An Approach of the Engine Charge Efficiency Ascertainment

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F2000A029

Seoul 2000 FISITA World Automotive Congress June 12-15, 2000, Seoul, Korea

An Approach of the Engine Charge Efficiency Ascertainment Radu Alboteanu, Cristian Petcu MASTER S.A., [email protected] Romania Based on experimental investigation on a car engine, it was established the relationship between airflow rate and pressure drop along the intake duct versus valve lift. To have an evaluation of charge efficiency, i.e. the theoretical and maximum potential flow of inlet duct during the suction stroke, a model considering the influence of inlet valve through area and came profile and inlet duct geometry was developed. A first method for estimation of charge parameters considers inlet duct and cylinder as two control volumes. The flow between the two control volumes is a function of flow characteristics through the inlet valve, experimental determined, assuming in each computation step the steady flow through the pipe. A second method assumes the unsteady flow through the duct and takes into account the pipe junctions for each cylinder and flow dynamics including the throttle. A two-step hybrid finite difference scheme was used to solve the differential system equations describing the specific processes. During engine tests the conditions considered in the assumptions seemed justified by reasonably good agreement with some quantities and qualitative data. Therefore the outcome of presented research was not only the improvement of engine performances but also the finding of a correlation between theoretical and experimental results. Keywords: engine, charge efficiency, modeling

INTRODUCTION An engine simulation model is useful in many ways in the research programs as well as during engine development, thinking also to the often expensive and sometimes not very efficient cost of measuring equipment. The ways for improving the rate of intake air, i.e. the proper matching of volume and length of the inlet duct, together with the control of inlet valve through area must be considered in such models. The analytical analyze of gas exchange processes means necessarily the determination of the air mass flow rate, i.e. an appropriate prediction of the inlet duct discharge coefficient. Therefore, a very useful input data for some models able to predict the engine charge efficiency is the theoretical and experimental ascertain of the discharge coefficient, as a global result appraise the capacity of an inlet duct. This problem coming from that evaluation is to find out if the global performance quantities as charge efficiency together with indicated thermal efficiency predicted by model agreed with experimental results from engines.

MODELING APPROACH STEADY FLOW In the quasi-steady flow simulation model the balance of energy for an ideal gas flow through the intake direct of an engine was evaluated. By using a coefficient to denote that part of total enthalpy due to the energy exchange that occurs before the inlet valve, the velocity immediate after the valve can be found from equation:

w v = 2 ⋅ c p ⋅ [Tadm − (1 − φ) ⋅ Tcyl ]

(1)

If the variable section controlled by intake valve is known, the flow rate of gas passing through the port can be calculated either as polytropic or isentropic process (in that case ϕ=0, n=k). Therefore, the expression of discharge coefficient as ratio between polytropic and isentropic flow is: n −1   n p 1 − (1 − φ ) ⋅  cyl   p     adm     μ= k −1   k 1 −  pcyl     p adm    

   p adm ⋅

  

 p cyl   p adm

  

p cyl

1 n

1 k

(2)

It can be seen that discharge coefficient µ depends upon:

− polytropic exponent, as a synthesis of friction losses due

to geometric configuration of inlet duct and valve controlled section; − coefficient ϕ; − the ratio between the fluid pressure, immediate after the valve through section and the pressure at the entrance into the duct. The sensitive element of that approach is the definition of polytropic exponent, as seen in the expresion:

n=

pcyl k⋅ ln padm n−1 2 2  A   p n  p pcyl  cyl  n  cyl   v   1 (1 φ)   ln −φ⋅ k − ⋅ k⋅   ⋅ p  ⋅  − − ⋅ p   padm A p  adm  adm     

(3)

The coefficient in that expression emphasize overall energy exchange into heat because of friction losses at the

duct entrance, along the pipe, into the bent of the duct inside the cylinder head and the expansion occurring in the valve through area. It can be calculated by using expressions reported in literature, mainly empirical. In steady flow test the coefficient φ, being a measure of energy exchange between fluid and environmental, can be neglected.

