Radial Temperature Research Articles

A Physics Informed Neural Network for Solving the Inverse Heat Transfer Problem in Gas Turbine Rotating Cavities

Abstract Recently, Physics-Informed Neural Networks have displayed great potential in delivering swift and accurate solutions for inverse problems. Here, a Physics-Informed Neural Network (PINN) was used to solve the inverse heat conduction problem in the rotating cavities of a aeroengine high-pressure compressor internal air system. The neural network was designed to receive experimentally captured radially distributed temperature profiles as inputs and predict the associated surface heat fluxes. The correctness of these predicted heat fluxes are assessed by numerically solving the direct heat conduction equation using a 2D Finite-Element model, thereby recovering the original temperature profiles. A comparative analysis is conducted between the predicted temperature profiles and the initial inputs. The physics informed neural network is trained using noise free synthetic data, created from a range of radial temperature curve fit coefficients, and subsequently tested on noisy experimental data at engine representative conditions. The predicted temperature values exhibit some good agreement with their respective actual counterparts. Furthermore, the sensitivity of model hyperparameters are explored to showcase the capability of the proposed approach. The results show that Physics- Informed Neural Networks exhibit reduced susceptibility to experimental uncertainties when addressing inverse problems, in contrast to inverse solution methods, and offer a possible new approach for analysis of experimental data if trained on a sufficiently large dataset.

FLOW AND HEAT TRANSFER IN ROTATING COMPRESSOR CAVITIES WITH INVERTED SHROUD-THROUGHFLOW TEMPERATURE DIFFERENCES

Abstract In an aero-engine compressor, co-rotating discs form cavities that interact with an axial throughflow of secondary air at low radius. In the high-pressure (HP) compressor the shroud is hotter than the throughflow (directed downstream to the turbine) and the radial temperature gradient creates buoyancy-induced flow at Grashof numbers ∼ 1013. Such flows can be unstable and typically take the form of counter-rotating vortex pairs separated by radial hot and cold plumes. However, in low pressure (LP) and intermediate pressure (IP) compressors the secondary air is directed upstream. In this inverse scenario the axial throughflow is hotter than the compressor discs, reversing the disc temperature gradient and eliminating the fundamental driver for buoyancy. Despite its practical application and importance, this inverse scenario has not been previously investigated. The University of Bath Compressor Cavity Rig has been uniquely designed to simulate such flows, measuring temperature and unsteady pressure in the frame of reference of the rotating discs. Bayesian and spectral analysis have determined the radial distribution of disc heat flux, as well as the asymmetry of the rotating vortex structures and their slip relative to the discs. Unexpectedly, the new data reveal the flow structure in cavities with positive and inverted temperature differences are fundamentally similar (albeit with reversed radial-temperature profiles). Isothermal cases identified a critical Rossby number (Ro), above which the flow structure in the cavity was dominated by a toroidal vortex. At sub-critical Ro, the flow structure for the inverted temperature gradient continued

Toward electron temperature profiles in hot-dense plasmas from x-ray spectral ensembles

High repetition rate laser systems enable new strategies for diagnosing plasma behavior with large datasets. Here, we define an ensemble technique that relies on randomized targeting of x-ray tracer micro-stripes. On each shot, a high-intensity laser pulse is focused on a solid target with Ti tracer stripes embedded in an Al foil, randomly targeting a micro-stripe, a portion of a stripe, or a gap between stripes. High-resolution, time-integrated x-ray spectrometers capture line emission from the portion of the micro-stripe that is heated to sufficiently high electron temperatures. Accumulation of many such cases is used to construct ensemble distributions of x-ray line intensities that encompass all relative offsets of the laser focus to the micro-stripe centers. Synthetic intensity distributions are likewise generated using collisional-radiative modeling. Bayesian fitting of modeled to measured intensity distributions establishes the most likely radial temperature profiles, enabling comparison to hydrodynamic models and calling into question the cylindrical symmetry of these micro-stripe-embedded systems. Ensemble techniques have significant potential for high-energy-density plasma diagnostics, especially with the advent of high repetition rate experiments.

