Assessment of the Methods for Dividing Indicated Mean Effective Pressure into High Pressure and Gas Exchange Portions Marco Wagner; Kistler Instrumente GmbH Hubert Fußhoeller; FKFS www.kistler.com Contents Motivation 3 Fundamentals 3 The BDC-BDC Method 4 The pV Intersection Point Method 5 The Witt/Shelby Method 6 Real Examples and Differences between the Methods 8 Possibilities for Using the Methods 10 References 11 2 www.kistler.com Assessment of the Methods for Dividing Indicated Mean Effective Pressure into High Pressure and Gas Exchange Portions Marco Wagner; Kistler Instrumente GmbH Hubert Fußhoeller; FKFS Motivation Fundamentals Indicated mean effective pressure (NMEP) represents a particu- To determine the NMEP from the pressure curve, the process larly important index value in connection with combustion analy- work is divided by the displacement. The work is calculated from sis and combustion engine indication. It describes the work pro- the circular integral pdV over the combustion cycle. duced due to combustion, and it allows different engines to be compared with one another independently of the displacement. pdV Since NMEP is an internal variable (based on the measured pres- ∫ W cyc cyc sure curve), it is independent of friction – unlike the measured pmi = = V V torque. On this basis, the friction mean effective pressure FMEP d d can be calculated from the difference between the brake mean If the NMEP is broken down into high pressure IMEP and gas effective pressure BMEP (calculated from the torque) and the H exchange IMEP , different subvalues are obtained depending on NMEP. L the method used; within one method, however, the same total NMEP is always obtained with all the breakdown variants on By breaking the indicated mean effective pressure down into high summation. pressure and gas exchange portions, further conclusions can be drawn from the respective sub-index values in various fields of development. However, the methods of arriving at the break- NMEP = IMEPH + IMEPL down may differ greatly. As well as the commonly used BDC- BDC and pV intersection methods, the Witt-Shelby method must The following index values may be adduced for a detailed assess- also be mentioned in this context. Moreover, because the values ment of the process: differ in all of these methods, the general question arises as to which of them can be described as the 'right' one. Users of com- The high pressure efficiency bustion analysis should consider this question, especially in the light of the increasing use of fully variable valve trains. W = H η H Q fuel The following sections describe and evaluate the methods just mentioned, and are intended to provide a basis for decisions re- to evaluate the high pressure process, where WH can be determi- garding each individual application case. ned through IMEPH, and Qfuel can be determined from the pro- duct of the fuel mass and the lower calorific value. The gas exchange efficiency η cyc NMEP = i = W = based on = ⋅ η L η i η L η H IMEPH η H W H or, more usually, the gas exchange work W L i.e. the size of the gas exchange area in the pV graph, or the gas exchange indica- ted mean effective pressure IMEPL to evaluate the gas exchange. www.kistler.com 3 The BDC-BDC Method The breakdown of NMEP according to the BDC-BDC method The high pressure work and the gas exchange work both contain corresponds to the classical breakdown into the portion labeled as Area C. This is a positive component in the high pressure portion and a negative component in the gas ex- • compression stroke and expansion stroke change portion. When the high pressure and gas exchange por- • exhaust stroke and intake stroke tions are added to obtain the total work or NMEP, the positive and negative components of Area C are eliminated. By definition (i.e. not necessarily in reality), the two portions Depending on the exhaust or intake timings, this method may – the high pressure and gas exchange portions – are calculated lead to erroneous interpretations – for example, of expansion or starting from bottom dead center: on the one hand, over the blowdown losses, or of gas exchange work. This is caused by the compression and expansion strokes and on the other, over the problem of attribution to the high pressure or the gas exchange exhaust and intake strokes, until bottom dead center is reached portion rather than by an incorrect calculation. again. In engines with variable valve timings, different effects may then The relevant equation to calculate the work is as follows: be produced during operation; in some cases, this problem may lead to incorrect countermeasures in the combustion process or the calibration of the electronic control unit. = pdV = pdV + pdV = W +W W cyc ∫ ∫ ∫ H BDC LBDC cyc H BDC −BDC LBDC −BDC and