Evaporation Source Term Research Articles

The interaction between evaporation and chemistry on two-stage auto-ignition of an n-heptane droplet

This paper investigates the interaction between droplet evaporation and chemical reactions on two-stage auto-ignition. A two-phase model is established by embedding evaporation source terms into a well-stirred reactor. Evaporation Damkholer number (Daeva) is first proposed to investigate auto-ignition characteristics because it controls the evaporation-induced decrease of gas temperature and the increase of available fuel vapor. Three auto-ignition modes are observed with increasing Daeva. Both mode 1# and 2# are two-stage auto-ignition and their difference is whether the evaporation is completed before (mode 1#, Daeva ≤ 1.0) or after the low-temperature auto-ignition (mode 2#, Daeva > 1.0). The feature of mode 1# is that the second auto-ignition delay is unchanged with increasing Daeva. However, the second delay sharply increases for mode 2#. The mode 3# has a slow evaporation and it is a single-stage auto-ignition due to the disappearance of low-temperature auto-ignition. Ambient pressure does not influence Daeva at the 1#-2# boundary (Daeva≈1.0), while an increased equivalence ratio slightly decreases the turning Daeva. Furthermore, a decreased total auto-ignition delay is observed in two special areas with increasing evaporation timescale due to the shortening of the first or second auto-ignition delay. In the end, a new estimation method for auto-ignition delays is proposed for three auto-ignition modes and its error is controlled in the range of ±10%.

LES of a turbulent lifted methanol spray flame using a novel spray flamelet/progress variable model

Turbulent spray flames are complex combustion configurations and are difficult to be accurately simulated. In this paper, we focus on further development and validation of the two-phase spray flamelet/progress variable (TSFPV) model, which is first proposed in our previous work and shows sound performance because it is able to consider the effect of droplet evaporation on the flamelet structure. A spray evaporation source term (SEST) model is improved in the present work to model the evaporation sources and is applied to the calculation of one-dimensional laminar counterflow flames to generate the spray flamelet library. The SEST model is validated on the configuration of two-dimensional counterflow spray flames, and the a priori and a posteriori results show good agreement with the solutions using the Lagrangian particle tracking (LPT) method. The effect of pre-vaporized fuel vapor is further considered in the spray flamelet library, in which both the spray and gaseous flame regimes are covered. The TSFPV model is well validated on the configuration of the laminar mixing layer by comparing the a priori and a posteriori results with detailed chemistry (DC) solutions. Large Eddy Simulation (LES) of the Sydney turbulent lifted methanol spray flame Mt2A is conducted using the TSFPV model. The flame lift-off is correctly captured and the final predicted lift-off height is very close to the experimental value. The predicted mean droplet velocities show good agreement with experimental measurements, and the rms velocities agree well with the experimental data at downstream locations with a late jet breakup. The droplet size increases along the downstream direction and this trend is well reproduced in the current simulation, though the local peak value of droplet size near the upstream shear layer is not well captured. The central jet temperature at upstream locations is also well predicted by the TSFPV model. Overall, the results show good agreement with the experimental measurements, which illustrates the potential of the TSFPV model for spray combustion modeling.

Thermodynamic effect on attached cavitation and cavitation-turbulence interaction around a hydrofoil

This paper aims to numerically investigate the thermodynamic effect on attached cavitation and cavitation-vortex interaction around a NACA0015 hydrofoil. Based on the isothermal cavitation model, the compressibility and thermodynamic effect are considered by adding the state equation and modifying the evaporation and condensation source term in the mass transport equation. The thermodynamic effect on the hydrodynamic performance and the cavity volume fluctuations, the temporal evolution of the unsteady cavitation, the temporal evolution of vortex structures in the hydrofoil wake, and the cavitation-vortex interaction are presented. The main features of the unsteady quasi-periodic cavitation behavior are illustrated for the isothermal and non-isothermal conditions. The new omega vortex identification method depicts the influence of the thermodynamic effect on the shedding structure around the wake of a hydrofoil. Furthermore, the cavitation-vortex interaction is examined to show the relationship.

