Homogeneous Relaxation Model Research Articles

Analysis of the exergy transfers in subcritical and transcritical CO[formula omitted] ejectors and their connection with the performance of the refrigeration cycle

Ejector refrigeration systems (ERSs) operating with carbon dioxide are notoriously challenging from both design and operation perspectives. In particular, the ejector itself gives rise to special attention since it directly affects the performance of the global system. In this study, the connections between local exergy transfers within the ejector and global cycle performance are investigated by using a novel multi-scale numerical approach. Computational Fluid Dynamics (CFD) is used to generate accurate predictions of the ejector operation with access to the local flow and heat transfer features. The exergy tube analysis is applied onto the simulation results, linking local transfers within the ejector to the results at the component- and cycle-scale. A state-of-the-art ejector thermodynamic model is then calibrated onto the CFD results, and employed to determine the physically possible operation of the ERS. In addition, the metastability impact on the exergy transfers and overall system performance is investigated by comparing the CFD results of the classical Homogeneous Equilibrium Model with those obtained with the Homogeneous Relaxation Model. Notably, it is found that at fixed ejector inlet conditions, there exits an outlet pressure that maximizes the exergy transfers from primary to secondary streams. Interestingly, this work shows for the first time that the maximum exergy gain of the secondary stream appears to correlate with the maximum coefficient of performance of the system, independently of the on- or off-design operation of the ejector. Moreover, metastability generally deteriorates the performance at both scales. The results of the present study serve to pave the way towards better ejector design objectives.

Impact of modelling assumptions in cavitating flow of simplified injector

Here, three-dimensional Reynolds-averaged Navier–Stokes (RANS) simulations are employed for in-nozzle flow modelling. The aim is to evaluate the capabilities and sensitivities of simulating in-nozzle flow phenomena by using homogeneous phase change models. Two commonly used homogeneous models are employed – (i) Homogeneous Equilibrium Model (HEM) and (ii) Homogeneous Relaxation Model (HRM) A simplified nozzle with reference experimental data is modelled in the developing, super cavitation, and hydraulic flip regimes using OpenFOAM. The influence of the inlet boundary condition and turbulence models are investigated. With HEM, three barotropic compressibility models are tested. The research seeks to understand the strengths and limitations of each approach by comparing different sub-models and their interactions with the flow fields and phase change phenomena. Ultimately, this study contributes to a better understanding of how different modelling choices can influence the accuracy and reliability of cavitation simulations using homogeneous phase change models. While the simulations demonstrated reliable predictions for low-order velocity statistics, substantial discrepancies were identified in the prediction of the cavitating region by both homogeneous models. Additionally, the relaxation model predicted only minor cavitation. In contrast, acceptable flow predictions were achieved using different barotropic compressibility models and inlet boundary condition types, as well as most RANS turbulence models, where the RNG k-ɛ model deviated more from the other turbulence models. Therefore, the added value of the present study is summarised as: (a) Four different cavitation regimes are simulated with HEM and HRM in a single study. (b) The more comprehensive HRM approach does not produce better velocity or cavitation predictions for a low-speed flow using the default relaxation time. (c) The choice of turbulence model can radically affect the cavitation prediction, in addition to velocity fields. (d) The HEM flow simulation has little sensitivity to the barotropic compressibility model.

A homogeneous relaxation model algorithm in density-based formulation with novel tabulated method for the modeling of CO2 flashing nozzles

Accurate prediction of the flow physics within nozzles and ejectors working with two-phase carbon dioxide remains particularly challenging. Indeed, the flashing phenomenon in the device often comes along with the formation of the metastable phase, which can severely affect both the flow physics, and the flow rate. Due to the particular challenges associated with building and operating two-phase carbon dioxide experimental setups, computational fluid dynamics constitutes a compelling alternative to study and predict nozzle and ejector flows. In this work, the metastability effects are modeled through a Homogeneous Relaxation Model for the first time expressed in density-based formulation, within the SU2 solver. The thermodynamic relations for the equation of state are tabulated using a novel quad-tree algorithm and directly coupled to the solver, ensuring fast and accurate predictions. The simulation tool is then validated against experimental nozzle pressure profiles and used to compare the commonly used Homogeneous Equilibrium Model to the Homogeneous Relaxation Model in terms of local flow topology and mass flow rates. Most notably, it was found that the Homogeneous Relaxation Model was able to better fit the experimental pressure profiles within the first part of the expansion.

