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Thermodynamic simulation of porous-medium combustion chamber under diesel engine-like conditions
Applied Thermal Engineering 153 (2019) 306–315
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Research Paper
Thermodynamic simulation of porous-medium combustion chamber under diesel engine-like conditions
T
⁎
M. Saghaei , A. Mohammadi Department of Mechanical Engineering, Shahid Rajaee Teacher Training University, Tehran 16758-136, Iran
H I GH L IG H T S
initial pressure decreases the delay and maximum temperature. • Higher gas temperature will reduce with decrease in the PM’s mean pore’s diameter. • The the porosity decreases the pressure peak and causes delay in combustion. • Decreasing • Fuels with lower reaction rate will become more efficient when used in PM engine.
A R T I C LE I N FO
A B S T R A C T
Keywords: Porous medium Homogeneous combustion Constant volume chamber Diesel
Currently, one of the most important issue of the diesel engines is the non-homogeneity of the in-cylinder fuel-air mixture. Non-homogeneous mixture causes the non-uniform heat release and high-temperature gradient in the combustion chamber that followed by the production of unburnt hydrocarbons, carbon monoxide, nitrogen oxides and soot. Homogenous combustion decreases the production of the emissions. One novel method for achieving homogenous combustion is the use of porous medium (PM) within the combustion chamber of engine so as to separate the mixture formation process from combustion process. The present article thermodynamically investigates the effect of utilizing PM in a constant-volume combustion chamber via solving the energy equations for both the solid and fluid phases considering the chemical reaction of the fuel combustion. At first, numerical result is validated according to the experimental result of diesel fuel injection in a constant-volume combustion chamber with PM. Then, effects of the initial mixture and PM temperature, the porosity of the PM, the mean pores diameter as well as the use of fuels such as decane, isooctane, methanol, ethanol, propane and hydrogen on combustion initiation, and also pressure and temperature of the combustion chamber studied.
1. Introduction The homogenous air-fuel combustion for achieving a uniform temperature and reducing of the pollutants is highly considerable for researchers. One method for creating homogeneous combustion is the use of porous medium within the combustion chamber. PM for its increasingly higher heat capacity as compared to gas possesses the ability of storing a high thermal energy. Also, it has a high surface area to volume ratio that causes an increase in the heat exchange. The high temperature of the PM inside the combustion chamber can provide the rapid evaporation of the liquid fuel and better mixture formation of the air-fuel that will eventually leads to the self-ignition of the mixture. Also, it can separate the processes of mixture formation and combustion that happen simultaneously in diesel engines. The ideal diesel combustion is usually considered as a constant-pressure process, but the ⁎
combustion occurs very fast when PM is employed inside the dieselengine combustion chamber for such a reason as the high solid-phase temperature and the exchange of the heat with the injected liquid-fuel. Combustion in presence of PM due to high reaction rate and lack of enough time for volume change can be considered approximately as constant-volume. In this case due to making use of PM, constant-volume combustion process taken into account in lieu of constant-pressure. Fig. 1 (Left) shows using of PM in combustion chamber of a diesel engine. Fig. 1 (Right) illustrates constant-volume combustion chamber that is equivalent with combustion process in a PM Diesel-engine. The idea of utilizing PM in diesel engine was proposed by Durst and Weclas [1,2]. They assembled a PM made of silicon carbide in the cylinder-head of a single-cylinder diesel engine. In the foresaid engine maximum chamber temperature was reduced from about 2200 K to 1500 K. The NOx pollutant was found decreased between 90% and 97%
Corresponding author. E-mail address: [email protected] (M. Saghaei).
https://doi.org/10.1016/j.applthermaleng.2019.03.024 Received 11 July 2018; Received in revised form 4 February 2019; Accepted 4 March 2019 Available online 05 March 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.
Applied Thermal Engineering 153 (2019) 306–315
M. Saghaei and A. Mohammadi
Nomenclature
Nuv
T t R V Q̇ h [X] cp P hv cs kg d u Re Pr
Greek symbols
Temperature Time Universal gas constant Combustion chamber volume Chamber heat transfer rate Enthalpy Concentration Constant pressure heat capacity Pressure Volumetric heat transfer coefficient Solid heat capacity Gaseous mixture thermal conductivity Mean pore’s diameter Velocity Reynolds Number Prandtl Number
ω̇ φ ε σ ρ μ λ
Nusselt Number
Production rate Porosity Emissivity coefficient of PM Stefan-Boltzman constant Density Dynamics viscosity Actual to Stoichiometry Air/Fuel Ratio
Subscripts g s FV PM
Gas phase Solid phase Free-Volume Porous-Medium
Fig. 1. Schematic presentation of constant volume PM chamber [18].
in-cylinder and PM through imposing modifications in the KIVA-3V code. Their work indicated that the PM structure is effective on the heat transfer between the gas and solid phases. Also, the valve-opening timings has to be definitely optimized so as to attain an optimal operation of the PM engine. Dhale et al. [12] performed experimental studies on the single-cylinder PM engines featuring direct diesel fuel injection. The pollutants considerably reduced and the cycle exhibited an increase in net of work in contrast to the normal operation of the engine. Weclas and Cypris [13] carried out an experimental research on the diesel fuel injection inside a constant-volume chamber assembled with a PM. Their work showed that the delay in combustion initiation is decreased with the increase in temperature and pressure in the combustion chamber. The heat transfer from PM to the fresh fuel-air mixture is a rapid process and the reaction occurs in a high rate therein. Mohammadi et al. [14–17] numerically tested the use of a PM in the combustion chamber of a direct injection methane-fueled engine. In their study, a PM and combustion chamber were modeled as 3D with unsteady-flow. The study results indicated that the PM reduces the maximum combustion temperature from about 2500 K to 1800 K. Also, combustion was carried out in highly lean equivalence ratios that are impossible in the normal operation of the engine. Weclas et al. [18] constructed a constant volume combustion chamber and assembled a PM therein. After increasing the temperature and pressure inside the chamber to a fixed value, they injected the diesel fuel and investigated the combustion process within free and PM chamber. Mohammadi et al.
and also an 80%-reduction was evidenced for CO, HC and soot were also found nearly eliminated entirely. Also, they succeeded in increasing the excess air by 2.3 times without flame quenching. Macek and Polasek [3–5] simulated engine by the use of PM for homogenizing and stabilizing the combustion with lean mixture. Their work indicated that NO formation increased due to locally high temperature in PM somewhat compensated by lack of oxygen, and extremely lean mixture is required if combustion takes place mostly in PM. Park and Kaviany [6] thermodynamically simulated a diesel engine via making use of PM. They employed the two-zone model and single-step methane combustion. Their work indicated that the use of the PM increases the thermal efficiency from 43% to 53%. In his experimental studies, Weclas [7,8] examined the effect of liquid fuel jet impingement with a highly porous material. He explained the states that the fuel jet might undergo upon hitting the PM. Liu et al. [9] tried to predict the efficiency of PM heat regeneration cycle. They compared the net output work of PM-cycle with the Otto-cycle and Diesel-cycle. Liu et al [10] applied the two-zone model featuring mass transfer between zones, heat transfer from the combustion chamber wall and heat transfer in the PM between the fluid and the solid in their simulations to simulate the working cycle of a PM engine. They noticed that the average temperature is higher inside the PM than in the cylinder which resulting in slightly more emissions of NO for existing excess air ratio of 1.6, which is still a problem for PM engine. Zhao et al. [11] numerically studied a compression ignition in a type of PM engine fueled with isooctane and periodic contact between
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equation pertaining to constant-volume chamber with no PM is as shown in Eq. (1) [25].
Table 1 Coefficient of single step global reaction of the used fuel. Fuel
Pre-exponential factor A
Activation temperature Ea/R (K)
m
n
Ref.
H2 C3H8 C8H18 C10H22 CH3OH C2H5OH
1.8·1013 8.6·1011 4.6·1011 3.8·1011 3.2·1012 1.5·1012
17,614 15,098 15,098 15,098 15,098 15,098
1.00 0.10 0.25 0.25 0.25 0.15
0.50 1.65 1.50 1.50 1.50 1.60
[26] [25]
(Q/ V ) + RT ∑i ω̇ i − ∑i (hi ω̇ i ) dT = dt ∑i ([Xi ](cp, i − R))
(1)
The global reaction has been applied to model the fuel combustion as shown in Eq. (2) [25].
