Real Fluid Effects Research Articles

Direct numerical simulation of supercritical carbon dioxide oxy-methane combustion

Supercritical CO2 (sCO2) oxy-methane combustion is a key component of zero-carbon technologies in direct-fired sCO2 power cycles, i.e., the Allam cycle which offers promising solutions for clean and sustainable energy production. The use of sCO2 as both working fluid and diluent to moderate the combustor exit temperature at high pressure and high preheat temperature in the Allam cycle poses a unique combustion behavior. The effects of high sCO2 dilution on sCO2 oxy-methane combustion behavior, flame propagation, and flame stability are not fully resolved due to experimental challenges at such extreme conditions. This study addresses this major challenge by providing an understanding of the effect of sCO2 dilution on supercritical mixing and the combustion behavior in sCO2 oxy-methane combustion. A direct numerical simulation (DNS) integrated with the real-fluid equation of state is developed to provide the first DNS dataset for the realistic operating conditions of sCO2 oxy-methane combustors designed by Southwest Research Institute. The combustion behavior shows that sCO2 dilution has a major impact on mixing, heat release rate, temperature, and flame thickness. A peak in the heat release rate is identified for a given air–fuel ratio and the lowest CO production for 75%–80% CO2 dilution which results in a maximum temperature of 2000 K. By comparing the results obtained from ideal- and real-fluid equation of state, this study shows that real-fluid effects can significantly affect density gradient distribution and heat release rate, impacting supercritical mixing and flame dynamics under high sCO2 dilution. The results provide crucial insight for designing future sCO2 oxy-combustors.

Small-scale turbulent characteristics in transcritical wall-bounded flows

Considerable efforts have been devoted to the understanding of the small-scale characteristics in turbulent flows. While the universality of small-scale quantities has been established for incompressible flows, their extension to high-pressure transcritical flows remains an open area of research. To address this question, we investigate the real-fluid thermodynamic effects on small-scale velocity statistics of high-pressure transcritical wall-bounded turbulence. We show that in the locally isotropic region for transcritical flows, low-order moments of small-scale statistics collapse for all cases and Kolmogorov's (1941) theory holds. However, real-fluid thermodynamic effects introduce deviations in the tails of the probability density function for the velocity derivative and, consequently, high-order moments of velocity gradients and dissipation rate in transcritical flows cannot collapse in the locally isotropic region. Analysis of the intermittency shows that the low-order structure functions in transcritical flows follow extended self-similarity, while the dependence of the intermittency factor on real-fluid effects is observed for high-order structure functions. The real-fluid effects on intermittency are explained by turbulent structures related to rare events. Additionally, the dissipation rate moments for transcritical flows follow a universal scaling with Reynolds number, and the scaling exponents are different from those of incompressible flows. These results extend the small-scale universality in incompressible flows (Schumacher et al., Proc. Natl Acad. Sci. USA, vol. 111, 2014, pp. 10961–10965) to realistic flows with significant changes in thermodynamic properties, and provide a physical underpinning of the scaling laws of small-scale statistics at transcritical conditions.

A computational fluid dynamic method for dense-phase carbon dioxide centrifugal pump

As an advanced approach for large-scale low-carbon utilization of fossil energy, the carbon capture, utilization and storage technology is a promising means to achieve the carbon-neutrality target by 2060. Among the most widely used approaches for carbon storage is the enhanced oil recovery technique, for which the centrifugal pump is used to inject high-pressure dense-phase carbon dioxide (CO2) into the stratum. This work focuses on real fluid effects and inter-stage matching deviation from the incompressibility assumption for a dense-phase CO2 centrifugal pump, of which the inlet condition is close to the fluid critical point. With a thermophysical-state table for CO2 based on the thermophysical-property database of the National Institute of Standards and Technology embedded into a computational fluid dynamics solver, a numerical simulation method for compressible dense-phase CO2 pumps is established. The developed method is validated in the 50kW main compressor for a supercritical CO2 cycle and then applied to the simulation of a multistage dense-phase CO2 pump designed for carbon storage. The stage with the most remarkable fluid compressibility is determined, which provides a priori basis for the follow-up design optimization of the pump. This work is of promising application prospect for design of advanced dense-phase fluid machinery.