A flashing flow model for the rapid depressurization of [formula omitted] in a pipe accounting for bubble nucleation and growth

Flashing flow is encountered in many industrial systems involving nozzles, valves and decompression of vessels and pipes. In the context of CO2 capture and storage (CCS), the design of safe and efficient CO2 transportation systems requires accurate flashing models, e.g., for safety analysis of pipe fractures and to predict the mass flow through relief valves. We propose a homogeneous flashing model (HFM) for flashing flow accounting for the underlying physical phenomena of the phase change: bubble nucleation, coalescence, break-up and growth. Homogeneous nucleation is modeled using classical nucleation theory and heterogeneous nucleation is approximated with constant rates of bubble creation and mass transfer from liquid to vapor. The flashing flow model is fitted for CO2 pipe depressurization data at various initial conditions. We find that the same, constant model parameters can be applied for the whole set of depressurization cases considered, as opposed to the conventional homogeneous relaxation model which typically is tuned on a case-by-case basis. For depressurization paths where the fluid state passes close to the critical point, we demonstrate that an accurate description of the flashing process along the length of the pipe can only be achieved when both homogeneous and heterogeneous nucleation are accounted for.

Optimization of the Flashing Processes in Mineral Metallurgy Based on CFD Simulations

In mineral metallurgy, the flashing unit is key to returning the slurry to atmospheric conditions. Its primary function is to achieve pressure letdown, and during the process, shock waves are generated to maximize energy dissipation. Investigating the location and expansion of shock waves is the focal point of this study due to their importance in flashing unit design. A CFD model coupled with a homogeneous relaxation model (HRM) was used to simulate the flashing process of mineral slurry. The flow behavior, including velocity, pressure, and the shape and location of the shock waves, were obtained using simulation under different unit design and operating parameters. These results would provide valuable insights into the design of flashing units and guidance for the safe operation and maintenance of devices.

Simulation of a homogeneous relaxation model for a three-phase mixture with miscible phases

Simulation of a homogeneous relaxation model for a three-phase mixture with miscible phases

A unified non-equilibrium phase change model for injection flow modeling

The homogenous relaxation model (HRM) is one of the most widely used models to describe the liquid‑gas phase transition. However, in its original formulation, it is unable to handle multispecies vapor-liquid equilibrium (VLE), which limits its applicability to single-component fluids. In this work, a unified non-equilibrium phase change model that considers the VLE of multicomponent mixtures is proposed building upon the HRM's structure. A time factor is introduced to mimic the effect of different phase change timescales due to different mechanisms, e.g., cavitation, flash-boiling, and evaporation. To assess the model's performance, computational fluid dynamics simulations of the internal and near-nozzle injection flow of the Engine Combustion Network's Spray G injector were performed using the nine-component PACE-20 fuel with both the unified model and the original HRM. The predicted fuel density in the near-nozzle region matched well with X-ray tomography measurements. The simulation results indicated that, whereas the HRM failed to capture the vaporization due to convective mixing between the fuel and ambient gas, the unified model performed well in predicting the mixing-driven vaporization and the corresponding evaporative cooling. Further comparisons using the nine-component fuel formula and a single-component fuel surrogate demonstrated the unified model's ability to predict preferential vaporization, which affects the predictions of local mixture composition and rate of vaporization. Finally, it is shown that the unified model is capable of representing multiple phase change mechanisms, and the relaxation time factor plays an important role in determining the degree of phase change due to the different mechanisms.

Modelling of two-phase expansion in a reciprocating expander

Two-phase expansion devices can be applied in a multitude of cycles which allow for an increase of the overall system efficiency in currently used heat and power cycles. The expanders that are mainly investigated for the purpose of two-phase expansion are the Lysholm and the reciprocating expanders. From these two, the reciprocating expander is challenging to model as there is a need to describe the non-equilibrium state of the phases during the expansion process. This study aims to fill the knowledge gap that exists for two-phase reciprocating expanders, by constructing a predictive model to describe the expansion process and the non-equilibrium phenomena occurring. The simulation framework makes use of a modified homogeneous relaxation model to describe the thermal non-equilibrium between the phases within the isolated working chamber. The model results are verified and compared to experimental data in literature with water as working fluid. Subsequently, Cyclopentane is selected as a more suitable candidate and a thorough analysis is presented. The simulation results predict a 15% lower work and a 10% higher mass intake per stroke of the expander compared to equilibrium working conditions. • A model is constructed to predict the evaporation rate of a two-phase mixture in a reciprocating expander. • The homogeneous relaxation model is applied and compared to the homogeneous equilibrium model. • The evaporation rate in a reciprocating expander is lower than expected, resulting in metastable conditions during the process. • The updated disequilibrium model predicts around 25% more mass intake and 8% lower work compared to the equilibrium model.

