The Effects of Intake Plenum Volume on the Performance of a Small Naturally Aspirated Restricted Engine Leonard J. Hamilton Jim S. Cowart Jasen E. Lee Ryan E. Amorosso U.S. Naval Academy, Annapolis, MD 21402
1
Intake tuning is a widely recognized method for optimizing the performance of a naturally aspirated engine for motorsports applications. Wave resonance and Helmholtz theories are useful for predicting the impact of intake runner length on engine performance. However, there is very little information in the literature regarding the effects of intake plenum volume. The goal of this study was to determine the effects of intake plenum volume on steady state and transient engine performance for a restricted naturally aspirated engine for Formula Society of Automotive Engineers (FSAE) vehicle use. Testing was conducted on a four cylinder 600 cc motorcycle engine fitted with a 20 mm restrictor in compliance with FSAE competition rules. Plenum sizes were varied from 2 to 10 times engine displacement (1.2–6.0 l) and engine speeds were varied from 3000 rpm to 12,500 rpm. Performance metrics including volumetric efficiency, torque, and power were recorded at steady state conditions. Experimental results showed that engine performance increased modestly as plenum volume was increased from 2 to 8 times engine displacement (4.8 l). Increasing plenum volume beyond 4.8 l resulted in significant improvement in performance parameters. Overall, peak power was shown to increase from 54 kW to 63 kW over the range of plenums tested. Additionally, transient engine performance was evaluated using extremely fast (60 ms) throttle opening times for the full range of plenum sizes tested. In-cylinder pressure was used to calculate cycle-resolved gross indicated mean effective pressure (IMEPg) development during these transients. Interestingly, the cases with the largest plenum sizes only took 1 to 2 extra cycles (30–60 ms) to achieve maximum IMEPg levels when compared with the smaller volumes. In fact, the differences were so minor that it would be doubtful that a driver would notice the lag. Additional metrics included time for the plenums to fill and an analysis of manifold absolute pressure and peak in-cylinder pressure development during and after the throttle transient. Plenums below 4.8 l completely filled even before the transient was completed. 关DOI: 10.1115/1.4001071兴
Introduction
Intake system tuning is a well known and cost effective method of increasing the performance of internal combustion engines without the use of mechanical turbochargers or superchargers for motorsports applications. In general, intake systems consist of an airbox or plenum chamber 共fed by a throttle body兲 and runners that lead from the plenum to each cylinder. Engine designers strive to take advantage of pressure wave dynamics in the intake system to increase the mass of air transferred to the combustion chamber over desired rpm ranges. While the actual wave dynamics are complex for a multicylinder engine, the intake system can be modeled as a simple Helmholtz resonator 关1兴. When the intake valve opens and the piston descends, a rarefaction or expansion wave travels upstream in the runner toward the plenum. Upon reaching the runner opening in the plenum, this wave is partially transmitted 共still as an expansion wave兲 into the plenum. At the same time, part of the original expansion wave is reflected as a compression wave that Contributed by the IC Engine Division of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received September 23, 2009; final manuscript received September 25, 2009; published online September 24, 2010. Editor: Dilip R. Ballal. The United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States Government purposes.
