TDC Determination in IC Engines Based on the Thermodynamic Analysis of the Temperature-Entropy Diagram

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1 SAE ECHNICAL AER SERIES DC Determination in IC Engines Based on the hermodynamic Analysis of the emperature-entropy Diagram M. azerout, O. Le Corre and S. Rousseau DSEE-Ecole des Mines de Nantes International Spring Fuels & Lubricants Meeting Dearborn, Michigan May 3-6, Commonwealth Drive, Warrendale, A U.S.A. el: (724) Fax: (724)

2 he appearance of this ISSN code at the bottom of this page indicates SAE s consent that copies of the paper may be made for personal or internal use of specific clients. his consent is given on the condition, however, that the copier pay a $7.00 per article copy fee through the Copyright Clearance Center, Inc. Operations Center, 222 Rosewood Drive, Danvers, MA for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law. his consent does not extend to other kinds of copying such as copying for general distribution, for advertising or promotional purposes, for creating new collective works, or for resale. SAE routinely stocks printed papers for a period of three years following date of publication. Direct your orders to SAE Customer Sales and Satisfaction Department. Quantity reprint rates can be obtained from the Customer Sales and Satisfaction Department. o request permission to reprint a technical paper or permission to use copyrighted SAE publications in other works, contact the SAE ublications Group. All SAE papers, standards, and selected books are abstracted and indexed in the Global Mobility Database No part of this publication may be reproduced in any form, in an electronic retrieval system or otherwise, without the prior written permission of the publisher. ISSN Copyright 1999 Society of Automotive Engineers, Inc. ositions and opinions advanced in this paper are those of the author(s) and not necessarily those of SAE. he author is solely responsible for the content of the paper. A process is available by which discussions will be printed with the paper if it is published in SAE ransactions. For permission to publish this paper in full or in part, contact the SAE ublications Group. ersons wishing to submit papers to be considered for presentation or publication through SAE should send the manuscript or a 300 word abstract of a proposed manuscript to: Secretary, Engineering Meetings Board, SAE. rinted in USA

3 DC Determination in IC Engines Based on the hermodynamic Analysis of the emperature-entropy Diagram Copyright 1999 Society of Automotive Engineers, Inc. M. azerout, O. Le Corre and S. Rousseau DSEE-Ecole des Mines de Nantes ABSRAC A thermodynamic methodology of DC determination in IC engines based on a motoring pressure-time diagram is presented. his method consists in entropy calculation and temperature-entropy diagram analysis. When the DC position is well calibrated, compression and expansion strokes under motoring conditions are symmetrical with respect to the peak temperature in the (,S) diagram. Moreover, in case of error on the DC position, a loop appears, which has no thermodynamic significance. Hence, an easy methodology has been conceived to obtain the actual position of DC. his methodology is applied to motoring measurements in order to present its performance, which are compared to usual methods. INRODUCION he recording of accurate indicator diagrams is very difficult but is of great importance. Among the many sources of error, a wrong DC position, leading to an incorrect (,V) diagram, has been recognized as the major source of error on thermodynamic calculation results such as IME (Indicated Mean Effective ressure), mass fraction burned or combustion duration. Hribernik [4] proposes a formulation giving the ratio between the IME error (in %) and the DC position error (in CA). [ ] IME error % 9 DCerror[ CA] (1) he main difficulty in locating DC is that the peak pressure under motoring conditions precedes the DC position (corresponding to the minimum volume) because of heat transfer and mass losses: it is the loss angle (figure 1). hus, previous studies [1] [2] [4] [6] [7] [9] have investigated several methods for determining the DC position. Figure 1. efinition of the DC phase lag error In this paper, the DC phase lag error ϕ is defined as the angle between the peak pressure with the actual DC and the peak pressure with a wrong DC, as shown on figure 1. BACKGROUND In 1967, Brown [1] identified the main sources of error in pressure measurements. One of them was the shift between pressure and crank angle. He proposed a correction using the polytropic exponent obtained from experimental data: ln( i ) ln( i + 1) n = ln( Vi + 1) ln( Vi ) (2) Stas [9] proposed another method based on polytropic coefficients calculated at the inflexion point occurring during the compression and expansion strokes (figure 2). 1

