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Investigations and analysis of working processes of two-stroke engines with the focus on wall heat flux.


Small displacement two-stroke engines are widely used as affordable and low-maintenance propulsion systems for motorcycles, scooters, hand-held power tools and others. In recent years, considerable progress regarding emission reduction has been reached. Nevertheless, a further improvement of two-stroke engines is necessary to cover protection of health and environment. In addition, the shortage of fossil fuel resources and the anthropogenic climate change call for a sensual use of natural resources and therefore, the fuel consumption and engine efficiency needs to be improved.

With the application of suitable analyses methods it is possible to find improving potential of the working processes of these engines. The thermodynamic loss analysis is a frequently applied method to examine the working process and is universally adaptable. Within this paper, a series production small displacement two-stroke engine is experimentally investigated on the test bench and adapted with measuring equipment in order to analyze the working process with focus on the wall heat flux. Due to high speed and vibrations, these investigations are complex. This publication considers an assessment of correlation predictability of heat transfer models, which are used in the thermodynamic loss analysis, by means of a comparison with experimental data. Thereto the measurement technique based on the surface temperature method applied to a small two-stroke engine is explained. From these investigations, the thermodynamic loss analysis regarding wall heat loss is reassessed and improvement potential is pointed out. Finally, an alignment of the thermodynamic loss analysis for small displacement two-stroke engines regarding the wall heat losses is performed. The results of the thermodynamic loss analysis demonstrate the occurring efficiency losses and therewith improvement strategies concerning the working process can be deduced.

CITATION: Piecha, P., Bruckner, P., Schmidt, S., Kirchberger, R. et al., "Investigations and Analysis of Working Processes of Two-Stroke Engines with the Focus on Wall Heat Flux," SAE Int. J. Engines 9(4):2016, doi:10.4271/2016-32-0028.


Due to the fact, that small displacement two-stroke engines are used in many applications as propulsion, it is essential to enhance the efficiency of these power units. The share of these small engine applications on total emissions and fuel consumption is not negligible. Therefore, the demand to apply a meaningful and accurate analysis to these propulsion systems is necessary to detect optimization potential.

Internal combustion engines (ICE) and their working process comprise complex thermodynamic and chemical sequences. The occurring combustion during the high-pressure phase, when all transfer ports are closed, is crucial for the conversion from chemical energy stored in fuel to effective work. The combustion process needs to be analyzed in detail, because, for instance, a fast combustion in combination with an increasing pressure and temperature gradient influences pollutant formation and wall heat losses rise. To get a deeper insight in this complex processes, chemical models, phenomenological approaches and combustion analysis can be included to the assessment [1]. For the analysis, different tools and system boundaries are applied depending on the topic [2]. For the assessment of the combustion processes, the thermodynamic loss analysis and the energy balance method are substantial tools. The use of the thermodynamic loss analysis as an analysis method is common and cost effective. The increased insight into this method leads to a continuous further development. As an example, in previously published literature the scavenging loss of two-stroke engines was introduced as a distinct loss [3] in the thermodynamic loss analysis. The accuracy of both thermodynamic loss analysis and energy balance analysis depends on the accuracy of the quantification of each particular efficiency loss. A verification of this analysis method and the comparison to measurements is mandatory to get a further improvement in accuracy and therefore an optimal opportunity to assess working processes regarding optimization potentials.

This paper focuses the subordinated wall heat loss in the thermodynamic loss analysis, because the wall heat loss plays, amongst others, a relevant role since it represents about 5-7 % of the efficiency losses. These investigations focus the assessment of high speed two-stroke engines with small displacements. Therefore, a two-stroke engine, which typically finds application in hand-held power tools, has been adapted, in order to determine the heat flux from the working gas to the combustion chamber walls. Vibrations and high speed make investigations more complex in comparison to other engine types (compare with [4, 5, 6]). For that reason, a comparison of correlation predictability with experimental data of such small displacement high speed engines hasn't been assessed in detail yet. To achieve this, different positions in the combustion chamber have been investigated regarding wall heat. For this analysis, sensors based on the surface temperature method had been used as measurement technique. On this basis, the measured heat transfer can be compared to the results of simulations carried out with the program CORA, developed by the Institute of Internal Combustion Engines and Thermodynamic (Graz University of Technology). Wherein, wall heat loss is calculated by use of empirical correlations, which can introduce errors in the estimation. The applied heat transfer types have been analyzed followed by a revision of the compliance with the measurement results and an assessment of the improvement potential.