UNSTEADY FLOW The unsteady flow model use the differential equations describing the specific processes into the exhaust and the intake systems of an engine, based on the laws of continuity of mass, conservation of momentum and energy, applied to a small control volume. The flow throughout pipes is practically 3-D, but to consider that in a model, the physical principles of all associated phenomena should be known. The complete theoretical solutions for 3-D steady and unsteady flows are extremely difficult. In case of unsteady flow analysis of engines inlet duct, it is usual to assume the flow to be effectively 1-D. This is not a very bad approximation if we take into consideration various losses by using empirical relations. The used analyze of unsteady flow describe scavenging and volumetric capacities of the engine. The system of hyperbolic partial differential equations, describing unsteady and non-rotational compressible fluid flow is: ∂ρ ∂t ∂w ∂t ∂p ∂t

+ ρ⋅

∂w ∂x

+w⋅

+w⋅

∂w ∂x

+ k⋅p⋅

+

∂w ∂x

∂ρ ∂x

+

∂p ∂x

− ⋅ w2⋅

2⋅π σ

INLET VALVE PORT FLOW Discussions: a. In case of the isentropic flow, it takes into account only the values of the pressure before and after the inlet valve port, considering a reversible adiabatic transform between inlet duct and the cylinder. The internal losses are neglected. The flow coefficient calculated in this case is called µisen b. In case of the irreversible adiabatic flow, the values of pressures and temperatures before and after the inlet valve port, considering the internal losses. We can define a coefficient of irreversibility “c”: 1-

Tcyl T adm

c=

 pcyl   p   adm 

1- 

(4)

− ρ⋅ q⋅ (k − 1) = 0

Generally is admitted that the most adequate method to solve hyperbolic partial equations when the boundaries are very abrupt, as in the case of an engine, is the “method of characteristics”. Despite these, we can solve unsteady flow problems using finite differences' schemes. A two-step hybrid method can be used to solve the above system. The computer program operates in two modes. At the steady flow conditions the program automatically determines also, the intake valve loss coefficient. After finding the loss coefficient, the program can then be run at off-design mode to predict performance of unsteady flow, depending on inlet condition supplied, as in case of the charge of the cylinders of a spark ignition engine. The finite difference schema can be useful for investigating the intake flow dynamics including the carburetor whose throttle influences the flow characteristic. The other constrictions play smaller roles. Hence it is assumed that the throttle is a very important source of discontinuity and the inlet duct is split into two parts, so that conditions on either sides of throttle can be considered boundary conditions for these. Flow can be in both the directions depending upon the pressure in the adjacent cells. For each pipe we can consider minimum two cells. The unsteady flow through the throttle suffers almost same pressure drops as in case of steady flows. It is very useful for calculations by defining a throttle loss coefficient.

k -1 k

∈ [0;1]

(5)

Considering the continuity equation between the valve port and the end cell: ρnc ⋅ w nc ⋅ Anc = μc ⋅ Av ⋅ ρcyl ⋅

ρ ⋅ w dσ ⋅ =0 σ dx

1 ∂p 2⋅π ⋅ + ⋅w⋅ =0 ρ ∂x ρ σ +w⋅

The carburetor is “reduced” to a cell of length equal to the others, but with equivalent cross-section as a function of the load of the engine. In addition the throttle forms the boundary of the two adjacent cells.

(

and B = c ⋅ 1 − πc

k/(k−1)

(

2⋅k ⋅ R ⋅ Tadm − Tcyl k −1

)∈ [0;1];

)

(6)

Hence, an equation in B of second degree, solved if the flow parameters in the end cell are predicted or known. To estimate the flow between the inlet duct and the cylinder, the values of the pressure and of the flow rate measured on a gas-dynamic stand are taken into account. The steady flows are estimated considering the system Eq.(4) solved with the hybrid finite differences schema. The inlet pipe with its branches and the inlet channels into the cylinder head is divided into 9 cells on each branch. In each cell, the properties are assumed uniform. The cross sections of these cells are different as the design of the duct is. At boundaries, at t+∆t data are complete only after specifying boundary conditions: isentropic or irreversible adiabatic flow through the inlet valve port. In case “b”, the program runs in “two steps”. In the first step, value of the flow rate is calculated after “c” is predicted using the calculated values of the flow properties in the “end cell”, and in the cylinder, in an iterative mode. µc is a result of this computation step, after a number of iterations necessary to evaluate the steady flow through the inlet duct (after these iterations the pressure in each cell remain constant). In addition, at the boundary the Lax Wendroff ‘s slope of any property is estimated. In the second step, the value of µc is used to correct the value of the inlet port area, and the value of “c” is finally found out. When the flow chokes, the value of flow rate is considered critical. In this case µc=µcrt. In case of isentropic flow, the program runs in a single step, to calculate µisen.

