HEAT TRANSFER modeling OF DIESEL ENGINE combustion …



HEAT TRANSFER MODELING OF A DIESEL ENGINE

The solution of heat transfer phenomena in Internal Combustion Engines is a very challenging task considering the number of systems (intake and exhaust ports, coolant subsystem, lubricant oil subsystem), the different heat transfer mechanisms (convection, conduction and radiation) and the quick and unsteady changes inside the cylinder that take place at the same time. These difficulties had led to a lot of experimental and theoretical work over the last years. A review of these works can be found in Borman and Nishiwaki [1], and Robinson [2].

Several authors [3-6] have documented the relevance of the understanding of heat transfer phenomena at the earlier stages of engine design, when the thermal endurance and stability of the composing combustion chamber parts have to be assured. Since engine efficiency and emissions are affected by the magnitude of engine heat transfer, which is directly related to the magnitude of combustion chamber wall temperatures [7-13], it is also during the design stage, that the strategies to control these temperatures, as well as heat and mass transfer involved in the engine cooling system, especially during cold start and transient regimes, must be envisaged. Among others, coolant temperature control is being considered as part of various technology solutions to control material temperatures, given the linear dependency between them [5, 14].

The definition of the requirements for the coolant temperature control and the engine control strategies require detailed knowledge about the thermal engine behaviour. So, an accurate prediction of the metal temperatures and heat flows through the cylinder head, piston and the cylinder liner boundaries is important to engine design, performance prediction and engine diagnosis.

Aforementioned explains the continuous work on engine heat transfer and thermal management carried out by many research groups. In the framework of a research program concerning heat transfer in Diesel engines, the authors [5, 6] already discussed the convenience of using a reduced thermal model for calculating the cylinder head, piston and liner temperature, while conducting combustion analysis. The aim of the present work is to improve the thermal resolution of the mentioned model, and also to extend its capabilities in order to incorporate it into a more comprehensive engine thermal management model. The developed tool can be used in the modelling of different cooling system architectures to assess their impact on oil, coolant and metal temperature, thus saving on extensive and time consuming test work. With this aim the following procedure has been chosen:

1. A more detailed partitioning of the engine geometry into nodes, without loosing the functionality and readiness of the program that characterize the concise wall temperature predictive model reported in [13].

2. The assessment of engine energy balances, as well as the rate of heat rejection to the coolant system.

As a result, in addition to the calculation of metal temperatures, the thermal model allows the calculation of the heat fluxes through combustion chamber elements (in which the engine enclosure has been divided) and engine boundaries and, in particular, with the calibrated engine predictive thermal model it can be estimated the engine heat rejection to the coolant.

The presentation of the work is organized as follows: first, a brief description of the electrical equivalent model of the engine is explained, including a brief explanation of the combustion chamber nodes. After that, the modelling of the boundary conditions is treated, that is: the model of heat transfer between the in-cylinder gases and combustion chamber walls; between the gas and the intake/exhaust runners; between the coolant and the liner and cylinder head; between the oil and the piston; between the oil and the liner; between the piston and the liner. Then, a short explanation of the model code is described, followed by a comparison between experimental and model results. Finally, the main conclusions of this work are given.

2. THE THERMAL MODEL.

The thermal model developed has been adjusted by means of a thorough experimental work on a specific four cylinder Diesel engine, in which its first cylinder was isolated from the other three and instrumented with 23 thermocouples in the cylinder liner, 16 thermocouples in the cylinder head, and 2 thermocouples in the piston (a detailed description of the set-up can be found in [16]. The main characteristics of this engine are given on table 1.

Table 1: Engine main characteristics

|Stroke |80 mm |

|Bore |75 mm |

|Maximum BMEP |1,96 MPa |

|Nominal speed |2000 rpm |

The model is a lumped parameter based on the electrical analogy as performed by other authors [18, 19, 20]. In this kind of models, the engine is treated as a thermal network formed by a finite number of physical nodes considered to be isothermal (resulted from an accurate geometrical discretization of components), linked by means of thermal resistors representative of thermal conductances. Nodes can be either capacitance nodes, possessing mass, or convective boundary nodes with specifying temperature. The heat in the network is transmitted from the source terms to the heat sink nodes through thermal resistors (convection or conduction resistors) with a dynamics dictated by the network topology and lumped capacitances.

To meet the correspondence between the actual system and its electrical analogous, engine piston, cylinder head and cylinder liner have been divided into elementary geometrical pieces (nodes) in accordance to the number of temperature sensors installed to experimentally validate the model, and taking care of meeting the Biot number criterion (to assure that the temperature is uniform over the node).

2.1. The FE model.

The models of the cylinder head, liner and piston were created by using a commercial 3D software. This allowed splitting these complex components into small parts and getting the mechanical characteristics such as connecting areas, distances between centres of mass, and masses of elements. Valves and injector were also decomposed into smaller parts. The cylinder liner was divided in the axial, circumferential and radial direction as shown in figure 1. The fact that only three quarters of the piston stroke was cooled was also taken into account. In total the cylinder liner is made up of 51 cylinder nodes. The nodes at the inside are connected with the piston through the segments.

|[pic] |[pic] |

|Figure 1. Cylinder liner decomposition |Figure 2. Piston decomposition |

The piston was divided in 6 nodes. In figure 2 the referred nodes are, from top to bottom, the bowl centre, the bowl rim, the piston crown, the piston centre, the ring waist housing the oil cooling gallery, and the piston skirt. With the contact area and the distance between the nodes, the conductances between them could be calculated. An axisymmetric temperature distribution was assumed for the piston and liner.