Nonlinear generalized piezothermoelasticity of spherical vessels made of functionally graded piezoelectric materials

The present study investigates the thermoelastic response of a heterogeneous piezoelectric sphere under thermal shock loading. Boundary conditions as well as loading are considered as symmetric; thus, the response of the sphere is expected to be symmetric. All of the properties of the thick-walled sphere, including mechanical, electrical and thermal properties, are considered dependent on the radial position, except for the relaxation time, which is considered a constant value along the radius. The governing equations of the sphere have been derived under heterogeneous anisotropic assumptions. The general form of the second law of thermodynamics, which is nonlinear in nature, and is called nonlinear energy equation is used. The number of the established equations is three, which includes the motion equation, energy equation and Maxwell electrostatic equation of Maxwell. These equations are obtained in terms of radial displacement, temperature difference and electric potential. The energy equation is derived based on Lord and Shulman theory with a single relaxation time. In the next step, by introducing dimensionless variables, the governing equations are provided in dimensionless presentation. Then these equations have been discretized using generalized differential quadrature method. Also, in order to follow the solution of the equations in time domain, Newmark method has been used. Since the system of equations is nonlinear, Picard algorithm is applied as a predictor-corrector mechanism to solve the nonlinear system of equations. Then numerical results are presented to investigate the propagation of mechanical, thermal and electric waves inside the heterogeneous sphere and also their reflection from the outer surface of the sphere. By examining the results, it can be seen that mechanical and thermal waves propagate with a limited speed, while the speed of electric wave propagation is infinite.

Predicting smoke temperature distribution beneath ceiling for a large subway station fire

Fire accident seriously threatens the stable operation and personnel security in the subway station, and clarifying the smoke temperature distribution is conducive to arranging reasonably fire alarm. In this study, model experiments and numerical simulations are conducted to investigate the ceiling temperature profiles, mainly altering the heat release rate (HRR) and fire locations in a large subway station. The repeatability of the experimental data is confirmed, and the numerical model is validated by the measurement data. During a fire happening in a large-wide space, the smoke movement beneath the ceiling can be divided into radial and one-dimensional flow, whose prediction models are proposed under fire source located at the center. On this basis, it can be found that the radial temperature profile is independent of fire source location. While, the one-dimensional temperature distribution model is modified by introducing the effects of transvers and longitudinal fire locations respectively. This work could provide data support and theoretical reference for clarifying the smoke movement for large subway station fire.

Toroidal mean flow and complex temperature distribution in a thermoacoustic core

Increasing the capacity of thermoacoustic machines (engines or refrigerators) requires increasing the diameter of the regenerator, which may result in non-uniform temperature distributions inside the regenerator. In the current study, the temperature is measured at different radial and axial locations inside the regenerator of a thermoacoustic refrigerator with a diameter of 148 mm. The working gas is a mixture of helium and Argon at a static pressure of 40 bar. Non-uniform radial temperature distributions are observed at different axial positions. Also, the predicted axial temperature distributions by a 1-D linear model (DeltaEC) do not agree with the measured temperature distributions. We suspect that the non-uniform radial temperature distribution generates a steady flow through the regenerator which increases the radial temperature non-uniformity and results in non-linear axial temperature distribution. Given the measured temperature distribution, the presence of a toroidal steady flow inside the regenerator is suspected. To confirm this hypothesis, the regenerator is divided into three segments connected in parallel in the DeltaEC model. Mean flows are added in each segment of the regenerator to simulate the presence of toroidal flow in the regenerator. The predicted temperature distributions from this modified DeltaEC model agree with the measured temperature distributions.

Internal radiation effect on semiconductor β-Ga2O3 crystals grown by the VB Method and anisotropic thermal stress

