Constant Temperature Boundary Condition Research Articles

Relative Stress Analysis of Gas Turbine Blade for Various Alloying Materials

Gas turbines provide a reliable and efficient production of power in both pilot power plants and aircraft propulsion. The operating cost of the modern gas turbines is greatly influenced by the durability of hot section components. To cope up with the increasing temperature, there has been an evolution of new generation blade materials. At elevated temperature conditions, thermal stress and resulting deformations can affect the power developed and efficiency. In this paper a finite element simulation has been made on a fixed blade profile to explore various factors affecting the turbine blade. Variety of existing and new generation materials have been considered a under a boundary condition of constant high pressure and high Operating temperature was varied between 1000°C-1400°C. The development of stress and deformation along with the heat flux have been studied for finding the most effective manufacturing alloy for gas turbines.

Evaluating the different boundary conditions to simulate airflow and heat transfer in Double-Skin Facade

The CFD simulation accuracy mostly depends on the appropriate setting of boundary conditions and numerical simulation parameters. This study shows the influence of two types of boundary condition settings on the CFD simulation results of Double-Skin Facade (DSF) for a specific problem. These two boundary settings are the constant temperature on the DSF surfaces called Boundary A, and Boundary B is defined via solar radiation using the Discrete Ordinate radiation Model (DOM). The paper verified both the numerical simulations using the experimental data. Comparing the numerical results of two types of boundaries with experimental data shows that both cases underestimated the values lower than 5.2 K and 0.1 m/s for the temperature and velocity respectively at the regarded measured points. Boundary A gives more accurate temperature prediction results, while Boundary B shows velocity magnitude closer to the measurements in the middle height of the cavity; the average temperature and velocity differences between the two boundary types are 0.6 K and 0.003 m/s respectively which are negligible. Finally, the selection of boundary conditions depends on study purposes, however, when the DSF is equipped with blinds and if there is not enough data in hand but the exact value of solar irradiation, using the Boundary B approach is suggested; it can provide reasonable results associated with multi-type of thermal boundary conditions at the same time. Furthermore, if the goal is to investigate the flow pattern in the DSF, Boundary B is argued to perform better than the constant temperature boundary condition.

The Effect of Inclination on Natural Convective Heat Transfer from a Slender Cuboid

A numerical study was undertaken of the naturally occurring laminar convective heat transfer from a slender cuboid with a relatively narrow cross-section (square) and an exposed top surface. The cuboid was perpendicularly placed on an adiabatic flat base plate and two types of surface boundary conditions were considered. The slender cuboid was inclined relative to the vertical axis at angles ranging from 0 to 180 degrees. The flow was considered symmetrical along the vertical axis of the slender cuboid. The equations governing the system were numerically solved in terms of dimensionless variables using FLUENT software. From the results obtained, mean Nusselt numbers over the slender cuboid were calculated using parameters such as: the Rayleigh number for heat flux, Ra*; the Rayleigh number, Ra; the slender cuboid dimensionless width, i.e., the ratio of the width to the height of the heated slender cuboid, W = w/h; and the position of the slender cuboid relative to the vertical, φ. Simulation results were produced for the boundary conditions of constant temperature, constant heat flux, and for Pr = 0.7. The effects of these parameters on the mean Nusselt number for the combined and for the individual surfaces of the slender cuboid are presented and the mean Nusselt numbers are correlated.

Design and Optimization of a Composite Heat Spreader to Improve the Thermal Management of a Three-Dimensional Integrated Circuit

Abstract This study establishes a numerical investigation of the optimal distribution of a limited amount of high thermal conductivity material to enhance the heat removal from 3D integrated circuits, IC. The structure of the heat spreader is designed as a composite of high thermal conductivity (Boron Arsenide) and moderate thermal conductivity (copper) materials. The volume ratio of high-conductivity inserts to the total volume of the spreader is set at a fixed pertinent ratio. Two different boundary conditions of constant and variable temperature are considered for the heat sink. To examine the impact of adding high-conductivity inserts on the cooling performance of the heat spreader, various patterns of the single and double ring inserts are studied. A parametric study is performed to find the optimal location of the rings. Moreover, the optimal distribution of the high-conductivity material between the inner and outer rings is found. The results show that for the optimal conditions, the maximum temperature of the 3D IC is reduced up to 10%; while at the same time, the size of the heat sink and heat spreader can be diminished by as much as 200%.