The CAD model of the cylinder head is represented in figure 3. It consists on fire deck, exhaust and intake runners and valves with their guides and the injector. All these elements are separated in two different parts: lower and upper. The cylinder head model was divided into 35 nodes. Because of the special interest the fire deck of the cylinder head, it was modelled in more detail. The partition is shown in figure 4.

|[pic] |[pic] |

|Figure 3. CAD model of the structural part of cylinder head corresponding|Figure 4. Cylinder head decomposition |

|to one cylinder. | |

2.2. Interactions and boundary conditions.

Thermal calculations include the determination of heat fluxes from in-cylinder gases to combustion chamber walls, the heat fluxes through the metallic parts, the convection from the intake and exhaust gases around the surfaces of valve stems, inner surfaces of valve seats and along the intake and exhaust port walls, and also the convection from the metallic parts to the cooling and lubricating oil media. Although the heat fluxes in combustion chamber have a periodically changing nature in time, the analysis is made assuming steady state loading using the cycle averaged values. This assumption is reasonable considering the speed of the periodical changes as compared to thermal inertia of all the components of cylinder head, piston and liner. The same assumption is valid for the exhaust and intake gases. Thermal contact interactions between valves and valve seats are described by heat flux [pic] from the solid face A to B, which is related to the difference of their surface temperatures [pic] and [pic], according to [pic], where [pic] is the contact heat-transfer coefficient.

1

1 Basic principles of nodal model.

For each component, the boundary conditions are specified, either by media (coolant, oil, etc.) temperature and heat transfer coefficient from the outside wall surface to the media, or by specified wall temperature on outside surface. In the model each node is connected to other nodes and boundary conditions. Once the structure is divided into nodes, the energy conservation equation can be written for each node. The sum of heat fluxes between nodes, convective heat fluxes and other heat fluxes in a time span [pic] equals the change in sensible energy of the node (eq. 1).

[pic] (1)

With [pic] the mass of node [pic], [pic] its heat capacity, [pic] the conductance between node [pic] and a node [pic], [pic] the heat transfer coefficient between node [pic] and a boundary [pic] and [pic] the corresponding contact area. At the right side the temperatures at the instant [pic] are used (the implicit formulation). The advantage of the implicit formulation is that the solution is unconditionally stable when simulating transitory behaviour. Because the model described here was also used for transitory calculations the implicit form was used.

For each of the n nodes of the model there is an equation like equation 1, forming a system of n equations and n unknown node temperatures. Equation 1 gives rise to a set of linearized, implicit equations of the form:

[pic] (2)

Where, [pic] and [pic] are [pic] conductance and capacitance matrixes, respectively. The ith diagonal element of the conductance matrix is the sum of all the conductive and convective conductances to node i. The element on the ith row and jth column is the conductance between nodes [pic] and [pic] with a minus sign.

[pic] (3)

[pic] and [pic] are column vectors of n elements with the old and new temperatures of the nodes. [pic] is a column vector with the sum of the heat fluxes to node [pic] on the ith row. This can be e.g. a heat flux generated by friction. [pic] is a column vector with the ith row the sum of the product terms [pic] for the convective boundary conditions of node [pic].

For stationary conditions, nodal thermal masses are not included in the equation 2, [pic], and equation 1 reduces to:

[pic] (4)

The assembly of the equations (2) and (4) is performed automatically based on general engine specifications and is solved implicitly for the temperature vector [pic], employing a Gaussian elimination procedure.

2 Modelling the boundary conditions.

The model to predict the temperatures of the metal parts, results in a thermal resistor network made up of 92 metallic nodes and 8 convective nodes, which represent the boundary conditions, characterized by their instantaneous media temperatures and film coefficients.

The conductances between the combustion chamber nodes and oil/coolant flows have been determined assuming that they depend on the boundary flows or the piston speed in a form like

[pic] (5)

With x representing the coolant flow or the piston speed, [pic] is a multiplicative factor and [pic] is an exponent to be fitted. [pic] is a constant conductance. [pic] is the series configuration of [pic] and the variable-dependent conductance. All conductances of the model are discussed in detail in the following paragraph.

Boundary condition between the gas and combustion chamber walls.

The changing nature of intake, in-cylinder and exhaust processes reflects in a change of the boundary conditions. To predict the mean wall temperatures during the engine working cycle, heat flows have to be calculated using cycle averaged boundary conditions. The mean heat flux ([pic]) between the gas and a wall permanently in contact with the gas (e.g. piston, cylinder head) is found integrating the instantaneous flux [pic] over a cycle.

[pic] (6)

With [pic] the instantaneous heat transfer coefficient as function of crank angle,[pic] the instantaneous gas temperature and [pic] the combustion chamber wall temperature.

Introducing a mean film coefficient ([pic]) and an apparent gas temperature ([pic]):

[pic] (7)

[pic] (8)

The mean heat flux can be written as:

[pic] (9)

So, the conductance between each of the nodes (piston and cylinder head) in contact with the in-cylinder gases is calculated as the product of this mean film coefficient times the area,[pic]. The apparent gas temperature ([pic]) is used as boundary condition.

The conductance between the in-cylinder gases and the internal nodes of the cylinder has been calculated bearing in mind that they are not in contact along all the cycle. So, apparent mean gas temperature and an apparent mean heat transfer coefficient for cylinder nodes have to be found. To this effect a function [pic] is used in the model. For every node of the cylinder liner, the function is defined such that:

[pic] (10)

[pic]

Figure 5. Schematic to illustrate the notation used in the modeling of the cylinder gas – liner interaction.

Being z the axial position along the liner measured from the fire deck, [pic] is the distance between the fire deck and the top of the piston for crank angle α (as illustrated in figure 5). With the δ-function, the mean gas temperature and heat transfer coefficient are defined for each position along the stroke. The mean heat flux at a distance z from the fire deck is

[pic] (11)

This can be written as:

[pic] (12)

With the mean heat transfer coefficient and gas temperature at a distance z from the fire deck:

[pic] (13)

[pic] (14)

Considering a node of the cylinder liner between a distance of z1 and z2 from the fire deck, the contact area is given by:

[pic] (15)

The mean film coefficient times the area gives the conductance that has to be put on the conductance matrix, [pic], for each node of the cylinder liner in contact with the cylinder gases in the model. The apparent gas temperature seen by the cylinder ring band, in which the node is located, is used as boundary condition, [pic].

