The gas-dynamic unsteadiness effects on heat transfer in the intake and exhaust systems of piston internal combustion engines

International Journal of Heat and Mass Transfer 115 (2017) 1182–1191

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The gas-dynamic unsteadiness effects on heat transfer in the intake and exhaust systems of piston internal combustion engines L.V. Plotnikov a,⇑, B.P. Zhilkin b a b

Ural Federal University, Turbines and Engines Chair, Ekaterinburg, Russia Ural Federal University, Heat Power Engineering and Heat Engineering Chair, Ekaterinburg, Russia

a r t i c l e

i n f o

Article history: Received 14 May 2017 Received in revised form 24 July 2017 Accepted 30 August 2017 Available online 8 September 2017 Keywords: Gas-dynamic unsteadiness Local heat transfer Gas exchange processes Intake and exhaust pipelines Internal combustion engines

a b s t r a c t This article presents the results of experimental research into the gas-dynamic and heat-exchange parameters of gas flows in the intake and exhaust pipelines of piston ICEs (internal combustion engine) taking into account the nonstationary nature of the gas exchange processes. Some characteristic times of transient processes (recovery time and relaxation time) are established during the gas flow recovery in round pipelines. Based on the obtained data, the degree of non-stationarity or unsteadiness of the gasdynamic processes in piston ICE pipelines can be established. It is demonstrated that there are two types of resolution for gas-dynamic unsteadiness. It is established that unsteadiness reduces the instantaneous local heat transfer intensity in the pipelines of piston ICEs by 1.3–2.5 times. A method is proposed for taking the thermomechanical unsteadiness into account in thermal calculations by applying the heat transfer mobility correction coefficient for classical equations that are used to calculate the local heat transfer coefficient. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction There are many different power machines and plants in which the operating process occurs in pulsating modes (the gas flows in their elements in a context of gas-dynamic unsteadiness). They include piston internal combustion engines (ICE), compressors, bladed machines and many others. At the same time, the gasdynamic unsteadiness significantly influences the transport process mechanisms in their gas-air paths. It is known that the deeper the unsteadiness, the more significant the non-equilibrium and, consequently, its effect on the transport mechanism [1]. Hence, there are two inter-related tasks. First, it is necessary to have remarkably clear indicators (criteria) that allow us to unambiguously determine the degree of unsteadiness of gas flows in the power machine paths in order to evaluate their actual technical and economic performance, calculate the gas exchange processes and effectively control them. Secondly, it is necessary to have an idea of the physical mechanisms of the effect of the gas-dynamic unsteadiness on the processes in gas-air paths of power machines in order to improve their processes and effectively influence them. ⇑ Corresponding author at: Ural Federal University, Ural Institute for Power Engineering, Turbines and Engines Chair, Mira Street, 19, Ekaterinburg 620002, Russia. E-mail addresses: [email protected] (L.V. Plotnikov), [email protected] (B.P. Zhilkin). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2017.08.118 0017-9310/Ó 2017 Elsevier Ltd. All rights reserved.

To date, these problems have been poorly covered in the published literature. Therefore, it is quite relevant to obtain initial information on the levels of unsteadiness of processes in the pulsating gas flows, develop criteria that determines the degree of the gasdynamic unsteadiness, update the physical transport mechanisms in gas-air paths and develop a methodology for taking into account the effect of the gas-dynamic unsteadiness of flows in pipelines of different configurations on local heat transfer. To a significant extent, the efficiency of piston internal combustion engines depends on the perfection of the processes taking place in their gas-air paths (in the intake and exhaust pipelines). The gas exchange processes (the air intake and exhaust gas release) in piston engines are high-frequency and non-steady. The gas exchange periods in modern piston engines account for hundredths of a second. The gas flow parameters in the intake and exhaust pipelines change periodically with frequencies of up to 100 Hz and higher. The flow accelerations and decelerations reach values of up to 150,000 m/s2. At the same time, it is known that the gas flow heat exchange rate under non-stationary conditions can be reduced by 2–4 times as compared with the steady-state case. For example, Valueva, proceeding from numerical modelling of gas dynamics [2] and heat exchange [3] of pulsating gas flows in pipelines of different configurations, has established a significant decrease in the heat transfer rate compared to a steady flow that can reach 2.5 times. Simakov [4] and Holley and Faghri [5] have

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Nomenclature w j p d n Kmh l

flow velocity, m/s flow acceleration, m/s2 static pressure, MPa pipeline diameter, mm engine crankshaft speed, rpm heat transfer mobility factor linear dimension, mm (measured from the gas flow pipeline inlet)

