Thermodynamic Model for Cold-Phase Influence on Light Vehicles’ Fuel Consumption

Abstract

The present and appropriate concern regarding climate changes resulting from the combustion of fossil fuels in light passenger vehicles raises the necessity to develop appropriate instruments to investigate probable and feasible solutions for fleet decarbonization. Given the direct relationship between fossil fuel consumption and greenhouse gas emissions have historically been determined through experimental tests in the laboratory following standard cycles, to enhance the vehicle’s energy efficiency these should be complemented by numerical simulation tools, as they demonstrate fast response and adequate correlation to experimentation. In this aspect, one of the biggest challenges of numerical simulation is quantifying the impact of the various phenomena that affect the vehicle operation during the cold phase, in which the internal combustion engine loses efficiency. This study proposes a thermodynamic model for simulating the fuel consumption of light vehicles during the cold phase of operation. Measured lubricant temperature, ignition spark retardation, exhaust valve timing, and coolant temperature in the vehicles along the drive cycle are the required input data for the model. This thermodynamic procedure makes it possible to quantify the impact on fuel consumption while driving the vehicle in cold operation. The cold phase, with a 505 s duration, is responsible for approximately a 21% increase in fuel consumption in a standard urban drive cycle. It is considered that the shorter the route, the more pronounced and significant the cold phenomena are, and the impact of vehicles frequently driven on short urban routes can be accurately estimated for future analyses.

1. Introduction

Numerous publications have studied the environmental impacts and decarbonization of different fuels for light-duty vehicles. For instance, Feliciano et al. [1] displayed the impact of biofuels in comparison to the Brazilian electricity matrix, revealing the possibility of ethanol and the alikeness of both vectors concerning their carbon footprint. Other authors, such as Rovai et al. [2], demonstrated that depending on the country, the use of electrification would not achieve a real gain in terms of carbon dioxide emissions. Furthermore, one of the critical factors of electrification that may or may not achieve full decarbonization is related to the electrical mix employed for vehicle use and battery manufacturing. Tabrizi et al. [3] evaluated a 30 to 60% reduction of the carbon footprint when the production moves from China to some European countries (Germany, Italy, and France). Finally, Sacchi et al. [4] demonstrated that current battery electric vehicles (hybrids) perform better than solely gasoline vehicles in 26 out of the 35 countries investigated (showing the importance of respecting regionalities) and raised remarks regarding the importance of future fuels from “green energy”, similar to those stated by Rovai et al. [2] with respect to regionalities. There are some important aspects of the degradation of batteries to take into consideration, as described by Shchurov et al. [5], with the subject stressed by Kaarlela et al. [6], where they discuss the potential of artificial intelligence in enhancing and supporting the circularity of electric vehicle batteries at their disposal or recycling. These issues must be taken into consideration in changing and assessing the real decarbonization effect [2], although electric vehicles show a better path for higher efficiencies in energy use (thanks to the wheels).

A concern with the increase in the thermal efficiency of internal combustion engines has been demonstrated in several literature analyses, as indicated by the review manuscripts [7,8], and concern with the technological improvement of the efficiency of performance [9], culminating with a taxation of CO₂ emissions, based on regression analyses conducted in Brazil [10], the European Union [8], and the United States [11].

The use of conventional light passenger vehicles with internal combustion engines in short, primarily urban, routes intensifies the influence of the cold-start and warm-up operation phase. Some literature in the area is available from recent years, as indicated in [12], although this is for diesel engines or biodiesel [13]. Guilherme et al. [14] experimentally demonstrated the influence of the cold-phase operation of conventional vehicles in the EPA75 cycle determined by the United States Environmental Protection Agency [15]. The significance of this usage condition is reinforced by the Brazilian standard NBR16567 [16], which considers that the average fleet usage for daily routes of less than 12 km accounts for 20%, with this percentage increasing to nearly 40% for routes of up to 24 km. These arguments show the importance of this subject. The urban driving cycle starts with the vehicle cold start, at a temperature between 20 °C and 30 °C, followed by vehicle operation in the urban cycle during the warm-up, in accordance with Brazilian technical standard NBR6601 [17]. As suggested by Roberts, [18], Ye and Mohamadian [19], and from traditional internal combustion engine literature such as Heywood [20] and Reif [21], during the critical cold period of operation, internal combustion engines lose efficiency because of a combination of phenomena such as (i) high engine friction due to the higher lubricant viscosity in lower temperatures (warm-up phase). (ii) A strategy to anticipate the catalytic converter light-off to achieve emissions control constraints, which is performed by spark ignition retardation and complemented by early opening of exhaust valves in engines equipped with variable valve timing in the exhaust camshaft. (iii) Engine hardware heating of its components and related parts, with energy from fuel combustion. (iv) Ensuring cold combustion stability by fuel enrichment during cold starts to promote the first combustion reactions, idle engine speed increase, and fuel enrichment to compensate for fuel condensation on the cold engine walls (lost fuel), ensuring a proper air/fuel mixture inside the combustion chamber.

