Strojniški vestnik - Journal of Mechanical Engineering 51(2005)7-8, 462-469 UDK-UDC 536.2 Izvirni znanstveni članek - Original scientific paper (1.01) The Use of a Phase Change Material within a Cylinder Wall in order to Detect Knock in a Gas SI Engine Jerome Bellettre , Eric Ollivier, Mohand Tazerout Department of Energetics and Environmental Engineering, Ecole des Mines de Nantes, La Chantrerie 4 rue Alfred Kastler BP 20722 44307 Nantes cedex, France, * Jerome.Bellettre@emn.fr Abstract The present paper studies the possibility to develop a new method of knock detection in a gas SI engine. This method is based on the increase in the wall heat flux when knock occurs. It also must be simple enough to be used by industry. In order to achieve this goal, a metallic Phase Change Material is put within the wall cylinder. The melting of the PCM means that knock has occurred and is persistent. The melting of such a phase change material would be easy to detect using industrial measurement tools. In this paper, numerical simulations of unsteady heat transfer across the cylinder wall are presented. Unsteady heat transfer from the hot gas to the wall chamber is simulated by a self-developed program. This program allows fixing instantaneous local heat flux values deduced from the literature in case of both normal and knocking combustion. Heat transfer across the cylinder wall is solved by the finite volume technique. Grid is validated by comparison with analytical results. Melting is treated by the Voller and Prakash model and Sodium is chosen as PCM. Among all the results, we can notice that an increase in the knock intensity changes the shape of the isothermal curves around and inside the PCM. This leads to an increase in the melting velocity with a higher rate than the increase in the heat flux. Introduction Knock is due to an unexpected combustion in Spark Ignition (SI) engines. It is a result of spontaneous ignition of a portion of end gas in the engine chamber, ahead of the propagating flame. The very rapid heat release implied by this abnormal combustion generates shock waves that can lead to the decrease in output, the increase in some pollutants and the destruction of the engine. Although knock has been more or less overcome in gasoline engines by controlling the fuel quality, gas engines are not safe from knock. Natural gas contains different gases (CH4, C2H6, etc.) with variable knock-resistance. Its composition varies widely with time and place. Consequently, an engine can start to knock if the gas reaches too low anti-knocking properties. A reliable method for the detection of knock in gas SI engine is then of high interest. The knock detection is currently based on data generated by accelerometers or cylinder pressure sensors [1, 2]. Due to its simplicity, accelerometry (vibration measurement) is largely employed in industry. Nevertheless, parasitic noises relative to engine operation often affect the quality of knock detection in this method. On the other hand, cylinder pressure data provide a direct and reliable way to analyze knock. The major disadvantage is that a suitable probe has to be provided in the engine cylinder that may reduce the engine lifetime [3]. Knock occurrence is accompanied by an important increase (up to 4 times higher) in the wall heat transfer inside the combustion chamber [4-6]. Thus, an alternative to the current methods could be the detection from analysis of the thermal signal measured near the outer side of the cylinder. However, the deadening effect of the cylinder wall makes such detection difficult [7-9]. Moreover even low knock intensity (with low increase in heat transfer) should be detected in order to protect reliably the engine. The use of a Phase Change Material (PCM), placed within the wall cylinder, can make this target reachable because the phase change is easy to detect with industrial tools. The present paper treats numerically the melting of a metallic PCM. It is divided into three main parts. Firstly, the background in the field of knock detection deduced from heat transfer analysis is presented. Secondly, the 462 Strojniški vestnik - Journal of Mechanical Engineering 51(2005) 7-8, 462-469 Nomenclature Cp specific heat capacity, J/kg.K Greek letters d depth of the slot, m a thermal diffusivity, m /s e wall thickness, m Ah latent heat of melting, J/kg h enthalpy, J/kg 0 crank angle, rad k thermal conductivity, W/m.K CO angular frequency, rad/s I connecting rod length, m p density, kg/m3 r crankshaft radius length, m T temperature, K Subscript t time, s e on the outer side of the wall w width of the slot, m i, i direction w/d width to depth ratio, - m time averaged X horizontal coordinate, m ext external y vertical coordinate, m w on the inner side of the wall modeling assumption and the validation of the model are detailed. Finally, model is exploited and main results are then exposed and discussed. Background In previous studies [7-9], we studied numerically the thermal signal in the coolant flow close to the outer side of the cylinder wall. A rib or a slot was made on the external surface in order to enhance the temperature variations. An example of sketch of those studies is presented in Fig. 1. We treated the case of a water-cooled