Supercritical hydrothermal combustion: Basic principles, characteristics and applications and development in energy and environment

Supercritical hydrothermal combustion technology is a new homogeneous combustion technology with high potential in the fields of efficient removal of organic waste, clean utilization of conventional fossil energy, and efficient recovery of heavy oil. This manuscript reviews the literature related to supercritical hydrothermal combustion in recent years, and focuses on evaluating the current status of experimental and numerical simulation studies on the characteristics of supercritical hydrothermal combustion, as well as the latest progress in engineering. It is pointed out that the reduction of ignition temperature and extinction temperature is the key to promoting the application of supercritical hydrothermal combustion technology, and the consideration of the real-fluid effects and turbulence-reaction interactions can correctly reflect the combustion process. In addition, supercritical hydrothermal combustion technology, as a source of heat and reaction medium supply, can realize the efficient removal of highly concentrated organic wastewater, the clean combustion of coal and in-situ hydrogen production, as well as the thermal recovery of heavy oil by multi-thermal fluids. At present, supercritical hydrothermal combustion forced ignition technology, reactor design guidelines, and corrosion prevention of key equipment are still the focus of future research, which is of great significance to promote the application.

Non-equilibrium flow of van der Waals fluids in nano-channels

The Enskog–Vlasov equation provides a consistent description of the microscopic molecular interactions for real fluids based on the kinetic and mean-field theories. The fluid flows in nano-channels are investigated by the Bhatnagar–Gross–Krook (BGK) type Enskog–Vlasov model, which simplifies the complicated Enskog–Vlasov collision operator and enables large-scale engineering design simulations. The density distributions of real fluids are found to exhibit inhomogeneities across the nano-channel, particularly at large densities, as a direct consequence of the inhomogeneous force distributions caused by the real fluid effects including the fluid molecules' volume exclusion and the long-range molecular attraction. In contrast to the Navier–Stokes equation with the slip boundary condition, which fails to describe nano-scale flows due to the coexistence of confinement, non-equilibrium, and real fluid effects, the Enskog–Vlasov–BGK model is found to capture these effects accurately as confirmed by the corresponding molecular dynamics simulations for low and moderate fluid densities.

Prediction of propagating flames under high-pressure conditions with real-fluid combustion modeling

The present study discusses computational fluid dynamics (CFD) modeling for combustion flows under high-pressure conditions, including supercritical pressure conditions. The real-fluid effects are considered in terms of thermodynamic properties, transport properties, and chemical kinetics. In the present model, the real-fluid effect on chemical kinetics is introduced via a modified equilibrium constant derived using the Gibbs free energy variation of chemical reactions and the fugacity. The results obtained with the present model are compared with available experimental data of high-pressure premixed H2/O2 propagating flames diluted by Ar or He. We demonstrate in the H2/O2/Ar flame case that the real-fluid model provides a better prediction accuracy for the negative pressure dependence of the mass burning rate compared to the ideal-gas model. The improved prediction accuracy is primarily attributed to the proper estimation of thermodynamic properties such as unburnt-gas enthalpy via an appropriate equation of state and a departure function. The negative pressure dependence of unburnt-gas enthalpy of the H2/O2/Ar mixture with the real-fluid model significantly affects the flame speed prediction under high-pressure conditions. On the other hand, although the H2/O2/He mixture shows a positive pressure dependence of enthalpy, differences in the mass burning rate between the real-fluid and ideal-gas models are not significant for the H2/O2/He flame case. In the He-diluted case, the real-fluid effect is undermined owing to the low density of the H2/O2/He mixture. Thus, the real-fluid effect appears differently in the prediction of propagating flames depending on the species composition and thermodynamic conditions. The present study suggests that the positive or negative pressure dependence of enthalpy (i.e., the isothermal Joule–Thomson coefficient) is a metric to identify the real-fluid effects that appear.

