Constant Property Model Research Articles

Device level assessment of Ni and Ni45Cu55 as electrodes in Mg2(Si,Sn)-based thermoelectric generators

Owing to efficient thermoelectric conversion, non-toxicity, low density and cost, Mg2(Si,Sn)-based solid solutions hold potential for mid-to-high temperature waste heat recovery. Yet, challenges arise from n-Mg2(Si,Sn) degradation at ≥400 °C caused by Mg loss and charge carrier reduction, particularly in Sn-rich compositions. To build a thermoelectric generator (TEG) stable up to 400 °C, we propose binary Mg2Si as the n-type leg. Using Ni45Cu55and Ni yields low electrical contact resistance (<5 µΩ.cm2) without altering the thermoelectric properties of n-Mg2Si. We fabricated two 2×2 leg TE modules with the same electrode/TE combination for the p-type legs and with Ni or Ni45Cu55 for their n-type legs and tested up to 400 °C, allowing for a direct comparison between these twoelectrodes for n-Mg2Si at the device level. Ni45Cu55 outperformed Ni, resulting in a peak power density of 0.79 W/cm2 at ΔT ∼375 K and an efficiency competitive to Mg2(Si,Sn)-only TEG.Comparative simulations using a constant property model revealed a strong reduction of internal losses when using Ni45Cu55as the electrode for n-Mg2Si as the main reason for the high performance. The presented design overcame challenges such as Mg sublimation at targeted application temperature or electrode induced defect formation, resulting in a stable TEG.

High-performance tellurium-free thermoelectric module for moderate temperatures using α-MgAgSb/Mg2(Si,Sn)

α-MgAgSb is a promising thermoelectric material with an average figure of merit above unity between room temperature and 573 K, making it attractive for low temperature waste heat recovery or temperature regulation applications. We demonstrate here the first α-MgAgSb/Mg2(Si,Sn)-based thermoelectric module, where Mg2(Si,Sn) was chosen as n-type counterpart due to its excellent thermoelectric properties, low weight, abundant, and eco-friendly constituents. By using this new material combination, a maximum conversion efficiency of 6.4% and maximum power of 0.68 W were achieved for a temperature difference of 275 K, superior to commercially available (Bi,Te,Sb)-based thermoelectric modules. The Constant Property Model was used to check the validity of the measurement results and to identify room for further improvement. The characterization of the prototype shows a relatively good match between measurement and calculation for most of the thermoelectric module performance parameters; however, the measured internal electrical resistance is around 10% higher than the predicted values, indicating opportunities for further enhancement.

Recent trends of ternary, quaternary half-Heusler thermoelectric materials and contact resistance effect on their power output efficiency

Climate change isone of the most pressing global issues, owing to the high carbon footprint generated during conventional power generation via coal consumption and gasoline-fuelled exhaust. Furthermore, nearly half of thetotal energy is lost as heat. Suitable thermoelectric (TE) devices can convert waste heat into green/clean energy. Moreover, these devices have no moving parts, require no maintenance, and are environmentally friendly. A better TE device's thermoelectric performance (zT) should be highly cost-effective for process scaling. Because of their low cost, narrow band gap, better contact engineering, decent electrical properties, and high mechanical performance, Half-Heusler (HH) compounds (space group Fm-3 m) have been considered the best candidate materials worldwide. However, these materials have a high thermal conductivity. The high thermoelectric performance of HH compounds was achieved through iso-electronic doping and nanostructuring, which reduced thermal conductivity significantly. The current report briefly overviews17, 18, 19, and 21 valence electron count (VEC) HH materials and their effects on thermal conductivity and zT. Finally, using cumulative temperature dependence (CTD) and constant property models (CPM), the theoretical estimation of power density and efficiency was calculated by considering the materials' thermoelectric performanceand contact resistance.