Journal of Engineering for Gas Turbines and Power
heads back to the cylinder. If the compression wave arrives at the intake valve before it closes, the increased pressure will effectively force more air into the cylinder 关2兴. This tuning effect or resonant supercharging leads to increased volumetric efficiency and torque. Meanwhile, the expansion waves will travel to the inactive branches 共with closed valves兲 and be reflected as expansion waves back to the active runner. These expansion waves reduce intake runner pressure and have the effect of reducing volumetric efficiency 关1兴. Typically, intake tuners focus on runner geometry 共length and/or cross section area兲 and plenum size and shape. An excellent overview of resonant supercharging is provided by Benajes et al. 关3兴. This method is particularly useful for vehicles competing in the Formula Society of Automotive Engineers 共FSAE兲 design series, where the extra weight and complexity of mechanical boost systems could be detrimental to overall performance. The FSAE series provides college students from around the world an opportunity to conceive, design, fabricate, and compete a small scale formula style vehicle based on a comprehensive set of design constraints. Several of the constraints pertain to engine and intake design. For example, engine size is limited to 610 cc and all intake air must pass through a restrictor of circular cross section 共20 mm for gasoline or 19 mm for E85兲 关4兴. Some excellent studies have been published to document the effects of intake tuning on a restricted engine suitable for use in the FSAE design series. Jawad et al. 关5兴 evaluated four different intake designs with a Honda™ CBR600 F4i engine coupled to a JANUARY 2011, Vol. 133 / 012801-1
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Table 1 2002 Honda™ CBR 600 F4i specifications Engine configuration Displacement Fuel system Cooling system Lubrication system Compression ratio Valves per cylinder Bore Stroke Valve timing IVO IVC EVO EVC
Inline four, 4 stroke, DOHC 600 cc EFI Water Wet sump 12:1 4 67.0 mm 42.5 mm 30 60 50 10
deg BTC deg ABC deg BBC deg ATC
water brake dynamometer. Their performance criteria were based on total area under the power curve for each configuration. They focused primarily on novel runner geometry approaches and did not document changes in plenum volume. McKee et al. 关6兴 provided a seminal contribution to optimization of this class of engines by experimentally evaluating the effects of diffuser length 共after the restrictor兲, runner length, camshaft modifications, and exhaust tuning. However, they selected a plenum volume of 3.5 l and did not vary it during testing. This decision was based on model predictions, which did not show much benefit by increasing plenum volume beyond this amount. The effect of plenum volume on engine performance was studied and reported by Ceviz 关7兴 as a basis for variable intake plenum technology. He installed plenum additions 共90 and 180 cc兲 to the original intake manifold of a 1.6 l four cylinder gasoline engine over a modest rpm range of 1250–3000 rpm. While he found that increasing plenum volume increased power at the mid-rpm range, plenum size had to be reduced for best performance at higher speeds. It should be noted that this engine was equipped with a carburetor and the author cited difficulty with proper air-fuel ratio control when changing plenum size. The objective of the current study is to determine the effects of plenum size on volumetric efficiency, torque, and power for a restricted intake 600 cc motorcycle engine for use in Formula SAE applications under steady state and transient operating conditions.
2
Experimental Setup
2.1 Experimental Apparatus. All testing was conducted using a 2002 Honda™ CBR600 F4i engine equipped with a MoTeC™ M4 engine control unit 共ECU兲. The engine characteristics are listed in Table 1. Engine performance parameters were measured using a Land and Sea™ water brake dynamometer coupled to the output shaft. The dynamometer was equipped with a load servo to maintain a specified rpm regardless of throttle position. The intake apparatus included a throttle body, an intake pipe with a circular 20 mm diameter restrictor, a custom variable volume intake plenum and four 0.05 m aluminum intake runners, as shown in Fig. 1. This runner length was chosen to produce peak torque at 10,000 rpm based on the following equation from Lumley 关1兴: L=
