Three-dimensional Temperature Field Research Articles

Analysis of Coupled Three-Dimensional Seepage and Temperature Fields in Fracture Network of Rock Mass

The coupling effect of seepage and temperature fields in fractured rock mass is a hot topic in the area of water conservancy, nuclear waste disposal and geothermal resources development. A coupling mathematical model of the seepage, flow temperature and rock mass temperature fields in the fracture network of rock mass is established based on the seepage and temperature interaction. A calculation program is developed and applied to calculate the seepage and temperature fields of the dam foundation of a water conservancy project. The interaction mechanism of the seepage, flow temperature and rock mass temperature fields is analyzed in this paper. Results show that the seepage field largely influences the temperature field, which can provide several suggestions for the deep underground disposal of nuclear waste, geothermal resources development and fractured rock mass in dam foundations. Considering the coupling effect of the seepage, flow temperature and rock mass temperature fields by the fracture network method is necessary.

The Dynamic-Implicit-Additional-Source (DIAS) method for multi-scale coupling of thermal-hydraulic codes to enhance the prediction of mass and heat transfer in the nuclear reactor pressure VESSEL

The paper describes a Dynamic-Implicit-Additional-Source (DIAS) method for a domain-overlapped multi-scale coupling of a system-code, sub-channel code, and CFD code aiming to improve the simulation of the thermal-hydraulics phenomena e.g. the heat, mass, solute transfer in the Nuclear Reactor Pressure Vessel (RPV). This method is developed to correlate the essential physical parameters predicted by the nuclear system thermal-hydraulic code with more precise data derived from sub-channel or Computational Fluid Dynamic (CFD) solutions, enabling the system-code to produce more realistic mass and heat transfer within the RPV. The DIAS-method is used in combination with the domain-overlapping coupling approach and it currently correlates four system-codes parameters: the coolant velocity, the pressure drop, the coolant temperature, and the boron concentration.The three-dimensional velocity and pressure fields predicted by a sub-channel or CFD codes are used to calculate the new friction and form loss coefficients on the fly (in the momentum equation) at all the overlapped edges in the system-code with increased accuracy. Additionally, the coolant temperature distribution predicted by the system-code is correlated based on the three-dimensional temperature field gained from the sub-channel or CFD codes by adding a dynamic-implicit heat source or sink to the energy equation. Such kind of source/sink was also added to the solubility equation of the system-code to predict the boron concentration based on the corresponding high-resolution fields provided by the high-resolution thermal-hydraulic solvers. All of the three newly added items are named as the Dynamic-Implicit-Additional-Source (DIAS) since they are not the traditional fixed-explicit appendixes to the original system of governing equation set but they are dynamically tuned and implicitly calculated along with the solution process.The complete DIAS-method was verified with an academic 3D coolant-mixing problem in a Reactor Pressure Vessel (RPV). Results obtained from the test cases indicate that the mass, heat and solute transfer in the RPV could be better predicted by the coupled codes with the DIAS method. Finally, the DIAS method is proved an efficient and powerful approach for multi-scale thermal-hydraulic coupling based on the domain-overlapping approach.

Reconstruction of the mesoscale variability of the Black Sea based on assimilation in the model of three-dimensional fields of pseudo-measurements of temperature and salinity

The paper presents the results of the analysis of the hydrophysical fields of the Black Sea, reconstructed in the reanalysis through the assimilation in the model of pseudo-measurements of temperature and salinity. Much attention was paid to assessing the reproduction of mesoscale eddies. To perform a retrospective analysis of hydrophysical fields, three-dimensional temperature and salinity fields obtained by the original method of joint analysis of data on sea-level anomalies and rare contact measurements were acquired in the model. To identify the eddy structures, an automatic identification procedure is used, based on the definition of closed streamlines in the velocity fields. The coordinates of the eddy, trajectories of motion, velocity, time of life and vertical structure are calculated.