First, the basics of thermodynamic loss analysis are explained and the occurring losses are illustrated. Subsequently, the energy balancing is performed and the wall heat loss is focused in detail. Therefore, different empirical correlations of heat transfer types are analyzed and compared to measurements to assess their predictability. In more detail, the measurement technology adapted to a high speed small displacement two-stroke engine and the basic principles of the heat flux measurement, including the surface temperature method, are explained. Finally, a comprehensive assessment of the accuracy of the applied heat transfer models is performed. The results are included in an adapted thermodynamic loss analysis with a revalued wall heat loss. In addition, a reassessed energy balance analysis of the two-stroke hand-held engine is conducted.


In this section, the theoretical basics regarding thermodynamic loss analysis and energy balance analysis are explained and the needed data is taken into account.

As described by Pischinger et al. [1] the corresponding losses within the thermodynamic loss analysis are differences in work, which get related to the energy added to the system in form of fuel. Thus, a detailed quantification of the particular efficiency loss is possible. A distinction is made between losses from imperfect combustion, real combustion, wall heat, gas exchange, scavenging losses and friction. Based on the distribution of losses, optimization measures concerning the design and combustion processes can be derived. Starting from the efficiency of an ideal engine with real charge, the effective efficiency is calculated through a subtraction of all losses. In [1] a detailed description of the basic methodology can be found and the physical relations of each loss are presented. Further considerations with similar approaches for the loss mechanisms had been developed and investigated by Weberbauer et al. [7] and Schiirg et al. [8].

For the analysis of the engine processes of an ICE a precise knowledge of many engine values, such as the charge mass along with the mixture and the conversion of energy, is essential. If scavenging losses [] occur (see figure 1). the fresh charge mass [m.sub.FR] at the beginning of the high-pressure phase is less in comparison to the delivered fresh charge mass [m.sub.FRdel]. These scavenging losses exist particularly for two-stroke engines with loop scavenging and are a substantial energetic loss, which is caused through the trapping efficiency of the fuel ([TE.sub.Fuel]). This fuel scavenging loss leads to higher emissions and a reduced efficiency.

The loss analysis methodology applied in this paper differs from previous approaches. Figure 2 shows a visualization of the thermodynamic loss analysis methodology. All calculations are based on the real masses and the real delivered fuel caloric value. In earlier approaches of Schmidt et al. and Winkler [12,13] the caloric value of fuel was decreased according the energy of fuel scavenging losses. That way, all losses, except the loss through scavenging losses, were referenced to the trapped fuel energy. The studies from Schmidt et al. [12] assigned the scavenging losses to imperfect combustion; Winkler [13] already distinguished the scavenging losses as a separate loss arranged below imperfect combustion (compare to figure 2). The applied methodology places the scavenging losses as a separate loss between losses due to real gas exchange and mechanical losses.

CORA, a 0D program, is used to calculate distinctive losses. Starting from the ideal engine process with real charge down to the loss from gas exchange, the trapped fuel energy is applied for calculations. The losses below the share of gas exchange, scavenging and friction losses, are calculated with the delivered fuel energy. The same air fuel ratio is used for all calculations steps.

In accordance with [1] and [7], constant-volume combustion is chosen as the ideal process for loss analysis of the ideal engine process with real charge. At the start of the high-pressure phase, the real engine is equivalent to the ideal engine with real charge, so that the same charge mass, temperature, pressure and gas composition, which leads to the same air-fuel and residual gas ratio, is available. The efficiency of the ideal engine provides for changes in efficiency through real charge and incomplete combustion due to lack of oxygen up to chemical equilibrium. A dissociation of the working gas during combustion is also considered for this.

In real processes, the chemical equilibrium is not reached and unburnt emissions additionally arise during combustion. This energy loss, due to unburnt fuel components, is counted as the efficiency loss through imperfect combustion. Moreover, it is an efficiency difference between incomplete combustion up to the chemical equilibrium and imperfect combustion. A further energy loss occurs due to of real combustion and depends on the duration of combustion (DOC), the shape of the heat release and the center of combustion (CoC). This loss is determined by calculating the real gross heat release by means of the measured cylinder pressure curve. Hence, the difference of efficiency of the adiabatic high-pressure process with constant volume combustion and real combustion is calculated [10]. Another loss mechanism - the wall heat loss - appears as a result of heat transfer from the gas to the combustion chamber walls. This wall heat loss and the loss through real combustion interact with each other. According to [1] an optimum regarding CoC depends on the wall heat loss and real combustion. With a CoC near the top dead center (TDC) losses due to real combustion are low, but in contrast wall heat losses increase because of higher temperatures in the combustion chamber. In this presented methodology, the wall heat loss is analyzed in detail. In this context, wall heat loss is calculated by use of semi empirical formulas, whereas different wall heat transfer models, Woschni [15], Woschni-Huber [16] and Hohenberg [17], are investigated. By comparing the applied transfer models to measurements, the best approach for small displacement two-stroke engines can be found and the accuracy of the methodology will be improved.