One-dimensional mathematical modeling of two-phase ejectors: Extension to mixtures and mapping of the local exergy destruction

The ejector is a process equipment frequently used in refrigeration processes. There is currently a knowledge gap on the efficiency of ejectors operating with mixtures. To address this knowledge gap, we present a one-dimensional ejector model for mixtures, defined by spatially distributed mass-, energy- and momentum-balances for different zones, which together constitute the full ejector geometry. The recently developed delayed homogeneous relaxation model is used to describe the two-phase transition in the motive and suction nozzles. For evaporation of pure CO 2 in the throat of the motive nozzle, the model yields an average error of 2.6% in the critical mass flow rate, which is significantly lower than the homogeneous equilibrium model that has an average error of 8.4%. A comparison to new experimental data shows that both models give excellent predictions of critical mass flow rates where condensation occurs in the throat, with an average error below 0.9%. New experimental data with CO 2 are presented, which are used to regress two parameters in correlations that describe the momentum transfer between the primary and secondary stream in the mixer and diffuser sections. This leads to accurate reproduction of the pressure lift in five different ejector geometries, with a mean error of 2.3%. By using nonequilibrium thermodynamics, we derive formulae for the local exergy destruction in the ejector. The largest exergy destruction is located in the mixer, and originates in transfer of momentum between the primary and secondary streams. The local exergy destruction profiles through the mixer and diffuser are highly non-uniform, and deviate from the established guidelines for energy-efficient design characterized by equipartition of exergy destruction. This reveals a potential to increase the performance of ejectors by suitable adjustments to their geometric design. The mathematical model validated for pure CO 2 is assumed to also be valid for mixtures rich in CO 2 . We show that minute concentrations of a second component can have a significant influence on the ejector performance. When fixing the inlet conditions and ejector geometry, we demonstrate that adding 2% H 2 to a mixture of CO 2 decreases the critical mass flow rate by 20%, while adding 2% SO 2 increases the pressure lift by 1 bar. • A state-of-the-art, one-dimensional ejector model for mixtures is presented. • New experimental data for ejector operation with CO2 improves the model. • Critical mass flow rates and pressure lifts from experiments reproduced within 3%. • Local mapping of exergy destruction with nonequilibrium thermodynamics. • Minute concentrations of a second component alter the ejector performance.

On the effect of mixing-driven vaporization in a homogeneous relaxation modeling framework

The homogeneous relaxation model (HRM) is one of the most widely used models to describe the liquid–gas phase transition in multiphase flows due to the occurrence of cavitation. However, in its original formulation, the HRM does not account for the presence of ambient gas species, which generally limits its applicability to the injector's internal flow where ambient gases are negligible. In this work, a mixing-driven vaporization (MDV) model was developed to extend the capability of the HRM in handling the mixing effect in the regions external to the nozzle, where vapor–liquid equilibrium for multi-species mixtures of fuel and ambient gas is considered. To assess the model performance, simulations of the Engine Combustion Network's Spray G injector were performed with the HRM and the MDV model under both flash-boiling and evaporating conditions. It was found that the MDV model led to a better match against x-ray measurements of fuel density in the near-nozzle region. In contrast to the HRM, the MDV model was able to reproduce the vaporization process in the mixing zone at the edge of the fuel jet, which aligns with the expected physics. This resulted in substantial differences in the prediction of other flow characteristics such as mixture temperature and pressure. Furthermore, this work demonstrates that evaporation timescales have a considerable effect on the MDV model's predictions, as shown by a parametric study in which a time factor was introduced to mimic the effect of different timescales due to different phase change mechanisms.