共a2 − v2兲 4aN
共1兲
where L is the intake length 共m兲, is the intake valve open duration 共rad兲 divided by , a is the speed of sound 共m/s兲, v is the velocity of air 共m/s兲 in the intake 共Lumley uses v ⬇ 0兲, and N is the engine speed 共rad/s兲. From Eq. 共1兲, predicted intake length to produce a torque peak at 10,000 rpm was 0.13 m. Since the intake path in the cylinder 012801-2 / Vol. 133, JANUARY 2011
Fig. 1 Intake system
head was 0.10 m, this would have required the intake runners to be only 0.03 m. To facilitate fuel injector placement, the actual runners were cut to 0.05 m as mentioned above. A 0–2 bar absolute Kistler™ piezoelectric pressure transducer was mounted in the plenum adjacent to the runner leading to cylinder No. 1 with a data rate of 40 kHz. An identical 0–2 bar absolute pressure transducer was placed midway in runner No. 1. This location was 0.12 m from the intake valve as it included the length of the cylinder head intake port beyond the runner base. Next, a 6052C Kistler™ pressure transducer was mounted in the cylinder head to read combustion chamber pressure in cylinder No. 1. In-cylinder pressure was used to calculate gross indicated mean effective pressure 共IMEPg兲 on a cycle resolved basis. An increase in IMEPg would correspond closely to the increase in torque felt by the driver during a throttle “stomp.” Thus, IMEPg was considered a principle metric in evaluating transient performance. Finally, an ECM™ 1200 oxygen sensor was mounted in the exhaust header approximately 0.12 m from exhaust valve to provide positive feedback to the ECU to maintain proper AFR control. The AFR target in the ECU was set to stoichiometric for all test points. Injector sequencing was selected to minimize pressure fluctuations in the fuel rail. The intake plenum was designed as a simple aluminum box with a movable ceiling to provide 9 discrete volumes for testing. The possible volumes were based on engine displacement and ranged from 2 共1.2 l兲 to 10 共6.0 l兲. In all cases, the entrance to the plenum via the restrictor was not changed; only the ceiling was raised or lowered to change plenum volume. The plenum can be seen in Fig. 1. A 45-mm throttle body fitted to the end of the restrictor was used for transient testing. A hand lever was used to actuate the throttle via a control cable. An electronically controlled stepper motor was considered for throttle “tip-in” but was not used as it was unable to achieve the very fast opening time desired 共60 ms兲. This throttle transient represented the fastest time physically achievable by the test team and was felt to meet or exceed the severity of transients that could be achieved in a real world application. Volumetric efficiency, a measure of engine air breathing capacity, was one of the desired parameters to be evaluated in this study as it directly relates to torque produced by an engine 关8兴. It is determined by dividing the actual mass of air consumed by the ideal air mass that could be drawn in based on displacement volume, as shown in Eqs. 共2兲 and 共3兲. Volumetric efficiency is Transactions of the ASME
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0.035
60 cal data linear fit
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-m) corrected torque (N
0.030
fuel flow (cc/shot)
0.025
50
0.020
0.015
y = 0.0036 x − 0.0039
0.010
R2 = 1
45 40 35 30 25
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1
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3
4
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7
8
9
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6 5
vol
pulse width (ms)
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e( um
3
L)
Fig. 2 Injector calibration at fuel pressure= 4.0 bars
2 1
˙ m V = air,actual ˙ air,ideal m where ˙ air,ideal = m
冉 冊
PairVdisp rpm 2 RTair
rpm 2
RPM
共3兲
minimum timing for best brake torque for the range of 1300– 12,500 rpm. Engine knock was not encountered on any of the test runs.