Continuing the thermodynamic loss analysis, the loss due to gas exchange contains losses caused by losses concerning expansion, compression, and low pressure. It is calculated by the difference of total indicated work and indicated high-pressure work. Starting from the ideal engine (step 1 in figure 2) down to the loss of gas exchange (step 5) the efficiency differences are based on the trapped fuel energy. The scavenging loss difference (step 6) is calculated with the trapped fuel mass and delivered fuel mass, so that the indicated efficiencies ([[eta].sub.i], [[eta].sub.iwoSL]) are related to different fuel energy amounts. Two-stroke engines especially suffer from scavenging losses in comparison to four-stroke engines. The friction loss is referenced to the delivered fuel mass und represents mechanical losses. Subtracting all efficiency differences from the efficiency of the ideal engine, the result is effective efficiency. This effective efficiency is the effective work of the engine divided by the delivered fuel energy.

Analytic Process with Thermodynamic Loss Analysis

The thermodynamic loss analysis is performed with experimental data. Amongst others, the cylinder pressure curve, the raw gas emissions, the delivered fuel mass and fresh air mass are mandatory. Besides, the amount of the residual gas in the cylinder is also necessary. As the measurement of the residual gas ratio is costly and laborious, it has not been performed in detail yet and is herein determined with a verified gas exchange simulation. After measurement and simulation, input data can be prepared for further analyses including a pressure curve analysis. For verification reasons, the quality of the input data is controlled by the energy balance method. Therefore, the cumulative gross heat release, derived from the measured pressure curve, is compared with the trapped fuel energy minus the energy from imperfect combustion. Subsequently, the thermodynamic loss analysis can be performed using the calculated gross heat release.


To evaluate the results of the thermodynamic loss analysis regarding wall heat losses, the heat flux for the applied small-displacement two-stroke engines needs to be investigated in more detail. For this, a suitable measurement technique must be selected and adapted to these high-speed engines. The demands for sensors are stringent, as the required response time is very short and the needed accuracy is high. Furthermore, the sensor itself must have the smallest possible size, so that the influences on the heat flux field and temperature level are negligible. The sensors must withstand the occurring temperatures and vibrations to have a sufficient durability [14]. In principle, there are two different measurement methods, which can be applied to ICEs to measure the heat flux in high resolution [18]. The first measurement technique is based on sensors measuring the surface temperature [2]. A second method is available, which measures the temperature drop through sensors with a thin thermal resistance layer inside. Due to packaging restrictions, when using small displacement two-stroke engines, this method is not applicable. In addition, these sensors have high production costs and a limited durability [14]. Therefore, sensors based on the surface method are preferred for the application in two-stroke engines.

For the determination of the heat flux in ICEs surface thermocouple sensors with a coaxial design, as shown in figure 3, are often used. With this design, the probe, when installed in the wall, is flush with the wall surface. The two thermocouple materials are electrically insulated by ceramic oxide powder (MgO), which makes up a layer of 12.7 [micro]m. The contact between the thermocouples is established by an evaporated thin metal layer (thickness of 1-2 [micro]m). These sensors are available with various thermocouples materials (Typ T, J; E, K and S) and variable junction plating materials (Cr, Ni, Pt, and Cu) at the hot junction [14].

Applying this surface sensors to small displacement two-stroke engines, sensors with a thermocouple material of Type K (temperature range: - 270 to + 1372 [degrees]C) and a diameter of 0.79 mm have been chosen. The sensors are adapted flush to the combustion chamber wall by small bores through the cylinder head. On this basis, temperature gradients can be measured during one cycle.

Basic Principles of the Surface Temperature Method

In the following, the basic principles of the transient wall heat flux from the gas-side to the combustion chamber wall, determined with measured temperature gradients, are described.

The surface temperature method is based on the commonly known Fourier differential equation for heat conduction and can be used to characterize the temperature field inside the wall of the combustion chamber. Therefore, it is assumed, that no heat source exists in the considered object and a one-dimensional heat flow in the combustion chamber wall is present. Temperature gradients occur only perpendicularly to the combustion chamber surface in x-direction. With these assumptions, the commonly Fourier differential equation is reduced to the following form:


In equation (1). [T.sub.w] is the wall temperature and t the time. Further, a is the thermal diffusivity of the wall material and is determined by a quotient of the thermal conductivity [lambda] and the product of the material density [rho] and the specific heat capacity [c.sub.[rho]] [14].


The transient heat flow through the combustion chamber wall can be calculated with the temperature gradient and the thermal conductivity:


For the periodic work process of the ICE and with the assumption of an infinitely extended wall, the differential equations above can be solved with a mathematic sequence. From this, the unsteady temperature field and the unsteady heat flux density field can be derived. The results are presented in equation (4) and (5).