A novel three-dimensional implicit numerical model of a borehole field heat exchanger that accounts for seasonal fluctuations of the soil temperature

This study proposes a new three-dimensional implicit numerical model to simulate a borehole field heat exchanger that accounts for seasonal fluctuations of the soil temperature. The model uses an alternating-direction implicit finite difference approach to perform the simulation. The effect of seasonal changes in the soil temperature is considered using an internal heat source term in the governing equations. The model is validated against several published in-situ tests as well as a laboratory experimental study and the results obtained from a TRNSYS version of the duct storage (DST) model, demonstrating an average error of less than 3%.The validated model is then applied to analyse the impact of accounting for seasonal soil temperature fluctuations at various borehole lengths and climate zones. This analysis compares the results obtained from a model that uses constant temperature boundary conditions against those from a model that contains the internal heat source term and uses adiabatic boundary conditions. A significant discrepancy between the outputs of the two models has been observed for shallow borehole heat exchangers (H < 60 m) and at locations with a high annual amplitude of the surface temperature variations (ΔTa > 5°C). Thus, the assumption of constant temperature at the ground surface is only appropriate for deep boreholes (H > 60 m) or at locations with a relatively low annual amplitude of the surface temperature variations (ΔTa < 5°C).

Analytical Thermal Boundary Condition for Quasi-Transient Simulation of Internal Flow Experiments

Transient thermochromic liquid crystal (TLC) experiments can provide high-fidelity spatially resolved heat transfer data for complex geometries, particularly where infrared techniques cannot be applied. One challenge when applying transient methods to internal geometries is the local definition of the driving gas temperature. The transient nature of the streamwise driving gas temperature profile has led to comparisons with steady-state computational fluid dynamics being questioned. This paper explores simulating the temporal behavior of transient TLC experiments directly. A novel technique is developed to account for differences in the gas and solid time scales, where surface temperature is calculated at each spatial location analytically from the surface heat flux, using an impulse response method assuming one dimensional, semi-infinite conduction. Postprocessing of the simulated surface temperature history is performed using the same method as experimentally, allowing for direct comparison. This analytical thermal boundary condition (ATBC) is applied to simulate a transient TLC experiment of a stationary superscaled rib turbulated internal cooling passage in a gas turbine engine. Traditional steady-state simulations were also performed with constant temporal and spatial temperature boundary conditions. Results show that calculations using the new ATBC and traditional steady-state method give very similar Nusselt number distributions and mean values in relation to the experimental data, suggesting the larger discrepancy between simulations and the experiments is not the definition of the driving gas temperature. Analysis of transient variation of Nusselt number indicated brief highly localized maximum variations up to 40%, although this was not found to significantly affect the mean values, and passage-averaged values converged to within 0.5% of the final value within 0.2 s.

A novel spiral channel with the growing waviness on the sidewalls for compact high-efficiency heat exchanger

Spiral channels are widely used as the core heat exchangers in latent thermal storage units. This study aims to develop a novel spiral channel characterized by wavy sidewalls for high-efficiency convective heat transfer in tube side. The amplitude of the wavy sidewalls is designed to grow from the inlet to the outlet along flow direction. The thermal characteristics in the spiral-wavy channel were numerically investigated under the boundary condition of constant wall temperature, since latent heat storage units mainly work under isothermal condition. The comparison was carried out between a smooth-spiral channel and a spiral-wavy channel in terms of the heat transfer capacity, friction factor, dimensionless temperature distributions and development of boundary layers. At a given heat transfer rate, the required length of the spiral-wavy channel is only 63.5% of that of the smooth-spiral channel, which implies that the energy density and efficiency of a heat storage unit can be improved remarkably. The increase in pressure drop brought by the spiral-wave channel is less important compared with the improvement of thermal performance, suggesting its potential in heat transfer enhancement and energy saving. The present work is expected to motivate the design of compact and high-efficiency heat exchangers for thermal energy storage and extraction.

