Development of Thermophysical and Transport ... - ACS Publications

Jul 13, 2012 - Department of Mechanical, Materials and Manufacturing Engineering, The University of Nottingham Malaysia Campus, Jalan Broga,...
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Development of Thermophysical and Transport Properties for the CFD Simulations of In-Cylinder Biodiesel Spray Combustion Harun Mohamed Ismail,† Hoon Kiat Ng,*,† Xinwei Cheng,† Suyin Gan,‡ Tommaso Lucchini,§ and Gianluca D’Errico§ †

Department of Mechanical, Materials and Manufacturing Engineering, The University of Nottingham Malaysia Campus, Jalan Broga, 43500 Semenyih, Selangor Darul Ehsan, Malaysia ‡ Department of Chemical and Environmental Engineering, The University of Nottingham Malaysia Campus, Jalan Broga, 43500 Semenyih, Selangor Darul Ehsan, Malaysia § Department of Energy, Politecnico Di Milano, Via Lambruschini 4, 20156 Milano, Italy ABSTRACT: This paper reports the development, validation, and application of the thermophysical and transport properties of coconut, palm, and soy methyl esters for fuel spray and combustion modeling under light-duty diesel engine conditions. The developed fuel library is implemented in an open-source CFD code. The fuel properties are validated for both constant volume combustion chamber and compression ignition (CI) engine operation at a wide range of conditions. Sensitivity analysis on the effects of individual fuel properties is also investigated under both conditions. The properties of interest for the study are density, vapor pressure, heat of vaporization, liquid heat capacity, vapor heat capacity, second-virial coefficient, liquid dynamic viscosity, vapor dynamic viscosity, liquid thermal conductivity, vapor thermal conductivity, surface tension, and vapor diffusivity. From these twelve physical and transport properties, only five have significant effects on fuel spray structure, combustion, and emission characteristics. These are vapor pressure, vapor diffusivity, surface tension, liquid density, and liquid dynamic viscosity. However, only vapor pressure and surface tension have the strongest influence on the mixture preparation process.

1. INTRODUCTION Increasingly stringent emissions legislations and depletion of petroleum reserves call for more efficient combustion systems as well as clean-burning fuels for ground transportation purposes. In recent years, biodiesel has generated immense interest within the automotive community as a viable substitute for fossil diesel.1 This is largely due to its physicochemical characteristics which closely resemble that of fossil diesel,2 permitting biodiesel to be used with minimal or no modifications on existing diesel engines. In addition, neat biodiesel and biodiesel blends are known to reduce particulate matter (PM), hydrocarbons (HC), and carbon monoxide (CO) emissions.3 Separately, some studies have indicated that an increase in nitrogen oxides (NOx) is observed3,4 when biodiesel fuels are tested on unmodified engines as compared to diesel fuel. There are also contrasting reports which have shown that biodiesel such as coconut methyl ester reduces exhaust-out NO x 5,6 emissions. Thus, there is a need for more comprehensive research work to conclusively determine the benefits and drawbacks of biodiesel.7,8 One such effort is the utilization of computational fluid dynamics (CFD) techniques to better understand and improve biodiesel fuel spray, combustion, and emission characteristics in compression ignition (CI) engines. For accurate in-cylinder CFD simulations of the biodiesel spray combustion process, three key elements must be captured. These are the in-cylinder air motion, the fuel spray and vapor structures, and finally, the fuel chemistry. The characteristics of fuel spray and vapor structures are deemed especially important, as they dictate the fuel vaporization rate, which in turn affects the ignition, combustion, and pollutant © 2012 American Chemical Society

formation processes. Fuel spray and vapor structures are predominantly governed by the thermophysical and transport properties of the fuel. Therefore, it is imperative to understand the influence of these properties of different biodiesel fuels as compared to fossil diesel. However, only very limited studies have been conducted to date to develop and establish the impact of thermophysical and transport properties of biodiesel fuels as reported in the literature.7−9 In particular, individual and collective effects of biodiesel fuel properties on combustion and emission behaviors are not well-defined. Additionally, there are limitations in the currently available thermophysical and transport properties of biodiesel fuels. Most of these properties were developed based on the mixture composition of soy7−9 or based on an “adapted” or approximated single-component molecule, for example methyl oleate (C 19H 36O 2) that represents rapeseed methyl ester.10 Fuel spray and combustion modeling using the approximated generic biodiesel fuel properties inherently result in a certain level of inaccuracy in the predictions. This is because different fuels have different levels of heavy, light, saturated, and unsaturated molecular compositions, which significantly affect the fuel properties and hence the spray structure. This was highlighted by Zhang et al.11 for multicomponent diesel fuel, in which preferential evaporation of the lighter components increases the amount of light-end components upstream of the spray plume while the heavy-end components are predominantly found within the region near the tip of the spray. Received: May 19, 2012 Revised: July 13, 2012 Published: July 13, 2012 4857

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Table 1. FAME Mixture Compositions and Critical Properties parameter

CME

PME

SME

Tb (K)

critical temperature (K)

critical pressure (bar)

critical volume (mL/mol)

lauric myristic palmitic stearic oleic linoleic linolenic critical temperature (K) critical pressure (bar) critical volume (mL/mol) normal boiling temperature (K)

0.53 0.2 0.12 0.065 0.085 − − 721.2 15.3 885.0 629.15

− 0.011 0.41 0.042 0.429 0.108 − 773.5 14.0 1064.0 609.15

− − 0.08 0.04 0.25 0.55 0.08 789.2 13.0 1084.4 619.15

535.15 568.15 611.15 625.15 622.15 639.15 639.15

695.33 724.11 767.05 775.59 774.40 798.46 801.68

14.21 14.21 14.21 14.21 14.08 13.95 13.83

789.5 901.5 1013.5 1125.5 1105.5 1085.5 1065.5

saturation of FAME. Table 1 illustrates the different compositions of saturated and unsaturated FAME in CME, PME, and SME, respectively. The biodiesel properties are computed by first calculating the thermophysical and transport properties of each FAME constituent as given in Table 1, and second by applying mixing rules to determine the properties of each biodiesel. Table 2 lists

