•A modified flamelet-progress-variable model for supercritical combustion.•Model validations based on data from laminar flames and turbulent combustion.•Model validations and numerical studies conducted in RANS framework.•Pressure effect on coaxial injection and combustion of LOx/methane.•Pressure effect on swirling injection and combustion of LOx/kerosene.Non-premixed turbulent combustion at a supercritical pressure is an important physicochemical phenomenon in many propulsion and power-generation systems. In this paper, a modified flamelet-progress-variable model, in which a simple term is proposed to approximately account for the extra turbulent mixing related to large density difference between two fluid streams, has been developed and incorporated into a single-phase general fluid numerical scheme in RANS framework for solving supercritical-pressure turbulent combustion of hydrocarbon fuels. The model was validated and then applied for studying the coaxial injection and turbulent combustion of LOx/methane and the swirling injection and turbulent combustion of LOx/kerosene at various supercritical pressures. Results indicate that for the coaxial injection and combustion of LOx/methane at a mixture ratio of 3, flame length decreases as chamber pressure increases, dictated by the penetration capability of the injected LOx stream. For the swirling injection and combustion of LOx/kerosene at supercritical pressures, flame moves closer to the injector as chamber pressure increases. This phenomenon at a higher pressure is similar to that caused by an increased inlet-flow swirling number. It suggests that increasing chamber pressure may lead to a shorter combustor for the turbulent combustion of LOx and hydrocarbon fuels.

•A CFD model to study heat transfer of nanofluid at supercritical pressure.•Weakened heat transfer at 3 MW/m2 and an inlet velocity of 25 m/s.•Enhanced heat transfer at 7 MW/m2 or an inlet velocity of 10 m/s.•Heat transfer phenomena dictated by thermophysical property variations.A numerical study has been conducted to examine the turbulent heat transfer of a nanofluid, methane-CuO, in a circular cooling tube at a supercritical pressure of 8 MPa, a phenomenon relevant to the rocket engine cooling application. Results reveal that at a surface heat flux of 3 MW/m2 and an inlet flow velocity of 25 m/s, the addition of nanoparticles decreases the heat transfer rate, dictated by significant increase of the nanofluid viscosity, which leads to the decreased turbulent viscosity in the near-wall buffer zone. As the surface heat flux is increased to 7 MW/m2 or the inlet velocity is decreased to 10 m/s, however, two physical phenomena of heat transfer improvement are observed in the nanofluid. The first phenomenon, which starts almost immediately from the beginning of the heated section, is controlled by strong increase of the nanofluid density, which results in the increased turbulent viscosity in the near-wall buffer zone. The second phenomenon is dictated by thermophysical property variations in the near-wall turbulent flow region as fluid temperature transits from the subcritical to supercritical state (the transcritical process). Results indicate potential applications of nanofluids in enhancing heat transfer at supercritical pressures.

•Transient fluid flows and heat transfer of n-decane at supercritical pressure.•Flow dynamics dictated by thermoacoustic oscillation and transient convection.•Surface heat flux strongly influences pressure oscillating magnitude.•Surface heating rate affects both oscillating magnitude and frequency.•Tube length and inlet flow velocity affect total transient responding time.Turbulent heat transfer of hydrocarbon fuel at supercritical pressure plays a crucial role in regenerative cooling of aerospace propulsion systems. In this paper, flow dynamics in transient heat transfer of n-decane at a supercritical pressure of 5 MPa has been numerically investigated, focusing on the effects of a number of key influential parameters, including the surface heat flux, surface heating rate, cooling tube length, and inlet flow velocity, on the transient responding behaviors. Results indicate that the transient responding process is dictated by two fundamental mechanisms: the initial thermoacoustic oscillation, which is caused by strong fluid thermal expansion, and the subsequent transient convection. The thermoacoustic oscillating magnitude increases as the surface heat flux, surface heating rate, and cooling tube length are increased, but it decreases as the inlet flow velocity is increased. The surface heating rate and cooling tube length also exert strong impacts on the oscillating frequency of the thermoacoustic wave. Moreover, the cooling tube length and inlet flow velocity significantly affect the second-stage transient convective process and thus the total transient responding time, which both increase as the cooling tube length is increased and/or the inlet flow velocity is decreased. Results obtained herein are helpful for fundamental understanding of the transient heat transfer mechanisms relevant to regenerative engine cooling processes.

