Acquisition of kHz-frequency two-dimensional surface temperature field using phosphor thermometry and proper orthogonal decomposition assisted long short-term memory neural networks

https://doi.org/10.1016/j.ijheatmasstransfer.2020.120662Get rights and content

Highlights

Abstract

A reconstruction technique of kHz time-resolved two-dimensional (2D) surface temperature field was achieved with the discrete point measurements and low sampling rate 2D thermographic phosphor (TP) thermometry measurements using a long short-term memory (LSTM) based artificial intelligence framework. The 2D surface temperature field of a 350 °C plate with a 2.5 Hz swing cooling jet was measured using TP thermometry at a sampling rate of 20 Hz. At the same time, high-frequency thermocouples with a sampling rate of 1 kHz were recorded for the construction of LSTM neural networks training and for validation. The 20 Hz 2D surface temperature field was analyzed with proper orthogonal decomposition to acquire the energy modes and model coefficients. The mode coefficients are then trained with the discrete but high-frequency time-resolved temperature information from the thermocouple by LSTM to acquire the time-resolved mode coefficients. Finally, the high-frequency time-resolved 2D surface temperature field is obtained by reconstructing modes and the time-resolved coefficients. The reconstructed result shows that the current technique can obtain high time-resolved and spatially resolved 2D surface temperature fields very well.

Introduction

As one of the basic physical parameters, the temperature is the foundation for understanding various physical phenomena such as chemical kinetics, combustion, heat transfer, and fluid mechanics. It is also the key indicator for evaluating the thermal performance of products in the industry. However, high-frequency time-resolved temperature acquisition, especially for the two-dimensional (2D) time-resolved temperature measurement, which has always been a difficult task as the limitation of the measurement technique. While for the study of internal combustion engines, gas turbines, material heat treatment, and thermal turbulence, accuracy acquisition of 2D high-frequency time-resolved temperature information is necessary. Recently years, with the development of coherent anti-Stokes Raman scattering (CARS) [1,2] and infrared spectrometer (IR) techniques, 2D time-resolved temperature measurement techniques have been initially realized in a laboratory environment by 2D-CARS [3,4], and 2D-IR [[5], [6], [7]]. Despite this, considering the high equipment cost (high-frequency high-energy laser or high energy diode pump), complicated system setup, and involuted post-processing process of the above technology, the practical application of these techniques is difficult. On the other hand, the measurement area of the above techniques is usually in μm or mm scale, which limits their future development. Thus, it is necessary to develop a new technique to realize a 2D time-resolved temperature acquisition technique.

Thermographic phosphor (TP) thermometry [[8], [9], [10]] is a newly developed temperature measurement technique, which has been applied in the area of surface [11] temperature measurement and fluid [12,13] temperature measurement due to its advantages of non-intrusiveness, high accuracy, and high spatial resolution and large area measurement. Its measurement is relatively simple, requiring only an excitation light source, a signal detector (spectrometer, photomultiplier tube (PMT), or camera), and appropriate phosphor. The precisions of TP measurement can be within 5% [[14], [15], [16]]. Especially for the lifetime based TP measurement, its measurement precisions have reached to within 1% [17]. Successful application included temperature measurement in combustion engine [18,19], jet cooling [20], film cooling [[21], [22], [23]], and fuel burning [24].