Modeling of 3D temperature field in butt welded joint of 6060 alloy sheets using the ANSYS program

In work, the modeling of a three-dimensional temperature field in a butt weld connection of two 6060 aluminum alloy sheets using Finite Element Method is presented. The calculations were performed for two welding methods: TIG (Tungsten Inert Gas) and MIG (Metal Inert Gas). The Goldak's double ellipsoidal heat source model has been used in modeling. The thermal-mechanical properties of the material were assumed to depend on the temperature. The Workbench, DesignModeler, Mechanical, Fluent and CFD-Post modules of the ANSYS program were used for numerical simulations. In the description of the geometry of joints, cube type elements were used, with density of grid in the heat affected zone. The parabolic shapes of face and root were assumed based on the literature and results of the experiment. The temperature distributions in cross-sections of welded joints as well as welding thermal cycles at selected points were analyzed. The results of numerical simulations were verified experimentally. Comparison of calculated and obtained in the experiment the characteristic limits of heat affected zones showed satisfactory compatibility. The directions of heat propagation determined by vectors of cooling rates coincide with the longitudinal axis of dendritic grains determined on the basis of metallographic tests.

Investigation on temperature field of unidirectional carbon fiber/epoxy composites during drilling process

The phenomenon of heat accumulation and transportation in the composite materials is a very typical and critical issue during drilling process. In this study, a three-dimensional temperature field prediction model is proposed using finite difference method, based on the partly homogenization hypothesis of material, to predict temperature field in the process of drilling unidirectional carbon fiber/epoxy (C/E) composites. According to the drilling feed motion, drilling process is divided into four stages to study the temperature distributing characteristics. The results show that the temperature distribution predicted by numerical study has a good agreement with the experimental results. The temperature increases with increasing the drilling depth, and the burn phenomena is observed due to the heat accumulation, especially at the drill exit. Due to the fiber orientation, an elliptical shape of the temperature field along the direction is found for both numerical and experimental studies of C/E composites drilling process.

Thermo-Mechanical Coupling Analyses for Al Alloy Brake Discs with Al2O3-SiC(3D)/Al Alloy Composite Wear-Resisting Surface Layer for High-Speed Trains.

In the present work, a theoretical model of three-dimensional (3D) transient temperature field for Al alloy brake discs with Al2O3-SiC(3D)/Al alloy wear-resisting surface layer was established. 3D transient thermo-stress coupling finite element (FE) and computational fluid dynamic (CFD) models of the brake discs was presented. The variation regularities of transient temperature and internal temperature gradient of the brake discs under different emergency braking conditions were obtained. The effects of initial braking velocity (IBV) and thickness of Al2O3-SiC(3D)/Al alloy composite wear-resisting layer on the maximum friction temperature evolution of the disc were discussed. The results indicated the lower temperature and thermal stress distributed uniformly on the wear-resisting surface, which was dominated by high conductivity and cooling ability of the Al alloy brake disc. The maximum friction temperature was not obviously affected by the thickness of the wear-resisting layer. The maximum friction temperature of the brake discs increased with the increase of the IBV, the maximum friction temperature and thermal stress of the brake discs is about 517 °C and 192 MPa at IBV = 97 m/s considering air cooling, respectively. The lower thermal stress and fewer thermal cracks are produced during the braking process, which relatively decrease the damage. The friction behavior of the tribo-couple predicted using FE method correlated well with the experimental results obtained by sub-scale testing.

A Study on the Heating Method and Implementation of a Shrink-Fit Tool Holder

A novel induction heating coil is proposed and designed as a shrink-fit tool holder. An electromagnetic field analysis of the coil with different winding methods is conducted using the ANSYS finite element analysis software and an appropriate coil structure is determined, based on the simulated electromagnetic field distribution cloud maps. The magnetic field in the X–Y plane is increased by one order of magnitude around the surface with the addition of the designed magnetic slot, as well as improving the magnetic leakage. The electromagnetic field strength in the middle of the coil is greatly increased, up to 2.312 × 104 A/m, by the addition of a designed magnetic ring covering the top of the coil. The distribution of the three-dimensional temperature field is obtained by the ANSYS workbench transient thermal analysis software, based on the selected coil. Hot-loading equipment used for shrink-fit tool holders are implemented with diameter-selection, power, and heating time-setting functions. Experiments on different types of tool holders are carried out to obtain optimal heating parameters and to verify the reliability of the implemented heating equipment. Through experimental testing, the inserting and pulling out temperature is found to be about 270 °C for the BT40-SF06 and about 285 °C for the BT40-SF10. According to the experimental results, the simulated temperature field is in good agreement with the measured result. The optimal heating parameters of the heating equipment are determined, which proves the correctness of the heating method of the shrink-fit tool holder.