A priori and a posteriori studies of a novel spray flamelet tabulation methodology considering evaporation effects

Turbulent spray flames are complicated combustion configurations involving many coupled processes including atomization, evaporation, mixing, chemical reactions, etc. Different flamelet models with intrinsically high computational efficiency have been proposed and extended to model spray combustion. One popular approach for flamelet modeling is based on the gaseous flamelet library, but the accuracy is not guaranteed for combustion with gas–liquid two-phase flows. The other approach is based on the spray flamelet library that takes into account the effects of evaporation on the flamelet structure, but problems related to the non-monotonicity of mixture fraction occur. We develop a novel tabulated spray flamelet/progress variable (TSFPV) model in the present work. An additional mixture fraction Zcarr (named carrier mixture fraction) is defined to describe the mixing process, and it proves to avoid the problem of non-monotonicity of the spray flame structure. The empirical formulas of mass and energy evaporation source terms are obtained and then applied to one-dimensional flames in order to create the flamelet library considering evaporation effects. The developed TSFPV model is validated via simulations of laminar spray counterflow flame and turbulent spray reactive jet in cross-flow, where strong interactions between spray droplets and flame occur and the traditional Flamelet/Progress Variable (FPV) model fails. The a priori and a posteriori studies of TSFPV model are conducted, and the model shows to achieve good agreement with the detailed chemistry solutions. The double-reaction spray flame structure can be captured correctly. The TSFPV model can also give sound quantitative predictions for temperature and minor intermediate products (such as OH, C2H2, and C2H4).

Response of spray number density and evaporation rate to velocity oscillations

A theoretical investigation of the effect of gas velocity oscillations on droplet number density and evaporation rate is presented. Oscillations in gas velocity cause a number density wave, i.e. an inhomogeneous, unsteady variation of droplet concentration. The number density wave, as it propagates downstream at the mean flow speed, causes modulation of the local evaporation rate, creating a vapour wave with corresponding oscillations in equivalence ratio. The present work devises an analytical formulation of these processes. Firstly, the response of a population of droplets to oscillations in the gas velocity is modelled in terms of a number density wave. Secondly, the formulation is extended to incorporate droplet evaporation, such that an analytical expression for the evaporation rate modulation is obtained. Subsequently, the droplet 1D convection-diffusion transport equation with the calculated evaporation source term is solved using an appropriate Green’s function to determine the resulting equivalence ratio perturbations. The dynamic response of equivalence ratio fluctuations to velocity oscillations is finally characterized in terms of a frequency-dependent transfer function. The aforementioned analytical approach relies on a number of simplifying approximations, nevertheless it was validated with good agreement against 1D Euler-Lagrange CFD simulations.

Effects of evaporation on chemical reactions in counterflow spray flames

The role of evaporation on chemical reactions in counterflow spray flames remains a key issue due to the non-linear inter-phase interactions through mass, momentum, and energy conservation. An extended chemical explosive mode analysis to illustrate the role of evaporation (ECEMA) was previously developed by separating the evaporation source term from non-chemical terms and projecting them onto the chemical explosive mode (CEM). Evaporation was found to promote chemical reactions when the fuel supply effect dominated the evaporative cooling and to inhibit reactions otherwise. In this work, ECEMA is applied to one-dimensional laminar and three-dimensional turbulent counterflow spray flames. For laminar cases, ECEMA is applied to multi-modal spray flame solutions including the distributed, collocated, and cool flame. The analysis for the collocated and cool flame shows similar behavior, namely, that evaporation inhibits chemical reactions due to heat absorption near the fuel injection region and enhances chemistry around the zero-crossing CEM. For the distributed flame, the promotion effect is observed for most of the domain. For the turbulent counterflow flame, three CEM regions are identified, namely, a hybrid region, an inhibition region, and a promotion region. In particular, for the hybrid region near the spray injection side, the contribution of evaporation to chemical reactions changes from inhibition to promotion. For the inhibition region in the middle, significant suppressing of chemical reactions by evaporation is observed. In the promotion region near the oxidizer side, evaporation remains promoting chemical reactions. For the case investigated, the dominant combustion modes are the assisted ignition and local extinction.