•Flow oscillations caused by significant fluid thermal expansion.•Strong pressure effect on property variations extends a transient process.•Flow oscillations become stronger at a higher surface heat flux.•Flow oscillations become stronger at a lower inlet flow velocity.•An increased pressure slightly decreases transient responding time.A numerical study has been conducted to analyze transient responding behaviors of fluid flow and heat transfer of the cryogenic methane at supercritical pressures, the physical phenomena closely related to the regenerative rocket engine cooling application. A steady-state cold flow is instantly enforced with a constant surface heat flux to activate the transient heat transfer process. The effects of surface heat flux, inlet flow velocity, and pressure on transient responses are studied in detail to obtain fundamental understanding of the underlying physical mechanisms. Results indicate that the increased fluid temperature during the heat transfer process leads to the significantly decreased fluid density at a supercritical pressure and consequently causes strong fluid thermal expansion, which results in flow oscillations. The strong pressure effect on thermophysical property variations in the supercritical-pressure heat transfer process, particularly in the trans-critical region, can lead to further extension of the transient responding process at a low inlet flow velocity and/or under a high surface heat flux. Flow oscillations become stronger and last longer under a higher surface heat flux and/or at a lower inlet flow velocity. An increased operating pressure slightly decreases the transient responding time. Under the tested conditions in the present work, the maximum transient response time is around 20 ms.

Regenerative cooling of the high-temperature components in propulsion and power-generation systems plays a paramount role in maintaining the reliability and durability of the systems. In this paper, a mathematical model is developed for studying fluid dynamics and heat-transfer characteristics of the aviation kerosene RP-3 at supercritical pressures. The model accommodates a detailed pyrolytic chemical reaction mechanism, which consists of 18 species and 24 elementary reactions (Jiang, R.; Liu, G.; Zhang, X.Thermal cracking of hydrocarbon aviation fuels in regenerative cooling microchannels. Energy Fuels 2013, 27, 2563−2577). Accurate calculations of thermophysical properties at supercritical pressures are properly incorporated. After rigorous model validations, numerical studies of turbulent heat transfer of RP-3 in a micro cooling tube at a supercritical pressure of 5 MPa are conducted under operating conditions of both constant wall heat flux and constant surface temperature to obtain a fundamental understanding of the complex physicochemical processes. Results indicate that the endothermic fuel pyrolysis, which prevails once the bulk fluid temperature rises above 750 K, dictates the fluid flow and heat-transfer process in the high fluid temperature region. Significant variations of the fluid thermophysical properties also make strong impacts; two scenarios of heat-transfer enhancement resulting from property variations under the tested conditions are analyzed. This work has fundamental and practical implications for effective thermal management in propulsion and power-generation systems.

Aviation kerosene is commonly used in combustion and regenerative engine cooling processes in propulsion and power-generation systems, including rocket, scramjet, and advanced gas turbine engines. In this paper, many surrogate models proposed in the open literature are examined for their applicability and accuracy in calculating thermodynamic and transport properties of the China aviation kerosene RP-3 at supercritical pressures, based on the extended corresponding-states methods. The enthalpy change from endothermic decomposition and low heating value from combustion of the jet fuel are also evaluated. Results from a number of simple and representative surrogate models, which contain species components ranging from 1 to 10, are analyzed in detail. Data analyses indicate that a surrogate model with four species is the best choice for thermophysical property calculations under the tested conditions, with fluid temperature up to 650 K at various supercritical pressures. The surrogate model is particularly accurate in predicting the pseudo-critical temperature of aviation kerosene RP-3 at a supercritical pressure. A simple surrogate model containing the n-decane species and a surrogate model containing 10 species are the other two acceptable options. The work conducted herein is of practical importance for theoretical analyses and numerical simulations of various physicochemical processes at engine operating conditions.

A numerical study of the counterflow diffusion flames of methane/air at both subcritical and supercritical pressures, which have very important applications in the air-breathing rocket and advanced gas turbine engines, is conducted to obtain fundamental understanding of the flame characteristics. The analysis is based on a general mathematical formulation and accommodates a unified treatment of general fluids thermodynamics and accurate calculations of thermophysical properties. Results reveal that the maximum flame temperature occurs on the fuel-rich side for low-pressure conditions and shifts toward the stoichiometric position when the pressure increases. The maximum flame temperature increases with an increasing pressure, but decreases with an increasing strain rate. The flame width is inversely proportional to the square root of the product of the pressure and strain rate as \({{\delta \propto 1} \mathord{\left/ {\vphantom {{\delta \propto 1} {\sqrt {p \cdot a} }}} \right. \kern-\nulldelimiterspace} {\sqrt {p \cdot a} }}\). The total heat release rate varies with the pressure and strain rate in a relationship of (Qrelease √(p·a)0.518. An increased pressure leads to a slightly more complete combustion process near the stoichiometric position, but its effect on NO production is minor. Under the test conditions, variations of the strain rate have significant impacts on the formation of major pollutants. An increased strain rate leads to the decreased mole fraction of CO in the fuel-rich region and significantly reduced NO near the stoichiometric position.