Two-Phase Volumetric Expanders: A Review of the State-of-the-Art

Two-phase expansion is the process where a fluid undergoes a pressure drop through or in the liquid–vapor dome. This operation was historically avoided. However, currently it is studied for a multitude of processes. Due to the volume increase in volumetric expanders, a pressure drop occurs in the fluid resulting in flashing phenomena occurring. These phenomena have been studied before in other processes such as two-phase flows or static flash. However, this has not been extensively studied in volumetric expanders and is mostly neglected. Even if data has shown this is not always neglectable depending on the expander type. The thermal non-equilibrium occurring can be modeled on different principles of flashing flows, such as the mixture model, boiling delay model, and homogeneous relaxation model. The main application area in current literature for volumetric two-phase expansion machines, is in low-temperature two-phase heat-to-power cycles. These cycles have shown benefit over classic options if expanders are available with efficiencies in the range of at least 75%. Experimental investigation of expanders in two-phase operation, though lacking in quantity, has shown that this is an achievable goal. However, the know-how to accomplish this requires more studies, both experimentally and in modeling techniques for the different phenomena occurring within these expanders. The present work provides a brief but comprehensive overview of the available experimental data, applicable flashing modeling techniques, and available models of volumetric two-phase expanders.

Transient nozzle flow analysis and near field characterization of gasoline direct fuel injector using Large Eddy Simulation

Injection duration in spark ignition engines is typically very short. Thus, understanding transient effects of the Gasoline Direct injection (GDi) process plays a major role in the analysis of the mixture formation and so combustion efficiency in this type of engines. Focusing on the opening and closing phases when the needle is moving up and downwards, there still are some uncertainties. For instance, the effect of wobble may lead to uneven distribution of fuel among the holes, and therefore differences in spray formation and even plume-to-plume interactions. Other factors that may affect the shape of the rate of injection and so the mixture formation are the time evolution of the upstream pressure (related to the injector dynamics) together with the detailed geometry of the needle and its seat. Experimentally addressing these issues nowadays remains challenging, if not impossible, so Computational Fluid Dynamics (CFD) are used to study this phase of the injection process. Large Eddy Simulations (LES) are selected to account for the effects of turbulence. Volume-of-Fluid (VOF) approach is used, not only to analyze the flow inside the nozzle, but also the first 2–5 mm of the spray. Homogeneous Relaxation Model (HRM) is employed to consider the mass exchange between liquid and vapor phases of the fuel inside the nozzle, if necessary. The Spray G operating condition of Engine Combustion Network (ECN) is used in this analysis. Statistics of several realizations are performed in order to extract significant conclusions. Results are validated against experimental data, and show the effects of the turbulence in the spray development. A strong interaction between jets, especially in the transitory phases of the simulation (opening and closing), is observed. Spray parameters, after averaging the different realizations, also accurately match the experimental results and previous simulations reported in the literature. One of these precisely captured effects is the deviation of the spray from the geometric axis of the orifice.

Analysis of elliptical diesel nozzle spray dynamics using a one-way coupled spray model

The elliptical nozzle has the potential ability to increase the air-fuel mixture quality. A one-way coupled spray model and Homogenous Relaxation Model (HRM) was adopted to investigate the spray behaviors and the air-fuel mixture progress in real diesel combustion chamber with the application of elliptical and circular diesel nozzle. The results indicated that the spray cone angle and the air entrainment mass of elliptical nozzle were larger than that of the circular nozzle, while the spray penetration of the elliptical nozzle which the aspect ratio is 1.5 and 2 was shortened by 11% and 8.3% as compared to circular spray respectively. Also, the air entrainment mass of the elliptical spray with a ratio of 1.5 and 2 increased by 60% and 35% as compared with circular spray respectively. Furthermore, the partial equivalent ratio and the high concentration area in the cylinder is reduced for elliptical nozzle, and the air-fuel mixture is more uniform. The fuel evaporation rate of elliptical spray is always higher than that of the circular spray.