EXPERIMENTAL

1.1

700 600 500

350 300 250

240 kg/h 320 kg/h

400 300

200 150 100 50

200 100 2

4 6 valve lift (mm)

8

4000 rpm

0.9 5000 rpm 5250 rpm

0.8

10

Figure 1 – Complex characteristic of a cylinder head. By processing these diagrams it was possible to have a response about the charge efficiency by considering the theoretical flow and maximum potential flow assured by the inlet duct during the intake air piston movement. The stand experiments were performed in a specially instrumented engine allowing access to different parts of intake manifold. Inlet air pressure versus crank angle data was gathered over a large number of cycles using piezoelectric transducers installed in two different sections of the intake duct (Fig. 2), by using a data acquisition system.

0

30

60 90 120 150 180 210 240 crank angle (degree)

Figure 3 – Mixture pressure history at the entrance into the intake manifold at full load. 1.1

0 0

1.0

-30

pressure (bar)

0

3500 rpm

0.7

400

20 kg/h 40 kg/h 140 kg/h

massflow rate (kg/h)

pressure drop (mmHg)

800

3000 rpm pressure (bar)

Due to limitation of space, only a small proportion of the total amount of experimental data collected during the study is included here. However the data shown are considered representative of all the results obtained. By means of determinations on steady-state flow test rig, there were established the complex characteristics that specify the relationship between airflow rate and pressure drop along the intake duct vs. valve lift (Fig.1).

3500 rpm

1.0

4000 rpm

3000 rpm

0.9 5250 rpm 0.8

5000 rpm 0.7 -30

0

30

60 90 120 150 180 210 240 crank angle (degree)

Figure 4 – Mixture pressure history at the exit of the intake manifold at full load. Charge efficiency at any given speed condition (Fig. 4), was determined by using a laminar flow measuring system. charge efficiency (%)

0.90 0.85

modified engine

0.80 standard engine 0.75 0.70 2000 2500 3000 3500 4000 4500 5000 5500 speed (rpm)

Figure 2 – The structure of tested manifold. The experiments covered a wide range of operating conditions, ranging from 2000 to 5250 r.p.m. and from 25 to 100 % load. Measurements of pressure were made for all these engine speeds, their history in the two measuring points being presented in Fig. 3 and 4.

Figure 5 – Effective charge efficiency for same engine equipped with two different cylinder heads. From all these series of tests, carried out under carefully controlled conditions, it was possible to find a good representation of how the flowing process actually occurs and to sustain the following conclusions.

RESULTS AND DISCUSSION

− the analytical coefficient are grouped on the entire range

By using analytical steady flow model and experimental data, a function was fit to produce an approximate relation and to calculate the average of intake air mass flows. The in cylinder state pressure due to piston motion was calculated by assuming polytropic process. For several applications, by using different constructive parameters, the results have shown that the most important factor affecting the charge efficiency is the ratio between valve-controlled section and the pipe cross section (Fig.6).

− otherwise

20 kg/h

0.95

140 kg/h

1

320 kg/h

0.9 0.85 standard valve majored valve

0.8 0.75 0.7 0

2

4 6 valve lift (mm)

10

8

discharge coefficient

discharge coefficient

1

of mass flows and valve lifts; in case of analytical coefficients, the experimental coefficient has evident standard deviations, especially at low valve lifts, due to measuring precision; − since the valve lifts are low, there is a good agreement between the two types of coefficients. For the purpose of the model it was used an average discharge coefficient curve as a convenient curve way to have a synthetic comparison between measured and predicted values with variation in both types of cylinder heads (Fig.8)

analytical evaluation 0.8 0.6

experimental evaluation

0.4

standard majored

0.2 0 0

Figure 6 – A comparison between the analytical charge efficiencies for polytropic flow rates in case of two geometric different inlet valves. An evaluation of the differences of the results either in case of analytical prediction and experimental testing have been made by a comparison between calculated and experimental discharge coefficients (Fig.7).