ω̇Fuel =
d [XFuel ] = −Aexp (−Ea/ RT )[XFuel ]m [XOxygen ]n dt
(2)
Constant coefficients of A, m, n for single-step oxidation of fuels in Eq. (2), were selected according to Table 1. After the Eqs. (1) and (2) were simultaneously solved, the changes in the gas temperature and the species generation and consumption rates were obtained. After updating the temperature and concentration of every species, pressure was computed according to Eq. (3) [25].
[19] investigated the direct diesel fuel injection into the constant-volume PM chamber. The results indicated that fuel will be scattered after injection with the existence of the PM and the fuel vapor will disperse inside the whole chamber. Zhao et al. [20] investigated a model wherein the PM had been assembled in the crown of the piston. Their work demonstrated the possibility of combustion in equivalence ratios of about 0.07 which was deemed impossible without the PM. Krishnaiah and Naik [21] performed an experimental study to investigate the effect of PM in diesel engines combustion chamber. They studied the experiment for part loads and full load conditions. They observed from the results that using PM inside chamber cause increased power deliver at reduced fuel consumption. Krishna et al. [22] investigated in an experimental study the effect of PM mounted to the crown of the piston. Their work showed that the diesel engines output can be increased by 10% with the use of PM. Mohammadi et al. [23,24] simulated direct diesel fuel injection in the constant-volume chamber for free and PM chambers. They also studied the emissions like NO, CO and soot, some pollutants are completely removed in the lean fuel-air mixture and they were found increasingly reduced in the very rich mixtures up to equivalent ratios of 2.3. In the present study thermodynamically simulated the combustion in a constant-volume PM chamber correspond to the operation conditions of diesel engines. The objective of the simulations, as well, is the investigation of the effect of PM in a constant volume chamber on the combustion initiation, pressure and gas temperature as well as PM temperature. Next, the effect of such parameters as the initial gas pressure, initial gas and the solid temperature, the porosity of the PM, the mean pore’s diameter of the PM, the effect of such fuels as hydrogen, propan, methanol, ethanol, isooctane and decane on combustion, and the sensitivity analysis have been investigated.
P=
∑ [Xi ] RT
(3)
i
2.2. Governing equations of porous medium combustion chamber To apply the PM in the combustion chamber, there was made use of modified gas energy equation (convective heat transfer term) and energy equation for PM (solid phase) was added thereto. The assumptions taken into account for the modeling process are:
• PM is made of Silicon-Carbide. • The combustion chamber is insulated. • PM only serves the regeneration of the energy. • The fuel combustion happens in a single-step reaction. • The radiation effect has only been presumed in solid phase. • The PM is in permanent contact with the intra-chamber mixture. • The air and the fuel are premixed and feature an identical temperature. • Heat capacity of the gaseous [27] and solid phase [28] depends on temperature. • The gas and solid phase energy equations are solved simultaneously and coupled.
The gas-phase energy equation in the presence of PM is calculated based on relation (4) [29]:
dTg
2. Mathematical model
=
dt The PM used in this simulation only acts as an energy regenerator. The PM and the gas inside the combustion chamber each have separated energy equations that solved coupled. The heat exchange between phases takes place via convection and the effect of radiation has also been taken into consideration only for the PM. The simulation process assumes a homogenous fuel-air mixture and this seems a logical presumption for such a reason as the use of PM. Combustion takes place as self-ignition due to the combustion chamber’s high initial temperature and pressure. A single-step oxidation was also applied for the combustion simulation. There was made use of NASA seven term polynomials to calculate the thermodynamic properties. The volumetric heat transfer coefficient calculated instantly according to chamber’s condition. The program code was written in C++ programming language. For validation of numerical simulation of code, experimental data [18] were used.
h v (Tg − Ts ) − φ ∑i (ω̇ i hi ) + φRTg ∑i ω̇ i ∑i [[Xi ](cp . i − R)]
(4)
The solid phase energy in the presence of the PM is calculated based on Eq. (5) [29]:
() A
−h v (Tg − Ts ) − εσ V (Ts4 − T04 ) dTs s = dt (1 − φ) ρs cs
(5)
()
A V s
is the ratio of surface area to volume of the PM, T0 is the where, temperature of the environment in which radiation occurs. The empirical relation (6) has been used to calculate the volumetric heat transfer coefficient [30]:
hv =
k g Nu v d2
(6)
Nusselt number, as well, is computed by the use of relation (7) [30]:
Nu v = 2 + 1.11Re 0.60 Pr 0.33
2.1. Governing equations of free-volume combustion chamber
(7)
The gas thermal conductivity, Reynolds number and Prandtl, as well, are calculated based on the instantaneous conditions of the gas inside the combustion chamber. The Reynolds of the chamber was related to the injected fuel velocity. Relation (8) is utilized to compute the Reynolds of the interior chamber [29]:
Since combustion inside a constant-volume chamber has been thermodynamically modeled. Therefore, only the energy equation and rate of reaction are required to be simultaneously solved. The energy 308
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Re =
dTg
ρg uc d μ
dt
(8)
Relation (9) simplifies the extracted Bernoulli equation wherein ρf is the fuel density, the intra-chamber pressure is denoted by pc and injector pressure is designated by pi [27].
2(pi − pc )
uc =
ρf
∑ [Xi ] RTg i
(11)
dTs = g (t , [Xi ], Tg , Ts ) dt
(12)
d [Xi ] = h (t , [Xi ], Tg ) dt
(13)
(9) 3. Validation of the results
Eq. (10) shows the gas pressure inside the chamber [25]:
P=
= f (t , [Xi ], Tg , Ts )
In the present study, two cases were considered, regular constantvolume chamber (free-volume) and PM inside constant-volume chamber (PM chamber). An amount of 23.8 mg decane, premixed with air, was considered in the chamber. PM had the porosity 90% and pores density of 8 ppi (pores per inch), and the initial temperature of the PM and the gaseous mixture of the free-volume and PM chamber was 500 °C. Self-ignition occurs due to the high temperature of the mixture. The comparison of the numerical gas temperature and pressure with the experimental data of Ref. [18] for such initial pressures of 1.6 MPa and 1.8 MPa has been illustrated in Fig. 2, note that the pressure is relative to the initial pressure. In Fig. 2-a because of the completely isolated chamber in simulation, as it is apparent in free-volume curve, so there is no temperature decrease after reaching maximum temperature. In the free-volume maximum point reached earlier than the experimental case, it shows that the is fuel consumed earlier than the actual value. It
(10)
2.3. Solving method of the equations Runge-Kutta fourth order method was employed to solve the solid and fluid phase energy equations in a PM and calculate the species concentrations (three nonlinear first-order differential equations). The following three Eqs. (11)–(13) are pertinent to solid and gaseous phase energy relationships as well as the species concentrations that are solved in a coupled manner. The time step used to update the energy and combustion equations was equal to 10−5 s. The step size of RungeKutta method for simultaneously solving the equations was assumed 10−6.
Fig. 2. Comparison between numerical results and test data. 309
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fuel causes to variation in chambers maximum pressure and maximum temperature. Note that the maximum pressure values are relative to initial pressure. In Fig. 3-a and -b, mass of the injected fuel is constant and lambda varies with the initial pressure. It is disclosed that by fixing the initial gas or solid temperature and increasing the other phase temperature, maximum chambers pressure increased. Due to constant mass of the injected fuel, lambda has not affected the maximum relative pressure by considering the fixed initial temperature of both phases of PM. In Fig. 3c and (3-d), initial temperature of the fuel-air mixture and PM are fixed and effect of variation of the fuel mass and initial pressure on the maximum temperature of both phase were considered. By investigation of the graphs, it is clear that increasing the injected fuel mass, increases the maximum gas temperature. Increasing the initial pressure causes increase in mass of the gaseous mixture, so chamber’s temperature decreases.
is made clear in an investigations that in this state, as well, the increasing in pressure and temperature in the simulations curve start with a mild slope from their beginning. The reason behind such a happening is the premixed mixture of the fuel and air as well as the high fuel temperature and also, the use of the single-step model for such a reason as the absence of intermediate reactions and species causes the numerical results deviate from test data, in which the pressure and temperature increase instantly with an intense slope. In Fig. 2-b, the entire conditions like the initial temperatures of the mixture and PM, the porosity percentage and fuel mass are similar to the 1.6 MPa state and there is only observed an increase in the chamber’s initial pressure to 1.8 MPa. Due to the fuel evaporation in experimental conditions, the temperature reduction happens, that has not been taken into consideration in this model. Because of the higher heat capacity of the PM as compared to gas, its temperature variations during the combustion reaction are much less than the gas temperature changes. Passing the maximum temperature and pressure of the interior chamber, both of the pressure and temperature curves find negative slopes due to the heat transfer from gas to PM featuring a lower temperature. So, with the passage of time, the slope of the simulation curve is found slightly higher immediately past the interior chamber’s maximum pressure and temperature point and that is because the heat transfer coefficient computed in the simulations is somewhat higher.