Numerical study of the hydrofoil cavitation flow with thermodynamic effects

High-temperature water exhibits evident thermodynamic effects during cavitation, which influences the cavitation flow and generates complex flow characteristics. To reveal the mechanism of thermodynamic effects on the cavitation flow in high-temperature water, a flow around NACA 0015 hydrofoil was simulated. Based on the existing isothermal cavitation model, the thermodynamic effects were considered by correcting evaporation and condensation source terms and coupling physical parameters with temperature. Numerical results obtained from the thermodynamic effect cavitation model agree well with the available experiments. A comparative analysis of performance characteristics, cavitation shape, and interphase mass transfer rate was performed. The thermodynamic effects on the cavitation flow of hydrofoil under different temperature were presented. The existence of the thermodynamic effects lowers the local temperature of the cavitation, reduces the vapor phase volume fraction of the cavitation area, and inhibits the development of cavitation. Moreover, a novel entropy production analysis was conducted to reveal the thermodynamic effects on the energy loss. The difference of local entropy production rate in the cavitation flow with and without thermodynamic effects was revealed. The analyses show that the existence of the thermodynamic effects reduces the energy loss owing to the reduction of the dissipation loss caused by the velocity gradient. When the thermodynamic effects are considered, the energy loss caused by the temperature gradient shows an increase; however, the proportion of this loss is still small.

A DNS evaluation of mixing and evaporation models for TPDF modelling of nonpremixed spray flames

In the present work, nonpremixed temporally evolving planar spray jet flames are simulated using both direct numerical simulation (DNS) and the composition transported probability density function (TPDF) method. The objective is to assess the performance of various mixing and evaporation source term distribution models which are required to close the PDF transport equation in spray flames. Quantities which would normally be provided to the TPDF solver by spray models and turbulence models are provided from the DNS: the mean flow velocity, turbulent diffusivity, mixing frequency, and cell-mean evaporation source term. Two cases with different Damköhler numbers (Da) are considered. The low Da case (Da-) features extinction followed by reignition while extinction in the high Da case (Da+) is insignificant. The TPDF modelling considers two mixing models: interaction by exchange with the mean (IEM) and Euclidean minimum spanning trees (EMST). Three models for distribution of the evaporation source terms are considered: EQUAL which distributes them in proportion to notional particles’ mass weight, NEW which creates new particles of pure fuel, and SAT which distributes the sources preferentially to notional particles close to saturation. It is found that the IEM model overpredicts the extinction when used with any evaporation model for both Da- and Da+ cases. The EMST model captures well the trend for extinction and reignition for the Da- case when it is coupled with the EQUAL evaporation model, but it overpredicts the extinction when coupled with the NEW or SAT evaporation model. For the Da+ case, all evaporation models reasonably capture the flame dynamics when coupled with EMST. The flame temperature in the mixture fraction space was examined to further assess the model performance. In general the EMST model results in narrow PDFs with little conditional fluctuation, while the IEM model produces bimodal PDFs with burning and partial extinction branches.

A computational framework for interface-resolved DNS of simultaneous atomization, evaporation and combustion

A computational framework for interface-resolved direct numerical simulations (DNS) of simultaneous atomization, evaporation and combustion process is proposed. The present work utilizes a level set method to implicitly capture the gas–liquid interface and the ghost fluid method (GFM) to accurately address jump conditions across the interface. Specific care has been devoted to the discretization of the convective term and diffusive term for the species and energy equations. The level set method with a sub-cell resolution of the interface is employed and a semi-Lagrangian scheme for the discretization of the level set equation with an evaporation source term is proposed. The one-step global reaction model of n-heptane is used for the vapor combustion. To the best of our knowledge, this is the first computational framework that has the capability to simulate spray combustion with an interface-resolved method. The present framework has been validated in several cases, including the one-dimensional evaporation and the static droplet evaporation for low ambient temperature, the Stefan problem, the Sucking problem, the evaporation of static and moving droplet for high ambient temperature, and the combustion of static and moving droplet. Finally, the integrated simulation of droplet collision and combustion is performed to evaluate the accuracy and robustness of the present method.

