Abstract This paper explores possible implementations of a quantum annealing-based algorithm, in the Quadratic unconstrained binary optimization method (QUBO) form, to solve the thermo-fluid dynamics problem associated with the design of critical components of aircraft environmental control systems, namely compact heat exchangers and ejectors (also known as jet pumps), used on rotary- or fixed- winged aircrafts environmental control system to mix two fluids and exchange thermal energy. The purpose of this paper is to introduce the implementation of the QUBO model based on compact heat exchangers lumped model and the SAE 1168–6 ejector design procedure, with the formalization of the mathematical problem and the comparison of results obtained with experimental tests, classical resolution approaches and the quantum optimized code, showing how the QUBO approach is an effective and efficient tools for design engineers tasked to design and validate equipment parameters.We start with a simple two-phase flow within a single-pass mini-channel heat exchanger, describing the mathematical formulation of the problem followed by a simplified implementation of the proposed quantum approaches, highlighting the main procedures of the calculation as well as the practical implications, advantages and disadvantages of the proposed method, e.g. a limited number of CFD simulations are required to evaluate air side heat transfer coefficient and pressure drop for particular designs within the defined design space, and the specific hardware required to implement the quantum process.
Abstract This paper explores possible implementations of a quantum annealing-based algorithm, in the Quadratic unconstrained binary optimization method (QUBO) form, to solve the thermo-fluid dynamics problem associated with the design of critical components of aircraft environmental control systems, namely compact heat exchangers and ejectors (also known as jet pumps), used on rotary- or fixed- winged aircrafts environmental control system to mix two fluids and exchange thermal energy. The purpose of this paper is to introduce the implementation of the QUBO model based on compact heat exchangers lumped model and the SAE 1168–6 ejector design procedure, with the formalization of the mathematical problem and the comparison of results obtained with experimental tests, classical resolution approaches and the quantum optimized code, showing how the QUBO approach is an effective and efficient tools for design engineers tasked to design and validate equipment parameters.We start with a simple two-phase flow within a single-pass mini-channel heat exchanger, describing the mathematical formulation of the problem followed by a simplified implementation of the proposed quantum approaches, highlighting the main procedures of the calculation as well as the practical implications, advantages and disadvantages of the proposed method, e.g. a limited number of CFD simulations are required to evaluate air side heat transfer coefficient and pressure drop for particular designs within the defined design space, and the specific hardware required to implement the quantum process.
Abstract This paper explores possible implementations of quantum computing technologies, namely the quantum annealing and the quantum walk search algorithm, to solve fluid dynamics problems related to the design and assessment of compact heat exchangers for aeronautical environmental control and thermal management systems, as well as several other science and engineering applications, e.g. oil and gas refinery process. The purpose of this paper is to introduce two alternative implementations to the already assessed numerical resolution of Navier–Stokes equations or the resolution of analog quantum mechanical problem, highlighting how the use of quantum annealing and a classification algorithm (quantum walk search algorithm) can be implemented for the resolution of a lumped-characteristic analytical model of the heat transfer inside a compact heat exchanger, also in case of two-phase refrigerant fluid, for the use during design phase of environmental control system, e.g. provide the design engineers with a relatively simple and quick to use tool, which provides a reasonable result with an easily interpretable physical meaning. We start with a simple two-phase flow within a single-pass mini-channel heat exchanger, describing the mathematical formulation of the problem followed by a simplified implementation of the proposed quantum approaches, highlighting the main procedures of the calculation as well as the practical implications, advantages and disadvantages of the proposed method, e.g. a limited number of CFD simulations are required to evaluate air side heat transfer coefficient and pressure drop for particular designs within the defined design space, and the specific hardware required to implement the quantum process.
This article aims to assess a quantum annealing algorithm proposed for the evaluation of the performance of refrigerant ejectors used in aircrafts environmental control systems to mix two streams at different pressures and temperatures, through the formalization of Society of Automotive Engineers (SAE) 1168/6 method in the quadratic unconstrained binary optimization model, including the extension for compressible fluids. The assessment includes the comparison with the traditional analytical methods based on SAE 1168/6 methodology as well as computational fluid-dynamics simulations of an existing ejector. The article shows how the behavior of the ejector can be evaluated with different independent approaches, namely experimental tests, analytical iterative and quantum-based methods, and the computational fluid dynamics (CFD) numerical simulations, with the quantum algorithm achieving reasonable practical results compared with the other methods, thus the article highlights how this method can be effectively implemented to solve thermo-fluid dynamic problems given its advantages and besides its intrinsic limitations.