5. The effects of various parameters on numerical results 5.1. The effect of mixture’s initial pressure In this section effect of mixture initial pressure on the pressure and gas temperature profiles versus time, are investigated. The porosity of PM is 90% and pore’s density is 8 ppi. Mass of decane as a fuel is 23.8 mg. The initial pressure inside the chamber ranged between 1.4 and 2.0 MPa. The PM and the gaseous mixture’s initial temperature was assumed 500 °C for all of the states. Fig. 4-a shows the effect of initial pressure on the pressure change versus time units. The pressure is relative value respect to the initial pressure. According to Fig. 4-a, it is clear that the initial pressure variations do not have much of an effect on the maximum pressure change and they only cause reductions in the combustion delays form 3.9 ms in
4. Sensitivity analysis Sensitivity analysis is the study of how uncertainty in inputs of numerical code causes to variations in outputs of numerical code and to check that the output results are reliable. In sensitivity analysis, porosity of the PM is 90% with pore’s density of 8 ppi, and the applied fuel is decane. As can be seen form Fig. 3 small changes in lambda, initial pressure, initial gas temperature, initial PM temperature, and mass of
Fig. 3. Sensitivity analysis. 310
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concentration and elevated reaction rate not only causes a reduction in the combustion time but it also decreases the maximum temperature inside the chamber due to elevating the mass of the air inside the chamber that leads to the reduction in the energy per every unit mass of the fluid. Furthermore, the increase in the initial pressure by 0.600 MPa causes the maximum temperature inside the chamber to be reduced from about 857 °C to 758 °C. Fig. 4-c depicts the effect of the initial pressure on the temperature of the solid phase in a time unit. It is clear from the Fig. 4-c that the PM’s maximum temperature change occurs at 10 ms. The reason behind this incident are the PM’s heat transfer coefficient and the temporal delay resulting from the gaseous phase’s heat transfer to the PM. The maximum temperature changes are at about 15 °C to 18 °C. The highest temperature of the PM belongs to the initial 1.4 MPa pressure because it is in this pressure that the chamber’s maximum temperature is higher and the amount of the heat transferred to the PM is also higher than the other states. The amount of the energy transferred to the PM is reduced with the increase in the initial pressure and the decrease in the maximum temperature inside the chamber. 5.2. The effect of the initial temperature of the PM Main aim of this section is to study the effect of solid phase temperature of PM on combustion initiation. The other is to investigate the effect of solid phase temperature of PM on maximum pressure and temperature. In this section, the initial pressure and temperature of the gaseous phase were considered fixed and it is the initial temperature of the solid phase that is changed so as to be investigated of its influence on the combustion chamber’s status. The fuel is decane and lambda value equals to 1.7. The initial temperature of the gaseous phase was always fixed at 450 °C and the solid phase’s temperature was in a range from 400 °C to 550 °C in every examination. The simulation results of the effect of the PM’s initial temperature on the gaseous phase’s pressure and temperature have been illustrated in Fig. 5. It is observed in Fig. 5 that combustion does not take place when the solid phase’s temperature is 400 °C that is because the initial temperature had been set at 450 °C. It was made clear with the increase in the simulation time that the combustion takes place in higher temperatures in which case the maximum combustion temperature is reached at 14.0 ms with a maximum temperature of 640 °C. It can be understood from the Fig. 5 that the minimum initial temperature of the PM should be 500 °C in order for the combustion to get started within the 10-millisecond time span. It is evident in the investigation of the solid and gas phases temperature variations that the change in the solid phase temperature exerts a considerable effect on the combustion initiation time. For example, with the gaseous phase being fixed and the solid phase temperature being increased from 450 °C to 500 °C, the delay in the combustion will be reduced by 5.4 ms. The reason behind such a happening is the heat transfer between the PM and the gas. The oxidation rates of the fuel and the air increase with the increase in the gas temperature and the reaction takes place more quickly. Also, it is clear that the increase in the solid phase’s temperature causes an increase in the maximum gas temperature for such a reasons as the increase in the gaseous phase’s internal energy elevation inside the chamber. Fig. 4. Initial pressure effect.
5.3. The effect of the initial temperature of air-fuel mixture
initial pressure 1.4 MPa to 2.9 ms in initial pressure 2.0 MPa. The reason for which is the increase in the air concentration that brings about an increase in the reaction rate and also a reduction in the main combustion time as shown in the relation (2). It is understood in the observation of the pressure variations in Fig. 4-a that the maximum pressure changes of all the states is about 0.745 MPa on average. Fig. 4b displays the effect of the initial pressure on the gas temperature versus time. It is made clear in the investigation of Fig. 4-b that the increase in the initial pressure of the gaseous mixture due to increased air
The present study investigated the effect of the initial temperature of gas on the temperature and pressure variations of the gaseous phase in a time unit assuming a fixed initial temperature of the PM. To do so, the initial pressure of the gas and temperature of the PM are assumed fixed and only the gas phase’s initial temperature is changed. The fuel is decane and lambda value equals to 1.7. The initial temperature of the PM is 400 °C and fixed, the initial temperature of the gas mix ranges from 450 °C to 525 °C. It is seen in an investigation of the Fig. 6 that the combustion does not begin over 10 ms when the initial temperature of 311
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Fig. 5. PM’s initial temperature effect.
mean pore’s diameter changes on the gas pressure and temperature in a time unit. The maximum pressure inside the combustion chamber is increased by 0.290 MPa with the increase in the mean pore’s diameter of PM from 2.7 mm to 5.5 mm. The increase in the pore’s density of the PM causes a higher heat transfer to the PM due to the reduction in the pore’s diameter and this brings about a delay in the combustion initiation time. It is made clear in a study of the Fig. 7 that the increase in the pore’s density from 8 to 10 ppi does not bring about a tangible difference except for a 0.042 MPa difference in the pressure and a 17 °C difference in temperature at 10 ms. The increase in the pore density from 10 to 20 ppi causes a reduction in the maximum pressure of the chamber by about 0.210 MPa and a decrease in the maximum temperature by about 87 °C but it will also bring a delay by about 1.2 ms in their times, as well. The increase in the density from 20 to 30 ppi decreases the maximum pressure of the chamber by about 0.073 MPa and lowers the maximum temperature by about 48 °C but it will also cause a delay by about half a millisecond in their times. The reasons why the combustion is delayed can be its distancing away from the free flame state and the decrease in the gas temperature resulting from the existence of the PM in the combustion chamber. There is more contact surface in lower pore diameters for the exchange of heat for gas and the PM can store more energy as a subsequent to which the upper limit of the chamber’s combustion temperature is decreased.
the gas is below 500 °C. The increase in simulation time does not have any effect on the initiation of combustion when the initial temperature of the gas is 450 °C. The combustion would start when the gas temperature is increased to 475 °C with the continuation of the simulation. The maximum temperature inside the chamber in this state would become 553 °C reached within 15 ms. The time required for reaching the maximum temperature inside the chamber would be decreased considerably by 10.1 ms with the increase in the temperature from 475 °C to 500 °C and there would be observed an increase by 167-degree in the maximum temperature. The increase in the initial temperature from 500 °C to 525 °C decreases the time required for reaching to the maximum combustion temperature by 2.7 ms and the maximum temperature will be also increased by 82-degree, and relative pressure inside the chamber to be increased by 0.119 MPa. Due to the existence of a PM in the combustion chamber and for such a reason that it possesses high heat capacity and usually a temperature lower than the gas inside the chamber, the temperatures of all the states converge towards a certain temperature that is the very temperature of the PM. 5.4. The effect of the mean pore’s diameter of PM In this state, the PM is assumed with a fixed 90-percent porosity and only the mean pore’s diameter of the PM is changed. The fuel is decane and lambda value equals to 1.7. Both the gas and PM have a temperature of 500 °C. The mean pore’s diameter of the PM ranges from 8 to 20 ppi and the mean pore’s diameter corresponding to each state has been written in front of it in millimeter. Fig. 7 demonstrates the effect of
5.5. The effect of porosity of the PM In this section, assuming a fixed mean pore’s diameter, the PM porosity percentage is changed so as to evaluate its effect on the
Fig. 6. Gaseous mixture initial temperature effect. 312
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Fig. 7. Mean pore’s diameter effect.