Analyzing the Performance of Thermoelectric Generators with Inhomogeneous Legs: Coupled Material–Device Modelling for Mg2X-Based TEG Prototypes

Thermoelectric generators (TEGs) possess the ability to generate electrical power from heat. As TEGs are operated under a thermal gradient, inhomogeneous material properties—either by design or due to inhomogeneous material degradation under thermal load—are commonly found. However, this cannot be addressed using standard approaches for performance analysis of TEGs in which spatially homogeneous materials are assumed. Therefore, an innovative method of analysis, which can incorporate inhomogeneous material properties, is presented in this study. This is crucial to understand the measured performance parameters of TEGs and, from this, develop means to improve their longevity. The analysis combines experimental profiling of inhomogeneous material properties, modelling of the material properties using a single parabolic band model, and calculation of device properties using the established Constant Property Model. We compare modeling results assuming homogeneous and inhomogeneous properties to the measurement results of an Mg2(Si,Sn)-based TEG prototype. We find that relevant discrepancies lie in the effective temperature difference across the TE leg, which decreases by ~10%, and in the difference between measured and calculated heat flow, which increases from 2–15% to 9–16% when considering the inhomogeneous material. The approach confirms additional resistances in the TEG as the main performance loss mechanism and allows the accurate calculation of the impact of different improvements on the TEG’s performance.

Efficiency Measurement and Modeling of a High‐Performance Mg2(Si,Sn)‐Based Thermoelectric Generator

Mg2(Si,Sn) is an attractive material class due to its excellent thermoelectric (TE) properties, its eco‐friendly constituents, its low mass density, and its low price. A lot of research has been done on optimizing its TE properties; however, works on its use in thermoelectric generators (TEG) are scarce. Herein, the first conversion efficiency measurement of a functional, fully Mg2(Si,Sn)‐based TEG, approaching a maximum value of 4% for an applied = 375 °C, is shown. A maximum power density of 0.9 W cm−2 (related to the cross‐sectional area of the TE legs) at =375 °C is also reported, which is among the highest performance of silicide‐based modules reported in literature. Efficiency measurements can be tricky due to the uncertainty of heat flow measurement and parasitic heat losses; therefore, assessing the measurement reliability by confronting it to theoretical calculations is necessary. TEG device simulation in a constant property model is used to compare measured data to expected values and a good match is found (&lt;1% deviation for current at maximum power, &lt;4% difference for maximum power output, deviation within measurement uncertainty range for heat flows and efficiency). The significant discrepancy between measurement and calculations of the inner electrical resistance reveals room for improvement. Cracks form due to thermally induced mechanical stress, which dramatically increase the inner electrical resistance. It is shown that by avoiding those cracks, the maximum power output and conversion efficiency of the TEG could be improved by 30%.

Effect of overburden spatial variability on field-scale geomechanical modeling of potential CO2 storage site Smeaheia, offshore Norway

Although geological CO2 sequestration is an essential solution for reducing anthropogenic carbon dioxide from the atmosphere, the method needs critical evaluation of injection-induced mechanical risks for safe and reliable CO2 storage. 3D field-scale geomechanical modeling is a preeminent solution for assessing mechanical risks of subsurface geological CO2 storage. However, data scarcity of seals and overburden rocks might limit building the 3D field-scale geomechanical model. This study focuses on seismic data-derived 3D field-scale geomechanical modeling of potential CO2 storage site Smeaheia, offshore Norway. The geomechanical properties inverted from seismic data are resampled in the 3D grid to consider spatial variabilities of seal and overburden rock properties. This method allows us to investigate the effect of overburden rock spatial variability imposed in seismic data on the 3D geomechanical model of Smeaheia. The model was built in Petrel-2019, while the one-way geomechanical simulation is iterated using the finite element method. Simplified constant overburden property models are also constructed to analyze the sensitivity of the overburden rock properties. The results reveal that the seismic data-driven spatially distributed overburden properties model workflow used in this study is a convenient and robust solution for 3D field-scale geomechanical modeling. The maximum vertical estimation of rock deformation is doubled in the simplified (isotropic) overburden rock property model compared to the new spatially variable (anisotropic) overburden rock property model. The Mohr-Coulomb failure envelope reveals that the new modeling approach is less prone to failure than the simplified (isotropic) model, which might influence the project decision. Moreover, our study demonstrates the importance of considering the spatial variability of overburden rock properties in building the 3D field-scale geomechanical model.