Greek symbols a heat-transfer factor, W/(m2
K) s time, s Subscripts x local parameter

also shown in their experimental works a significant reduction in heat transfer under the non-stationary conditions with respect to different thermal engineering problems. Detailed research into the physical mechanism for reducing the heat transfer rate of pulsating flows in pipelines are devoted to a number of works by Kraev [6,7]. He explains the decrease in the heat transfer intensity by three separate effects: the effect on the convective heat exchange of transient heat conduction; the dynamic rearrangement of the gas flow structure in the boundary layer at a constant flow rate; and flow changes. At the same time, Kraev emphasises that the mechanism of the effect of acceleration and deceleration of the flow on turbulence has not yet been fully explained [7]. Moreover, some works provide other results that indicate that the gas-dynamic unsteadiness does not significantly affect the heat transfer rate in pipes or leads to its growth by 30–40% in comparison with the steady flow. For example, the numerical simulation by Wang and Zhang [8] established that the local heat transfer factor increases by an average of 30% with a pulsating gas flow. Similar data were obtained by Russian researchers Mikheev et al. [9] based on experimental research. Similar results can also be found in the well-known publications of Park et al. [10] and Chung et al. [11], in which it was shown that the gas-dynamic unsteadiness does not essentially affect the local heat transfer intensity. It should be noted that the data described above were obtained in a laboratory environment without reference to specific technical or technological machinery, or, more precisely, without reference to the type of unsteadiness typical of the processes in a particular machine. It should be noted that insufficient focus has been on the study of gas dynamics and heat transfer of gas flow in the intake and exhaust systems of internal combustion engines (ICE). This is because the improvement of heat transfer in the cylinder was initially more relevant and effective from the point of view of improving the technical and economic performance of piston engines. At the moment, engine manufacturing has reached such a level that an increase in any engine index by at least a few tenths of a percent is a serious achievement for professionals. Therefore, at present, researchers and engineers are looking for new possibilities of improving the ICE processes. One of such possibilities, according to the authors, is the study and improvement of processes in the intake and exhaust pipelines of engines in the gas-dynamic unsteadiness context. As noted above, the gas exchange processes in the engines are pulsating and unsteady, therefore it is not entirely correct to study the gas-dynamic and heat-exchange characteristics of the gas flow in gas-air paths only in the steady-state conditions and/or using quasi-stationary approaches by numerical

–

e bb res rel st unst 1 2

averaged parameter value equivalent (hydraulic) diameter initial exhaust overpressure recovery time relaxation time steady flow unsteady flow the parameter related to the sensor near the channel wall the parameter related to the sensor in the centre of the channel

Abbreviations ICE internal combustion engine

simulation. The information on the gas exchange processes in piston ICEs under unsteady conditions are very limited and very contradictory. The classic experiments by Ricardo [12] and Zass [13] performed in the early 20th century can be referred to as the first research into the air flow in the cylinder of a piston engine. They studied the twist of the flow in a cylinder using a vane anemometer depending on the engine crankshaft speed. Later, some research into gas dynamics and heat exchange of flows in steady-state gas flow conditions was initiated and followed by the development of mathematical models for one-dimensional gas exchange process modelling [14]. Since the development of computer and measuring equipment, the thermal anemometry method has become widely used in the study of unsteady-state and turbulent flows including in gas-air paths of piston internal combustion engines [15]. The development of software packages for the mathematical modelling of gas dynamics and heat transfer has led to a large number of gas exchange process studies with their help [16]. Unfortunately, only some works verify results obtained on the basis of numerical modelling based on experimental studies [17]. This paper considers the characteristics of gas-dynamic unsteadiness in relation to thermal-mechanical processes in the intake and exhaust systems of piston internal combustion engines. The study is aimed at clarifying the physical mechanism of pulsating currents and establishing the regularities in the variation of the gas-dynamic and thermal characteristics of the flows in the intake and exhaust channels in the gas-dynamic unsteady conditions for improving the gas exchange quality in piston ICEs. The key objectives of the research are as follows: – to identify the physical features of the gas dynamic conditions of heat transfer of the high-frequency and pulsing flow in the gas-air tracts of piston engines; – to establish the degree of the gas-dynamic unsteadiness of gas flows in the intake and exhaust pipelines of piston engines; – to develop a methodology for taking into account the effect of the gas-dynamic unsteadiness of flows in pipelines of different configurations on the local heat transfer. By solving the problems, it will be possible to expand the knowledge base on thermophysical processes in the course of gas flows under unsteady-state conditions, provide the basis for the development of engineering methods for calculating the intake and exhaust systems of engines, and also allow the development of perspective piston engine designs with heat recovery of exhaust gases.