fuels for the same lambda 1.6 on temperature profile, are compared. It can be understood from the study of the Fig. 9 that for all of the fuel types, increasing the lambda value by adding mass of the air in the combustion chamber, maximum temperature of the gas decreased. Also for all fuels (except hydrogen) increasing lambda causes reduction in the main combustion time. According to Table 1 for hydrogen combustion it is obvious that, oxidizer concentration exponent (n) is lower than fuel concentration exponent (m), hence fuel concentration has more effect than air concentration. So, the hydrogen profile’s temperature differs from the others fuel profile’s temperature. It is disclosed from Fig. 9 combustion delay for methanol and hydrogen are approximately close but maximum temperature of methanol is about 101 °C higher. Methanol and hydrogen have lower ignition delay in comparison with the other studied fuels. Propane and ethanol are close in term of the ignition delay but ethanol’s maximum temperature occurs about 0.3 milisecond lower than propane. On the other hand, the temperature profiles of decane and isooctane are very similar in terms of ignition delay and also maximum value of temperature.
gaseous phase changes of temperature and pressure inside the chamber. In the present study, the solid and gaseous phases have the same temperature, i.e. 500 °C, and the fuel is decane and lambda value equals to 1.5. The PM has a porosity in a range from 80% to 95%. Fig. 8 depicts the effect of PM’s porosity percentage variations on the pressure and temperature inside the chamber in a time unit. It can be understood from an investigation of the curves that the increase in the porosity makes the combustion behavior approach the free flame state. The increase in the porosity percentage is equal to the increase in the gaseous phase’s share of the combustion chamber and the reduction of the solid phase’s quotient therein. The result of increasing the porosity percentage, as well, would be the reduction in the energy storage area in the PM and increase in the pressure inside the chamber. Also, the more the porosity percentage is increased the lesser the time required for the initiation of the combustion due to the transferring of lesser heat to the PM. According to the Fig. 8, it can be seen that the maximum relative pressure will be increased by about 0.152 MPa and its corresponding delay will be about 0.9 ms with the increase in the porosity from 80% to 95%, it also causes the maximum temperature inside the combustion chamber to be increased from 771 °C to 842 °C. The main reason behind this increase in temperature and pressure is the reduction in the energy storage in the solid.
6. Conclusion The present study deal with the modeling of combustion in a constant-volume chamber featuring PM, through considering a PM chamber, to thermodynamically solve the single-step combustion and energy equations at the same time for solid and gaseous phase and radiation just for the solid phase. The study examined the effects of such parameters as initial gas pressure, the initial gas and PM temperatures, the PM’s percentage of porosity, mean pore’s diameter of the PM as well as the effects of such fuels as hydrogen, propane, methanol, ethanol, isooctane and decane on combustion and also sensitivity analysis of the code. The followings are the simulation findings:
5.6. The effect of the fuel type In this section, fuels such as hydrogen, propane, methanol, ethanol, isooctane and decane have been studied under fixed initial conditions. The initial temperature of the gas and PM for all of the state is 475 °C and PM porosity is 90% with pore density 8 ppi. The effect of the lambda variations from 1.4 to 2.0 on the temperature of the combustion chamber have been investigated. In addition, the results of the various
Fig. 8. Porosity percentage effect. 313
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Fig. 9. Effect of the fuel type.
(1) Assuming a fixed initial temperature of the PM and the gas mixture, when the initial pressure was higher, the lesser time required for the combustion. Also, higher initial pressure rates were accompanied by lower maximum temperatures inside the chamber. The effect of the initial pressure on the intra-chamber maximum relative pressure was low and almost negligible. (2) Assuming a fixed gas temperature, the higher PM’s temperature causes lesser delay in the combustion initiation. On the other hand, the increase in the initial temperature of the PM caused increase in the maximum temperature and pressure inside the combustion chamber. (3) The maximum temperature inside the combustion chamber is reduced with the decrease in the mean pore’s diameter (increase in the pore’s density). Also, the temperature increase curve enjoys a milder slope up to the point where the temperature inside the chamber peaks and this is indicative of the idea that the combustion distances away from the explosive-like state and flame is more smoothly released. The effect of the mean pore’s diameter reduction
is displayed in the form of more delay in the main combustion initiation. (4) The combustion behavior gets closer to the free flame state with the increase in the porosity percentage. Assuming fixed temperature of the two phases and also fixed mean pore’s diameter, the increase in the porosity causes increase in the maximum temperature and pressure inside the chamber. In terms of the time required for the initiation of the combustion, the increase in the solid phase quotient causes a slight delay in the combustion time. (5) It is understandable with investigation of different fuels that, combustion in PM chamber may not be effective enough with fuels with explosive behavior and low ignition delay such as hydrogen. References [1] F. Durst, M. Weclas, A new type of internal combustion engine based on the porousmedium combustion technique, Proc. Inst. Mech. Eng., Part D: J. Automobile Eng. 215 (1) (2001) 63–81, https://doi.org/10.1243/0954407011525467. [2] F. Durst, M. Weclas, A new concept of IC engine with homogeneous combustion in
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[3] [4]
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https://doi.org/10.1115/ices2012-81150. [17] A. Mohammadi, A. Jazayeri, M. Ziabasharhagh, Numerical study of combustion and emission in a porous medium engine, in: The Eighth KSME-JSME 2012 Thermal and Fluids Engineering Confrerence, Songdo Convensia Center, Incheon, Korea, 2012. [18] M. Weclas, J. Cypris, T.M.A. Maksoud, Thermodynamic properties of real porous combustion reactor under diesel engine-like conditions, J. Thermodyn. 2012 (2012), https://doi.org/10.1155/2012/798104. [19] A. Mohammadi, M. Benhari, Simulation of combustion in a porous reactor, in: ASME 2014 12th Biennial Conference on Engineering Systems Design and Analysis, American Society of Mechanical Engineers, doi: 10.1115/esda2014-20205, 2014, pp. V002T11A014-V002T11A014. [20] L. Zhou, M.Z. Xie, K.H. Luo, Numerical study of heat transfer and combustion in IC engine with a porous media piston region, Appl. Therm. Eng. 65 (1) (2014) 597–604, https://doi.org/10.1016/j.applthermaleng.2013.12.066. [21] B.V. Krishnaiah, B.B. Naik, Performance and emission analysis of porous media combustion chamber in diesel engines for different fuel blends, Int. J. Mech. Eng. Technol. (IJMET) 7 (3) (2016) 200–212. [22] K. Krishna, B. Sudheer Prem Kumar, K. Vijaya Kumar Reddy, P. Vijaya Rao, R. Gugulothu, A review of porous-media combustion technology applied to IC engine, Int. J. Eng. Res. 5 (2) (2016) 491–494. [23] A. Mohammadi, M., Benhari, M.N. Khajavi, Numerical study of combustion in a porous medium with liquid fuel injection, in: ASME 2017 International Mechanical Engineering Congress and Exposition, American Society of Mechanical Engineers, doi: 10.1115/imece2017-72483, 2017, November, pp. V008T10A033V008T10A033. [24] A. Mohammadi, M. Varmazyar, R. Hamzeloo, Simulation of combustion in a porous-medium diesel engine, J. Mech. Sci. Technol. 32 (5) (2018) 2327–2337, https://doi.org/10.1007/s12206-018-0444-x. [25] S.R. Turns, An Introduction to Combustion, McGraw-hill, New York, 1996. [26] N.M. Marinov, C.K. Westbrook, W.J. Pitz, Detailed and global chemical kinetics model for hydrogen, in: Proceedings of the Eighth International Symposium on Transport Phenomena in Combustion, edited by S. H., 1995. [27] A. Burcat, B. Ruscic, Third millenium ideal gas and condensed phase thermochemical database for combustion (with update from active thermochemical tables) (No. ANL-05/20), Argonne National Lab.(ANL), Argonne, IL (United States). doi: 10.2172/925269, 2005. [28] B.K. Jang, Y. Sakka, Thermophysical properties of porous SiC ceramics fabricated by pressureless sintering, Sci. Technol. Adv. Mater. 8 (7–8) (2007) 655, https://doi. org/10.1016/j.stam.2007.08.003. [29] M. Saghaei, Thermodynamic Simulation of Porous-Medium Combustion Chamber Operation under Diesel Engine-like Conditions, MSc diss., Shahid Rajaei Teacher Training University, Tehran, Iran, 2017. [30] X. Fu, R. Viskanta, J.P. Gore, Measurement and correlation of volumetric heat transfer coefficients of cellular ceramics, Exp. Therm. Fluid Sci. 17 (4) (1998) 285–293, https://doi.org/10.1016/s0894-1777(98)10002-x.
