View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Universidade do Minho: RepositoriUM 2004-01-0617 THERMODYNAMIC ANALYSIS OF AN OVER-EXPANDED ENGINE Jorge J.G. MARTINS, Dept. Eng. Mecanica – Un. Minho Krisztina UZUNEANU Universitatea “Dunarea de Jos” of Galati Bernardo Sousa RIBEIRO, Universidade do Minho Ondrej JASANSKY, Thecnical University of Liberec Copyright © 2003 SAE International ABSTRACT Special attention must then be taken in the study of the part load conditions in engines, specially for automotive When the exhaust valve of a conventional spark ignition applications. It will be useful to understand which is the engine opens at the end of the expansion stroke, a large most efficient working cycle at light and part load, so quantity of high pressure exhaust gas is freed to the these working conditions may be used as specifications atmosphere, without using its availability. An engine that during car engine design. could use this lost energy should have a better efficiency. The major problem of the conventional S.I. engine at part The equations for an over-expanded cycle (Miller cycle) load is the throttling process and the consequential low are developed in this paper, together with equations for pressure at the end of the compression stroke. the Otto cycle, diesel cycle and dual cycle, all at part load, so they can be compared. The Miller cycle is based on the Otto cycle, having an expansion stroke which is longer than the compression Furthermore, indicated cycle thermodynamical stroke [1]. Intake valve is kept opened during a comparisons of a S.I. engine at part load (Otto cycle at significant part of the piston movement during half load), a S.I. engine at WOT (with half displacement) compression, so that part of the mixture contained in the and two over-expanded S.I. engines (with different cylinder is sent back to the inlet manifold, allowing the compression strokes) are examined and compared, with reduction of mixture mass that is “trapped” in the the aim of extending the referred theoretical cycle cylinder. The volume of “trapped” mixture corresponds to comparisons. the cylinder volume at the closure of the intake valve. Another way of implementing this cycle consists on INTRODUCTION closing the intake valve during the admission, long before BDC. The descent of the piston will create a depression inside the cylinder, achieving the atmospheric Spark ignition and compression ignition engines are still pressure somewhere during compression, near the the main power for automotive applications. The heavy position where the intake valve was closed on the traffic in cities and the high output of their engines does downward movement of the piston. not allow cars to use all the potential of their engines, working for most of the time at low loads. The standard S.I. engine that are used in cars are prepared to have the The new developments in variable valve timing (BMW best efficiency at full load, but as they are used very Valvetronic - [2]) and the possibility of compression ratio often at light loads, the amount of energy lost due to this change (SAAB) [3] allows the Miller cycle to be used at inefficiency is significant. the most effective (efficient) conditions at all times. The detailed investigation of this cycle as well as the expressions that describe it, are not matters usually explained in internal combustion engines literature [4]. A (expansion-compression ratio - σ), which is a set of equations was developed allowing the description characteristic parameter of the Miller cycle: of the Miller cycle [5], as well as the definition of the main variables that influence its development. Equations V V presented herein result of the application of σ = BDC = 5 (1.3) thermodynamic laws, without using other variables that VADM V1 influence the cycle performance (for example non- instantaneous combustion, heat transfer and internal From the parameters defined in (1.1) and (1.2) comes: friction). ε g ENGINE GEOMETRIC PARAMETERS σ = (1.4) ε tr In an internal combustion engine (Figure 1) with a fixed geometry the compression ratio (here named geometric Which means that σ also shows the relation between ε – g) is unique and defined by: geometric compression ratio