Recent advancements in quantum computing have demonstrated significant potential for solving combinatorial optimization problems, like the quadratic knapsack problem, a constrained binary optimization problem. However, current quantum and quantum-inspired algorithms often require transforming these constrained problems into an unconstrained form, known as Quadratic Unconstrained Binary Optimization (QUBO). Such transformations can significantly impact the algorithms’ speed and efficiency. In this study, we evaluate five existing transformation methods and propose four novel approaches. We assess all nine methods using Simulated Annealing and find that three of our approaches outperform existing methods in terms of execution time and the quality and quantity of feasible solutions found. Additionally, we tested these transformations on quantum annealers, which were unable to solve even small problem instances, due to limitations in connectivity and error rates. However, our results highlight the advantages of the new approaches, which reduce the total number of variables in the QUBO representation. This is a critical factor for enhanced performance on emerging quantum hardware, since it also reduces the required number of qubits and the embedding chain lengths.
Recent advancements in quantum computing have demonstrated significant potential for solving combinatorial optimization problems, like the quadratic knapsack problem, a constrained binary optimization problem. However, current quantum and quantum-inspired algorithms often require transforming these constrained problems into an unconstrained form, known as Quadratic Unconstrained Binary Optimization (QUBO). Such transformations can significantly impact the algorithms’ speed and efficiency. In this study, we evaluate five existing transformation methods and propose four novel approaches. We assess all nine methods using Simulated Annealing and find that three of our approaches outperform existing methods in terms of execution time and the quality and quantity of feasible solutions found. Additionally, we tested these transformations on quantum annealers, which were unable to solve even small problem instances, due to limitations in connectivity and error rates. However, our results highlight the advantages of the new approaches, which reduce the total number of variables in the QUBO representation. This is a critical factor for enhanced performance on emerging quantum hardware, since it also reduces the required number of qubits and the embedding chain lengths.
This paper introduces an innovative approach to explore the capabilities of Quantum Annealing (QA) for trajectory optimization in dynamic systems. The proposed method involves transforming trajectory optimization problems into equivalent binary optimization problems using Quadratic Unconstrained Binary Optimization (QUBO) representation. The procedure is general and adaptable, making it applicable to a wide range of optimal control problems that entail the satisfaction of dynamic, boundary, and path constraints. Specifically, the trajectory is discretized and approximated using polynomials. In contrast to the conventional approach of determining the polynomial degree (n) solely based on the number of boundary conditions, a specific factor is introduced in our method to augment the polynomial degree. As a result, the ultimate polynomial degree is calculated as a composite of two components: n = l + (m−1), where m denotes the count of boundary conditions and l signifies the number of independent variables. By leveraging inverse dynamics, the control required to follow the approximated trajectory can be determined as a linear function of independent variables l. As a result, the optimization function, which is represented by the integral of the square of the control, can be formulated as a QUBO problem and the QA is employed to find the optimal binary solutions.
Recent advancements in quantum computing have demonstrated significant potential for solving combinatorial optimization problems, like the quadratic knapsack problem, a constrained binary optimization problem. How- ever, current quantum and quantum-inspired algorithms often require transforming these constrained problems into an unconstrained form, known as Quadratic Unconstrained Binary Optimization (QUBO). Such transfor- mations can significantly impact the algorithms’ speed and efficiency. In this study, we evaluate five existing transformation methods and propose four novel approaches. We assess all nine methods using Simulated An- nealing and find that three of our approaches outperform existing methods in terms of execution time and the quality and quantity of feasible solutions found. Additionally, we tested these transformations on quantum annealers, which were unable to solve even small problem instances, due to limitations in connectivity and error rates. However, our results highlight the advantages of the new approaches, which reduce the total num- ber of variables in the QUBO representation. This is a critical factor for enhanced performance on emerging quantum hardware, since it also reduces the required number of qubits and the embedding chain lengths.