porous-medium (PM), in: 5th Int. In Symposium COMODIA-2001, Nagoya, Japan, 2001. J. Macek, M. Polášek, Via homogeneous combustion to low NOx emission, in: Proceedings of EAEC congress–CD-ROM. Bratislava: SAITS, Vol. 1, 2001, pp. 1–10. J. Macek, M. Polášek, Simulation of Porous Medium Combustion in Engines, Publications. Josef Bo zek Research Center, Czech Technical University in Prague, 2001. M. Polášek, J. Macek, Homogenization of combustion in cylinder of CI engine using porous medium (No. 2003-01-1085), SAE Technical Paper, 2003, doi: 10.4271/ 2003-01-1085. C.W. Park, M. Kaviany, Evaporation-combustion affected by in-cylinder, reciprocating porous regenerator, J. Heat Transfer 124 (1) (2003) 184–194, https:// doi.org/10.1115/1.1418368. M. Weclas, B. Ates, V. Vlachovic, Basic aspects of interaction between a high velocity Diesel jet and a highly porous medium (PM), in: 9th International Conference on Liquid Atomization and Spray Systems, ICLASS, 2003. M. Weclas, High velocity CR Diesel jet impingement on to porous structure and its utilization for mixture homogenization in IC engines, in: DITICE Workshop: Drop/ wall Interaction: Industrial Applications, Experiments and Modeling, Bergamo (Italy), 2006, May. H. Liu, M. Xie, D. Wu, Thermodynamic analysis of the heat regenerative cycle in porous medium engine, Energy Convers. Manage. 50 (2) (2009) 297–303, https:// doi.org/10.1016/j.enconman.2008.09.023. H. Liu, M. Xie, D. Wu, Simulation of a porous medium (PM) engine using a two-zone combustion model, Appl. Therm. Eng. 29 (14) (2009) 3189–3197, https://doi.org/ 10.1016/j.applthermaleng.2009.04.021. Z. Zhao, C. Wang, M. Xie, Numerical study on the realization of compression ignition in a type of porous medium engine fueled with Isooctane, Fuel 88 (11) (2009) 2291–2296, https://doi.org/10.1016/j.fuel.2009.06.002. A.A. Dhale, G.K. Awari, M.P. Singh, Analysis of internal combustion engine with a new concept of porous medium combustion for the future clean engine, Therm. Sci. 14 (4) (2010) 943–956, https://doi.org/10.2298/tsci1004943d. M. Weclas, J. Cypris, Combustion of diesel spray: low-and high-temperature oxidation processes for free diesel injection and in porous reactors, in: DIPSI Workshop 2011. Droplet Impact Phenomena & Spray Investigations, Università degli studi di Bergamo, 2011, pp. 66–72. A. Mohammadi, A. Jazayeri, M. Ziabasharhagh, Numerical simulation of porous medium internal combustion engine, ASME-JSME-KSME 2011 Joint Fluids Engineering Conference, American Society of Mechanical Engineers, 2011, pp. 1521–1529, , https://doi.org/10.1115/ajk2011-03079. A. Mohammadi, A. Jazayeri, M. Ziabasharhagh, Numerical simulation of combustion with porous medium in IC engine, Fuel Combust. Sci. Res. J. 5 (1) (2012) 71–85. A. Mohammadi, A. Jazayeri, M. Ziabasharhagh, Numerical simulation of direct injection engine with using porous medium, Proceedings of the ASME Internal Combustion Engine Division Spring Technical Conference, 2012, pp. 785–795, ,
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Thermodynamic simulation of porous-medium combustion chamber under diesel engine-like conditions
T
⁎
M. Saghaei , A. Mohammadi Department of Mechanical Engineering, Shahid Rajaee Teacher Training University, Tehran 16758-136, Iran
H I GH L IG H T S
initial pressure decreases the delay and maximum temperature. • Higher gas temperature will reduce with decrease in the PM’s mean pore’s diameter. • The the porosity decreases the pressure peak and causes delay in combustion. • Decreasing • Fuels with lower reaction rate will become more efficient when used in PM engine.
A R T I C LE I N FO
A B S T R A C T
Keywords: Porous medium Homogeneous combustion Constant volume chamber Diesel
Currently, one of the most important issue of the diesel engines is the non-homogeneity of the in-cylinder fuel-air mixture. Non-homogeneous mixture causes the non-uniform heat release and high-temperature gradient in the combustion chamber that followed by the production of unburnt hydrocarbons, carbon monoxide, nitrogen oxides and soot. Homogenous combustion decreases the production of the emissions. One novel method for achieving homogenous combustion is the use of porous medium (PM) within the combustion chamber of engine so as to separate the mixture formation process from combustion process. The present article thermodynamically investigates the effect of utilizing PM in a constant-volume combustion chamber via solving the energy equations for both the solid and fluid phases considering the chemical reaction of the fuel combustion. At first, numerical result is validated according to the experimental result of diesel fuel injection in a constant-volume combustion chamber with PM. Then, effects of the initial mixture and PM temperature, the porosity of the PM, the mean pores diameter as well as the use of fuels such as decane, isooctane, methanol, ethanol, propane and hydrogen on combustion initiation, and also pressure and temperature of the combustion chamber studied.
1. Introduction The homogenous air-fuel combustion for achieving a uniform temperature and reducing of the pollutants is highly considerable for researchers. One method for creating homogeneous combustion is the use of porous medium within the combustion chamber. PM for its increasingly higher heat capacity as compared to gas possesses the ability of storing a high thermal energy. Also, it has a high surface area to volume ratio that causes an increase in the heat exchange. The high temperature of the PM inside the combustion chamber can provide the rapid evaporation of the liquid fuel and better mixture formation of the air-fuel that will eventually leads to the self-ignition of the mixture. Also, it can separate the processes of mixture formation and combustion that happen simultaneously in diesel engines. The ideal diesel combustion is usually considered as a constant-pressure process, but the ⁎
combustion occurs very fast when PM is employed inside the dieselengine combustion chamber for such a reason as the high solid-phase temperature and the exchange of the heat with the injected liquid-fuel. Combustion in presence of PM due to high reaction rate and lack of enough time for volume change can be considered approximately as constant-volume. In this case due to making use of PM, constant-volume combustion process taken into account in lieu of constant-pressure. Fig. 1 (Left) shows using of PM in combustion chamber of a diesel engine. Fig. 1 (Right) illustrates constant-volume combustion chamber that is equivalent with combustion process in a PM Diesel-engine. The idea of utilizing PM in diesel engine was proposed by Durst and Weclas [1,2]. They assembled a PM made of silicon carbide in the cylinder-head of a single-cylinder diesel engine. In the foresaid engine maximum chamber temperature was reduced from about 2200 K to 1500 K. The NOx pollutant was found decreased between 90% and 97%
Corresponding author. E-mail address: [email protected] (M. Saghaei).
https://doi.org/10.1016/j.applthermaleng.2019.03.024 Received 11 July 2018; Received in revised form 4 February 2019; Accepted 4 March 2019 Available online 05 March 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.
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Nomenclature
Nuv
T t R V Q̇ h [X] cp P hv cs kg d u Re Pr
Greek symbols
Temperature Time Universal gas constant Combustion chamber volume Chamber heat transfer rate Enthalpy Concentration Constant pressure heat capacity Pressure Volumetric heat transfer coefficient Solid heat capacity Gaseous mixture thermal conductivity Mean pore’s diameter Velocity Reynolds Number Prandtl Number
ω̇ φ ε σ ρ μ λ
Nusselt Number
Production rate Porosity Emissivity coefficient of PM Stefan-Boltzman constant Density Dynamics viscosity Actual to Stoichiometry Air/Fuel Ratio
Subscripts g s FV PM
Gas phase Solid phase Free-Volume Porous-Medium
Fig. 1. Schematic presentation of constant volume PM chamber [18].
