Fuel Efficiency Evaluation of Gas Turbine Engine Based Hybrid Vehicles
Michael Ben Chaim1, Efraim Shmerling2 and Alon Kuperman3*
1
Department of Mechanical Engineering and Mechatronics 2
3
Department of Computer Sciences and Mathematics
Department of Electrical Engineering and Electronics
*
Corresponding Author, Email:
[email protected], Tel: +972-526-943234 Ariel University Ariel, 40700
Abstract - The purpose of the contribution is evaluating the fuel efficiency of gas turbine engine based hybrid vehicles, which can be manufactured utilizing modern technologies. An analytical equation for calculating fuel consumption is derived taking into account specific properties of hybrid vehicles. European Union Directives and regulations of the United Nations Economic Commission for Europe are adopted to evaluate the fuel efficiency. The equation is first verified by calculating the mileage of several commercial hybrid passenger vehicles and then applied to gas turbine based hybrid vehicles. It is revealed that even though gas turbine engine possesses relatively poor efficiency, reduced turbine-generator weight results in a lower overall weight of the vehicle, leading to fuel consumption decrease. The estimated fuel efficiency of gas turbine engine based vehicles is shown to be on a par with the efficiency of widely employed diesel and gasoline engine based vehicles.
Keywords - gas turbine, hybrid vehicle, urban driving cycle, fuel economy.
1. Introduction The idea of using gas turbine (GT) engines in ground vehicles is not novel; a lot of research on gas turbine based hybrid engines have been performed in the past. Toyota demonstrated the hybrid technology in 1975 and Volvo Cars built a concept car in 1990 (Watanabe et al. 1985; Society of Automotive Engineers 1980; Cheng et al. 1997). Nevertheless the idea has not received much attention recently from either researchers or manufacturers (Christodoulou et al. 2011). The main reason is the fact that GT engines are inferior to piston engines in terms of fuel efficiency, which is undoubtedly the most important engine performance indicator (Capstone Turbine Corporation 2011; Schwaller 1977; Granet et al. 2004). Nevertheless, the emergence and rapid developments of full hybrid and plug-in hybrid electric vehicles (HVs) whose electric drive train supplies the acceleration energy, leaving the engine to operate in the optimal mode almost all the time by supplying the average vehicle power demand - make this idea worthy of serious consideration (Wong 2001). When comparing GT engines in HVs to piston engines, it must be emphasized that GT engines have several important and widely recognized advantages. A GT can develop greater speeds (105 rpm is a typical value (Capstone Turbine Corporation 2011)), allowing significant mass reduction of both the engine and generator and as a result of the vehicle as a whole (Thern et al. 2007; Tesla Motors Inc. 2011). Other important advantages that have been mentioned in the literature include higher environmental performance, smaller amount of engine parts and ease of upgrade when switching to other fuels (Granovskii et al. 2006; Gupta 1997). As for the relatively high initial cost of GT engines, calculations show that it is offset by higher mileage before overhaul and lower cost of technical maintenance (Chen et al. 1998).
Currently, two major sets of regulations are applied in Europe, binding all the vehicle manufacturers. These are EU Directives and the norms and regulations of the UN ECE, which are applicable in most countries worldwide. The calculations proposed in the paper are governed by Directives of UN ECE. According to UN ECE requirements and the above directives, fuel consumption is normally indicated in three traffic modes: urban, non-urban, and mixed traffic and appropriate tests are conducted on a chassis dynamometer workbenc (UNECE 2011). According to the above mentioned rules and regulations, the ECE Type 1 test is employed for Europe Dynamometer Operating Cycles. The test consists of two parts, Elementary Urban Cycle and Extra Urban Driving Cycle (USEPA 2011). The first part of ECE Type 1 test is considered in the manuscript. In order to estimate the fuel efficiency of GT engines in HVs, an equation for calculating fuel consumption is derived in the manuscript. Unlike conventional fuel efficiency equations described in the literature, the proposed equation takes into account the above mentioned specific characteristic of fully hybrid and plug-in HVs regarding the average and acceleration powers splitting between the engine and electric drive train. The manuscript reveals that GT engine based hybrid vehicles’ fuel economy may be on a par with that of diesel and gasoline engine based vehicles. This is a convincing argument in favor of the suggestion that reliable low-power GT engines, the production of which has been made possible by the recent advances in the development of the theory of turbomachinery and the combustion theory, as well as the development of modern technologies in metallurgy and in the field of composite materials, have the potential of successfully replacing piston engines in HVs (Lefebvre et al. 2010; Polyzakis et al. 2008).