On the understanding of a cryogenic two-phase LOX/GH2 flame: Parametric sensitivity, characteristic scaling and phase instability

This study concerns the cryogenic hydrogen combustion in subcritical pressure conditions, with practical relevance to rocket engine applications. A cryogenic two-phase flame in the counterflow configuration is calculated and analyzed with the consideration of real-fluid effects and heat/mass transfer across the liquid-gas interface. The effects of pressure, strain rate, fuel inlet temperature, and heat loss on the flame characteristic behaviors are examined. It is found that the vaporization rate of liquid oxidizer scales with the square-root of pressure (p) times strain rate (ast), and is not a limiting factor for combustion. The total heat release scales with past at lower strain rates while with p4/5ast1/3 at higher strain rates. The significant results on the phase-stability of cryogenic flame are also established. It is found that the unstable phase, in terms of vapor-liquid equilibrium, arises in the vicinity of the liquid-gas interface; however, all unstable-phase states still stay in the metastable region of the phase diagram. For all the flame solutions considered in this study, no thermochemical state enters the spinodal region.

Numerical Predictions of Mean Performance and Dynamic Behavior of a 10 MWe SCO2 Compressor With Test Data Validation

Abstract High-fidelity aerodynamic analysis has been demonstrated for mean performance and unsteady dynamics in a sCO2 compressor designed by Hanwha Power Systems Americas for a 10 MWe Concentrating Solar Power plant. Simulations were performed with crunchcfd® software tool that was matured to accurately model near critical real fluid effects in sCO2. Pretest predictions for mean performance were validated with test data collected later. Performance predictions were accurate and captured sensitivity of the efficiency to inlet temperature of CO2 as well as steep drop-off at high flow rates due to condensation in the inlet throat. Detailed analysis was performed to understand the source of these performance losses at near critical conditions. Unsteady dynamic effects in the compressor at off-design conditions were also identified and quantified. In particular, a system wide “condensation surge” condition was detected at high flow coefficients that results in large amplitude pulsations with accompanying mass flow fluctuations at low frequencies and has potential to cause damage in closed-loop systems.

Theoretically based correction to model test results of OWC wave energy converters to account for air compressibility effect

The oscillating-water-column (OWC) wave energy converter with air turbine has been object of extensive development. The spring-like effect of air compressibility in the chamber is related to the density–pressure relationship. It is known to significantly affect the power performance of the full-sized converter, and is rarely accounted for in model testing. A method is presented to correct results from physical model testing for effects of air compressibility. It combines linear theory in the frequency domain and hydrodynamic coefficients, together with air thermodynamics. A new concept of linear turbine simulator aerodynamically equivalent to the orifice simulator is introduced in the theory. Corrections for non-linear real-fluid effects may be accounted for from comparisons with data from wave tank testing. The method was validated in a case study involving published data from OWC model testing with regular waves of different periods and amplitudes in a wave flume. Theoretically based corrections were found to well predict the air compressibility effects upon power performance. Air compressibility may negatively or positively affect power conversion depending on whether the wave period is larger or smaller than a critical value accurately predicted by the theory.

Scaling laws of statistics of wall-bounded turbulence at supercritical pressure: Evaluation and mechanism

A growing body of studies support that the real fluid effects related to the abrupt density changes in supercritical fluids significantly affect statistical properties of turbulence, yet developing appropriate scaling laws for wall-bounded turbulence at supercritical state is still difficult. In the present study, we conduct direct numerical simulations on channel flows of supercritical fluids to evaluate the usefulness of classical scaling developed for variable-property flows. We find that the expressions based on semi-local scaling [ϕ=f(y*,Reτ*) and ϕ=f(y*,Reτ*,Pr*)] fail to collapse the statistical profiles at supercritical pressure. We analyze the mechanism of the failure of semi-local scaling by quantifying the modulations of turbulent structures of supercritical fluids due to changes in fluid properties. The intensified ejection and sweep of low-speed streaks destabilize the stream-wise streaks and reduce the stream-wise coherence, changing the statistics and affecting the usefulness of semi-local scaling. To shed light on the scaling laws of fluctuating velocities, we finally examine the hypotheses in Townsend wall-attached eddy theory in the context of flows at a supercritical state. It is found that the attached eddies are self-similar near-wall structures, which result in the logarithmic profiles of stream-wise and span-wise velocity fluctuations; the population density of the attached eddies can be well approximated by an exponential scaling.

