Abstract
Low-pressure exhaust gas recirculation (LP-EGR) systems are applied to diesel engines because they reduce nitrogen oxide emission by lowering the internal temperature of the cylinder by mixing the oxides with intake air. However, low-temperature ambient conditions include a large amount of vapor in the mixed gas flowing into the intercooler; when heat is exchanged, the water vapor condenses and is adsorbed on the surface of the intercooler fin to form a liquid film. Condensation occurs as the thermal resistance between the vapor and solid surface increases with the thickness of the liquid film and causing a corrosion due to condensation of the surface. In this study, the amount of condensation was predicted through calculations based on thermodynamic studies. Factors that can cause condensation inside the intercooler (fuel, air, and LP-EGR) were selected as variables. A mathematical formula was established to predict the convergence form of condensation or the amount of condensation over time at various temperature and relative humidity conditions. The formula predicted the condensation amount in the intercooler of the diesel engine, compared it to the actual amount of condensation in the test evaluation with an error of less than 4%. Additionally, because the formula can predict the amount of condensation by changing the heat exchange area of the intercooler, the application range of the formula was expanded to predict the condensation in the intercoolers of gasoline vehicles with different heat exchange areas and fuel types. The condensation error was within 2%, indicating a high consistency. Validation of the formula predicts a reliable amount of condensation under various operating and ambient temperature conditions, which means that both the time and cost of the test evaluation require the determination of the cause before solving the actual condensation problem.
1. Introduction
The threat of climate change because of carbon emissions is rising; the carbon dioxide emitted by burning fossil fuels leads to the greenhouse effect [1]. U.S. economist William Dawbney Nordhaus estimated a temperature increase of less than 2°C to achieve carbon neutrality. Global policy-making aimed to achieve carbon neutrality has been on a surge [2]. In particular, the automobile industry is reducing carbon emissions to achieve zero emission as per the regulations introduced by the European Union. Figure 1 shows that enhanced regulations for nitrogen and carbon emissions from diesel engines were applied as of 2014 [3]. As the regulations become stricter, diesel engines require an exhaust gas recirculation (EGR) system that recirculates the exhaust gas to reduce nitrogen oxide emission. The EGR systems facilitate exhaust recirculation by applying high-pressure exhaust gas recirculation (HP-EGR) or low-pressure exhaust gas recirculation (LP-EGR) [4, 5]. LP-EGR involves passing a gas through the turbocharger, mixing it with the charged intake air, and flowing into the combustion chamber. Mixed gases aid in reducing nitrogen oxide emission and improving fuel efficiency by lowering the internal temperature of the combustion chamber [6]. In addition, LP-EGR has been applied to gasoline direct injection (GDI) to reduce knocking in gasoline engines because it is effective in controlling combustion owing to its low turbocharger efficiency and excellent mixing with air [7, 8]. However, because humid air from the ambient environment and the LP-EGR system contains water vapor, some problems arise when a mixed gas is introduced into the vehicle [9]. Therefore, the charge air cooler (CAC) and intercooler, which are heat exchanger auxiliary devices of an internal combustion (IC) engine into which a high-temperature mixed gas is introduced, carry water vapor. Recently, heat exchangers have been required to maintain efficiency and durability; however, there are various disadvantages owing to internal water vapor and difficulties, such as loss of function [10–13]. Gürbüz et al. performed a series of tests on the exhaust waste heat recovery using a thermoelectric generator (TEG) in a propane-fueled spark-ignition (SI) engine. In this paper, ensured the evaporation of propane and to increase the temperature differences by increasing the cold surface activity of TEG, creating a novel design by placing copper serpentine pipes in each Ec_hex to allow propane to pass through the TEG [14]. Ahmet Baturalp and Habib analyzed the heat exchangers having different fin number and arrangement by computational fluid dynamic method. This paper had introduced the surface temperature and distribution of hot side (exhaust) heat exchanger in the thermoelectric generator where electrical energy is generated from the exhaust waste heat energy of the spark-ignition engine. According to the results of the computational fluid dynamic analysis performed for the designed exhaust exchanger arrangement, the reverse direction serial plate arrangements having six flow guiding fins and 15°, 30°, and 45° angled raindrop geometries have more optimum values in terms of heat exchanger surface temperature, distribution, and pressure drop in the exchanger compared to other models [15]. Warey et al. focused to investigate whether surface condensation of water vapor could be used to remove the accumulated deposit mass from various types of deposit layers typically encountered in EGR coolers. This study shows that the surface condensation of water vapor can lead to significant removal of certain deposit layers from the cooler walls and, thus, mitigate fouling of the EGR cooler. It could be used as regeneration strategy for periodic on-board regeneration of fouled EGR coolers [16]. Although the role of an intercooler is to cool the high-temperature mixed gas introduced through the compressor of a turbocharger to improve fuel efficiency and power, the vapor content in the mixed gas decreases below the saturation temperature during heat exchange in low-temperature environment, causing a phase change. The phase change forms a liquid film by adsorbing the condensation on the inner wall surface of the intercooler. As the thickness of the liquid film increases, it acts as a thermal insulation between the water vapor and the solid surface. Consequently, the heat exchange efficiency of the intercooler deteriorates, and the temperature of the mixed gas is not sufficiently reduced. Furthermore, some residual condensation flows into the combustion chamber, causing surface corrosion and misfiring of the engine. Thus, it has been identified as a prime cause of the deteriorating combustion performance. Therefore, as the condensation in heat exchangers is becoming an issue for various industrial groups, advanced research is required for its academic understanding and analysis.
