Arabian Journal for Science and Engineering https://doi.org/10.1007/s13369-018-3254-7
RESEARCH ARTICLE - MECHANICAL ENGINEERING
Volumetric Efficiency Optimization of Manifold with Variable Geometry Using Acoustic Vibration for Intake Manifold with Variable Geometry in Case of LPG-Enriched Hydrogen Engine Sahar Hadjkacem1 · Mohamed Ali Jemni1 · Mohamed Salah Abid1 Received: 9 September 2017 / Accepted: 9 April 2018 © King Fahd University of Petroleum & Minerals 2018
Abstract A proper design of the engine intake system can provide the best engine performance. The modeling of inlet system is very important for the evaluation of the engine performance. It is known that the wave dynamics of intake system influences the engine performance. In the present work, the acoustic supercharging phenomenon is applied to optimize the volumetric efficiency of an engine converted into LPG–hydrogen blend. The effect of the intake plenum length on the engine performance is investigated. In fact, an analytical resolution of acoustic waves is used to perform the optimal length for several engine speeds. This resolution is based on the impedance method. In a second step, a simulation of the pressure wave evolution in the intake pipe is carried out using the method of characteristic in order to validate the lengths analytically found. After that, a validation is achieved through experimental data. The results showed that an optimum length calculated by the analytical method gives a maximum in-cylinder velocity (0.649 m at 750 rpm and 0.696 m at 1000 rpm). Keywords Gas engine · Intake manifold · Variable geometry · Acoustic · Supercharging
1 Introduction Improving engine performance, reducing fuel consumption costs and decreasing emissions are the primary objectives of vehicle manufacturers. Several techniques are adopted. Among them, the use of gaseous alternative fuels is found to be very promising. However, converting a conventional engine fueled with gasoline or diesel into a gas engine can cause a reduction in the engine efficiency [1,2]. For this purpose, increasing the volumetric efficiency presents a solution for this problem. The geometry of the intake manifold is among the methods influencing the engine performance [3– 5]. Optimized intake manifolds provide a better flow motion to the combustion chamber. It is consisted generally of a plenum and runners which lead to each cylinder. The lengths of plenum or runners must be carefully chosen as they will
B 1
Sahar Hadjkacem
[email protected] Laboratory of the Electromechanical Systems, Mechanical Department, National School Engineers of Sfax, University of Sfax, BP 1173, Avenue of Soukra, 3038 Sfax, Tunisia
determine the resonant frequencies of the manifold. When the engine is run at a speed where one or more of these resonances is excited, the volumetric efficiency and the intake noise level can be affected [6]. In IC engine, the valve and piston motions of the intake system produce pressure waves that propagate inside the intake manifold. This phenomenon can impact the engine performance and especially the volumetric efficiency [7]. At the opening of the intake valve, expansion waves are developed and spread to the other end of the intake pipe. These expansion waves may be reflected as positive pressure waves at the end of manifold and propagated back to the cylinder end of the pipe [8]. Previous and recent researches have largely studied the effect of the acoustic tuning and influence of pressure wave action on the volumetric efficiency [9–12]. For instance, Harrison et al. [13] employed a linear acoustic model to obtain a better understanding of the nature of acoustic wave dynamics. They used this model to improve the inlet volumetric behavior. On the other hand, Yin et al. [14] developed one-dimensional models of wave propagation in inlet pipes to simplify the understanding of this phenomenon. Computational tools should be developed to take into account this kind of phenomenon.
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Previous studies have mostly employed one-dimensional gas dynamic schemes to evaluate the acoustic wave behavior [15–17]. The gas dynamics flow equations are obtained by: the continuity equation, the momentum equation, and the energy equation [18]. Historically, the method of characteristics is used to solve these gas dynamic equations [18–20]. The process reduces partial differential equations to a family of ordinary equations, permitting a solution to be included from initial data [21]. In this paper, the acoustic supercharging phenomenon is adopted to optimize the volumetric efficiency of an engine converted into LPG–hydrogen blend. The initial manifold of this engine is modified in a variable geometry by varying the length of the plenum. This method is also used to calculate the optimal lengths corresponding to the engine critical regimes. The optimal lengths are performed using an analytical resolution of acoustic waves, whose resolution is based on the impedance method. In a second step, the method of characteristics is used to simulate the pressure wave evolution in the pipes. After that, the experimental data are adopted to validate the numerical results.