Within these equations, x is the wall depth and [omega] the angular velocity related to the work cycle. [A.sub.i] and [B.sub.i] are Fourier coefficients and C is the constant for the averaged heat flux density. The order is denoted by the index i. In this case, it is legitimate to assume an infinitely extending wall, because the temperature and the heat flow decrease exponentially with the wall depth x [14].

Substituting x with the value 0 in equation (4) and (5) gives the temperature curve and heat flux on the wall of the combustion chamber side. Furthermore, the constants [A.sub.i] and [B.sub.i] are calculated through a Fourier analysis, wherein measured temperature curves also serve as boundary conditions. In this case, C is identified by the average gas temperature, which has been calculated through the pressure curve analysis within the thermodynamic loss analysis. For this, a two zone combustion model is considered. It should be noted that local gas temperatures are not taken into account. However, the model approach, which uses the average gas temperature, has shown sufficient results [14]. Therefore, the assumption can be made, that the heat flow equals zero, when the gas and wall temperature are the same. Beside this method, determining constant C with the calculated gas temperature, there are other measuring techniques. For example, with a heat flow sensor in a defined distance, where the constant part of the heat flow is measured through the combustion chamber wall, so that C can be derived.

Application to Small Two-Stroke ICE

The heat flux measurement has been applied to a small displacement two-stroke engine taking the theoretical background into account. High speed and vibrations increase the complexity of the measurements compared to other engines types. Therefore, a high resolution measurement chain is used and the mounted sensors have to withstand the vibrations. A one cylinder air-cooled engine of a brush cutter from STIHL has been chosen for this analysis. This engine uses an electronic carburetor for mixture formation. A stratified scavenging system with Schnurle-type loop-scavenging is applied, due to higher trapping efficiencies [19]. The technical data is shown in table 1.

For the application of the surface temperature method, it is important to reference the results of the measured temperature curves to the measuring area. At the same time, it is necessary to install many sensors for comparability reasons. Therewith, the regional mean wall heat flow, which is calculated through different local curves, can be compared to the results of the simulation (motor process analysis). Therefore, different measurement positions have been investigated.

The cylinder head surface of the combustion chamber can be divided in two main parts; the combustion chamber sphere and the sphere of the squish gap (see figure 4, figure 5 and figure 6). In the combustion chamber head seven sensors are located in total, three in the combustion chamber sphere and four in the squish gap sphere. The number of sensors reflects a compromise in order to ensure sufficient information and minimal influence to the heat flux. Other examples in literature use less than seven sensors [4, 5, 14, 20], therefore, the number of sensors deemed to be sufficient. Two of the squish gap sensors (squish gap inlet 1 and squish gap outlet 1) are positioned in the inner ring of the squish gap sphere. The squish gap inlet 2 and squish gap outlet 2 sensors lie in the outer ring of the squish gap sphere. Local influential factors can be examined with this arrangement and the temperature gradients from inside to outside can be estimated. Furthermore, an evaluation of the flame propagation is possible. In this way, local heat flows and a mean heat flow of the cylinder head can be determined.

Figure 5 shows an example of a thermocouple sensor adapted through the cylinder head; here the sensor is mounted opposite the spark plug. If several sensors are applied, a determination of mean heat flow requires a division of the combustion chamber in different segments related to the respective sensor. This way, a weighted average of wall heat flows, as presented in formula (6), can be calculated [1].


For the investigated two-stroke engine, the sphere of the combustion chamber at the cylinder head (yellow area figure 6) is subdivided in three equal parts (blue striped area [A.sub.ccs]). The squish gap sphere is subdivided in four equal parts (red striped area [A.sub.SGS] figure 6) Each subdivided surface is related to one sensor position and is used for the weighted calculation of the mean wall heat flow.

Measurement Results

Based on the preceding considerations, the measurements have been performed on the test bench for all outlined positions. Care has been taken, that the sensors are flush to the combustion chamber wall and sooting or carbon deposits are obviated. Two relevant operating points for this two-stroke engine have been chosen. On the one hand the operating point with maximum torque at 6000 RPM and on the other hand the operating point with maximum power at 9500 RPM. Both operating points have been operated with a lambda of [lambda] = 0.85, which is common for those type of engines. The results are compiled in figure 7 and figure 8.