and the trapped compression ratio. In the Otto cycle the value of this V V parameter is one, since that theoretically expansion ε = BDC = 5 g (1.1) equals compression. VTDC V2 OTTO CYCLE AT PART LOAD Spark Ignition engines when working at idle or at light loads usually lower the intake pressure of air to reduce load. When engines work under the Otto cycle this pressure reduction on the engine charge may be obtained by throttling, keeping the mixture at stoichiometric conditions, so that the three-way catalytic converter can work at optimal conditions. This will lead to a reduction on the intake pressure, and during the intake stroke the engine will work as an air pump. The reduction of the intake pressure leads to a reduction of the mass of air and fuel (assuming a stoichiometric mixture) trapped in the cylinder. In the p-V diagram of this cycle (Figure 2), the pumping work (negative) is represented by the area defined by 1’-6-7-1-1’ (or 5-6-7-1-5), while the positive work is 5-1’-2-3-4-5 (or 1-2-3-4-1). Figure 1 – p-V diagram of a Miller cycle. When studying the Miller cycle, due to the cycle operation (effective admission is shorter than the piston stroke), we have to consider another compression ratio that is the effective compression ratio (here named trapped - εtr ). This one is defined in the same manner described in (1.1), but instead of considering the V BDC , it is considered the cylinder volume at beginning of compression (where the pressure is still atmospheric). It results then: V V ε = ADM = 1 (1.2) tr VTDC V2 Figure 2 - p-V diagram of the Otto cycle at part load. In this kind of cycle it is necessary to enter with the relation between expansion and compression Analyzing the work involved in this cycle: 1 ⋅Q + A LHV W = W + W + W + W + W + W (2.1) 1 2'1 34 51 ' 6'1 71 11 ' where: B = F is a constant (the mixture is ⋅ R T1 All the terms will be throughoutly analyzed. The first always stoichiometric) term, which corresponds to the compression from the atmospheric pressure until p 2 is considered an isentropic γ γ γ V process: ⋅ = ⋅ = ⋅ 3 = ⋅τ p3 V3 p 4 V4 p 4 p3 p1 V p ⋅ V − p ⋅ V 4 = '1 '1 2 2 W 2'1 (2.2) γ −1 And the work involved in this process may be written as: Considering: γ V ⋅τ p ε⋅ ⋅ 1 − ⋅τ p ⋅ V 1 ε 1 1 1 = = W34 γ γ − p γ V 1 (2.7) p = p V = V 1 p = p ε⋅ ε = 1 '1 0 '1 1 2 1 ⋅τ ⋅ p V p V γ−1 0 2 = 1 1 ()ε −1 γ −1 Comes: The exhaust process is considered an isobaric process. 1 To simplify the analysis this work was divided in two γ p γ− ⋅ 1 − ⋅ ε⋅ 1 parts, from 5 to 1’ and from 1’ to 6. Thus the work can be p 0 V1 p1 V1 p determined as: W = 0 (2.3) 2'1 γ − 1 1 p γ = ⋅ ()− = ⋅ 1 − For the expansion stroke, also considered an isentropic W51 ' p0 V '1 V5 p0 V1 1 (2.8) p process, it comes: 0 p ⋅ V − p V W = 3 3 4 4 (2.4) And 34 γ −1 1 V p γ Considering: W = p ()V − V = p 1 − V ⋅ 1 = 6'1 0 6 '1 0 ε 1 p0 p T γ V τ = 3 = 3 p = ⋅τ p ε⋅ V = 1 (2.9) p T 3 1 3 ε 1 2 2 p γ = ⋅ 1 − 1 p0 V1 The increase of temperature/pressure in combustion. ε p 0 Q − = m ⋅ c ⋅ T( − T ) = m ⋅ Q (2.5) 2 3 v 3 2 f LHV The pumping work from the intake stroke can be described as an isobaric process and it becomes: It leads to: V m W = p ⋅ ()V − V = p ⋅V − 1 = ()γ −1 ⋅ ⋅ Q 71 1 1 7 1 1 ε A LHV T 1+ (2.10) τ = 3 = 1+ F = 1 γ−1 (2.6) = ⋅ − T ε ⋅ p ⋅ ∆V p1 V1 1 2 1 ε ()γ − ⋅ = + 1 B 1 γ−1 ε The first part of the compression from p 1 up to the atmospheric pressure, p 0, is described as an isentropic process. ⋅ − ⋅ We can present an equation that gives the load for the p1 V1 p '1 V '1 W = = Otto cycle at part load: 11 ' γ −1 1 W 1 (β −1)⋅ (ε −1) ε⋅ γ−2 p γ (2.11) = − (2.16) ⋅ − ⋅ ⋅ 1 β γ−1 p1 V1 p0 V1 W ⋅β B⋅ ()ε −1 p max = 0 γ −1 The values of efficiency of this cycle are plotted against β and against load on Figure 3 and Figure 4, respectively Considering equations (2.3), (2.7), (2.8), (2.9), (2.10) and for an engine with ε =12. (2.11), the work (2.1) of this cycle can be determined as: p ⋅ V γ− ε W = 1 1 ()τ −1 ⋅ ()ε 1 −1 − V ⋅ ()p − p = γ −1 1 0 1 ε −1 B γ− ε = p ⋅ V ⋅ ()ε 1 −1 − V ⋅ ()p − p 1 1 ε γ−1 1 0 1 ε −1 (2.12) The efficiency is calculated as: W η = = O Q H Figure 3 – Thermal efficiency of Otto cycle at part load as a function of B γ− ε ⋅ ⋅ ()ε 1 − − ⋅ ⋅ ()β − (2.13) pressure ratio.