The conductance between the valves and the seats Kvalves–head is the product of a contact time factor, the valve seat area (Aseats) and a contact conductance (Kseat): Kvalves–head=f.Aseats.Kseat. For the contact resistance, Kseat, a value of 3000 W/m2 K was used [21].

Gas-wall heat transfer.

The film coefficient, hgas, necessary to calculate the conductance between the gas and the walls, is obtained with an enhanced version of Woschni equation [22]:

[pic](16)

Here, D is the bore; Tg the instantaneous gas temperature calculated with the measured in-cylinder pressure, p; [pic] is the mean piston speed; cu is the tangential velocity at the cylinder wall due to swirl; VT is the displacement volume; Tivc, pivc and Vivc are the gas temperature, pressure and cylinder volume at intake valve closing (IVC) and p0 is the in-cylinder pressure under motoring conditions.

In the wall temperature model the heat transfer coefficient between the gas and the walls is calculated with the previously described formula using the instantaneous gas temperature,[pic], and pressure, [pic], from a home made combustion predictive program. Then the cycle average heat transfer coefficient and gas temperature are calculated.

Runner – air heat transfer

The heat transfer between the runners and the gas is highly non stationary. Especially in the exhaust where very high gas velocities are reached during the blow down. Because the generated turbulence lasts even after valve closing, formulas based on the instantaneous speed cannot describe adequately the heat transfer in this pulsating flow and in this work the method proposed by Reyes [23] was used. The velocity is calculated as a sum of the actual velocity and the previous velocities multiplied with their respective dissipation coefficients (17).

[pic] (17)

The average velocity [pic] is calculated with the instantaneous velocity [pic] and the previous average velocity [pic]:

[pic] (18)

Being c the dissipation constant. With the time averaged speed, the Reynolds and Nusselt numbers are calculated.

[pic] (19)

[pic] (20)

The instantaneous speed is obtained from the combustion analysis program. The heat transfer coefficients and temperatures for the intake and exhaust gases, obtained from the Nusselt number, are averaged over a cycle in a way analogous to the one used to obtain the in-cylinder mean film coefficient ([pic]) and the apparent gas temperature ([pic]).

Coolant – wall heat transfer

Along three quarters of the stroke the cylinder liner are refrigerated by water. The correlation for the corresponding conductance (Klin,i–cool) takes into account the coolant flow dependent convection. A similar conductance (Khead,i–cool) exists between the cylinder head nodes in contact with the coolant and the coolant itself. Forced convection is the dominant regime in the coolant circuit and is described with the widely used Dittus-Boelter correlation [24].

[pic] (21)

In the model the possibility of occurrence of the local boiling effects was neglected. The decision was taken considering the complexity of the problem resulting in significant deviations of coefficient values calculated according to the different equations and the multiplicity of variables needed, not all easy to assess.

Oil – Piston heat transfer.

The piston is cooled in two ways. Part of the heat is led away through the segments to the liner and finally to the coolant. The bigger part, though, is transferred to the oil. In the engine under study the oil is sprayed to the entrance of a gallery in the piston crown from an oil cooling jet.

To find the heat transfer coefficient hoil-pis, based on the boundary layer theory, an expression of the form[pic] for the convective heat transfer in the piston gallery is used. Since no tests were done with which the value of exponent n could be determined, it was decided to consider the factor Prn as a part of the constant. The expression for the Nusselt number then takes the following form:

[pic] (22)

The Nusselt number in the coolant gallery is defined as[pic], the Reynolds number as[pic]. Where dgal is the internal diameter of the oil gallery and koil and υoil are the conductivity and viscosity of the oil, respectively.

Based on the work of Kajiwara [25], using the piston temperature measurements, the correlation for the conductance between the oil and the piston was sought in the form:

[pic] (23)

Where Sp is the mean piston speed. The parameters Cpis-oil and Exppis-oil determine the piston speed dependent conductance between the piston and the oil. The constants are results of the optimisation routine.

Liner – oil heat transfer.

Oil is continuously splashed against the cylinder wall and, in the piston some channels coming from the cooling gallery feed the third groove. So the cylinder wall is continuously wetted with oil. This oil is heated by the cylinder wall and scrapped of during the downward stroke. For this conductance (Klin-oil), a piston speed dependence was taken into account just like for the oil – piston heat transfer. During the optimization phase of the model this speed dependence did not appear to be very significant and only the constant part was included in the model. An equivalent heat transfer coefficient, hlin–oil, for this mechanism can be extracted from the following expression:

[pic] (24)

Piston – cylinder liner heat transfer

Because measurements were available of both the piston and the liner temperature, an empirical model could be fitted to the data. It was supposed that the segments have a conductance Kseg per unit of length. The possible influence of the piston speed was turned to be not significant. Hence the conductance between a node of the piston “Pis_i” and a node of the liner “Lin_j” which make contact through a segment is given by the following formula:

[pic] (25)

Where, tcon is the contact time between the segment and the liner node, Tcycle the duration of a cycle, αLin_j the angular width of the liner node and D the bore. The contact time is calculated from the instantaneous piston position taking into account the position of the segment and the axial position of the liner node.

Cylinder head – cylinder liner heat transfer

Heat conduction between the cylinder liner and the cylinder head is possible through the gasket (Klin–head). This conductance did not appear to be significant and was not considered in the model.

3

4 3. THE COMPUTATIONAL PROGRAM.

As was mentioned in the previous paragraph the model developed is a combination of theoretical and experimental work. Fitting the model to particular engine temperature measurements, it has been taking care of representing the conductances involved in the optimization process, as functions of geometrical and operational parameters of the engine, so that the model can be readily applied to other engines with similar geometry and power as a generic template. Also a set of scale factors and relationships has been provided in the program to adjust new engine geometries and materials.