Finite-size evaporating droplets in weakly compressible homogeneous shear turbulence

We perform interface-resolved simulations of finite-size evaporating droplets in weakly compressible homogeneous shear turbulence. The study is conducted by varying three dimensionless physical parameters: the initial gas temperature over the critical temperature $T_{g,0}/T_c$ , the initial droplet diameter over the Kolmogorov scale $d_0/\eta$ and the surface tension, i.e. the shear-based Weber number, $We_{\mathcal {S}}$ . For the smallest $We_{\mathcal {S}}$ , we first discuss the impact on the evaporation rate of the three thermodynamic models employed to evaluate the gas thermophysical properties: a constant property model and two variable-properties approaches where either the gas density or all the gas properties are allowed to vary. Taking this last approach as reference, the model assuming constant gas properties and evaluated with the ‘1/3’ rule is shown to predict the evaporation rate better than the model where the only variable property is the gas density. Moreover, we observe that the well-known Frössling/Ranz-Marshall correlation underpredicts the Sherwood number at low temperatures, $T_{g,0}/T_c=0.75$ . Next, we show that the ratio between the actual evaporation rate in turbulence and the one computed in stagnant conditions is always much higher than one for weakly deformable droplets: it decreases with $T_{g,0}/T_c$ without approaching unity at the highest $T_{g,0}/T_c$ considered. This suggests an evaporation enhancement due to turbulence also in conditions typical of combustion applications. Finally, we examine the overall evaporation rate and the local interfacial mass flux at higher $We_{\mathcal {S}}$ , showing a positive correlation between evaporation rate and interfacial curvature, especially at the lowest $T_{g,0}/T_c$ .

Numerical Modeling and Experimental Validation of a Supercritical CO2-Lubricated Hydrodynamic Journal Bearing

Abstract The supercritical carbon dioxide (sCO2) Brayton cycle is an attractive thermal cycle for compact power generation applications due to its high efficiency and power density. Hydrodynamic gas journal bearings are attractive for this application due to their simplicity. Lubricating the bearings with sCO2 from the primary loop would be ideal, as this would eliminate the need for a separate lubricant source or complex seals and pumps to reduce the bearing lubricant pressure below the operating pressure of the primary loop. However, few studies in the literature have examined the behavior of a hydrodynamic journal bearing lubricated with supercritical fluid and none have experimentally demonstrated the operation of such a bearing. This paper describes the development of a simple numerical model of a hydrodynamic journal bearing operating under laminar conditions. The model incorporates the real gas properties of sCO2 and therefore can be used to qualitatively investigate the impact of operation near the critical point and the scaling relationships between inlet pressure and the bearing drag and stiffness. The model predictions are compared to results that would be obtained by assuming constant fluid properties in order to assess the effects on bearing performance of the large gradients in properties that occur near the critical point and to determine over what range of inlet conditions the constant-property simplification is valid. The modeling results show that bearing drag and stiffness rise linearly throughout the subcritical regime, but sharply rise by approximately 50% at the critical pressure. However, the behavior predicted by the real gas model closely matches those obtained from the constant-property model (CPM) for all conditions that are more than 3 kPa away from the critical pressure. To validate the prediction that bearing operation follows the same scaling relationships near the critical pressure as at low pressure, a test assembly consisting of a turbomachine driven by a motor and supported on tilt-pad hydrodynamic gas journal bearing was operated in a CO2 environment at 35 °C with pressures up to 7.336 MPa. The bearing operated smoothly and did not exhibit signs of instability such as whirl. Coast down measurements were conducted to estimate the bearing drag at various pressures up to 5.612 MPa. The bearing coefficient of friction, f, inferred from these tests increased with system pressure from 0.359 at atmospheric pressure to 0.619 at 5.612 MPa. The peak bearing Reynolds number during operation was approximately 400. These results indicate that hydrodynamic bearing operation using sCO2 is possible without significant reduction in bearing performance; however, further testing should be carried out in order to validate the model results concerning bearing stiffness.