Application of Taguchi method in the numerical analysis of fluid flow and heat transfer around a flat tube with various axial ratios

In this paper, the behavior of airflow over flat and circular tubes is investigated in terms of aerodynamics and heat transfer simultaneously to determine the most effective factors and their optimum levels. Three types of flat tubes, with axial ratios of 1.5, 2, and 2.5, are considered in comparison with circular tubes. Two boundary conditions of constant temperature and constant heat flux are applied on the tube wall. By using the Taguchi method and analysis of variance (ANOVA), the L16 array is investigated statistically. The drag force coefficient, the Nusselt number, and the thermal-hydraulic performance are calculated, as well as the optimal values and contributions of design variables. The results show that, while the axial ratio has a major effect on the drag force, it has little impact on the rate of heat transfer, and the tube wall boundary condition would be more effective. However, the axial ratio of the tube has the greatest impact on thermal-hydraulic performance. In terms of flow behavior, the vortex shedding phenomenon is eliminated in most cases of flat tubes. By utilizing the Taguchi method and statistical analysis, the volume of calculations is reduced by 50% without considering the reduction of data analysis time.

Effect of viscosity on entropy generation for laminar flow in helical pipes

Entropy generation for fully developed laminar flow in a helical pipe carrying high viscous fluid under constant temperature boundary conditions is investigated analytically. This work focuses on geometrical, fluid, and thermal aspects and their influence on irreversibilities in helical coils. The effect of viscosity on the irreversibilities and its influence on the operating parameters of the helical coil are studied with the second law of thermodynamics. The most commonly used relationships for estimating viscosity change due to temperature are selected for analysis. The entropy generation and avoidable exergy destruction in each case are presented. Bejan number is plotted for varying viscosities under different wall temperatures for both heat transfer to and from the fluid. The thermodynamic potential of improvement based on avoidable and unavoidable exergy destruction concepts showed that the potential of improvement for heating and the cooling condition is considerable for a given operating condition in helical tubes. The selected model for estimating viscosity influences the optimum operating wall temperature, thereby giving an insight into a selection of a proper viscosity model. The optimum helical number is not affected by fluid properties and wall temperature. The heat transfer to pumping ratio is evaluated and it is found that the optimal value is influenced by the change in viscosity.

Development of an Efficient Conjugate Heat Transfer Modeling Framework to Optimize Mixing-Limited Combustion of Ethanol in a Diesel Engine

Abstract Mixing controlled combustion of alcohol fuels has been identified as a promising technology based on their low propensity for particulate and NOx production, but the higher heats of vaporization and auto-ignition temperatures of these fuels make their direct use in diesel engine architectures a challenge. To realize the potential of alcohol-fueled combustion, a computational fluid dynamics (CFD) modeling framework is developed, validated, and exercised to identify designs that maximize engine thermal efficiency. To evaluate the use of thermal barrier coatings (TBCs), a simplified one-dimensional (1D) conjugate heat transfer (CHT) modeling framework is employed. The addition of the 1D CHT model only increases the computational expense by 15% relative to traditional approaches, yet offers more accurate heat transfer predictions over constant temperature boundary conditions. The validated model is then used to explore a range of injector orientations and piston bowl geometries. Using a design of experiments (DoE) approach, several designs were identified that improved fuel–air mixing, shortened the combustion duration, and increased thermal efficiency. The most promising design was fabricated and tested in a Caterpillar 1Y3700 single-cylinder oil test engine (SCOTE). Engine testing confirmed the findings from the CFD simulations and found that the co-optimized injector and piston bowl design yielded over 2-percentage point increase in thermal efficiency at the same equivalence ratio (0.96) and over 6-percentage point increase at the same engine load (10.1 bar indicated mean effective pressure (IMEP)), while satisfying design constraints for peak pressure and maximum pressure rise rate.

Impact of Additive Manufacturing on Internal Cooling Channels With Varying Diameters and Build Directions

AbstractThe use of additive manufacturing (AM) processes, such as direct metal laser sintering, provides the design freedom required to incorporate complex cooling schemes in gas turbine components. Additively manufactured turbine components have a range of cooling feature sizes and, because of the inherent three-dimensionality, a wide range of build angles. Previous studies have shown that AM built directions influence internal channel surface roughness that, in turn, augment heat transfer and pressure loss. This study investigates the impact of AM on channel feature size and builds direction relative to tolerance, surface roughness, pressure losses, and convective cooling. Multiple AM coupons were built from Inconel 718 consisting of channels with different diameters and a variety of build directions. An experimental rig was used to measure pressure drop to calculate friction factor and was used to impose a constant surface temperature boundary condition to collect Nusselt number over a range of Reynolds numbers. Significant variations in surface roughness and geometric deviations from the design intent were observed for distinct build directions and channel sizes. These differences led to notable impacts in friction factor and Nusselt number augmentations, which were a strong function of build angle.