Gallium oxide crystals are semitransparent semiconductors with good optical and electrical properties, which allow their use for several technological applications. During the growth process of β-Ga2O3 crystals, internal radiation plays a crucial role that affects the growth process and then the crystal quality. In this work, the effect of the melt and the crystal transparency on the vertical Bridgman growth of β-Ga2O3 oxide is thoroughly studied. Using a global 2D/3D finite element model, temperature, melt flow, melt-crystal interface, and three-dimensional anisotropic thermal stress are computed at different growth stages. At each stage, four cases are considered, namely, opaque melt and crystal, semi-transparent melt and opaque crystal, semitransparent crystal and opaque melt, and finally semitransparent melt and crystal. The role of internal radiation in each case at different growth stages is then highlighted separately and then coupled together. It was found that the melt-crystal interface is shifted from a convex shape at the early stage to a nearly plane and then to a concave shape at the last stage. The melt flow is then changed from two rolls pattern at the beginning to a single-roll structure at the last stage. Thermal stress of the as-grown ingot is decreased during the growth due to the decrease of temperature non-linearities. Internal radiation inside the crystal acts to increase the melt-crystal interface convexity at the early and middle stages of the growth process and leads to a decrease in its concavity at the final stage. However, the melt transparency leads to the opposite effects, i.e., it decreases the interface convexity at the early stage and increases the interface concavity at the final stage. As a result, for semitransparent crystal and melt, the interface is between the two previous cases. The calculated thermal stresses are found to be more affected by the transparency of the crystal than the melt as the absorption coefficient of β-Ga2O3 crystal is smaller than that of the melt. At all stages, the thermal stresses are found to be larger for the opaque case due to the increase of temperature non-linearities in the crystal. Large values are found at the bottom and the lower part of the periphery. Furthermore, internal radiation inside the melt plays a major role during the early growth stage due to the large liquid volume. It reduces the melt flow intensity close to the free surface where the shear stress is combined with the buoyant force and leads to the flattening of the interface decreasing then the radial temperature gradients, which leads to small attenuation of the thermal stress. At the final stage, the transparency of the melt plays the opposite role due to the increase of the interface concavity which leads to an increase in both of the temperature gradients and the thermal stress inside the crystal. Due to the crystal anisotropy, and especially to the large thermal expansion coefficient in the [010] direction, the 3D thermal stress values are found to be larger in this direction, especially in the bottom part of the ingot. Comparisons with available experimental and numerical works are provided in this paper.

Investigation on Wax Deposition Risk in Shale Oil Well During Production Test

Abstract During production test of the shale oil well, the low temperature environment in the wellbore is likely to cause wax precipitation of shale oil, and in turn disrupt the normal production test, increase the operating costs and risks. In view of this problem, by considering the gas-liquid flow, radial heat transfer and temperature gradient etc, a temperature and pressure field model of shale oil wellbore was established, and a prediction method of wax deposition zone in the shale oil wellbore during production test was proposed. Furthermore, by using the production data of a shale oil well with wax deposition in the South China Sea during production test, the accuracy of the model in calculating the fluid temperature and pressure of the wellbore with wax deposition was verified. The wellhead temperatures calculated by the model had a maximum error of 9.31%, and the bottom-hole pressures calculated by the model had a maximum error of 7.52%, indicating the model has high calculation accuracy. The model was used to analyze the sensitivities of wax deposition to the time and rate of production, water content and the ratio of gas to oil. It is found that the wax deposited in wellbore increases in thickness with the production time, is more strongly affected by production rate and water content, but less affected by the ratio of gas to oil. The research results can provide support for preventing wax deposition during production test of shale oil wells.

Numerical Approach of the First Instability Appearance in Inclined Taylor–Couette System

The present study numerically investigates the three-dimensional forced and mixed convection heat transfer in an inclined Taylor–Couette system (η=0.5 and Γ=20) submitted to a radial temperature gradient. The main objective of this study is to determine the effect of the angle inclination duct on the thermal and dynamic fields. Several cases have been dealt with depending on the inclination angle to detect the critical Reynolds number in each case. The model of the conservation equations with their boundary conditions is numerically solved by the finite volume method with a second-order spatiotemporal discretization. The results show that, in forced convection, the effect of the inclination angle is inexistent on the velocity field. However, with the presence of buoyancy effects, which impact flow stability and the transition to turbulence, the inclination influences both velocity and temperature fields. It also shows that selecting the vertical position of the annulus is preferable to obtain hydrodynamic stability in mixed convection. At the same time, from the thermal point of view, it is preferable to select the horizontal position to get dynamic and thermal stability.