The continuous technological advancement of vehicles towards the tradeoffs between efficiency and performance are pushed by Brazilian regulations [22,23]. As pointed out by Salvo Junior et al. [24] and by Mosquim and Mady [9,25], this will have important future implications. It will lead to a reduction in the impact of cold phenomena using lower-viscosity lubricants and aluminum-made engines, while also increasing the cold impact due to challenging pollutant emission regulations as demanded globally, including those imposed by the Brazilian vehicle emission control program PROCONVE [26]. The cold-start phase in vehicles with internal combustion engines has a relatively small impact on fuel consumption in the combined cycle (urban and highway), as specified by the Brazilian standard NBR7024 [16], resulting in a 2% increase in fuel consumption. Contrarily, during the initial phase of the standard urban driving cycle EPA75 [15], the impact of the cold-start phase is significant, leading to an over 20% increase in fuel consumption. These figures demonstrate the critical role of the vehicle’s driving cycle in the effects of the cold-start phase, especially on short routes where the cold-start phase leads to substantial penalties in fuel consumption.

The proposed model enables numerical simulations to predict the impact of vehicle fuel consumption during the cold phase, making an innovative and significant contribution to the area. Conventional simulations only consider hot and stabilized conditions based on inputs from dynamometer engine bench tests. Developing an experimentally validated thermodynamic model to estimate the impact of the cold phase on the efficiency of internal combustion engines allows for improving traditional life-cycle analyses based on homologated fuel consumption results. The potential advantages of decarbonization through the electrification of the light-vehicle fleet are more pronounced in urban usage [2], conditions that are more sensitive to short journeys, and consequently, cold phases, in which the fuel consumption measurement in the laboratory is not representative.

2. Methods

The one-dimensional (1-D) numerical simulation of energy expenditure is crucial for predicting fuel consumption and supporting the implementation of technologies to meet regulations while developing light vehicles. One of the challenges in simulating vehicle fuel consumption is accurately determining higher fuel usage during the cold phase. The engine’s entire load curve and brake-specific fuel consumption map were experimentally acquired on the dynamometer bench at steady-state and hot conditions. This method is traditionally used in literature, as explained by [1], making it possible to achieve quality results with simulations that consider the vehicle’s dynamics behavior, draft, test routines, and different powertrain technologies.

In order to determine the impact of the cold phase in conventional and hybrid vehicles, a numerical simulation model was developed and implemented inside the GT-Drive module of the commercial software GT-Suite v2023 developed by Gamma Technologies, as illustrated in Figure 1.

This model, based on experimental input data measured in the vehicle, such as lubricant temperature, ignition spark timing, exhaust valve opening, and coolant temperature, allows the estimation of the impact of cold-start fuel consumption. Therefore, the thermodynamic model adjusts the engine efficiency map under hot, nominal operating conditions to consider the cold phenomena, which include higher lubricant viscosity and engine friction, the catalytic converter heating strategy until light-off, and the engine hardware heating up to steady condition. Lubricant temperature measurements were performed inside the engine with a type K thermocouple inserted with the engine oil dipstick and immersed in the engine oil pan. We also measured, directly from the engine’s control unity, the spark ignition timing, the exhaust valve timing, and the engine coolant temperature. For data acquisition in the vehicles, we chose the ETAS Inca software (v7.3). The INCA software was chosen because it is the same console used for ECU calibration, specifically for catalyst heating strategy investigation in this work. This instrumentation already has data acquisition capability. Nevertheless, any other data acquisition system with a 10 Hz sampling rate would be feasible.