In figure 7, the temperature curves of each sensor position are plotted versus the crank angle of one cycle. 0 [degrees] crank angle is referred to TDC. The temperature curves have been first filtered and subsequently averaged over a certain number of cycles. It can be seen, that the curves of the squish gap inlet sensor positions (squish gap inlet 1 and squish gap inlet 2) reach a level of about 280 [degrees]C and they do not differ much from each other. The temperature rise of the inlet sensor in the combustion chamber sphere is higher in comparison to the rise of the squish gap positions. As might be expected, the level of the temperature curve of the outlet position is the highest (compare to [20]), because thermal exhaust heats up the outlet side. In contrast, the inlet side is cooled by the incoming charge. The average temperature curve is diagramed in black and is further used for comparison with the results from the simulation of the thermodynamic loss analysis. At 6000 RPM, the stationary temperature, measured at the spark plug seat, reaches a relatively high temperature level referred to common two-stroke engines of about 246 [degrees]C.

For the operating point at 9500 RPM, the temperature curves are presented in figure 8. Here, the stationary temperature at the spark plug seat is 262 [degrees]C. In principle, similar trends, as seen at 6000 RPM, can be derived. The squish gap measurements need to be particularly noted, because they show a lower temperature rise than before. This behavior is associated with the shorter duration of the flame propagation with higher speed. The duration, when the flame reaches the sensors in the squish gap, is shortened. Despite lower rises of temperature curves, the absolute level of each temperature curve is higher. The outlet position reaches a maximum temperature of about 470 [degrees]C on the wall of the combustion chamber.

To be able to estimate further insights, the presentation of the temperature curves has been changed, in order to standardize the curves to the same level at - 30 [degrees] crank angle. The rise of each curve and a shift towards earlier or later crank angles can be easier compared in this visualization. By these means, the flame propagation and temperature gradients are more obvious. At first, the temperature differences are presented for the operating point at 6000 RPM (see figure 9).

The outlet curve has the highest increase and therefore a higher temperature drop from 30 [degrees] to - 30 [degrees] crank angle in comparison to the other curves. The minimum temperature point is reached at - 30 [degrees] crank angle. This high temperature drop is an indicator of high heat dissipation. The squish gap inlet curves have a slower temperature drop. This can be caused by secondary reactions and a later combustion end in the squish gap sphere. Additionally the wall heat transfer is lower, due to low turbulence and the existing thermal boundary layer. The various curves have different starting points for a drastic temperature increase. This sharp increase of temperature is caused by the flame propagation in the combustion chamber. A trend can be observed. The flame reaches the outlet side first, followed by the opposite spark plug position, further the inlet side and finally the squish gaps. A decisive difference between the squish gap positions cannot be deduced. Higher temperatures at the exhaust side, where the thermal energy gets out of the system, result in a hot outlet and thus enable the benefit of chemical reactions inside the combustion chamber at the outlet side. The minimum temperature point of the squish gap inlet 2 curve is at about - 100 [degrees] crank angle. Around this crank angle position, the intake port closes (IPC) and the charge gets compressed. Up to the outlet temperature curve, the minimum temperature point of each curve moves from - 100 [degrees] towards - 30 [degrees] crank angle. The minimum point for each curve is different due to different temperature levels at each position. The minimum point of the temperature difference curve is reached, when the gas temperature exceeds the wall temperature. At higher temperature levels, this point is shifted towards TDC.

The next diagram (figure 10) shows the temperature difference curves at 9500 RPM. Here, each temperature rise decreases by almost 1 [degrees]C, compared to 6000 RPM. Simultaneously, the curves show a minimal drift towards TDC, due to higher speed. Moreover, all temperature rises of the squish gap positions drop below the temperature curve of the inlet position. In total, the squish gap curves have different characteristics comparing the 6000 RPM and 9500 RPM operating point. This is an indicator for changing flow conditions in the squish gap area. The temperature curves on the squish gap outlet side behave similar and almost have the same starting point, when the positive temperature gradient, due to flame propagation, increases. The curves of the inlet squish gap positions change at 9500 RPM, so that the temperature increases up to ~ 4 [degrees]C.

Calculated Wall Heat Flux

Based on the measured temperature curves at different positions, the wall heat flux density of each position has been determined. In addition, the weighted averaged heat flux density has been calculated (black line) according to formula (6). The heat flux densities have been analyzed at 6000 RPM as well as at 9500 RPM.

The results for the operating point at maximum torque are displayed in figure 11. Considering all curves, a heat flux from the cylinder head wall towards the gas inside the combustion chamber only occurs in the crank angle range outside - 50 [degrees] and 90 [degrees]. During the rest of the crank angle range, the cylinder head is exclusively heated up by compression and combustion. The maximum heat flux varies between ~100 and ~ 440 W/[cm.sup.2]. At the outlet heat flux curve, a post heating phase is evident. The wavy curves in the phase after 30 [degrees] crank angle result from data handling and filtering. The peaks of the heat flux densities at each position are located closely with regard to the crank angle. The average heat flux density is similar to the inlet curve and increases up to a heat flux of~ 250 W/[cm.sup.2].