Liu et al. conducted experiments to characterize the effect of initial ice roughness on an aircraft model by measuring the thickness distribution of dynamic water and ice flow on the surface of airfoil wings and observed that the ice roughness formed on the surface of the initial wings delays and shortens the primary wave formation in the water film flow [17]. Nakakita et al. presented a model for predicting the approximate flow of fluid on an aircraft wing surface and introduced the model and an extensive ice-shaped path in aeroicing simulations to predict the effects of moisture content, droplet size, and pressure elevation [18]. Yue et al. studied the high-humid aerodynamic effect on the performance of marine wind turbine blades through computational fluid dynamic (CFD) analysis and found that the condensation around the edge of the blade causes higher drag, which results in turbine performance degradation [19]. Hochart et al. conducted a study on the performance of wind turbines under condensation conditions and explained that the installation of only one-third of the blade ice-making system could avoid freezing, maintain 90% of the blade aerodynamic performance, and reduce heat energy costs [20]. Most studies in the aviation industry and wind power facilities using turbines have the problem of frozen condensation on the wing and blade surfaces exposed to external environments; therefore, the identification of these characteristics and phenomena of condensation is the primary motive.
In addition, various studies have been conducted on industrial groups using air-conditioning and refrigeration systems. Shin and Ha conducted a study on water behavior owing to condensation at the contact angle at the surface in various fin-tube heat exchangers and concluded that the water adsorption rate could be considerably reduced by improving the hydrophilicity of the surface and designing the heat exchanger with fewer fins [21]. Briggs and Bui conducted a study on the vapor condensation of supercooled liquid columns applied to the thermal design of shell-tube condensers and observed the change in condensate temperature by varying the distance between two consecutive tubes [22]. Wang et al. emphasized that low-temperature corrosion is a key factor influencing the performance and stability of heat exchangers for industrial waste heat recovery systems and selected the acid dew-point temperature and vapor condensation properties as key parameters for conducting numerical studies on acid condensation and corrosion properties on three-dimensional fine-tuned surfaces. By studying the effects of the variables, it was confirmed that the inflow rate of the tube gas and concentration of acidic vapor affected the acid dew point, and the temperature of the tube wall and the concentration of water vapor affected the concentration of the condensed acid solution [23]. Previous studies in the field primarily focused on reducing condensation and the variations in condensation deposited inside and outside the heat exchanger.
In addition, various numerical and experimental studies have been conducted because the EGR cooler, a heat exchanger of vehicles, affects the combustion control depending on the fin type and condensation strength of the hydrocarbon series. Serrano et al. conducted a study to develop and validate a three-dimensional CFD simulation model that could predict water condensation in a mixture of air entering the T-joint of an LP-EGR. A sensitivity study of the angle of intake throttle valve was conducted to obtain quantitative and qualitative results from the model validation for condensation occurrence [24, 25]. In particular, Han et al. conducted a study on the effect of hydrocarbon condensation on the pollution of the EGR cooler and heat exchange efficiency and suggested a temperature corresponding to the stabilization of condensation at various hydrocarbon contents (ppm). It was found that a high contamination density of hydrocarbon condensation improved the heat exchange efficiency [26]. To observe changes in the evolution of deposits on the side of the EGR cooler, Paz et al. analyzed the local thickness, roughness, and density of the contaminated layer during hydrocarbon condensation and found that the thickness of the contaminated layer decreased in the area near the outlet early in deposit formation when high hydrocarbon concentrations were considered. Hydrocarbon condensation in the early stages was 1.9 times higher than the density of deposits produced over a long period [27]. In addition, H. Song and S. Song used a one-dimensional engine simulation to build a real-time condensation model based on heat transfer analysis around the intercooler and optimized a dual-loop EGR control strategy to reduce nitrogen oxides. In addition, by performing a worldwide harmonized light-duty test process simulation, results were obtained for reducing condensation and increasing fuel consumption efficiency [28]. Previous studies on the occurrence of condensation in vehicles have primarily been conducted from a local perspective of each major component. However, compared to the other areas in which condensation is actively studied, most of the research has been conducted to identify and avoid condensation rather than solving the problem itself from the perspective of the vehicle engine; therefore, the available research on condensation issues is insufficient. As a result, a mathematical approach is required to observe the condensation occurring inside the intercooler from the perspective of the vehicle engine, and efforts are required to predict the amount of condensation over time under transient conditions.
