## Abstract

The twenty-first century started with many downsizing applications. This important trend in the engine technology has been constantly developed. There are questions about limits and on the other hand new solutions in the face of new materials, tribological discovery, lubrication oils, turbo- or supercharging, new control electronic system of the engine run, higher accuracy in designing, etc. Some of parameters of thermodynamics of working cycle and thermal load according to the downsizing engine parameters were considered in this article. The downsizing impacts on fuel economy and emission were analysed, too. The investigations were carried out with own measured data (i.e. pressure inside inlet manifold, temperature of engine wall) as well as data from references (for example material properties) and at the end the simulations were done. The essential achievements of the work are (a) downsizing factor (DSF) was defined first time in this article (nobody before), (b) because of possibility of exceeding thermal load in piston (as an example engine part) the changes of DSF has to be restricted to almost 0.95 giving changes of 0.85 for base cylinder diameter and 0.90 ratio of base volume for stroke, (c) the main goal of downsizing to reduce CO_{2} emission was results of all tests but it show only 10% benefit, and (d) it is possible to optimise the downsizing technology. So, the next research work will be focused on changes of super- and turbocharging as well as lean mixture combustion for better optimisation of downsizing.

## Introduction

The engine technology named downsizing occupies a significant position in the worldwide idea of reducing carbon dioxide emission as well as saving up fuels. It saves manufacturing costs per power unit, too.

The idea of downsizing the engine (which means reducing main dimensions of the engine) reducing the swept volume with mainly the same or higher torque and power of the engine has been well known since the 1990s [1–3]. However, there are numerous limitations of this technology and they might be overcome only when new advanced solutions are available [4, 5].

In gasoline engines, essential limitations are as follows: knocking, thermal and mechanical loads of the engine components, response time of turbocharging as well as reliability and durability of the engine parts [6].

In case of diesel engines, the most important limitations of applying the technology of downsizing are thermal loads and consequently the right type of cooling as well as the emission of particulate matter and nitrogen oxides which are in contradiction with the idea of reducing CO_{2} [7, 8].

The main task for engineers working on downsizing is to control ignition and combustion process, e.g. the controlled homogeneous auto-ignition supercharged engine (CHAISE), to control timing and lift of valves—the variable valve timing (VVT), to control recovering energy—the exhaust gas recirculation (EGR), variable and mixed charging—the VS or variable supercharging and turbocharging (VST), to change compression ratio—the variable compression ratio (VCR), to control the procedure START/STOP, switching off cylinders (the dynamic downsizing), emission reduction, e.g. the gasoline direct injection (GDI). There are also so called indirect interventions, e.g. applying alcohol fuels to gasoline engines taking into consideration higher resistance against knocking and larger speed of fuel burning which improves thermal efficiency [9].

Reducing dimensions of the combustion chamber with simultaneous growth of mean effective pressure definitely influences thermodynamics of combustion process as well as it puts into consideration the thermal load of the engine components.

By that project, I would like to join the discussion about limitations of downsizing from the thermodynamic standpoint. The conclusions which are in accordance with the title of the article have been presented after the author's own research based on multi-variants computer simulation, carried out at the Division of Motor Vehicles and Internal Combustion Engines, the Wroclaw University of Technology (Poland).

## Thermal load of combustion engine

*Q*is the heat transfer,

*Q*

_{HV}is fuel heating value,

*B*

_{o}is dose of fuel in time unit and ξ is the coefficient of heat utilisation in combustion chamber.

Local thermal loads, relating to individual parts of the engine, characterise heat exchange on their surfaces as well as heat penetration into metal depth. They depend on

- — heat conductivity,
- —geometry of the combustion chamber and the relation of dimensions,
- —velocity of combustion gases inside the chamber,
- —course of the burning process.

The analysis of thermal loads in the engine as the whole object as well as in its separate components is based on different kinds of heat exchange conditions such as conduction, convection, radiation and diffusion [4, 10–12].

*Q*, transferred in the definite direction, is formulated by Fourier's law (2). where λ

_{m}is the thermal conductivity of medium;

*s*is thickness of layer of medium;

*A*is surface area of the barrier for heat transfer;

*T*

_{1},

*T*

_{2}are temperature on surfaces of studied barrier and τ is the time.