In line with the discussion above, the reported work here is based on coconut methyl ester (CME), palm methyl ester (PME), and soybean methyl ester (SME) to represent biodiesel fuels with low, moderate, and high degree of unsaturation, respectively. To the authors’ best knowledge, there is a lack of comprehensively validated fuel properties of neat CME, PME, and SME available in the public domain for simulation studies. There are also very limited studies in archival literature which quantify the comparison of the physical properties effects for CME, PME, SME, and diesel. For these reasons, the fuel properties of CME, PME, and SME are first developed and validated against experimental data of a constant volume combustion chamber and a wide range of conditions for a CI engine. Then, a set of numerical experiments are performed to investigate the sensitivity of individual and collective fuel properties under both the constant volume and CI engine conditions. In-depth analyses are conducted to study the behavior of each fuel by isolating the chemistry effects in the simulations. Quantifiable comparisons are made on the behavior of different fuels under identical conditions which are independent of the chemical effects and only influenced by the differences in the thermophysical and transport properties.

Table 2. Proposed Estimation Methods for Thermophysical and Transport Properties of Biodiesels thermophysical and transport properties

2. DEVELOPMENT OF BIODIESEL PROPERTIES Fuel spray and vapor structures are typically influenced by 12 thermophysical and transport properties. The properties generally depend on the molecular groups present in the fuel, for example, petroleum diesel consists of hundreds of molecules including n-heptane, n-decane, and isooctane. However, developing accurate thermophysical and transport properties of various real fuels is challenging because fuel consists of an intricate mixture of long hydrocarbons molecules with hundreds of constituents. One way of alleviating this problem is by using the appropriate surrogate fuel species. In this approach, the fuel is assumed to be made of not hundreds but rather a few important groups, each with their own unique molecular structure. A similar approach is utilized in this study, whereby the thermophysical and transport properties of CME, PME, and SME are determined based on their chemical compositions and structures over a wide temperature range. One of the main challenges in determining biodiesel properties is that the properties vary according to the origin feedstock and are highly influenced by the molecular structures of the constituent organic compounds. Biodiesels from different feedstock typically have different fatty acid methyl ester (FAME) compositions. Each feedstock has a unique composition of carbon single and double bonds, which is linked to the level of

1 2 3 4 5

critical properties liquid density vapor pressure surface tension liquid viscosity

6 7 8 9 10 11 12 13

latent heat of vaporization liquid thermal conductivity liquid heat capacity vapor heat capacity vapor viscosity vapor thermal conductivity vapor diffusivity second-virial coefficient

computation method Lydersen method9,14 Rackett equation14 Antoine equation12 equation proposed by Allen et al.15 Orrick and Erbar method, Nissan and Grunberg method9,14 Pitzer accentric correlation14 Robbins and Kingrea method14 Van Bommel correlation16 Rihani and Doraiswamy method14 correlation from Chung et al.17 correlation from Chung et al.17 Wilke-Lee correlation14 Tsonopolous method14

the thermophysical and transport properties developed in this study and the methods utilized. Here, all the correlations that are utilized to calculate the properties are valid for the range of interest, which is between 280 and 780 K unless otherwise specified. To determine the critical properties, the normal boiling points of CME, PME, and SME are first derived using a modified correlation of normal boiling point based on the number of carbons by Yuan et al.12 Here, the required normal boiling point for each FAME constituent is obtained from Graboski and McCormick.13 Then, the critical properties of each FAME constituent that forms CME, PME, and SME are computed from the modified Lydersen’s method9,14 as presented in Table 1. Finally, the Lee−Kesler mixing-rule14 is applied to determine the overall critical properties for each biodiesel. The critical properties of these biodiesels are important because properties beyond the critical points cease to be valid and also because they are required to predict other thermophysical and transport properties. Based on the critical properties and normal boiling points, the 12 thermophysical and transport properties are developed using the methods summarized in Table 2. Figure 1a−l shows 4858

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Figure 1. Thermophysical and transport properties of CME, PME, and SME as compared to C14H30 for (a) vapor pressure, (b) heat of vaporization, (c) liquid density, (d) surface tension, (e) liquid viscosity, (f) liquid heat capacity, (g) liquid thermal conductivity, (h) vapor heat capacity, (i) vapor viscosity, (j) vapor thermal conductivity, (k) vapor diffusivity, and (l) second-virial coefficient.

heat of vaporizations of PME and SME are generally higher than diesel surrogate throughout the temperature range of interest. On the other hand, the latent heat of vaporization of CME tends to converge toward the latent heat of vaporization of diesel surrogate as temperature increases but has a lower value than that of C14H30 at the critical temperature point. Liquid densities of CME, PME, and SME are predicted using the modified Rackett equation.14 The densities of all three biodiesels are usually higher than C14H30 up to 580 K, as shown in Figure 1c. However, C14H30 has a higher density value at higher temperatures above 580 K. Because biodiesels have higher densities, this may contribute to the variations in fuel spray injection, the break-up process, and the ignition-delay period (ID) between the fuels. Surface tensions for CME, PME, and SME are calculated using the equation proposed by Allen et al.15 In general, the surface tensions of all three biodiesels are higher than that of C14H30 at all temperatures as illustrated in Figure 1d. Again, this may cause significant differences between CME, PME, SME, and C14H30 in the spray break-up process.

the developed thermophysical and transport properties of CME, PME, and SME in comparison to that of tetradecane (C14H30), which is as a common surrogate for diesel fuel. First, vapor pressures of CME, PME, and SME are predicted using the Antoine equation12 as illustrated in Figure 1a. The vapor pressure of each FAME constituent is computed, and the Lee− Kesler mixing rule is then utilized to calculate the vapor pressure of the three fuels. From Figure 1a, biodiesel fuels have lower vapor pressure than C14H30 at a temperature range between 280 K and 580 K due to the absence of volatile components in biodiesel.13 At higher temperatures however, the vapor pressures increase significantly to maximum values at critical temperature. Generally, the computed vapor pressures of all three biodiesels are lower than that of C14H30. Nonetheless, CME has a similar vapor pressure range to that of C14H30 between 380 K and 580 K. These attributes may influence fuel spray evaporation process significantly. Latent heat of vaporizations at normal boiling point for CME, PME, and SME are estimated using the Pitzer acentric factor correlation,14 and are shown in Figure 1b. The latent 4859