in-cylinder and PM through imposing modifications in the KIVA-3V code. Their work indicated that the PM structure is effective on the heat transfer between the gas and solid phases. Also, the valve-opening timings has to be definitely optimized so as to attain an optimal operation of the PM engine. Dhale et al. [12] performed experimental studies on the single-cylinder PM engines featuring direct diesel fuel injection. The pollutants considerably reduced and the cycle exhibited an increase in net of work in contrast to the normal operation of the engine. Weclas and Cypris [13] carried out an experimental research on the diesel fuel injection inside a constant-volume chamber assembled with a PM. Their work showed that the delay in combustion initiation is decreased with the increase in temperature and pressure in the combustion chamber. The heat transfer from PM to the fresh fuel-air mixture is a rapid process and the reaction occurs in a high rate therein. Mohammadi et al. [14–17] numerically tested the use of a PM in the combustion chamber of a direct injection methane-fueled engine. In their study, a PM and combustion chamber were modeled as 3D with unsteady-flow. The study results indicated that the PM reduces the maximum combustion temperature from about 2500 K to 1800 K. Also, combustion was carried out in highly lean equivalence ratios that are impossible in the normal operation of the engine. Weclas et al. [18] constructed a constant volume combustion chamber and assembled a PM therein. After increasing the temperature and pressure inside the chamber to a fixed value, they injected the diesel fuel and investigated the combustion process within free and PM chamber. Mohammadi et al.
and also an 80%-reduction was evidenced for CO, HC and soot were also found nearly eliminated entirely. Also, they succeeded in increasing the excess air by 2.3 times without flame quenching. Macek and Polasek [3–5] simulated engine by the use of PM for homogenizing and stabilizing the combustion with lean mixture. Their work indicated that NO formation increased due to locally high temperature in PM somewhat compensated by lack of oxygen, and extremely lean mixture is required if combustion takes place mostly in PM. Park and Kaviany [6] thermodynamically simulated a diesel engine via making use of PM. They employed the two-zone model and single-step methane combustion. Their work indicated that the use of the PM increases the thermal efficiency from 43% to 53%. In his experimental studies, Weclas [7,8] examined the effect of liquid fuel jet impingement with a highly porous material. He explained the states that the fuel jet might undergo upon hitting the PM. Liu et al. [9] tried to predict the efficiency of PM heat regeneration cycle. They compared the net output work of PM-cycle with the Otto-cycle and Diesel-cycle. Liu et al [10] applied the two-zone model featuring mass transfer between zones, heat transfer from the combustion chamber wall and heat transfer in the PM between the fluid and the solid in their simulations to simulate the working cycle of a PM engine. They noticed that the average temperature is higher inside the PM than in the cylinder which resulting in slightly more emissions of NO for existing excess air ratio of 1.6, which is still a problem for PM engine. Zhao et al. [11] numerically studied a compression ignition in a type of PM engine fueled with isooctane and periodic contact between
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equation pertaining to constant-volume chamber with no PM is as shown in Eq. (1) [25].
Table 1 Coefficient of single step global reaction of the used fuel. Fuel
Pre-exponential factor A
Activation temperature Ea/R (K)
m
n
Ref.
H2 C3H8 C8H18 C10H22 CH3OH C2H5OH
1.8·1013 8.6·1011 4.6·1011 3.8·1011 3.2·1012 1.5·1012
17,614 15,098 15,098 15,098 15,098 15,098
1.00 0.10 0.25 0.25 0.25 0.15
0.50 1.65 1.50 1.50 1.50 1.60
[26] [25]
(Q/ V ) + RT ∑i ω̇ i − ∑i (hi ω̇ i ) dT = dt ∑i ([Xi ](cp, i − R))
(1)
The global reaction has been applied to model the fuel combustion as shown in Eq. (2) [25].
ω̇Fuel =
d [XFuel ] = −Aexp (−Ea/ RT )[XFuel ]m [XOxygen ]n dt
(2)
Constant coefficients of A, m, n for single-step oxidation of fuels in Eq. (2), were selected according to Table 1. After the Eqs. (1) and (2) were simultaneously solved, the changes in the gas temperature and the species generation and consumption rates were obtained. After updating the temperature and concentration of every species, pressure was computed according to Eq. (3) [25].
[19] investigated the direct diesel fuel injection into the constant-volume PM chamber. The results indicated that fuel will be scattered after injection with the existence of the PM and the fuel vapor will disperse inside the whole chamber. Zhao et al. [20] investigated a model wherein the PM had been assembled in the crown of the piston. Their work demonstrated the possibility of combustion in equivalence ratios of about 0.07 which was deemed impossible without the PM. Krishnaiah and Naik [21] performed an experimental study to investigate the effect of PM in diesel engines combustion chamber. They studied the experiment for part loads and full load conditions. They observed from the results that using PM inside chamber cause increased power deliver at reduced fuel consumption. Krishna et al. [22] investigated in an experimental study the effect of PM mounted to the crown of the piston. Their work showed that the diesel engines output can be increased by 10% with the use of PM. Mohammadi et al. [23,24] simulated direct diesel fuel injection in the constant-volume chamber for free and PM chambers. They also studied the emissions like NO, CO and soot, some pollutants are completely removed in the lean fuel-air mixture and they were found increasingly reduced in the very rich mixtures up to equivalent ratios of 2.3. In the present study thermodynamically simulated the combustion in a constant-volume PM chamber correspond to the operation conditions of diesel engines. The objective of the simulations, as well, is the investigation of the effect of PM in a constant volume chamber on the combustion initiation, pressure and gas temperature as well as PM temperature. Next, the effect of such parameters as the initial gas pressure, initial gas and the solid temperature, the porosity of the PM, the mean pore’s diameter of the PM, the effect of such fuels as hydrogen, propan, methanol, ethanol, isooctane and decane on combustion, and the sensitivity analysis have been investigated.
P=
∑ [Xi ] RT
(3)
i
2.2. Governing equations of porous medium combustion chamber To apply the PM in the combustion chamber, there was made use of modified gas energy equation (convective heat transfer term) and energy equation for PM (solid phase) was added thereto. The assumptions taken into account for the modeling process are:
• PM is made of Silicon-Carbide. • The combustion chamber is insulated. • PM only serves the regeneration of the energy. • The fuel combustion happens in a single-step reaction. • The radiation effect has only been presumed in solid phase. • The PM is in permanent contact with the intra-chamber mixture. • The air and the fuel are premixed and feature an identical temperature. • Heat capacity of the gaseous [27] and solid phase [28] depends on temperature. • The gas and solid phase energy equations are solved simultaneously and coupled.
The gas-phase energy equation in the presence of PM is calculated based on relation (4) [29]:
dTg
2. Mathematical model
=
dt The PM used in this simulation only acts as an energy regenerator. The PM and the gas inside the combustion chamber each have separated energy equations that solved coupled. The heat exchange between phases takes place via convection and the effect of radiation has also been taken into consideration only for the PM. The simulation process assumes a homogenous fuel-air mixture and this seems a logical presumption for such a reason as the use of PM. Combustion takes place as self-ignition due to the combustion chamber’s high initial temperature and pressure. A single-step oxidation was also applied for the combustion simulation. There was made use of NASA seven term polynomials to calculate the thermodynamic properties. The volumetric heat transfer coefficient calculated instantly according to chamber’s condition. The program code was written in C++ programming language. For validation of numerical simulation of code, experimental data [18] were used.
h v (Tg − Ts ) − φ ∑i (ω̇ i hi ) + φRTg ∑i ω̇ i ∑i [[Xi ](cp . i − R)]
(4)
The solid phase energy in the presence of the PM is calculated based on Eq. (5) [29]:
() A
−h v (Tg − Ts ) − εσ V (Ts4 − T04 ) dTs s = dt (1 − φ) ρs cs
(5)
()
A V s
is the ratio of surface area to volume of the PM, T0 is the where, temperature of the environment in which radiation occurs. The empirical relation (6) has been used to calculate the volumetric heat transfer coefficient [30]:
hv =
k g Nu v d2
(6)
Nusselt number, as well, is computed by the use of relation (7) [30]:
Nu v = 2 + 1.11Re 0.60 Pr 0.33
2.1. Governing equations of free-volume combustion chamber
(7)
The gas thermal conductivity, Reynolds number and Prandtl, as well, are calculated based on the instantaneous conditions of the gas inside the combustion chamber. The Reynolds of the chamber was related to the injected fuel velocity. Relation (8) is utilized to compute the Reynolds of the interior chamber [29]:
Since combustion inside a constant-volume chamber has been thermodynamically modeled. Therefore, only the energy equation and rate of reaction are required to be simultaneously solved. The energy 308
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Re =
dTg
ρg uc d μ
dt
(8)
Relation (9) simplifies the extracted Bernoulli equation wherein ρf is the fuel density, the intra-chamber pressure is denoted by pc and injector pressure is designated by pi [27].