Water management is an important issue in the polymer electrolyte membrane (PEM) fuel cell, which is considered as a promising alternative power source for future automotive applications. In this article, lattice Boltzmann simulations are conducted to examine the interfacial phenomena in liquid water transport in porous materials of a PEM fuel cell. Numerical results clearly indicate that large perforated pores through the porous diffusion layers can serve as a convenient liquid water transport pathway and thus assist in liquid water removal. An interconnected horizontal and vertical pore combination is especially beneficial to liquid water transport through the porous layers in flooding conditions. Therefore, liquid water transport in a PEM fuel cell may be effectively managed through well engineered interfacial structures in porous materials.Highlights► Conducted lattice Boltzmann simulation on interfacial phenomena in porous layers. ► Large perforated pores serve as a convenient pathway for liquid water removal. ► A horizontal and vertical pore combination can assist in water management.

This paper provides a comprehensive review on the research and development in multi-scale numerical modeling and simulation of PEM fuel cells. An overview of recent progress in PEM fuel cell modeling has been provided. Fundamental transport phenomena in PEM fuel cells and the corresponding mathematical formulation of macroscale models are analyzed. Various important issues in PEM fuel cell modeling and simulation are examined in detail, including fluid flow and species transport, electron and proton transport, heat transfer and thermal management, liquid water transport and water management, transient response behaviors, and cold-start processes. Key areas for further improvements have also been discussed.

A two-phase lattice Boltzmann model is employed for direct numerical simulation of liquid water transport in the turning regions of serpentine gas channels in proton exchange membrane (PEM) fuel cells. Two different types of serpentine gas channels with either a smooth U-shaped or a sharp right-angled turning region are examined. Numerical results indicate that a smooth U-shaped turning region is beneficial to liquid water removal in a serpentine gas channel. An increased gas stream velocity or channel surface contact angle can further assist the process. Liquid water tends to accumulate in the sharp right-angled turning region because of the acting direction of the gas shear force. Increased gas stream velocity and surface contact angle are not very helpful for liquid water removal in the right-angled turning region under all the tested conditions. This numerical study is intended to provide improved fundamental understandings of liquid water transport mechanisms in serpentine gas channels of PEM fuel cells.Highlights► Simulated liquid water transport in turning regions of serpentine gas channels. ► A smooth U-shaped turning region is beneficial to liquid water removal. ► Increased gas stream velocity or surface contact angle assists the process. ► Liquid water tends to accumulate in the sharp right-angled turning region.

Liquid water transport in gas channels may influence and even prevent gas supply in a proton exchange membrane (PEM) fuel cell, so significantly affect cell operation. A two-phase two-dimensional lattice Boltzmann model is employed in this paper to simulate the development and interaction of two liquid droplets in a gas channel of a PEM fuel cell, focusing mainly on parametric effects, including the gas flow velocity, initial droplet distance, different micropore combinations, and the gas diffusion layer (GDL) surface wetting properties, on liquid droplet transport behaviors. Results confirm that an increased gas stream velocity and liquid pore distance may prevent liquid droplet interaction and enhance liquid water removal. Numerical simulations further indicate that different pore size combinations may promote droplet interaction, particularly with a large pore in front of a small one. On the contrary, a more hydrophobic GDL surface can decrease liquid droplet interaction, benefit liquid water removal, and consequently improve PEM fuel cell water management.

In this paper, a two-phase two-dimensional PEM fuel cell model, which is capable of handling liquid water transport across different porous materials, is employed for parametric studies of liquid water transport and distribution in the cathode of a PEM fuel cell. Attention is paid particularly to the coupled effects of two-phase flow and heat transfer phenomena. The effects of key operation parameters, including the outside cell boundary temperature, the cathode gas humidification condition, and the cell operation current, on the liquid water behaviors and cell performance have been examined in detail. Numerical results elucidate that increasing the fuel cell temperature would not only enhance liquid water evaporation and thus decrease the liquid saturation inside the PEM fuel cell cathode, but also change the location where liquid water is condensed or evaporated. At a cell boundary temperature of 80 °C, liquid water inside the catalyst layer and gas diffusion media under the current-collecting land would flow laterally towards the gas channel and become evaporated along an interface separating the land and channel. As the cell boundary temperature increases, the maximum current density inside the membrane would shift laterally towards the current-collecting land, a phenomenon dictated by membrane hydration. Increasing the gas humidification condition in the cathode gas channel and/or increasing the operating current of the fuel cell could offset the temperature effect on liquid water transport and distribution.