The code to model the thermal behaviour of the engine has been written in C++. Its structure is summarized in figure 6. The inputs of the program are: a file with the names of the tests, the wall temperatures of which will be calculated; CALMEC (home made predictive computer application) output files with the instantaneous temperature and pressure in the combustion chamber for every test; a file that contains the measured mean variables representative of the running condiction, including prescribed coolant and oil temperatures; a file that describes the discretization of cylinder liner, cylinder head and piston and, finally, a file with the parameters of the model, needed to calculate convective conductances.

[pic]

Figure 6. Structure of the computational program used for the model [15].

The program can be used either in predictive mode, or in an optimization mode. In the optimization mode, the parameters of the model affecting convective conductances (with the capability to be extended to other new parameters of interest) are adjusted in a way that the error between the calculated and measured temperatures of a known set of tests is minimal. The program uses the Nelder-Mead simplex algorithm [26] to optimize the parameters.

In the predictive mode, temperatures and heat fluxes can be calculated for any given engine, provided its geometrical information and the instantaneous and mean variables are known.

For all the tests in the file “Tests.txt” the program calculates the temperatures, and the results are compared with the measurements. For the cylinder liner the predicted temperature at a thermocouple location is calculated by three-dimensional interpolation between the surrounding nodes. This interpolation uses the position of the nodes and the thermocouple. To compare measurements and predictions in the cylinder head and piston a weighting procedure is performed between the nodal temperatures of close related nodes.

With the engine used to tune the model up, the values of the optimized parameters are those referred in table 2.

Table 2. Optimized values of conductance parameters used in the model.

|Cte_lin2head |0 |

|h_cool2cyl |0.524482 |

|h_cool2FD |1.218676 |

|h_cool2Exh |0 |

|Cte_pis2oil |721.422607 |

|Exp_pis2oil |0.687376 |

|Kpis2lin |3.875552 |

|h_lin2oil |864.868713 |

4. RESULTS AND DISCUSSION.

The experimental work comprises two stages. The first stage is intended to provide engine steady state temperature measurements to run the computational program in the optimization mode. The outcome of this stage is the attainment of the optimized model to predict the thermal behaviour of Diesel engines geometrically similar to that used in the model development process.

In the second stage, another set of tests is used to obtain measurements of the engine temperatures over elementary transient step changes with the aim of assessing the predictions of the model for heated engine transient operation. Known the initial and final points of transient engine operation, the model with the optimized parameters is used to calculate temperature evolution of the engine temperatures and heat fluxes for a given transient time. An interpolation procedure in the time domain, allows a comparison of predicted and experimental transient thermal responses of the engine.

For the first stage, the program is run in the predictive mode and the predicted temperatures are compared to the measured ones, obtaining the model temperature errors separately for piston, liner and cylinder head, as well as the global model error. After that, the program is requested to optimize the initial model parameters in the optimization mode, and the resulted optimized parameters are re-entered to the model to recalculate the engine temperatures and obtain the global error, the final errors in the predictions of piston, liner and fire deck temperatures, the heat fluxes between engine nodes and the engine heat balance.

For the second stage, the program is run in the predictive transitory mode, after optimizing the model parameters.

The test matrix with the mean variables used during the optimization process of the thermal model for the engine under study is presented in table 3. 32 steady state tests were conducted with variation of the speed and load. The temperatures of the 32 tests are compared to those obtained experimentally for all measured points.

Table 3. Mean variables of the tests performed and used to tune the model up.

|Test |Speed |

|a) |b) |

|[pic] |[pic] |

|c) |d) |

|Figure 7. Predicted and measured temperature distributions in the liner at various axial locations for 12 %, 33 %, and 65 % of BMEP: |

|a) between cylinders side, b) intake side, c) exhaust side, d) clutch side. |

The dependence of liner wall temperature on load is exemplified in figure 8, for two operation points with the same engine speed of 3000 rpm, and mean effective pressures of 3,08 bar and 11,76 bar, correspondingly (tests 10 and 12, respectively). The predictions agree with the measured data at a good level. As was previously said main discrepancies may be attributable to the variation of heat transfer coefficient for the liner coolant interface, less important at low loads.

|[pic] |[pic] |

|a) |b) |

|[pic] |[pic] |

|c) |d) |

|Figure 8. Predicted and measured temperature distributions in the liner at various axial locations as the load changes at a constant |

|speed of 3000 rpm, a) between cylinders side, b) intake side, c) exhaust side, d) clutch side. |

The sensitivity of the model to the speed changes as compared to the measured values is represented in figure 9 for two operation points with the same mean effective pressure of 2,6 bar and engine speeds of 1520 and 3500 rpm, correspondingly (tests 3 and 24, respectively). The match of predicted and measured temperatures is good, more accurate at low speeds.

|[pic] |[pic] |

|a) |b) |

|[pic] |[pic] |

|c) |d) |

|Figure 9. Predicted and measured temperature distributions in the liner at various axial locations as the speed changes at a constant|

|mep of 2,6 bar, a) between cylinders side, b) intake side, c) exhaust side, d) clutch side. |

Liner temperatures as well as all others increase with speed and load. The gradient is more significant in the upper part of liner. Higher engine loads translate in an increase of temperatures but with a higher gradient in the upper portion of the liner; higher engine speeds more equally distribute wall temperatures along the stroke.

The computed temperatures of the liner in the cross sectional area are in good agreement with experimental results, as can be inferred from the temperature plot in figure 10, where temperatures for four orthogonal points in the liner at a distance of 44 mm and a penetration depth of 3,5 mm, for load cases 1 a12, have been represented. It is observed that major discrepancies in the predicted temperatures as compared to measured values appear for liner nodes between cylinder nodes, especially at high loads.

[pic]

Figure 10. Distribution of liner node temperatures in the cross sectional area of the cylinder 1 at a distance of 44 mm from the fire deck, 3,5 mm penetration depth.

