Identification Of Heat Flux Research Articles

Identification of the surface heat flux of charring ablative materials using dynamic Bayesian network based on multisource information fusion

In order to solve the dual uncertainty problem between heat flux and thermophysical properties in the identification of the heat flux of charring ablative materials, a dynamic Bayesian network (DBN) based on multisource information fusion is proposed. The method is divided into two stages, with thermophysical properties identified in the former stage and the heat flux identified in the latter stage. A one-dimensional pyrolysis layer model is adopted to characterize the ablation process of materials. In the DBN, the multisource information of surface recession and temperature history data are considered as observation nodes. Sensitivity analysis is used to determine the key parameters in each time step in the DBN, and only key parameters are identified in the corresponding time step. Thus, with the increase of types of information and the decrease of the number of simultaneous identification parameters, the identification accuracy can be improved. The method was verified by numerical and experimental cases. In the numerical cases with noise and experimental cases, the maximum error of using the proposed method was 3.27% and 2.55%, respectively. Compared with only considering the temperature information, the relative errors of the identification results considering multisource information fusion were reduced by 83.95% and 47.53%, respectively.

Defect model modification method for thermal protection system with surface heat flux identification

Thermal protection systems (TPS) have become a key issue in ensuring the reliability of hypersonic flights. Aimed at monitoring the thermal loads and possible defects for TPS, a defect model modification method with surface heat flux identification is proposed in this paper. Firstly, by the measured temperature from a distributed sensor network and the initial TPS model, the surface heat flux was identified with the Levenberg–Marquardt Method (LMM). If there existed outliers in the identified heat flux distribution, it can be visually indicated that the defect occurred. Then, defects were represented by shape parameters and can be determined by the model modification from the knowledge of the identified heat flux and the measured temperature. The effectiveness of the proposed method was verified numerically using TPS containing a surface defect. Meanwhile, the effects of various factors on the identified results were investigated in detail, such as defect sizes, defect shapes, sensor locations, and real aerodynamic heating. Finally, the proposed method was successfully applied to an experiment, and results demonstrated that the proposed method can achieve good identification results by experimentally measured temperature.

Heat Flux Identification of Aircraft Structure with Artificial Neural Network Compensation

Aerodynamic heating measurement of reusable hypersonic vehicles has always been an important aspect of hypersonic vehicle design. In this paper, a mechanistic-model-based heat flux identification method with artificial neural network (ANN) compensation is established to determine the spatially distributed heat flux of the aircraft structure. A one-dimensional heat conduction model is used to estimate heat flux by a robust and efficient algorithm integrating Tikhonov regularization with Levenberg–Marquardt method. The one-dimensional estimated heat flux has large errors for not considering multidimensional heat conduction effects. The proposed mechanistic-model-based method is then utilized to compensate the multidimensional heat conduction by ANN. The performance of the proposed method will be assessed by the determination of the heat flux of a two-dimensional plate and aircraft structure. Results show that compared with the one-dimensional inversion results, ANN compensation method can significantly improve the accuracy of estimated heat flux and is also applicable for larger levels of heat flux. The proposed compensation method is an effective technique to identify the nonuniform surface heat flux of multidimensional structures.

A quick surface heat flux estimation method for typical structures of high-speed aircrafts

Surface heat flux estimation of high-speed aircrafts is an inverse problem and high system ill-posedness usually leading to instability and low accuracy. In this study, an efficient method is proposed to solve it stably. The heat flux identification equation is established based on the superposition principle. Tikhonov regularization method with the parameter determined by generalized cross validation is applied to reduce the sensitivity to measurement error. A calibration method is presented to correct the pulse sensitivity coefficient matrix so that the estimation method can be used for complex three-dimensional structures. Numerical studies demonstrate the efficiency and accuracy.