Structure of the thermal boundary layer in turbulent channel flows at transcritical conditions

Enhanced fluctuations, steep gradients, and intensified heat transfer are characteristics of wall-bounded turbulence at transcritical conditions. Although such conditions are prevalent in numerous technical applications, the structure of the thermal boundary layer under realistic density gradients and heating conditions remains poorly understood. Specifically, statistical descriptions of the temperature field in such flows are provided inconsistently using existing models. To address this issue, direct numerical simulations are performed by considering fully developed transcritical turbulent channel flow at pressure and temperature conditions that cause density changes of a factor of up to$O(20)$between the hot and cold walls. As a consequence of the proximity of the Widom line to the hot wall, significant asymmetries are observed when comparing regions near the cold wall and near the hot wall. Previous transformations that attempt to collapse the near-wall mean temperature profiles among different cases to a single curve are examined. By addressing model deficiencies of these transformations, a formulation for an improved mean temperature transformation is proposed, with appropriate considerations for real fluid effects that involve strong variations in thermodynamic quantities. Our proposed transformation is shown to perform well in collapsing the slope of the logarithmic region to a single universal value with reduced uncertainty. Coupled with a predictive framework to estimate the non-universal shift parameter of the logarithmic region usinga prioriinformation, our transformation provides an analytic profile to model the near-wall mean temperature. These results thus provide a framework to guide the development of models for wall-bounded transcritical turbulence.

Simulation study on the cryogenic liquid nitrogen jets: Effects of equations of state and turbulence models

Based on the open source software OpenFOAM, a new computational fluid dynamics (CFD) solver is developed for trans/supercritical jets. Considering the real-fluid effects, the pressure Poisson equation is modified using two real-fluid equations of state (EOSs). Turbulent flows of liquid nitrogen jets are studied by different turbulence models based on Reynolds Average Navier-Stokes (RANS) under trans/supercritical pressure conditions, and the iterative calculation of pressure–velocity-density coupling is implemented by the extended PISO algorithm. The simulation results of different EOSs are compared with the experimental data, and the performance and accuracy of different EOSs coupling with five different turbulence models applied to trans/supercritical jets are analyzed and quantified. The results indicate that the selection of real-fluid EOS is more significant and important than the turbulence model for the numerical performance. Analysis of three cases under different operating conditions shows that none of the conventional RANS models always give satisfactory results, and all need to be extended to adapt to various characteristics under trans/supercritical conditions.

A High-Fidelity Modeling Tool to Support the Design of Oxy-Combustors for Direct-Fired Supercritical CO2 Cycles

Abstract The challenge in the design of oxy-combustors for direct-fired supercritical CO2 (sCO2) cycles is in addressing disparate performance metrics and objectives. Key design parameters to consider include, among others, injector design for mixing and flame stability, split of recycled CO2 diluent between injectors and cooling films, target flame temperatures to control noncondensable products, and strategies to inject the diluent CO2 for film cooling and thermal control. In order to support novel oxy-combustor designs, a high-fidelity yet numerically efficient modeling framework based on the CRUNCH CFD® flow solver is presented, featuring key physics-based submodels relevant in this regime. For computational efficiency in modeling large kinetic sets, a flamelet/progress variable (FPV) based tabulated-chemistry approach is utilized featuring a three-stream extension to allow for the simulation of the CO2 film cooling stream in addition to the fuel and oxidizer streams. Finite rate chemistry effects are modeled in terms of multiple progress variables for the primary flame as well as for slower-evolving chemical species such as NOx and SOx contaminants. Real fluid effects are modeled using advanced equations of states. The predictive capabilities of this computationally tractable design support tool are demonstrated on a conceptual injector design for an oxy-combustor operating near 30 MPa. Simulations results provide quantitative feedback on the effectiveness of the film cooling as well as the level of contaminants (CO, NO, and N) in the exhaust due to impurities entering from the injectors. These results indicate that this framework would be a useful tool for refining and optimizing the oxy-combustor designs as well as risk mitigation analyses.

