Finite Element Heat Research Articles

A High-Temperature Assessment of Air-Cooled Unsteady Pressure Transducers

This paper discusses the problem of measuring unsteady pressure in a high-temperature environment using standard transducers. Commercially available cooling adapters for these transducers use water as the cooling medium to provide thermal protection. This arrangement is suitable only for some test bed applications and not suitable for integration into in-flight active control systems. An assessment of the cooling effectiveness of a commercial water-cooled adapter using air as the cooling medium is presented using an experimentally validated finite element heat transfer model. The assessment indicates survival of an air-cooled transducer, itself rated to 235°C, at source flow temperatures up to 800°C.

The Effect Of Chamber Components On Wafer Temperature Response In An Rtp System

ABSTRACTIn recent years, simulation techniques have emerged as useful tools for the design of semiconductor equipment. However, the need for rapid assessment of potential designs stretches the capability of even the most advanced tools currently available to the limit. In this paper, a simplified model of a rapid thermal processing (RTP) system that significantly reduces the execution time is presented. The model is based on a coupling of semi-analytical expressions for radiation fluxes with a one-dimensional finite element heat transfer model for wafer and slip-free ring temperatures. Results showing the effects of plate reflectivity and slip-free ring emissivity on wafer temperature are presented. It is shown that the simplified model yields results that are in agreement with detailed two-dimensional simulations of the same geometry.

A 3D Cellular Automaton algorithm for the prediction of dendritic grain growth

Two- and three-dimensional (3D) Cellular Automaton (CA) algorithms are proposed for modelling the growth of dendritic grains from the liquid phase. These CA growth algorithms are validated for simple thermal situations by comparing the predicted grain shapes with those deduced from analytical models. The insight obtained by the 3D approach is demonstrated by studying the extension of a single dendritic grain in a squared platform (i.e. at a section change of a casting mould) under various conditions. In particular, the effects of crystallographic orientation, thermal gradient, velocity of the isotherms and growth kinetics are shown. This 3D CA growth algorithm, coupled with finite element heat flow calculations, will become a major tool for the prediction of dendritic grain structures in solidification processes.

Superheater minimum stress unit start-up option of coal-fired power plant

In the operation of coal-fired power plants, the provision of selecting the superheater minimum stress unit start-up option is presented in this paper. This stress minimization is necessary for tomorrow's business climate, of the electric-supply industry, with expanding deregulation and competition both domestic arid global. The start-up option recommended in the present paper is meant to influence the power plant automation in start-up and firing temperature controls. The stress temperatures characteristics for final superheater outlet temperatures are approximated and three selected unit start-up options are identified. The paper presents a practical mathematical formulation of the superheater heat transfer equilibrium. This is done for the unit start-up segment that is the low boiler continuous maximum rating (C.M.R.) range (0–20%). The mathematical formulation of the matrix equilibrium is modelled in the paper as a conductivity spring and a capacity spring opposed by heat fluxes. The heat flow equilibrium equation derived in the present paper is a nonlinear system in which the thermal properties vary with the superheater temperatures. A detailed solution is presented in the paper. Consequently, the paper presents two superheater axisymmetric finite element heat transfer and stress analysis models along with heat transfer and stress analysis results. The paper suggests that automation should include faster plant start-up according to the unit start-up option with the fastest firing rate, which yields minimum stress.

大規模水圧破砕で造成された亀裂の進展範囲と形状の推定

A hydraulic fracturing test was conducted in 1992 at the Hijiori hot dry rock test site. In this test, water was injected into injection well HDR-1. The depth of the injection well was about 2, 200m, and the maximum ternperature of the well was about 270 degC. The main fracture, which was extended along natural joints, was initiated from the bottom hole and a radius of the fracture was estimated to be about 500m from the acoustic emission observation. In this paper, the radius of the fracture, and the pressure, permeability and aperture distribution within the fracture was estimated by numerical simulation. The FEHM (Finite Element Heat and Mass transfer) code was used to estimate the radius of the growing fracture and a pressure distribution within the fracture. The Gangi bed-of-nails model was used to relate the fracture aperture to the fluid pressure. The permeability of the fracture was then calculated from the fracture aperture using Lomize's friction factor. A pressure history match between measured and calculated value was obtained. The simulation result shows that the radius of the fracture at the end of the experiment was about 500m, which agrees well with observations. The estimated apertures of the fracture at the vicinity of the well were 1.4mm and 2.6mm when the injection water rates were kept constant at 6kg/s and 20kg/s, respectively. In this simulation, three fitting parameters were used to match the pressure history. The sensitivities of three parameters on the simulation results were also examined.