2(pi − pc )
uc =
ρf
∑ [Xi ] RTg i
(11)
dTs = g (t , [Xi ], Tg , Ts ) dt
(12)
d [Xi ] = h (t , [Xi ], Tg ) dt
(13)
(9) 3. Validation of the results
Eq. (10) shows the gas pressure inside the chamber [25]:
P=
= f (t , [Xi ], Tg , Ts )
In the present study, two cases were considered, regular constantvolume chamber (free-volume) and PM inside constant-volume chamber (PM chamber). An amount of 23.8 mg decane, premixed with air, was considered in the chamber. PM had the porosity 90% and pores density of 8 ppi (pores per inch), and the initial temperature of the PM and the gaseous mixture of the free-volume and PM chamber was 500 °C. Self-ignition occurs due to the high temperature of the mixture. The comparison of the numerical gas temperature and pressure with the experimental data of Ref. [18] for such initial pressures of 1.6 MPa and 1.8 MPa has been illustrated in Fig. 2, note that the pressure is relative to the initial pressure. In Fig. 2-a because of the completely isolated chamber in simulation, as it is apparent in free-volume curve, so there is no temperature decrease after reaching maximum temperature. In the free-volume maximum point reached earlier than the experimental case, it shows that the is fuel consumed earlier than the actual value. It
(10)
2.3. Solving method of the equations Runge-Kutta fourth order method was employed to solve the solid and fluid phase energy equations in a PM and calculate the species concentrations (three nonlinear first-order differential equations). The following three Eqs. (11)–(13) are pertinent to solid and gaseous phase energy relationships as well as the species concentrations that are solved in a coupled manner. The time step used to update the energy and combustion equations was equal to 10−5 s. The step size of RungeKutta method for simultaneously solving the equations was assumed 10−6.
Fig. 2. Comparison between numerical results and test data. 309
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fuel causes to variation in chambers maximum pressure and maximum temperature. Note that the maximum pressure values are relative to initial pressure. In Fig. 3-a and -b, mass of the injected fuel is constant and lambda varies with the initial pressure. It is disclosed that by fixing the initial gas or solid temperature and increasing the other phase temperature, maximum chambers pressure increased. Due to constant mass of the injected fuel, lambda has not affected the maximum relative pressure by considering the fixed initial temperature of both phases of PM. In Fig. 3c and (3-d), initial temperature of the fuel-air mixture and PM are fixed and effect of variation of the fuel mass and initial pressure on the maximum temperature of both phase were considered. By investigation of the graphs, it is clear that increasing the injected fuel mass, increases the maximum gas temperature. Increasing the initial pressure causes increase in mass of the gaseous mixture, so chamber’s temperature decreases.
is made clear in an investigations that in this state, as well, the increasing in pressure and temperature in the simulations curve start with a mild slope from their beginning. The reason behind such a happening is the premixed mixture of the fuel and air as well as the high fuel temperature and also, the use of the single-step model for such a reason as the absence of intermediate reactions and species causes the numerical results deviate from test data, in which the pressure and temperature increase instantly with an intense slope. In Fig. 2-b, the entire conditions like the initial temperatures of the mixture and PM, the porosity percentage and fuel mass are similar to the 1.6 MPa state and there is only observed an increase in the chamber’s initial pressure to 1.8 MPa. Due to the fuel evaporation in experimental conditions, the temperature reduction happens, that has not been taken into consideration in this model. Because of the higher heat capacity of the PM as compared to gas, its temperature variations during the combustion reaction are much less than the gas temperature changes. Passing the maximum temperature and pressure of the interior chamber, both of the pressure and temperature curves find negative slopes due to the heat transfer from gas to PM featuring a lower temperature. So, with the passage of time, the slope of the simulation curve is found slightly higher immediately past the interior chamber’s maximum pressure and temperature point and that is because the heat transfer coefficient computed in the simulations is somewhat higher.
5. The effects of various parameters on numerical results 5.1. The effect of mixture’s initial pressure In this section effect of mixture initial pressure on the pressure and gas temperature profiles versus time, are investigated. The porosity of PM is 90% and pore’s density is 8 ppi. Mass of decane as a fuel is 23.8 mg. The initial pressure inside the chamber ranged between 1.4 and 2.0 MPa. The PM and the gaseous mixture’s initial temperature was assumed 500 °C for all of the states. Fig. 4-a shows the effect of initial pressure on the pressure change versus time units. The pressure is relative value respect to the initial pressure. According to Fig. 4-a, it is clear that the initial pressure variations do not have much of an effect on the maximum pressure change and they only cause reductions in the combustion delays form 3.9 ms in
4. Sensitivity analysis Sensitivity analysis is the study of how uncertainty in inputs of numerical code causes to variations in outputs of numerical code and to check that the output results are reliable. In sensitivity analysis, porosity of the PM is 90% with pore’s density of 8 ppi, and the applied fuel is decane. As can be seen form Fig. 3 small changes in lambda, initial pressure, initial gas temperature, initial PM temperature, and mass of
Fig. 3. Sensitivity analysis. 310
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concentration and elevated reaction rate not only causes a reduction in the combustion time but it also decreases the maximum temperature inside the chamber due to elevating the mass of the air inside the chamber that leads to the reduction in the energy per every unit mass of the fluid. Furthermore, the increase in the initial pressure by 0.600 MPa causes the maximum temperature inside the chamber to be reduced from about 857 °C to 758 °C. Fig. 4-c depicts the effect of the initial pressure on the temperature of the solid phase in a time unit. It is clear from the Fig. 4-c that the PM’s maximum temperature change occurs at 10 ms. The reason behind this incident are the PM’s heat transfer coefficient and the temporal delay resulting from the gaseous phase’s heat transfer to the PM. The maximum temperature changes are at about 15 °C to 18 °C. The highest temperature of the PM belongs to the initial 1.4 MPa pressure because it is in this pressure that the chamber’s maximum temperature is higher and the amount of the heat transferred to the PM is also higher than the other states. The amount of the energy transferred to the PM is reduced with the increase in the initial pressure and the decrease in the maximum temperature inside the chamber. 5.2. The effect of the initial temperature of the PM Main aim of this section is to study the effect of solid phase temperature of PM on combustion initiation. The other is to investigate the effect of solid phase temperature of PM on maximum pressure and temperature. In this section, the initial pressure and temperature of the gaseous phase were considered fixed and it is the initial temperature of the solid phase that is changed so as to be investigated of its influence on the combustion chamber’s status. The fuel is decane and lambda value equals to 1.7. The initial temperature of the gaseous phase was always fixed at 450 °C and the solid phase’s temperature was in a range from 400 °C to 550 °C in every examination. The simulation results of the effect of the PM’s initial temperature on the gaseous phase’s pressure and temperature have been illustrated in Fig. 5. It is observed in Fig. 5 that combustion does not take place when the solid phase’s temperature is 400 °C that is because the initial temperature had been set at 450 °C. It was made clear with the increase in the simulation time that the combustion takes place in higher temperatures in which case the maximum combustion temperature is reached at 14.0 ms with a maximum temperature of 640 °C. It can be understood from the Fig. 5 that the minimum initial temperature of the PM should be 500 °C in order for the combustion to get started within the 10-millisecond time span. It is evident in the investigation of the solid and gas phases temperature variations that the change in the solid phase temperature exerts a considerable effect on the combustion initiation time. For example, with the gaseous phase being fixed and the solid phase temperature being increased from 450 °C to 500 °C, the delay in the combustion will be reduced by 5.4 ms. The reason behind such a happening is the heat transfer between the PM and the gas. The oxidation rates of the fuel and the air increase with the increase in the gas temperature and the reaction takes place more quickly. Also, it is clear that the increase in the solid phase’s temperature causes an increase in the maximum gas temperature for such a reasons as the increase in the gaseous phase’s internal energy elevation inside the chamber. Fig. 4. Initial pressure effect.