In recent years, the study of TP began to focus on high-frequency time-resolved 2D temperature measurement. A 6 kHz time-resolved point TP measurement has been performed for the first time by Fuhrmann et al. [25] in 2011 using a lifetime-based method. And it was then applied to measure cylinder head temperatures within an optically accessible internal combustion engine under fired operation [26]. Based on the slope of the exponential anti-Stokes emission tail of the phosphorescence, a spectral based phosphor thermometry technique with 5 kHz sampling rate for point measurements has been developed by Yan et al. [15]. The only reported 2D high-frequency TP measurement was from Abram et al. [14], which realized a 3kHz 2D TP temperature measurements of gas using the intensity ratio method. And it was then successfully be applied to the temperature field measurements in the flow emanating from angled and trenched film cooling holes [23]. Limited by the equipment and luminescent characteristics of phosphor material, the lifetime method with more advantages in measurement accuracy and spatial resolution [27] is still limited to high-frequency point measurement. If a high-frequency temperature field acquisition based on the phosphorescence lifetime can be achieved, the prospects for temperature measurement will become very broad. And its application value will be very attractive since it has advantages of high-accuracy, non-contact, two-dimensional, high temporal resolution, high spatial resolution. To make this purpose, an alternative option is to introduce neural network algorithms into the measurement to obtain data with high temporal resolution.

Neural networks have been effectively combined with measurement in the past decade [28,29]. Although most of them focus on fluid mechanics, this method of combining measurement with neural networks shows excellent performance in the temporal and spatial resolution enhancement [[30], [31], [32], [33]]. Based on the long short-term memory (LSTM) neural networks, Deng et al. [32] realized a 2kHz time-resolved flow field acquisition using the data from a 5 Hz 2D-PIV and 2 kHz discrete point measurement. Similarly, the time-resolved flow field around a circular cylinder was acquired by Jin et al. [34] using bidirectional recurrent neural networks (RNNs) with 5 Hz PIV measurement data and high-frequency probes measured data. These studies provide a feasible approach to get a time-resolved field with high accuracy using neural networks and show that neural networks could be applied in a complex experimental field to acquire a high-frequency time-resolved filed information [35]. Among many neural networks algorithms, long short-term memory (LSTM) neural networks, as one of the powerful neural networks algorithms for processing time sequence data, is considered the most effective tool for the temporal resolution enhancement, especially when it been combined with proper orthogonal decomposition (POD) [36]. POD [37,38] could decompose the dynamic data set obtained from multiple measurements to obtain a set of low-dimensional optimal basis that can represent the original complex dynamic system. Since POD is mathematically optimal for any given data set, POD assisted LSTM is feasible for nonlinear unsteady response predictions and reconstructions [29]. As in the study of Jin X et al. [34], the time-resolved flow field around a circular cylinder was reconstructed using recurrent neural networks combined with POD coefficients. The high-frequency velocity-probe signals were selected as the inputs of the network and the POD coefficients are the outputs. The time-resolved flow filed was reconstructed successfully with the first few POD modes, in which the strategy is similar with Deng et al. [32]. Mohan and Gaitonde [39] proposed an approach that combined LSTM and POD coefficients to build the reduced-order-mode for turbulent flow control. They successfully predicted the changing regularity of the POD coefficients using LSTM networks with the input of the previous POD coefficients. However, to the best of the author's knowledge, most of the studies are focused on velocity field measurement. Few studies have been conducted on neural-network-based high-frequency time-resolved temperature field acquisition, especially for the study combining with advanced TP temperature measurement technique.

In this study, network-based high-frequency time-resolved 2D surface temperature field acquisition using low-frequency phosphor thermometry and high-frequency thermocouples was tried for the first time. To acquire a time-resolved swing-jet cooling temperature field, a 20 Hz 2D-surface temperature measurement using TP and 1 kHz points-temperature measurement using 7 thermocouples was conducted. During the data process, a set of POD mode and mode coefficients are obtained at first by performing POD decomposition on the low-frequency 2D surface temperature results. After that, the data of high-frequency point measurement is filtered using the 2D surface temperature sampling frequency, and the discrete-point temperature results at the same frequency as the low-frequency 2D surface temperature measurement are obtained. Taking the discrete point temperature measurement results obtained by screening as input and low sampling rate mode coefficients as output, an LSTM mode is then established by neural network training. The original high-frequency discrete points are input into the LSTM mode to obtain the high-frequency POD modal coefficients. Finally, the high-frequency POD modal coefficients and the POD modal obtained in the first step are reconstructed, and the high-frequency 2D information field is successfully obtained. The reconstructed temperature field shows excellent time-resolved and spatially resolved performance. The current method developed a TP-AI combined 2D surface temperature measurement technique, which provides a new way to obtain high-frequency 2D surface temperature field information. The currently developed AI-assisted TP temperature measurement method is a non-contact, high frequency and high spatial resolution in-situ surface-temperature measurement method. It could provide the high-frequency 2D surface temperature information with a simple phosphor coating and several thermocouples. And because it measures temperature based on the decay of phosphorescence, it will not be affected by infrared radiation and other noise light, which makes the measurement accuracy very high.