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2. Experimental facilities and measuring instruments In the experimental research into transient processes in the nonstationary gas flows in pipelines, a transient process typical of gas-exchange systems of piston engines was chosen as the model process, namely, the restoration of flow when a valve opens after a pause. In this case, the typical unsteadiness is due to the cyclic nature of the piston engine cycle. The peculiarities of the flow pulsations typical of the internal combustion engine cycles are that the gas flow for a long time is completely stopped by the valve mechanism (the channel cross section overlaps), and then it is restored again when the valve opens after a pause. During the operation of piston engines, the time, during which the valve is open (there is a gas flow), is about 40% of the entire cycle time. Fig. 1 shows a diagram of a test unit for studying the transient processes in pipelines. The air from compressor 1 was supplied to tank-receiver 2, which was equipped with an internal lattice to stabilise the flow. Then the air was supplied to cylinder wind box 3 (with a honeycomb). From there, air was supplied through the channel in cylinder head 4 into pipeline 5 (a total length of 1000 mm and a diameter of 30 mm), in which the heat loss anemometer sensors were installed. The non-stationary (accelerating) flow mode in the channel was created with the controlled bypass valve 6. In the pipeline in question, four control cross-sections were selected at the distances lx from the channel inlet of 150 mm, 300 mm, 600 mm and 900 mm: two heat loss anemometer sensors were installed (Fig. 2). In this case, the measuring thread of one of the heat loss anemometers was on the axis of the channel perpendicular to the flow in it. The other measuring thread was installed at a distance of 0.2d from the channel wall in the same position as the flow direction. The experimental procedure for the test unit described above (see Fig. 1) is as follows. The compressor was started, then followed the time adjustment to the exhaust of the flow in the pipeline in question to the stationary mode, which was monitored by heat loss anemometers. Then the bypass valve was closed and the air was discharged into the atmosphere, bypassing the pipeline in question. Again, the exposure was maintained until flow steadiness was achieved. Then the valve was opened sharply, and air was directed to the pipeline in question. In the experimental research into unsteady gas dynamics and instantaneous local heat transfer with respect to piston internal combustion engines, the air intake process and the exhaust gas process, which take place in the intake and exhaust systems, were chosen as research aims. For the experimental research into gas dynamics and the local heat transfer in the intake and exhaust systems of piston engines, experimental facilities representing the full-scale models of a single-cylinder piston engine were designed and manufactured (Fig. 3). The prototype was a two-cylinder engine with the piston

Fig. 1. Diagram of a test unit for studying the transient processes in pipelines: 1 is the compressor; 2 is the tank-receiver; 3 is the cylinder wind box; 4 is the cylinder head of the crankshaft engine; 5 is the pipeline in question; 6 is the bypass valve.

Fig. 2. Configuration of the area of interest: 1 is the cylinder wind box; 2 is the cylinder head of the crankshaft engine; 3 is the engine valve; 4 is the pipeline in question; 5 is the heat loss anemometer sensor for measuring the flow velocity near the wall; 6 is the heat loss anemometer sensor for measuring the flow velocity along the channel section.

diameter of 82 mm and the piston stroke of 71 mm produced by the Russian VAZ company. The gas distribution mechanism of the experimental installations is borrowed from the engine in question. Valve timing (intake and exhaust valve opening and closing) and lifting the valves of the units corresponded to those for the prototype engine. The crankshaft was driven by an electric motor, the speed of which was regulated by a frequency converter in the range of 600–3000 rpm. The experimental research into processes in the intake and exhaust systems of piston engines was carried out in stationary and pulsating blowdown modes. In the steady-state flow mode, the intake or exhaust valve of the piston engine was fixed in the extreme upper (open) position, and the air flow was created by an air exhauster sucking air from the cylinder (intake) or by a compressor injecting air into the cylinder (discharge). In the pulsating air flow mode in pipelines created by the rotation of the engine’s crankshaft, the valves opened and closed according to the nominal valve timing phases. The research was carried out for different rotational speeds of the crankshaft from 600 rpm to 3000 rpm at various constant excess pressures at the exhaust pbb from 0.05 MPa to 0.2 MPa. The air temperature in the intake pipeline was about 22–24 °C, and in the exhaust one 36–40 °C. Due to the poor level of knowledge and the insufficient amount of experimental data on processes in the gas-air paths of piston engines that take into account the gas dynamic unsteadiness, it was methodologically advisable, as a starting point, to choose a traditional straight pipe with a circular cross section. The length of the pilot pipe was 450 mm, the internal diameter of the intake pipe 32 mm and that of the exhaust pipe 30 mm. To collect and process the experimental data, an automated system based on an analogue-to-digital converter was created. A tachometer was used to measure the rotational speed and angle of rotation of the crankshaft. To determine the instantaneous airflow velocity wx and the local heat transfer factor ax, a constanttemperature thermal anemometer of the original design protected by the Russian Federation patent was used [18]. The thermal anemometry method was chosen for studying gas dynamics and the local heat transfer of gas flows was selected on the basis of the literature and the existing approaches to the unsteady flow research. The thermal anemometry method for the study of gas dynamics and local heat transfer of gas flows was chosen proceeding from the analysis of the literature and existing approaches to the study of unsteady-state flows. Thus, the classical monograph by Bradshaw [19] considers various constant temperature thermoanemometer systems and gives recommendations on their use in the study of turbulent flows. A number of articles related to the experimental research into turbulent flows present up-to-date