Simulation analysis of gas-solid two-phase flow and reaction in a novel catalytic cracking reactor

A gas-solid two-phase flow reaction model was developed to evaluate the performance of a novel catalytic cracking reactor in the residue-to-chemicals (RTC) process. Coupled TFM, EMMS drag, and 12-lump kinetic models were employed to simulate the flow reaction process. The reaction temperature and product yields at the reactor exit aligned well with real industrial RTC reactor test results, indicating the reliability and effectiveness of the coupling model. Catalyst particles formed an internal circulation structure in the reactor, increasing the instantaneous catalyst-to-oil ratio. The reactor exhibited low axial and radial temperature gradients with higher reaction temperatures, accelerating the catalytic cracking rate and enhancing the selectivity for high-value products. The effects of the catalyst-to-oil ratio, catalyst inlet temperature, and feedstock mass flow rate on the flow reaction process were optimized. Results showed that both the catalyst-to-oil ratio and catalyst inlet temperature influenced the overall catalyst velocity distribution. Within the limit range, increasing the catalyst-to-oil ratio increased feedstock conversion, gasoline, LPG, dry gas, and coke yields, but decreased diesel yield. Conversely, increasing the feedstock mass flow rate showed opposite trends. Different trends in product yields were observed with varying inlet catalyst temperatures, with optimal product distribution at 973.15 K.

Photoevaporation of protoplanetary discs with PLUTO+PRIZMO I. Lower X-ray--driven mass-loss rates due to enhanced cooling

Photoevaporation is an important process for protoplanetary disc dispersal, but there has so far been a lack of consensus from simulations over the mass-loss rates and the most important part of the high-energy spectrum involved in driving the wind. We aim to isolate the origins of these discrepancies through carefully benchmarked hydrodynamic simulations of X-ray photoevaporation with time-dependent thermochemistry calculated on the fly. We conducted hydrodynamic simulations with pluto where the thermochemistry is calculated using prizmo . We explored the contribution of certain key microphysical processes and the impact of employing different spectra previously used in literature studies. We find that additional cooling results from the excitation of O by neutral H, which leads to dramatically reduced mass-loss across the disc compared to previous X-ray photoevaporation models, with an integrated rate of $ M sun yr^ $. Such rates would allow for longer-lived discs than previously expected from population synthesis. An alternative spectrum with less soft X-ray produces mass-loss rates around a factor of two to three times lower. The chemistry is significantly out of equilibrium, with the survival of H into the wind being aided by advection. This leads to H becoming the dominant coolant at 10s au, thus stabilising a larger radial temperature gradient across the wind as well as providing a possible wind tracer.

Low-current gliding DC discharge in high-speed flows

Abstract A low-current gliding discharge (current range 1–5 A) in high-speed air flows of 100–250 m s−1 was experimentally studied. A high-voltage direct current source with a maximum voltage of 4.5 kV was used to create the discharge. The average electron concentration n e ∼ 1014 cm−3 and the plasma ionization degree were determined by measuring the Stark broadening of the hydrogen H β line (λ Hβ = 486.1 nm). The estimates of the electric field (E ∼ 100 V cm −1 ÷ 600 V cm−1) in the discharge positive column were found using time-synchronized high-speed video recordings and oscillograms. The gas rotational temperature T g = 7000–9500 K and the vibrational temperature T v = 7000–11 000 K were estimated using optical emission spectroscopy. Time-resolved spectroscopy is used to investigate the effective plasma channel spatial regions from which the N, NH, N2 +, O and OH molecules radiate. The difference of the obtained radii indicates the presence of a radial temperature gradient and inhomogeneous plasma composition in the discharge cross section. The possibility of using of gliding discharge to ignite hydrocarbon-air mixtures in the ramjet engines combustors has been experimentally demonstrated.

The impact of induction heating time on the temperature distribution of high-temperature alloy discs

Abstract The induction heating time is directly related to the temperature uniformity of high-temperature alloy disc components. Therefore, investigating the influence of induction heating time on the temperature field distribution of disc components provides guidance for temperature control strategies in the forming process. In this study, the finite element analysis software COMSOL Multiphysics was employed to examine the impact of induction heating time on the radial and thickness-wise temperature fields of GH4169 discs. The results indicate that the heating time affects the thickness of the heating layer, and appropriately extending the heating time can improve the temperature uniformity in the thickness direction, achieving a temperature difference of ±5 °C in the disc component thickness direction under certain conditions. When the heating time ranges from 1229 s to 1239 s, the temperature in the R=30 mm to R=100 mm range reaches the suitable forging temperature.