Study on Influences of Water Temperature on Stress Distribution for High Arch Dam in Impounding Period

Water temperature affects not only the water quality and ecological balance of the reservoir, but the temperature and stress field distribution of the high arch dam during water storage and operation management. During low water storage and initial operation, the concrete in reservoirs over 100 m deep in particular can easily crack or expand because of low temperature reservoir water. This paper studies the water temperature distribution law of the reservoir during initial storage by establishing a three-dimensional fluid dynamics model. Based on this, this paper explores the three-dimensional temperature field and stress field of the dam body during the storage period, the causes of cracking, and stress distribution in key parts of the arch dam.

TheDiaTo (v1.0) – a new diagnostic tool for water, energy and entropy budgets in climate models

Abstract. This work presents the Thermodynamic Diagnostic Tool (TheDiaTo), a novel diagnostic tool for investigating the thermodynamics of climate systems with a wide range of applications, from sensitivity studies to model tuning. It includes a number of modules for assessing the internal energy budget, the hydrological cycle, the Lorenz energy cycle and the material entropy production. The routine takes as inputs energy fluxes at the surface and at the top of the atmosphere (TOA), which allows for the computation of energy budgets at the TOA, the surface and in the atmosphere as a residual. Meridional enthalpy transports are also computed from the divergence of the zonal mean energy budget from which the location and intensity of the maxima in each hemisphere are calculated. Rainfall, snowfall and latent heat fluxes are received as inputs for computation of the water mass and latent energy budgets. If a land–sea mask is provided, the required quantities are separately computed over continents and oceans. The diagnostic tool also computes the annual Lorenz energy cycle (LEC) and its storage and conversion terms by hemisphere and as a global mean. This is computed from three-dimensional daily fields of horizontal wind velocity and temperature in the troposphere. Two methods have been implemented for the computation of the material entropy production: one relying on the convergence of radiative heat fluxes in the atmosphere (indirect method) and the other combining the irreversible processes occurring in the climate system, particularly heat fluxes in the boundary layer, the hydrological cycle and the kinetic energy dissipation as retrieved from the residuals of the LEC (direct method). A version of these diagnostics has been developed as part of the Earth System Model eValuation Tool (ESMValTool) v2.0a1 in order to assess the performances of CMIP6 model simulations, and it will be available in the next release. The aim of this software is to provide a comprehensive picture of the thermodynamics of the climate system, as reproduced in the state-of-the-art coupled general circulation models. This can prove useful for better understanding anthropogenic and natural climate change, paleoclimatic climate variability, and climatic tipping points.

Experimental verification of three-dimensional temperature field reconstruction method based on Lucy-Richardson and nearest neighbor filtering joint deconvolution algorithm for flame light field imaging

Non-intrusive flame detection technique, such as radiation imaging, can measure large flame in boilers or engines. Flame light field imaging is a new type flame detection method based on radiation imaging. Using this method, a multi-view flame light field image can be obtained in a single capture, and the three-dimensional temperature field of the flame can be calculated using a reconstruction algorithm. In this study, experiments are conducted to verify the temperature reconstruction method using the Lucy–Richardson and nearest neighbor filtering joint deconvolution algorithm based on the refocused flame light field images. It was found that, in terms of the temperature trend and range, the results for different flame sections can be reconstructed to be comparable to the results using the non-negative least squares method. Although the flame shapes are non-axisymmetric corresponding to working conditions, the temperature reconstruction method using refocused light field images can effectively reflect these changes.