Contact metamorphism surrounding the Alta Stock; finite element model simulation of heat- and 18 O/ 16 O mass-transport during prograde metamorphism

Results of calcite-dolomite geothermometry and oxygen isotope studies of marbles in the southern portion of the contact aureole surrounding the Alta stock (Utah) provide evidence for extensive hydrothermal metamorphism in this part of the aureole. Simulation of these two independent data sets with two-dimensional, finite element fluid flow and heat transport models constrains the pattern of fluid flow, minimum permeability, and the permeability structure in this part of the aureole. Model results demonstrate that intrusion of the stock into a homogeneous, isotropic permeability medium yields peak metamorphic temperatures significantly lower than those measured in the marbles and significant {sup 18}O depletions both above and below the Alta-Grizzly thrust system. The latter contradicts the observations in the south aureole that {sup 18}O depletions in the marbles are restricted to marbles below the Alta-Grizzly thrust; dolomitic marbles above the thrust retain original sedimentary values up to the intrusive contact. Models with horizontal permeability barriers above the Alta-Grizzly thrust and extending over the top of the Alta stock are capable of reproducing the observed thermal and {delta}{sup 18}O profiles in the southern aureole. The presence of such horizontal barriers reduces the predominantly vertical fluid flow and heat transfer that would occur in amore » homogeneous and isotropic permeability medium, forcing fluid flow and heat transfer laterally away from the upper flanks of the stock. Such horizontal flow patterns are necessary to produce significant {sup 18}O depletion above the thrust, and to provide the necessary lateral heat transfer to duplicate the observed temperature profile. Best fit model results to the observed thermal and {delta}{sup 18}O profiles provide several new insights into the dynamics of fluid circulation and hydrogeologic characteristics of the southern Alta aureole during prograde metamorphism.« less

Uplift of the Colorado Plateau due to lithosphere attenuation during Laramide low‐angle subduction

The Colorado Plateau is blanketed by Phanerozoic marine and nonmarine strata as young as Cretaceous that are now exposed at elevations of about 2 km. Crustal thickening due to magmatism and horizontal crustal shortening was far less than necessary to cause this uplift, which is commonly attributed to the consequences of mantle lithosphere thinning and heating. The Colorado Plateau and the midcontinent region around Iowa consist of Precambrian bedrock overlain by a similar amount of Paleozoic platformal strata, and thus both regions once had similar lithospheric buoyancy. Mesozoic sedimentation increased the crustal thickness and lithospheric buoyancy of the Colorado Plateau relative to the midcontinent region. Backstripping calculations yield elevation without these sediments and lead to a calculated elevation difference between the two areas of about 1200 m, which represents unexplained plateau uplift. Review of constraints on uplift timing finds little support for a late Cenozoic uplift age and allows early to middle Cenozoic uplift, which is consistent with uplift mechanisms related to low‐angle subduction that ended in the middle Cenozoic. Finite element heat flow calculations of low‐angle subduction and lithosphere attenuation, using a range of initial lithosphere thicknesses and degree of attenuation, indicate that required uplift can result from tectonic removal of about 120 km of mantle lithosphere from an initially 200‐km‐thick lithosphere. This allows for partial preservation of North American mantie lithosphere with its distinctive isotopic signature in some late Cenozoic volcanic rocks and is consistent with normal Pn velocities in the uppermost mantle beneath the plateau.

Experimental verification of models for induction heating of continuous‐carbon‐fiber composites

AbstractHeating of continuous‐carbon‐fiber‐reinforced polymers (CFRPs) by the application of an alternating magnetic field has been shown to be due to dielectric losses in the polymer. Models that predict thermal generation in these composites are input to a finite element heat transfer analysis, providing the predicted transient thermal profile in the plane of the laminate. The validity of the global thermal generation model is established through an experimental test matrix in which various specimen configurations are evaluated and compared with theoretical predictions of transient surface temperatures.