The experimental measurements were performed with a vehicle speed profile based on EPA75. This cycle is made up of three phases: the 1st phase; the 2nd phase, a period with the engine turned off; and the 3rd phase (with the car already “warm”). The first and third phases have the same speed profile and last 505 s, with the first phase starting with a cold start after a minimum period of 12 h turned off to ensure that the entire car has a stabilized temperature between 20 and 30 °C, and the third phase beginning with a hot start after the soak period in the cycle. Hence, comparing the 1st and 3rd phases means quantifying the differences in the effects of the cold phase.

In the 1st (cold) and 3rd (hot) phases, the higher fuel consumption in the 1st phase is determined by cold phenomena. For the experimental procedure, we used a Brazilian compact sport utility light passenger vehicle, 2022 MY, usually sold in Brazlian market (the model is not necessarily relevant for the conclusions) equipped with a four-stroke 1.0-liter spark-ignition flex-fuel engine, with direct injection and turbocharged, running on E22, with an aluminum engine block and cylinder head, coupled with a torque converter to a six-speed automatic transmission. Finally, we used the carbon balance method to calculate vehicle fuel consumption at an emissions laboratory.

2.1. Hot-Phase Simulation and Experimental Mathematical Model Correlation

The vehicle fuel consumption was firstly simulated in the hot phase, integrating the instantaneous fuel consumption from the engine experimental map through the 3rd phase of EPA75 [15]. The vehicle mathematical model considers:

• Engine-specific fuel consumption mapped in dynamometer in steady-state conditions.
• Full-load engine curve.
• Engine idle speed.
• Fuel cut-off strategy.
• Torque demand as function of gas pedal position.
• Transmission efficiency maps.
• Dynamic torque converter curves.
• Torque converter lock-up according to transmission control unity (TCU) maps.
• Measured gear shifting.
• Measured vehicle speed profile.

The vehicle fuel consumption simulation results in the hot phase were compared with the experimental results measured in the vehicle. The first and second lines of

Table 1. Simulation results that are input to the model proposed in this manuscript.

	1st Phase (Cold)	Increase in Fuel Consumption (%)	3rd Phase (Hot)
Measurement (bag)	1.209	-	1.0
Hot simulation	0.977	-	0.979
Hot simulation adjustment	0.999	-	1.0
Lubricant temperature	1.054	5.5	-
Catalyst ignition	1.085	8.6	-
Catalyst evvt	1.095	9.7	-
Engine hardware	1.209	21.1	-

show a 2.15% fuel consumption deviation in the 3rd-phase simulation. This simulation deviation is considered acceptable given the uncertainties:

• Engine mapping uncertainty.
• Vehicle production variability.
• Vehicle testing variability.
• Dynamic transient maneuvers.
• Engine torque reserve applied specifically in vehicle.
• Auxiliary load difference between dynamometer and vehicle (e.g., alternator).

The simulation model was adjusted by this 2.15% factor and run for the 1st and 3rd phases, representing the theoretical 1st phase except the cold phenomena; the values of the third line of Table 1 show a strong similarity between the 1st and 3rd phases in terms of test execution, which means close gear shifting and vehicle speed profiles. Table 1 shows the contribution of each cold phenomenon considered on vehicle fuel economy, detailed below, achieving 21.1% higher values in the cold phase according to measurements in the vehicle.

2.2. Lubricant Temperature Effect

The lubricant’s higher viscosity in cold temperatures is one of the leading causes of the internal combustion engines’ efficiency decrease in the cold phase [18]. According to [20], the model of lubricant kinematic viscosity ($\nu$) is a function of its temperature ($T_{lub}$) for the considered SAE 5W40, according to Equation (1).

$${\nu }_{lub}={0.15}^{\left({\displaystyle \frac{1018.74}{125.91+T_{lub}}}\right)}$$

(1)