Computational investigation of real fluid effects in cryogenic laminar premixed CH4–O2 flames

This study investigates the effects of real fluid thermodynamic and transport properties on the structure and propagation of canonical planar, unstretched, premixed methane-oxygen flames at transcritical conditions, which is relevant to the ignition phase in a liquid rocket engine. The ideal gas law is inapplicable at such extreme conditions, and real fluid thermodynamic and transport properties are required to accurately model the combustion physics at supercritical conditions.The computational framework used in this study integrates real fluid property estimation into the steady-state, freely-propagating flame solver available in the Cantera combustion suite [Goodwin et al., 2017]. The Peng-Robinson equation of state provides closure for the thermodynamic terms in the governing equations. High-pressure thermal conductivity and mass diffusivity coefficients are obtained using the Chung and Takahashi correlations, respectively. A mixture-averaged mass diffusion model is assumed, while neglecting the Soret and Dufour effects. The reaction rate terms are modeled with the standard Arrhenius ideal gas kinetics model using the CH4–O2 mechanism from Lindstedt. The effects on laminar flame structure are presented. It is found that the choice of chemical mechanism has a much greater influence on mass burning rates than the real fluid effects. Real fluid properties produce lower mass burning rates by just ∼10% near the critical region, while the laminar flame speeds are reduced by a factor of ∼5. It is shown that using dilute gas transport properties in combination with a real fluid equation of state and differential diffusion effects may cause a qualitatively different, non-monotonic density profile in the flame.

Detecting parametric resonance in a floating oscillating water column device for wave energy conversion: Numerical simulations and validation with physical model tests

The wave energy sector has faced enormous technological improvements over the last five decades, however, due to the complexity of the hydrodynamic processes, current numerical models still have limitations in predicting relevant phenomena. In particular, floating spar-type wave energy converters are prone to large undesirable roll and pitch amplitudes caused by a dynamic instability induced by parametric resonance. Detecting this phenomenon accurately is essential as it impacts drastically on power extraction, structural loads and mooring forces. This paper presents the validation of results from a numerical model, capable of detecting parametric resonance, using experimental data. Experiments were carried out for a scaled model of the Spar-buoy OWC (Oscillating Water Column) device at a large ocean basin. The buoy uses a slack-mooring system attached to the basin floor. The scaled turbine damping effect is simulated by a calibrated orifice plate. Two different buoy draft configurations are considered to analyse the effect of different mass distributions. The numerical model considers the nonlinear Froude-Krylov forces, which allows it to capture complex hydrodynamic phenomena associated with the six-degree-of-freedom motion of the buoy. The mooring system is simulated through a quasi-static inelastic line model. Real fluid effects are accounted for through drag forces based on the Morison’s equation and determined from experimental data. The comparison of results from regular-wave tests shows good agreement, including when parametric resonance is detected. Numerical results show that parametric resonance can produce a negative impact on power extraction efficiency up to 53%.

Heat-induced planar shock waves in supercritical fluids

We have investigated one-dimensional compression waves, produced by heat addition in quiescent and uniform initial conditions, in six different supercritical fluids, each taken in four states ranging from compressible pseudo-liquid fluid to ideal gas. Navier–Stokes simulations of a canonical semi-infinite domain flow problem, spanning five orders of magnitude of heating rate, are also carried out to support the theoretical analysis. Depending on the intensity of the Gaussian-shaped energy source, linear waves or shock waves due to nonlinear wave steepening are observed. A new reference heating rate parameter allows to collapse in the linear regime the whole dataset, together with the existing experimental data, thanks to its absorption of real-fluid effects. Moreover, the scaling strategy illustrates a clear separation between linear and nonlinear regimes for all fluids and conditions, offering motivation for the derivation of a unified fully predictive model for shock intensity. The latter is performed by extending the validity of previously obtained theoretical results in the nonlinear regime to supercritical fluids. Finally, thermal to mechanical power conversion efficiencies are shown to be proportional, in the linear regime, to the fluid’s Gruneisen parameter, which is the highest for compressible pseudo-liquid fluids, and maximum in the nonlinear regime for ideal gases.