An ML-based approach for inverse identification of heat flux in machining

This study presents an efficient and robust inverse approach to obtain the heat flux distribution on the tool rake face in oblique cutting including the tool nose radius. In this approach, Machine Learning (ML) is used to establish the relation between the parameters associated with the heat flux distribution and the error functions expressing the deviation between the embedded thermocouple measurements and Finite Element (FE) simulations. The dependency of the algorithm on the number of input data, the optimization strategy, and the overall performance of the approach are studied. The results show a clear potential of the proposed ML-based inverse identification approach.

Experimental study on critical heat flux during flow boiling of R134a in a vertical helically coiled tube

This paper carried out an experimental study on the critical heat flux during flow boiling of R134a in a vertical helically coiled tube. The length, inner diameter, coil diameter, and pitch of the test tube were 1.85 m, 8 mm, 205 mm, and 25 mm, respectively. Experiments cover the mass flux range of 190–400 kg·m−2·s−1, heat flux of 15–55 kW·m−2, inlet pressure of 0.8–1.1 MPa, and inlet vapor quality of 0.01–0.35. The effects of critical heat flux identification method, mass flux, system pressure, and inlet vapor quality on critical heat flux were presented. The critical heat flux obtained by the wall temperature rise method was larger than that obtained by the wall temperature oscillation method. The deviation of the critical heat flux corresponding to two methods, including wall temperature rises sharply above 10 ℃ and wall temperature drastic oscillation, was about 20% under the present experimental conditions. The critical heat flux increased with mass flux while it decreased with the inlet vapor quality and pressure. The experiment data were compared with four existing empirical correlations. A new correlation is proposed for critical heat flux prediction in vertical helical tubes.

Identification of heat flux and heat transfer coefficient during water spray cooling of horizontal copper plate

Heat transfer coefficient (HTC) and heat flux (HF) at the copper plate during water-air assisted spray cooling from 700 °C to the ambient temperature was evaluated. For the HTC and HF identification the inverse method has been implemented. A self-developed computer code based on finite element method (FEM) has been used to solve the heat conduction problem. The FEM solver utilizing linear and nonlinear shape functions has been first compared with the analytical solution to the plate cooling. Further, the reduced finite element model employed in the inverse solution has been compared with the reference model for plate cooling under variable in time and space HTC. The boundary condition at the water spray cooled surface obtained from earlier researches has been employed in the uncertainty tests. The conducted tests have allowed determining the uncertainty of the inverse solution to HTC. A part of research includes the experimental study, which consist of the temperature measurements inside the copper plate during water spray cooling. The measured temperatures have been used as an input data for the local HTC and HF identification and development of a local HTC and HF models. The models have allowed retrieving the water flux rate, fluid pressure and the nozzle to plate distance influence on the boiling curve parameters. The boundary condition models define HF and HTC as functions of a local plate surface temperature.

An inverse meshfree method for heat flux identification based on strain measurement

A new method for identification of unknown heat fluxes is proposed in this paper. The proposed identification method is based on the measured strains, rather than the usual temperature measurements. The basic idea of this work is that the thermal response of systems is much slower than their mechanical response. This means that when a heat flux is applied to a sufficiently constrained member, the strain field develops much faster than the temperature field. Therefore, the time variations of the applied heat flux can be better identified if the strain measurements are utilized. Especial attention is paid to problems in which large heat fluxes or thermal shocks are applied to a structure. In such problems, a large temperature gradient develops near the boundary and a rigorous analysis is required in order to obtain accurate distribution of the temperature and strain fields. In this work, an efficient meshfree method is used for fast and accurate analysis of the associated direct problems.

Solving of Two-Dimensional Unsteady Inverse Heat Conduction Problems Based on Boundary Element Method and Sequential Function Specification Method

The boundary element method (BEM) and sequential function specification method (SFSM) are used to research the inverse problem of boundary heat flux identification in the two-dimensional heat conduction system. The future time step in the SFSM is optimized by introducing the residual error principles to get the more accurate inversion results. For the forward problems, the BEM is used to calculate the required temperature value of discrete point; for the inverse problems, the impacts of different future time steps, measuring point position, and measuring error on the inversion results are discussed. Furthermore, the comparison is made for the optimal future time step obtained by introducing the residual error principle and the inherent future time step. The example analysis shows that the method proposed still has higher accuracy when the measuring error exists or the measuring point position is far away from the boundary heat flux.