According to Shayler et al. [30] and Taylor [31], the engine friction mean effective pressure (FMEP) is affected by oil viscosity, according to Equation (2), adopting either kinematic or dynamic viscosity (specific mass variations considered negligible) [20]. The power index (i) in Equation (2) takes into account not only the viscosity influence but also the lubricant friction additives’ impact on engine friction, varying from 0.19 to 0.30, with 0.25 being a usual value according to Taylor [31].

$${\displaystyle \frac{FMEP}{{FMEP}_{hot}}}={\left({\displaystyle \frac{{\nu }_{lub}}{{\nu }_{lub,hot}}}\right)}^i$$

(2)

The FMEP is calculated using Equation (3). Considering $k=2$ for a 4-stroke engine, engine speed (n), and engine displacement ($V_d$).

$$FMEP={\displaystyle \frac{k{\dot{W}}_{eff}}{n\pi V_d}}$$

(3)

The power index in Equation (2) was experimentally determined specifically for the engine used in the single tested vehicle. The experimental results are shown in Figure 2; note that there are no error or uncertainty analyses since it is a proof of concept with only one measure due to the costs of each test. Although the comparison between the first and third phases of the emissions test may be subject to test uncertainty, we choose not to analyze this because they take place in the exact same test vehicle, with the same driver, and in the same test cell on the same day. Furthermore, emissions tests are proper if there are no violations of the speed range that the vehicle must concede throughout the test. All tests used in the study are tamper-free. Determining index i in Figure 2 involved tests on a bench dynamometer. These tests were subject to the uncertainties of the AVL FUEL EXACT PLUS 300 equipment for consumption measurement and the AVL INDY S33 for torque measurement ($\tau$). Both software are available in Orlanda Bérgamo St., 1062, São Paulo, Brazil, manufactured Using this specific, high-precision equipment ensures the accuracy of the measurements. The experimental validation of the impact of catalyst heating was conducted in the same vehicle, with the identical driver, and in the identical test cell. On subsequent days, the first day was with the original engine control unity ECU calibration, and the second was with the calibration that turns off the catalyst heating strategy.

Our understanding is that the experimentally determined value of the coefficient is not a one-size-fits-all solution but a specific factor that varies for different engines and tribological systems. The most important conclusion is that this coefficient is within the literature-recommended range. Hence, different engines and tribological systems would demand specific coefficients. The method used to determine the parameters is described in the following few paragraphs, where Equation (4) relates brake-specific fuel consumption (BSFC), fuel mass flow (${\dot{m}}_{fuel}$), and effective power (${\dot{W}}_{eff}$), which are constant during the experiment.

$$BSFC={\displaystyle \frac{{\dot{m}}_{fuel}}{{\dot{W}}_{eff}}}$$

(4)

Assuming the engine thermal efficiency (${\eta }_t$) remains constant, the engine global efficiency (${\eta }_g$) increases with increasing lubricant temperature, as shown by the reduction in BSFC, as a consequence of engine mechanical efficiency (${\eta }_m$) improvement (lower friction), according to Equation (5).

$${\eta }_g={\eta }_t\times {\eta }_m$$

(5)

When the coolant temperature stabilizes, the heat transfer from the combustion chamber to the coolant can be considered constant, resulting in the engine indicated power (${\dot{W}}_i$) from Equation (6), where the engine thermal efficiency value from the last 30 s is used for a lower heating value of fuel ($LHV$).

$${\eta }_t={\displaystyle \frac{{\dot{W}}_i}{{\dot{m}}_{fuel}LHV}}=cte={\eta }_{t,hot}$$

(6)

As engine indicated power (${\dot{W}}_i$) is the sum of effective power (${\dot{W}}_{eff}$) and friction (${\dot{W}}_{fric}$) power, in the Equation ${\dot{W}}_i={\dot{W}}_{eff}+{\dot{W}}_{fric}$ friction power can be experimentally determined by Equation (7) during engine warm-up.

$${\dot{W}}_{fric}={\eta }_{t,hot}{\dot{m}}_{fuel}LHV-{\dot{W}}_{eff}$$

(7)