Lagrangian conditional moment closure model with flame group interaction for lifted turbulent spray jet flames

A new Lagrangian conditional moment closure (CMC) model is developed for multiple Lagrangian groups of sequentially evaporating fuel in turbulent spray combustion. Flame group interaction is taken into account as premixed combustion by the eddy breakup (EBU) model in terms of the probability of finding flame groups in the burned and the unburned state. Evaporation source terms are included in the two phase conditional transport equations, although they turn out to have negligible influence on the mean temperature field during combustion. The Lagrangian CMC model is implemented in OpenFOAM [1] and validated for test cases in the Engine Combustion Network (ECN) [2,3]. Similar ignition delays and lift-off lengths are predicted by the incompletely stirred reactor (ISR) and the Eulerian CMC models due to relatively uniform conditional flame structure in the domain. The improved Lagrangian CMC model shows no abrupt reaction or oscillatory behaviour with an appropriate model constant K and gives results in better agreement with measurements lying between the predictions by ISR and Lagrangian CMC without flame group interaction.

On the generalisation of the mixture fraction to a monotonic mixing-describing variable for the flamelet formulation of spray flames

Spray flames are complex combustion configurations that require the consideration of competing processes between evaporation, mixing and chemical reactions. The classical mixture-fraction formulation, commonly employed for the representation of gaseous diffusion flames, cannot be used for spray flames owing to its non-monotonicity. This is a consequence of the presence of an evaporation source term in the corresponding conservation equation. By addressing this issue, a new mixing-describing variable, called the effective composition variable η, is introduced to enable the general analysis of spray-flame structures in composition space. This quantity combines the gaseous mixture fraction Zg and the liquid-to-gas mass ratio Zl, and is defined as . This new expression reduces to the classical mixture-fraction definition for gaseous systems, thereby ensuring consistency. The versatility of this new expression is demonstrated in application to the analysis of counterflow spray flames. Following this analysis, this effective composition variable is employed for the derivation of a spray-flamelet formulation. The consistent representation in both effective composition space and physical space is guaranteed by construction and the feasibility of solving the resulting spray-flamelet equations in this newly defined composition space is demonstrated numerically. A model for the scalar dissipation rate is proposed to close the derived spray-flamelet equations. The laminar one-dimensional counterflow spray-flamelet equations are numerically solved in η-space and compared to the physical-space solutions. It is shown that the hysteresis and bifurcation characterising the flame structure response to variations of droplet diameter and strain rate are correctly reproduced by the proposed composition-space formulation.

분무 증발을 이용한 칩 냉각 향상에 대한 수치적 연구

The heat transfer enhancement of heat sink with mist flow is studied numerically by solving the conservation equations for mass, momentum and energy in the continuous and dispersed phases. A Lagrangian method is used for tracing dispersed water droplets in the heat sink and an Eulerian species transport model for air and steam mixture. The continuous and dispersed phases are interacted with the drag and evaporation source terms. The computed results show that addition of evaporating mist droplets enhances the cooling performance of heat sink significantly.