The subject vehicle has the problem of condensation inside the intercooler in an environment with ambient low temperatures, and over time, the occurrence of condensation tends to converge owing to the efficiency degradation of the heat exchanger. Before physically solving these field claims, a mathematical approach is required, and thermodynamic equations that can encompass the overall system of the vehicle are applied to predict the amount of condensation occurring inside the intercooler. The aim is to establish a generalized formula capable of predicting condensation in various heat exchangers. This paper is continuous with the research of this research team conducted previously [10]. However, the differentiation from the previously conducted research results is as follows. Previous studies dealt with the flow phenomenon in front of the compressor based on a calculation formula model, not the CFD approach. In addition, if existing research was conducted only on diesel engines, this study established as calculation formula model for diesel engines. Furthermore, after expanding to a gasoline engine and applying it, its consistency was compared and analyzed.
In this study, various operating conditions were selected to consider the combustion characteristics at which the lambda is high in the operation area where the frequency of the diesel engine is high. When the air containing water vapor flows into the intercooler in a low-temperature environment, the relative humidity is considered to confirm the characteristics of condensation generation. The molecular formula of the LP-EGR containing water vapor was determined through mass balance, and the condensation tendency was determined according to the LP-EGR ratio among the mixed gases flowing into the intercooler. In addition, the generating factor of condensation was transformed into a function to which temperature variables were applied, and the characteristics of the change in the cumulative amount of condensation over time were confirmed. Finally, the calculation formula was completed using a mathematical approach for evaluating the amount of condensation in the intercooler of a gasoline engine to confirm its applicability to the changes in various types of intercoolers and fuel species. Figure 2 presents an overview of this study. The first process involved a vehicle test evaluation of the company target engine, which confirmed the occurrence of condensation inside the intercooler, and thus, hourly condensation generation data were obtained. In the second process, a modification was performed to predict condensation generation through thermodynamic correlation based on the condensation generation data, and its validity was verified by establishing a generalized mathematical formula for predicting condensation. Finally, the amount of condensation other than the test evaluation was predicted, and the accuracy of the mathematical formula was obtained through additional comparison.
2. Materials and Methods
2.1. Experimental Method
The target engine with four cylinders (2.0 L) and a diesel engine with a high compression ratio of 16 : 1 was selected; the detailed specifications of the engine are listed in Table 1.
This study secured data on diesel engine vehicles using a dynamometer. Fuel meter and temperature conditioner set of AVL was used to measure the flow rate and temperature of fuel. For accurate flow measurement and exhaust analysis of EGR gas, HORIBA’s MEXA 7500DERG system was used, and exhaust gas can control temperatures in the range of -35°C to 60°C. In addition, D2t OSIRIS is used as a combustion analysis equipment to secured data generated from combustion inside the cylinder, such as the engine’s maximum pressure and indicated mean effective pressure. All flow rates are controlled through the flow by gas meter of ALV. The flow rate measurement range is 0.2~2,400 L/min, and the measurement error is less than 1.5%, indicating high accuracy. Data collected by measuring all physical phenomenon are sampled as signals and converted into digital forms through DASAN’s Automation DAQ system. To confirm the occurrence of condensation in a low-temperature environment, a driving environment was constructed by mounting a vehicle in a wind tunnel facility capable of controlling temperature and relative humidity, as shown schematically in Figure 3.
Table 2 lists the operating area conditions measured during the test to complete the mathematical formula. Three operating conditions were considered with constant speed: 1300 rpm and 80 kmph, 1500 rpm and 60 kmph, and 1620 rpm and 100 kmph. In addition, 58.9 kg/h of air flow rate and 7.64 kg/h of LP-EGR mass were measured at 1300 rpm; approximately 78.6 kg/h of air flow rate and 11.5 kg/h of LP-EGR mass were measured at 1500 rpm, and 97.7 kg/h of air flow rate and 14.4 kg/h of LP-EGR mass were measured at 1620 rpm. The vehicle’s speed, air mass, and LP-EGR mass were performed through engine dynamometer experiments and measured at the front and rear ends of each component to received data.
Figure 4 shows the operating conditions for each ambient temperature and relative humidity (R/H) applied in the test evaluation. The loads for the operating conditions of 1300 rpm, 1500 rpm, and 1620 rpm are marked with red points. The test evaluation of 1300 rpm was done under two operating conditions: ambient temperatures of 0°C (R/H 100%) and 5°C (R/H 88%). The test evaluation of 1500 rpm was done under four operating conditions: with ambient temperatures of -3°C (R/H 100%), 5°C (R/H 88%), 10°C (R/H 45%), and 15°C (R/H 25%). Finally, the test evaluation was conducted at two ambient temperatures, 0°C (R/H 100%) and 10°C (R/H 45%), under 1620 rpm, and the test evaluation was conducted at eight points. Gray represents the point at which additional condensation is predicted after establishing the calculation formula. In addition, for the test evaluation, the vehicle was driven for 3 hours at each point, and the condensation generation data were collected by draining the water and removing the intercooler hourly. The characteristics of the condensation generation data show a tendency for condensation generation to converge over time under the corresponding operating conditions. This is because when the mixed gas passes through the heat exchange area inside the intercooler, the heat exchange efficiency decreases owing to the film condensation, and the amount of condensation decreases after a certain period. Therefore, a mathematical approach is required to predict not only the amount of condensation generated over time but also the convergence phenomenon of condensation.