2 Generality of the Acoustic Supercharging The acoustic supercharging is beneficial when the pressure wave, which is reflected in the intake pipes, falls in phase with the depression wave caused by the descent of the piston, all at the moment of opening of the valve. Morse et al. [22] noted that supercharging effect occurs only if the valve closes when the pressure is greater than the atmospheric one. Harrison et al. [6,13] used a linear acoustic model to obtain a better understanding of the nature of the acoustic wave dynamics.
3 Engine Geometry Modeling The geometric model used consists of the intake system of a CLIO 2 engine with a pipe that changes the inlet system length. The characteristics of the engine are illustrated in Table 1. This engine is modified from gasoline configuration into gaseous bi-fuel LPG configuration in a first step. After that, it is adapted to a hydrogen operation with a mass fraction equal to 20% of the total gas intake. As shown in Fig. 1, the intake manifold is equipped with a variable length plenum, which has a diameter of 35 mm. The engine is run at different speeds ranging from 750 to 3000 rpm. The manifold geometry variation is linked to the plenum length variation (the runners lengths are fixed). In order to study the impact of the plenum length on the volumetric efficiency, a pipe with variable lengths is tested.
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Table 1 Characteristics of the studied engine Engine parameters
Value
Engine (four cycle)
CLIO 2 D7F 1.2
Displacement (dm3 )
1.2
Bore/stroke (mm)
69/76.8
Intake valve open
4
Compression ratio
9.65:1
Rated speed (rpm)
2500
Maximum intake valve lift (mm)
8.8
Inlet valve diameter (mm)
33
Valve seat angle (degree)
120
Intake manifold diameter (mm)
45
4 Gas Dynamic Modeling Natural supercharging is a technique that optimizes the volumetric efficiency of the internal combustion engine. This technique is related to the optimization of the inlet system length. For this reason, the simulation of the pressure waves in the inlet pipe is necessary. The flows into the inlet circuit are generally simplified and considered to be one dimensional. The study of unsteady inlet flow helps optimize the intake manifold. The inlet manifolds can be studied using the resolution of unsteady flow one-dimensional equations. These equations are: the continuity equation, the momentum equation, and the energy equation. They can be written as follow [13]:
∂ρ ∂V ρV d A ∂ρ +V +ρ + =0 ∂t ∂x ∂x A dx ∂V ∂ρ ∂V ∂ρ d A ρ +V + 2ρV + V2 ∂t ∂t ∂x ∂ x dx ρV 2 V ∂p − 4λ =− ∂x 2D |V | ∂p ∂p +V ρ(γ − 1)(q + V F) = ∂t ∂x ∂ρ ∂ρ − c2 +V ∂t ∂x
(1)
(2)
(3)
ρ density, p pressure, V axial velocity, A cross section area, λ friction coefficient, D inlet pipe diameter, γ specific heat ratio, F force of friction, q heat quantity, c celerity of sound. The methods of solving previous equations are various, among which are the acoustic analytical method of determining the optimal lengths of the intake pipes and the numerical method of characteristics to simulate the propagation of the pressure waves.
Arabian Journal for Science and Engineering Fig. 1 Geometry modeling
1 2 3 4 5 6
4.1 Acoustic Method
Table 2 Optimum lengths of inlet system
The “acoustic” approach is an essential element for the study of the vibratory phenomena. The optimal length of the plenum depends on the resonance of the acoustic vibrant waves in the intake pipe. This phenomenon is directly related to the behavior of the acoustic waves and their propagation in the intake pipes. A system of linearized acoustic equations depends on two variables and interesting for engine filling is obtained [18]:
∂ 2 ∂ ∂t (δ p) + ρc ∂ x (δV ) = ∂ ∂ ρ0 ∂t (δV ) ∂ x (δ p) = 0
0
(4.a) (4.b)
(4)
Due to a pressure variation caused by a wave, a velocity variation passage is generated in the in-cylinder flow. This variation depends on specific characteristics in acoustic impedance. The specific acoustic impedance “Z” of a gaseous midst is written in the following form: Z=
δ p ρ0 c0 f I (c0 t − x) + f II (c0 t + x) = AδV A f I (c0 t − x) − f II (c0 t + x)
(5)
f I and f II represent progressive disruption functions and depend only on the variable V . The pressure disruptions created by the acoustic wave are functions of “x” abscissa of the intake pipe section and time “t”. In the case of a harmonic acoustic wave, the characteristic impedance of a pipe is time independent; it depends only on the abscissa of the section. In this study, the intake pipe is considered as a pipe (with a length equal to “l”) closed at the first extremity (x = 0) and open at the second (x = l). Since the boundary conditions of this tube, a system of equations will be held:
Variable pipe Plenum Runners Head pipe Combustion chamber Total inlet length
At x = 0, δ p0 = 0 ⇒ Z 0 = 0 At x = l, δUl = 0 ⇒ Z l → ∞
(6.a) (6.b)
(6)
Engine speed (rpm)
750
1000
2500
3000
Length (m)
0.694
0.696
0.89
0.747
Based on the above conditions, the length of the optimum pipe for having the acoustic supercharging phenomenon is: L=
(2k + 1) c0 4 fr
(7)
k harmonic vibration, that is an integer. At a given engine speed, the period of vibration is given by: tf =
720 − θa 6n
(8)
n engine speed (rpm), θa the total opening angle of the valve (degree). 1 tf c0 (2k + 1)c0 c0 = = fr = L 4L 4L 2k+1 4 2k+1 L = 4cf0r (11.a) ⇒ L L 2k+1 = 2k+1 (11.b)
fr =
(9) (10)
(11)
From Eq. (11.a), the optimal lengths can be calculated for each engine speed (see Table 2). The calculated lengths from Eq. (11.b) are the lengths checking an acoustic supercharging which varies according to k. After choosing these lengths, 1D simulation will be developed to verify the analytical results. These results are verified from a 1D simulation based on the characteristic method. A specific code has been developed to perform this simulation.