On the role of thermo-transport properties in the convective/absolute transition of heated round jets

The effect of thermodynamic and transport properties on the convective-to-absolute transition in heated round jets is investigated with the spatio-temporal linear stability theory, by considering three sets of properties with increasing complexity. Present models include (i) a constant property model often used in the literature, (ii) a simplified model with variable properties, and (iii) a more accurate equilibrium air mixture model, accounting for dissociation reactions in the flow. A family of arbitrary single-stream and dual-stream jet profiles, representative of typical configurations studied in the literature, is investigated and adapted to each model. Our results show that considering a variable viscosity and thermal conductivity has a destabilizing effect on absolute instabilities in the viscous regime. Furthermore, this destabilization is stronger for the outer mode in dual-stream jets than for the inner mode or the jet-column mode in single-stream jets. With sufficient heating (S &amp;lt; 0.3), results obtained with the equilibrium model strongly depart from those of calorically perfect gas models and display absolute domains deformed by the chemical activity. For absolute instabilities triggered by the baroclinic torque such as jet-column and inner modes, the convective-to-absolute transition is shifted toward thinner and hotter configurations, while the opposite is observed for the outer mode. Finally, we observe a dependence of the equilibrium model stability properties on the static pressure.

Melt-Spun SiGe Nano-Alloys: Microstructural Engineering Towards High Thermoelectric Efficiency

Silicon-germanium (SiGe) alloys are prominent high-temperature thermoelectric (TE) materials used as a powering source for deep space applications. In this work, we employed rapid cooling rates for solidification by melt-spinning and rapid heating rates for bulk consolidation employing spark plasma sintering to synthesize high-performance p-type SiGe nano-alloys. The current methodology exhibited a TE figure-of-merit (ZT) ≈ 0.94 at 1123 K for a higher cooling rate of ∼3.0 × 107 K/s. This corresponds to ≈ 88% enhancement in ZT when compared with currently used radioisotope thermoelectric generators (RTGs) in space flight missions, ≈ 45% higher than pressure-sintered p-type alloys, which results in a higher output power density, and TE conversion efficiency (η) ≈ 8% of synthesized SiGe nano-alloys estimated using a cumulative temperature dependence (CTD) model. The ZT enhancement is driven by selective scattering of phonons rather than of charge carriers by the high density of grain boundaries with random orientations and induced lattice-scale defects, resulting in a substantial reduction of lattice thermal conductivity and high power factor. The TE characteristics of synthesized alloys presented using the constant property model (CPM) and CTD model display their high TE performance in high-temperature regimes along with wide suitability of segmentation with different mid-temperature TE materials.

Numerical investigation of transient phase-change transpiration cooling based on variable properties of coolant

Aimed at promoting the practical application of transpiration cooling technology in the field of active thermal protective system of hypersonic vehicles, this study presents a comprehensive numerical approach combining two-phase mixture model (TPMM), local thermal non-equilibrium (LTNE) assumption and variable properties of coolant to investigate the transient transpiration cooling problems with phase change. The real variable physical properties of coolant as functions of temperature and pressure are taken into consideration based on the data from the National Institute of Standards and Technology (NIST). The model is verified by comparing with the numerical and experimental data in previous researches. Results suggest that a new phenomenon of “reverse temperature distribution” in two-phase region is observed in the transient simulation considering variable properties. Comparison between the constant-property model and variable-property model indicates the necessity of the real variable physical properties, especially at low-pressure conditions with large differential pressure gradient. Meanwhile, the simulation with a non-uniform heat flux boundary condition reveals the mechanism of heat transfer deterioration. A gap of liquid outflow is formed after vapor generation, next moves along the outlet, then disappears and finally regenerates. The non-uniform heat flux will certainly lead to an uneven pressure distribution, resulting in the deterioration of local heat transfer in the porous matrix.

Transient air natural convection in asymmetrically heated vertical channels

A numerical analysis of natural convection in air in a vertical channel asymmetrically heated at uniform heat flux is carried out in this work. One channel wall is heated whereas the other one is adiabatic, and the problem is transient, two-dimensional and laminar. Constant and variable property models are considered. For both models, numerical solution is obtained by means the commercial CFD code Fluent. An extended computational domain is considered in order to simulate the far field conditions and it consists of the channel geometry with an upstream reservoir and a downstream reservoir. Simulations are achieved for Rayleigh number, Ra, values in the range 102–106 and results are showed as temperature profiles along the heated wall as a function of time, stream function and temperature fields. The present analysis allows to improve the knowledge of the effects related to the variable properties on the inlet and outlet zone and consequently inside the channel by numerical investigation during the development of fluid dynamic and thermal fields which are strongly linked. The results give quantitative information on the errors due to the use of constant properties model with respect to the variable properties model in natural convection in asymmetrical heated vertical channels.