discharge coefficient

1

40 kg/h

20 0.8

140 kg/h 240 kg/h

0.6 320 kg/h 0.4 0.2 0

2

4 6 valve lift (mm)

8

10

Figure 7 – The discharge coefficient as ratio between measured and theoretical airflow rate vs. valve lift in case of a cylinder head. To be observed a significant deviation of experimental coefficient from analytical determination especially in the range of less mass flows and large valve lifts. As can be seen on complex characteristics in these range the subcritical flows occurs at pressure ratio close to 1. By comparative analyze there are to be pointed out that:

2

4

h [mm]

6

8

10

Figure 8 – A comparison between the average measured and analytical charge coefficient in case of two different cylinder heads. The trends from experimental evaluation are different from the analytical prediction, the values being 40 – 50% lower at high valve lifts. The explanation of the poor agreement is an over estimation of calculated adiabatic air mass flow due the considering of a much larger conventional geometric valve through area. The unsteady analyze offers the possibilities to find out the links between πc, µc and µcrt for each value of h at any mass flow rate. The values of µc calculated with unsteady model for the quasi-steady flows, are used to estimate the flow parameters in unsteady conditions as they are in the inlet system of an i.e. The unsteady model applied on the quasi steady flows, based on the experimental data on gas dynamic stand, was very important, because offers the possibilities of modeling the unsteady flows into the intake system. For these reasons, the values of the flow coefficient found out on the irreversible hypotheses are used in each step of computation to determine the effective area of flow through the inlet port. The characteristics presented below are interpolated in each step of computation. The values of irreversibility coefficient are found out in an iterative mode, as in case of quasi steady flows. In fig. 9 πc vs. h is presented for each value of the flow rate measured on the stand. Every curve presented represents the values of πc for constant flow rate, for each value of h tested.

crt

/ c

πC

1 0.9 0.8 0.7 0.6 0.5 0.4 0

2

4

6 h [mm]

20 kg/h

40 kg/h

240 kg/h

320 kg/h

10

8

1 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.6

0.7

0.8

1

0.9

πC

140 kg/h

Figure 12 - μc / μcrt approximation vs. πc

C

The comparison between two cases of the unsteady model (Fig.10) at flow rate of 40 kg/h shows that value of µc calculated with irreversible hypothesis is higher. 0.9 0.8 0.7 0.6 0.5 0.4 0.3

flow rate [kg / h]

Figure 9 – Characteristic πc vs. h 350 300 250 200 150 100 50 0

π c = 0,7

π c = 0,85

0.5 0

2

4

6

2

3.5

5

6.5

8

9.5

h [m m ]

10

8

π c = 0,8

h [mm] irreversible

Figure 13 – Comparison between measured and calculated flow rate for different values of πc

isentropic

Figure 10 – Comparison irreversible and isentropic values.

C

The value of µc vs. h in case of the irreversible flow assumption is presented in Fig.11. 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.5

2

3.5

5

6.5

8

The calculated value of the flow rate considers the values of critical ratio, critical value of µc and πc vs. h, using the irreversible model of the flow through the inlet valve. For unsteady flows, the irreversible model and the values of πc, µc and the ratio µc/µcrt, are used. The flow properties in each cell of the inlet duct and into the cylinder are found out, for any running engine regime. As a result of the model “the history” of the pressure in each (Fig.14) is in accordance with the experimental data.