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Fig. 3. 3D model (a) and photograph (b) the test unit for investigating processes in piston engines: 1 is the electric drive; 2 is the intake pipeline; 3 is the cylinder head; 4 is the cylinder; 5 is the crankshaft.

electronic schemes of thermoanemometers for the study of unsteady-state flows [20], experimental setups and methods for calibrating the sensors of a thermoanemometer are described [21], a comparison of different types of thermal anemometers is made, and the possibility of their use in specific cases is reviewed [22]. The applicability of the thermal anemometry method for studying pulsating flows in gas-air tracts of piston engines is shown in monographs [23–25]. For example, the monograph by Vikhert et al. [23] provides a detailed description of the thermoanemometer sensors and their locations for the investigation of flows in the intake channels of piston engines, whereas the monograph by Draganov et al. [24] and Heywood [25] provide experimental data (air velocity or exhaust gas velocity) for the intake and exhaust systems of various internal combustion engines obtained by the thermal anemometry method. In our case, the sensitive element of the heat loss anemometer sensors was a nickel-chromium filament with a diameter of 5 lm and a length of 5 mm. To measure the air flow velocity, a sensor with a free thread placed perpendicular to the axis of the pipeline was used. To determine ax, a sensor mounted flush was used with the wall of the pipeline and with a thread lying on a fluoroplastic substrate. The local heat-transfer factor was determined with the indirect calibration method according to S.S. Kutateladze, which is based on the basic indicator of the local heat transfer rate of a well-studied reference process, for which a permanent-set heat transfer in a long rectilinear tube of circular cross section was chosen for the case (l/d = 50). A detailed description of the technique for determining the local heat transfer factor is presented in Appendix A. The maximum systematic error in measuring speed wx was 5.4% and the local heat-transfer factor ax was 10.0%. A detailed calculation of the experimental errors for the study is presented in Appendix B. A more detailed description of the test units, the instrumentation base and an evaluation of its high-speed response are given in the author’s monograph [26].

It is established that immediately after opening the bypass valve there was a sharp increase in air velocity, while its values for some time exceed the average speed w (the so-called ‘overspeed’). After that, the air velocity stabilizes: its instantaneous values fluctuate around the mean. These flow regularities are typical of all control sections and airflow velocities. With the dependences wx = f (s), two characteristic times of the transient process were determined: the flow recovery time sres and the relaxation time srel. The time up to when the flow velocity in the pipe first reaches the mean velocity value was taken as the flow recovery time sres. The flow relaxation time srel after overspeed was considered to be the time for setting the oscillations of the instantaneous velocities about the mean value wx . Thus, for each control section, two values of the characteristic times were obtained, one for the flow along the axis, the other for the flow near the pipe wall. Fig. 5 shows the dependence of the recovery time and relaxation time on the length of a pipe for an average air velocity of 20 m/s. It follows from the graphs in Fig. 5 that at this flow rate the recovery time sres of relaxation srel increases monotonically as long as the control section moves away from the pipe inlet. If at lx = 150 mm, sres1 is 38 ms, then at lx = 900 mm, sres4 is 83 ms. It should be noted that the recovery time is significantly longer than the transit time of the sound wave from the channel inlet to the mounted sensors, which is between 0.5 ms and 4.5 ms. According to the authors, this indicates the special structural conditions for flow stabilisation in such hydraulic systems. The probability of this mechanism is indicated by a small difference (within the experimental accuracy) of sres along the axis and near the pipe wall. Thus, it should be assumed that if forced pulsations of the gas flow in a pipe up to 150 mm long have a period much shorter than

3. Typical time of transient processes in the unsteady gas flow in pipelines Fig. 4 shows the dependence of the airflow velocity wx in the channel at the time after the opening of the bypass valve and air supply to the pipe in question (the data were obtained with the test unit as shown in Fig. 1). Dependencies are created with the steady flow and mean velocity wx = 20 m/s in the control section at a distance x = 300 mm from the pipe inlet. Similar oscillograms were obtained for all control sections and airflow velocities.

Fig. 4. Dependence of the local (lx = 300 mm) instantaneous gas flow velocity wx in the pipe on time s: 1 is the heat loss anemometer data with a thread in the centre of the channel; 2 is the heat loss anemometer data with a thread near the wall.