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t
This code was carried out with the “Matlab” programming software. The functions and mathematical procedures are integrated into this software. The pressure wave’s evolution along the inlet pipe can be plotted using this code.
C+
Equations (1) and (2) are two hyperbolic nonlinear partial differential equations. V and p are considered as the main variables of flow. It is necessary to express the density of the mixture ρ according to the fluid pressure for solving these equations numerically. The computer program calculates the unsteady motion in the inlet system using the method of characteristics. Equations (1) and (2) may be written in a characteristic form as: = V +c (12.a) dV + c dρ = 0 (12.b) ρ dx (13.a) dt = V − c dV − c dρ = 0 (13.b) ρ dx dt
(12) (13)
The sign “+” is for the waves coming from the upstream end although the “−” is for the waves coming from the downstream end. It can be said that there are two curves C + and C − , which are the respective integral curves of the differential equations: C+ ⇔
ρP − ρR = 0, ρR (x P − x R ) = (V R + c) (t P − t R ),
(V P − V R ) + c
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(14) (15)
S x i-1
i
i+1
Fig. 2 Characteristics lines
ρ P − ρS = 0, ρR (x P − x S ) = (VS + c) (t P − t S ) . V P − VS + c
(16) (17)
As Eqs. (1) and (2) are nonlinear, the characteristics are curved on the (x, t) plane. Therefore, the integration is carried out by means of an iterative trapezoidal rule. As a result, the values of V p and ρ P at the point P are obtained: ⎧ ⎨ V P (i) − V (i − 1) + c ρ P (i)−ρ(i−1) = 0 ρ(i−1)
(18.a)
⎩ V p (i) − V (i
(18.b)
+ 1) + c ρ P (i)−ρ(i+1) ρ(i+1)
=0
(18)
The pressure will be calculated with the following equation of acoustic celerity: c=
Equations (12.b) and (13.b) determine the evolution of velocity and pressure depending on time and space. They are called compatibility equations or evolution equations. They are not valid only when Eqs. (1) and (2) are satisfied, respectively. It is more favorable to be solved numerically. Figure 2 shows the lines C + and C − in the plane (x, t). It is advantageous to visualize the development of the solution in the independent plane variables (x, t). Since V = V (x, t) and C = C[ p(x, t)] are functions of the point (x, t), the lines C + AND C − appear in this plan as curved lines. These lines are called characteristic lines along which Eqs. (12.a) and (13.a) are checked. It is assumed that the conditions (x, t, V , ρ) at the points R and S are known. The characteristic lines from R and S intersect at a point P whose coordinates are unknown. By integrating Eqs. (12) and (13), they can be written for both signs in four finite difference equations:
C-
R
dx dx = V + c C− ⇔ = V −c dt dt
Δt
P
t + Δt
4.2 Characteristic Method
Δx
γP ρ
(19) C
where γ = Cvp · C p and Cv are the isobaric and isochoric thermal capacities of gas. The celerity of sound can also be calculated using the equation of state, the coefficient γ , the specific constant of the gas R and temperature T (◦ K): c=
γ RT
(20)
For air–LPG–H2 mixture: γ = 0.95 × γair + 0.04 × γLPG + 0.01 × γHydrogen R = 0.95 × Rair + 0.04 × RLPG + 0.01 × RHydrogen To determine the solution in the two extreme sections, boundaries conditions have to be introduced: – The inlet system is considered as a pipe of length l, closed at the first end (x = 0) and open at the second (x = l).