4.2. Temperatures for the fire deck nodes.

Through the fire deck the heat flow is transferred from the combustion chamber to the rest of the nodes of the cylinder head, including intake and exhaust pipes, and coolant.

The comparison of predicted (obtained by interpolation of the nodal results) and measured temperatures of fire deck nodes of the cylinder head, taken at depths of 3,5 mm and 8,7 mm, for all the experimental test conducted, is presented in figure 11. In general it can be said that the fire deck temperatures are well rendered, especially for low loads. The average error in the prediction of the fire deck temperatures is 7,5 ºC, which is low for the applicability of the model (Procurar traer aquí las conclusions de Jaime sobre sensibilidad con CALMEC a las predicciones de temperature de pared). The higher errors correspond to the node represented by the injector hole at the exhaust side, at 8,7 mm (with an average value of 21,35 ºC), and between intake and exhaust valves (with an average value of 7,02 ºC). The error plot for all the tests conducted under steady state operation points is shown in figure 12.

|[pic] |[pic] |

|[pic] |[pic] |

|[pic] |[pic] |

Figure 11. Predicted and measured temperatures in the cylinder head nodes.

[pic]

Figure 12. Plot of the errors in the prediction of fire deck temperatures for the measuring points.

The predicted temperatures of cylinder head fire deck nodes, for three representative operation points: 12 %, 33 %, and 65 % of BMEP (tests Nº 1, 6 and 13 in table 2, respectively) is presented in figure 13. The higher temperatures correspond to the exhaust valve. To illustrate the sensitivity of the thermal response of the fire deck nodes load changes, it is presented in the figure 14 the variation of fire deck node temperatures as the load is changed from 3,08 to 11,76 bar at a constant speed of 3000 rpm (tests 10 and 12, respectively). To illustrate the sensitivity of the fire deck temperatures to the speed regime changes, the behavior of the temperatures for the referred nodes is presented in figure 15, where the test points correspond to a speed variation from 1520 rpm to 3500 rpm with a mean effective pressure of 2,6 bar (tests 3 and 24, respectively).

[pic]

Figure 13. Temperatures for the fire deck nodes predicted by the model.

|[pic] |[pic] |

|Figure 14. Temperatures for the fire deck nodes predicted by the |Figure 15. Temperatures for the fire deck nodes predicted by the model at a |

|model at a constant speed and two different mean effective |constant mep and two different engine speeds. |

|pressure values. | |

4.3. Temperatures for the piston nodes.

The steady-state predicted and measured temperatures in the piston nodes, where thermocouples were placed, are compared in the figure 16 for all the experimental tests performed. For the bowl rim, the temperatures are well predicted, while for the bowl bottom the temperatures are overpredicted. This overprediction of the bowl bottom temperatures has an acceptable magnitude though. The behaviour of temperature predictions for these nodes are zoomed in figure 17 for three working operating points corresponding to 12 %, 33 %, and 65 % of BMEP.

|[pic] |[pic] |

|Figure 16. Predicted and measured temperatures in the piston nodes. |

[pic]

Figure 17. Predicted and measured temperatures in the piston nodes for 12 %, 33 %, and 65 % of BMEP.

The sensitivity of the thermal response of the piston nodes to the load is illustrated in figure 18, as the load is changed from 3,08 to 11,76 bar at a constant speed of 3000 rpm. To illustrate the sensitivity of the piston nodes to the speed regime changes, the behavior of the temperatures for the referred nodes is presented in figure 19, where the test points correspond to a speed variation from 1520 rpm to 3500 rpm with a mean effective pressure of 2,6 bar.

|[pic] |[pic] |

|Figure 18. Sensitivity of piston node temperatures to speed changes at |Figure 19. Sensitivity of piston node temperatures to load changes at |

|constant load. |constant engine speeds. |

Figures 20 and 21 show a good agreement between calculated and measured piston node temperatures along all the test history, with a mayor degree of overprediction for the piston bowl bottom.

|[pic] |[pic] |

| | |

|Figure 20. Test history of predicted and measured temperatures of the |Figure 21. Test history of predicted and measured temperatures of the |

|piston bowl rim. |piston bowl bottom. |

Figure 22 shows the variation of temperature errors for piston bowl rim and piston bowl bottom for a history of tests. Since the program uses only two experimental piston temperatures of a total of 41 ones in the entire engine (it was not possible to connect enough sensors to match all the elements of the meshed model), to collectively calibrate the global thermal model and give well-conditioned predictions of the engine thermal behavior, it is not likely to approximate all the measures with the same degree of accuracy. Although a reevaluation of the weighting factors for the temperatures could improve the predictions, it is true that a more detailed calibration of the engine model could be made introducing friction model data from an engine of known dimensions and masses, or obtaining experimental friction data.

[pic]

Figure 22. Error history in the temperature predictions of the piston bowl rim and piston bowl bottom nodes.

The behavior of the temperatures predicted by the model for all the nodes in which de model has been descretized is presented in figure 23. A larger number of temperature measurements with good distribution uniformity in the piston could improve the predictions if the objectives of the research were to have a refined piston model.

[pic]

Figure 23. Predicted temperatures of the piston nodes for a test history.

A summary of the errors in the predictions of cylinder head (not only the fire deck), the piston and liner temperatures as well as the total error of the model is plotted in figure 24. Mean errors in the evaluation of combustion chamber wall temperatures are summarized in table 4, being the error in the prediction of piston temperatures the larger one followed by the error in the prediction of cylinder head temperatures. Liner temperatures give the best predictions. The global mean error is lower than 10 ºC, and is representative for the operation points encountered by Diesel engines during the city driving cycles. Results are very satisfactory. In fact, this error is low enough to allow the model to be used for research purposes in Diesel engine combustion predictive and diagnosing programs. Also, the information of the model permits to write the energy balance and the heat fluxes between the components.