Numerical investigation on the impact of variable particle radiation properties on the heat transfer in high ash pulverized coal boiler through co-simulation

Co-simulation of the high-temperature heat and mass transfer processes in coal-fired boilers using CFD together with process-level models of the water/steam circuit is a promising approach to investigate off-design conditions. In the present work, a 1D discretized two-phase model of the water flows in the evaporator and radiative superheaters was developed. This was coupled with a detailed furnace combustion and heat transfer CFD model. The coupled models are used to investigate the impact of variable particle emissivity and scattering efficiency on the evaporator and radiant superheater process conditions, including the furnace steam generation rate and final steam temperature. The results are compared with the case where the radiation properties of the particles are assumed to be constant, thereby highlighting the importance of accounting for the variations in the particle properties throughout the process. The case study boiler is that of a real 620 MWe subcritical power plant firing coal with a high ash content (41 %wt). The results show that the constant property model results in a predicted furnace heat load that is 6.5% lower than the experimental value, while the conversion-dependent model is only 0.7% lower than the experimental value.

Brownian models effect on turbulent fluid flow and heat transfer and entropy generation of water/boehmite alumina nanofluid inside enclosure

PurposeThe purpose of this paper is to study the effects of using different Brownian models on natural and mixed convection fluid flow and heat transfer inside the square enclosure filled with the AlOOH–water nanofluid.Design/methodology/approachDue to fulfill of this demand, five different models for the effective thermal conductivity and viscosity of the nanofluid are considered. The following results are presented for the Ra=107 to 1010 and Ri=0.01 to 100, whereas the volume fraction of the nanoparticles is varied from φ = 0.01 to 0.04.FindingsAccording to the obtained results, increasing of Rayleigh number and reduction of Richardson number leads to the higher values of the average Nusselt number and entropy generation. Also, it is realized that, variation trend of the average Nusselt number and entropy generation in all cases is increasing by growing the volume fraction. It is found that the obtained average Nusselt numbers and entropy generations with Koo and Kleinstreuer are the highest among all the studied cases, and it is followed by Patel, Vajjha and Das, Corcione and Maxwell–Brinkman models, respectively.Originality/valueBased on the results of present investigation, the Nusselt number difference predicted between the Maxwell–Brinkman model (as constant-property model) and Koo and Kleinstreuer model is about 7.84 per cent at 0.01 per cent volume fraction and 5.47 per cent at 0.04 per cent volume fraction for the Rayleigh number equal to 107. The entropy generation difference predicted between the two above studied model is about 8.05 per cent at 0.01 per cent volume fraction and 5.86 per cent at 0.04 per cent volume fraction for the Rayleigh number equal to 107. It is observed that using constant-property model has a significant difference in the obtained results with the results of other variable-property models.

An analytical model of heat and mass transfer from liquid drops with temperature dependence of gas thermo-physical properties

An analytical model for heating and evaporation of a single component liquid drop is developed. The model accounts for the temperature dependence of density, diffusivity, thermal conductivity and specific heat of the gas species. The effect of variable properties on heat and evaporation rates is analysed and a comparison with the prediction of the classical constant property model is reported for six different species and different operating conditions. The model allows to evaluate the effect of the choice of the gas mixture averaging parameter (the relative weight of free stream and drop surface conditions) on the prediction of the constant property model, and a way to optimise the choice is proposed. The results can be extended to non-spherical drop and examples are reported.

Numerical Simulation of Transpiration Cooling within Variable Property of Water and Steam

Transpiration cooling with coolant phase change provides a wide range of applications in effective thermal protection. Water is usually employed as the coolant and experiences huge temperature and pressure changes during the transpiration cooling process. Mathematical model and numerical approach of transpiration cooling with phase change in consideration of the real variation of water thermodynamic properties are established in this paper, and compared with the constant property model. The IWAPS Industrial Formulation 1997 is used to calculate the thermodynamic properties of water in wide ranges of temperature and pressure. The numerical results obtained indicate some thermodynamic properties vary significantly with temperature and pressure, leading to higher phase change temperature and coolant driving force. With the increase of mass flow rate, the two property models exhibit the similar changing trend in temperature and pressure and there is a lag in the start and end positions of phase change.