Large eddy simulation of dilute reacting sprays: Droplet evaporation and scalar mixing

Large eddy simulation (LES) of turbulent reacting sprays is performed to investigate the interactions of droplet evaporation and subfilter scalar mixing processes. A stochastic method is proposed to generate the subfilter fluctuations in gas-phase reactive scalars in the framework of a mixture-fraction-based combustion model. The subfilter fluctuations of the gas-phase temperature and composition, seen by droplets, are used to refine the estimates of the interphase heat/mass transfer rates. Gas-phase combustion is described by the flamelet progress variable approach. The effects of droplet evaporation on subfilter scalar mixing are considered by solving the transport equation for the subfilter mixture fraction variance. The mixture fraction that is valid instantaneously in both the gas and the liquid phases is adopted and its implication on the modeling of the evaporation source term in the subfilter variance equation is discussed. The modeling approach has been applied to the Sydney dilute reacting sprays. To account for uncertainty in the modeling of scalar dissipation rates in spray flames, a parametric study is performed for the constant in the scalar dissipation model for the subfilter variance equation. The effects of subfilter fluctuations on droplet evaporation are found to depend on the inflow condition of the pre-evaporated gas-phase mixture and the liquid injection rate in the present dilute reacting sprays.

New spray flamelet equations considering evaporation effects in the mixture fraction space

New flamelet equations for spray combustion considering evaporation effects are derived in the mixture fraction space based on the instantaneous Eulerian transport equations for gas phase and Lagrangian descriptions for droplets. The novelty of these equations lies in some source terms related to evaporation which were neglected in previous studies. The influences of spray evaporation on flamelet structures are demonstrated by solving the steady spray flamelet equations. It is found that the evaporation source term may shift or even create new reaction zones, increase the chemical reaction rate, and change the profiles of scalars in the mixture fraction space. These comprehensive effects should be included in future spray combustion modeling.

Lagrangian conditional statistics of turbulent n-heptane spray combustion in different injection conditions

3D DNS is performed for n-heptane sprays that go through ignition and combustion in different injection conditions. Conditional statistics are obtained for multiple Lagrangian groups of sequentially evaporating fuel in the group and the collective combustion regime. Ignition occurs close to but leaner than the most reactive mixture fraction for fuel of the longest residence time and low scalar dissipation rates. Combustion propagates with strong interaction among neighboring groups after ignition of the preceding flame group in the given conditions. Multiple flame groups are required for accurate description of combustion of a spray over long injection duration or multiply injected sprays. Reasonable agreement is shown between DNS and model predictions of conditional evaporation and scalar dissipation rates in the range of meaningful probabilities. Budgets are checked for all component terms in the balance equation of conditional sensible enthalpy with evaporation source terms.

LES-CMC of a dilute acetone spray flame

A combined Large-Eddy-Simulation (LES) – Conditional Moment Closure (CMC) method has been applied to model spray combustion. Additional source terms in the CMC transport equation that originate from the evaporation of the fuel have been modelled and their influence on flame structure and global quantities such as temporally averaged temperature profiles has been analysed. The predictions of a laboratory spray jet flame are generally good, the temperature profiles are in good agreement with measurements, and predictions of droplet velocities are satisfactory. The evaporation source term leads to a flux in mixture fraction space and peak temperatures are shifted towards higher mixture fraction regions. The results, however, also highlight some limitations associated with mixture fraction as a single conditioning variable for mixture fraction based approaches if applied to liquid fuel combustion.

A MODIFIED KUBOTA CAVITATION MODEL FOR COMPUTATIONS OF CRYOGENIC CAVITATING FLOWS

In order to predict the cavitating flow characteristics in cryogenic fluids more exactly, a revised cavitation model considering the thermal effect with modified the evaporation and condensation source terms is established, which is based on Kubota cavitation model. The computations for cavitating flows in liquid nitrogen are conducted around an axisymmetric ogive by employing Kubota cavitation model and the revised cavitation model, respectively. The computational results are compared with the experimental data to evaluate the revised cavitation model. It is found that for the results of the revised cavitation model due to considering the thermal effects, the evaporation becomes smaller and the condensation becomes larger, the cavity length is shorter and the cavity interface becomes more porous compared with the results of original Kubota model. The results of the revised cavitation model are more accordant with the experimental data, and it dictates that the revised cavitation model can describe the process of mass transport more accurately in the cavitation process in cryogenic fluids and it is applicable for computations of cavitating flows in cryogenic fluids flow.