共4兲
冉 冊
12000
Fig. 4 Torque-rpm and plenum volume sweep
A fuel injector calibration test was performed to determine actual fuel flow for a given pulse width. For this calibration, the fuel rail was pressurized to 4.0 bar and a single injector was activated for 1000 “shots” into a graduated cylinder to get an accurate volumetric fuel flow rate for various pulse width values. The result of this calibration is shown in Fig. 2. Notice that the curve intercepts the x-axis at 1.1 ms, which represents the opening time for these injectors. Using this calibration relationship yields the following equation for fuel mass flow rate: ˙ fuel = fuel共0.0036PW − 0.0039兲 m
6000
10000
共2兲
Since the engine was not equipped with a mass airflow sensor, fuel flow rate and AFR were used to determine actual air flow through the engine using equation ˙ air,actual = AFR ⫻ m ˙ fuel m
4000
8000
共5兲
where PW is the fuel pulse width in milliseconds. For all testing, spark timing was set according to the curve shown in Fig. 3. This curve represents experimentally derived
2.2 Experimental Procedures. All testing was performed in a climate controlled test cell with the engine fully warmed up. Prior to each test period, test cell temperature and barometric pressure were recorded. Standard SAE correction factors were used for all performance results. Plenum volumes were varied from 1.2 l to 6.0 l in 0.6 l increments for steady state testing and 1.2 l increments for transient testing. Special care was taken to ensure that all seams and access holes were sealed prior to testing. For steady state testing, the engine was stabilized at wide open throttle from 3000 rpm to 12,500 rpm at 500 rpm intervals. For transient tests, the engine was stabilized at 4000 rpm before the throttle was fully opened in 60 ms. Dynamometer controls were set to simulate acceleration loading on flat terrain. Acceleration fueling was adjusted to ensure proper AFR control throughout the transient. Intake and combustion chamber pressures, absorber torque, fuel pulse width, and AFR were recorded for each test run. Commercial premium gasoline with a 共R + M兲 / 2 octane rating 共average of research and motoring octane number兲 of 94 was used for all test points.
3
Results and Discussion
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Fig. 3 Spark timing curve
Journal of Engineering for Gas Turbines and Power
3.1 Full rpm Sweep. Figures 4 and 5 show graphical representations of the effects of plenum size on torque at various engine speeds. At low rpm, the smaller plenum appears to produce higher torque than the large plenum although the effect is modest. However, above 7000 rpm, it is clear that torque tends to increase significantly as plenum size increases. This effect is more pronounced at higher rpm. In fact, at the maximum rpm tested, torque dropped from 48 N m to 36 N m when comparing the largest and smallest plenums; a 25% loss in torque. It is also evident that there are two distinct torque peaks; one at approximately 6500 rpm and the second near 10,000 rpm. It is also interesting to note that the peak torque speed location has a very weak dependence on plenum size. For the 6.0 l plenum, torque peaks at 54.5 N m at 10,000 rpm, while the 1.2 l plenum results in a peak of 48.5 N m at 9500 rpm. As discussed earlier, this is because runner length is the primary factor in determining the frequency 共driven by engine rpm兲 for resonant supercharging 关3兴. Later in this paper, the effects of plenum size on engine perJANUARY 2011, Vol. 133 / 012801-3
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70
60
6.0L plenum
6.0L plenum 55
60
50
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power (kW)
torque (Nm)
45
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RPM
Fig. 5 Comparison of torque between smallest and largest plenums tested
Fig. 7 Comparison of power output between smallest and largest plenums tested
formance operating at 9500 rpm will be more closely examined. Figure 6 shows a similar rpm and plenum sweep with power as the variable of interest. As before, plenum size has little effect until approximately 7000 rpm, as shown in Fig. 7. At the higher engine speeds, the increase in power with plenum size is dramatic. Peak power output increases from 54 kW for the 1.2 l plenum to 63 kW for the 6.0 l plenum—an increase of 17%. Note that plenum size appears to have a greater effect on the engine speed for peak power than it did on peak torque. In fact, for the smaller plenums, power peaked at approximately 11,000 rpm while the larger plenums drove the rpm for peak power out to 12,500 rpm. This is largely due to the precipitous reduction in torque for the small plenums at high rpm seen in Fig. 4. Another interesting metric is comparison of integrated area under the torque and power curves over the useful rpm range. This metric is useful in evaluating the overall advantage offered by a particular plenum size. Recall that in Fig. 5 the large plenum clearly held the advantage at high rpm but the smaller plenum showed a modest advantage in the low rpm range. Figure 8 shows integrated area 共normalized to the 1.2 l plenum兲 for both torque and power for engine speed ranging from 3000 rpm to 12,500 rpm. From this chart, it is clear that gains in torque and power are relatively modest for plenum volume up to 3.6 l or 6 times engine
displacement. However, increasing plenum volume up to 8 or 10 times displacement produces a relatively large increase in performance based on integrated area. When compared with the 1.2 l plenum, the 6.0 l plenum produces a 5% and 8% increase in area under the torque and power curves, respectively.