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C14H30, while the vapor thermal conductivities of biodiesels are lower than that of C14H30. Vapor diffusivity is predicted using the Wilke−Lee relation.14 The differences in vapor diffusivities among the three biodiesel fuels are not as significant as between all the biodiesels and the C14H30. From Figure 1k, the three biodiesels generally have vapor diffusivities lower than that of C14H30. The second-virial coefficient is the coefficient that is used in the gas expansion equation. The second-virial coefficients for the FAME constituents are computed using the Tsonopoulos method.14 The simple mixing-rule is then utilized to determine the overall second-virial coefficients of CME, PME, and SME, as illustrated in Figure 1l.

Liquid viscosity is determined using two different approaches depending on the reduced temperature, Tr. Here, Tr is defined as the ratio of fuel temperature to critical temperature, Tc (T/ Tc). At low reduced temperatures when Tr < 0.7, the liquid viscosity of each FAME constituent is determined using the Orrick and Erbar method.9,14 Meanwhile, the Letsou and Stiel method is applied to compute liquid viscosity for Tr > 0.7.14 Finally, the Grunberg and Nissan method9,14 is used to determine the liquid viscosities of the FAME mixtures that constitute CME, PME, and SME, respectively. From the calculated results, all the biodiesels have higher viscosities than C14H30 at lower temperatures. Figure 1e shows that there is a large difference in liquid viscosity within the temperature range from 280 K to 380 K. Fuel is typically injected at temperatures between 300 K and 320 K, and therefore significant differences in fuel flow within the injector are expected between biodiesels and C14H30 at this lower temperature range. Also, substantial differences in the droplet break-up process and wall-film characteristics between the two fuels are predicted. All the biodiesel fuels are observed to have reduced viscosities at higher temperatures, which tend to converge closely to that of C14H30. Liquid heat capacities of the three biodiesel fuels are calculated based on a function of number of carbon atoms and temperature.16 The liquid heat capacity of each FAME constituent is computed, and the mixing-rule is then applied to determine the liquid heat capacity for each biodiesel, as depicted in Figure 1f. A higher heat capacity indicates that the fuel takes a longer time to be heated and vice versa. From Figure 1f, the difference in liquid heat capacity between diesel surrogate and biodiesel fuels increases as temperature increases. Biodiesel fuels typically have lower heat capacities, and thus the rate of temperature rise of the fuel droplets is higher as compared to C14H30 fuel droplets for the same amount of heat input. Vaporization rate of biodiesel is therefore enhanced. Liquid thermal conductivity is predicted using the Robbins and Kingrea method14 for each FAME constituents of all the fuels. Next, the volume fraction of each FAME constituent for biodiesels is calculated using the Li equation.14 The values obtained are then used to compute the overall liquid thermal conductivities of CME, PME, and SME, as given in Figure 1g. In CFD spray simulations, liquid thermal conductivity is used to determine the heat transfer between the drop’s interior and its surface where a transient temperature distribution is assumed.8 All three biodiesels have liquid thermal conductivities lower than that of C14H30. Hence, heat transfer within each droplet of biodiesel is expected to be lower than that in C14H30 fuel droplets. Vapor heat capacities for the fuels are estimated by using the Rihani and Doraiswamy method,14 as can be seen in Figure 1h. Vapor heat capacity influences the heat transfer from the surrounding gas to the drop surface.8 The correlation utilized to compute the vapor heat capacities is valid for the range of interest between 280 and 1080 K. From the computed results, CME has lower vapor heat capacity throughout the temperature range as compared to C14H30. In contrast, PME and SME have similar vapor heat capacity values as C14H30. Vapor viscosity and vapor thermal conductivity for the three biodiesels are calculated using the Chapman−Enskog kinetic theory17 and are highlighted in Figure 1i and Figure 1j, respectively. This correlation is suitable for dilute and low pressure gases. Here, the biodiesels are assumed as dilute low pressure gases because dense gases are known to be polar gases. The vapor viscosities of biodiesels are higher than that of

3. NUMERICAL VALIDATIONS AND APPLICATION OF THE DEVELOPED FUEL PROPERTIES Validations of the developed thermophysical and transport properties of the biodiesel fuels are conducted at two levels. First, the validation is performed using three-dimensional (3D) CFD simulations on Chalmers high-pressure/high-temperature (HP/HT) constant volume experimental setup. This is carried out to prove the validity of the fuel properties in terms of fundamental spray attributes such as spray penetration length, vapor penetration length, and vapor distribution. The second validation is accomplished by 3D CFD simulations of a lightduty CI engine fueled with pure CME, PME, and SME biodiesels and their blends. Here, the properties are validated based on comparison between the experimental and simulated combustion and emission profiles. In the validation process, the diesel fuel properties are taken to be that of C14H30 whereas for the neat biodiesels, the developed properties of CME, PME, and SME are utilized. For the B50 blends of biodiesel fuels, neat biodiesel properties are “mixed” with C14H30 fuel properties using the multicomponent modeling approach at 50 vol % biodiesel to diesel blending ratio. To gain fundamental understandings of the effects of thermophysical and transport properties that are independent of fuel chemistry, sensitivity analyses on the individual properties are performed under constant volume and engine simulations. Here, 12 fuel properties are tested: density, vapor pressure, heat of vaporization, liquid heat capacity, ideal gas heat capacity, second-virial coefficient, dynamic viscosity, vapor dynamic viscosity, thermal conductivity, vapor thermal conductivity, surface tension, and vapor diffusivity. For this purpose, neat PME is chosen here as the base fuel. Sensitivity analysis for each property is performed by substituting one property of the base fuel to that of diesel surrogate (C14H30) while all the other properties are retained to that of the base fuel. This is an approach similar to that reported by Ra et al.8 An important point to note here is that when any one property associated with the Clausius−Clapeyron equation is changed, adjustment needs to be made to the other coupled properties as well, such that the equality of the equation is not violated.8 The list of adjusted properties is given in Table 3. For the combustion chemistry, the BOS-V2 mechanism containing 113 species and 399 reactions with integrated NOx reaction kinetics as proposed by Harun et al.18 is utilized to represent the CME, PME, and SME fuel chemistry for the validation exercise. Here, the different fuels are simulated by varying the mass composition ratio of saturated and unsaturated components with respect to the individual fuel type18 for all the simulations. However, the mass ratio of saturated to unsaturated component for the fuels is maintained 4860