2.2. Mass Balance and Formula Set-Up
Because data corresponding to the operating conditions, such as the air flow rate and LP-EGR mass, were measured using a flow meter, it was necessary to maintain the mass balance of the IC engine under each operating condition for establishing a generalized equation for predicting the occurrence of condensation. Figure 5 shows the IC engine circulation diagram based on a diesel engine in terms of mass flow through which the mass balance can be confirmed by focusing on the mixed gas flowing into the intercooler. From the view point of combustion, the mass balance is summarized in Equations (1), (2), and (3). The ratio of LP-EGR in fuel to that in air was determined by assuming that the molecular composition of reactants is the same as CO2, O2, H2O, and N2. This was later used to determine the state of each LP-EGR molecule in the product of the combustion reaction.
The mass flow rate flowing into the intercooler was calculated as follows:
The system is explained through mass balance, and it is necessary to formulate a mathematical formula. Therefore, the mathematical formula for condensation prediction in the intercooler was formulated in the order of output parameter, calculation sheet, and output data and can be understood through the schematic diagram in Figure 6.
Input parameter describes the operating conditions, ambient conditions, and heat exchanger conditions. This is a necessary parameter when calculating through a thermodynamic equation based on a mass balance. The first operating conditions require RPM, fuel mass, air mass, and HP/LP-EGR mass. In addition, fuel species can be selected to obtain a chemical reaction formula for combustion, and this study applied the C12H24 molecular that is most suitable for simulating diesel fuel. In the second ambient conditions, the pressure of the ambient air (kPa), the temperature of the ambient air (°C), and the relative humidity (%) of the surrounding air are needed. This is an important factor in which the temperature and humidity contained in the air in the atmosphere affect condensation changes and constitutes an environment necessary for research through the temperature and humidity controller of the wind tunnel test. Third, the heat exchanger conditions are described. It specifies the components to which condensation occurs, and the required data are the front and rear pressure (kPa) and the temperature (°C) of the front and rear of the intercooler. And the most important parameter in the heat exchanger condition is the heat exchanger area (m2). The heat exchanger area means the area through which the mixed gas with air and EGR gas pass in the intercooler, and in this calculation formula, it means the area of the tube and the fin in the tube, excluding the area at the entrance and exit of the intercooler. The intercooler measured the internal area using the inventor tool.
The first input parameter describes the operating, ambient, and heat exchanger conditions. Operating conditions were applied to the engine characteristics by expressing the RPM, fuel mass, air mass, HP/LP-EGR mass, and fuel specifications. In particular, the most suitable C12H24 molecular formula for the chemical reaction was applied to simulate the fuel type of the diesel engine. Ambient conditions include the pressure, temperature, and relative humidity of the surrounding air. In addition, the front/rear pressure, temperature, and heat exchange area of the intercooler can be expressed under the heat exchanger conditions. The next step is calculation sheet; the LP-EGR molecular formula was derived through the lean combustion reaction equation and the mass balance of the diesel engine. The molecular formula of the mixed gas flowing into the intercooler was primarily determined by the sum of the air molecular formula calculated under ambient conditions. Subsequently, the saturation temperature at which condensation occurred was calculated based on the mole fraction of H2O in the mixed gas molecular formula and organized to predict the condensation. Therefore, it is possible to verify the molecular formula of the mixed gas flowing into the intercooler and the amount of condensation generated per hour using the final output data.
2.3. Determination of Molecular Formula and Condensation Equation
The second step in the formula for predicting the amount of condensation is to derive the molecular formula of the mixed gas flowing into the intercooler. The mixed gas molecular formula is the sum of the air and LP-EGR molecular formula, each of which uses thermodynamic equations for pressure, temperature, and relative humidity to determine the number of states in the molecules. Based on the Clausius–Clapeyron equation, the partial pressure () of saturated water vapor in the air is calculated using the temperature () and relative humidity () of the ambient air [29].
As the total humid air is assumed to be the sum of water vapor and dry air, the mass of water vapor in the humid air can be calculated using absolute humidity; the formulas for absolute humidity () and water vapor mass () are described in Equations (7) and (8).
Using these formulas, the mass of water vapor in the air can be obtained, and it is assumed that dry air (excluding water vapor in the total air content) consists of oxygen and nitrogen. In particular, the mass of oxygen and nitrogen in dry air was determined by applying a mass ratio of 23.2% oxygen and 76.8% nitrogen using Equations (9) and (10) to determine the molecular formula of the mixed gas flowing into the intercooler.
