1. Introduction
The reduction in exhaust gas emissions has become a critical issue in diesel engines due to environmental problems around the globe. Strict emission regulations are, therefore, imposed on diesel engines by many countries for passenger cars, trucks, marine machineries, and construction machineries. Particularly for construction machineries, in Europe and the U.S., Post Stage-V and Tier 5 regulations will be phased in, which would restrict NOx emissions strictly in cold operating conditions [
1,
2].
The urea-SCR system is one of the most popular after-treatment systems for the NOx reduction in diesel engines [
3,
4]. It injects the urea–water solution (normally composed of 32.5% urea and 67.5% water) into the exhaust gas and induces the evaporation and thermal decomposition of the urea–water solution by the thermal energy of the exhaust gas that forms ammonia (NH
3), as shown in Equation (1).
The ammonia can be used as the reduction agent of NOx so that the final emission products through the tailpipe can be nitrogen (N
2) and water (H
2O), as shown in Equations (2) and (3).
The evaporation and decomposition performance of the urea–water solution is affected by the atomization of urea–water sprays [
4,
5,
6]. In conventional urea-SCR systems, advanced injection strategies and mixers have been widely employed to promote the atomization and local homogeneity of urea–water sprays [
4,
5,
6,
7,
8]. On the other hand, the exhaust gas temperature is another critical factor affecting the evaporation and decomposition performance of urea–water sprays, which becomes inferior in cold operating conditions [
9,
10].
The EHC has been introduced as a measure to increase the operating temperatures of three-way catalysts (TWCs) in gasoline engines during the cold start [
11,
12,
13]. It has also been applied to diesel oxidation catalysts (DOC) and urea-SCR systems to enhance the evaporation and decomposition performance of the urea–water solution, particularly in cold start conditions by increasing the exhaust gas temperature [
14,
15,
16,
17]. The evaporation and decomposition performance can be further enhanced by injecting the urea–water solution directly into the heater in the EHC so that the thermal energy of the heater can be used.
Considerable previous studies have investigated the chemical processes and temperature regimes associated with the evaporation, thermal decomposition, and undesired deposit formation of urea–water sprays for urea-SCR systems [
18,
19,
20,
21,
22,
23,
24,
25,
26,
27]. The evaporation of urea–water droplets can be initiated at 373 K, which is the saturation temperature of the water at the atmospheric pressure. The droplet evaporation time can become shorter upon the increase in surrounding gas temperature and the decrease in urea–water droplet size [
18,
19,
20,
21]. The thermal decomposition of urea can be initiated at a temperature over 410 K and forms the biuret and cyanuric acid in order based on the progress of decomposition [
18,
19,
20,
21,
22,
23,
24]. The completion temperature of urea decomposition varies based on the residence time of the feed gas stream. For example, the complete thermal decomposition of urea can be achieved at the temperature of around 623 K when the residence time of the feed gas stream is 0.1 s [
24]. The formation of urea deposits is governed by the wall film temperature and urea concentration of the urea–water solution. The composition of urea deposits varies with the wall film temperature based on the progress of thermal decomposition [
25,
26,
27].
The results of previous fundamental studies can be referred to for the optimized design and control of EHC-based urea-SCR systems in various operating conditions such as exhaust gas temperature and flow rate, and electric power supplied to the heater. To accomplish the complete evaporation and decomposition of urea–water solution without the formation of a urea deposit, the thermal conditions in the EHC such as surface temperature and exhaust gas temperature distribution should be characterized first so that the accumulated knowledge of previous studies can be linked and used for the optimization of EHC-based urea-SCR systems. Particularly for the urea-SCR system adopting the direct injection of a urea–water solution to the EHC, the surface temperature distribution of the EHC becomes the most critical factor that must be characterized.
Figure 1 illustrates the structure of the EHC-based urea-SCR system which injects the urea–water solution directly into the heater. The EHC has a circular outer shape and contains a bundle of thin corrugated heater foils. The heater foils are rolled and stacked to maximize the effective area of heat transfer between the heater and exhaust gas which forms the fine flow cells inside the EHC. The size and structure of flow cells determine the flow conditions and convective heat transfer between the heater surface and exhaust gas, which in turn determine the heater surface temperature and outflowing exhaust gas temperature. It is a quite difficult task to characterize the heat transfer characteristics in the EHC in various geometric and operating conditions due to the complicated internal structure of the EHC.