Numerical analysis of the influence of two-phase flow mass and heat transfer on n-heptane autoignition

This paper investigates the influence of liquid fuel presence on the autoignition of n-heptane/air mixtures over a wide range of conditions encountered in internal combustion engines. To this end, evaporating droplet physics and skeletal chemistry mechanisms are simultaneously solved considering a homogeneous constant-pressure reactor. A skeletal mechanism is introduced to account for specific kinetics behavior in the Negative Temperature Coefficient (NTC) region. The impact of mass and heat source terms during evaporation is emphasized by comparing a two-phase flow scenario with a purely gaseous case. The competition between fuel vapor availability and the evaporation-induced gas temperature decrease is specific to two-phase flow autoignition. On the one hand, droplet evaporation delay restricts the gaseous local fuel/air equivalence ratio and consequently the kinetics runaway. On the other hand, temperature reduction due to evaporation may either reduce or enhance chemical reactivity, depending on the local thermodynamic conditions lying either inside or outside the NTC region. By simultaneously accounting for evaporation source terms and skeletal chemistry, we can reproduce the already experimentally observed transformation of the NTC region into a Zero Temperature Coefficient (ZTC) region depending on thermodynamic conditions and droplet size. The ZTC phenomenon appears when combustion heat-release starts before complete droplet evaporation. Since the ZTC behavior can be captured using the point source approach, in which droplets are considered only as zero-dimensional source terms of mass and energy, the present results pave the way for future exploration of NTC chemistry in sprays with a direct numerical simulation of discrete particles considering detailed chemistry and turbulent flows.

Combustion Simulation of a Diesel Engine in the pHCCI Mode with Split Injections by the Spatially Integrated CMC Model

Simulation is performed for a diesel engine in the partial homogeneous charge compression ignition (pHCCI) mode with split injections. The spatially integrated CMC model involves an additional heat loss term for the conditional enthalpy and the evaporation source terms for the mean mixture fraction variance. Two flame structures are defined to consider different evaporation and flame histories of the two split injection fuel groups. An independent transport equation is solved for each fuel vapor group with no mutual interaction between flame structures. The local mean mixture fraction and its variance determine the probability density functions (PDF) and the scalar dissipation rates (SDR). Calculated pressure traces show reasonable agreement with measurements for different loads and ratios between the two split injections. The overpredicted rate of pressure rise at ignition is attributed to simultaneous burning of all combustible premixture in the CMC model. The flammable limits are applied to consider extinction of lean mixture, wall film, or other possible factors for incomplete combustion of the pilot injection fuel, which burns completely after mixing with the second main injection fuel. Further research may be required for improved spray atomization and wall film models, which play a significant role in heat release and emissions of pHCCI engines.

Surrogate model‐based strategy for cryogenic cavitation model validation and sensitivity evaluation

AbstractThe study of cavitation dynamics in cryogenic environment has critical implications for the performance and safety of liquid rocket engines, but there is no established method to estimate cavitation‐induced loads. To help develop such a computational capability, we employ a multiple‐surrogate model‐based approach to aid in the model validation and calibration process of a transport‐based, homogeneous cryogenic cavitation model. We assess the role of empirical parameters in the cavitation model and uncertainties in material properties via global sensitivity analysis coupled with multiple surrogates including polynomial response surface, radial basis neural network, kriging, and a predicted residual sum of squares‐based weighted average surrogate model. The global sensitivity analysis results indicate that the performance of cavitation model is more sensitive to the changes in model parameters than to uncertainties in material properties. Although the impact of uncertainty in temperature‐dependent vapor pressure on the predictions seems significant, uncertainty in latent heat influences only temperature field. The influence of wall heat transfer on pressure load is insignificant. We find that slower onset of vapor condensation leads to deviation of the predictions from the experiments. The recalibrated model parameters rectify the importance of evaporation source terms, resulting in significant improvements in pressure predictions. The model parameters need to be adjusted for different fluids, but for a given fluid, they help capture the essential fluid physics with different geometry and operating conditions. Copyright © 2008 John Wiley & Sons, Ltd.