Prediction of grain structures in various solidification processes

Grain structure formation during solidification can be simulatedvia the use of stochastic models providing the physical mechanisms of nucleation and dendrite growth are accounted for. With this goal in mind, a physically based cellular automaton (CA) model has been coupled with finite element (FE) heat flow computations and implemented into the code3- MOS. The CA enmeshment of the solidifying domain with small square cells is first generated automatically from the FE mesh. Within each time-step, the variation of enthalpy at each node of the FE mesh is calculated using an implicit scheme and a Newton-type linearization method. After interpolation of the explicit temperature and of the enthalpy variation at the cell location, the nucleation and growth of grains are simulated using the CA algorithm. This algorithm accounts for the heterogeneous nucleation in the bulk and at the surface of the ingot, for the growth and preferential growth directions of the dendrites, and for microsegregation. The variations of volume fraction of solid at the cell location are then summed up at the FE nodes in order to find the new temperatures. This CAFE model, which allows the prediction and the visualization of grain structures during and after solidification, is applied to various solidification processes: the investment casting of turbine blades, the continuous casting of rods, and the laser remelting or welding of plates. Because the CAFE model is yet two-dimensional (2-D), the simulation results are compared in a qualitative way with experimental findings.

Chlorine-36 Investigations of Groundwater Infiltration in the Exploratory Studies Facility at Yucca Mountain, Nevada

ABSTRACTChlorine-36, including the natural cosmogenic component and the component produced during atmospheric nuclear testing in the 1950's and 1960's (bomb pulse), is being used as an isotopie tracer for groundwater infiltration studies at Yucca Mountain, a potential nuclear waste repository. Rock samples have been collected systematically in the Exploratory Studies Facility (ESF), and samples were also collected from fractures, faults, and breccia zones. Isotopie ratios indicative of bomb-pulse components in the water (36Cl/Cl values > 1250 × 10-15), signifying less than 40-yr travel times from the surface, have been detected at a few locations within the Topopah Spring Tuff, the candidate host rock for the repository. The specific features associated with the high 36Cl/Cl values are predominantly cooling joints and syngenetic breccias, but most of the sites are in the general vicinity of faults. The non-bomb pulse samples have 36Cl/Cl values interpreted to indicate groundwater travel times of at least a few thousand to possibly several hundred thousand years. Preliminary numerical solute-travel experiments using the FEHM (Finite Element Heat and Mass transfer) code demonstrate consistency between these interpreted ages and the observed 36Cl/Cl values but do not validate the interpretations.

Analysis of critical heat flux during subcooled boiling for finned fuel elements

Experimental and analytical studies were performed to determine the critical heat flux (CHF) during subcooled boiling on finned fuel elements. Tests were conducted in a vertical, concentric-annulus test section consisting of a glass tube containing a finned heater element with either six, eight, or ten longitudinal fins. The phenomena leading to CHF are described and the parametric trends are discussed. A two-dimensional finite-element heat transfer model using the Galerkin method was used to analyse the experimental data to obtain CHF values. A dimensionless correlation was derived to predict the CHF values during subcooled boiling. Over 90% of the predicted CHF values agreed with those obtained from the two-dimensional analysis within ±30%.

A comparative finite element heat conduction analysis of laminated composite plates

A Galerkin finite element formulation is applied to the heat conduction problem in laminated composite plates. The laminate conductivity is formed from those of the constituent fibre and matrix. Both steady and transient heat conduction phases are analysed. In each phase four different types of planar finite elements are used and a suitable numerical example is chosen to compare their performances. In other numerical examples the effect of stacking sequence on the temperature field for a metal matrix composite plate is closely studied.