Applying the three-dimensional (3D) computational fluid dynamics (CFD) can be considered to perform this kind of flow and heat transfer analysis in the EHC, but there are some challenges to applying the CFD. First, CFD is time-consuming and expensive, particularly for the flow analysis in complicated fine structures, since it requires extremely small grid sizes to resolve the physical phenomena. Second, it is difficult to select and combine the proper models since too many parameters are engaged in the models, so the verification and calibration of model prediction results are troublesome. Last, it is difficult to investigate the effects of various geometric and operation parameters in a systematic and efficient way, which is needed for the model-based design and control of the EHC. In that sense, simplified one-dimensional (1D) theoretical models can be suitable for that purpose if the prediction accuracy of the models is acceptable. The 1D modeling works have been performed previously for the EHC system coupled with a three-way catalyst (TWC) in gasoline engines [
11,
12,
13]. However, the studies mostly focused on the analysis of the catalyst temperature distribution inside the TWC, not in the EHC. The EHC has been regarded merely as a heat source for the TWC. Up to now, little attention has been paid to analyzing the thermal conditions in the EHC, which exert a critical impact on the evaporation and thermal decomposition of urea–water droplets, particularly in EHC-based urea-SCR systems adopting the direct injection of a urea–water solution to the EHC.
The current study introduces a 1D analysis scheme to characterize the heater surface temperature distribution in the EHC in various EHC geometric and operating conditions such as the flow cell diameter and length of the EHC, electrical power supply to the EHC, and exhaust gas temperature and flow rate in the EHC inlet. The energy conservation and conventional theories of forced internal convection are employed as base models for the 1D analysis with assumptions of steady-state operation, uniform heat flux from the heater to the exhaust gas, negligible thermal resistance of the heater, and constant fluid properties [
28,
29]. To implement the analytical approaches to the EHC with complicated structures, a tiny flow cell in the EHC is extracted for the analysis. The analyzed surface temperature results at the EHC outlet are compared with the measurement results to validate the adequacy of the analysis platform and the accuracy of prediction results. Then, the effects of various geometric parameters and operating conditions on the surface temperature distribution in the EHC are analyzed and discussed. The originality of the current study lies in the introduction of an analysis scheme to characterize the thermal conditions inside the EHC in a systematic and efficient way, and the analysis and discussion of the effects of geometric and operation parameters on the thermal conditions in the EHC that have not been thoroughly investigated in previous studies.
3. Measurements
Experiments were performed to measure the heater surface temperature distribution at the EHC outlet (
), and a picture of the experimental setup is presented in
Figure 5a. Simulated exhaust gases were generated by the ultra-lean combustion of liquified petroleum gas (LPG). The LPG was used for the generation of exhaust gas to control the exhaust gas flow rate and temperature with more ease because with the premixed combustion, it is easier to control those parameters. The premixed LPG combustion was performed in a constant volume chamber to control those parameters by varying the supplying flow rates and equivalence ratio of the LPG–air mixture in the chamber. The exhaust gas temperatures were measured in front of the EHC using a thermocouple. The heater surface temperature distributions were measured in the EHC outlet using an infrared (IR) camera (FLIR Systems Co., Ltd., Wilsonville, OR, USA, THermaCAM S65) after the surface temperature reaches a steady-state condition. Unfortunately, the surface temperature distribution at the EHC inlet is not measurable because the EHC inlet is invisible due to the existence of an exhaust pipe. The temperature measurement results of the IR camera at four locations of the EHC outlet (black cross-marks in
Figure 5b) were averaged to obtain the representative temperature result at each condition.
Table 2 shows the measurement conditions of heater surface temperature at the EHC outlet. The measurement variables are
,
, and
. Due to the control difficulties of
and
from the simulated exhaust gases, the measurements were performed in limited conditions. The
and
of the EHC used for the measurement were 2.7 mm and 20 mm, respectively. The
of 20 mm was chosen to estimate the validity of model prediction results in the marginal condition in which the effect of
might appear (see
for each condition in
Table 2). The data are used for the model validation, and the results are presented in the following section.
The local average and deviation results of
measured using the IR camera are presented in
Figure 6. The results show that the local deviation of
is a maximum of 8.64% in the measurement conditions, which demonstrates the local uniformity of
. This near-uniform surface temperature distribution can be from the uniform heat generation of the heater and the negligible stray heat transfer from the EHC to the surroundings. It implies that the current analysis scheme and model simplifications are adequate.
4. Results and Discussion
In this section, the adequacy of 1D prediction results is discussed first by comparing them with the measurement results. Then, the effects of EHC geometric ( and ) and operation parameters (, and ) on distribution in the EHC are presented and discussed based on the 1D analysis results.
4.1. Validation of 1D Analysis Results
Figure 7 compares the prediction and measurement results of
in the conditions given in
Table 2. The error rates of the prediction results are also presented. For the simplicity of 1D model analysis, the properties of exhaust gases are assumed as those of air since the properties of simulated exhaust gases are quite close to those of air in the ultra-lean combustion conditions (maximum 3%, 8%, and 7% difference in Pr,
k, and
ρ in given flow conditions).
The results show that, in general, the predicted
from the 1D model matches quite well with the measurement results, but the error rate increases with the increase in
, especially at the high flow rate condition (see
Figure 7b). The increased error at the high
condition can result from the increased heat loss to the surroundings due to the higher temperature of the EHC and housing. However, the error rates in the applied conditions are limited to a maximum of 5%, which indicates that the 1D analysis scheme suggested in the current study has over 95% reliability in the operating conditions of the 4L class heavy-duty diesel engine. This reliability would increase further for the smaller engines in which exhaust gas flow rates and maximum applicable heater powers are lower.
