Inverse identification of boundary conditions in a scramjet combustor with a regenerative cooling system

Cui, Miao; Mei, Jianqin; Zhang, Bowen; Xu, Bing‐Bing; Zhou, Ling; Zhang, Yuwen

doi:10.1016/j.applthermaleng.2018.02.038

Cited by 27 publications

(3 citation statements)

References 49 publications

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“…Compared with experimental measurements, numerical simulations could significantly reduce cost and save time. Numerical studies indicated that for a regenerative cooling combustor, the boundary conditions and heat transfer of the combustor wall could be solved by the gradient-based method [11]. The numerical investigation of Wang et al [12] indicated that the wall heat flux is greatly influenced by the flow and combustion characteristics, which leads to the high non-uniform distribution of heat flux in the supersonic combustor.…”

Section: Introductionmentioning

confidence: 99%

A Parametrical Study on Convective Heat Transfer between High-Temperature Gas and Regenerative Cooling Panel

Wang

Zhang

et al. 2021

Energies

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Thermal protection is still one of the key challenges for successful scramjet operations. In this study, the three-dimensional coupled heat transfer between high-temperature gas and regenerative cooling panel with kerosene of supercritical pressure flowing in the cooling channels was numerically investigated to reveal the fundamental characteristics of regenerative cooling as well as its influencing factors. The SST k-ω turbulence model with low-Reynolds-number correction provided by the pressure-based solver of Fluent 19.2 is adopted for simulation. It was found that the heat flux of the gas heated surface is in the order of 106 W/m2, and it declines along the flow direction of gas due to the development of boundary layer. Compared with cocurrent flow, the temperature peak of the gas heated surface in counter flow is much higher. The temperature and heat flux of the gas heated surface both rises with the static pressure and total temperature of gas. The heat flux of the gas heated surface increases with the mass flow rate of kerosene, and it hardly changes with the pressure of kerosene. Results herein could help to understand the real heat transfer process of regenerative cooling and guide the design of thermal protection systems.

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Section: Introductionmentioning

confidence: 99%

A Parametrical Study on Convective Heat Transfer between High-Temperature Gas and Regenerative Cooling Panel

Wang

Zhang

et al. 2021

Energies

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“…However, in practice, it is difficult to measure the upstream conditions due to the challenges in diagnostic at harass environment and the constraints of cost. Therefore, computational tools aiming at the inference of unknown information based on available measurements have been developed and are often termed as inverse models [1,2,3]. Conventional inverse modeling methods are usually limited to a few unknown parameters and suffering from the curse of dimensionality since the computational cost increases significantly as the number of unknown quantities increases.…”

Section: Introductionmentioning

confidence: 99%

Neural Differential Equations for Inverse Modeling in Model Combustors

Zhang

et al. 2021

Preprint

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Monitoring the dynamics processes in combustors is crucial for safe and efficient operations. However, in practice, only limited data can be obtained due to limitations in the measurable quantities, visualization window, and temporal resolution. This work proposes an approach based on neural differential equations to approximate the unknown quantities from available sparse measurements. The approach tackles the challenges of nonlinearity and the curse of dimensionality in inverse modeling by representing the dynamic signal using neural network models. In addition, we augment physical models for combustion with neural differential equations to enable learning from sparse measurements. We demonstrated the inverse modeling approach in a model combustor system by simulating the oscillation of an industrial combustor with a perfectly stirred reactor. Given the sparse measurements of the temperature inside the combustor, upstream fluctuations in compositions and/or flow rates can be inferred. Various types of fluctuations in the upstream, as well as the responses in the combustor, were synthesized to train and validate the algorithm. The results demonstrated that the approach can efficiently and accurately infer the dynamics of the unknown

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“…Inverse problems are widely used in technological problems, such as cooling blades in turbines (Frąckowiak and Ciałkowski, 2018; Frąckowiak et al , 2015b), analysis of heat flow in pipes (Cebula et al , 2018; Jaremkiewicz and Taler, 2017; Taler et al , 2016) and other components of boilers (Taler et al , 2017). Solution of the inverse problem is also used to analyse the heat flow in a scramjet combustor with a regenerative cooling system (Cui et al , 2018) and in mini channels (Hożejowska et al , 2009; Maciejewska and Piasecka, 2017). It can be a basis for development of calculation methods enabling to obtain stable solutions to inverse problems minimizing the sensitivity of these solutions to disturbances to measurement data.…”

Section: Introductionmentioning

confidence: 99%

Stable method for solving the Cauchy problem with the use of Chebyshev polynomials

Joachimiak

Ciałkowski

Frąckowiak

2019

HFF

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Purpose The purpose of this paper is to present the method for solving the inverse Cauchy-type problem for the Laplace’s equation. Calculations were made for the rectangular domain with the target temperature on three boundaries and, additionally, on one of the boundaries, the heat flux distribution was selected. The purpose of consideration was to determine the distribution of temperature on a section of the boundary of the investigated domain (boundary Γ1) and find proper method for the problem regularization. Design/methodology/approach The solution of the direct and the inverse (Cauchy-type) problems for the Laplace’s equation is presented in the paper. The form of the solution is noted as the linear combination of the Chebyshev polynomials. The collocation method in which collocation points had been determined based on the Chebyshev nodes was applied. To solve the Cauchy problem, the minimum of functional describing differences between the target and the calculated values of temperature and the heat flux on a section of the domain’s boundary was sought. Various types of the inverse problem regularization, based on Tikhonov and Tikhonov–Philips regularizations, were analysed. Regularization parameter α was chosen with the use of the Morozov discrepancy principle. Findings Calculations were performed for random disturbances to the heat flux density of up to 0.01, 0.02 and 0.05 of the target value. The quality of obtained results was next estimated by means of the norm. Effect of the disturbance to the heat flux density and the type of regularization on the sought temperature distribution on the boundary Γ1 was investigated. Presented methods of regularization are considerably less sensitive to disturbances to measurement data than to Tikhonov regularization. Practical implications Discussed in this paper is an example of solution of the Cauchy problem for the Laplace’s equation in the rectangular domain that can be applied for determination of the temperature distribution on the boundary of the heated element where it is impossible to measure temperature or the measurement is subject to a great error, for instance on the inner wall of the boiler. Authors investigated numerical examples for functions with singularities outside the domain, for which values of gradients change significantly within the calculation domain what corresponds to significant changes in temperature on the wall of the boiler during the fuel combustion. Originality/value In this paper, a new method for solving the Cauchy problem for the Laplace’s equation is described. To solve this problem, the Chebyshev polynomials and nodes were used. Various types of regularization of this problem were considered.

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Inverse identification of boundary conditions in a scramjet combustor with a regenerative cooling system

Cited by 27 publications

References 49 publications

A Parametrical Study on Convective Heat Transfer between High-Temperature Gas and Regenerative Cooling Panel

A Parametrical Study on Convective Heat Transfer between High-Temperature Gas and Regenerative Cooling Panel

Neural Differential Equations for Inverse Modeling in Model Combustors

Stable method for solving the Cauchy problem with the use of Chebyshev polynomials

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