_{m}is an experimental factor which characterises this kind of heat exchange for solid substances (including metal) and it is related to temperature and pressure. For example AK12 (popular aluminium alloy used in engines) can be described as follows [13]:

The convection is the mechanism of heat exchange which dominates in liquids and gases. This is transportation of heat through moving particles which cause heat transfer by contacting each other or the barrier. The measure of convection can be the speed of movement of particles which is variable in the section of flow: from stormy in the central part, across laminar, until to achieve motionless layer on the surface of the barrier.

_{k}characterises the heat exchange by convection. This coefficient expresses the quantity of heat passed from gas or liquid to the unit of surface area of the solid barrier at the unit of difference of temperature between medium and the barrier (Newton's law of cooling). where α

_{k}is the convective heat transfer coefficient;

*A*is surface area of the barrier for heat transfer;

*T*

_{1},

*T*

_{2}are temperature on surfaces of studied barrier and τ is the time.

The coefficient α_{k} is an empirical value and can be expressed by criteria numbers as follows: Nusselt's *Nu*, Prandtl's *Pr*, Reynold's *Re.*

_{k}in the combustion chamber within the engine is formula given by Woschni [14, 15]. where

*D*is the cylinder diameter,

*w*is average speed of air–fuel mixture in combustion chamber,

*p*(

*φ*

_{i}) is temporary value of pressure inside combustion chamber,

*T*(

*φ*

_{i}) is temporary value of temperature inside combustion chamber and

*φ*

_{i}is the value of crank angle of turn of crankshaft in the working cycle of engine.

The thermal radiation is the type of heat transfer which depends on properties of absorbing irradiated surface, its emissivity and the transparency. In the combustion chamber, the following processes can be distinguished:

- — exchange of energy by radiation among the chamber element (walls),
- —emission of hot exhaust gases including the flame in the chamber,
- —emission of radiation of particulate matters as products of fuel burning in exhaust gases.

_{f}(φ

_{i}) is the relative emissivity of the flame where

*p*(φ

_{i}) is the temporary pressure inside combustion chamber,

*l*

_{p}is average distance of flame in combustion chamber. where

*V*is the volume of burning space,

*A*

_{k}is area of the combustion chamber

*Q*, the heat transfer coefficient is created as supplementary and it depends on convection and conduction processes (11) where

*A*

_{m}average surface area of cross section of barrier,

*l*length of the cylinder liner,

*r*

_{z}external radius of the cylinder liner,

*r*

_{w}inner radius of the cylinder liner,

*k*

_{z}supplementary coefficient of the heat transfer,

*T*

_{1},

*T*

_{2}temperature on surfaces of the studied barrier, τ time, α

_{1}, α

_{2}convective heat transfer coefficients for zones of 1 and 2 in relation to the barrier,

*s*

_{i}thickness of layer, called ‘

*i*’ within the barrier, λ

_{i}thermal conductivity of layer named ‘

*i*’ within the barrier.

*Q*

_{1}and exit

*Q*

_{2}:

*c*

_{p}is specific heat for constant pressure, d

*x*, d

*y*, d

*z*are changes of unit dimensions of studied parts, ρ is density of material and d

*T*is the changes of temperature in the changes of time of dτ

*x*”), the formula (13) might be presented as Fourier's equation for unsteady state (14). and the expression (15) is called coefficient of thermal diffusion.

According to Woschni's definition [14, 15], heat load in the combustion engine requires qualification of temperature changes of air–fuel charge (*T*) at space with closed valves and for some assumptions, connected with air–fuel mixture:

- — air–fuel mixture is in thermal equilibrium at any time,
- —air–fuel mixture can be treated as perfect gas,
- —combustion chamber is closed space from thermodynamic standpoint (the same quantity of air–fuel mixture at any time).

*p*is the pressure of gas,

*V*is volume of burning space,

*T*is temperature of air–fuel mixture,

*b*is current coefficient of change of moles number for air–fuel mixture,

*n*

_{1}is total number of moles of air–fuel mixture at the beginning of compression cycle and

*MR*is universal gas constant.

_{i}), temperature

*T*can be marked according to the formula (17):

*p*(φ

_{i}) specifies pressure course following

*pV*-diagram, measured at the test stand in a laboratory. The remaining factors depend on constructional parameters of the engine, e.g. the swept volume

*V*(φ

_{i}) which is changed according to formula (18) and in which the compression ratio is of high importance as well as the clearance volume: where

*V*

_{k}is the clearance volume, ∊ is compression ratio,

*L*is length of connecting rod and

*R*is the crank radius.