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and can be found in the literature.19 The second-stage simulations are carried out for a quiescent, bowl-in-piston light-duty diesel engine, with a compression ratio of 19.1:1 and a displacement volume of 347 cm3. Four equally spaced injector holes deliver the required fuel. The engine operates at speeds between 1500 to 3500 rev/min and loads between 0.5 to 2.5 kW. The engine is air cooled, and the bore and stroke dimensions are given as 80 mm and 69 mm, respectively. Table 4 summarizes the specification of the research engine used here. The experimental tests and measurements of the engine are reported elsewhere.5,6 3.2. Computational Mesh and Initial Conditions. Chalmers Constant Volume HP/HT Chamber. A full 3D mesh of the constant volume combustion chamber is generated with a constant cell size of 4 mm, as shown in Figure 2a.

Table 3. Adjusted Properties for Sensitivity Analysis under the Clausius−Clapeyron Equation test property

adjusted property

liquid heat capacity vapor heat capacity heat of vaporization vapor pressure

heat of vaporization heat of vaporization liquid heat capacity liquid heat capacity and heat of vaporizationa

a

By only adjusting liquid heat capacity, numerical errors are obtained; hence, both heat of vaporization and liquid heat capacity are adjusted for this case.

at 0.5:0.5 similar to that of the base fuel in order to decouple the chemistry effect in the sensitivity analysis. As such, the effects of chemistry are eliminated and any changes observed in ID and spray structure are solely attributed to the differences in the thermophysical and transport properties. 3.1. Experimental Setup. First, simulations are conducted for the validation exercise of spray characteristics using the Chalmers HP/HT chamber.19 The HP/HT spray rig is an optically accessible unit through which pressurized, preheated air flows at 0.1 m/s. The rig is considered quiescent before fuel is injected over a period of 3.5 ms at a fuel injection pressure of 1200 bar. The in-chamber conditions are controlled at pressure and temperature of 50 bar and 830 K, respectively. Further details on the experimental setup are summarized in Table 4

Figure 2. Computational domain for the (a) Chalmers HP/HT constant volume combustion chamber (full mesh) and (b) Nottingham Research Engine (90° sector mesh).

Table 4. Experimental Conditions and CFD Test Range Nottingham Test Engine

Simulations are carried out using the adaptive local mesh refinement (ALMR) technique20,21 to allow high mesh resolution where fuel−air mixing takes place, while the overall grid size is only increased slightly. An initial computational mesh has to be provided first, where the size should be adequately fine to correctly reproduce the geometrical domain to be simulated and the main details of the initial flow field. A geometric field is chosen as an error estimator, and when its values lie in a user-specified interval, the parent cell is split into eight child cells by introducing new nodes at the cell centroid and at the mesh face centers. An arbitrary level of refinements can be chosen by the user as well as the maximum number of cells to control the mesh size. Grid unrefinement is also possible when the values of the error estimator are outside the specified interval. The geometric field used as a refinement criterion is represented by the total fuel mass fraction (liquid and gas) in each cell. The consistency and reduced grid dependency provided by the ALMR approach have been extensively illustrated in past studies.20,22 The simulated computational domain consists of a box, where the size is 40 × 40 × 100 mm and all initial conditions are maintained identical to the experimental case. In particular, the chamber air density is 0.7246 kg/m3, pressure is 50 bar, and temperature is 830 K. Nottingham Research Engine. A 90° sector mesh is generated to take advantage of the symmetry imposed by the four equally spaced injector nozzle holes installed centrally. A hexahedral mesh type is utilized to construct the engine mesh, as shown in Figure 2b. At intake valve closing (IVC) time, the initial pressure and temperature are 1.23 bar and 300 K, respectively. During the compression and expansion strokes, the dynamic mesh layering is adopted to keep an optimum mesh size for the entire simulation.22−24 Here, the mesh with a

engine type light-duty diesel piston type bowl-in-piston cylinder head type flat cylinder head displacement volume per-cylinder 347 cm3 compression ratio 19.1: 1 stroke 69 mm connecting rod length 114.5 mm intake valve closing (IVC) −140° ATDC exhaust valve opening (EVO) 140° ATDC engine speed 1500−3500 rev/min Chalmers HP/HT Constant Volume Chamber domain constant volume volume 2L chamber pressure 50 bar chamber temperature 830 K injector vertically aligned, single hole nozzle diameter 0.14 mm injection pressure 1200 bar injection durations 3.5 ms injection temperature 313.15 K fuel types palm (B100), diesel (B0) Validation Conditions for Nottingham Test Engine load (kW)

speed (rev/min)

fuel (B100)

fuel (B50)

0.5 0.5 0.5 1.5 1.5 1.5 2.5 2.5 2.5

2000 2000 2000 2000 2000 2000 2000 2000 2000

CME PME SME CME PME SME CME PME SME

CME PME SME CME PME SME CME PME SME 4861

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Figure 3. Variation of CME, PME, SME, and C14H30 in (a) liquid axial penetration length, and (b) evaporation rate and evaporated mass at EOI.