A conjugate heat transfer analysis of performance for rectangular microchannel with trapezoidal cavities and ribs

A numerical investigation has been taken up to assess the efficacy of a design innovation for rectangular microchannel heat sink by applying the concepts of maximization of thermal performance (TP) and minimization of entropy generation (EG). The channel is conceived as a serial arrangement of modifying units, each with a rib symmetrically located between trapezoidal cavities (TRC) on opposite side walls. Based on SIMPLEC algorithm for the flow along with conduction through the bounding walls and the internal ribs, a three dimensional laminar-flow conjugate heat-transfer study has been carried out between Reynolds number (Re) of 140 and 600 following a validation against a representative numerical and experimental study. A comparison among the predictions of constant fluid property model and models incorporating their realistic variations with temperature has shown the cooling to be dominated by convection, of course more strongly at higher Re. Substantially higher thermal conductivity of copper than that of silicon have revealed moderate increase in bulk fluid temperature and even lower increase of substrate temperature. Four different rib structures have been considered that are rectangular (RR), backward triangular (BTR), forward triangular (FTR) and diamond (DR). The predictions against Re indicated the best TP with diamond rib combination (TRC-DR) and the highest EG with backward triangular rib combination (TRC-BTR). A notable contribution of this work is establishing the concept of minimization of EG under the constraint of given pumping power to be equivalent to the concept of maximization of TP. The effects of parametric variations of relative width and length of cavity and relative width and pitch of rib have been investigated and the highest TP has been predicted around Re of 328.

Modeling wellbore heat exchangers: Fully numerical to fully analytical solutions

The successful modeling of wellbore heat exchangers requires tight coupling between the formation heat conduction and the wellbore thermal dynamics. In this paper, we developed three representative solutions: a fully numerical solution that treats both formation and wellbore numerically, a semi-numerical solution that treats formation analytically and wellbore numerically and a fully analytical solution that treats both formation and wellbore analytically. The outlet temperature, pressure, and heat flow rate predicted by the three solutions are compared. The results of this comparison indicate that the fully numerical solution is the only accurate solution for the early transient time. After the system reaches quasi-steady state, temperature and heat flow estimated from all three solutions are in very good agreement. The analysis of transient fluid properties and mass flow rates revealed that constant fluid property model cannot accurately estimate the pressure loss for the system. The newly proposed fully analytical solution is applied in an economic analysis problem for calculating the optimal insulation thickness and mass flow rate to minimize the cost of generated power.

Residence time distribution in packed bed microreactor – Lattice Boltzmann model validation

An analytical model for heating and evaporation of a single component liquid drop is developed. The model accounts for the temperature dependence of density, diffusivity, thermal conductivity and specific heat of the gas species. The effect of variable properties on heat and evaporation rates is analysed and a comparison with the prediction of the classical constant property model is reported for six different species and different operating conditions. The model allows to evaluate the effect of the choice of the gas mixture averaging parameter (the relative weight of free stream and drop surface conditions) on the prediction of the constant property model, and a way to optimise the choice is proposed. The results can be extended to non-spherical drop and examples are reported.

Laminar convective heat transfer characteristic of Al2O3/water nanofluid in a circular microchannel

In this study, laminar convective heat transfer characteristics Al2O3/water nanofluid in a circular microchannel is investigated using a two-phase (discrete phase) model. The computational fluid dynamic code FLUENT (ANSYS) is employed to solve the coupled momentum and energy equations with the boundary conditions of uniform wall heat flux and velocity at channel inlet. Detail analysis is done showing variation of wall temperature, fluid bulk mean temperature, heat transfer coefficient, Nusselt number, shear stress, friction, pressure drop, entropy generation etc. along the microchannel at two particle volume concentrations (1% and 4%) of the nanofluid. Comparison of results is provided between base and nanofluid and also for two cases, one with constant property and the other with variable temperature thermal conductivity and viscosity. Results show that heat transfer is enhanced in case of the nanofluid with low entropy generation and the heat transfer parameters increase with increase in nanoparticle volume concentration and Reynolds number. However, use of nanofluid also causes increase in pressure drop and shear stress. A comparison of the constant and variable property model showed that heat transfer is further enhanced; entropy, shear stress and pressure drop further decrease when temperature dependent properties of the nanofluid are considered instead of constant properties.