70
3.2 Plenum Comparison at 9500 rpm. Next, the effect of plenum size on engine performance at 9500 rpm was closely evaluated. This engine speed was chosen because it corresponded to nominally the highest torque region across the plenum sizes tested. Figure 9 shows the effect of plenum size on volumetric efficiency and power at 9500 rpm. Note that it is not necessary to also plot torque as that would show an identical trend as power since rpm is fixed. It is interesting to see that volumetric efficiency shows only modest gains as plenum size is increased until 4.8 l 共8 engine displacements兲 is exceeded. Beyond that size, volumetric efficiency jumps from 0.83 to 0.95, a relative increase of 14.5%. A similar trend is noted for power. Once a plenum size of 8 engine displacements 共4.8 l兲 is used, power increases by nearly 5%. Overall, power increased from 47 kW to 53 kW across the full range of plenum volumes tested at this engine speed. This corresponds to a 12.7% increase in power with no other modifications to the engine. The fast response plenum pressure traces shown in Fig. 10 are helpful in understanding this significant effect. In this figure, normalized pressure is plotted for several plenums over the range of crank angle degrees 共CADs兲 corresponding to the open intake
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)
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Fig. 6 Power-rpm and plenum volume sweep
012801-4 / Vol. 133, JANUARY 2011
Fig. 8 Comparison of normalized integrated area under torque and power curves for various plenum sizes
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0.978
volumetric efficiency
0.976
56
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0.974
avg P/Patm volumetric efficiency
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corrected power
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corrected power (kW)
volumetric efficiency
0.96
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0.970 0.88 0.968 0.86 0.966 0.84
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48
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0.78 0
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plenum volume (L)
Fig. 11 The effect of normalized intake pressure on volumetric efficiency at 9500 rpm
Fig. 9 Plenum volume sweep at 9500 rpm
valve. In this case, CAD= 0 deg corresponds to top center. The dotted line, representing the smallest plenum, shows two deep pressure troughs; one just after intake valve opening and another one as the piston approached bottom center. The next two bigger volumes, 3.6 l and 4.8 l, show a similar 共but less significant trough兲 just after IVO. These two cases show much higher pressures even as the piston is descending implying greater resonant charging. Finally, the largest plenum shows very little pressure drop just after IVO and a significant peak just before intake valve closing also caused by resonant charging. Qualitatively, it appears that the largest plenum provides the greatest average pressure throughout the intake valve open period. This advantageous pressure profile is likely the result of beneficial wave dynamics that occur in the larger plenum chamber known as resonance charging 关9兴. Due to the confined space in the smaller plenums, strong reflection of expansion waves from neighboring cylinders 共with closed intake valves兲 may cause interference waves that reduce the strength of compression waves in the primary runner thereby negating the beneficial effects of resonant charging to some extent. This may account for the reduced volumetric efficiency measured for the 2.4 l plenum, as seen in Figs. 9 and 11. It is likely that the reflections of expansion waves in the larger plenums are not as strong as those in the smaller plenums and therefore do not degrade resonance charging. To quantify these pressure trends, normalized pressure was averaged across the entire intake valve open period and compared for the various plenum sizes. Figure 11 provides a summary of these averages and shows that they increase significantly as ple-
num volume increases. Also plotted in this figure is volumetric efficiency. It is evident that the trend in normalized pressure averaged over the intake valve open period corresponds directly with an increase in volumetric efficiency. Thus, intake runner pressure can be used as a measure of intake system effectiveness. 3.3 Transient Response. Figure 12 shows a representative throttle transient conducted during this evaluation. Note that throttle “tip-in” is very fast 共60 ms兲 and appears to be essentially linear based on the throttle position sensor. Relative air-fuel ratio remains stable during and after the throttle transient even for several cycles beyond those shown in the figure. This was an important consideration in order to rule out fueling effects as a possible contributor to IMEPg development trends. As manifold absolute pressure 共MAP兲 rises, peak in-cylinder pressure rapidly builds. In order to be considered suitable for data analysis and comparison, each throttle transient had to begin during the intake stroke 共of cycle 0兲 and have a 60 ms opening duration. Figure 13 shows cycle-resolved IMEPg development for various plenum sizes during and after the 60 ms throttle transient. In each case, cycle 0 indicated the start of the throttle transient. The smallest plenum showed nearly immediate IMEPg increase while the largest plenum showed approximately one cycle delay initially. Later in the transient, the 6.0 l plenum took 1–2 more cycles or 30–60 ms longer to achieve the same IMEPg as the 1.2 l plenum. The three middle plenum volumes, 2.4 l, 3.6 l, and 4.8 l tended to be grouped together between these extreme cases. By the sixth cycle, the differences were practically indistinguishable.