cell size of 2 × 2.5 mm is utilized throughout the simulation process because further mesh refinement increases the computing time but does not produce significant increase in the level of accuracy.18 Computation is performed over the closed part of the engine cycle only. 3.3. Computational Model Formulations. Simulations are carried out using the Lib-ICE code, which is a set of libraries and solvers developed under the OpenFOAM technology for internal combustion (IC) engines.22 Governing equations of mass, momentum, and energy for the gas phase are discretized and solved by means of the finite volume method in an Eulerian way, while the Lagrangian approach is adopted to model the evolution of the fuel spray. For combustion process, each computational cell is assumed to be a homogeneous system and a detailed chemical mechanism is used to estimate by the autoignition and the mixing-controlled combustion phases. The chemical reaction rates are calculated by an ordinary differential equation (ODE) stiff solver using an operator-splitting technique. For each time-step Δt, the ODE solver maps the initial composition ψ0 = ψ(t0) to the reacted value ψ(t0 + Δt) which is a unique function of ψ0 called the reaction mapping, R(ψ0). The composition array is defined by ψ{Yi,..., YNs, p, T}, where Yi is the species mass fraction, Ns the number of species, T the temperature, and p is the pressure. However, directintegration of detailed chemistry is computationally demanding. For this reason, the proposed combustion model works in combination with the TDAC algorithm.24−26 Such approach combines mechanism reduction and tabulation techniques that are both performed on-the-fly in each cell during the simulation. Significant speed-up factors compared to directintegration are ensured (>300), allowing detailed chemical mechanisms to be used for simulations of practical devices such as the IC engines. The in-cylinder flows and turbulence effects are computed using the Reynolds-averaged Navier−Stokes approach with RNG k−ε turbulence model, whose choice is motivated by its capability to correctly account for swirling effects.18,27 The heat transfer from the in-cylinder gases to the chamber walls is modeled by the Han−Reitz approach, where the temperature wall function is formulated to account for the in-cylinder variable-density turbulent flow conditions.28 To predict incylinder NO evolution, the extended-Zeldovich mechanism is integrated into the reduced combustion kinetics of BOS-V2. Here, the NO formation mechanism also includes the NO formation via N2O pathways. Finally, a phenomenological model is used to predict soot emissions. In particular, the

Hiroyasu approach is used to describe the formation of soot, while the oxidation process is estimated through the Nagle− Strickland and Constable model. To obtain comparable soot data set, both the experimental and simulated data set are normalized using eq 1, Here, Xi is the normalized soot data, Zi is the input or output variable and λ1, λ2 are the ranges of the function.29 The data is normalized between the range of 0 and 1 such that the experimental and computed data are within the same scale. ⎛ Z − Z min ⎞ i i ⎟ Xi = λ1 + (λ 2 − λ1)⎜ max min ⎝ Zi − Zi ⎠

(1)

For spray modeling, the Huh−Gosman model is used to describe the injection and atomization processes.22,30 In particular, the turbulence conditions for the liquid fuel jet are computed at the injector exit. With these quantities, the initial cone-angle is estimated. Droplets are injected with the same nozzle diameter, their diameter is reduced, and new small droplets are stripped from them due to the atomization process. The model consists of several constants that can be adjusted to match experimental data of spray penetration at evaporating conditions for the tested fuels. For this study, the model constants C4 and C5 are adjusted to 3 and 2, respectively, such that agreement with the current experimental conditions is achieved. Here, the model constant C4 is used to compute the atomization time scale and C5 is utilized to compute the decrease in parent droplet diameter with respect to time. Secondary break-up is modeled, accounting for both Kelvin− Helmoltz and Rayleigh−Taylor instabilities. Further details about spray model implementations and validations can be found in the literature.18,22−24,31

4. RESULTS AND DISCUSSION 4.1. Validation and Analysis of Fuel Properties under Constant Volume Conditions. To understand the fuel spray behavior that is independent of the combustion process, noncombusting constant volume simulation tests are conducted first. Through these tests, the behavior of different fuels in terms of spray structure is captured solely with respect to the heat transfer from the surrounding air to the fuel droplets. From the simulations, it is found that PME has the highest liquid axial penetration length followed by SME, CME, and C14H30 as shown in Figure 3a. On the other hand, Figure 3b shows that C14H30 has the highest vaporization rate followed by CME, SME, and PME. The primary reason for the observed 4862

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trends is that biodiesels generally have larger droplets (indicated by greater values of Sauter mean diameter (SMD), d32) as compared to C14H30 as depicted in Figure 4. To

Figure 5. Experimental/computed vapor and liquid axial penetration lengths for the reacting spray jet of PME.

Figure 4. Sauter mean diameters of liquid fuel droplets for CME, PME, SME, and C14H30.

demonstrate the difference in SMD values between the fuels, a set of correlations between the SMD values of CME, PME, and SME to that of C14H30 surrogate is derived. At any SMD value of C14H30 (x), the SMD values of CME, PME, and SME are given by eqs 2, 3, and 4, respectively. On the basis of this correlation, CME, PME, and SME have larger SMD values as compared to C14H30. Hence, biodiesel fuels have lower surfaceto-volume ratio as compared to C14H30, which results in the observed lower vaporization rate. CME, d32 = 0.9674x + 1.6629

(2)

PME, d32 = 1.0188x + 1.6677

(3)

SME, d32 = 1.0738x + 0.9193

(4)

Figure 6. Experimental/computed liquid axial penetration length for the reacting spray jets of CME, PME, SME, and C14H30.

properties of the test fuels because the chemistry effects have been decoupled. The CME and SME fuel properties are validated qualitatively because only the PME and diesel experimental data are available. In terms of fuel vaporization rate, trends similar to that of the noncombusting spray are observed. The vaporization rates of all the test fuels are enhanced from the ignited gas mixtures. For combusting sprays, the vaporization rate generally follows the order of C14H30 > CME > SME > PME as shown in Figure 7. Nevertheless, the differences in evaporated fuel mass at the end-of-injection (EOI) between the tested fuels are negligible. In summary, it is found that the differences in fuel properties have profound effects during the early stage of fuel injection up to the start of the combustion (SOC) point. At the later stage of the fuel injection period, spray structure and vaporization is predominantly affected by the burning rate and in-chamber temperature. 4.2. Sensitivity Analysis of Fuel Properties under Constant Volume Conditions. As highlighted in section 3, the sensitivity analysis of each property is performed by substituting one property of the base fuel (PME) to that of diesel surrogate (C14H30) while all the other properties are maintained to that of the base fuel (PME). The results of this sensitivity analysis under constant volume conditions are