The rest of the article is organized as follows. The analytical derivation of fuel consumption estimating equation is presented in Section 2. The validity of the equation is verified in Section 3 and is applied to estimating the fuel economy of GT engine based HVs in Section 4. The manuscript is concluded in Section 5.
2. Estimating Fuel Consumption According to the conventional ground vehicle theory, fuel consumption is usually determined assuming that the car is in a "continuous acceleration" mode, i.e. the internal combustion engine supplies both average power and peaking power, demanded by accelerations. While adequate for conventional cars, this approach is inaccurate for full hybrid and plug-in hybrid vehicles due to their special technical properties. In such vehicles, the engine operates during most of the time in an optimal mode, while the peaking power source (rechargeable batteries and/or ultracapacitors) are used to supply the acceleration power (Ehsani et al. 2010; Gaevsky et al. 2007). Here, the assumption that the engine operates in optimal mode constantly (leading to an underestimation of fuel consumption) is counterbalanced by neglecting the regeneration energy (results in an overestimation of fuel consumption). The validity of such suppositions will be supported by the next Section results.
Fig. 1: Vehicle power profile decomposition
In this subsection, a modified fuel consumption equation is derived, taking into consideration fuel economy assessment technologies, as stated in EU Directives and in norms and regulations of the UN ECE.
The fuel consumption on a flat road (liters per distance interval of X km) is typically estimated according to the following expression (Ehsani et al. 2010; Gaevsky et al. 2007)
QS =
g e × ( Prl + Pw + Pa ) × X [l ], 1000 × Va ×ht × r f
(1)
where ge is the average specific fuel consumption, [g/kWh]; Prl is the average vehicle power consumed in overcoming the rolling resistance, [kW]; Pw is the average vehicle power consumed in overcoming the aerodynamic drag, [kW]; Pa is average vehicle power consumed in overcoming the inertial acceleration, [kW]; ηt is the mechanical drive train efficiency; ρf is the fuel density, [kg/l]; Va is the average vehicle speed, [km/h].
Equation (1) implies that the acceleration power is supplied by the engine; hence the average specific fuel consumption is non-optimal. Therefore, the equation is inapplicable for HVs. It is suggested that fuel consumption estimate per 100 km interval may be determined using total energy expenditure Es as follows. The overall consumed
energy is separated into two components: energy required for overcoming the forces of resistances E1 and kinetic energy required for accelerations E2, i.e.
Es = E1 + E2 ,
(2)
where E1 is the energy required to overcome the rolling resistance and aerodynamic drag at 100 km interval, [J]; E2 is the kinetic energy required for episodic accelerations at 100 km interval, [J].
The first energy component is determined by dividing the 100 km distance into I subintervals and summing the energies of each as (Ehsani et al. 2010). æ v (t ) E1 = å ò ç mv × g × f r × i + 0.5 × r a × CD × A f ç 3.6 i =1 Ti è I
ì v (t ) ü ×í i ý î 3.6 þ
3
ö ÷÷dt [ J ], ø
where vi(t) is the instantaneous vehicle speed at subinterval i, [km/h]; Ti is the i-th subinterval duration [sec]; mv is the vehicle mass, [kg]; fr is the rolling resistance coefficient; CD is the aerodynamic drag coefficient; ρa is the air density, [kg/m3];
(3a)
Af is the vehicle frontal area, [m2]; g is the acceleration of gravity, [m/s2].
Assuming there are J accelerations per 100 km, the acceleration energy is calculated by
E2 =
mv × g m 2 × 3.62
J
å (V j =1
2 2
- V12 ) j [ J ],
(3b)
where γm is the mass factor of the car, which equivalently converts the rotational inertia of rotating components into translation mass (Ehsani et al. 2010); V2 is the speed after acceleration, [km/h]; V1 is the speed before acceleration, [km/h].