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Fig. 5. Dependence of the recovery time sres (a) and relaxation srel (b) along the pipe length lx for the average flow velocity in the channel of 20 m/s: 1 is the sensor in the centre of the channel; 2 is the sensor near the channel wall.

sres1 = 38 ms, then the flow should be characterised as a flow with a high degree of unsteadiness. According to the authors, this indicates that the transitional flow mode in the channels of the power plant has not yet been completed, and the flow is under the influence of another perturbation. Conversely, if the flow pulsations represent a much longer period than sres, then the flow should be considered quasi-steady (with a low degree of unsteadiness). In this case, before the appearance of the perturbation, the transient hydrodynamic mode has time to complete and the flow to level. Finally, if the flow pulsation period is close to the value sres, then the flow should be characterised as unsteady with an increasing degree of unsteadiness. Thus, the correlation of the characteristic times and the period of forced pulsations of the gas flow can be used to estimate the degree of gas dynamic unsteadiness. 4. Influence of gas dynamic unsteadiness on processes in the intake and exhaust systems of piston engines Let us consider how the typical times (sres and srel) can be used to estimate the gas flow unsteadiness in the intake and exhaust pipes of piston engines. Let us analyse the dependence wx = f (s) at n = 3000 rpm (Fig. 6). As can be seen, for a given crankshaft speed, the duration of the entire intake process is 0.0162 s, and the discharge process is 0.0136 s. The transient hydrodynamic process in the pipes begins immediately after valve opening. In both cases (intake, exhaust), the most dynamic rise can be recorded (the time interval during which a sharp increase in the flow velocity occurs), after which the flow velocity increase is replaced by its decrease. For more details on the gas dynamics of the intake and exhaust processes, see article [27]. As was established earlier, for the flow mode and hydraulic system configuration, the flow recovery time is 0.025–0.028 s, i.e. it is about two times longer than the gas

exchange processes, not to mention the relaxation time. Thus, it should be considered that the intake and exhaust processes in piston engines occur with a high degree of unsteadiness. The data on the flow acceleration in the gas-air paths also testifies to the high degree of unsteadiness of the gas exchange processes (Fig. 7). For example, the maximum flow acceleration values for the considered configuration of the exhaust system reach 40,000 m/s2 at a crankshaft speed of n = 1500 rpm. However, for n = 3000 rpm these values reach as little as 60,000 m/s2. In the intake system, the maximum flow acceleration values reach 120,000 m/s2 at a crankshaft speed of n = 3000 rpm. It is noteworthy that the flow acceleration values are almost always slightly higher than those of deceleration. To estimate the degree of influence of the gas-dynamic unsteadiness on the heat transfer rate in the intake system of a piston engine, we can compare the dependences of the local heat transfer rate ax on the air flow rate wx for different air flow modes in the intake pipeline (Fig. 8). In this figure, in the pulsating modes, the average integral values of the heat transfer rate and the air flow rate for 100 pulsation periods were used for comparison. It was found that there had been significant differences between the local heat transfer rate values obtained with the stationary purges of the intake pipeline and the mean integral values of ax in the pulsating flow: the difference reaches 2.5 times at speeds wx from 40 to 60 m/s. This is also described in article [28]. It is noteworthy that the local heat transfer rate intensity in the case of steady flow is greater than for a non-steady flow at all air flow rates. Thus, it is established that gas-dynamic unsteadiness leads to a decrease in the local heat transfer intensity. In addition, by the dependence ax = f(wx) for an unsteady flow, the following trend can be traced. Up to an airflow velocity of 22 m/s, the local heat transfer rate increases with the same intensity at all crankshaft speeds; then at medium and high n we can isolate the stabilisation zone ax, a peculiar plateau with a subsequent intensive growth.

Fig. 6. Dependence of the local (lx = 140 mm) airflow velocity wx in the intake (a) and exhaust (b) pipes on the time s at a crankshaft speed of 3000 rpm.

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Fig. 7. Dependence of the local (lx = 140 mm) acceleration of the air flow wx in the intake (a) and exhaust (b) pipes on the time s at a crankshaft rotation speed of 3000 rpm.

Fig. 8. Dependence of the local (lx = 110 mm) heat transfer rate ax on the air flow rate wx in the intake pipe of the piston engine: 1 – n = 600 rpm; 2 – n = 1500 rpm; 3 – n = 3000 rpm - - - - steady flow; —— pulsating flow.

Based on the data, it should be concluded that, firstly, the stationary research methods cannot fully reflect the transport mechanisms that arise in pulsating flows with a high degree of the gas-dynamic unsteadiness inherent in piston engines. Secondly, it should be assumed that unsteadiness is aggravated in time but it cannot accumulate indefinitely and should somehow be resolved thus affecting the processes in the pipelines. It is established that during the release process in an internal combustion engine, the gas-dynamic unsteadiness is resolved in a critical manner. According to Fig. 9a, the mechanism for resolving unsteadiness at low values of n can be traced, first, cycles that are similar to each other (release processes) occur, and then a critical cycle can be seen; i.e. a special oscillogram, or more precisely an oscillogram with a special section (circled with an oval in the figure). Fig. 9b also shows the dependence of the local gas flow rate wx on the time s in the discharge pipeline but at a crankshaft rotation speed of 3000 rpm. At high values of n, the unsteady-state resolution mechanism changes slightly. The oscillograms of the release processes are evolutionarily deformed, namely each subsequent cycle differs significantly from the previous one. The constantly deformed sections of the gas flow velocity oscillograms are also marked by ovals (Fig. 9b). Thus, the unsteady-state resolution mechanism depends on the frequency of the perturbation, and is therefore not purely acoustic. The nature of the gas-dynamic unsteadiness of the exhaust process exerts its influence on the heat-exchange characteristics (in particular, the local heat-transfer rate) in the piston engine exhaust pipeline. In order to analyse this, we turn to Fig. 10, which shows the dependence of the local heat-transfer rate ax on the time s at different rotational speeds of the crankshaft n for the excess pressure pbb = 0.1 MPa. From Fig. 10 it can be seen that the thermal unsteadiness resolution also occurs in a critical manner. On the dependences