Because biodiesel fuel droplets have larger diameters, the droplets have greater momentum to travel further into the combustion chamber which contributes to the longer liquid penetration length. This observation may have significant effect on the ID period, magnitude of peak premixed controlled combustion (PMC), and early NOx formation under normal CI engine conditions. Here, longer spray penetration length may lead to better air utilization and mixing due to the entrainment of fresh charge into the spray jets further downstream. However, it may also lead to spray impingement on the piston wall surface. Wall impingement is not desired because it reduces fuel efficiency and increases unburned hydrocarbon (UHC) formation. Further investigation on the combusting fuel spray shows that good levels of agreement between the experimental and computed data for liquid and vapor axial penetration lengths are achieved during the earlier part of the simulation, as shown in Figure 5 for PME as an illustration. However, marginal error is observed later in the simulation due to the relatively large cell size when utilizing the ALMR approach. The CME surrogate has a similar spray structure as C14H30 surrogate, while SME is similar to that of PME as seen in Figure 6. Here, PME and SME have longer spray penetration lengths as compared to CME and C14H30. This is solely due to the difference in physical 4863

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Additionally, any changes in the individual fuel properties result in negligible effects on the spray and vapor structure after the diffusion flame has fully developed (after 2 ms). This is depicted in Figure 8a,g. The reason for this is that under a fully developed flame, the vaporization rate is predominantly governed by the burning rate and the effect of fuel properties becomes less important. From this study, vapor pressure, vapor diffusivity, surface tension, liquid density, and liquid dynamic viscosity are found to affect the spray structure. A change in vapor heat capacity was reported to have significant effects on the spray structure and combustion process elsewhere.8 However, the change in vapor heat capacity has been observed to produce negligible effects on the spray structure and combustion process under the constant volume condition here. Therefore, vapor pressure, vapor diffusivity, surface tension, liquid density, liquid dynamic viscosity, and vapor heat capacity are further tested for the sensitivity analysis under CI engine conditions to better understand the influence of these properties on fuel spray, combustion, and emission characteristics. 4.3. Validation and Analysis of Fuel Properties in a CI Engine. Eighteen engine test points are utilized to validate the proposed fuel properties for a total of six biodiesel fuel types. The test fuels are neat CME, PME, and SME and 50 vol % of CME, PME, and SME in diesel fuel. When the tested biodiesel fuel changes from CME to PME and SME, the level of unsaturation of the fuel is changed from 20% to 50% and 80%, respectively, to match the typical unsaturation levels present in the actual biodiesels. The engine speed is maintained at 2000 rev/min, and engine loads are varied from low (brake mean effective pressure (bmep) of 0.86 bar and brake power of 0.5 kW) to mid (bmep of 2.59 bar and brake power of 1.5 kW) and high (bmep of 4.32 bar and brake power of 2.5 kW), as summarized in Table 4. Figure 9a−f shows the comparison of the in-cylinder pressure trace and heat-release rate (HRR) between the experimental and simulated results for the six test fuels at three different engine loadings. Good levels of accuracy are achieved in the prediction of the pressure trace, heat-release profile, and emission characteristics for all the fuels as shown in Figure 9a−f and Figure 10a−f, respectively. The ID period and the peak pressures are predicted accurately for the entire tested loads. The maximum percentage error between the experimental and computed peak pressures is below 4.5%. As engine loading is raised, the fuel spray injection period is prolonged to accommodate the increase in the fuel mass delivered. Consequently, the combustion characteristic changes from the PMC phase to the mixing-controlled combustion (MCC) phase as shown in Figure 9a−f, whereby the diffusion flame is present for a longer period. This trend is captured accurately by the simulation in which the shift from the PMC phase to the MCC phase is clearly predicted for all the test fuels. However, a certain level of variations between the experimental and predicted data during the high temperature stage is observed. This is because the experimental HRR data are smoothened,18 which reduces the magnitude but at the same time increases the width of the experimental peak HRR. Figure 10a−f illustrates the calculated and measured exhaustout NOx and soot emissions at exhaust valve opening (EVO) time. Typically, the observed error is within the range of 10− 15% for both NOx and soot. However, maximum errors of 20% for NOx and 30% for soot are recorded. The general trend of soot for all the tests is predicted well, as can be seen in Figure

Figure 7. Evaporation rate and evaporated mass at EOI for the reacting spray jets of CME, PME, SME, and C14H30.

illustrated in Figure 8a−g, where the effects of the 12 fuel properties on the combusting fuel spray structure are demonstrated. Figure 8a indicates that none of the individual properties have any immediate effects on the vapor axial penetration length. However, Figure 8b−e shows that other spray structures are significantly affected by mainly five fuel properties. These properties are vapor pressure, surface tension, liquid density, liquid dynamic viscosity, and vapor diffusivity. Vapor pressure is found to be the most influential parameter out of the five aforementioned properties as evident in Figure 8b−d,f. From Figure 1a, the vapor pressure of C14H30 is significantly different from the base fuel (PME). This property governs the fuel mass fraction at the drop surface and consequently the evaporation until the boiling temperature (or critical temperature under supercritical ambient pressure conditions) is reached.8 It is also observed from the vapor pressure sensitivity test that the number of parcels in the system is reduced significantly, as highlighted in Figure 8f. There are typically two reasons for the reduction in the number of parcels in a control volume, which can be attributed to the higher vaporization rate and lower fuel droplet break-up rate. Here, the higher vaporization rate is the dominant factor which reduces the number of parcels in the control volume as shown in Figure 8b,d. Further sensitivity analysis shows that the change in surface tension to that of C14H30 affects droplet break-up rate more profoundly as compared to other properties. The reduction in surface tension from PME to that of C14H30 increases the droplet break-up rate which leads to smaller drop size as indicated in Figure 8e and enhances vaporization considerably as shown in Figure 8b. In addition, a change in surface tension also affects the SOC timing, whereby a relatively shorter ID and smaller temperature change are recorded as compared to the base fuel in Figure 8d. Finally, Figure 8b−e demonstrates that changes in liquid density, liquid dynamic viscosity, and vapor diffusivity have certain degrees of influence over the ID, SMD, and vaporization rate. However, this is not as significant as the impact of vapor pressure or surface tension. The other seven tested properties, namely heat of vaporization, liquid heat capacity, vapor heat capacity, second viral coefficient, vapor dynamic viscosity, liquid thermal conductivity, and vapor thermal conductivity are shown to have minimal impacts on the spray structure. 4864