[pic]

Figure 24. Errors in the temperature predictions of combustion chamber walls.

Table 4. Mean errors in the predicted temperatures of engine metallic parts.

|Error_Liner |Error_head |Error_Pis |Error_total |

|(ºC) |(ºC) |(ºC) |(ºC) |

|3.871875 |7.3853125 |10.84375 |7.3675 |

In figure 25 the surface averaged temperatures of the cylinder liner, piston and fire deck are presented for an extended set of tests. The model allows calculating the heat fluxes through the combustion chamber walls. In the following paragraph it will be presented the heat flux balance for all the nodes used in the model.

[pic]

Figure 25. Mean temperatures of the cylinder liner, piston and cylinder head for an extended set of tests.

4.4. Heat fluxes through node boundaries.

Knowledge about geometry, thermal properties of material, conductances, and node temperatures is utilized in the model to find the partitioning of the heat rejected to the combustion chamber walls. So, the model can be easily interfaced with engine combustion predictive and diagnostics programs. Heat crossing any node interface of the discretized model can also be found. To give an example of this model feature, based on a particular operational condition of the engine, mep = 3,93 bar and 1500 rpm (test Nº 1 in table 3), heat fluxes of importance for the heat energy balance will be detailed here.

Table 5 shows the global heat transfer balance in the main components of the combustion chamber, for the given engine operation condition (test Nº 1).

Table 5. Heat fluxes through combustion chamber walls (W), derived directly from the model.

|From cylinder gases to liner |419.102953 |

|From cylinder gases to piston |668.630687 |

|From cylinder gases to fire deck |508.402046 |

|From exhaust gases to cylinder head |294.044094 |

|From cylinder head to intake air |15.805118 |

|Total heat flux received by the combustion chamber walls |1874.37466 |

In the steady state running conditions the total heat flux to the combustion chamber walls plus the heat flux from exhaust gases to cylinder head are transferred in the end to the engine coolant. This is currently one of the most important outcomes of the program to be utilized, since it is a primary input to the design and analysis of engine cooling systems.

In the model presented, the cylinder liner model is decomposed into five longitudinal sections or cylinder ring bands. The heat to the cylinder liner transferred according to this geometrical partitioning is presented in table 6 for two running conditions (tests Nº 1 and 13). It can be seen that almost 50 % of the heat through the cylinder liner is transferred by the upper 10 % of the liner surface in contact with the gases. A more refined partitioning of the liner along its length can be set in the program.

Table 6. Heat fluxes from cylinder working gas through liner surfaces.

|Test |1500 rpm, 4,93 bar |3000 rpm, 11,74 bar |

|Cylinder belt |Heat flux (W) |% |Heat flux (W) |% |

|I |201.952 |48.187 |667.435 |46.709 |

|II |88.737 |21.173 |302.344 |21.159 |

|III |61.567 |14.690 |215.432 |15.076 |

|IV |43.684 |10.423 |156.377 |10.944 |

|V |23.163 |5.527 |87.342 |6.112 |

|Total |419.103 |100 |1428.931 |100 |

A coarse description of the paths followed by the heat flow from cylinder gases to the piston surfaces is as appears in table 7.

Table 7. Heat fluxes through piston surfaces.

|Piston surface |Heat flux, W |% |

|Piston central pik |53.324 |7.975 |

|Piston bowl rim |98.018 |14.66 |

|Piston core node |93.432 |13.974 |

|Piston upper crown |423.858 |63.392 |

|Total heat flux through piston surfaces |668.632 |100 |

Heat flowing to the piston from cylinder gases is then transferred, one part to the oil through piston oil gallery and piston under crown surfaces, and the other part to the cylinder liner through piston-ring-liner interfaces, as depicted by table 8.

Table 8. Heat fluxes through piston-ring-liner interfaces.

| |Head flux (W) |% |

|Heat flux from piston to oil |559.783 |83.72 |

|Total Heat flux from piston to cylinder liner |108.848 |16.28 |

|Total heat flux through piston surfaces |668.632 |100 |

| | | |

|Heat flux from upper piston ring belt to cylinder liner |59.485 |54.65 |

|Heat flux from lower piston ring belt to cylinder liner |49.363 |45.35 |

|Total Heat flux from piston to cylinder liner |108.848 |100 |

The cylinder liner receives heat from cylinder gases and piston ring belts. This heat, in turn, is transferred from the cylinder liner to the coolant and to the oil, as presented in table 9.

Table 9. Heat fluxes from cylinder liner to the oil and coolant.

| |Head flux (W) |% |

|Heat flux from cylinder gases to the liner |419.103 |79 |

|Heat flux from piston to cylinder liner |108.848 |21 |

|Total heat flux received by the cylinder liner |527.951 |100 |

| | | |

|Heat flux from cylinder liner to coolant |310.2575 |58.77 |

|Heat flux from cylinder liner to oil |217.694 |41.23 |

In the model developed it is assumed that all the energy transferred by the cylinder and exhaust gases to the cylinder walls goes to lubricating oil and coolant heating. The lubricating oil receives heat from cylinder liner and piston in the proportions depicted in table 10.

Table 10. Heat fluxes to lubricating oil.

| |Head flux (W) |% |

|Heat flux from cylinder liner to oil |217.694 |28 |

|Heat flux from piston to oil |559.783 |72 |

|Total Heat flux to oil |777.477 |100 |

The gas energy balance for the cylinder head is presented in table 11. As can be seen an important part of the heat flux to the cylinder head comes from the exhaust gases, almost 35 %.