9.5

h [mm]

1.15

40 kg/h 240 kg/h crit ical value

Figure 11 – Characteristic μc vs. h The curve of µcrt can be approximated with any mathematics function, and is useful to estimate the value of µc in any case for the same engine. This is possible using the approximation of πc for each value of h at any value of the flow rate, and the approximation of the ratio between µc and µcrt (Fig. 12) We can have a comparison between measured (continue line) and calculated flow rate (Fig.13)

pressure [bar]

20 kg/h 140 kg/h 320 kg/h

1.05 0.95

m 22 0.2 m 7 6 0.1 m 11 1 . 0 m 56 0.0 m 0 0 0.0

0.85 0.75 0

90

180

270

crank a ngle

360

450

540

630

720

Figure 14 – History of pressure on the first branch of the inlet manifold

CONCLUSION Reported here was a part of the research, work carried out at MASTER S.A., to find out how acting on distributing system parts the engine output should be improved. Upon reviewing the performance, several conclusions can be made. Considering approaches expressed in the literature, there were used characteristic quantities to have an objective comparison and evaluation of different charging systems and to make the thermodynamic analysis easier. All these characteristic quantities provide uniformly applicable criteria for the thermodynamic assessment of any charging system and, what is very important, they are compatible with the conventional definition of engine and charge efficiency. The research work concerning the intake airflow processes brought about not only the improvement of engine performances but also a coherent correlation between theoretical and experimental results. The theoretical research made it possible a correct evaluation of some mathematical relation that can be used for further development of new models. The application of the developed model, including analytic determination of discharge coefficient, is very convenient and may eliminate the supplementary cost in acquiring special investigation systems. Very good comparisons were obtained between measured and predicted global quantities such as effective pressure and indicated thermal efficiency with variations in both engine speed and overall air-fuel ratio. For a spread range of engine speed at full load the prediction of charge efficiency was in good agreement with the stand tests results.

NOMENCLATURE c cp h k m n p [N/m2] q[[J/(kg·s)]

− − − − − − − −

t [s] wv [m/s] wnc x [m] Anc Av Apipe R Tadm

− − − − − − − − −

Tcyl σ [m2] ϕ

− − − −

μ

−

the irreversibility coefficient; specific heat at constant pressure; the rise of the inlet valve; adiabatic exponent; mass flow rate; polytropic exponent; pressure; the gain in energy due to heat transfer across pipe walls per unit mass of gas; time; velocity in the valve port; velocity in the end cell; dimension along the pipe axis; cross section area of the end cell; valve port area; cross section area of the pipe; gas constant; temperature before the inlet valve port, or in end cell temperature into the cylinder; cross-section area of the pipe. coefficient denoting part of total enthalpy of flow process into the intake duct; coefficient of energy exchange into heat because of friction losses; discharge coefficient;

ρ [kg/m3] − density; η [N·s/m2] − dynamic viscosity coefficient; − flow coefficient through the inlet valve µc port; − flow coefficient corresponding to the µcrt critical conditions; − pressure ratio πc

REFERENCES [1] Lax, P.D., and Wendroff, E. 1964. Difference schemes with higher order accuracy for solving hyperbolic equations. Communications on Pure and Applied Mathematics. 17, 381. [2] Negrea, V. 1973. Determinarea analitica a coeficientilor de debit pentru supapele de admisiune ale motoarelor cu ardere interna. Buletinul Stiintific IPB, Tom 18(32), fasc. 2.,Bucharest [3] Peyret, R. 1990. Computational Methods for Fluid Flow. Springer Werlag, New York, inc. [4] Bulaty, T., Widenhorn, M. and Corbeàn, J.M. 1993. Berechnung der Instationären Strömung in Verzweigten Auspruffsystemen. MTZ 54: 192 - 201. [5] Radcenco, V. 1994. Termodinamica Generalizată. Editura Tehnica, Bucharest. [6] Kowalewicz, A. 1980. Systemy spalania szybkoobrotowych tlokowych silnikow spalinowych. Wydawnictwa Komunikcji Lacznojci, Warsaw. [7] Alboteanu, R., Teodorescu, L., Andreescu, Cr., Oprean, M. 1997. The Analysis of the Possibilities of Increasing 1557cmc DACIA Engine Power Output by Modifications of Distributing System. Revista Inginerilor de Automobile, Vol. VII nr.1-2, Bucharest. [8] Petcu, Cr. 1999. A numerical solution of isentropic 1-D unsteady flows in pipes. The 17th International Conference "Science and Motor Vehicles '99", Constantza