Supercritical convective heat transfer of hydrocarbon propellants plays a key role in the regenerative cooling technology development in aerospace applications. In this paper, a numerical study of the supercritical forced convective heat transfer of a typical hydrocarbon fuel, n-heptane, has been conducted based on a complete set of conservation equations of mass, momentum, and energy with accurate evaluations of the thermophysical properties. The present fundamental numerical study focuses on the effects of many key parameters, including the inlet pressure, inlet velocity, wall heat flux, and the inlet fluid temperature, on the supercritical heat transfer processes. Results indicate that under supercritical heat transfer processes, heat transfer deterioration could occur once the wall temperature or the fluid temperature in a large near-wall region reaches the pseudo-critical temperature, and increasing the fluid pressure would enhance heat transfer. The conventional empirical Gnielinski expression could only be used for supercritical heat transfer predictions of n-heptane under very limited operational conditions. It is found in the present numerical study that a supercritical heat transfer expression for CO2, H2O, and HCFC-22 applications can generally be employed for predicting the supercritical heat transfer coefficient of n-heptane when the inlet velocity is higher than 10 m/s.

A multi-dimensional two-phase PEM fuel cell model, which is capable of handling the liquid water transport across different porous materials, including the catalyst layer (CL), the micro-porous layer (MPL), and the macro-porous gas diffusion medium (GDM), has been developed and applied in this paper for studying the liquid water transport phenomena with consideration of the MPL. Numerical simulations show that the liquid water saturation would maintain the highest value inside the catalyst layer while it possesses the lowest value inside the MPL, a trend consistent qualitatively with the high-resolution neutron imaging data. The present multi-dimensional model can clearly distinguish the different effects of the current-collecting land and the gas channel on the liquid water transport and distribution inside a PEM fuel cell, a feature lacking in the existing one-dimensional models. Numerical results indicate that the MPL would serve as a barrier for the liquid water transport on the cathode side of a PEM fuel cell.

In this paper, a transient multiphase multi-dimensional PEM fuel cell model has been developed in the mixed-domain framework for elucidating the fundamental physics of fuel cell cold start. Cold-start operations of a PEM fuel cell at a subfreezing boundary temperature of −20 °C under both constant current and constant cell voltage conditions have been numerically examined. Numerical results indicate that the water vapor concentration inside the cathode gas channel affects ice formation in the cathode catalyst layer and thus the cold-start process of the fuel cell. This conclusion demonstrates that high gas flow rates in the cathode gas channel could increase fuel cell cold-start time and benefit the cold-start process. It is shown that the membrane plays a significant role during the cold-start process of a PEM fuel cell by absorbing the product water and becoming hydrated. The time evolutions of ice formation, current density and water content distributions during fuel cell cold-start processes have also been discussed in detail.

In this paper, a multiphase multidimensional PEM fuel cell model for cold-start simulations has been employed for numerical analyses of the non-isothermal self-start behaviors of a PEM fuel cell from subfreezing startup temperatures, focusing on the coupled phenomena of the ice formation and temperature increase inside the cell. The roles played by many key influential parameters, including the water vapor concentration in the cathode gas channel, the initial water content inside the membrane, the operating current density, and the startup cell temperature, are carefully examined. Numerical results indicate that decreasing the interfacial water vapor concentration at the gas diffusion layer and gas channel surface on the cathode side of the cell would delay ice precipitation and prolong the cell operation time. Decreasing the operation current density and the initial water content inside the membrane, and increasing the startup cell temperature are beneficial for the non-isothermal cold starts of the PEM fuel cell and could lead to successful self-starts.

In this paper, a transient two-phase non-isothermal PEM fuel cell model has been developed based on the previously established two-phase mixed-domain approach. This model is capable of solving two-phase flow and heat transfer processes simultaneously and has been applied herein for two-dimensional time-accurate simulations to fully examine the effects of liquid water transport and heat transfer phenomena on the transient responses of a PEM fuel cell undergoing a step change of cell voltage, with and without condensation/evaporation interfaces. The present numerical results show that under isothermal two-phase conditions, the presence of liquid water in the porous materials increases the current density over-shoot and under-shoot, while under the non-isothermal two-phase conditions, the heat transfer process significantly increases the transient response time. The present studies also indicate that proper consideration of the liquid droplet coverage at the GDL/GC interface results in the increased liquid saturation values inside the porous materials and consequently the drastically increased over-shoot and under-shoot of the current density. In fact, the transient characteristics of the interfacial liquid droplet coverage could exert influences on not only the magnitude but also the time of the transient response process.