The following process determines the molecular formula of LP-EGR in the emitted gas through the combustion reaction equation, and the ratio of LP-EGR can be obtained through the combustion reaction equation of only the fuel mass and air mass using the previous mass balance. Because diesel engines pursue combustion under conditions in which the equivalence ratio is lean, lean combustion containing water vapor is applied; the combustion reaction formula when the fuel is 1 mole is given as follows:
The combustion reaction equation includes the air required for complete combustion and the residual air that does not participate in the combustion based on the fuel amount. In addition, after the equilibrium of the combustion reaction equation is achieved, the total mass of water vapor in air is obtained using thermodynamic equations, and water vapor is added to both sides of the equation. Therefore, the products involved in combustion, residual dry air, and water vapor are derived as reactants. The molecular formula of LP-EGR can be derived by dividing the ratio of LP-EGR in the reactant, and the molecular formula of the mixed gas flowing into the intercooler is determined by the sum of the molecular formulas of air and LP-EGR. Condensation occurs in two forms: films and droplets. Film condensation gradually increases its thickness on the surface and forms a liquid layer that provides thermal resistance; however, droplet condensation does not form a liquid film with thermal resistance. Therefore, droplet condensation can obtain a heat transfer rate 10 times higher than that of film condensation. However, considering gravity and surface treatment, it is difficult to maintain droplet condensation, which changes to film condensation over time; therefore, the design of the heat transfer method assumes the occurrence of film condensation on the plate [30, 31]. Additionally, various assumptions were made in this equation to predict the condensation: (1) the changes in the kinetic and potential energies of the fluid flow were ignored; (2) assuming that the wall of the heat exchanger is thin, the temperatures of the inner and outer walls were considered equal; (3) the saturation and wall temperatures were maintained at constant values, and the temperature of the liquid film varied linearly; (4) heat transfer through the liquid film was achieved by pure conduction (no convection occurs inside the liquid film); (5) the flow of the condensed matter was laminar, and properties of the liquid were constant; and (6) the acceleration of condensed matter was ignored. means the saturation temperature of vapor. The saturation temperature can determine the partial pressure of H2O by multiplying the mole fraction of H2O generated from the EGR molecular formula with the intercooler inlet pressure (). In addition, the saturation temperature corresponding to the partial pressure of H2O can be found through the psychrometric chart. The partial pressure of H2O is calculated as follows:
The latent heat of vaporization is the heat from which the water vapor of a unit mass is condensed and released and generally emits more heat than the condensed material. Rohsenow calculated the modified latent heat of vaporization through a relationship between the specific heat () of the liquid and the temperature difference between the saturation temperature () and wall temperature () given by the following equation [32]:
The specific heat of the liquid represents the characteristics of the liquid and can be obtained from the average film temperature (), which is the average temperature of the liquid. The average film temperature is calculated as follows:
Therefore, condensation () can be defined through the relationship between heat transfer () and the modified latent heat of vaporization (), which is given as follows:
Heat transfer in condensation has a convective form according to Newton’s law of cooling; therefore, convective heat transfer is applied, and the equation for convective heat transfer is as follows:
Convection contains variables that are important for condensation growth. The heat exchange area () of the intercooler is the region where heat transfer occurs. The convection heat transfer generated by various types of intercoolers can be confirmed by considering the heat exchange area as a variable. The variable is the convective heat transfer coefficient, which impacts the growth and change in condensation the most; however, it does not indicate the state in which a substance can be defined, that is, the amount of state. This value is determined experimentally and is affected by all variables affecting convection, the geometry of the surface, and the amount of fluid state. In particular, in the relationship between convective heat transfer and conduction heat transfer, the correlation between the thickness of the condensation film and the convective heat transfer coefficient can be confirmed. In the heat transfer equation representing conduction, it can be seen that is the thickness of the condensation film and is inversely proportional to the convective heat transfer coefficient. Therefore, in this formula, the convective heat transfer coefficient was selected as the factor for the generation and growth of condensation, and the change in the amount of condensation over time was calculated based on the change in the convective heat transfer coefficient.
2.4. Arrangement of Convection Heat Transfer Coefficient
The convection heat transfer coefficient is calculated through empirical relations; therefore, the condensation equation can be calculated inversely based on the condensation generation measured through test evaluation to obtain convection heat transfer coefficients over time as follows:
Figure 7(a) shows the convection heat transfer coefficient for the eight points of the test evaluation based on the operating conditions over time. The convection heat transfer coefficient tends to decrease over time. However, because there is no tendency for the driving conditions, it is necessary to construct a relational expression for the variables to apply these data to the calculation formula. Therefore, based on the temperature difference between the saturated and the wall temperatures, the convection heat transfer coefficients for the eight points were listed in the increasing order of temperature difference. In addition, these data apply a trend line such that the convection heat transfer coefficient is related to the time change to reflect the amount of condensation generated over time. A trend line was applied to eight points, and the type of exponentiation with the highest accuracy was selected among the types of trend lines. and are constants derived from each trend line.