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Fig. 10 Normalized plenum pressure for various plenum volumes during intake valve open event for cylinder No. 1
Journal of Engineering for Gas Turbines and Power
Fig. 12 Transient response for 1.2 l plenum
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18
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8 6 4
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2 0
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Fig. 13 Effect of plenum volume on the gross indicated mean effective pressure development
It is believed that even experienced drivers would be unable to detect any acceleration lag differences between the various plenum volumes tested. Figure 14 shows the effect of plenum volume on peak incylinder pressure during and after the throttle transient. Peak pressure trends naturally followed the same behavior as IMEPg development. Plenum volumes 1.2 l and 6.0 l were separated by 1 to 2 cycles and the other three volumes were grouped together in the middle. Figure 15 shows the increase in manifold absolute pressure triggered by the throttle transient for each of the plenum volumes. The pressure values shown are averages taken from several runs at each plenum volume. The throttle transient begins at the start of cycle 0 and is completed by the start of cycle 2, as shown by the vertical line on the graph. For the two smallest plenums, it is clear that MAP exceeds 1.0 bar even before the throttle is fully open. In fact, MAP appears to overshoot ambient conditions suggesting a ram tuning effect that would ultimately benefit engine transient response. By the end of cycle 2, the other plenums had reached maximum pressure. Figure 16 shows a detailed view of intake manifold pressure development with respect to percent of total throttle opening. Unlike the data shown in Fig. 15, these data points were taken from a single representative run for each plenum volume. This was done to avoid “smoothing out” the pressure profiles by averaging
5
6
7
Fig. 15 Cycle-resolved MAP development
them. As a result, pressure pulses occurring during the transient are evident. As shown before, for the smallest two plenums, atmospheric pressure is achieved even before the throttle is fully opened. The remaining plenums appear to be achieving or approaching atmospheric pressure by the time the throttle is opened fully. This indicates that ample intake air is available for combustion by the time the throttle transient has been completed for the majority of the plenum sizes tested. Examining the time it takes to fill each plenum 共defined by reaching atmospheric pressure兲 during the throttle transient further supports this fact, as shown in Fig. 17. Note that all but the two largest plenums are actually full before the throttle is fully open.
4
Conclusions
In summary, there are two main conclusions that can be drawn regarding the effect of plenum volume on the performance of a small naturally aspirated engine. First, an increase in plenum volume resulted in a significant increase in steady state engine torque and volumetric efficiency for the majority of the engine’s operating speed range. In particular: • • •
60
Torque was shown to improve at all engine speeds above 6500 rpm. Maximum torque increase was 31% at 12,500 rpm when comparing the 6.0 l plenum to the 1.2 l plenum. Plenum size did not significantly affect torque peak location. 1.1
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Fig. 14 Effect of plenum volume on the peak in-cylinder pressure development
012801-6 / Vol. 133, JANUARY 2011
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Fig. 16 Manifold transients
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80
fill time (msec)
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throttle transient complete
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Fig. 17 Time to fill plenum during the 60 ms throttle transient for various plenum volumes
•
Increased torque and volumetric efficiency correlated directly to higher average intake pressure observed during the entire intake valve open event for the larger plenums. This enhancement was likely due to the resonant charging effect. For the smaller plenums, this effect was diminished by the effect of neighboring cylinders.