As shown in Figure 2, the testing was performed on the engine at a constant speed/ rotation (n) and effective torque (${\tau }_e$) of 2000 rpm and 60 Nm, respectively. During the warm-up phase, the lubricant temperature varied from 35 to 100 °C. The engine coolant temperature varied from 22 °C at engine start to 87 °C, controlled by the thermostatic valve. The intake air temperature remained around 22 °C during the test, with viscosity evaluated from Equation (1). The AVL FUEL EXACT PLU300 equipment measured instantaneous fuel consumption during the test, resulting in plotting points of the brake-specific fuel consumption (BSFC). As the effective power remained constant throughout the test, the reduction observed in BSFC represents an increase in the engine global efficiency. Assuming that the engine thermal efficiency remains constant after the coolant temperature stabilizes at 87 °C (indicated by thermal efficiency, ${\eta }_t=cte$) in Figure 2, the increase in engine global efficiency can be explained by the increase in mechanical engine efficiency with the reduction in lubricant viscosity, and its consequent reduction in engine friction (Equation (2)). Comparing the engine friction in hot conditions (FMEP_hot) measured in a motoring test on an active dynamometer AVL INDY S33 (same locations of other AVL equipment’s) with the calculated FMEP during the engine warm-up, it is possible to experimentally determine the viscosity power index (i) in Equation (1). The difference in lubricant temperature measured in the vehicle in the cold and hot phases (Figure 3) results in additional torque ($\Delta {\tau }_{lubricant}$) being applied on the engine during the cold phase due to higher engine friction, calculated by Equation (8) and applied to the engine crankshaft in the simulation model. This additional friction torque accounted for a 5.5% increase, as shown in Table 1.

$$\Delta {\tau }_{lubricant}=\left[{\left({\displaystyle \frac{{\nu }_{lub,cold}}{{\nu }_{lub,hot}}}\right)}^i-1\right]{\displaystyle \frac{V_d}{4\pi }}FME{P}_{hot}$$

(8)

2.3. Catalyst Heating to Anticipate Light-Off

The pollutant conversion efficiency through a catalytic converter depends on its component temperature. Engine cold starting followed by warm-up operation, which occurs in the first phase of the urban test cycle, is the most critical condition for vehicles equipped with internal combustion engines, not only because of the cold-operation phenomena but also because of the time required to heat the catalytic converter until it reaches the light-off temperature. This is the temperature at which pollutants are converted most efficiently into non-polluting gases.

Specific engine control strategies operate immediately after cold start for a short period, less than one minute, to anticipate the catalytic converter light-off in the considered vehicle. During this short period, the ECU (engine control unit) manages the engine’s operation with lower efficiency, although with higher energy release to the exhaust gases, with the undesirable impact of higher fuel consumption.

The increase in energy released through exhaust gases is achieved by delaying the ignition spark timing and anticipating the exhaust valve’s opening before the end of the expansion stroke in engines equipped with variable exhaust camshaft timing. This use of a catalyst-heating strategy is expected for most applications currently available in the Brazilian market. In the future, we expect an electrical heating system (eCAT) installed at the catalyst inlet, powered by 12 VDC or 48 VDC, pushed by more significant restrictions on pollutant emission limits in the Brazilian market imposed by the Brazilian Ministry of the Environment [32] and Brazilian National Environmental Council [26]. The catalyst heating strategies of ignition or exhaust valves are independent and complementary, which justifies analyzing each separately.

The maximum internal combustion engine efficiency is achieved for an ignition timing that operates the engine at its maximum brake torque (MBT), as explained by [20]. During combustion, the burn-flame evolution increases pressure and temperature inside the combustion chamber, which converts it into work during the piston expansion stroke. The conversion efficiency of the cylinder pressure in expansion work strongly depends on the crankshaft angle at which combustion starts, determined by the spark ignition timing. Retarding the spark ignition timing results in lower engine torque but higher energy released through exhaust gases, enhancing catalytic converter light-off. The sensitivity of the engine’s overall efficiency to the spark timing retard depends on several factors: engine geometric characteristics, compression ratio, intake and exhaust systems, fuel properties, and other physical phenomena. In order to simplify the multiple variables into a single sensitivity curve, this study considered an average curve, experimentally determined, of engine efficiency as a function of spark ignition angle that varies from MBT to the maximum spark ignition retardation, determined by the combustion stability limit. From the ignition timing measurement in the vehicle throughout the cold and hot phases of the EPA75 test cycle, with an excerpt from this measurement illustrated in Figure 4, the impact of the catalyst heating strategy by spark ignition retardation on fuel consumption can be determined considering the experimental curve of the global engine efficiency reduction as a function of spark retardation ($\Delta {\eta }_g$).