In this paper, a two-phase non-isothermal PEM fuel cell model based on the previously developed mixed-domain PEM fuel cell model with a consistent treatment of water transport in MEA has been established using the traditional two-fluid method. This two-phase multi-dimensional PEM fuel cell model could fully incorporate both the anode and cathode sides, properly account for the various water phases, including water vapor, water in the membrane phase, and liquid water, and truly enable numerical investigations of water and thermal management issues with the existence of condensation/evaporation interfaces in a PEM fuel cell. This two-phase model has been applied in this paper in a two-dimensional configuration to determine the appropriate condensation and evaporation rate coefficients and conduct extensive numerical studies concerning the effects of the inlet humidity condition and temperature variation on liquid water distribution with or without a condensation/evaporation interface.

A three-dimensional mixed-domain PEM fuel cell model with fully-coupled transport phenomena has been developed in this paper. In this model, after fully justified simplifications, only one set of interfacial boundary conditions is required to connect the water content equation inside the membrane and the equation of the water mass fraction in the other regions. All the other conservation equations are still solved in the single-domain framework. Numerical results indicate that although the fully-coupled transport phenomena produce only minor effects on the overall PEM fuel cell performance, i.e. average current density, they impose significant effects on current distribution, net water transfer coefficient, velocity and density variations, and species distributions. Intricate interactions of the mass transfer across the membrane, electrochemical kinetics, density and velocity variations, and species distributions dictate the detailed cell performances. Therefore, for accurate PEM fuel cell modeling and simulation, the effects of the fully-coupled transport phenomena could not be neglected.

In this paper, a three-dimensional PEM fuel cell model with a consistent water transport treatment in the membrane electrode assembly (MEA) has been developed. In this new PEM fuel cell model, the conservation equation of the water concentration is solved in the gas channels, gas diffusion layers, and catalyst layers while a conservation equation of the water content is established in the membrane. These two equations are connected using a set of internal boundary conditions based on the thermodynamic phase equilibrium and flux equality at the interface of the membrane and the catalyst layer. The existing fictitious water concentration treatment, which assumes thermodynamic phase equilibrium between the water content in the membrane phase and the water concentration, is applied in the two catalyst layers to consider water transport in the membrane phase. Since all the other conservation equations are still developed and solved in the single-domain framework without resort to interfacial boundary conditions, the present new PEM fuel cell model is termed as a mixed-domain method. Results from this mixed-domain approach have been compared extensively with those from the single-domain method, showing good accuracy in terms of not only cell performances and current distributions but also water content variations in the membrane.

A simplified isotropic numerical treatment for solving the anisotropic electron transport phenomenon in PEM fuel cells has been proposed. In order to maintain appropriate lateral current distribution, the in-plane electronic conductivity in the catalyst and gas diffusion layers is utilized, while an extra contact resistance is added between the gas diffusion layer (GDL) and the current-collecting land to compensate the reduced through-plane electronic resistance. This simplified method is also applicable for solving the anisotropic heat transfer phenomenon in PEM fuel cells, and it improves numerical convergence and stability in three-dimensional large-scale simulations.

The regenerative cooling technology is a promising approach for effective thermal protection of propulsion and power-generation systems. A mathematical model has been used to examine fluid flows and heat transfer of the aviation kerosene RP-3 with endothermic fuel pyrolysis at a supercritical pressure of 5 MPa. A pyrolytic reaction mechanism, which consists of 18 species and 24 elementary reactions, is incorporated to account for fuel pyrolysis. Detailed model validations are conducted against a series of experimental data, including fluid temperature, fuel conversion rate, various product yields, and chemical heat sink, fully verifying the accuracy and reliability of the model. Effects of fuel pyrolysis and inlet flow velocity on flow dynamics and heat transfer characteristics of RP-3 are investigated. Results reveal that the endothermic fuel pyrolysis significantly improves the heat transfer process in the high fluid temperature region. During the supercritical-pressure heat transfer process, the flow velocity significantly increases, caused by the drastic variations of thermophysical properties. Under all the tested conditions, the Nusselt number initially increases, consistent with the increased flow velocity, and then slightly decreases in the high fluid temperature region, mainly owing to the decreased heat absorption rate from the endothermic pyrolytic chemical reactions.