Effects of the Mean Flow on Martian Transient Eddy Activity: Studies with an Idealized General Circulation Model

Abstract The extent to which the eddy statistics of the Martian atmosphere can be inferred from the mean state and highly simplified assumptions about diabatic and frictional processes is investigated using an idealized general circulation model (GCM) with Newtonian relaxation thermal forcing. An iterative technique, adapted from previous terrestrial studies, is used to generate radiative equilibrium temperatures such that the three-dimensional time-mean temperature fields of the idealized model match means computed from the Mars Analysis Correction Data Assimilation (MACDA). Focusing on a period of strong Northern Hemisphere eddy activity prior to winter solstice, it is found that the idealized model reproduces some key features of the spatial patterns of the MACDA eddy temperature variance and kinetic energy fields. The idealized model can also simulate aspects of MACDA’s seasonal cycle of spatial patterns of low-level eddy meridional wind and temperature variances. The most notable weakness of the model is its eddy amplitudes—both their absolute values and seasonal variations are quite unrealistic, for reasons unclear. The idealized model was also run with a mean flow based on output from the Geophysical Fluid Dynamics Laboratory (GFDL) full-physics Mars GCM. The idealized model captures the difference in mean flows between MACDA and the GFDL Mars GCM and reproduces a bias in the more complex model’s eddy zonal wavenumber distribution. This implies that the mean flow is an important influence on transient eddy wavenumbers and that improving the GFDL Mars GCM’s mean flow would make its eddy scales more realistic.

Heat Source Modeling in Selective Laser Melting.

Selective laser melting (SLM) is an emerging additive manufacturing (AM) technology for metals. Intricate three-dimensional parts can be generated from the powder bed by selectively melting the desired location of the powders. The process is repeated for each layer until the part is built. The necessary heat is provided by a laser. Temperature magnitude and history during SLM directly determine the molten pool dimensions, thermal stress, residual stress, balling effect, and dimensional accuracy. Laser-matter interaction is a crucial physical phenomenon in the SLM process. In this paper, five different heat source models are introduced to predict the three-dimensional temperature field analytically. These models are known as steady state moving point heat source, transient moving point heat source, semi-elliptical moving heat source, double elliptical moving heat source, and uniform moving heat source. The analytical temperature model for all of the heat source models is solved using three-dimensional differential equations of heat conduction with different approaches. The steady state and transient moving heat source are solved using a separation of variables approach. However, the rest of the models are solved by employing Green’s functions. Due to the high temperature in the presence of the laser, the temperature gradient is usually high which has a substantial impact on thermal material properties. Consequently, the temperature field is predicted by considering the temperature sensitivity thermal material properties. Moreover, due to the repeated heating and cooling, the part usually undergoes several melting and solidification cycles, and this physical phenomenon is considered by modifying the heat capacity using latent heat of melting. Furthermore, the multi-layer aspect of the metal AM process is considered by incorporating the temperature history from the previous layer since the interaction of the layers have an impact on heat transfer mechanisms. The proposed temperature field models based on different heat source approaches are validated using experimental measurement of melt pool geometry from independent experimentations. A detailed explanation of the comparison of models is also provided. Moreover, the effect of process parameters on the balling effect is also discussed.

Thermal behavior and grain evolution of 24CrNiMoY alloy steel prepared by pre-laid laser cladding technology