Arabian Journal for Science and Engineering
a
Optimized length=0.694 m
8
b
8
Optimized length=0.696 m
6
6
4
4
Pr (mbar)
Pr (mbar)
Initial length
2 0 -2
0
0,02
0,04
0,08
0,1
-2
0
0,02
0,04
Optimized length=0.89 m
d
Initial length
0,08
Time (s)
Time (s)
8
0,06
CIVT (s)
-6
6
8
Optimized length=0.747 m Initial length
6 4
Pr (mbar)
4
Pr (mbar)
0
CIVT (s)
-6
2 0 -2
2
-4
-4
c
0,06
Initial length
0
0,005
0,01
0,015
0,02
0,025
0,03
2 0 -2 -4
-4
CIVT (s)
-6
0
0,005
0,01
0,015
0,02
0,025
CIVT (s)
-6
Time (s)
Time (s)
Fig. 3 In-cylinder air relative pressure. a n = 750 rpm, b n = 1000 rpm, c n = 2500 rpm, d n = 3000 rpm
5 Meshing and Hypothesis The subdivision of the space domain is represented by: x =
L N
(21)
where L is the domain length of the pipe and N the number of selected meshes. The time domain mesh is represented by: Dt =
dx c0
(22)
where c0 is the sound celerity. In this work, a condition of instantaneous increase in the pressure is considered related to the sudden closure of the intake valve.
6 Simulation Results In this part, the evolutions of pressure waves along the intake system starting from the plenum input until variable the intake valve are presented. These evolutions are developed for three cases of in-cylinder flow: pure air, air–LPG
blend, air–LPG–hydrogen blend. These results were taken for engine speeds at 750 rpm (starting speed), 1000 rpm, 2500 rpm (nominal speed corresponding to the maximum torque) and 3000 rpm (acceleration speed corresponding to the maximum power).
6.1 Pressure Wave Evolution for Pure Air Figure 4 shows the pressure wave evolution along the inlet pipes. These evolutions are presented for the optimal lengths corresponding to the engine speeds. Based on Fig. 3, it is noticed that the waves for all the engine speeds begin with maximum pressure amplitude (pressure waves), which justifies that the sudden closing of the intake valve causes this abrupt change in pressure. Using the optimized length, it has been observed that there is a maximum amplitude at the propagation time end (moment of valve opening). The existence of maximum amplitudes indicates that where is an acoustic or natural supercharging. This type of wave helps to direct the flow to the combustion chamber, which leads to the increase in the volumetric efficiency. The existence of minimal amplitudes indicates that the pressure waves prevent the incoming flow which reduces the volumetric efficiency. It has been noted that the wave propagation periods decrease when the engine speed decreases.
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Arabian Journal for Science and Engineering Pure air Air_LPG
8 6
Pr (mbar)
4 2 0 -2
0
0,005
0,01
0,015
0,02
0,025
0,03
0,035
-4
CIVT (s) -6
Time (s)
Fig. 6 Comparison of pure air and air–LPG–hydrogen relative pressure at engine speed = 750 rpm
Fig. 4 Comparison of pure air and air–LPG blends relative pressure at engine speed = 2500 rpm
6
Optimized length=0.89 m
8
Initial length
4
Pr (mbar)
6
Pr (mbar)
4 2
2 0 -2
0 -2
0
0,005
0,01
0,015
0,02
0,025
Pure air Air_LPG_H2
8
0,03
0,035
0
0,005
0,01
0,015
0,02
0,025
0,03
0,035
-4
CIVT (s) -6
-4
Time (s)
CIVT (s) -6
Time (s)
Fig. 7 Comparison of pure air and air–LPG–hydrogen relative pressure at engine speed = 2500 rpm
Fig. 5 Relative pressure variation for initial length and optimized length of the plenum at engine speed = 2500 rpm
Pure air Air_LPG_H2
8 6
6.2 Pressure Wave Evolution for Air–LPG Blends
6.3 Pressure Wave Evolution for Air–LPG–Hydrogen Blends The in-cylinder flow is taken as an air–LPG–hydrogen. The percentage of hydrogen taken for this study is 20% of the total gas intake. The engine speeds studied in this section start at
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Pr (mbar)
In this section, simulation focuses on the study of the reel blend operation (Fig. 4). The engine starts its operation with just an air–LPG mixture. The results presented are about 2500 rpm, which is the most significant engine speed (for maximum torque). The maximal amplitude is conserved so that the mixture always checks the natural supercharging. The harmonic wave propagation increases compared to the pure air, which causes an increase in the velocity of the particle entering the combustion chamber. Figure 5 shows the effect of the use of an optimal length in the intake circuit for the nominal speed. It is noted that there is a variation in the length of the plenum influence on the pressure wave behavior since there is a maximum amplitude just before the opening of the intake valve.