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Figure 8. Constant volume sensitivity analysis of reacting spray jets by examining the effects of individual fuel properties on (a) vapor axial penetration length, (b) evaporated mass, (c) temperature, (d) rate-change in temperature, (e) Sauter mean diameter, (f) number of parcels, and (g) liquid axial penetration length.

10a−f. For engine-out NOx, the prediction accuracy is lower at low engine load. At higher engine load, NOx is predicted with a high degree of accuracy where the maximum percentage error is only 4.6% for diesel and 6.2% for neat PME at mid and high engine loads, respectively. Also, it is observed from Figure 6c that soot level is over predicted for the B50 blend of CME. The discrepancy between experimental and simulated data here is

believed to be attributed to the error in the computed burning rate and energy release during the MCC phase. Among the test fuels, B50 blend of CME produces the longest MCC phase. From the HRR plot, there are certain degrees of deviation in the predicted and experimental HRR profiles especially during the MCC phase. Because soot is known to be produced within the rich core of the reacting spray jets during the MCC phase, 4865

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Figure 9. Pressure trace and HRR for low, medium, and high load at 2000 rev/min for (a) CME (B50), (b) PME (B50), (c) SME (B50), (d) CME (B100), (e) PME (B100), and (f) SME (B100).

insignificant effect on the vaporized fuel mass at EOI. Contrary to that, the collective change in fuel properties to that of C14H30 gives the highest vaporized fuel mass at EOI (97.13%) as opposed to the base PME fuel (91.98%). Figure 12 shows the variation in peak PMC when an individual fuel property is substituted with that of C14H30. Individual fuel properties exert stronger influence on the PMC phase than on the MCC phase. Table 5 summarizes the order of variation in the peak PMC values with the individual properties. When vapor pressure value is raised to that of C14H30, the fuel is considered more volatile, as it has a greater vaporization rate. Here, the proportion of ideal fuel−air mixture required for autoignition is formed at a higher rate. This leads to a shorter ID period, thus lowering the peak HRR of the PMC phase when compared with that of the base fuel. However, changes in vapor heat capacity, liquid dynamic viscosity, and surface tension produce similar ID periods, although the values of peak PMCs are not the same. Among the three cases, highest and lowest peak PMC are produced when sensitivity tests are conducted for liquid dynamic viscosity and surface tension, respectively, as shown in Table 5. This can be explained using the vaporization curve up to SOC as seen in Figure 13. Comparing the three cases at the early stages of vaporization, surface tension has the most effect on vaporization rate, followed by liquid dynamic viscosity and then vapor heat capacity. As evaporation progresses, the trends are reversed whereby the greatest influence on vaporization rate is now given by the vapor heat capacity, followed by the liquid dynamic viscosity and then surface tension. Both surface tension and liquid viscosity are known to exert substantial influence over the droplet break-up process. A reduction in surface tension as shown in Figure 1d increases the vaporization rate due to enhanced fuel droplet break-up rate, forming smaller droplets as compared to the base fuel. However, the change in liquid dynamic viscosity has more profound impact on the droplets break-up and evaporation processes as

any error in the MCC phase prediction can lead to an error in the soot computation. 4.4. Sensitivity Analysis of Fuel Properties in a CI Engine. Sensitivity analysis of individual fuel properties under engine conditions is performed for vapor pressure, vapor diffusivity, surface tension, liquid density, liquid dynamic viscosity, and vapor heat capacity. Only 6 out of the 12 fuel properties are deemed important and hence investigated here because all the properties have been assessed previously in the constant volume chamber study. Furthermore, extensive computing time is required here as compared to the constant volume combustion simulations due to the use of a semidetailed mechanism consisting of 113 species and 399 reactions,18 a control volume cell size of 2 × 2.5 mm, and the topological changes of the dynamic mesh throughout the expansion stroke. As mentioned previously, the PME surrogate is maintained as the base fuel. Hence, comparison is made to the base fuel when each property is substituted with the property of C14H30 surrogate in this sensitivity analysis. Figures 11−15 show the results of the simulations in terms of the ID period, percentage of vaporized fuel mass at EOI, HRR profile, pressure trace, and vaporization rate up to SOC as well as levels of NO and normalized soot. Based on Figure 11a, the ID error between predicted and measured PME is only 4.17%. However, the error is amplified to 18.06% when all the fuel properties are changed to C14H30 because of the collective effect of reducing the ID period by 14.49%. In evaluating the significance of the individual properties, vapor pressure, density, and vapor diffusivity induces as much as 14.49%, 13.04%, and 13.04% errors in ID, respectively, as compared to the base PME fuel. On the other hand, vapor heat capacity, liquid dynamic viscosity, and surface tension have negligible influence on ID. Further investigation reveals that at EOI timing, changing the vapor pressure, density, surface tension, vapor diffusivity, and liquid dynamic viscosity increases the vaporized fuel mass as illustrated in Figure 11b. Here, vapor heat capacity has 4866

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Figure 10. NOx emission index and normalized soot of diesel, CME, PME, and SME fuel blends for (a) B50 blend at low load (0.5 kW), (b) B50 blend at mid load (1.5 kW), (c) B50 blend at high load (2.5 kW), (d) B100 at low load (0.5 kW), (e) B100 at mid load (1.5 kW), and (f) B100 at high load (2.5 kW).