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The convection heat transfer coefficient can be derived as a function of the trend line, and the shape of the function can be confirmed from Figure 7(b). The characteristic of the convection heat transfer coefficient function is that the smaller the temperature difference in the initial stage, the larger the convection heat transfer coefficient; however, the value of the heat transfer coefficient tends to converge after a certain period. If the temperature difference is large, the initial value of the heat transfer coefficient is small, and the width of the slope decreases sharply. Thus, it may be confirmed that the difference between the saturation temperature and the wall temperature, which is affected by the ambient temperature, affects the determination of the initial convection heat transfer coefficient. The tendency of the convection heat transfer coefficients to decrease over time indirectly shows that the thickness of the condensation film increases through the convection heat transfer coefficient, which is inversely proportional to the thickness of the condensation film. Therefore, the thickness of the condensation film on the surface of the heat exchanger increases thereby deteriorating the heat exchange efficiency and reducing the amount of condensation generated over time.
To establish a generalized condensation prediction formula, the convection heat transfer coefficient function was updated by predicting seven points for other ambient temperatures using the formula, in addition to the eight points for measuring condensation. The convection heat transfer coefficient function first calculates the difference between the saturation temperature and the wall temperature corresponding to the seven points and then applies interpolation to predict the value of the function for the intermediate value of the variable using condensation and time as variables. It is possible to derive convection heat transfer coefficients generated from the heat exchanger at a specific time for various ambient temperatures and operating conditions through a mathematical approach that considers condensation and time as variables. Similarly, the convection heat transfer coefficient function is listed in the descending order based on the temperature difference between the saturation and wall temperatures. Figure 8 shows the convection heat transfer coefficient function form of all 15 points for 4 hours. Therefore, the difference between the saturated and wall temperatures was derived through calculations, and the function was applied to the formula to estimate the function within the temperature difference of the convection heat transfer coefficient function.
3. Results and Discussion
3.1. Validation of the Test
Using thermodynamics and heat transfer principles, a formula for predicting the condensation in a heat exchanger was established. This formula proved reliable and was validated based on the amount of condensation generated in the heat exchanger of a diesel engine through a test evaluation. The amount of condensation generated over time did not show the actual value owing to the security policy of the vehicle company; therefore, normalization was performed through maximum and minimum scaling of the condensation data. The normalization ranged from the minimum value of 1 to the maximum value of 100 when the data of all condensations was available. All specific values were scaled by applying maximum and minimum normalization expressions between 1 and 100. The normalization equation for obtaining an element () of a specific condensation () is given as follows:
Figure 9 shows the comparison of the amount of condensation generated for the eight points of the test evaluation with the calculation equation. In the test evaluation, the amount of condensation generated over 3 hours is indicated by the solid line. The amount of condensation derived from the calculated formula was predicted for a total of 4 hours, and the results are indicated by the dotted lines. Figure 9(a) shows a trend that the condensation value predicted at 1300 rpm at the ambient temperatures of 0 and 5°C has a slope similar to the actual amount of condensation. In addition, the error range of the condensation is at least 0.49% and at most 1.77%. Figure 9(b) shows the result at 1500 rpm for a total of four points corresponding to the ambient temperatures of -3, 5, 10, and 15°C. The actual amount of condensation was compared with the predicted amount of condensation using the calculation formula. In particular, the actual amount of condensation corresponding to the ambient temperature of 15°C decreases over time. The amount of condensation predicted by the formula also shows a similar value in decreasing form. Figure 9(c) shows the results at the ambient temperatures of 0 and 10°C at 1600 rpm. The amount of condensation predicted by the formula corresponds with the amount of actual condensation. This result indicates that the condensation value converges after 1 hour under each operating condition. As shown in Table 3, the errors can be checked over time under each operating condition with a maximum error of 3.5%. Therefore, the formula shows a reasonable margin of error for verifying the validity of this result.