The unique thermal behavior during the multi-layer laser rapid manufacturing process brings about unique microstructure for the as-produced parts. In this paper, a comprehensive three-dimensional self-consistent transient temperature field model of 24CrNiMoY alloy steel by pre-laid laser cladding technology (PLLC) was established, and the reliability of model was verified by the experiment. The simulation results showed that as scanning speed increased (5, 7, 9 mm/s), the peak temperature, dimensions and liquid lifetime of the molten pool decreased, while the G × R increased and G/R decreased at the same position. With increasing layer, the peak temperature of molten pool and the temperature of the whole domain increased gradually until forming a dynamic balance. The contrast experimental results showed that with scanning speed increased, the average size of equiaxed grain increased (4.682, 5.012, 5.462 μm) and the average aspect ratio of columnar grain decreased (11.890, 11.411, 10.593). During the multi-layer process, grain growth modes were different along the deposition sections. The structure in parallel scanning direction mainly consisted of equiaxed grains, while in the overlapping direction were equiaxed and columnar grains. There was a clear columnar-to-equiaxed transition (CET) boundary that controls the change in grain types. The grain growth behavior of a multi-layered in vertical scanning direction section was different from that of a single track. All the above results illustrated that temperature field had a significant effect on the thermal behavior during PLLC process, which affected the grain evolution of 24CrNiMoY alloy steel.

Joint method for reconstructing three-dimensional temperature of flame using Lucy-Richardson and nearest neighbor filtering using light-field imaging

The real-time measurement and reconstruction of three-dimensional temperature are essential when studying the combustion process inside a flame. In the proposed sectioned flame light field imaging model, flame sections are reconstructed based on the characteristics identified using the Lucy-Richardson or nearest neighbor filtering methods, or a joint method involving a combination of both, to improve on the accuracy of two-dimensional temperature reconstruction. Compared to the results of a previous work, the proposed method increases the resolution in the depth of field direction and the extraction of the flame temperature of all sections from the same height ensures the accuracy of the reconstructed temperature distribution across the cross-section of the flame. The relative error when compared to the actual flame is less than 10%. Thus, this approach allows the accurate estimation of the three-dimensional temperature distribution inside a flame, and enables the rapid and effective reconstruction of the three-dimensional temperature field.

Analysis of the Thermal State of a Heating Element of Transformer Type

The solution of a simulation problem and the analysis of three-dimensional temperature field in a heating element of transformer type are considered. The design of a three-phase heating element with a spatial magnetic system is presented. The features of model construction using ANSYS software package are described. The results of simulation of temperature field in the heating element with the power of 25 kW are shown and analyzed. It is revealed that the temperature field in the area of primary winding is distributed unevenly and there are regions of local overheating. A heat removal from these regions is carried out by two main paths. The heat removal intensity and the distribution of heat fluxes depend on the current density in the jumper, which closes the elements of the secondary winding. Taking this into account, recommendations for selecting the electromagnetic loads in the active parts of the heating element and improving the design of electrical equipment are presented. To justify the modes of operation of the heating element as a part of heating unit of a stand-alone heat-supply system, the interrelation between the flow rate of the heat-transfer agent and the power of the heating element was revealed, which makes it possible to limit the maximum temperature in areas of local overheating and prolong the operation life of electrical equipment.

Three-Dimensional Velocity and Temperature Field Measurements of Internal and External Turbine Blade Features Using Magnetic Resonance Thermometry

Magnetic resonance thermometry (MRT) is a maturing diagnostic tool used to measure three-dimensional temperature fields. It has a great potential for investigating fluid flows within complex geometries leveraging medical grade magnetic resonance imaging (MRI) equipment and software along with novel measurement techniques. The efficacy of the method in engineering applications increases when coupled with other well-established MRI-based techniques such as magnetic resonance velocimetry (MRV). In this study, a challenging geometry is presented with the direct application to a complex gas turbine blade cooling scheme. Turbulent external flow with a Reynolds number of 136,000 passes a hollowed NACA-0012 airfoil with internal cooling features. Inserts within the airfoil, fed by a second flow line with an average temperature difference of 30 K from the main flow and a temperature-dependent Reynolds number in excess of 1,800, produces a conjugate heat transfer scenario including impingement cooling on the inside surface of the airfoil. The airfoil cooling scheme also includes zonal recirculation, surface film cooling, and trailing edge ejection features. The entire airfoil surface is constructed of a stereolithography resin—Accura 60—with low thermal conductivity. The three-dimensional internal and external velocity field is measured using an MRV. The fluid temperature field is measured within and outside of the airfoil with an MRT, and the results are compared with a computational fluid dynamics (CFD) solution to assess the current state of the art for combined MRV/MRT techniques for investigating these complex internal and external flows. The accompanying CFD analysis provides a prediction of the velocity and temperature fields, allowing for errors in the MRT technique to be estimated.