Lattice Boltzmann simulation of natural convection melting in a cubic cavity with an internal cylindrical heat source

In this work, natural convection melting in a cubic cavity with an internal cylindrical heat source is studied numerically by employing the two-relaxation-time lattice Boltzmann (LB) method. In numerical simulations, natural convective melting of pure Gallium in a three-dimensional enclosure is first considered to validate the present LB model. Then, effects of some key parameters, including the thermal boundary conditions at the walls of the outer enclosure, the location and the placement direction of the inner cylinder are numerically studied and analyzed. It is found that the full melting time obtained for the case of the constant temperature boundary condition is larger than that obtained for the case of the adiabatic boundary condition. In addition, the variation of the location of the inner cylinder plays an essential role in full melting time, and when the inner cylinder is located at the center of the cavity, the full melting time obtained in such a case is always smaller than the other cases. Further, the streamlines as well as the distributions of the temperature obtained for different conditions are also presented and discussed.

Heat transfer from a particle in laminar flows of a variable thermal conductivity fluid

We revisit the classical problem of steady-state heat transfer from a single particle in a uniform laminar flow with the assumption that the thermal conductivity of the fluid changes linearly with the temperature. We use a combination of asymptotic and scaling analyses to derive approximate expressions for the dimensionless heat transfer coefficient, i.e., the Nusselt number Nu, of arbitrarily shaped particles. The results cover the entire range of the Peclet number Pe. We find that, for a constant temperature boundary condition and fixed geometry, the Nusselt number is essentially equal to the product of two terms, one of which is only a function of Pe while the other one is nearly independent of Pe and mainly depends on the proportionality constant of the conductivity-temperature relation. We also show that, in contrast, when a uniform heat flux is imposed on the surface of the particle, Nu can be estimated as a summation of a Pe-dependent piece and one that solely varies with the proportionality constant.

Entropy generation analysis in a single-turn pulsating heat pipe considering phase change modeling

Pulsating heat pipes are one of the most important solutions for the daily increasing demand for high-performance cooling systems. Despite numerous studies in this field, most of the previous works, including experimental and numerical studies, take constant heat flux boundary condition into account and neglect thin-film boiling and condensation. Furthermore, an improvement in accuracy is essential for the models that consider constant temperature boundary condition. In order to satisfy the essence of accuracy improvement in modeling of constant temperature boundary condition PHPs, the present study models a single-turn pulsating heat pipe numerically, which is based on the best predictor correlations for flow boiling and condensation. Moreover, a thin liquid film is considered in the calculation of mass transfer from vapor plugs, because of annular flow assumption. All fundamental equations, except liquid-slug-energy equation, are solved explicitly. Comparison of displacement of the liquid slug, with the previous works, indicates an increase in both amplitude and frequency. In contrast to the previous mathematical models, acceptable agreement between empirical data and the present mathematical model has been demonstrated. Furthermore, entropy generation analysis has been carried out to achieve optimum operating conditions and the results have been presented for different pipe diameters. These data also depict the effect of diameter on the properties of PHP, besides entropy generation analysis. Bejan number for simulations has been derived to show heat transfer share in entropy generation. It is shown that the share of heat transfer in entropy generation also increases by the diameter.

High pressure turbine blade internal cooling in a realistic rib roughened two-pass channel

