain new macroscopic model describing the effective behavior of the fluid in the system. In particular, the generalized version of the Kirchhoff’s law is derived giving the explicit formula for the junction pressure. The error estimate for the asymptotic approximation is also provided. Mathematical analysis presented here can be applied to a general viscosity–pressure relation satisfied by other empiric laws.

97 MATHEMATICS AND COMPUTING↗