The other strategy adopted for catalyst heating is the early opening of the exhaust valve during the expansion stroke. Considering the maximum work during the expansion stroke is obtained by opening the exhaust valve slightly after the engine bottom dead center (BDC), early exhaust valve opening, before BDC, increases energy rejection through exhaust gases for catalyst heating to the detriment of work generation and engine efficiency, shortening the expansion stroke, and consequently, increasing fuel consumption. An excerpt of the measurement of exhaust valve opening in the vehicle, shown in Figure 5, demonstrates the exhaust valve before the engine bottom dead center (°BBDC) during the cold phase compared with the regular exhaust valve opening, in general, after bottom dead center (°ABDC) in the hot phase, as a reference.

The resultant impact factor of the catalyst heating strategies (${\Delta }_{catalyst}$), spark ignition retard (${\Delta }_{{\eta }_g}$), and early exhaust valve (${\Delta }_{evvt}$), on the engine’s fuel consumption map is determined by Equation (9), which multiplies the engine fuel map in the simulation model. The small values usually applied to ${\Delta }_{evvt}$ make the assumption of a linear impact on fuel consumption acceptable.

$${\Delta }_{catalyst}={\displaystyle \frac{1}{\frac{\left(100\%-{\Delta }_{{\eta }_g}\right)}{100\%}\frac{\left({180}^o-{\Delta }_{{\eta }_{evvt}}\right)}{{180}^o}}}$$

(9)

The numerical simulation for the impacts of the catalyst heating strategy on fuel consumption are discretized in Table 1 for spark retardation impact (+catalyst ignition, on the 5th line) and for early exhaust valve opening impact (+catalyst evvt, on the 6th line). The overall simulation result for the catalyst heating impact on fuel consumption is about 4.2% with the proposed model. An experimental validation of the catalyst heating impact was performed comparing the fuel economy test results in the emissions laboratory, for the same car, with the catalyst heating strategy disabled by calibration data applied on a programmable ECU, which resulted in about a 4.0% impact on fuel economy, close to the simulation results.

2.4. Engine Hardware Heating

The last stage of the proposed mathematical model for the cold-phase phenomena impact on vehicle fuel consumption considers the heating of the engine hardware components, which represents an 11.4% increase in fuel consumption calculated by subtracting the values of the 5th and 6th lines of Table 1. The detection of the heating stage of the engine hardware components can be achieved by measuring the engine coolant temperature from a coolant temperature sensor installed close to the engine coolant outlet. Figure 6 comparatively illustrates the engine coolant temperature in the cold and hot phases, which takes about 300 s in the tested vehicle.

The amount of fuel energy that, instead of being transformed into work inside the combustion chamber, is transferred to heat engine hardware components, and penalizes fuel consumption, can be calculated by the fuel mass flow (${\Delta }_{fuel,hardware}$) in Equation (10).

$$\Delta m_{fuel,hardware}={\displaystyle \frac{UA\left(T_{{coolant}_{HOT}}-T_{{coolant}_{COLD}}\right)}{LHV}}$$

(10)

The fuel energy transferred to the components can be mathematically modeled, in a simple way [33], by assuming the product of the global heat transfer coefficient and the thermal exchange area (UA) as constant, the instantaneous coolant temperature in the cold phase compared to the hot phase measured in the vehicle (Figure 6), and the fuel lower heating value (LHV) of 38.92 MJ/kg according to [34]. The main simplification of this model involves using the direct temperature difference instead of the logarithmic average temperature difference and a constant value for the global heat transfer coefficient independent of engine temperature, since the calculus is conducted for the coolant.