Simplified rectangular or square channels are commonly adopted for studying turbine blade internal cooling characteristics under constant temperature or constant heat flux boundary conditions, but the effects caused by those simplifications have not been considered in detail. This paper used a numerical method to study blade internal cooling in a realistic rib roughened two-pass channel of a Pratt & Whitney Energy Efficient Engine high-pressure turbine blade under turbine design conditions. The purposes are two-fold: 1) to investigate the effects of the types of wall boundary condition on blade internal heat transfer, including coupled wall, constant temperature wall, and constant heat flux wall; 2) to present the internal heat transfer and pressure losses in the channel with two types of rib roughened walls, i.e., Model A with 60-degree inclined ribs and Model B with 60-degree V-shaped ribs. Both stationary and two rotating conditions with rotation number Ro= 0.1 and 0.2 are considered. The turbulence model is Shear Stress Transport k-ω model. The results revealed that: 1) The types of wall boundary conditions have large effects on blade internal cooling performance. At the stationary condition, the maximum difference in local normalized Nusselt number (Nu/Nu0) on the trailing surface can be as large as 44.4% between the coupled wall and constant temperature at the inlet pass, and 50% between the coupled wall and constant heat flux at the outlet pass. Under blade rotations, the large difference in Nu/Nu0 remains on the trailing surface, while on the leading surface only minor difference exists. 2) At the stationary condition, the maximum difference in Nu/Nu0 between the trailing surface and leading surface for Model A 51.3%, and Model B 40.7%. 3) At the stationary condition, in the inlet pass, the results of Mode A and B are close to the simplified channels. In the outlet pass, a relatively large discrepancy exists between the two ribbed models and their corresponding simplified channel results. 4) Blade rotation results in a large increase in Nu/Nu0 on the trailing surface in the inlet pass and bend regions of the three models. The maximum change in Nu/Nu0 reaches over 100% for each model, which is significantly higher than that of the simplified channels. 5) The friction factor of the two ribbed models decreases with the rotation number. The difference in pressure drop and friction factor between the two ribbed models also decreases with the rotation number.

Experimental investigation of enhancing influence of Al2O3 nanoparticles on the convective heat transfer in a tube equipped with twisted tape inserts

In this study, the heat transfer rate of Al2O3-water nanofluid-flow in a tube with twisted tape inserts is experimentally examined. The twisted tape insert can cause a swirling region in the fluid-flow which will enhance the heat transfer coefficient. On the other hand, the twisted tape inserts have a great influence on the pressure drop. It is known that nanoparticles and twisted tape inserts may both increase the heat transfer rate of the fluid. Thus, in this study, it is tried to demonstrate the combined effect of both phenomena, experimentally. In this way, the Al2O3-water nanofluid is used as the carrier liquid in a tube equipped with various twisted tape inserts of different pitches and twist ratios. Moreover, the influence of nanoparticles? volume fractions was studied in the turbulent regime of a tube with the constant temperature boundary condition.

Numerical investigation on conjugate heat transfer in octet-shape-based single unit cell thick metal foam

Present study reports flow and thermal transport characteristics of metal-foam based on Octet-shaped unit cell (porosity ~ 0.97) for electronic cooling application with water as the working fluid. Conjugate simulations were carried out on a single cell thick lattice frame comprising of four consecutive connected unit cells in the streamwise direction. Simulations were performed for flow velocity range of 2–8 cm/s with the substrate subjected to a heat flux of 10 W/cm2, for two different solid-phases corresponding to solid-to-fluid thermal conductivity ratios (ks/kf) of 37 and 288. A control-volume-based energy balance method was adopted for calculation of global and cell-based convective heat transfer coefficient in the conjugate simulations, where the global heat transfer coefficient was ~ 2900 W/m2K for ks/kf~288 and ~ 2100 W/m2K for ks/kf~37, both for flow velocity of 8 cm/s. The cell-based heat transfer coefficient showed a sharp declining trend typical of developing flow. The interfacial heat transfer coefficient (hsf) on the fibers and the substrate-endwall was also obtained through separate simulations imposing constant heat flux and constant temperature boundary conditions on the walls. The averaged hsf on fiber walls and substrate-endwall was ~ 8700 W/m2K and ~ 2000 W/m2K, respectively, corresponding to average flow velocity of 8 cm/s.

The Influence of Leg Shape on Thermoelectric Performance Under Constant Temperature and Heat Flux Boundary Conditions