4 Figure 2. ressure vs. crank angle under motoring conditions Figure 3. ressure vs. crank angle under motoring conditions According to Stas, this methodology allows to locate DC with an accuracy of about ± 0.1 CA. Note that the calculation of polytropic coefficients uses d 2 V and ( dv ) 2, which can cause numerical errors. he location of DC can be determined using the symmetry of the pressure-time diagram under motoring conditions. It is the method used by the MACAO software OSIRIS [7]. It constitutes pairs of points (A, A ), (B, B ), and so on. oints A, B are on the compression curve of a motoring cycle, A, B are on the expansion curve (figure 3). he pressure in A and A is the same. hen, it calculates by linear regression the straight line passing through the center of segments [A, A ], [B, B ], he intersection between this line and the crank angle axis gives the thermodynamic DC. his angle must be corrected to give the actual DC location. OSIRIS calculates this correction on the basis of the engine characteristics, the peak pressure and the inlet pressure. Calibration results from most of methods depend on the heat transfer coefficient. For instance, inchon [6] proposed a calibration based on the IME and the peak pressure: θ DC 1 K = π = θ A A max m r c p IME + K maxmax max ( ) ( ) his method uses Woschni's correlation with a corrective factor of 1.7. Its accuracy is then very dependent on the accuracy of the heat transfer correlation. max u 0 0 (3) In that context, the purpose of the method proposed in this paper is to present a general method to determine the DC position using an experimental pressure-time diagram under motoring conditions and the analysis of its transformation into temperature-entropy diagram. Such a method is fully independent of any heat transfer correlation or polytropic exponent calculation. HERMODYNAMIC MODEL A thermodynamic model for motoring simulations has been developed and simulates the whole engine cycle, from the inlet to the exhaust. It corresponds to a onezone thermodynamic model for performance predictions but with no combustion, Heywood [3], and Ramos [8]. In cylinder gas are assumed to be ideal gas, and specific heats are supposed to depend on the temperature only: 2 3 Cp + = (4) he ideal gas law and the first principle of thermodynamics applied to the chamber respectively give cylinder pressure and temperature: p V = m r (5) m Cv & & & = pv Qw + u m& cyl (6) In equation (6), p V & is the work due to in-cylinder gas, and Q & is heat losses through the chamber walls. w Assuming that leakage is negligible, the change of the mass in the control volume is only due to flow-rates through inlet and exhaust valves: m& = δ valve C d A valve upst 2γ Rp 2 / γ Rp ( γ 1) Rupst γ + 1 / γ (7) 2

5 where C d is a constant valve discharge coefficient, A valve ( θ) is the geometrical valve flow area taken as a function of sine, and δ valve equals 1 during intake, -1 during exhaust and 0 during the other strokes. he pressure ratio R is defined according to : p δ valve Where the sonic pressure ratio is defined by: (8) upst upst 2 Rp lim upst = 1 γ upst + (9) he subscript upst designates the manifold during intake and the cylinder during exhaust. he heat transfer to the walls under motoring conditions is due to convection: γ γ 1 & Qw = hg S w ( w ) (10) he wall temperature is assumed constant and uniform. he heat transfer coefficient is calculated with Hohenberg s correlation: 0. 8 [ ] p( θ ) S p hg ( θ ) = V( θ ) ( θ ) (11) he instantaneous cylinder volume and heat exchange surface between gas and chamber walls are known analytically with respect to the engine s geometrical characteristics and to the crankshaft angle. Input and output of the predictive model are summarised on figure 4. his model allows simulating engine cycles under motoring conditions with actual and wrong DC. EMERAURE-ENROY DIAGRAM During compression and expansion strokes, the in cylinder mass is supposed constant, and the temperature is obtained from the pressure diagram (either numerically or experimentally) using a reformulation of eq (5): pv = mr 0. 8 (12) Figure 4. redictive model from Le Corre and al. [5] max 1 = max 2 = > 0 (13) wo points ( 1, 2) are defined in part of other of the peak temperature max, such as (figure 5): Note that the peak temperature is not necessary located at DC. he specific entropy leads to: d S = C d p R d (14) Near DC, the change of the volume can be neglected. Under these conditions: d d = (15) As is small, specific heat C p and C v can be assumed constant. During the compression stroke, equation 14 becomes: 3

6 ( ) 1 d Smax 1 = Cp R max = ( Cp R) ln ( 1 ) max (16) Using a first order aylor's development, equation (16) can be rewritten: ( ) Smax 1 = R Cp max (17) he same assumptions are applied to the expansion stroke: S max 2 = ( R C Equations 17 and 18 lead to: (18) S max 1 = S max 2 (19) Equation 19 shows that the entropy varies symmetrically around the peak temperature. In other words, the temperature-entropy diagram must be completely symmetrical with respect to. max p ) max Figure 6. Simulated (,S) diagram with different DC phase lags As shown on figure 7, the loop still exists until a DC phase lag of 0.45 CA is observed. Figure 7. Simulated (,S) diagram with different DC phase lags Figure 5. Simulated (,S) diagram under motoring conditions with the actual DC calibration When an error exists on the DC position, simulations show that a loop appears in the (,S) diagram. his loop has no thermodynamic significance. Figure 6 presents four (,S) diagrams, one with the actual DC position, three other curves with a wrong DC position (error of +1, and +0.5 CA). In the three last cases, a loop appears, which size increases with the error on the DC position. he existence of this loop appears to be a new way to locate DC. But one must verify the robustness of this way before conceiving a new methodology. In order to be validated, the new method is then compared to other existing methods and is applied to an experimental pressure-time diagram. ESS OF ROBUSNESS hree variables are tested. he first one is the engine throttle. he second one is the in cylinder mass since this value is difficult to known accurately. he last one is the volumetric compression ratio, in order to extend the method to any kind of engines. 4