The fuel consumption per 100 km in terms of energy expenditure is determined from (Ehsani et al. 2010).
QS =
ES [l ], he.ave ×ht × H l
where ηe,ave is the average engine efficiency; Hl is the fuel calorific value, [J/l].
(4)
Substituting (1)-(3) into (4), and noting that in case of HV the engine efficiency is maximal at all time, the general expression for HV fuel consumption per 100 km is obtained as (5)
1 QS = h e,max ×ht × H l
3 vi (t ) mv × g m ïì I æ ì vi (t ) ü ö + 0.5 × ra × CD × Af × í íå ò çç mv × g × f r × ý ÷÷dt + 3.6 2 × 3.6 2 î 3.6 þ ø ïî i =1 Ti è
with ηe,max being the maximal engine efficiency.
ïü 2 2 ( V V ) [l ]. ý å 1 2 j j =1 ïþ J
3. Theory Verification In order to examine the validity of the above mentioned assumptions and the feasibility of conclusions based on (5), fuel consumption of several existing HVs was calculated using (5) and compared to the available experimental data (USDE 2011). The UN/ECE Elementary Urban Cycle, shown in Fig. 1 was adopted.
50
velocity [km/h]
40 30 20 10 0 0
50
100 time [sec]
150
Fig. 2: UN/ECE Elementary Urban Driving Cycle
The main characteristics of the cycle are summarized in Table 1 (UKDT 2011). According to Fig. 2, the cycle consists of four non-zero constant state speed intervals and three following accelerations: 0 – 15 km/h, 0 – 32 km/h and 0 – 50 km/h (decelerations are neglected). In addition, since the total distance of a cycle is approximately 1 km, the cycle is repeated 100 times to cover 100km, i.e. I = 300 and J = 700 are substituted in (5). Table 1: Main characteristics of UN/ECE Elementary Urban Driving Cycle
Parameter
Value
Total distance Total time Driving time Standing time Accelerating time Average speed Maximum speed Number of acceleration intervals Number of total nonzero intervals
994.6 m 195 s 150 s 45 s 53 s 18.4 km/h 50 km/h 3 7
The results of the verification are given in Table 2. It can be concluded that the values calculated by (5) are very close to the experimental ones (the maximum deviation is less than 5%), which proves that Eq. (5) can be adopted for fuel consumption prediction. Table 2: Fuel consumption of different hybrid vehicles
Hybrid Vehicle Type Honda Insight Toyota Prius Lexus GS 450 Ford Fusion Honda Civic
Fuel Consumption, l/100 km from (UKDT 2011) from (5) 3.90 3.73 4.90 5.10 7.90 7.54 6.55 6.55 5.35 5.32
4. Application to Gas Turbine Based Hybrid Vehicles 4.1. Determining the vehicle mass According to (5), in order to determine the fuel consumption of HV equipped with various heat engines, it is important to identify the mass of the vehicle. A GTequipped vehicle benefits from a reduced weight due to the low specific mass of both the GT and associated generator. The mass of the generator can be estimated as (Zwyssig et al. 2005; Tuysuz et al. 2010)
P×r g , m = 0.09 g C ×n
(6)
where P is the engine power, [W]; ρg is the average density of rotor materials, [g/cm3]; C is the torque-per-volume constant, [N∙m/cm3]; n is the engine rotational speed, [rpm].