hence W +W NMEP = H BDC LBDC = IMEP + IMEP Vd H BDC LBDC Figure 1: High pressure work, gas exchange work and total work including Area C with the BDC-BDC method (from left to right) 4 www.kistler.com The pV Intersection Point Method With the intersection point method, the process is broken down There is no breakdown into high pressure or gas exchange por- into work that can be gained or work that has to be performed, tions, nor can a relationship with ideal comparative processes be starting from the intersection point between the compression line established. and the exhaust line. In terms of thermodynamics, processes that run to the right sup- The work is calculated according to ply work W + whereas work W - must be performed for processes that run to the left. = = + = + + − Wi ∫ pdV ∫ pdV ∫ pdV Ws Ws 0−720 S−SH S−SL from which follows the calculation of the divided mean effective pressures: W + +W − NMEP = s s = IMEP + IMEP Hs Ls Vd The determination of the intersection point required to calculate the divided work proves difficult and/or is not always unambi- guous. Figure 2: Breakdown of work in terms of thermodynamics into work that can be gained or that must be performed, with the pV intersection point method Figure 3: Unambiguous and multiple intersection finding www.kistler.com 5 Figure 3 shows, on the left, the gas exchange and parts of the The Witt/Shelby method is based on an extension of the BDC- high pressure for a typical partial load operating point. The red BDC method. It allows a full breakdown of the process into the dot indicates the intersection point that is to be found. The inter- high pressure and gas exchange portions. According to Witt/ section point that is found is unambiguous for the pressure curve Shelby, the high pressure portion comprises all combustion- shown. However, it can be seen that a critical point with a 'near' related components, and the gas exchange-related components intersection point can be found along the compression line, in the (like the expansion losses) are fully extracted. It is therefore easy direction of increasing volume. With only a slight change in the to identify a deterioration in combustion, caused for example by pressure curve during the exhaust phase, this could lead to the diminishing swirl or delayed combustion. This method also finding of a different intersection point. To illustrate this clearly, a enables good evaluation of processes that are otherwise difficult critical profile for the exhaust phase is superimposed in blue in Fi- to interpret, such as early close of intake valve or late close of gure 3, on the right. A somewhat larger pressure oscillation amp- intake valve. litude in the exhaust phase produces three possible intersection points. The directional dependency of the intersection point that The fundamental basis of this method is the extrapolation of the is found is also clearly recognizable. In this case, it has proven ap- pressure curves, based on the polytropic equation: propriate to perform the search from TDC towards BDC along n the compression line. p ⋅V = const This makes it possible to ensure the smallest possible variation Different methods can be used for this purpose, based either on width for the intersection points that are found. As can be seen in logarithmic pressure curves or on the differentiated form of the Figure 3 (bottom), further problems may occur in the case of su- polytropic change of state equation. In either case, the objective percharged engines with a positive gas exchange loop. In the is to determine the ideal pressure curve. The work from open/ profile shown in blue, the question arises as to how the small close timing to BDC can then be calculated. area shaded in light blue should be evaluated. Is it positive or ne- gative work? Should the first or second intersection point be cho- 1. Numerical integration over the section points of the ideal sen? For profiles with a purely positive gas exchange cycle pressure curve (marked in red), it makes sense to find the intersection at BDC, 2. Calculation with the equation to calculate the work along although the BDC limit position can cause difficulties with the fin- one isentrope ding algorithm. Ideally, there is a transition here from the inter- n−1 n ⋅ section point method to the BDC-BDC method. p 1 p W = 1 V ⋅ 2 −1 n −1 p1 With this method too, in case of variable timings, phenomena that really should be ascribed to the gas exchange may be assig- ned to the high pressure portion in certain cases, and vice-versa. 3. Formation of the numerical integral of the real curve This could also lead to misinterpretations, depending on the 4. Forming the differential area supplies the incremental com- pression work (ICW) or the expansion work engine's operating mode.