Differences appear when looking at the heat flux density diagram of the operating point at 9500 RPM (figure 12). An increase of heat flux density of the inlet side already occurs at - 80 [degrees] crank angle. The maximum values of the heat flux density rise, i.e. similar quantity of heat gets dissipated through a shorter duration of time due to higher speed. Coincidently, the averaged heat flux density at 9500 RPM reaches a higher peak of almost 320 W/[cm.sup.2], due to higher turbulence and a smaller thermal boundary layer at the combustion chamber wall. Except the squish gap inlet 1 curve, the maximum heat flux densities appear at a crank angle range between 15 [degrees] and 20 [degrees]. All squish gap curves, except for the squish gap outlet 1 curve, are below the measurement points inside the sphere of the combustion chamber. In addition, the outlet squish gap curves show a higher heat flux density in comparison to the inlet squish gap side. Comparing the inlet side and the outlet side separately, the squish gap positions, placed closer to the combustion chamber sphere (inlet 2 and outlet 2), point out a higher wall heat flux than the positions near the cylinder running surface (inlet 1 and outlet 1).

Altogether, the heat flux density at different positions of the combustion chamber wall has been determined for two operating points. Furthermore, averaged heat flux densities through the cylinder head have been calculated, enabling a comparison with the thermodynamic loss analysis.


In the following, the results of the thermodynamic loss analysis based on a small displacement two-stroke engine with stratified scavenging from STIHL are described. Hence, an estimation regarding a suitable approach for a wall heat transfer model of small displacement two-stroke engines can be derived. The optimization potential of the analysis method regarding accuracy and the two-stroke engine itself are demonstrated. An overview of the energy balance and the thermodynamic loss analysis of the brush cutter engine, with each loss from imperfect combustion down to effective efficiency, is given.

The averaged heat flux densities for both operating points, which result from the measurements, can be used for a first comparison. The averaged measured heat flux densities for one cycle have been taken to calculate the heat quantities from the gas side to the cylinder head. These heat quantities can be used to compare with the results of the thermodynamic loss analysis. The thermodynamic loss analysis calculates the heat transfer between the internal surfaces and the working fluid, which is mainly caused by forced convection, by means of Newton's law. It states that heat flux is proportional to the difference of gas temperature [T.sub.G]( [phi]) and wall temperature [T.sub.w]([phi]). The gas-wall temperature difference is multiplied by the heat transfer coefficient [[alpha].sub.G,w]([phi]).

[q.sub.G,w]([phi]) = [[alpha].sub.G,w]([phi])[[T.sub.G]([phi]) - [T.sub.w]([phi])] (7)

Within this heat flux equation (7), the heat transfer coefficient has been calculated by use of unadapted model approaches from Woschni [15], Woschni-Huber [16], and Hohenberg [17]. These models are based on empirical correlations and theoretical considerations of similarity and use temperature dependent polynomial approaches. Moreover, values like average piston speed or piston displacement are used. A detailed specification of the heat transfer models is cited in the appendix (see equation (8), (9), (10), (11), (12)). The results of the heat flux analysis are compared within the crank angle range of the high pressure phase, the range in which the thermodynamic loss analysis is carried out. Heat flows outside this crank angle range have not been considered in this heat quantity analysis. The results for both operating points are summarized in figure 13 and figure 14.

It is obvious that results, calculated with different wall heat transfer models, do not fit to the measured wall heat quantity. This finding is independent of the operating point. For the 6000 RPM operating point, the heat quantity curve of the heat transfer model from Woschni-Huber points out the best result. Woschni and Hohenberg show heat quantities considerably below the measured curve. At the speed of 9500 RPM all heat quantities are also below the measured curve, but, compared to 6000 RPM, Hohenberg and Woschni show similar results. It becomes clear that adjustments are necessary.

In addition to this heat quantity investigation, the results of the energy balance analysis confirm these discrepancies (shown in table 2). The energy balance evaluates the high-pressure process by comparing the gross heat release based on the measured pressure curve with the trapped fuel energy diminished by energy lost due to imperfect combustion [3]. By applying an energy balance, an assessment of the quality of the used data is possible. If the data is either not sufficiently precise or falsified or the selected model approach is inadequate, the energy balance analysis provides implausible results. The results of the energy balance do not reach a sufficient outcome in the herein used unadapted model approaches for the wall heat transfer. Due to this consideration and compared with the measurements, it is justifiable to apply adjustments to the heat transfer models. The amount of energy dissipating through the wall is higher than the results of the thermodynamic loss analysis. These differences can be explained by the development process of the wall heat transfer models. Initially, the models have been developed for diesel engines. Thereupon, they have been adapted to gasoline engines. A further and detailed development and adjustment to small displacement two-stroke engines with high speeds and air cooling has not been implemented yet. Therefore, the current results regarding the wall heat flux are unsuitable.