Fig. 9. Change in the local (lx = 110 mm) gas flow rate wx in the exhaust pipeline in time s at the exhaust overpressure pbb = 0.1 MPa and different speeds of the crankshaft n: a is 1500 rpm; b is 3000 rpm.

Fig. 10. Change in the local (lx = 110 mm) heat-transfer rate ax in the exhaust channel in time s under excess pressure at the exhaust pbb = 0.1 MPa and various crankshaft speeds n: a – 1500 rpm; b – 3000 rpm.

ax = f(s), the oscillograms, which differ significantly from the others, are circled by ovals, as in the case with the gas flow velocity. It should be noted that the local heat transfer factor is characterised by thermal inertia expressed in the appearance of two consecutive oscillograms which differ significantly from the others. At high speeds of the engine’s crankshaft (Fig. 10b), on the dependences ax = f(s), as expected, the thermal unsteadiness resolution occurs gradually or more smoothly. The constantly deformed sections of the oscillograms of the local heat-transfer rate are identified by ovals (Fig. 10b). In the opinion of the authors, the kinks and plateaus on the dependences ax = f(wx) (see Fig. 8) are related to the unsteadystate resolution mechanism.

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Thus, it can be concluded that in the release process in a piston ICE, the coupled thermal mechanical unsteadiness expressed in the nature of the change in the gas-dynamic and heat-exchange parameters of the flow can be recorded. Based on this, it is becoming relevant how the thermomechanical unsteadiness in the design calculation of the local heat-transfer rate in the intake and exhaust pipelines of piston engines should be taken into account. 5. Accounting for the unsteadiness of processes in the gas-air paths of the piston internal combustion engines At the moment, there are a rather large number of empirical equations for the calculation of heat transfer for long round tubes with a steady flow in them. Empirical dependencies for calculating the Nusselt number for steady-state gas flows in pipelines of different configurations can be found in the monographs by Incropera et al. [29], Isachenko et al. [30], Kutateladze [31] and Shah et al. [32]. Their calculation of the heat-transfer rate gives them essentially different results; therefore, in engineering practice, based on a company’s regulatory documents, a specialist (or scientist) selects the form of the equation which is considered the most reliable for their case. It should also be emphasised that the equations in their pure form are not applicable to pulsating currents because they are obtained at stationary purges and, accordingly, do not take into account the gas-dynamic unsteadiness effects. At the same time, as shown above, the heat-transfer rate of the flow in the unsteady conditions typical of piston engines can differ from the steady case by 2–4 times. Accordingly, one of the methods for calculating the local-heat transfer rate in the exhaust pipelines of piston engines under unsteady conditions is to obtain empirical equations based on the experimental data [26]. However, this method has not yet achieved methodological completeness and is very labour-consuming. Therefore, the authors propose to introduce a correction factor Kmh, the heat-transfer mobility factor, which is determined as:

K mh ¼ ax unst =ax st ; where ax unst is the value of the local heat transfer factor for a nonstationary (pulsating) gas flow, W/(m2
K); ax st is the value of the local heat-transfer rate for the steady gas flow, W/(m2
K). It should be emphasised that the Kmh factor should be experimentally determined anew in each specific case. In the framework of the paper, the dependences of the Kmh mobility factor on the gas flow velocity in the exhaust pipeline (d = 30 mm, lx = 110 mm) of a piston engine (cylinder diameter 82 mm, piston stroke 71 mm) for various crankshaft speeds were obtained (Fig. 11).

Fig. 11. Dependence of the heat-transfer mobility factor Kmh on the gas flow speed in the exhaust channel of the piston ICE with excess pressure at the outlet pbb = 0.1 MPa for various speeds of the crankshaft n: 1 is 600 rpm; 2 is 1500 rpm; 3 is 3000 rpm.

Thus, the method proposed by the authors for determining the local heat-transfer rate with allowance for the thermomechanical unsteadiness will consist of the following: – based on scientific and technical literature or regulatory documents, an expert chooses the design equation for calculating the local Nusselt number (the local heat-transfer rate) for the steady flow which is most suitable for its case and performs the respective calculation of ax; – then, to account for the effect of the gas-dynamic unsteadiness, the expert multiplies the calculated ax by the mobility heattransfer rate Kmh; – the value of Kmh further becomes regulatory based on the process development results.