7 1. ARIAL OEN HROLE hree open throttles have been analyzed. he robustness of the method is important at partial open throttle since it can be impossible or dangerous to obtain motoring cycles at wide open throttle (WO) for some kind of engines (gas engines with carburetor for example). Even if a mass error is introduced, figure 9 shows that the loop exists for a shift of +0.5 CA and is always vanished for a shift of CA (figure 10). Figure 8. Simulated (,S) diagram for different open throttles Figure 10. Simulated (,S) diagram for different incylinder masses his means that the error on the mass inside the cylinder has no effect on the loop. Since the loop exists for any throttle (figure 8), this method can be applied on motoring cycles obtained at partial open throttle. 2. IN-CYLINDER MASS Errors can be done in the calculation of the mass contained in the cylinder. hese are mainly due to errors on the inlet flow-rate measurement and to assumptions made to estimate the mass of residual gas. Moreover, the in-cylinder mass is not constant during compression and expansion strokes because of leakage. he following sensitivity study uses the following definition: 3. COMRESSION RAIO In order to apply the method to any kind of engines, the loop must be independent of the compression ratio. Simulated (,S) diagrams for three different compression ratios have shown that the loop exists for all of them (figure 11). Mass used = Mass rue ( 1 Mass Error) Figure 11. Simulated (,S) diagram for several compression ratios In any case, the loop is vanished for an error on the DC position of CA. he three tests of sensitivity allow concluding that this new method can be applied for any kind of engine, at any open throttle. Figure 9. Simulated (,S) diagram for different incylinder masses 5

8 COMARISON WIH HE OLYROIC EXONEN MEHOD he (,S) diagram can easily be compared to the polytropic exponent curvature. Figure 12 shows the evolution of the polytropic exponent versus crankshaft angle proposed by Hribernik [4] for an ideal adiabatic cycle. In the polytropic exponent diagram, the curve with no error of phase could be interpreted as a negative error of phase on DC (figure 14). So, in order to apply its method to real engines cycles, Hribernik [4] explained how to transform the measured pressure-time history into adiabatic pressure-time history. Figure 12. Simulated (n,θ) diagram for an ideal cycle He wrote that "the curves lie in the quadrants II and IV when the phase lag error is positive and in the quadrants I and III when the error is negative" Note that, the hyperbolic aspect of the polytropic exponent is due to its formula (equation 2). he curve (n,θ) is a horizontal line for an actual DC in this case (adiabatic cycle). For an actual calibration and an ideal adiabatic cycle, the (,S) diagram becomes a vertical line, as shown on figure 13. Figure 14. Simulated (n,θ) diagram for a real cycle with heat transfer his underlines the interest of the (,S) diagram, which avoids such confusion (figure 6), and shows the limits of the polytropic exponent diagram. MEHODOLOGY FOR HE CALIBRAION OF DC A new methodology can be proposed if one remarks that: ( ) ( ) max scomp = s = min s max exp (20) When the compression stroke is described, one retains ( ) ( ) s max the maximum of entropy max s comp. his value is compared to the value of the entropy s max at the peak temperature. If max s comp is superior to (case a on figure 15) then the DC position must be decreased by a constant step of 0.1 CA. his operation must be iterated until the convergence. Note θ lim this angle, (case B). Finally, adding θ lim and CA gives the actual calibration (case C). Figure 13. Simulated (,S) diagram for an ideal cycle 6

9 occur during these strokes, as the cylinder gas temperature is higher than the wall temperature. Being given that the criteria for a negative DC phase lag is difficult to obtain but not for a positive DC phase lag, the new methodology proposed in this paper is essential. ES RESULS he method has been tested on a SI engine. ressuretime diagrams have been recorded with OSIRIS with an acquisition every 1 CA. Engine characteristics are the following: Designation Ignition Admission Lister-etter S1 SI Natural Aspiration Displacement Volume 633 cm 3 Number of cylinders 1 Bore B 95.3 Stroke S 88.9 Engine Speed 1500 RM Figure 15. Schematic (,S) diagrams according to the correction on the DC position he following point must be underlined: this methodology assumes that initially, the peak pressure under motoring conditions is before the actual DC position. his condition is imperative since the loop does not exist for negative DC phase lag (figure 16). he data acquisition system for the cylinder pressure is composed by: a Sensor AVL QH32D, gain 25.28pC/Bar Range BAR a iezo Amplifier AVL 3066A01, gain 400pC/V with no reference of pressure a Druck type X Range 2.5 BARA inside inlet manifold to give the reference of pressure he first transformation in the (,S) diagram can be done (figure 17). A loop appears in this diagram: the DC position is wrong. Figure 16. Simulated (,S) diagram with positive DC phase lag In this case, an anomaly in a thermodynamic point of view appears on the entropy variation during the compression stroke (positive instead of negative) and at the expansion stroke (idem). his phenomenon can not Figure 17. Initial experimental (,S) diagram 7