4 2 0 -2 -4 -6
0
0,005
0,01
0,015
0,02
0,025
0,03
0,035
CIVT (s)
Time (s)
Fig. 8 Comparison of pure air and air–LPG–hydrogen relative pressure at n = 3000 rpm
speed (750 rpm), nominal speed (2500 rpm) and acceleration speed (300 rpm). Figures 6, 7, 8 and 9 show the evolution of the pressure waves along the intake path. From these figures, it has been noted that the addition of LPG enriched with hydrogen justifies the optimal lengths calculated by the analytical method, due to the existence of a maximum amplitude just at the end of the wave propagation time: this is the opening time of the intake valve. Such a wave helps to direct the flow to the combustion chamber. In addition, it is noted that the period of wave increases when working with the mixture
Arabian Journal for Science and Engineering Optimized length=0.89 m
8
Table 3 Experience engine characteristics
Pr (mbar)
Initial length
6
Parameters
Value
4
Engine
Ford Kent/Valencia OHV 26C 77
2
Displacement (dm3 )
1.2
Intake advance opening (degree) 12 0 -2
0
0,005
0,01
0,015
0,02
0,025
0,03
0,035
Intake closing delay (degree)
-4
Time (s)
Fig. 9 Relative pressure variation for initial length and optimized length of the plenum at engine speed = 2500 rpm
In-cylinder velocity (m/s)
14
CIVT (s) -6
35
n= 750 rpm n= 1000 rpm
13,5 13 12,5 12 11,5 11 10,5 10 0,6
0,62
0,64
0,66
0,68
0,7
Inlet system length (m)
Fig. 11 In-cylinder flow velocity inside cylinder for 750 and 1000 rpm speed
Fig. 10 Test bench of experience engine
which is explained by the increase in the fluid particle speed. This increase is due to the addition of hydrogen, which is a too light gas compared to other gases, which optimizes the flow rate entering the combustion chamber. Figure 10 indicates the effect of the use of an optimal length in the intake circuit for the nominal speed. It is noted that the variation in the length of the plenum influences the pressure waves behavior since there is a maximum amplitude just before the opening of the intake valve.
7 Experimental Validation of the Pipe Length The studied intake manifold is mounted on a test bench of an engine moved by an electric motor with a speed reducer to validate the analytical calculation performed previously. This engine is of FORD type, with four cylinders. Its characteristics are detailed in Table 3. This engine has almost the same intake system of geometric specification as the CLIO 2 engine (see Fig. 10). The air flow velocity measurement is displayed using a thermal anemometer, specific for a very
low air velocity which helps measure the speed between 0.2 and 20.0 m/s. The engine speeds are calculated using a motor drive, which can reach a power of 9.2 kW and a torque max 144 N m. It helps calculate the speeds in a range of 150– 1400 rpm. Figure 11 presents the variation of the in-cylinder velocity with the inlet system length. The experimental results confirm the analytical approach. From this figure, an optimum length calculated by the analytical method gives a maximum in-cylinder velocity (0.649 m at 750 rpm and 0.696 m at 1000 rpm). Therefore, the optimal lengths numerically calculated are validated by the experiment.
8 Conclusion Several engine manufacturers are focused on variable intake manifold geometry due to their improvement on engine performance, especially the volumetric efficiency. The optimization of this parameter is directly related to the control of filing process. The filling analysis of an internal combustion engine is linked to the modeling of pressure waves in the inlet systems. In this study, the effect of the intake manifold geometry on the engine volumetric efficiency is identified. The acoustic method is adopted to find the inlet system lengths of the volumetric efficiency of an engine converted into LPG– hydrogen blend. After that, a simulation of the pressure wave evolution in the inlet system is carried out using the method of characteristics in order to analytically validate the found
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lengths. Moreover, the validation of the numerical results is performed with experimental data. Subsequently, the intake system length must be equal to 0.89 m at the maximum torque operation, in order to improve the volumetric efficiency. Acknowledgements The authors wish to thank MIRAGE society for their help during the engine tests and financial assistance. The authors also acknowledge to National School of Engineers of Sfax (ENIS) and Laboratory of the Electromechanical Systems (LASEM) for supporting this research and simulation facilities.
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