Global energy resource consumption is increasing rapidly, and wasted energy (the portion not used for useful services) comprises a significant fraction of the energy consumed. Much of the wasted energy is in the form of heat. Thermoelectric devices offer the potential to convert this wasted heat into electricity, and they can be used for thermal management by pumping heat. The shape of thermoelectric devices, particularly the active semiconducting material units (or thermoelectric legs) within the device, has remained largely unchanged. However, the advent of new manufacturing techniques such as additive manufacturing enables customizable device shapes. Given these new manufacturing capabilities, exploring atypical, or non-rectangular, leg geometries becomes increasingly relevant. This work focuses on understanding the effect of different thermoelectric leg designs on thermoelectric device performance. Various leg shapes were studied for their thermal and electrical performance under different thermal boundary conditions. The shapes studied include rectangular prisms, rectangular prisms with interior hollows, trapezoids, hourglass, and Y-shapes. Temperature gradients and the electrical potentials of the thermoelectric legs are determined using the COMSOL Multiphysics Thermoelectric Module. Both fixed temperature and fixed heat flux boundary conditions were examined numerically. Among the geometries investigated, the hourglass-shaped thermoelectric leg, subjected to a fixed temperature boundary condition, is found to have the best thermal and electrical performance. The hourglass-shaped leg results in more than double the electrical potential and maximum power compared to the conventional rectangular shape when the cold side experiences a natural convection boundary condition. Under a fixed heat flux boundary condition on the hot side, a trapezoid-shaped leg results in almost double the electrical potential and a 50% increase in the power output compared to the conventional leg shape. Varying boundary conditions, which reflect different device operating conditions, result in different performance values for the same leg shapes. These findings underscore the importance of leg geometry on electrical and thermal performance of a thermoelectric leg, as well as the importance of considering the device operating condition when selecting the best leg shape.

Spectral method solutions of a variable aspect ratio duct flow in a uniform transverse magnetic field with two different thermal boundary conditions

Abstract A laminar electrically-conducting flow inside an electrically-insulated rectangular duct in a uniform transverse magnetic field with both uniform surface temperature and uniform heat flux boundary conditions are considered numerically. The problem with aspect ratios of the range from 1:10 to 10:1 and Hartmann number M up to 1000 is solved using a highly accurate technique which is spectral method. The flow variables are expanded in terms of linear combinations of Chebyshev polynomials chosen to satisfy the boundary conditions implicitly. The resulting equations are collocated using the Gauss points to produce a system of nonlinear algebraic equations which is solved iteratively using Gauss elimination. Convergence properties of the numerical method reveals that for aspect ratio of less than 4 to 1, the flow is well resolved with as small as 29 by 29 Chebyshev polynomials; however, as the aspect ratio increases to more than 4 to 1, the number of polynomials required for an adequate resolution can be as high as 49 by 49 polynomials. It is found when the magnetic field is turned on, the pressure drop, in general, increases with the field for different aspect ratios. However, the pressure drop increase will be slower near the aspect ratio of 10. Also, the heat transfer increases with the field for most of the cases, but for some cases the field will have adverse effect on the heat transfer, particularly, for constant surface temperature boundary condition at aspect ratio > 4 and M 4 and M

Heat pipe failure accident analysis in megawatt heat pipe cooled reactor

The heat pipe cooled reactor is an advanced reactor design which is nearly solid-state with an array of in-core heat pipes for passive heat transfer. The local heat pipe failure probability is certainly high over the reactor lifetime. Therefore, the reactor design must include consideration of heat pipe failure accidents which needs to be explored in-depth. The Monte Carlo neutron transport code RMC was used with the general finite element analysis software ANSYS Mechanical to analyze the thermal/mechanical characteristics of a megawatt heat pipe cooled reactor for both normal and heat pipe failure conditions. The simulations were verified against a previous study with the predicted temperature distributions being consistent with each other with an absolute error of less than 3 K. Further analyses show that a 2-D model simulation can also well represent the 3-D model for heat pipe failure accident analyses. Sterbentz et al. (2017) simplified the heat pipe model with a constant temperature boundary condition along the evaporator wall of 950.15 K regardless of the heat load or heat pipe operating temperature. Therefore, a heat pipe subroutine was added to the codes to predict the heat pipe temperatures during a heat pipe failure accident. The results show that the heat pipe failure will cause larger temperature rises and stress concentrations. The heat pipe wall temperatures in the core differ from each other with the differences between the heat pipe loads during normal heat pipe operation and with failures reflecting the local effect of the heat pipe failures. The operating conditions far from the failure area are little affected (<20 K temperature change) by a single heat pipe failure. The effects of the heat pipe failure on the reactor core reactivity and local power distribution were also analyzed with a reactivity change of less than 5 pcm and a local power change of less than 0.1%. Therefore, the heat pipe failure can be analyzed in steady-state simulations with unchanged power distributions.