_{v}is the charging ratio,

*V*

_{s}is swept volume,

*p*

_{ot}is ambient pressure,

*L*

_{t}is theoretical quantity of mole of air,

*B*

_{o}is dose of fuel in time unit,

*MR*is universal gas constant and

*T*

_{ot}is the ambient temperature.

The similar dependence (relations to cylinder diameter and stroke) can be observed for coefficients of heat convection and emissivity [13, 14, 17].

Therefore, it is obvious that the downsizing technology affects thermodynamic factors of the engine working cycles and its operational parameters.

## Downsizing technology

In general meaning, downsizing technology should be understood as a process of reduction of any size in machinery to get expected result, e.g. mass reduction or better performance, etc. When referring to the combustion engine downsizing stands for reducing swept volume with mainly the same or higher torque and power of the engine for reduction of CO_{2} emission and fuel consumption as well as to save manufacturing costs per power unit. I recognise three typical downsizing forms: changing cylinder diameter only, changing piston stroke only and changing both of them. The project presented here is aimed at examining the influence of changes of the downsizing factor (DSF), understood as relation of cylinder diameter to piston stroke on basic operating parameters of the engine. To fulfil the goal of the project, the matrix of changes of the DSF was created (Table 1). Many simulations were carried out whilst estimating the changes of, e.g. maximum temperature of air–fuel mixture, convective heat transfer coefficient, mean effective pressure, specific fuel consumption, emission of carbon dioxide.

The matrix of changes of DSF

Relative change of piston stroke S | Relative change of cylinder diameter D | ||||
---|---|---|---|---|---|

1.00 | 0.95 | 0.90 | 0.85 | 0.80 | |

1.00 | Basis | X | X | X | X |

0.95 | X | X | X | X | X |

0.90 | X | X | X | X | X |

0.85 | X | X | X | X | X |

0.80 | X | X | X | X | X |

Research was referred to the real engine Fiat 1.1 dm^{3} with following parameters: *V*_{s} = 1108 cm^{3}; *D* = 70 mm; *S* = 72 mm; *P*_{e} = 40 kW/5500 rpm; *M*_{o} = 88 Nm/3500 rpm; ∊ = 9.6; pressure at the beginning of compression 1.15 MPa.

That engine, assembled in car Fiat Seicento Sporting, was theoretically examined in the downsizing technology according to data matrix described in Table 1.

In the numerical research, many indexes were simulated depending on the DSF as follows: pressure of turbocharging, reduction of compression ratio, changes of cooling system by heat transfer from hot chamber walls to the fresh air–fuel mixture at the beginning of working cycle, etc.

## Results

The research results of the downsizing simulation are presented in the relative scale which is the consequence of applying the same thermodynamic theory of combustion engine, the analysis of thermal loads, measuring techniques, etc (Fig. 1).

In Fig. 2, the line and the areas illustrate the changes of DSF in the range of 0% (lack of downsizing) in the left bottom corner of graph up to 50% (the strong downsizing) placed in the right upper corner. Together with the change of DSF, the increase of charging was analysed up to 44% which gave the same level of increasing pressure at the end of intake stroke and nearly 10% rise of pressure at the end of the compression. The compression ratio was reduced by about 18% and mechanical efficiency was improved by 4%. The fresh air–fuel mixture was about 40% less heated from the hot chamber walls. These downsizing interventions caused the growth of many parameters as follows: 4.4% for filling ratio, 18% for maximum pressure of the cycle with simultaneously the same temperature of the circulation (maximum value falls down about 1% only). The average effective pressure increased significantly—about 50%. The power of engine grew up by about 50%, too. Effective efficiency was improved by about 1.5% whilst the reduction of fuel consumption was observed at the same level.

The multi-case analysis was organised to report the possible optimisation of the downsizing technology. Only some results (as three-dimensional graphs) of study are introduced in this article.

There are the changes of power in function of changes of *D** and *S** (Fig. 3), the changes of specific fuel consumption versus *D** and *S** (Fig. 4), the changes of mean effective pressure (Fig. 5).

The graphs of thermal load factors versus DSF were also built as follows: the changes of convective heat transfer coefficient in relation to DSF (Fig. 6), the changes of heat flux through piston crown (Fig. 7) as well as the changes of emission of carbon dioxide in exhaust gases (Fig. 8).

In general revision of analysed thermal load parameters and engine operating indexes, the range of changes of diameter and stroke should be from 0.8 to 0.85.

## Summary

In the global discussion of the reduction of CO_{2} emission as well as fuel consumption by combustion engines, concept of downsizing takes very important place.