Section snippets

Lifetime based phosphor thermometry

Phosphor thermometry is a non-contact temperature measurement technique that uses the relationship of phosphorescence and temperature to measure temperature [[8], [9], [10]]. Based on the phosphorescent characteristics, the measurement methods mainly include the intensity-based method, lifetime-based method, and rise-time method. In this study, the high-accuracy lifetime-based method was used. As shown in Fig. 1, the lifetime method is based on the dependency of a phosphorescent lifetime (or

Phosphor and coating

Commercially available Mg4FGeO6:Mn4+ (MFG) (CRE Jiangsu, China) is used in this study. The molar concentration of Mn4+ in current MFG is 0.01% and the average diameter of the MFG particle is 6 μm. During the preparation of temperature sensing coating, MFG particle was mixed with Hydroxypropyl cellulose (HPC) binder (ZYP Coatings Inc., Oak Ridge, USA) in a mass ratio of 1:3 and sprayed onto a 10 cm  ×  20 cm aluminum plate using an airbrush. In order to improve bonding and signal strength, the

Calibration results

Fig. 6 shows the calibration results of phosphor MFG. Eight calibration points (with each point representing an average of ten measurements) were arranged from 296 to 623 K. A linear fit was used. The adjusted R-Square for the fit is 0.996. It can be seen that the phosphorescence lifetime decreases gradually as the temperature rises. The red bars in the figure represent the uncertainty of calibration which is calculated with the 10 repeated calibrations. The repeatability of the entire

Results of POD analysis

To acquire the mutually orthogonal POD modes and low sampling rate POD mode coefficients, POD analysis was conducted on a larger number of 2D fluctuation temperature fields in this study. A POD eigenvalue represents the intensity level of its corresponding mode, while the POD modes were considered as basic temperature oscillations. As mentioned in the section of ‘High-frequency 2D temperature field reconstruction’, it needs to make sure that there are enough samples for POD decomposition.

Conclusions

A novel kHz-frequency 2D surface temperature field acquiring technique was introduced in this study. 1 kHz thermocouples and 20 Hz 2D surface phosphor thermometry were used in this study to capture the point-discrete high-frequency temperature and low-frequency 2D surface temperature information respectively. POD-assisted LSTM mode was then used to establish the relationship between the high-frequency temperature signals of discrete points and the high-frequency time-resolved POD mode

Author contributions

T. Cai and Z. Deng contributed equally for doing experiments and preparing the manuscript. Y. Park and S. Mohammadshahi contributed data processing and analysis. Y. Liu contributed for discussion of results and proof-reading the manuscript. K.C. Kim contributed for supervising experiments, discussion of results and proof-reading the manuscript.

Supporting material

Dynamic results of 2D fluctuation temperature field measured by TP-20 Hz (gif)

The whole dynamic process of the 2D fluctuation

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could influence the work reported in this paper.

Acknowledgment

This work was supported by the National Research Foundation of Korea (NRF) grant, which is funded by the Korean government (MSIT) (No. 2020R1A5A8018822, No. 2018R1A2B2007117). Support was also provided by the Korea Research Fellowship Program from NRF (KRF-2019H1D3A1A01071033).

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