6. Conclusions In this research, a technique for the experimental study of thermomechanical processes of gas flows under the conditions of gas-dynamic unsteadiness was developed, and a full-scale experimental setup was designed to study gas dynamics and heat exchange of gas-exchange processes in piston ICEs. The main task of the work was to refine the physical mechanism of pulsating currents and establish the features of the change in the gas-dynamic and thermal characteristics of the flows in the intake and exhaust pipelines of piston engines. The research was conducted using an automated system for collecting and processing experimental data. The constant-temperature thermal anemometer was the main measuring device. The conducted research package produced the following main results: 1. A methodology was developed for a comparative evaluation of the degree of gas-dynamic unsteadiness of gas flows in pipes based on the characteristic times; with its help, it is established that the processes in piston engines during intake and exhaust proceed with a high degree of unsteadiness, which determines the heat transfer mechanism. 2. It was established that during the gas exchange processes in gas-air paths of the internal combustion engines the resolution of gas dynamic unsteadiness occurs in a critical manner. 3. It is established that the gas-dynamic unsteadiness typical of the gas-air tracts of piston engines significantly reduces the heat-transfer rate. Differences in the values of the local heattransfer rates of gas flows in the steady and pulsed flow modes are in the range of 1.3–2.5 times. 4. A method is proposed for taking into account the influence of unsteadiness with the help of a correction factor, the heattransfer mobility factor to the calculation results using the classical equations for calculating the local heat-transfer rate (the Nusselt number). 5. The data on the intensity of the instantaneous local heat transfer in the gas-air paths of piston internal combustion engines can be used for: – calculation of the values of air heating and cooling of exhaust gases in the intake and exhaust processes of, respectively; – prediction of the local heat transfer in exhaust systems of piston engines with heat recovery of exhaust gases which will increase their effectiveness; – determination of the dynamics of distribution of temperature stresses in the parts and modules of gas-air paths and, accordingly, finding the thermal stresses in them; – development of the perspective intake and exhaust systems for the modernisation of existing engines or the development of new ICEs.

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Acknowledgement The work was supported by the Russian Foundation for Basic Research (Grant No. 16-38-00004).

Conflict of interest Corresponding author of the manuscript confirms that no actual or potential conflict of interest including any financial, personal or other relationship with other people or institutions within three years of beginning the submitting paper. Appendix A. Local heat transfer factor method A detailed description of the procedure for experimentally determining the local heat transfer factor in this study is presented in this appendix. The paper uses a well-proven thermal anemometry method as the basis for determining the intensity of heat transfer in the intake and exhaust systems of piston ICEs. It is known that the small dimensions of the detecting element of the thermoanemometer sensor do not introduce any significant changes in the nature of the gas flow; high sensitivity makes it possible to record fluctuations of the values with small amplitudes and high frequencies; the simplicity of the hardware scheme makes it possible to reliably record the electrical signal from the output of the thermoanemometer for storing and subsequent processing on a personal computer. It should be noted that the high speed of the filamentary sensor was the decisive factor in its selection because other types of sensors did not provide the necessary time resolution. The thermal anemometry method for the study of gas dynamics and local heat transfer of gas flows was selected based on the analysis of the reference literature (in particular, the scientists Hince I. O., Povh I.L., Bradshaw P., Frejmut P.) and the existing approaches to the study of turbulent flows. For this research, the authors developed an original fixed temperature anemometer protected by a patent of the Russian Federation (Patent No. 81338 RU). As noted above, a constant-temperature thermoanemometer was used to determine the local heat transfer factor ax. The sensitive element of the thermoanemometer sensors was a nichrome filament with a diameter of 5 lm and a length of 5 mm. The filament was on a fluoroplastic substrate, the surface of which was mounted flush with the pipeline wall (Fig. A1). It should be noted that the filament diameter was less than the average microroughness of the substrate. The preliminary calculation, analysis and pilot experiments have shown that it is not possible to arrange the implementation of the known techniques for the direct determination of the local heat transfer factor using wire sensors in this case. Direct determination of the heat transfer factor for the removed heat flux led to disproportionately large values of the factor since a heated local microelement creates around itself a thermal-mechanical environment different from an extended hot wall. Therefore, in this study, the determination of the local heat transfer factor was based on the indirect calibration based on the known empirical relationships, i.e. by the method proposed by S.S. Kutateladze. It is based on the basic indicator of the local heat transfer of a well-studied process, the reference process, in which the steady-state heat transfer in a long straight pipe (l/d  50) with a circular cross section which was chosen for this case. Thus, in this case the calibration consisted in relating the calculated heat transfer factor a (W/(m2
K)) for the long straight pipe and the signal value from the thermoanemometer sensor U (V).

Fig. A1. The diagram of installation of the thermal anemometer sensor for determining the local heat transfer factor in the pipeline of a piston engine: 1 is the pipeline; 2 is the fluoroplastic substrate; 3 is the nickel-chromium filament.