Theoretical and numerical analyses of thermal stresses and temperature variations in disc cutter cutting composite strata under thermal-force multi-fields

Composite strata consisting of hard and soft rock are common during shield cutter excavation. The friction cutting process generates a large amount of cutting heat, high temperature will produce thermal stresses and thermal expansion in the disc cutter ring, resulting in wear and deformation of the cutter, reducing its rock breaking performance. From the perspective of thermal-force change in cutter, This study establishes the theory of frictional heat generation and the theory of thermal stress of elastomer to analyse the frictional heat generation and derive the thermal stress theory of elastomer model in cutter. Numerical simulations were carried out to analyse the thermal-force multi-field coupling process considering the influencing factors such as penetration, cutting time, rock strength, etc. Solve the heat conduction equation and radial temperature field distribution from the heat transfer perspective. The comparative study of theoretical analysis, numerical simulation and experimental values shows that the theoretical and numerical results of thermal stress and temperature field distributions are consistent, which verifies the reasonableness of the theoretical derivation and numerical model.

Turbulent pipe flow and heat transfer of a binary mixture at supercritical pressure: Influences of cross-diffusion effects

Cross-diffusion effects, including Soret and Dufour effects, are enhanced around the pseudo-critical temperature (Tpc) of a binary mixture. Their influences on heat transfer at supercritical pressure have been scarcely studied. To bridge this gap, large-eddy simulations (LES) are conducted to investigate forced convective heat transfer of a CO2–ethane mixture at supercritical pressures in a circular pipe subject to a uniform heat flux. Both heating and cooling conditions, along with varying initial concentrations and thermodynamic pressures, are included in the simulations. The LES results reveal that the Soret effect causes concentration separation, resulting in a concentration boundary layer. The magnitudes of the thermodiffusion factor (kT) and the radial temperature gradient control the intensity of separation, which is more pronounced at near-critical pressure and high heat flux. Since kT is significant only around Tpc, downstream decay of the concentration separation is observed as the loci of T=Tpc migrate away from the wall so that the local radial temperature gradient diminishes. The primary factors affecting heat transfer are the variations in thermal conductivity and isobaric specific heat resulting from concentration separation. In contrast, the Dufour effect and the accompanying inter-diffusion play negligible roles. In deterioration scenarios, the bulk Nusselt number (Nub) shows a maximum relative drop of 8%, whereas in enhancement scenarios, Nub shows a maximum relative increase in 10%, with both deterioration and enhancement decaying downstream. Cross-diffusion effects have negligible impacts on density and streamwise velocity, but noticeably alter streamwise velocity fluctuation and turbulent kinetic energy.

Numerical investigation of heat transfer characteristics of hydrogen flow in a randomly packed bed

In this study, two randomly packed beds with small tube-to-particle diameter (D/d) ratios of D/d = 4 (PB-4) and D/d = 5 (PB-5) are constructed using the discrete element method (DEM). The pore-scale heat transfer characteristics of hydrogen flow at low pore Reynolds numbers (Rep < 100) are investigated using a DEM-CFD simulation approach, with the temperature-dependent thermo-properties of hydrogen being considered. Distinct local channeling flow patterns are revealed by detailed analyses of the flow fields in PB-4 and PB-5. The overall friction factors for both beds are found to agree well with empirical correlations. Notably, a faster spatial temperature increase is exhibited by PB-5, with a larger D/d ratio, as evidenced by a shorter axial distance for fully-heated hydrogen flow compared to PB-4. For the pore-scale heat transfer in the packed beds, the radial temperature profiles are compared at various heights of the packed beds depending on the radial porosity oscillation, in which the wall effect should be especially considered in the near-wall region. Furthermore, the axial pore-scale Nusselt number (Nup,axial) exhibits an inverse fluctuation with the axial porosity oscillation. Finally, the global Nusselt numbers (Nu) in the packed beds are analyzed under different operating conditions, which are in good agreement with empirical correlations.