3. Results and Discussions

Figure 7 shows the effect of each cold phenomenon on fuel consumption during the cold phase in dotted lines and the sum of them in a continuous line (mathematical model). An experimental validation of the cold-phase’s impact on vehicle fuel consumption is difficult to perform due to the continuous fuel consumption measurement uncertainties in dynamic driving. Alternatively, continuous fuel flow estimation through the injectors, performed by the engine electronic control system (ECU), can be considered for comparison, although with uncertainty in the applied data. The consumed fuel estimated by ECU (ECU curve in Figure 7) is originally below the measured data but it can be adjusted by a multiplicative factor (ECU adjusted curve in Figure 7) to achieve the same final measured and reliable value in the emissions laboratory bag, the red square (measured) in Figure 7. A clarification of the red square value for higher fuel consumption during the first (cold) phase compared to the third (hot) phase is experimentally determined in the vehicle emissions laboratory by the carbon balance method of tailpipe emissions. This is the most reliable experimental value and is the recommendation for normative measurements used for vehicle homologation.

It is possible to observe a deviation between the proposed mathematical model and the adjusted ECU estimation between 80 and 300 s in Figure 6. This period includes the engine lubricant and engine coolant warm-up. As the fuel consumption estimate by the ECU considers the fuel flow through the injectors, one hypothesis for this deviation in fuel consumption in Figure 6 is the fuel vapor from the blow-by system. According to Rovai et al. [35], Engler-Pinto et al. [36], and Guilherme and Franchi [37], this phenomenon of vaporization of lubricant fuel dilution during the engine warm-up period is significant, and although less critical when using E22 gasoline, it is enhanced by direct fuel injection [38].

Figure 8 quantitatively summarizes the contribution of each of the analyzed phenomena on vehicle fuel consumption during cold-phase operation throughout the compared cold and hot tested cycles, lasting 505 s. The phenomena of higher engine friction with cold lubricant (lubricant), heating of the catalyst due to spark ignition retardation (catalyst ignition) and early exhaust valve opening (catalyst evvt), and heating the engine hardware components (engine hardware) present specific and characteristic contributions to increased fuel consumption along the test cycle. Figure 8 illustrates the increase in fuel consumption both continuously over the test time but also discretely for six specific distances covered. Figure 8 also contains a quarter-pie-shaped graph with the percent share of each cold phenomenon.

It can be seen in Figure 8 that the fuel consumption increase at the beginning of the cold phase exceeds 300%; consider, however, that this variation refers to the small total amount of consumed fuel at this point in the test, highlighting that the engine operates with relatively low fuel consumption at idle speed. At this initial step of the cycle there is heat transfer to components due to the greater temperature gradient and the higher viscous friction of the lubricant, due to, respectively, lower coolant and lubricant temperatures. At the end of the 505 s test it was concluded that cold operation with E22 increased fuel consumption by 21.1% compared to hot operation.

4. Concluding Remarks

The thermodynamic procedure proposed to estimate the impact of engine cold operation on fuel consumption is based on the following phenomena: (i) higher engine friction occurs for low lubricant temperature, and consequently, higher viscosity; (ii) the engine electronic control strategies to anticipate catalyst light-off based on ignition spark retardation and early exhaust valve opening; (iii) energy from fuel consumed to heat the engine hardware. These analyses combined represent a distinguishing feature of this manuscript and a guideline for future analyses that intend to evaluate the CO₂ and pollutant emissions during the cold-phase start.

These combined phenomena resulted in 21.1% higher fuel consumption due to engine cold operation by the end of a 505 s standard urban test cycle, the first phase of the EPA75 cycle, and presented a good correlation with experimental validation in a vehicle. This thermodynamic model can predict an increase in fuel consumption as a function of driven distance, in addition to discretizing the most pronounced phenomena along the drive cycle. For a concise drive cycle of about 0.5 km, cold operation could impact fuel consumption by more than 100%. The methodology for estimating the increase in fuel consumption during the cold phase of vehicle operation developed in this cycle also applies to other drive cycles as long as specific experimental input data are available. Although the model has been developed based on the first phase of the EPA75 cycle, it can be applied to longer cycles. The reason is mainly because the lubricant temperature did not reach a steady state within 505 s.

The catalyst light-off model is even applicable to compare and optimize ECU application data, balancing the earliest light-off and the fuel consumed. The last stage of the modeling can be applied to investigate engine hardware heating on fuel economy and to optimize engine components and materials. The following research steps are based on developing a thermodynamic model that does not require experimental measurements in the vehicles, allowing us to simulate and estimate the fuel consumption simulation in any drive cycle.