An option for adaption exists by scaling the calculated wall heat transfers of the different wall heat transfer models with a factor. In the program CORA, used for thermodynamic loss analysis, a so called wall heat transfer factor exists, which multiplies the calculated wall heat quantity by a factor. To get a minimum difference between the measured wall heat quantity and the wall heat calculated according to each model, a factor (see table 3) for Woschni, Woschni-Huber and Hohenberg has been determined. With this adjustment the heat transfer models give an adapted heat quantity. Moreover, the results of the energy balance analysis for both operating points show good results with the optimized wall heat transfer models.

In table 3 the different wall heat transfer factors are listed. The factors differ for each wall heat model and operating point and lie in a range of 1.2-1.75.

The smallest adjustment occurs for the Woschni-Huber model. At higher speeds, all factors are lower, due to changing flow conditions, which are not properly taken into account by the wall heat transfer models. The considered models are not laid out for this kind of engines. With the adapted factors the known trend gets confirmed, so that with higher speeds wall heat transfer coefficients rise due to positively changing flow conditions (see table 3). The influence of the wall heat transfer factor can be estimated by comparing the wall heat transfer coefficient without and with adjustment. The temporal development of the heat quantity cannot be taken as an indicator of a suitable wall heat transfer model, as all adjusted wall heat quantity curves do not differ much from each other. Due to the fact, that the Woschni-Huber model requires the smallest adjustments, this adjusted model is used for the thermodynamic loss analysis.

On this basis, the adapted thermodynamic loss analysis with the determined wall heat factors and the energy balance analysis are conducted and the results are presented in figure 15. The same air-fuel ratio of [gamma] = 0.85 has been adjusted for these investigations. Figure 15 shows the outcomes of the energy balance analysis for the brush cutter engine at the operating points 6000 RPM and 9500 RPM.

Decisive differences occur at different speeds in scavenging loss and thermal exhaust energy. The share of energy regarding scavenging corresponds with the trapping efficiency and therefore the operating point at 9500 RPM has a smaller energy loss due to scavenging. These two-stroke engines are designed to have the highest trapping efficiency at the point of maximum power. The thermal exhaust gas enthalpy increases proportionally at higher speeds, because of higher gas temperatures of the exhaust gas. Furthermore, the effective efficiency rises from 19 % to 21 % comparing the point of maximum torque and maximum power.

Beside the energy balance analysis, a thermodynamic loss analysis has been performed (see figure 16). Starting from the effective efficiency, the share of energy loss by friction is 3.1 % at 6000 RPM and 5.2 % at 9500 RPM. In accordance with the energy balance analysis, the loss due to scavenging decreases to the operating point of maximum power. The gas exchange losses are within the same range for both operating points. Comparatively, the share of wall heat loss makes up a large part for both points. Due to various flow conditions, the proportion of wall heat loss is higher at 6000 RPM. Losses due to real combustion and imperfect combustion lie in a similar range.

Concluding, the brush cutter engine is already highly developed and scavenging losses are very low. Nevertheless, a further improvement in effective efficiency would be worth looking at. Besides, the wall heat makes up a big proportion. Further development steps should also focus on this energy loss.

On the basis of this research, especially with attention to the different wall heat transfer factors at different speeds, it becomes obvious, that the existing heat transfer models are not suitable for this kind of engines. The wall heat transfer relations for these small engines with high speeds are not properly reproducible. The adjustment with different wall heat factors is only applicable, when intense measurements are undertaken. In this case, good results can be achieved with an adjustment through measurements.


In the course of this publication, the accuracy of the thermodynamic loss analysis regarding wall heat loss of two-stroke engines is assessed. Therefore, the correlation predictability of wall heat transfer models is opposed to experimental data. For this, the surface temperature method to measure the wall heat flux is adapted to a small two-stroke combustion engine and the boundary conditions are described. In contrast to other combustion engines, the high speed and vibrations make the adaption more complex.

A detailed analysis of different positions in the combustion chamber has been realized. On the basis of these measurements, an averaged wall heat flux through the combustion chamber head has been calculated. These results of the wall heat flux investigation have been compared with common wall heat transfer correlations (Woschni, Woschni-Huber and Hohenberg) used in the thermodynamic loss analysis. The accuracy of the applied wall heat transfer models has been assessed and revealed the necessity of adaptions. A possible adaption for the wall heat transfer model is introduced to guarantee sufficient accuracy for the thermodynamic loss analysis for high speed small displacement two-stroke engines.

Finally, the thermodynamic loss analysis with adapted wall heat transfer models has been exemplarily applied to a two-stroke engine with external mixture formation. Discrepancies in energy balance analysis for the adapted wall heat transfer models are pointed out. Two operating points - maximum torque and maximum power - have been investigated in order to deduce the results. The distribution of different loss mechanisms down to the effective efficiency indicates optimization potentials for this brush cutter engine. It becomes clear, that wall heat loss plays a relevant role and, therewith, necessitates the assessment of accuracy.