A coupled finite element-cellular automaton model for the prediction of dendritic grain structures in solidification processes

A new algorithm based upon a 2-dimensional Cellular Automaton (CA) technique is proposed for the simulation of dendritic grain formation during solidification. The CA model takes into account the heterogeneous nucleation, the growth kinetics and the preferential growth directions of the dendrites. This new CA algorithm, which applies to non-uniform temperature situations, is fully coupled to an enthalpybased Finite Element (FE) heat flow calculation. At each time-step, the temperature at the cell locations is interpolated from those at the FE nodal points in order to calculate the nucleation-growth of grains. The latent heat released by the cells and calculated using a Scheil-type approximation is fed back into the FE nodal points. The coupled CA-FE model is applied to two solidification experiments, the Bridgman growth of an organic alloy and the one-dimensional solidification of an Al-7wt% Si alloy. In the first case, the predicted boundaries between grains are in good agreement with experiment, providing the CA cell size is of the order of the dendrite spacing. For the second experiment, the quality of the coupled CA-FE model is assessed based upon grain structures and cooling curves. The columnar-to-equiaxed transition and the occurrence of a recalescence are shown to be in good agreement with the model.

肘折高温岩体に形成された人工貯留層の亀裂面の熱交換面積の推定

At the Hijiori Hot Dry Rock test field in Yamagata prefecture, a three month circulation test (Exp. 9102) was conducted in 1991, using a injection well SKG-2, and three production wells HDR-1, HDR-2and HDR-3. During Exp. 9102, pressure, temperature and flow rate were periodically surveyed in the production wells with the PTS (Pressure, Temperature and Spinner) combination tool. Several flow paths were recognized from the PTS surveys and flow rate and temperature changes during Exp. 9102 were obtained.To estimate the heat extraction area, which consisted of several flow paths in the Hijiori HDR reservoir, a model was developed for each flow path using both Finite Element Heat and Mass Transfer Code (FEHM) and Gringarten's model. Calculations were repeated, changing the heat extraction area, until the temperature of production well obtained the best match of Exp. 9102.By matching the observed temperature in the producing zones, important features were observed. There were several flow paths in which the heat extraction area remained constant. Other flow paths, however, experienced an increase in heat extraction area. The main flow paths were produced in wells HDR-2 and HDR-3.These paths had about the same length to heat transfer area ratio. During Exp.9102 very little heat transfer interaction between the fractures was observed.

Simulation of heat transfer in the unsaturated zone : Zyvoloski, G Proc 1st Annual Topical Meeting on High Level Radioactive Waste Management, Las Vegas, 8–12 April 1990V1, P611–617. Publ La Grange Park: ANS/ASCE, 1990

Heat transfer can play an important role in fluid flow near the emplacement site of high-level nuclear waste. The effects on far- field flow can be important in understanding net moisture fluxes above the repository zone. The convection in the unsaturated zone at the Yucca Mountain site was responsible for this movement. If this is so, then the convection could provide a mechanism for drying the rock above the repository zone and thus provide a buffer for heavy rainfall events. In addition, the convection would increase the movement of gaseous radionuclides such as {sup 14}CO{sub 2}, tritiated water vapor, and {sup 129}I (Weeks, 1987). Because of the complexity of the problem, numerical models were required to calculate gas flow and vapor transport at the site. Kipp previously modeled this problem using the code HST3D. This code represents the flow of a single-phase fluid with both heat- and mass-transfer effects included. Water density and partial pressure effects are accounted for by the virtual temperature method. In this paper, the problem was simulated using the code FEHMN, a finite-element heat- and mass-transfer code being developed for the Yucca Mountain Project. The work described in this paper was done in preparation of the upcoming problem to be formulated for the Performance Assessment Calculation Exercise. 5 refs., 9 figs., 1 tab.

A study of the effect of partial loss of protection on the fire resistance of steel columns

Missing fire protection material on steel structural members is generally recognized as a problem, though little information is available to quantify the effect. A finite element heat transfer analysis is used to compare the thermal response of steel columns with lost protection material when exposed to the ASTM E-119 furnace environment. Based on the predicted thermal response and using thermal endpoint criteria specified in ASTM E-119, estimates are made of the fire resistance of each column with varying amounts of missing protection. Relatively small proportional losses of fire protection material are required before significant reductions in fire resistance are realized. The degradation in fire resistance is most significant for light-weight columns and for cases where the fire protection material is missing from the flange rather than web.