Machine learning accelerated turbulence modeling of transient flashing jets

Modeling the sudden depressurization of superheated liquids through nozzles is a challenge because the pressure drop causes rapid flash boiling of the liquid. The resulting jet usually demonstrates a wide range of structures, including ligaments and droplets, due to both mechanical and thermodynamic effects. As the simulation comprises increasingly numerous phenomena, the computational cost begins to increase. One way to moderate the additional cost is to use machine learning surrogacy for specific elements of the calculation. This study presents a machine learning-assisted computational fluid dynamics approach for simulating the atomization of flashing liquids accounting for distinct stages, from primary atomization to secondary breakup to small droplets using the Σ−Y model coupled with the homogeneous relaxation model. Notably, the models for thermodynamic non-equilibrium (HRM) and Σ−Y are coupled, for the first time, with a deep neural network that simulates the turbulence quantities, which are then used in the prediction of superheated liquid jet atomization. The data-driven component of this method is used for turbulence modeling, avoiding the solution of the two-equation turbulence model typically used for Reynolds-averaged Navier–Stokes simulations for these problems. Both the accuracy and speed of the hybrid approach are evaluated, demonstrating adequate accuracy and at least 25% faster computational fluid dynamics simulations than the traditional approach. This acceleration suggests that perhaps additional components of the calculation could be replaced for even further benefit.

Two-phase nozzles performances CFD modeling for low-grade heat to power generation: Mass transfer models assessment and a novel transitional formulation

The use of two-phase nozzles for low-grade heat valorization by electricity production increases the energy recovery rate using Trilateral Flash or Wet to Dry cycles. A model benchmark for nozzle flow rate and efficiency estimation was conducted on experimental data from the literature. These data come from a series of tests made on geothermal energy production water two-phase nozzles. A new transitional bubble-to-droplet interfacial area density formulation (TA-BD model) is presented by the paper. It is compared to three models from literature. Two nozzles operating with different inlet and outlet conditions were modeled. The calibration flexibility and the robustness of the models are discussed in association with physical analysis. The paper shows how the models using single or redundant adaptation parameters fail to provide good results simultaneously on flow rate and efficiency. It appeared that the TA-BD model is the more flexible and robust. The Homogeneous Relaxation Model (HRM) model gives also good results. Furthermore, TA-BD model gives the lowest average discrepancies. Especially at the best efficiency point of the first test case, TA-BD model shows<1% discrepancy where the HRM model has 18% discrepancy in efficiency. The TA-BD model appeared to be easier to calibrate than the HRM model. Finally, regarding the proposed TA-BD model, the sensitivity to the geometry and operating conditions shows that the interfacial area density formulation could be completed to include the effect of nozzle's section profile, the effect of the inlet temperature on bubbles number density, and the effect of outlet pressure on the droplets number density.

Choked liquid flow in nozzles: Crossover from heterogeneous to homogeneous cavitation and insensitivity to depressurization rate

The critical mass flow rate is the maximum flow rate that can pass through a constrained geometry such as a nozzle. For liquid CO2, it has been shown that homogeneous relaxation models systematically underpredict the critical mass flow rate. In this work, we demonstrate that a delay of the phase transition is necessary to reproduce experiments. To analyze this in further detail, two methodologies are presented: (1) the delayed homogeneous relaxation model (Delayed HRM), and (2) the metastable isentrope model (MIM). Delayed HRM is a relaxation model that can readily be incorporated into a spatially distributed description of the fluid flow, e.g. in ejectors. MIM assumes isentropic flow and instantaneous equilibrium up to the limit of metastability, and yields a geometry-independent critical mass flux as the solution of a set of algebraic equations. We compare the two methodologies to available experimental data on the critical mass flow rates of CO2 and H2O through nozzles, finding that they give nearly identical predictions. This suggests that the critical mass flow rate is mostly determined by the achievable degree of metastability before onset of phase change, and is rather insensitive to dynamic variables such as the depressurization rate or the rate of relaxation towards equilibrium. Using the limit of metastability predicted by homogeneous nucleation theory works well at high temperatures, rendering the methodologies completely predictive. They deviate on average 11% from experimental data on CO2, and thus outperform homogeneous relaxation models by a large margin, even when the latter employs several fitted parameters. Especially good agreement was found with experiments that employ a lubrication oil, which is hypothesized to suppress heterogeneous nucleation. The limit of superheat at lower temperatures must be described by heterogeneous nucleation theory. For water and CO2 we find a crossover between homogeneous and heterogeneous nucleation at T≈590 K and T≈285 K respectively. Moreover, the predicted limit of superheat falls on a single curve in the temperature–pressure space of water, and we present an empirical correlation of this curve. By combining this expression with the above methodologies, we obtained an average deviation of 3% with available experimental data on H2O mass flow rates.