4.2. Effects of EHC Geometric Parameters on Surface Temperature Distributions
Based on the proven reliability, the effects of EHC geometric parameters such as and on the surface temperature distribution are discussed based on the 1D analysis results.
Figure 8a presents the effect of
on the surface temperature distribution in the EHC. The results in a fixed condition of the other parameters (
= 800 L/min,
= 473 K,
= 2 kW,
= 50 mm) are only presented here since the results trend of
effect appears equivalent regardless of the condition. The results show that
does not affect the slope of the surface temperature with
x in the fully developed condition. As shown in Equation (9), the slope of
is linearly dependent on
.
has a linear relationship with
, which is proportional to the square of
. Based on Equation (5),
is proportional to
because
is proportional to the square of
, as shown in Equation (15). Thus, the slope of
in Equation (9) becomes independent of
. On the other hand,
-intercept in Equation (9) increases upon the increase in
since
is proportional to
. As a result, the larger
causes a higher
in the fully developed region. However, the increase in
is only around 40 K even with a nearly 3 times larger
. The effect of
on
is insignificant due to the substantially high
in the inlet (
), although the
increases linearly upon the increase in
(see Equation (9)).
Figure 8b presents the effect of
on the surface temperature distribution in the EHC. Only the results in a fixed condition of the other parameters (
= 800 L/min,
= 473 K,
= 2 kW,
= 2.7 mm) are presented. The results show that the slope of
decreases with the increase in
because the
, the only factor affecting the slope in Equation (9), is inversely proportional to
, as shown in Equation (5). The decrease in the slope and
causes the lower
at longer
in all regions of the EHC. Again, the effect of
on
is insignificant due to the substantially high
in the inlet (
).
Overall, the effect of appears to be much more critical on the surface temperature distribution compared to that of . The most relevant factor associated with this result trend is , which represents the heat generation potential of the heater material. The results indicate that reducing the can be effective to increase the heater surface temperature in the fixed and conditions. However, it should be confirmed when applying the short if the heater material has sufficient durability against the high heat load.
4.3. Effects of Operation Parameters on Surface Temperature Distributions
The effects of operation parameters such as
,
, and
on surface temperature distribution in the EHC are investigated for the EHC with
of 2.7 mm and
of 20 mm.
Figure 9a presents the effect of
and
on
and
in the fixed
of 523 K. The
is not varying with
because the
-intercept in Equation (9) is independent of
. On the other hand, the
decreases with the increase in
because the slope in Equation (9) is inversely proportional to
(or
). The larger
causes the higher
and
, but the degree of increase appears much larger for
.
Figure 9b presents the effect of
and
on
and
in the fixed
of 800 L/min. The higher
increases both
and
, and the increase rate against
appears almost identical for
regardless of
. This is because the
is placed in the
-intercept and does not affect the slope itself in Equation (9). The effect of
appears in a similar fashion to that in
Figure 9a.
An interesting point to discuss here is that the increase in is not as significant as that of in all conditions. Even with the application of maximum allowable heater power (2 kW), the increase rate of is only limited to 8.5% in its maximum. It indicates that the impingement location and jet-wall interaction of urea–water injection in the EHC should be carefully designed not to place the large portion of urea–water droplets near the EHC inlet in which the evaporation of urea–water solution would be inferior, and the possibility of urea deposit formation would be high.
4.4. Discussion
In the above sections, the 1D analysis scheme characterizing the surface and exhaust gas temperature distribution in the EHC is introduced, which is based on energy conservation and conventional theories of forced internal convection. Novel approaches have been applied to extract the tiny flow cell in the EHC for the analysis and scale the gas flow rate and heater power to the flow cell based on known operation factors. Although some assumptions and simplifications are applied in the 1D analysis, the validation results show a high prediction accuracy in the operation conditions of the 4L diesel engine. The prediction accuracy of this analysis scheme would be further guaranteed for the smaller size engines. Even for the larger size engines, the analysis scheme can be used, but the effect of different flow conditions should be considered because the flow rate (
) can become higher and the flow cell diameter (
) can become larger. In that case, the flow condition can be changed to turbulent due to the larger
. Even in the turbulent flow conditions, the same analysis scheme can be applied, but the
should be newly defined. The Dittus–Boelter equation presented in Equation (20) or the other correlations can be used to define the
in the turbulent flow conditions [
31,
32].
The 1D analysis scheme can analyze the effect of various geometric and operation parameters on the thermal conditions in the EHC in a systematic and efficient way. The operation map can be built shortly based on the 1D analysis scheme that can be used to determine the optimized condition in various operating conditions to accomplish the complete evaporation and decomposition of the urea–water solution, and to avoid the formation of urea deposit. For that purpose, the 1D analysis scheme can also be coupled with the prediction models of evaporation and decomposition of the urea–water solution, and urea deposit formation.