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3.2. Prediction of Condensation
The possibility of condensation prediction was validated using the proposed formula. In addition, condensation was predicted in the ambient temperature range to widen the prediction range of the formula, and no test evaluation was conducted in the relevant operating area. The formula predicts the condensation at seven additional points. Figure 10 shows the results of predicting condensation corresponding to five ambient temperatures between -3 and 15°C for each of the three operating areas. The solid black line represents the prediction of condensation in the current trial evaluation of eight points, and the solid red line represents the prediction of condensation for the additional seven points. All condensation amounts were determined using a normalization formula. Figure 10(a) shows the amount of condensation generated from the ambient temperature in the range of -3 to 15°C at 1300 rpm, and the characteristics of the condensation change can be confirmed. The initial condensation at -3 to 5°C occurs from 55 or higher and tends to increase up to 73 over time, confirming that the occurrence range of condensation is large. It can be attributed to the relative humidity ratio of the corresponding ambient temperature that is 88 to 100%, thereby implying that the air is rich in water vapor content. However, the range of change in the occurrence of condensation at ambient temperatures of 10 and 15°C is relatively small. This is because the relative humidity at ambient temperatures of 10 and 15°C is 45 and 25%, respectively, and the water vapor content of the air is low. Figure 10(b) shows the amount of condensation at the ambient temperature at 1500 rpm. The amount of initial condensation between the ambient temperature of -3 and 5°C is 60 or higher, which indicates that a larger amount of condensation occurs compared with that at 1300 rpm. This is a result of the relatively large inflow of air containing water vapor. In addition, similar to that at 1300 rpm, the amount of condensation decreases as the ambient temperature increases, indicating that a small amount of water vapor is introduced owing to the decrease in the relative humidity of the ambient air as the temperature increases. Figure 10(c) shows a relatively large change in the occurrence of condensation over time at 1620 rpm compared with other operating conditions and tends to increase up to 80. The reason for the large amount of condensation is that the air flow rate and LP-EGR mass are relatively large compared with other operating areas under the 1620 rpm operating condition, and the mixed gas flowing into the intercooler includes a large amount of water vapor. In addition, the amount of change in condensation decreases over time under all three operating conditions. The condensation converges after 1 hour because of various causes. Owing to the influence of gravity, liquid droplets are pulled down and accumulate in the lower sections of the heat exchanger or adhere to the surface of the heat exchanger via surface tension, forming a film that can increase in thickness over time. In addition, the flow velocity of the fluid passing through the heat exchanger may also play a role in the condensation convergence. This study assumes that a mixed gas of air and LP-EGR containing water vapor forms a liquid film in the heat exchange area and shows that condensation converges owing to the increase in the thickness of the liquid film over time using the convection heat transfer coefficient. It was confirmed that the relative humidity according to the ambient temperature was a factor influencing condensation.
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3.3. Additional Test to Improve the Reliability of the Formula
The amount of condensation for each operating area has been predicted according to the ambient temperature using the formula. However, it is necessary to examine whether the amount of condensation predicted by the formula corresponds to the actual amount. Therefore, to improve the prediction reliability of the formula, an additional test was performed to compare the amounts of condensation. For this test, two operating conditions were selected: 1500 rpm, which runs at a constant speed of 60 km/h, and 1570 rpm, which runs at a constant speed of 50 km/h. The ambient temperature was 0°C, and the test evaluation was performed for 3 hours by applying the same conditions of 100% relative humidity. Figure 11 shows the results of the comparison between the amount of condensation measured through the test evaluation and that predicted using the formula under the relevant operating conditions. Figure 11(a) shows the result obtained at 1500 rpm. The condensation values from the test evaluation results converge over time. In addition, the condensation results predicted by the formula correspond with the test evaluation results. The error range has an estimated minimum error of 2.37% within 1 hour and maximum error of 4% within 3 hours. In particular, the maximum error of 4% is calculated by applying the maximum and minimum normalizations of condensation; when converted into an actual value, the error is approximately 3.7%, which generates less condensation. Figure 11(b) shows the results at 1570 rpm. Similar to 1500 rpm, the amount of condensation converges over time. The actual condensation value is larger than the amount of condensation in the calculation formula within 2 hours.
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Although there is a limitation that the formula cannot reflect all the actual thermodynamic phenomena because of its assumptions, the convergence form of condensation generated over time is narrower and shows a reasonable range of condensation error. The minimum error is 0.85%, and the maximum error is 3.21%, which has a narrower error range than that of the previous operating conditions, and the error over time is shown in Table 4. The comparison of the amount of condensation through an additional test evaluation provides a basis for improving the reliability of the formula. This formula considers the operating and ambient conditions as variables and enables quick calculations based on the thermodynamic equations thereby reducing the time cost for evaluating the amount of condensation. In addition, the condensation predicted by the formula can yield an approximate value similar to the actual amount of condensation, which is the basis for responding to the field claims required by the company.
3.4. Extension for the Applicability of a Formula
This formula is aimed at predicting the amount of condensation despite the variations in the different types of intercoolers and fuel types applied to IC engines. Therefore, a formula applied to gasoline vehicles was used to determine the amount of condensation in the intercooler. Table 5 lists the heat exchange area and operating conditions of the gasoline-vehicle intercooler used in the test evaluation. In particular, the heat exchange area of the intercooler of the gasoline vehicle was approximately 2.27 m2, which was smaller than that of the diesel vehicle. The ambient temperature applied to the test evaluation was 5°C, and the relative humidity was 100%. In addition, the combustion reaction equation was calculated by selecting the molecular formula of C8H15.4, which accurately represented the characteristics of gasoline. Figure 12 compares the amount of condensation predicted using the calculation formula with the results of the condensation measured through the test evaluation. The amount of condensation measured through the test evaluation generates a large value of approximately 62 after 1 hour, and the values converge thereafter. This tendency is similar to that observed in diesel vehicles. The convergence of condensation is caused by the decrease in the convection heat transfer coefficient owing to the formation of a condensate film inside the intercooler, which decreases over time. The results of the condensation amount predicted through the formula verify this and are similar to the test evaluation results. In particular, the error in the condensation prediction is 0.95% at 1 hour, 0.89% at 2 hours, and 1.13% at 3 hours; therefore, the amount of condensation is predicted with extremely high accuracy. The results of the predicted condensation amount, even in the intercooler of gasoline vehicles, show the possibility of extending the application of the proposed formula and verify its accuracy.