Table 11. Heat transfer between cylinder head and working gases.

| |Head flux (W) |% |

|Heat flux from cylinder gases to fire deck |508.402046 |64.63 |

|Heat flux from exhaust gases to cylinder head |294.044094 |34.37 |

|Heat flux to intake air from cylinder head |-15.805118 |2 |

|Total heat flux received by the cylinder head walls |786.641022 |100 |

The detailed description of the heat flows leads us to the determination of the heat transmitted to the coolant, as presented in the table 12. It is noteworthy that the cylinder liner participates with less than 20 % in that heat flow. More than 80 % of the heat transferred to the coolant comes equally from the cylinder head and oil. Almost 16 % of the heat transferred to the coolant comes from the exhaust gases. 58,56 % of the heat transferred to coolant comes from the metallic parts, the 41,44 % remaining comes from the oil.

Table 12. Heat transferred by the engine to the coolant.

| |Head flux (W) |% |

|Heat flow from cylinder head to coolant |786.64 |41.97 |

|Heat flow from cylinder liner to coolant |310.26 |16.55 |

|Heat flow to coolant coming from combustion chamber walls |1096.90 |58,56 |

|Heat flow from oil to coolant |777.476 |41.44 |

|Total heat flow received by coolant per cylinder |1874.375 |100 |

|Total heat flow to coolant due to combustion in all the engine cylinders |7399.287 | |

The detailed heat balance presented can be performed for every point of operation, making the model suitable to analyse engine cooling systems at any given load operation of a vehicle in which the engine would be installed.

In figure 26 they are shown the heat fluxes through combustion chamber walls for the extended set of tests run under stationary conditions. In figure 27 the predicted total heat flux through combustion chamber walls is compared to the heat rejected by the coolant, calculated with the in and out coolant temperatures, coolant properties and coolant flow. The difference between these two curves stands for the result of heat exchanged between cylinder head and intake and exhaust gases, then transmitted to coolant.

|[pic] |[pic] |

|Figure 26. History of heat fluxes through combustion chamber walls for |Figure 27. Comparison between heat fluxes through combustion |

|the test used in the optimization of the model |chamber walls and heat rejected to coolant. |

Given the availability of the information related to brake effective power and fuel consumption for the tests performed, the heat losses through combustion chamber walls were related to the effective power developed by the engine and to the equivalent power introduced with the fuel. In figures 28 and 29 these useful relationships are presented. A representative set of tests could be used to predict the thermal map of the engine under modelling.

|[pic] |[pic] |

|Figure 28. Heat losses through combustion chamber walls related to|Figure 29. Heat losses through combustion chamber walls related to|

|brake effective power. |energy introduced with the fuel power, to be used in combustion |

| |analysis. |

|[pic] |[pic] |

|Figure 30. Heat losses through combustion chamber walls, brake |Figure 31. Heat rejected to the coolant referred to equivalent |

|mean effective power and power introduced with the fuel for a set |power introduced with the fuel for a set of operation points, to |

|of operation points. |be used in engine efficiency analysis. |

4.5. Transitory results.

After the model has been optimized for the steady state conditions the model can be used to analyse the engine thermal response predictions of the engine under transient conditions. Node temperatures and heat flux variations over any transient step determined by any play of initial and final load operation conditions can be calculated. A time-step length of 1 second was used in these calculations as a compromise between computation efficiency and prediction accuracy (calculation of the Fourier number for the presumed most risky nodes was done). The experimental measurements obtained for a set of 31 transient engine processes between known initial and final conditions were used to assess the model. For this tests the readings of the 39 thermocouples (for the transient tests difficulties were encountered with the measurements of piston temperatures) used were registered during a sufficient period over which the given set of operating conditions were applied on the system.

In general, although there is still room for improvement, a satisfactory degree of agreement is found between theoretical predictions and experimental measurements under all conditions tested.

In figure 32 transition temperatures (at 4500 rpm speed transition from 2 bar mep to 8 bar mep, and at 1000 rpm speed transition from 3 bar mep to 10 bar mep) for the cylinder liner measurements at two extreme longitudinal locations are shown. It can be seen that the model overpredicts the temperature evolution for the upper part, especially at high speeds and loads. This is caused in part by the error at steady state conditions, and in part also by the small number of segments taken in the lumped parameter model in the longitudinal dimension of the liner, which determines the accuracy of temperature resolution. However, the excursion of the response in a trend of a first order thermal element is acceptable. Obviously a refinement of the cylinder mesh would approach closer the time constants, but at the expense of the computational cost. Results for the lower part of the liner, where the static errors are lower, are satisfactory.

In figure 33 they are also illustrated temperature evolution for all the liner nodes were experimental information was available. The heat transfer gradient for the first two axial positions (ie, at 8 mm and 25 mm) is high when compared with the heat transfer gradient at other positions.

|[pic] |[pic] |

|Figure 32. Transient temperatures for a couple of extreme liner nodes |Figure 33. Transient temperatures for cylinder liner nodes. |

|under two transient processes. | |

In figure 34, 35 transient temperatures for the fire deck nodes are presented. The thermal response of the model is somewhat faster as compared to the experimental traces. It is more favourable the prediction for the exhaust valve seat node. Time constants can be considered favourable.

|[pic] |[pic] |

|Figure 34. Transient temperatures for the exhaust valve seat under two |Figure 35. Transient temperatures for the node between exhaust valves |

|transient processes. |under two engine transient processes. |

In figure 36, 37 transient temperatures for two fire deck nodes are presented. Plot 37 illustrates two speed transitions at constant load, from 1100 to 2700 rpm, and from 1040 to 4000. The thermal response of the model anticipates experimental traces. As was mentioned before the accuracy of transient response is limited by the accuracy of steady state response, which is affected also by the coarseness of the lumped parameters model.

|[pic] |[pic] |

|Figure 36. Predicted and measured transient temperatures for the |Figure 37. Predicted and measured transient temperatures for the |

|exhaust valve seat under two transient processes. |exhaust valve seat under two transient processes. |