5.3. The effect of the initial temperature of air-fuel mixture
initial pressure 1.4 MPa to 2.9 ms in initial pressure 2.0 MPa. The reason for which is the increase in the air concentration that brings about an increase in the reaction rate and also a reduction in the main combustion time as shown in the relation (2). It is understood in the observation of the pressure variations in Fig. 4-a that the maximum pressure changes of all the states is about 0.745 MPa on average. Fig. 4b displays the effect of the initial pressure on the gas temperature versus time. It is made clear in the investigation of Fig. 4-b that the increase in the initial pressure of the gaseous mixture due to increased air
The present study investigated the effect of the initial temperature of gas on the temperature and pressure variations of the gaseous phase in a time unit assuming a fixed initial temperature of the PM. To do so, the initial pressure of the gas and temperature of the PM are assumed fixed and only the gas phase’s initial temperature is changed. The fuel is decane and lambda value equals to 1.7. The initial temperature of the PM is 400 °C and fixed, the initial temperature of the gas mix ranges from 450 °C to 525 °C. It is seen in an investigation of the Fig. 6 that the combustion does not begin over 10 ms when the initial temperature of 311
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Fig. 5. PM’s initial temperature effect.
mean pore’s diameter changes on the gas pressure and temperature in a time unit. The maximum pressure inside the combustion chamber is increased by 0.290 MPa with the increase in the mean pore’s diameter of PM from 2.7 mm to 5.5 mm. The increase in the pore’s density of the PM causes a higher heat transfer to the PM due to the reduction in the pore’s diameter and this brings about a delay in the combustion initiation time. It is made clear in a study of the Fig. 7 that the increase in the pore’s density from 8 to 10 ppi does not bring about a tangible difference except for a 0.042 MPa difference in the pressure and a 17 °C difference in temperature at 10 ms. The increase in the pore density from 10 to 20 ppi causes a reduction in the maximum pressure of the chamber by about 0.210 MPa and a decrease in the maximum temperature by about 87 °C but it will also bring a delay by about 1.2 ms in their times, as well. The increase in the density from 20 to 30 ppi decreases the maximum pressure of the chamber by about 0.073 MPa and lowers the maximum temperature by about 48 °C but it will also cause a delay by about half a millisecond in their times. The reasons why the combustion is delayed can be its distancing away from the free flame state and the decrease in the gas temperature resulting from the existence of the PM in the combustion chamber. There is more contact surface in lower pore diameters for the exchange of heat for gas and the PM can store more energy as a subsequent to which the upper limit of the chamber’s combustion temperature is decreased.
the gas is below 500 °C. The increase in simulation time does not have any effect on the initiation of combustion when the initial temperature of the gas is 450 °C. The combustion would start when the gas temperature is increased to 475 °C with the continuation of the simulation. The maximum temperature inside the chamber in this state would become 553 °C reached within 15 ms. The time required for reaching the maximum temperature inside the chamber would be decreased considerably by 10.1 ms with the increase in the temperature from 475 °C to 500 °C and there would be observed an increase by 167-degree in the maximum temperature. The increase in the initial temperature from 500 °C to 525 °C decreases the time required for reaching to the maximum combustion temperature by 2.7 ms and the maximum temperature will be also increased by 82-degree, and relative pressure inside the chamber to be increased by 0.119 MPa. Due to the existence of a PM in the combustion chamber and for such a reason that it possesses high heat capacity and usually a temperature lower than the gas inside the chamber, the temperatures of all the states converge towards a certain temperature that is the very temperature of the PM. 5.4. The effect of the mean pore’s diameter of PM In this state, the PM is assumed with a fixed 90-percent porosity and only the mean pore’s diameter of the PM is changed. The fuel is decane and lambda value equals to 1.7. Both the gas and PM have a temperature of 500 °C. The mean pore’s diameter of the PM ranges from 8 to 20 ppi and the mean pore’s diameter corresponding to each state has been written in front of it in millimeter. Fig. 7 demonstrates the effect of
5.5. The effect of porosity of the PM In this section, assuming a fixed mean pore’s diameter, the PM porosity percentage is changed so as to evaluate its effect on the
Fig. 6. Gaseous mixture initial temperature effect. 312
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Fig. 7. Mean pore’s diameter effect.
fuels for the same lambda 1.6 on temperature profile, are compared. It can be understood from the study of the Fig. 9 that for all of the fuel types, increasing the lambda value by adding mass of the air in the combustion chamber, maximum temperature of the gas decreased. Also for all fuels (except hydrogen) increasing lambda causes reduction in the main combustion time. According to Table 1 for hydrogen combustion it is obvious that, oxidizer concentration exponent (n) is lower than fuel concentration exponent (m), hence fuel concentration has more effect than air concentration. So, the hydrogen profile’s temperature differs from the others fuel profile’s temperature. It is disclosed from Fig. 9 combustion delay for methanol and hydrogen are approximately close but maximum temperature of methanol is about 101 °C higher. Methanol and hydrogen have lower ignition delay in comparison with the other studied fuels. Propane and ethanol are close in term of the ignition delay but ethanol’s maximum temperature occurs about 0.3 milisecond lower than propane. On the other hand, the temperature profiles of decane and isooctane are very similar in terms of ignition delay and also maximum value of temperature.
gaseous phase changes of temperature and pressure inside the chamber. In the present study, the solid and gaseous phases have the same temperature, i.e. 500 °C, and the fuel is decane and lambda value equals to 1.5. The PM has a porosity in a range from 80% to 95%. Fig. 8 depicts the effect of PM’s porosity percentage variations on the pressure and temperature inside the chamber in a time unit. It can be understood from an investigation of the curves that the increase in the porosity makes the combustion behavior approach the free flame state. The increase in the porosity percentage is equal to the increase in the gaseous phase’s share of the combustion chamber and the reduction of the solid phase’s quotient therein. The result of increasing the porosity percentage, as well, would be the reduction in the energy storage area in the PM and increase in the pressure inside the chamber. Also, the more the porosity percentage is increased the lesser the time required for the initiation of the combustion due to the transferring of lesser heat to the PM. According to the Fig. 8, it can be seen that the maximum relative pressure will be increased by about 0.152 MPa and its corresponding delay will be about 0.9 ms with the increase in the porosity from 80% to 95%, it also causes the maximum temperature inside the combustion chamber to be increased from 771 °C to 842 °C. The main reason behind this increase in temperature and pressure is the reduction in the energy storage in the solid.
6. Conclusion The present study deal with the modeling of combustion in a constant-volume chamber featuring PM, through considering a PM chamber, to thermodynamically solve the single-step combustion and energy equations at the same time for solid and gaseous phase and radiation just for the solid phase. The study examined the effects of such parameters as initial gas pressure, the initial gas and PM temperatures, the PM’s percentage of porosity, mean pore’s diameter of the PM as well as the effects of such fuels as hydrogen, propane, methanol, ethanol, isooctane and decane on combustion and also sensitivity analysis of the code. The followings are the simulation findings:
5.6. The effect of the fuel type In this section, fuels such as hydrogen, propane, methanol, ethanol, isooctane and decane have been studied under fixed initial conditions. The initial temperature of the gas and PM for all of the state is 475 °C and PM porosity is 90% with pore density 8 ppi. The effect of the lambda variations from 1.4 to 2.0 on the temperature of the combustion chamber have been investigated. In addition, the results of the various
Fig. 8. Porosity percentage effect. 313
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Fig. 9. Effect of the fuel type.
(1) Assuming a fixed initial temperature of the PM and the gas mixture, when the initial pressure was higher, the lesser time required for the combustion. Also, higher initial pressure rates were accompanied by lower maximum temperatures inside the chamber. The effect of the initial pressure on the intra-chamber maximum relative pressure was low and almost negligible. (2) Assuming a fixed gas temperature, the higher PM’s temperature causes lesser delay in the combustion initiation. On the other hand, the increase in the initial temperature of the PM caused increase in the maximum temperature and pressure inside the combustion chamber. (3) The maximum temperature inside the combustion chamber is reduced with the decrease in the mean pore’s diameter (increase in the pore’s density). Also, the temperature increase curve enjoys a milder slope up to the point where the temperature inside the chamber peaks and this is indicative of the idea that the combustion distances away from the explosive-like state and flame is more smoothly released. The effect of the mean pore’s diameter reduction
is displayed in the form of more delay in the main combustion initiation. (4) The combustion behavior gets closer to the free flame state with the increase in the porosity percentage. Assuming fixed temperature of the two phases and also fixed mean pore’s diameter, the increase in the porosity causes increase in the maximum temperature and pressure inside the chamber. In terms of the time required for the initiation of the combustion, the increase in the solid phase quotient causes a slight delay in the combustion time. (5) It is understandable with investigation of different fuels that, combustion in PM chamber may not be effective enough with fuels with explosive behavior and low ignition delay such as hydrogen. References [1] F. Durst, M. Weclas, A new type of internal combustion engine based on the porousmedium combustion technique, Proc. Inst. Mech. Eng., Part D: J. Automobile Eng. 215 (1) (2001) 63–81, https://doi.org/10.1243/0954407011525467. [2] F. Durst, M. Weclas, A new concept of IC engine with homogeneous combustion in
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