Heat Flux Identification at the Charge Surface During Heating in Chamber Furnace

AbstractIn this study, a method of determining the heat flux, which reaches the surface of a charge, has been presented with the use of an inverse analysis. The research on the heating process of a square 15HM steel charge was conducted in a natural gas-fired laboratory furnace. The inverse solution was based on the search of the minimum standard error between the measured and the calculated temperatures. The temperature of the charge has been calculated by the finite element method, solving the heat conduction equation for a square charge heated on all the surfaces. As a result, the mean value of the heat flux on each of the heated surfaces of the charge was estimated.

The heat flux identification problem for a nonlinear parabolic equation in 2D

We consider the heat flux identification problem (HFIP) based on the boundary measurements for a nonlinear parabolic equation in 2-dimensional space. The standard linearization algorithm is applied to the nonlinear direct problem. The method of Conjugate Gradient Algorithm, based on the gradient formula for the cost functional, is then proposed for numerical solution of the inverse heat flux problem. Numerical analysis of the algorithm applied to the inverse problem in typical classes of flux functions is presented. Computational results, obtained for random noisy output data, indicate how the iteration number of the Conjugate Gradient Algorithm can be estimated. Numerical results illustrate bounds of applicability of proposed algorithm, as well as its efficiency and accuracy.

On inverse boundary thermal conductivity problem of recovery of heat fluxes to the boundaries of anisotropic bodies

A method for solution of the inverse boundary thermal conductivity problem of recovery of the heat fluxes to the structural components of aircraft fabricated of anisotropic materials is proposed. The method is based on a previously obtained analytical solution of a 2D nonstationary thermal conductivity problem in an anisotropic fin under boundary heat transfer. The method consists in parametric identification and finite-element approximation of the dependence of the heat flux on the spatial variable. A regularizing algorithm is developed that permits identification of heat fluxes with large, up to 10%, errors in the experimental temperature values. The results obtained in numerical experiments are analyzed.

Experimental disc heat flux identification on a reduced scale braking system using the inverse heat conduction method

This work focuses on the local heat fluxes on a disc during braking conditions. The generated heat and the temperature field are identified using an inverse heat conduction method coupled to temperature measurements inside the disc. Function specification is used to estimate the boundary conditions in the model without any prior information on the flux intensity and the evolution regarding the time and the position on the sliding surface. Disc heat flux identifications are performed for different braking conditions (sliding speed and normal pressure) on a High-Speed Tribometer. The temperature values are obtained using a telemetry system that allows inductive data transfer. The influence of the braking conditions on the heat repartition and the surface temperature is discussed.

Experimental heat flux identification from a braking system

This article presents the branch eigenmodes reduction method (BERM) applied to the identification of the heat flux dissipated during the friction between a disc rotating at variable speed and two brake pads. Temperature measurements used to identify fluxes in the disc and in the pad come from experimental data. One of the method's strength lies in its ability to greatly reduce the dimension of the numerical problem, while maintaining a satisfying precision on the whole computation domain. The reduction of the model enables us to perform the identification in a time compatible with real-time. The identified heat flux is coherent with the mechanical increase due to friction. Small discrepancies observed at the beginning of the friction sequence can be explained by wear.

On-line heat flux identification from a rotating disk at variable speed

This paper presents the Branch Eigenmodes Reduction Method (BERM) applied to the identification of a heat flux in an advection–diffusion model, with time dependent parameters. The treated application is a 2D disc brake whose velocity and thermal solicitations are time dependent. One of the method’s strength lies in its ability to greatly reduce the dimension of the numerical problem, while maintaining a satisfying precision on the entire computation domain. In the considered case, the inverse problem difficulties come from the transport phenomena which requires the use of very small time steps for its numerical resolution. In order comply with the on-line identification objective, a filtering technique is used.