Because of technical difficulties it was not possible to measure piston temperatures under transient conditions. The predicted piston response at constant load under a change of speed is plotted in figure 38. The lower heat capacity of the piston rim allows it to have a quicker response as compared to piston bowl bottom. In figure 39 transient evolutions of mean temperatures related to cylinder liner, cylinder head and piston are given for a transition from operation conditions corresponding to test Nº 32 to those of the operation condition Nº 1 in table 3. The mean piston temperatures are the more sluggish, though the upper part of the piston can have a quicker response.

|[pic] |[pic] |

|Figure 38. Predicted transient temperatures for the exhaust valve |Figure 39. Predicted transient temperatures for the cylinder liner, |

|seat under two transient processes. |cylinder head and piston under two transient processes. |

For the already warmed engine, transient total heat flow through combustion chamber walls establishes very fast, as is illustrated in figure 40 (the combustion process may take from 0,2 to 1,5 seconds to get its steady state). For the transition regimes the time constants for the engine nodes have an average of 35 – 65 seconds, not considering the time taken for the combustion process to reach its steady state condition, which is small as compared with this elapsed time.

In the figure 41 transient heat flux evolution as the engine is subjected to a random driving cycle arranged with a set of validated transitional processes is plotted. This can serve as an example of the applicability of the model to simulate the thermal behaviour of the engine over elementary step changes and stair-step changes in operating conditions, or even to evaluate the thermal response of the engine over a normalized driving cycle.

|[pic] |[pic] |

|Figure 40. Transient heat flux for a given change of operational |Figure 41. Transient heat flux evolution as the engine is subjected to a |

|conditions. |stair step schedule of operating conditions. |

Finally, to study the potential of developed thermal model for the prediction of engine thermal performance a second engine was tested with the basic characteristics presented in table , 85 mm bore, 88 mm stroke, 1,96 MPa maximum break mean effective pressure, 2000 rpm nominal speed. Results of the predicted heat fluxes from exhaust gases to the cylinder head, heat flux to the oil, heat flux through combustion chamber walls, and heat losses to the coolant for an arbitrary set of tests is plotted in figure 42. In the same plot the brake engine power of the tests is drawn also.

Table 13: Second engine main characteristics

|Stroke |88 mm |

|Bore |85 mm |

|Maximum BMEP |1,96 MPa |

|Nominal speed |2000 rpm |

[pic]

Figure 42. Presentation of power and heat balance for the second engine.

The computed mean temperatures of the cylinder liner, fire deck and piston for the second engine are illustrated in figure 43. For each combustion chamber wall (piston, head, liner), the mean heat flux over a thermodynamic cycle to the wall area has been also obtained.

[pic]

Figure 43. Mean surface averaged temperatures of combustion chamber walls.

In the progress of our work, the modelling of engine warm-up is under research. Figure 44 shows the temperature variation of the cylinder head, liner, piston, coolant, oil, and external wall surface temperature of the cylinder head, in the first 1180 seconds engine warm-up period. The shapes of the curves are encouraging.

[pic]

Figure 44. Time dependence of predicted mean surface averaged temperatures of combustion chamber walls, and measured temperatures of coolant and external surface of the cylinder head.

To gather experimental information for the modelling of engine warm-up, mean variables and instantaneous values of in-cylinder variables have been recorded during a real warm-up process. To have the mean variables for every point in the warm-up process, time averaged values of measurements taken during an actual warming-up process were utilized. It was assumed that during this transition period, for a given time averaged mep, the instantaneous in-cylinder pressures are identical for steady and unsteady operations. In fact during the warm-up, mep is affected by the friction mean effective pressure itself depending on the oil viscosity. It must be reminded that our model does not accounts for friction as an independent heat source.

It was assumed that, given the rapidity with which the processes take place inside the cylinder as compared to the time taken by any operation conditions to become stable, the cycle-averaged heat transfer coefficient and temperature were still valid for warm-up transient conditions. An engine can perform a significant number of complete thermodynamic gas cycles prior to being noticeable affected by transient thermal conditions resulting from a change in engine operating conditions.

The assumption made above is additionally allowed by the high speed features of the data acquisition system used to acquire the experimental data, very high as compared to the times of change of mean variables.

5. CONCLUSIONS.

A lumped parameter thermal model (lumped capacity method), obtained as an extension of the three nodes concise wall temperature model performed and reported by our research group [15], has been implemented and validated using experimental data issuing from thermal steady state and transient conditions. Global measurements of engine variables from the test bench along with instantaneous values of in-cylinder media properties, effective valve sections, flows, and local measurements of temperatures in the engine solid masses, coolant and oil were used during the development process. The updated model allows a higher degree of discretization and provides local and global heat flow and temperature field information to support not only energy, but also other relevant issues as thermal loads required for structural analysis, thermal management studies, and interfacing to engine cooling systems models. The model uses a geometric template that can be used for a set of engines with certain degree of structural and geometrical similarity.

To appreciate the predictive capability of the model, there were compared measured and calculated metallic temperatures for 32 different steady state tests and 31 transient processes. The heat transferred to the coolant was also calculated as the final end of the engine heat balance. A second engine was used to validate thermal steady state and transient predictions. The model gives numerical results closed to the experimental ones on a wide range of operating conditions. The model can be used as a design tool for thermal performance optimization and energy management system.

The next phase of the research project is the development of a reduced order thermal system in which the presented developed model will be coupled to an external to the engine radiator cooling loop, completing an engine cooling system. This will allow studying the impact of different cooling strategies on on oil, coolant and metal temperature.

Actual engine speeds, mep and other mean variables, as well as instantaneous in-cylinder parameters for an engine subject to the acceleration schedule of NEDC have been experimentally recorded, and used to predict the engine metal temperatures evolution and heat balance, given the availability of the model. This part of the work shown the predictive capability of the model to assess the warming-up process of Diesel engines. The refining of this feature is under work.

Further study and enhancement of the program comprises a more detailed calibration of the engine model, introducing friction model data from an engine of known dimensions and masses, and a more accurate prediction of the component thermal transients interfacing the model to the back of an engine cycle simulation model.

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