Summarized, the thermodynamic loss analysis has been optimized with regard to the wall heat loss, leading to the increased accuracy of the analysis - not only of the wall heat loss but also as a whole. This enables a more detailed analysis method for high speed two-stroke engines. The investigations reveal that a new correlation for a wall heat transfer model for small displacement and high speed two-stroke engines is a future-oriented approach.


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Institute of Internal Combustion Engines and Thermodynamics, University of Technology Graz

Pascal Piecha

Phone: +43 316 873 30258

Fax:+43 316 873 30202


This study was performed within the framework of the K-project ECO-Powerdrive-2, which is funded by the Austrian government, the Styrian, and the Upper Austrian government within the excellence initiative COMET. The working process calculation is done by the software CORA (Combustion Optimization Research and Analysis), which has been developed by the Institute for Internal Combustion Engines and Thermodynamics at University of Technology Graz.


[A.sub.ccs] - Area combustion chamber sphere

[A.sub.SGS] - Area squish gap sphere

CoC - Center of Combustion

CORA - Combustion Optimization Research and Analysis.

DOC - Duration of combustion

EPC - Exhaust port closing

EPO - Exhaust port opening

ICE - Internal combustion engine

IPC - Intake port closing

LCV - Lower calorific value


[m.sub.CYL] - Cylinder charge

[m.sub.EXH] - Exhaust charge







[] - Scavenging charge


RPM - Revolutions per minute

TDC - Top dead center

TE - Trapping efficiency

[TE.sub.Fuel] - Trapping efficiency fuel

[W.sub.IC] - Work of imperfect combustion

[W.sub.RC] - Work of real combustion

[W.sub.WH] - Work of wall heat

[W.sub.GE] - Work of gas exchange

[[DELTA][eta].sub.GE] - Gas exchange efficiency difference

[[DELTA][eta].sub.IC] - Imperfect combustion efficiency difference

[[DELTA][eta].sub.M] - Mechanical efficiency difference

[[DELTA][eta].sub.RC] - Real combustion efficiency difference

[[DELTA][eta].sub.SL] - Scavenging loss efficiency difference

[[DELTA][eta].sub.WH] - Wall heat efficiency difference

[[eta].sub.e] - Effective efficiency

[[eta].sub.i] - Indicated efficiency

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] - Indicated efficiency without scavenging loss










[C.sub.1] - Dimensionless constant for the high pressure phase

[C.sub.2] - Dimensionless constant depending on engine type

d - Bore diameter

IMEP - Indicated mean effective pressure

p - Cylinder pressure fired operation

[p.sub.0] - Cylinder pressure unfired operation

T - Current local averaged gas temperature

[T.sub.1] - Current local averaged gas temperature at start of compression

V - Crank angle based piston displacement

[V.sub.1] - Piston displacement at start of compression

[V.sub.c] - Compression volume

[V.sub.PD] - Piston displacement

v - Characteristic speed

[] - Piston speed

Pascal Piecha, Philipp Bruckner, Stephan Schmidt, and Roland Kirchberger Graz University of Technology

Florian Schumann, Stephan Meyer, and Tim Gegg Andreas Stihl AG & Co KG

Stefan Leiber BRP-Powertrain GmbH & Co KG

Table 1. Technical data of investigated engine

Application         Brush cutter

Cylinder             1
Displacement        45.6 [cm.sup.3]
Compression          9.5
Bore-/stroke ratio   0.68
Max. power           2.2 kW @ 9500 RPM
Mixture formation   Stratified, carburetor

Table 2. Energy balance analysis results with unadapted wall heat
transfer models

               Energy balance discrepancy

Hohenberg      -15.2%    -10.5%
Woschni        -13.5%    -10.0%
Woschni-Huber  -12.4%     -8.4 %

Table 3. Wall heat transfer factors and wall heat transfer coefficients

                Wall heat transfer factor

Hohenberg       1.75      1.51
Woschni         1.50      1.44
Woschni-Huber   1.36      1.20

                Wall heat transfer coefficient

Hohenberg       401       551
Woschni         417       540
Woschni-Huber   486       666

                Wall heat transfer coefficient
                adjusted [W/[m.sup.2]K]

Hohenberg       702       831
Woschni         627       780
Woschni-Huber   663       797
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Author:Piecha, Pascal; Bruckner, Philipp; Schmidt, Stephan; Kirchberger, Roland; Schumann, Florian; Meyer,
Publication:SAE International Journal of Engines
Article Type:Report
Date:Dec 1, 2016
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