Real-fluid effects on standing-wave thermoacoustic instability

We have performed high-order compressible Navier–Stokes simulations of a thermoacoustically unstable resonator employing in transcritical conditions. The parameter space spans the range of base pressures and temperature differences up to 200 K, with thermodynamic and transport properties obtained from the Peng–Robinson equation of state and Chung’s model. The set-up is a classic standing-wave thermoacoustic resonator, which has been optimized resulting in a minimum temperature difference required to sustain the instability of 23 K. Strong real-fluid effects in the thermoacoustic response in the linear regime are observed: (i) the thermoviscous functions need to depend on the complex eigenvalue (and not just the angular frequency) for linear theory to accurately predict the growth rate observed in the Navier–Stokes simulations, due to a high growth-rate-to-frequency ratio; (ii) the growth rate and frequency vary in a non-monotonic fashion with respect to and ; (iii) the pressure eigenmode amplitude tends to flatten out, and the pressure–velocity phase difference smoothly transitions from to at the average pressure node location; and (iv) the sharp change in base acoustic impedance at transcritical conditions introduces a discontinuity in the eigenmodes’ spatial derivative. The energy budgets illustrate, for a given , the increase of the acoustic power produced, but also of the heat input required, for thermodynamic conditions approaching the critical point. Finally, intense mass transport events at transcritical conditions are shown to entail thermodynamic and convective nonlinearities, which do not, however, govern the limit cycle physics, dominated instead by nonlinear minor losses.

Real-fluid effects on laminar diffusion and premixed hydrothermal flames

This paper is aimed to investigate the real-fluid effects on both diffusion and premixed laminar hydrothermal flames. The real-fluid effects are examined in three aspects, including the equation of state (EOS), thermodynamic, and transport properties. Results show that, for diffusion flames, the introduction of non-ideal EOS is the most significant adjustment as it modifies the flame location, while the correction of thermodynamic and transport properties has minor impacts on the flame structure. For premixed flames, the real-fluid models have limited influence on the temperature and species distributions but significantly affect the flame speed, which is mainly due to the density modification of the unburned mixture by the real-fluid EOS. Finally, the Lewis numbers are derived and the evaluation results show that laminar hydrothermal flames are sensitive to the Lewis number assumption and the non-unity Lewis number method can properly describe the differential diffusion effects for hydrothermal flames.

Numerical study of the counterflow diffusion flames of methanol hydrothermal combustion: The real-fluid effects and flamelet analysis

Counterflow diffusion flames of methanol hydrothermal combustion are investigated to improve the understanding of hydrothermal flames. It is indicated that the thermodynamic properties by the Peng-Robinson equation of state and the modified transport properties can reduce the flame temperature by about 500 K. The Takahashi correlation for mass diffusivity is found to be appropriate for hydrothermal combustion through comparison with the experimental data of Wellig et al. (J. Supercrit. Fluids, 2009, 49, 1). Compared to the Kolmogorov length scale in the experimental combustor, the thickness of the calculated counterflow flame is ten times larger, which means that the flame would be affected by the turbulence. The flame stable range is also reproduced well by the developed hydrothermal counterflow flame model. In the end, a Flamelet Generated Manifold (FGM) table is generated, promising to provide good closure of the non-equilibrium chemical source term in further turbulent flame simulations.

Wave-induced real-fluid effects in marine energy converters: Review and application to OWC devices

The performance assessment of industrial marine energy converters involves the integrated treatment of their hydrodynamic design and the optimization of their device hulls. Nowadays, such tasks require extensive experimental work and simulation plans, consuming considerable resources and time. In this comprehensive review of integrated approaches to numerical and experimental testing, the advantages and disadvantages of existing tools, from full-scale prototype and wave tank models to Computational Fluid Dynamics (CFD) and potential flow simulations, are all analysed. Likewise, current challenges such as experimental scale effects, numerical viscosity, and turbulence treatment are all studied. The novelty of this research is an integrated approach that employs experimental wave tank tests to validate a numerical wave tank model based on CFD that serves to calibrate a fast potential flow solver with Morison's correction terms. The model allows running, on tight resources, the necessary simulation for the design and optimisation of marine energy converters under multiple sea state conditions. Given the operating regimes of conventional marine energy converters, the results show that the influence of turbulence may be small, due to the unsteady nature of the oscillatory boundary layer flows.