The idea of engine modification with sustaining the engine operation performance or increasing power and torque in the same time is well known since the beginning of 1990s. There were technological solutions which are still developed to eliminate many technical limitations connected with downsizing.

The minimisation of size of engine with increasing break mean effective pressure has to be analysed from the thermal load's point of view. So, there were researches carried out by the staff of the Wroclaw University of Technology in Poland. Some labs tests and multivariable simulations were organised to looking for downsizing optimum. All results were transformed to percentage scale to be relative for considered factors and parameters.

This project shows that in downsizing design, it is necessary to watch the thermal effects.

Based on the presented material, it is worth to consider downsizing from the range of 80–90% of bore and piston stroke changes, giving DSF equals 8:9. For these parameters effective power is essential higher than entry value up to 50%. The same result was estimated for heat flux through piston crown. The physical and chemical processes in the downsized engine were simulated for supercharging with 44% of increasing of pressure at the end of intake stroke, almost 10% rise of pressure at the end of compression, reduction of compression ratio of 18% to protect engine against knocking, etc. So, the thermal load of engine was recognised as well as operating engine indexes as dependent variables. For example the maximum temperature of charge during whole cycle was minimised of 1.5% and it gave reduction of total convective heat transfer coefficient α_{k} of 6–8%. The results of supercharging and cooling were improving charging ratio of almost 5% and increasing pick of pressure of 18% as well as brake man effective pressure of 53%.

The main goal of downsizing to reduce CO_{2} emission was results of all tests but it show only 10% benefit.

So, the next research work will be focused on changes of super- and turbocharging as well as lean mixture combustion for better optimisation of downsizing.

## List of symbols

##### Variables

A | Surface area of the barrier for heat transfer |

A_{m} | Average surface area of cross section of barrier |

A_{k} | Area of the combustion chamber |

b | Current coefficient of change of moles number for air–fuel mixture |

B_{o} | Dose of fuel in time unit |

c_{p} | Specific heat for constant pressure |

D | Cylinder diameter |

D* | Change of diameter |

dx, dy, dz | Changes of unit dimensions of studied parts |

dT | Temperature changes in the time interval dτ |

k_{z} | Supplementary coefficient of the heat transfer |

l | Length of the cylinder liner |

l_{p} | Average distance of flame in combustion chamber |

L | Length of connecting rod |

L_{t} | Theoretical quantity of mole of air |

M_{o} | Engine torque |

MR | Universal gas constant |

n_{1} | Total number of moles of air–fuel mixture at the beginning of compression cycle |

p | Pressure of gas |

p_{ot} | Ambient pressure |

P_{e} | Engine power |

p(φ_{i}) | Temporary pressure inside combustion chamber |

Q | Heat transfer |

Q_{HV} | Fuel heating value |

R | Crank radius |

r_{z} | External radius of the cylinder liner |

r_{w} | Inner radius of the cylinder liner |

s | Thickness of layer of medium |

s_{i} | Thickness of layer, called ‘ |

S | Piston stroke |

S* | Change of piston stoke, |

T | Temperature of air–fuel mixture |

T_{1}, T_{2} | Temperature on surfaces of studied barrier |

T(φ_{i}) | Temporary value of temperature inside combustion chamber |

V | Volume of burning space |

V_{k} | Clearance volume |

V_{s} | Swept volume |

T_{ot} | Ambient temperature |

##### Greeks

α_{k} | Convective heat transfer coefficient |

α_{1}, α_{2} | Convective heat transfer coefficients for zones of 1 and 2 in relation to the barrier |

γ | Molar coefficient of the rest of exhaust gases |

δ | Coefficient of changes of mole number of fresh charge |

∊ | Compression ratio |

∊_{f}(φ_{i}) | Relative emissivity of the flame |

η_{v} | Charging ratio |

λ_{i} | Thermal conductivity of layer named ‘ |

λ_{m} | Thermal conductivity of medium |

ξ | Coefficient of heat utilisation in combustion chamber |

ρ | Density of material |

τ | Time |

φ_{i} | Value of crankshaft angle of turn of crankshaft in the working cycle of engine |

w | Average speed of air–fuel mixture in combustion chamber |

##### Abbreviations

DSF | Downsizing factor DSF = |

rpm | Revolution per minute |

CHAISE | Controlled homogeneous auto-ignition supercharged engine |

VVT | Variable valve timing |

EGR | Exhaust gas recirculation |

VS or VST | Variable super- and turbocharging |

VCR | Variable compression ratio |

GDI | Gasoline direct injection |

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