4. Conclusions
The proposed thermodynamic formula in this study predicted the amount of condensation generated by the heat exchange in the intercooler of a diesel engine vehicle. Predicting the condensation amount using the formula offers the advantage of reduced time and cost compared with the test evaluation method. Additionally, the mathematical formula that can predict condensation can be used over a wide range of applications because of the inclusion of terms such as the operating area, ambient temperature, relative humidity, and time. The purpose of this study is to identify the cause of condensation and how condensation occurs before reducing the condensation. The novelty is to determine what effect the thermodynamic governing equation has in calculating condensation and what are the key factors that affect condensation formation the most. In addition, this study is of great significance in that these thermodynamic governing equations have been converted into usable functions through a mathematical approach that affects condensation formation. This perspective is thought to be the result of the empirical research paper by explaining what the researcher found when analyzing the data. Figure 13 shows the results of this study. The amount of condensation generated by the intercooler of the diesel vehicle based on the ambient temperature and time was mapped and expressed as a contour line. The conclusions of this study are as follows: (1)In establishing the mathematical formula, the air mass and LP-EGR mass contain as much water vapor as the ratio of the relative humidity, and the saturation temperature determined by the ambient temperature affects the amount of condensation. The ambient temperature is closely related to humidity, and when the temperature is below 0°C, the humidity is 100% which contains a large amount, but as the temperature increases, the humidity decreases and contains a small amount of vapor(2)The film formed owing to condensation caused a thermal resistance that hindered the heat exchange efficiency of the intercooler, and the generation of condensation could be expressed through the convection heat transfer coefficient, which was inversely proportional to the film condensation. The convection heat transfer coefficient is a variable that can be derived through empirical correlation and calculated using the amount of condensation corresponding to the eight points of test evaluation. The initial convection heat transfer coefficient for each operating condition varied depending on the temperature difference between the saturation and wall temperatures. Therefore, to determine the shape in which the actual condensation converged, a function that can trend the amount of condensation was derived using the time and temperature differences as variables. The slope of the convection heat transfer coefficient graph tends to decrease as the temperature difference increases. A decrease in slope means that the amount of condensation converges after as certain period of time, and the same phenomenon could be confirmed in the test evaluation(3)The comparison of the formula and test evaluation results demonstrated that the condensation amount increased rapidly until 1 hour but converged after 1 hour due to the thermal resistance of the condensed water film. The initial condensation form was affected by the ambient temperature and relative humidity. The relative humidity was 100% when the ambient temperature was below 0°C, and the amount of initial condensation was large owing to the high relative humidity. At approximately 10°C or higher, the relative humidity rapidly decreased to less than 45%, and the initial amount of condensation was relatively reduced by approximately 30% compared with that in the low-temperature region. The results obtained using formula were verified using the test evaluation results with a ≤4% error in the amount of condensation(4)The condensation was predicted by applying the calculation formula to gasoline vehicles with different intercooler heat exchange areas and fuel species. The error in the amount of condensation generated was up to 1.14%. Thus, the results were similar to those of the test evaluation. This perspective proves the reliability of the formula and indicates the extended scope of application to predict condensation. In future studies, condensation of heat exchangers will be more specifically predicted. It is possible to determine the location where condensation occurs inside the intercooler by applying a phase change model through computational fluid dynamic (CFD) analysis. The tendency of condensation to occur will be determined by changing the arrangement of fins and the heat exchange area. CFD analysis will show how viscosity and tension of water affect condensation formation. As an additional study, it is necessary to confirm the formation of condensation in the LP-EGR cooler before exhaust gas enters the intercooler. Therefore, it is necessary to check the phenomenon of condensation and deposition of the unburned hydrocarbon and the effect of condensation of the hydrocarbon on the corrosion of the heat exchanger
Nomenclature
| : | Mass (kg) |
| : | Partial pressure (kPa) |
| : | Relative humidity (%) |
| : | Absolute humidity (kg water vapor/kg dry air) |
| : | Modified latent heat of vaporization (kJ/kg) |
| : | Latent heat of vaporization (kJ/kg) |
| : | Average film temperature (°C) |
| : | Heat transfer (J/s) |
| : | Material’s conductivity (W/m°C) |
| : | Thickness of condensation (m) |
| : | Convection heat transfer coefficient (W/m2°C) |
| : | Heat exchanger area (m2) |
| : | Saturation temperature (°C) |
| : | Intercooler wall temperature (°C). |
Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that there is no conflict of interest regarding the publication of this paper.
Acknowledgments
This work was supported by the Chosun University (Grant No. K207469004-1).