Fig. A2. The calibration dependence ax = f(U) for measuring local heat transfer factors in pipelines.

The base value of the heat transfer factor (Nusselt number) was calculated by means of empirical dependence [24]:

Nux ¼ 0:022Re0:8 Pr0:43 e; where Nux ¼ akxx
d is the Nusselt number; ax is the local heat-

exchange factor, W/(m2
K); d is the inner diameter of pipe, m; kx is the thermal conductivity factor of gas, W/(m
K); Pr is Prandtl number; e = f(x/d) is the correction factor for the length of the channel; Re ¼ w
d mx is Reynolds number; where w is average velocity, m/s;

mx is kinematic viscosity coefficient, m2/s.

When calibrating the thermoanemometer sensors to determine the local heat transfer factor, the following values were measured, i.e. flow temperature, barometric pressure, local flow rate and voltage from the calibrated sensor. The experiments were carried out in 10 modes. At the same time, the air flow rate varied from 0 to 120 m/s. Thus, a calibration curve in the form of a functional connection of voltage at the output of the thermoanemometer U and the local heat transfer factor ax was obtained (Fig. A2). The obtained calibration dependence was used to study the local heat transfer in the intake and exhaust systems of internal combustion engines.

Appendix B. Estimated experimental error The calculation of the error in determining the basic physical quantities in this study is presented in this appendix.

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When evaluating the experimental error, two main types of relative errors are usually considered: systematic and random. The systematic error component is a constant or variable value according to a certain law. However, a huge number of sources of systematic errors makes it practically impossible to fully analyse their effect on the measurement results; therefore, it is only feasible to estimate the magnitude of the systematic errors. The systematic error value for this method is usually estimated by procedural error and by the error of the measuring tools determined by their accuracy class. In this study, the systematic error was evaluated according to the data sheets of the instrument manufacturing plants, according to the reference data, and, if unavailable, the relative systematic error was determined as the ratio between the half of the scale value of the instrument scale and the smallest value measured. Unfortunately, most sources do not provide the exact characters of the error, so in this study these errors were taken as an estimate of the relative systematic error, which led to some (due to a random error) overestimation. In a complex measuring circuit, the total error was calculated by the formula:

d¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Xn di ; i¼1

where di is the relative errors of individual links including calibration, n is the number of measurements. The estimation of the maximum relative systematic error of the initial data is given in Table B1. The systematic error of the calculated values was estimated according to the relationships [33] between the root-meansquare errors of the initial and calculated values. The results of the estimation are given in Table B2. For values that result from indirect measurements, first, based on the initial data, the population was calculated from the values; then the random error value was determined from it.

No

Value

Instrument or source

Error d, %

1 2

Barometric pressure Differential pressure in the flow Air temperature

Barometer Micromanometer and transducer

0.1 2.5a

Measuring system with thermocouple and potentiometer Calipers

1.0

Thermoanemometer of constant temperature Inductive transducer Thermophysical reference book

5.4b

4 5 6 7

Linear dimensions of the channel Air flow velocity in the channel Engine crankshaft speed Thermophysical properties of substances

s Dx ¼ t pffiffiffi ; n where t is the Student’s coefficient for a given probability p and number of measurements n (for P(Dx) = 0.9 and n = 10: t = 1.8); s is the mean square error of a series of measurements:

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 i¼1 ðx  xi Þ s¼ ; n1 where xi is nth measurement, x is the average of n measurements, Pn i x ¼ ni1 . The maximum random error in calculating the main indicator, the local heat transfer factor in the channel was 1.6%. Since at present there is no sufficiently accurate and justified way of combining random and systematic errors, which are the errors of various origin, the magnitude of the total error was not estimated. In this study, a number of conclusions were obtained by the method of comparison; therefore, the reliability of the conclusions is limited only by random errors; since their number turned out to be insignificant, it was not necessary to involve the dispersion analysis apparatus. In general, the estimation of the experimental error showed that the selected experimental technique would provide sufficient reliability of the results obtained. References

Table B1 Estimation of the relative systematic error of the initial values.

3

Before the basic set of experiments, trial experiments were carried out, 10 measurements were made in several modes and geometric parameters. The confidence probability value was chosen equal to P(Dx) = 0.9 because only it has a single-valued relationship with the standard deviation for the most commonly used distribution laws. The boundaries of the confidence interval were determined by the relationship as follows,

0.6

2.5 2.0

a The error is given taking into account the calibration error (1.1%) and the conversion into a digital code (2.2%). b The error is given taking into account the error of converting the analogue signal into a digital code.

Table B2 Estimates of the relative systematic error of the basic design values. No

Parameter

Error d, %

1 2 3 4

Equivalent (hydraulic) diameter Air-flow rate through pipeline Local heat transfer factor Hydraulic resistance coefficient

0.9 6.2 10.0a 5.2

a Accuracy for the technique with a thermocouple providing the maximum systematic error.

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