INFRARED RADIATION OF SF6AND ITS APPLICATION TO GAS-FILLED DOUBLE-PANE WINDOWS

Interest in using sulfur hexafluoride (SF6 as a gas-fill in multipane windows has raised questions concerning the calculation of heat transfer rates through such windows. The infrared absorption characteristics of this gas make the heat transfer analysis much more complicated. In order to account for the absorption effect, we measured the spectral absorptivity of several infrared-active bands of sulfur hexafluoride at low resolution and a temperature of 298 K. We correlated the spectral absorption data with the Edwards exponential wide-band model and with the Elsasser narrow-band model, and incorporated the wide-band model into a one-dimensional, finite-element heat transfer model. The finite-element heat transfer model considered combined conduction and radiation effects in a double-pane window, and was used to evaluate the overall heat transfer coefficients of double-pane windows filled with SF6; CO2, or air. The numerical results show good agreement with the experimental results

高温岩体抽熱システムの評価のための現場試験とモデル化

A 15-day flow test (Exp. 8805) was conducted at the hot dry rock reservoir created by hydraulic fracturing at the bottom of injection well, SKG-2 at Hijiori test field in Yamagata Prefecture. The depth of SKG-2 well was about 1, 800m and the bottomhole temperature was about 250°C. Water was circulated at the flow rate of 0.5 t/min for first 10 days and then increased to 1.0 t/min. During the circulation test, fluid pressure, temperature and flow rate were measured at the wellheads of injection well, SKG-2 and production well, HDR-1. Production well temperature increased throughout the test and reached a maximum of 175°C, while the water recovery was about 40%.To evaluate the reservoir performance during Exp. 8805, two models were introduced: one is applied above 1, 500m depth and the other below 1, 500m depth, because we can analyze the performance above 1, 500m as two wells model and must introduce three-dimensional model for the reservoir created in hot dry rock. First, we calculate water temperature in SKG-2 well at the depth of 1, 500m using WBHT (Wellbore Heat Transfer Code). Then, the reservoir performance was simulated by placing two wellbores, SKG-2 and HDR-1 in the finite element mesh of FEHM (Finite Element Heat and Mass Transfer Code) at their relative positions. After the data match to this circulation test, one year simulation was conducted to predict the reservoir performance. Finally, the temperature of production fluid at the wellhead of HDR-1 well was calculated by the WBHT. The results showed that the wellhead temperature of production well reached 180°C and kept almost constant at the flow rate of 0.5 t/min and the recovery of 40%, while it reached 202°C and decreased to 185°C when the flow rate was 1.0 t/min and recovery was 38%.

Sizing Design Sensitivity Analysis of Linear Steady Heat Transfer Systems Using Established Finite Element Codes

Abstract A method for design sensitivity analysis of linear steady-state heat transfer systems is presented. To carry out computation of the sensitivity expressions derived in this paper, only postprocessing data from established finite element heat transfer codes are required. It is shown that design sensitivity computations can be performed efficiently without having to embed design sensitivity software into the finite element heat transfer code. Heat conduction is considered with convection boundary conditions. For heat transfer systems made up of one or more component types, sizing design variables such as thickness and cross-sectional areas of components of individual members, heat conductivities of materials, and surface convection coefficients are considered. A distributed parameter approach to design sensitivity analysis is used to retain the continuum formulation throughout the derivation of design sensitivity results. Expressions for design sensitivity of a general functional are thus derived in the continuum setting, using both direct differentiation and adjoint variable methods, which can be evaluated numerically using analysis results from established finite element heat transfer analyzers. The methods do not require differentiation of element thermal conductivity matrices in conventional finite element models. For numerical implementation, only the adjoint variable method is considered. Accurate design sensitivity results are obtained without the uncertainty of numerical accuracy and high cost associated with selection of finite difference perturbations.

Finite element model for thermal system in real time operation diesel piston

This study presents a finite element heat transfer model for the prediction of piston temperature distributions in a real time operation engine. The thermal boundary conditions are specified adequately in the model for various operations. The time-mean, area-averaged gas temperature and heat transfer coefficient could be obtained from the engine simulation. The ambient temperatures along the piston ring belt and skirt were estimated with a formula and the corresponding heat transfer coefficients were arrived at through equivalent thermal circuit analysis. The model is also calibrated and the predicted and measured temperatures compared for the operating engine. The predictions are reasonable, providing confidence in the use of the simulation model.