Second, increasing plenum size resulted in negligible delays in transient engine response. Specifically: •
• •
Torque development was only delayed by 1 to 2 engine cycles 共⬃60 ms兲 when comparing the largest and smallest plenum volumes. Effect of plenum size on manifold filling time during the throttle transient was modest. In fact, plenums smaller than 4.8 l completely filled before the transient was complete. It is highly doubtful that even an experienced driver would notice a real world difference in acceleration lag when comparing the plenums tested.
Acknowledgment The authors would like to thank Mr. John Hein and Mr. Charlie Baesch of the U.S. Naval Academy Propulsion Lab for providing support and access to engine test facilities.
Nomenclature a ⫽ speed of sound 共m/s兲
Journal of Engineering for Gas Turbines and Power
⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ V ⫽ ⫽
ABC AFR ATC BBC BC BTC CAD DOHC ECU EFI EVC EVO FSAE IMEPg MAP L ˙ m N Patm PW TC v Vdisp WOT
after bottom center air fuel ratio after top center before bottom center bottom center before top center crank angle degrees dual overhead cam engine control unit electronic fuel injection exhaust valve closing exhaust valve opening Formula Society of Automotive Engineers gross indicated mean effective pressure 共bar兲 manifold absolute pressure 共bar兲 intake runner length 共m兲 mass flow rate 共kg/s兲 engine speed 共rad/s兲 atmospheric pressure fuel injector pulse width 共ms兲 top center air velocity in intake runner 共m/s兲 displacement volume wide open throttle intake valve open duration 共rad兲 / relative air-fuel ratio 共AFRactual / AFRstoic兲 volumetric efficiency density 共kg/ m3兲
References 关1兴 Lumley, J. L., 1999, Engines: An Introduction, Cambridge University Press, Cambridge, UK, Chap. 4. 关2兴 Heywood, J. B., 1988, Internal Combustion Engine Fundamentals, McGrawHill, New York, Chap. 6. 关3兴 Benajes, J., Reyes, E., Galindo, J., and Peidro, J., 1997, “Predesign Model for Intake Manifolds in Internal Combustion Engines,” SAE Paper No. 970055. 关4兴 http://students.sae.org/competitions/formulaseries/rules 关5兴 Jawad, B., Dragoiu, A., Dyar, L., Zellner, K., and Riedel, C., 2003, “Intake Design for Maximum Performance,” SAE Paper No. 2003-01-2277. 关6兴 McKee, R. H., McCullough, G., Cunningham, G., Taylor, J. O., McDowell, N., Taylor, J. T., and McCullough, R., 2006, “Experimental Optimisation of Manifold and Camshaft Geometries for a Restricted 600cc Four-Cylinder FourStoke Engine,” SAE Paper No. 2006-32-0070. 关7兴 Ceviz, M. A., 2007, “Intake Plenum Volume and Its Influence on the Engine Performance, Cyclic Variability and Emissions,” Energy Convers. Manage., 48, pp. 961–966. 关8兴 Yagi, S., Ishizuya, A., and Fujii, I., 1970, “Research and Development of High-Speed, High-Performance, Small Displacement Honda Engines,” SAE Paper No. 700122. 关9兴 Neuber, H. J., Endres, H., and Breuer, M., 1994, “New Variable Intake and Mixture Formation System for Multi-Valve SI Engines,” SAE Paper No. 940449.
JANUARY 2011, Vol. 133 / 012801-7
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