Solution of three-dimensional temperature and turbulent velocity field in continuously cast steel billets with electromagnetic stirring by a meshless method

This paper demonstrates the development of meshless Local Radial Basis Function Collocation Method (LRBFCM) for solution of three dimensional (3D) turbulent molten steel flow and solidification under the influence of electromagnetic stirring (EMS) and its application to continuous casting process of steel billets. A mixture continuum approach is used to formulate the coupled set of macroscopic equations for mass, momentum, energy, turbulent kinetic energy, and dissipation rate in Cartesian coordinates. The mushy zone is treated as a Darcy porous media. The explicit Chorin fractional step method is used to resolve the pressure-velocity coupling. The LRBFCM uses explicit time discretization and spatial discretization with shape-adaptive multiquadrics radial basis functions collocation on non-uniform seven-noded influence domains, and displacement-adaptive upwind scheme. The Lorentz force due to EMS is provided by a one-way coupling by Elmer software. The advantages of the meshless method are trivial adaptation of the nodal densities, simple upgrade to 3D from previous two-dimensional models, and high accuracy. A study on the influence of changing the EMS parameters on the calculated temperature and velocity fields is performed. The paper confirms the ability of LRBFCM meshless solution of a realistic 3D multiphysics industrial problem with complicated swirling flow pattern.

Near-infrared measurement of axisymmetric temperature field formed by free convection from a 1-mm-diameter heating sphere in water

This paper presents a method of reconstructing transient, three-dimensional axisymmetric temperature fields in water formed by laminar free convection from a small heating sphere. This method is based on the temperature dependence of the water absorption coefficient at a near-infrared wavelength of 1150 nm. The horizontal line profiles of the absorbance at this wavelength, obtained using a unidirectional transmission imaging technique, were approximated with multi-Gaussian functions to robustly and efficiently apply the inverse Abel transform. In the experiment, a 1-mm-diameter steel sphere in water was heated by electromagnetic induction. The reconstruction results show the formation of spherical temperature distributions within the thermal conduction regime, followed by the occurrence of upward free convection, leading to a laminar plume. The size and shape of the plume depended on the heat generation rate in the sphere. These results were analyzed and verified through a comparison with the results of a numerical simulation on the temperature and flow fields.

Calculation and Analysis of Rotor Thermal Static Field for Inter-Turn Short Circuit of Large Hydro-Generator Excitation Winding

Rotor winding inter-turn short circuit a common fault in hydro-generators. This fault would change the temperature, stress, and other thermal fields of a rotor and threaten the safe operation of the generator. In this paper, the Three Gorges hydro-generator is taken as an example. Mathematical models of three-dimensional temperature field and thermal stress field of rotor magnetic poles are established based on heat transfer theory and solved by finite element method. The temperature field, thermal deformation, and thermal stress distribution of magnetic poles in rotor winding inter-turn short circuit are calculated. On the basis of the calculation, the effects of the different turn numbers and positions of short circuit on the temperature, thermal deformation, and thermal stress of rotor magnetic poles are further studied. It is concluded that the thermal stress of the winding adjacent to the shorted turn would decrease, the thermal stress of the winding farther away from the shorted winding would increase, and so on. The results of this paper can provide references for inter-turn short circuit fault diagnosis and lay a foundation for the further studies of related faults.

Three-dimensional Green’s functions for a point heat source in a trimaterial

We propose a simple yet effective method to derive the three-dimensional temperature field induced by a steady point heat source in a trimaterial composed of an intermediate layer of finite thickness sandwiched between two semi-infinite media. The heat source can be located either in the upper semi-infinite medium or in the intermediate layer. The resulting analytical solutions remain valid for the electrostatic problem of a point electric charge in a trimaterial and are used to obtain the Coulomb force in this case.