According to (Tuysuz et al. 2010), Eq. (6) is a fair approximation for engines rated at from several hundred watts up to tens of kilowatts. The mass of the engine is estimated as (Schwaller 1977; Granet et al. 2004) P . m = e 1000 × m
(7)
The ranges of specific mass µ are summarized in Table 3 (Schwaller 1977; Granet et al. 2004) for various engine types along with rotational speeds and engine
efficiencies. Note that newly developed diesel engines for several hundred kilowatt hybrid drives may reach 42% efficiency, however the efficiencies of diesel engines rated at several tens of kilowatts are as indicated in the Table. The average density of rotor materials and the torque-per-volume constants are assumed to be the same for the three mentioned engine types and possess the values of 7.5 g/cm3 and 0.036 N∙m/cm3, respectively. Table 3: Technical parameters of various engines
Type of engine Diesel Gasoline GT
Rotor speed n, [rpm] 3960 4980 90000
Specific mass μ, [kW/kg] 0.50-0.62 0.65-0.77 5-7
Engine efficiency, ηe 0.25-0.30 0.25-0.30 0.20-0.25
In order to determine the mass ratio of different vehicles, assume that the total mass (mv) of the HV with a GT is 1000 kg and the rating of the engine is 50 kW. Hence, in order to determine the mass of a vehicle equipped with a different type of engine, the mass of the engine and the generator is added to the mass of the GT-based vehicle without its engine and generator. For example, according to Table 4 the total mass of a diesel engine based hybrid vehicle is calculated using the following: 90.9 + 170.5 + (1000 – 10 – 9.4) = 1242 kg. Note that the generator and engine masses in Table 5 were calculated according to Eqs. (6) and (7), respectively and the specific mass in Eq. (7) was chosen as the median value of the range, given in Table 3. Table 4: Mass of components and vehicles with various engines
Type of engine Diesel Gasoline GT
Engine mass me, [kg] 90.9 71.4 10
Generator mass mg, [kg] 170.5 117.2 9.4
Total vehicle mass mv, [kg] 1242 1169.2 1000
4.2 Estimated fuel consumption of generic hybrid vehicles with different engine types The calculations were performed by applying (5) to UN/ECE Elementary Urban Driving Cycle. Vehicle masses, given in Table 4 and parameters, presented in Table 5 were adopted. The resulting fuel consumptions are summarized in Table 6. Table 5: Summary of parameters used in calculations
Engine
ηe
Diesel
0.28 0.93 34∙106 0.018 0.3
1.6 1.2
Gasoline 0.28 0.94 36∙106 0.018 0.3
1.6 1.2
GT
ηt
Hl
fr
ρa·CD Af
0.23 0.95 36∙106 0.018 0.3
γm
1.6 1.08
Table 6: Calculated fuel consumption
Type of engine Fuel consumption l/100km Diesel 5.07 Gasoline 4.46 GT 4.39
Fuel consumption Mpg 46.39 52.74 53.53
4.3 Discussion According to the data, presented in Table 6, it can be concluded that modern GT engine based HVs may be as good as gasoline engines and better than diesel engines in terms of fuel consumption, despite the lower engine efficiency of GT compared to piston engines. This is due to the fact that employing GT engines leads to significant vehicle mass reduction (as demonstrated in Table 4), which significantly improves fuel consumption. Given the widely recognized advantages of GT engines described above, it can be concluded that they can successfully compete with piston engines in HVs.
5. Conclusion Fuel efficiency of modern gas turbine engine based hybrid vehicles was estimated in the manuscript and compared to the fuel efficiency of the piston engine based hybrid vehicles. An equation for calculating fuel consumption of fully hybrid and plug-in hybrid vehicles was derived. It was assumed that the acceleration energy is provided by the electrical drive train, leaving the fuel-based source to supply the average power of the vehicle. The equation was verified by calculating the mileage of several commercial hybrid passenger vehicles, and comparing the results to the available test results. It was revealed that the results are close when adopting an urban driving cycle according to the European Union Directives and regulations of the United Nations Economic Commission for Europe. Then the equation was applied to calculating fuel efficiency of a generic gas-turbine engine based hybrid vehicle. The relatively poor efficiency of gas turbine was offset by reduced turbine-generator weight, resulting in a lower overall weight of the vehicle, leading to fuel consumption decrease. Estimated fuel efficiency of gas turbine engine based vehicles was shown to be similar to the efficiency of widely employed diesel and gasoline engine based vehicles. Based on the results, given the advantages of gas turbines, which include higher environmental performance and lower weight, it can be concluded that gas turbine engines may have the potential of replacing piston engines in hybrid cars.
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