10 A first correction of -0.1 CA is applied (figure 18). Figure 18. Experimental (,S) diagram with a correction of 0.1 CA Figure 20. Experimental (,S) diagram for the actual DC Figure 21 shows the actual (, V) diagram. After several corrections, the limit diagram is obtained (figure 19). Figure 21. Experimental (,V) diagram with actual DC Figure 19. Experimental (,S) diagram with a correction of -1.3 CA As simulations have shown that the loop disappears for a DC phase lag of 0.45 CA, the actual correction that should be applied to the physical position of the crankshaft angle encoder is 1.75 CA. Note that it is impossible to obtain the conditions required by the automatic procedure of OSIRIS for locating DC (3000 rev/min, 25% WO, no fuel injection), since the engine speed is imposed by the generator at 1500 rev/ min. Despite this, the difference observed between OSIRIS procedure and the new methodology is only CA. With this correction, the experimental temperatureentropy diagram is fairly symmetric with respect to the peak temperature (figure 20). Figure 22. Experimental (, θ) diagram with actual DC 8

11 he usual method [7] is in accordance with the calibration since the pressure diagram versus crankshaft angle is symmetric (figure 22). In addition, the polytropic exponent evolution is in accordance too, especially in the quadrants II and IV (figure 23). Figure 23. Comparison between experimental and simulation on (n,θ) diagram ACCURACY OF HE NEW MEHOD he last point of this work concerns the accuracy of this method. Stas's method [9] should have an accuracy of ±0.1 CA. Hribernik's method [4] should have a precision of ±0.025 CA. A correction step of 0.1 CA has been chosen. It determines the accuracy of the method, since CASE B figure 15 will be reached with a maximum error equal to the step, i.e. 0.1 CA. hus, the authors evaluate the accuracy of the new method at ±0.1 CA. CONCLUSION he interpretation of the temperature-entropy diagram is a right way to obtain the DC position. In fact, a physical error on the crankshaft encoder induces a loop, which has no thermodynamic sense. On this basis, a simple algorithm is proposed to obtain the actual DC position. wo advantages can be underlined in relation with previous papers. Firstly, this new methodology is robust and independent of heat transfer coefficient and mass losses. Secondly, the algorithm is easy to implement and does not generate numerical difficulties or errors. It has been applied with success on a real engine. REFERENCES 1. W.L. Brown Methods for Evaluating Requirements and Errors in Cylinder ressure Measurement, SAE aper N M.F.J. Burnt and A. L. Emtage Evaluation of IME Routines and Analysis Errors SAE aper N J. Heywood Internal Combustion Engine Fundamentals, McGraw-Hill International Editions, 1988, ISBN A. Hribernik Statistical Determination of Correlation Between ressure and Crankshaft Angle During Indication of Combustion Engines, SAE aper N O. Le Corre, S. Rousseau and C. Solliec One Zone hermodynamic Model Simulation of a Stationary Spark Ignition Gas Engine : Static and Dynamic erformances, SAE aper N inchon Calage hermodynamique du oint Mort Haut des Moteurs à iston Revue de l'institut du étrole, Vol 39, N 1, Janv-Fev OSIRIS Guide Version 2.0, Copyright MACAO J. Ramos, Internal Combustion Engine Modeling, Ed. Hemisphere ublishing Corporation, 1989, ISBN M. J. Stas hermodynamic Determination of.d.c. in iston Combustion Engines SAE aper N NOMENCLAURE p Mpa: ressure V m 3 : Volume θ CA: Crank Shaft Angle K: emperature n -: olytropic exponent r J/kg/K: Mayer Coefficient c p J/kg/K: Specific Heat at Constant ressure c v J/kg/K: Specific Heat at Constant Volume s J/kg/K: Entropy m kg: Mass inside the cylinder DC: op Dead Center IME BAR: Indicated Mean Effective ressure WO: Wide Open hrottle ϕ CA: hase Lag Error CR: Compression Ratio Q w W: Heat losses man: Manifold upst: Upstream 9

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