Figure 1e, where most droplet break-up occurs in this temperature region.8 C14H30 has a higher vapor diffusivity, which enhances evaporation because higher vapor diffusivity increases vapor dispersion to the surrounding area at a greater rate. This leads to an elevated peak PMC as compared to the base fuel case, as depicted in Table 5 and Figure 12. Conversely, when the density of the base fuel is reduced to that of C14H30, the peak PMC is correspondingly lowered. As density is reduced, fuel droplets tend to have lower momentum to travel further across the combustion chamber, hence producing shorter spray penetration length. This leads to poorer air utilization which limits the combustion efficiency. The individual fuel property has significant influence on the location of peak pressure but not on the magnitude of peak pressure for all the test cases as evident in Figure 14.

Table 5. Effects of Individual Fuel Properties under Engine Conditions rank

peak PMC/ (J/θ)

1 2 3 4 5

19.00 19.96 20.85 21.42 23.89

6 7 8

24.70 26.22 26.68

parameter C14H30(diesel) surface tension vapor heat capacity vapor pressure liquid dynamic viscosity density PME (base fuel) vapor diffusivity

ID/(CAD @ 2000 rev/min, 1.5 kW) 5.9 6.8 6.8 5.9 6.8 6 6.9 6

compared to surface tension. The reason for this is because the substituted viscosity values of C14H30 are significantly lower than those of the base fuel at lower temperatures as indicated in 4867

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Figure 11. Effects of individual properties on (a) ID and ID percentage error, and (b) vaporized fuel mass at EOI.

Figure 12. Effects of individual properties on heat-release rate.

Figure 14. Effects of individual properties on pressure trace.

On the basis of these results, it is clear that the accuracy of the prediction will be highly dependent on the accuracy of the individual fuel property. This is vital especially for low load conditions where the fuel injection period is typically short and the in-cylinder combustion is mainly dominated by the PMC phase. In contrast, the HRR profile shows that none of the individual fuel properties has significant influence on the combustion characteristics during the MCC phase as shown in Figure 12. When the individual fuel properties are varied, none of the vaporization rate curve matches closely to that of C14H30 or PME. Additionally, investigation into the emission characteristics indicates that soot predictions are highly affected by changes in vapor pressure (underpredicted) and liquid dynamic viscosity (overpredicted), which is demonstrated in Figure 15.

Meanwhile, NO predictions are significantly affected by density, vapor pressure, liquid dynamic viscosity, and surface tension. Then again, the greatest difference in NO predictions is induced by the coupled effect of all the fuel properties of the C14H30 surrogate rather than the individual fuel properties. In short, the synergetic effects of all the properties are more important even though individual fuel properties affect the spray and vapor structures as well as the combustion process to a certain extent. This is especially true for high load conditions where the fuel injection period is typically long and the incylinder combustion is mainly dominated by diffusion burn. Hence, the prediction accuracy will be largely dependent on the coupled effects of all the properties. Therefore, it is imperative

Figure 13. Effects of individual properties on evaporation rate up to SOC. 4868

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Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS

This work was supported by the Ministry of Science, Technology and Innovation (MOSTI) Malaysia under the grant no. 03-02-12-SF0045. The Faculty of Engineering at the University of Nottingham Malaysia Campus is also acknowledged for its support toward this project.

■ Figure 15. Effects of individual properties on normalized soot and NO concentrations.

to accurately determine all the required fuel properties for different biodiesels. It is also important to note that simulations of various biodiesel combustion using physical and transport properties of diesel fuel are not appropriate to accurately describe the in-cylinder spray, combustion, and emissions behaviors.

5. CONCLUSIONS This paper reports the development, validation, and applications of the thermophysical and transport properties of CME, PME, and SME for fuel spray and combustion modeling in diesel engine applications. The developed fuel library is implemented in the OpenFOAM open source code. From the sensitivity analysis of 12 thermophysical and transport properties, only five properties give significant effects on the spray structure, combustion, and emission characteristics. The properties are vapor pressure, vapor diffusivity, surface tension, liquid density, and liquid dynamic viscosity. Among these, only vapor pressure and surface tension are the most influential parameters on mixture preparation, combustion, and emissions formation processes. Biodiesel fuels are found to have larger fuel droplets size, longer spray penetration, lower vaporization rate, and longer ID as compared to their diesel counterpart. This is mainly due to higher liquid viscosity, higher surface tension, and lower vapor pressure. This eventually affects the spray break-up process, vaporization rate, and hence mixture preparation, which leads to longer ID. As demonstrated, the collective thermophysical and transport properties of biodiesels are very different from fossil diesel. The collective differences in the properties have substantial effects on the fuel mixture preparation and therefore affect the combustion and emission characteristics significantly. Combustion simulations of biodiesel fuels using the thermophysical and transport properties of fossil diesel are not able to accurately describe the corresponding in-cylinder events. In conclusion, even though individual fuel properties affect the spray and vapor structures, as well as combustion process to a certain degree, the synergetic effects of all the properties is more important. Therefore, it is necessary to accurately describe all the required biodiesel fuel properties for each biodiesel fuel for in-cylinder CFD simulation of the reacting spray jet.

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NOMENCLATURE ALMR = adaptive local mesh refinement ATDC = after top-dead center CAD = crank angle degree CFD = computational fluid dynamics CO = carbon monoxide CO2 = carbon dioxide CME = coconut methyl ester CI = compression ignition EOI = end-of-injection FAME = fatty acid methyl ester HC = hydrocarbon ID = ignition delay ISAT = in situ adaptive tabulations MCC = mixing-controlled combustion phase ME = methyl ester MEDM = modified eddy-dissipation model N2 = nitrogen NO = nitrogen monoxide O2 = oxygen PM = particulate matter PMC = premixed combustion phase PME = palm methyl ester SMD (d32) = Sauter mean diameter SME = soybean methyl ester SOC = start of combustion TDAC = tabulation of dynamic-adaptive chemistry UHC = unburned hydrocarbon Xi = normalized data Zi = maximum/minimum data λ1, λ2 = normalization range REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*Tel: +603 89248161. Fax: +603 89248017. E-mail: hoonkiat. [email protected]. 4869

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