An inverse method for non linear ablative thermics with experimentation of automatic differentiation

Thermal Protection System is a key element for atmospheric re-entry missions of aerospace vehicles. The high level of heat fluxes encountered in such missions has a direct effect on mass balance of the heat shield. Consequently, the identification of heat fluxes is of great industrial interest but is in flight only available by indirect methods based on temperature measurements. This paper is concerned with inverse analyses of highly evolutive heat fluxes. An inverse problem is used to estimate transient surface heat fluxes (convection coefficient), for degradable thermal material (ablation and pyrolysis), by using time domain temperature measurements on thermal protection. The inverse problem is formulated as a minimization problem involving an objective functional, through an optimization loop. An optimal control formulation (Lagrangian, adjoint and gradient steepest descent method combined with quasi-Newton method computations) is then developed and applied, using Monopyro, a transient one-dimensional thermal model with one moving boundary (ablative surface) that has been developed since many years by ASTRIUM-ST. To compute numerically the adjoint and gradient quantities, for the inverse problem in heat convection coefficient, we have used both an analytical manual differentiation and an Automatic Differentiation (AD) engine tool, Tapenade, developed at INRIA Sophia-Antipolis by the TROPICS team. Several validation test cases, using synthetic temperature measurements are carried out, by applying the results of the inverse method with minimization algorithm. Accurate results of identification on high fluxes test cases, and good agreement for temperatures restitutions, are obtained, without and with ablation and pyrolysis, using bad fluxes initial guesses. First encouraging results with an automatic differentiation procedure are also presented in this paper.

Heat flux characterisation in hot jet and flame/wall interaction by IHCP resolution coupled with infrared measurements

The aim of this work is to develop a method dedicated to the identification of heat fluxes between turbulent flames and 3D solids in order to improve the conception of aeronautic structures designed to endure and sustain fire events. Transient temperature modelling inside the impinged structure can only be realistic if the convective and radiative heat fluxes used as boundary conditions of the numerical model are accurately known. To do so, these two different heat transfer contributions are to be separated from the total heat flux information, obtained by solving an IHCP (Inverse Heat Conduction Problem). The inverse technique that was implemented for this study is based on adding back-face infrared measurements data as observation equation, thus closing this ill-posed problem. Infrared camera provides an accurate temperature map, allowing high resolution heat flux mapping without perturbing the impingement zone. The number of unknowns initially equal to the camera resolution is reduced by solving the problem in the cosine space thanks to Discrete Cosine Transform. As for the resolution of this multidimensional transient IHCP, Beck's inverse algorithm has been coupled to future time-steps stabilisation method. Flame to wall heat transfer knowledge is improved thanks to the study of a dedicated test bench composed of a propane / air burner on the one hand, and a 14kW air heater on the other hand. To take into account the spatial non-uniformity of the adiabatic wall temperature used in Nusselt calculation, a new adiabatic wall temperature computation is presented and compared to Nusselt calculations based on constant reference temperature. In the scope of this study, we present the comparison between propane/air flame and hot round isothermal air jet impinging perpendicularly on a titanium plate.

A method of rapid identification of heat fluxes

In design, development, and operation of crucial engineering systemssubjected to high heat fluxes, it is often necessary to observe the thermal state of the object in real time. The authors suggest an approach that is based on the methodology of solution of inverse heat-conduction problems (IHCP) and is a special adaptation of these methods for solution of observation problems. The approach is based on the idea of the possibility of identifying the current thermal state of the object with the use of measurements that are chronologically close to the current time, which leads to formulation of the retrospective boundary-value IHCP in a local time interval. A solution to this problem is considered, and results and estimates of the accuracy of simulation are presented.

Spline identification of heat fluxes

A method is discussed for the determination of one-dimensional transient heat fluxes from the experimentally measured temperature using a spline approximation of the heat flux with subsequent application of the procedures of parametric identification.