engine running at 1500 rpm and full load. Its stroke is 170 mm and bore is 152 mm. The computational domain (Fig. 1) includes the cylinder liner, (made of cast iron), the water jacket (10 mm wide) and the cylinder head (made of aluminum). The representation of the latter is very simplified because only its contribution to the vertical heat flux in the cylinder liner has to be taken into account. A cavity [8] or a rib [9] was machined at the top dead center on the outer External forced convection Cylinder head 'aluminium) Cylinder wall feast- iron) Cylinder axis Coolant outlet Coolant flow (waters External wall of the coolant duct Cool ant inlet surface of the cylinder liner. The coolant flow is vertical and extents from the bottom to the top of the cylinder liner along the external side of the cylinder. Calculations have shown that a two-dimensional plane representation was equivalent to a 2D asymmetric one so the coolant is assumed to flow in a 10 mm wide rectangular duct. The heat transfer from the hot burnt gas to the chamber walls is simulated by a self-developed program that allows fixing instantaneous heat flux values deduced from the literature in case of both normal and knocking combustion. An example of heat flux is plotted in Fig. 2. In all the studied case, knock occurs one time every two cycles. The combustion starts when the piston reaches top dead center and its duration is 0.033s (corresponding to 30° Crank Angle at 1500 rpm). The equation of the piston movement (Eq. 1) is given by: y = rXcos6' + /xA/l-(r//)2x(sin6')2 (1) where y is the vertical position of the piston, 0 the crankshaft angle and r and / the lengths of the crankshaft radius and of the connecting rod. A D = 10 mm cylinder head / front face of the groove /, i 1 L groove floor y / W cylinder wall jS 3 mm r s rear face of the groove „ 'e = 5 mm -^ I I Fig. 1 Sketch of a previously studied configuration [8] The use of a phase change material within a cylinder wall in order to detect knock in a gas si engine 463 Strojniški vestnik - Journal of Mechanical Engineering 51(2005) 7-8, 462-469 0,1 0,2 0,3 t [s] 0,4 0,5 Fig 2. Unsteady heat flux imposed for a semi knocking combustion (50%) [8] According to Eq. (1), only 31.64 mm of the wall height can face the combustion, during the combustion period. This distance is divided into five parts. The heat flux received by each one is a function of the time they are exposed to the combustion. The associated heat flux is assumed to have sinusoidal variation with time during the combustion period. The two previously obtained main results are summarized here. More details can be found in reference [7-9]. Firstly, in the case of a square slot machined on the outer wall surface, Fig. 3 shows the resulting temporal variations of temperature in the coolant, 0.5 mm above the floor. Only variations due to knocking combustion can be seen. Those variations are the highest in point 1 (see Fig. 3a) which is situated in the upstream corner of the groove. At this location, they are 3 times higher than for a 2 mm thick smooth plane wall (Fig. 3b). This is due to the low velocity of the flow that makes the fluid stagnant. The passage of the fluid in this location of the groove occurs after a larger residence time along the cavity floor compared to other points. Moreover, the location of point 1 coincides with streamlines that skim the cavity floor. 0.08 0.06 0.04 0.02 0 -0.02 -0.04 -0.06 -0.08 Loubar et al. [9] studied the effect of a rib placed in the outer side of the wall. They found a similar result. A surface roughened gives good results in terms of amplitude amplification. The temperature variations are approximately 20 times those obtained with smooth surface at the same location (Fig. 4). The presence of recirculation in downstream of the rib (Fig. 4) makes the residence time of the fluid in contact of the wall more important. Consequently, the fluid has got more time to collect the thermal signal. As in Ollivier et al. [8], they found that the best location regarding amplification is located in the upstream left corner of the recirculation. Even if thermal signal amplitude inside the coolant may be significantly increased compared to a smooth wall case, we must notice that temperature variations are always weak within the water (around 0.2 K in the best case). This is due to the important deadening effect of the metallic wall. Consequently, it would be difficult to detect knock by measuring such variations using industrial measurement tools. The use of the phase change phenomena in order to detect knock occurrence can lead to the development of method that requires less accuracy regarding the thermal sensors. Thus, the melting of PCM placed within the wall cylinder is now going to be numerically treated. Modeling assumption The principle of the proposed technique is illustrated in Fig. 5. A cavity filled with a Phase Change Material (PCM) is placed within the cylinder wall. The melting temperature of the PCM should be chosen in order to be solid in the case of normal combustion. In the chosen configuration, there is no need to simulate the heat transfer within the coolant flow. The computational domain is then reduced to the cylinder wall (made in cast iron) and the cylinder head (made in aluminum, cf. Fig. 5). /~\ r^ w/ d = 1, point 1 / i J / \ / \ 1 \ / \ /, _^ \ / ^^ \ U , \ H I A 1/ \\ / v / \ • i\ \ \ / v \\ "J\ I" 1 \{ \ 1 / / 1 \ l\ \l J \ smoot h plane V wall 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9 [s] b) Fig. 3 a) Recording points in the square slot (yvld = 1)[8] b) Temporal temperature variations for a 2 mm thick smooth plane wall and in point 1 of the square slot [8] 464 Bellettre J. - Ollivier E. - Tazerout M. Strojniški vestnik - Journal of Mechanical Engineering 51(2005) 7-8, 462-469 0.10 0.08 0.06 0.04 0.02 0.00 -0.02 -0.04 -0.06 -0.08 -0.10 0.0 -Smouth surface ¦¦Roughened surface \ / \ ; \ / \ i \ i \ i \ i i i i 1 1 1 1 i "i \ j i / \ i \ j \ i \ i \ i \ i \ i \ i \ i \ i \ \ \ \ \ \ \ 0.1 0.2 0.3 t(s) 0.4 I Recording point Fig. 4 Temporal variation of temperature in the fluid (0.5 mm from the wall) and recirculation zone downstream the rib [9] Eq. (2) governs the computational domain: heat transfer in the whole dPh a , ar c ^~= ^— k~\— ~su (2) where h and T are respectively the enthalpy and the temperature of the material; cp its specific heat, p the density and k the thermal conductivity. S& is a source term. The thermal properties p, cv, and Z depend only on the material nature because of the low temperature gradients observed outside the combustion chamber [4-10]. Moreover, the mesh is structured and has got 20 cells in the thickness of the cylinder wall. ----------r 2 mir 2 mm 2 mm 5 mm cylinder head (Al) closed cavity cylinder liner (cast iron] coolant flow Fig 5. Studied configuration The melting of the PCM is treated by the Voller and Prakash [10] model. Its allows to calculate the source term of Eq. (2), Sh. It uses an enthalpy formulation methodology and a fixed grid to solve mushy region phase change problems. Boundary conditions The cylinder head and the cylinder wall cooling is taken into account by "external convection" boundary conditions. The external heat transfer coefficient and temperature are respectively: hext — 2500 W/m2K (corresponding to forced convection with liquid) and Text — 353 K (corresponding to the temperature regulation of coolant in an actual engine). Unsteady heat transfer from the hot burnt gases to the chamber wall is simulated by the previously presented self-developed program. Four types of combustion are simulated: a normal combustion and knocking combustion with three levels of knock intensity. In case of knocking combustion, cyclic variations (generally met in engine operation) are taken into account by imposing successively a high and a low peak heat flux value. Table 1 summarizes all the peak heat flux values that are used in this study. Their are deduced from literature [6]. Table 1. Peak heat fluxes for the four different types of combustion [6]_______________________________________ Type of combustion Peak Heat Flux (MW/m2) Low Value High Value Normal 2.5 2.5 Knocking (low intensity) 2.5 3.5 Knocking 3.5 (moderate intensity) 5 Knocking (high intensity) 5 8 The use of a phase change material within a cylinder wall in order to detect knock in a gas si engine 465 Strojniški vestnik - Journal of Mechanical Engineering 51(2005) 7-8, 462-469 Numerical technique The energy equation (Eq. (2)) is solved by the finite volume technique. The time dependent term is integrated using a 1st order implicit scheme. The time step is fixed at 10"4 s (corresponding to 30 steps during one combustion period with engine cycle period of 0.08 s). Four iterations per time step were adopted because more iterations do not improve the convergence of computations. This choice gives good results while preserving a reasonable calculation time. predicted. Moreover the numerical results appeared to be independent of the mesh within the range 20-40 cells in the wall width. T(x,t) =T0-(T0 -Te)- — + 5> 0-'le) — e ^ 2'a (An ¦ cos(« cot-x in-co i----------- + Bn ¦ sin(» cot-x 2a (5) Mesh validation The accuracy of the model has to be checked before being used for the simulation of the PCM melting. Thus, the numerical results are confronted to an analytical solution in a simplified ID case without cavity. The combustion chamber wall constitutes a frontier between hot gases and water coolant flow. Its thickness is e. It is assumed to be isotropic and can be considered, in this step, as a semi-infinite plan in order to make the problem mono-dimensional. On one side, the temperature varies periodically (combustion chamber), on the other it remains constant (coolant flow). The mesh validation for the conduction problem consists in the confrontation of the calculated temperature field within the wall thickness with analytical solutions deduced from the resolution of the unsteady heat conduction equation in an one dimensional case (Eq. (3)): dT(x, t) = a d2T(x, t) -------------------------- dt dx (3) where a is the thermal diffusivity of wall material (cast-iron in the present case) and x the position from the internal side of the wall. The boundary conditions can then be written as: - T(0,t) = TJt), at x=0 - T(e,t) — Te — const, at x — e The periodic variations of temperature on the inner side of the wall can be expressed as a Fourier Series in the following form (Eq. (4)): Tw(t) = T0 + ^An-cos(«¦co-t) + Bn-sin(« cot) (4) n=\ where