Surface heat flux prediction through physics-based calibration: part 1- theory

Frankel, J. I.; Keyhani, M.; Elkins, Bryan

doi:10.2514/6.2012-222

Cited by 10 publications

(11 citation statements)

References 26 publications

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“…Depending on the method used, ht can be determined from analytical models or calibration measurements [10,20,21]. When performing a time discretization with θ marking the duration of a time step and t the measurement time, the convolution integral in Eq.…”

Section: Theorymentioning

confidence: 99%

Theoretical Stability Analysis for Inverse Heat Conduction Problems Using the Condition Number

Fuchs

Löhle

Fasoulas

2015

Journal of Thermophysics and Heat Transfer

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In this paper, an analysis of the conditioning of methods solving the inverse heat conduction problem is shown. A method is developed that connects the stability of the inverse solution, measured by the condition number, to the physical properties of the problem. The approach is based on norm and eigenvalue analysis of the matrix representation of the discretized inverse heat conduction problem. This formula can be applied to methods that are based on the utilization of the heat kernel. It can be used in order to determine the optimal setup for surface heat flux measurements.regularized by sequential function estimation method A VC = A regularized by van Cittert scheme a ij = element of A c = specific heat capacity d = distance to the nearest surface, mm g = arbitrary function h = fundamental solution, K · m 2 ∕J h a = regularized time-discrete fundamental solution, K · m 2 ∕J h p = numerical time discrete fundamental solution, K · m 2 ∕J k = thermal conductivity, W∕m · K _ q = surface heat flux density, W∕m 2 T = temperature, K t = time, s t f = regularization time, s t p= penetration time, s x, y, z = spatial variables, mm α = thermal diffusivity, m 2 ∕s δA = modeling error δ _ q = surface heat flux error δT = temperature measurement error θ = time-step size, s θ 0 = regularization time shift, s κ = condition number λ = eigenvalue ξ, τ = integration variables ρ = density, kg∕m 3 χ = dimensionless time-step size; α · θ∕d 2 k · k F = Frobenius norm k · k 1 , k · k ∞ = operator norms k · k 2 = spectral norm

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Section: Theorymentioning

confidence: 99%

Theoretical Stability Analysis for Inverse Heat Conduction Problems Using the Condition Number

Fuchs

Löhle

Fasoulas

2015

Journal of Thermophysics and Heat Transfer

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“…Theoretical research on boiling mechanisms provided the foundations for heat flux estimation 15 – 18 . However, the intrinsic complexity of the dynamic boiling phenomena has limited those theoretical studies to very simplified models 19 , 20 . With numerical simulations, single to multi-bubble physics are investigated for detailed characterization of heat flux 21 – 23 .…”

Section: Introductionmentioning

confidence: 99%

Deep learning predicts boiling heat transfer

Suh

Bostanabad

Won

2021

Sci Rep

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Boiling is arguably Nature’s most effective thermal management mechanism that cools submersed matter through bubble-induced advective transport. Central to the boiling process is the development of bubbles. Connecting boiling physics with bubble dynamics is an important, yet daunting challenge because of the intrinsically complex and high dimensional of bubble dynamics. Here, we introduce a data-driven learning framework that correlates high-quality imaging on dynamic bubbles with associated boiling curves. The framework leverages cutting-edge deep learning models including convolutional neural networks and object detection algorithms to automatically extract both hierarchical and physics-based features. By training on these features, our model learns physical boiling laws that statistically describe the manner in which bubbles nucleate, coalesce, and depart under boiling conditions, enabling in situ boiling curve prediction with a mean error of 6%. Our framework offers an automated, learning-based, alternative to conventional boiling heat transfer metrology.

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“…Inverse problems naturally arise as one attempts to reconstruct the cause of a phenomenon from observables. These problems occur in many fields and contexts that include vibrations (Brownjohn et al, 2016; Chaigne, 2016; Jingjing, 2019; Vyas and Wicks, 2001; Woods and Lawrence, 1997) and heat transfer (Frankel and Keyhani, 2017; Frankel et al, 2013, 2017). Single equation and systems of equations are naturally formulated in the modeling of dynamic systems (Woods and Lawrence, 1997).…”

Section: Introductionmentioning

confidence: 99%

“…The calibration integral equation (Frankel and Keyhani, 2017; Frankel et al, 2013, 2017) was designed to resolve the so-called “inverse heat conduction problem” (Beck et al, 1985) associated with boundary condition reconstruction given in-depth measurements. In the context of vibrations, the inverse problem would be stated as “What is the forcing or driving function of a system given discretely measured temporal displacement, velocity, or acceleration data contaminated with noise?” Frankel and his colleagues (2013, 2017) have theorized and experimentally validated a novel parameter-free inverse methodology for the inverse heat conduction problem (Frankel and Keyhani, 2017; Frankel et al, 2013, 2017) based on partial differential equations (Sneddon, 1995).…”

Section: Introductionmentioning

confidence: 99%

“…This regularization works by introducing an l2 norm penalty, thus penalizing solution magnitude. The Tikhonov method is within a matrix paradigm, whereas the calibration integral equation uses a “time-marching” paradigm (Jacquelin et al, 2003; Frankel and Keyhani, 2017; Frankel et al, 2013, 2017). In practice, these paradigms are identical, but the resulting methods have their own resulting strengths.…”

Section: Introductionmentioning

confidence: 99%

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Estimating the forcing function in a mechanical system by an inverse calibration method

Rice

Frankel

2021

Journal of Vibration and Control

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This article proposes and demonstrates a calibration-based integral formulation for resolving the forcing function in a mass–spring–damper system, given either displacement or acceleration data. The proposed method is novel in the context of vibrations, being thoroughly studied in the field of heat transfer. The approach can be expanded and generalized further to multi-variable systems associated with machine parts, vehicle suspensions, translational and rotational systems, gear systems, etc. when mathematically described by a system of constant property, linear, time-invariant ordinary differential equations. The analytic approach and subsequent numerical reconstruction of the forcing function is based on resolving a parameter-free inverse formulation for the equation(s) of motion. The calibration approach is formulated in the frequency domain and takes advantage of several observations produced by the dimensionality reduction leading to an algebratized system involving an input–output relationship and a transfer function possessing all the system parameters. The transfer function is eliminated in lieu of experimental data, from a calibration effort, thus leading to a reduction of systematic errors. These parameter-free, reduced systematic error aspects are the distinct and novel advantages of the proposed method. A first-kind Volterra integral equation is formed containing only the unknown forcing function and experimental data. As with all ill-posed problems, regularization must be introduced for system stabilization. A future-time technique is instituted for forming a family of predictions based on the chosen regularization parameter. The optimal regularization parameter is estimated using a combination of phase–plane analysis and cross-correlation principles. Finally, a numerical simulation is performed verifying the proposed approach.

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Surface heat flux prediction through physics-based calibration: part 1- theory

Cited by 10 publications

References 26 publications

Theoretical Stability Analysis for Inverse Heat Conduction Problems Using the Condition Number

Theoretical Stability Analysis for Inverse Heat Conduction Problems Using the Condition Number

Deep learning predicts boiling heat transfer

Estimating the forcing function in a mechanical system by an inverse calibration method

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