MC/sub-channel coupling for steady state and transient simulation of Xi’an Pulsed Reactor

The Monte Carlo (MC) code RMC and sub-channel code CTF are coupled for Xi’an Pulsed Reactor (XAPR) pulse and depletion simulation. A python script is developed to handle data exchange through files. $3.45 pulse and $2 pulse are simulated with the pulsed state core. The pulse peak power and the Full Width at Half-Maximum (FWHM) results are compared with experiments as a validation and good agreement is achieved. Detailed 3-D power and temperature distributions are also obtained. Results show that the core power peak is close to the pulse rod where the reactivity is introduced. The radial power peak of each rod is at the boundary because of the self-shielding effect. The rod temperature distribution follows the same trend with the power, and the coolant temperature is not changed during the pulse period of about 0.12 s, which suggests that the heat transfer plays a negligible role in such a short time. For the steady state core, depletion simulation is carried out for the lifetime of the first fuel cycle of 120 Effective Full Power Days (EFPD). Validation is done by calculating the temperature distribution and the differential worth of the regulating rod at 0 EFPD, which both agree well with experiments. Results show that the power distribution is almost unchanged over time, only slightly more flat, indicating the material is not greatly depleted. The temperature distribution of the core generally agrees with the power distribution, except the radial temperature peak of each rod is at the center because heat is conducted outwards at steady state. Detailed coolant temperature distribution is obtained thanks to the utilization of CTF. Temperatures at the assembly boundary and near the central water chamber is noticeably lower than the other part, which is not shown in the parallel multi-channel models.

A novel instrumentation approach for achieving in-situ temperature sensing of a Li-ion cylindrical cell under immersion cooling

Battery thermal management systems are critical for high-performance electric vehicles, where the ability to remove heat and homogenize temperature distributions in single cells and packs are key considerations. Immersion cooling, which immerses the battery in a dielectric fluid, can improve cooling efficiency compared to air cooling. However, stringent instrumentation standards make in-situ monitoring under immersion cooling a difficult challenge. This study proposes a novel cell instrumentation method based on the integrated combination of three O-rings, which for the first time achieves in-situ temperature sensing of batteries under oil-immersed cooling conditions. Reliability of the sealing system and instrumentation methodology is ensured by leakage tests and oil corrosion assessment. Data such as cell impedance and discharge capacity also support the success and reliability of the instrumentation process without affecting the battery performance. Compared with natural air cooling, immersion cooling can reduce the temperature rise during battery operation by >10 °C under high C-rate discharge conditions. However, this is accompanied by an increase in radial temperature gradient. The temperature gradient of the cell with oil immersed reaches a maximum of >7 °C, while the temperature gradient under natural cooling under the same test conditions is only 3 to 4 °C. This leads to intensified temperature inhomogeneity of the cell, which may accelerate the local ageing and degradation. Our instrumentation approach contributes to a deeper understanding of the thermal behaviour of batteries under direct immersion cooling, aiding the development of more advanced cooling strategies and associated battery thermal management models.

Physical and mechanical response of large-diameter shield tunnel lining structure under non-uniform fire: A full-scale fire test-based study

When a fire occurs in an underground shield tunnel, it can result in substantial property damage and cause permanent harm to the tunnel lining structure. This is especially true for large-diameter shield tunnels that have numerous segments and joints, and are exposed to specific fire conditions in certain areas. This paper constructs a full-scale shield tunnel fire test platform and conducts a non-uniform fire test using the lining system of a three-ring large-diameter shield tunnel with an inner diameter of 10.5 m. Based on the tests, the temperature field distribution, high-temperature bursting, cracking phenomena, and deformation under fire conditions are observed. Furthermore, the post-fire damage forms of tunnel lining structures are obtained through the post-fire ultimate loading test, and the corresponding mechanism is explained. The test results illustrate that the radial and circumferential distribution of internal temperature within the tunnel lining, as well as the radial temperature gradient distribution on the inner surface of the lining, have non-uniform distribution characteristics. As a result, the macroscopic phenomena of lining concrete bursting and crack development during the fire test mainly occur near the fire source, where the temperature rise gradient is the highest. In addition, the lining structure has a deformation characteristic of local outward expansion and cannot recover after the fire load is removed. The ultimate form of damage after the fire is dominated by crush damage from the inside out of the lining joints in the fire-exposed area. The above results serve as a foundation for future tunnel fire safety design and evaluation.

Investigation of Dislocation Behaviors in 4H-SiC Substrate during Post-Growth Thermal Treatment

Dislocation behaviors after post-growth thermal treatment were investigated by X-ray topography and KOH etching. Generation of prismatic dislocations were observed in X-ray topography, and density of basal plane dislocations (BPDs) increases with annealing temperature and radial temperature gradient. Distribution of newly generated BPDs in the wafer after thermal treatment is correlated to the resolved shear stress arising from radial temperature gradient.