Computational fluid dynamics study of CO2 dispersion with phase change of water following the release of supercritical CO2 pipeline

Accidental release of pressurized CO2 pipeline in carbon capture and storage involves the interaction of phase change and heavy-gas dispersion. However, the effect of the phase change of water vapor in air on the performance of cold CO2 dispersion is usually neglected. In this study, a three-dimensional two-phase computational fluid dynamics (CFD) model is developed to evaluate the cold CO2 dispersion by considering the phase change of water. A phase-change model based on the homogeneous relaxation model is used to describe the evaporation and condensation of water. The effects of terrain roughness, atmospheric stability, and turbulence models on the dispersion are also considered. The numerical results show that the model that uses the k–ω turbulent equations is superior to the other models. The results in which the phase change of water is considered exhibit a better agreement with the data from the experiments than those that do not consider it. The model is subsequently used in urban areas, which results in over-predicted CO2 concentration in the near field and under-predicted CO2 concentration in the far field when the phase change of water vapor is considered than that when it is neglected. Therefore, we proposed that the phase change of water vapor in the atmosphere should not be overlooked in the more accurate modeling of cold CO2 dispersion.

A homogeneous relaxation low mach number model

In the present paper, we investigate a new homogeneous relaxation model describing the behaviour of a two-phase fluid flow in a low Mach number regime, which can be obtained as a low Mach number approximation of the well-known HRM. For this specific model, we derive an equation of state to describe the thermodynamics of the two-phase fluid. We prove some theoretical properties satisfied by the solutions of the model, and provide a well-balanced scheme. To go further, we investigate the instantaneous relaxation regime, and prove the formal convergence of this model towards the low Mach number approximation of the well-known HEM. An asymptotic-preserving scheme is introduced to allow numerical simulations of the coupling between spatial regions with different relaxation characteristic times.

Experimental investigation of self-pressurized propellant injection into a simulated rocket motor combustion chamber

Behaviour of self-pressurized nitrous oxide (N2O) injection through a sharp-edged channel intended to replicate a rocket motor injector has been studied using carbon dioxide (CO2) as an analog fluid. Experimental data was collected from 14 separate experiments which varied pressure upstream and downstream of the injection channel. The experimental data was used to determine the accuracy of previously developed two-phase flow models found in the literature, including the homogeneous relaxation model (HRM), the homogeneous equilibrium model (HEM), and the delayed equilibrium model (DEM). The HRM was determined to be the best model for predicting flashing water flows, but it required adjustment of its vapourization rate equations to properly represent the CO2 flashing flows. A genetic algorithm was used to fit the HRM vapourization rate coefficients to the experimentally measured mass flow rate and pressure distribution. The modified HRM model developed in this work has been used to show a relationship between mass flow rate and injector geometry for a range of operating conditions relevant to rocket motor applications.

The effect of the divergent-convergent GDI injector on inner flow and spray characteristics at high injection pressure

ABSTRACT The effects of Divergent-Convergent (D-C) nozzle parameters on the inner flow and spray characteristics of GDI (Gasoline Direct Injection) injector were studied under the condition of high injection pressure of 40 MPa. Homogeneous Relaxation Model (HRM) was used to explore the GDI orifice inner cavitation flow and nozzle exit flow parameters. A one-way coupled spray model was adopted to study the GDI spray behaviors. From these results, the cavitation density in the orifice decreases with the increase of the medium diameter ratio Km, while the discharge coefficient and the orifice exit velocity increases with the increase of Km. Moreover, the nozzle exit average velocity increases with the increase of Xm, and the nozzle exit average velocity with the Km of 1.5 is about 14.1% larger than that of the cylindrical nozzle. While the changing of the Xm has no effect on the nozzle exit average velocity for the same median diameter ratio. Additionally, the turbulent kinetic energy at the nozzle exit decreases with the increase of Km, especially the turbulent kinetic energy for the D-C nozzle with Km of 1.5 is about 17.1% smaller than that of the cylindrical nozzle. In addition, the D-C nozzle with Xm of 0.5 held the smallest turbulent kinetic energy. Also, the Sauter Mean Diameter (SMD) decreases with the decrease of Km at the initial injection stage. However, the spray SMD increases with the decrease of Km, and the SMD decreases with the increase of Xm at the late injection stage. Furthermore, the SMD of D-C nozzle is smaller than that of the cylindrical nozzle at the late injection stage.