Energy balance in reciprocating engines

Modern engines in cogeneration applications are almost always turbocharged to improve performance Credit: Niigata Power Systems
Modern engines in cogeneration applications are almost always turbocharged to improve performance
Credit: Niigata Power Systems


Detailed knowledge of a cogeneration installation’s energy balance can help inform the decision and installation-design process. In the second of a series of articles, Jacob Klimstra provides the necessary background knowledge for an installation driven by a reciprocating gas engine.


Installations that combine the production of electricity and heat are generally chosen for economic reasons. The owner tries to create a profit via the optimum conversion of fuel energy into useful energy. It is a no-brainer that the costs of running the installation should be lower than purchasing electricity from the grid and producing heat locally with a boiler. For a proper decision and installation-design process, detailed knowledge of a cogeneration installation’s energy balance – showing the ratio of power and heat, as well as the temperature level of the heat produced – is required. This article offers the necessary background knowledge for an installation driven by a reciprocating gas engine.

Fuel efficiency

Reciprocating engines are also called internal combustion engines or piston engines. Most engines that drive cogeneration installations run on a gaseous fuel that is mixed with air and subsequently compressed by a piston moving inside a cylinder. After compression, the combustible mixture is ignited by a spark plug and burns, and the resulting high-pressure cylinder contents subsequently push the piston back.

The net result of a complete engine cycle is an amount of work that is transferred to the load via the shaft of the engine. In the case of CHP, the load is an electricity generator. The typical four-stroke spark-ignited engine was invented by the German travelling salesman Nicolaus August Otto in 1876, amazingly via a trial and error process. (The story of Otto is comprehensively described in the book “Gebàƒ¤ndigte Kraft”.)

Later, people with an engineering background tried to explain the efficiency of the engine process with thermodynamic theory. The idealised thermodynamic process of the engine consists of a suction-compression-combustion-expansion-expulsion step. The efficiency of such a standard cycle is fully determined by a characteristic medium property k and the compression ratio àŽµ. The medium property is the dimensionless ratio of specific heats k = cp/cV. The value of k equals 1.4 for standard air. The compression ratio àŽµ of the engine is a volume ratio: the maximum volume of the engine cylinder contents divided by the minimum volume. The equation that gives the idealised efficiency àŽ· of converting fuel energy into work for the standard cycle is:


Even many engineers find it difficult to believe that this equation contains no temperature or pressure values at all, but just a medium property and a design property.

Figure 1 gives the fuel efficiency of the idealised engine cycle for a range of compression ratios. At least in theory, very high fuel efficiencies can be reached if the compression ratio is high enough. In the idealised cycle, no heat is lost to the cylinder walls and no friction losses occur in the moving parts. This means that the fraction of the fuel energy that is not converted into work will be available in the exhaust gas. For the idealised cycle, the temperature of the exhaust gas could be 1000à‚°C in case of a cycle efficiency of 50% and 500à‚°C in case of a cycle efficiency of 75%.

Figure 1: Fuel efficiency of the idealised Otto engine cycle, depending on compression ratio àŽµ and medium property k
Figure 1: Fuel efficiency of the idealised Otto engine cycle, depending on compression ratio àŽµ and medium property k

The real engine process

In practice, reciprocating gas engines hardly ever use a compression ratio higher than 12. Much higher compression ratios induce very high pressures and temperatures in the cylinders, which can lead to melting of the cylinder material and overstressing of the engine construction. Moreover, compressing an ignitable mixture to very high temperatures and pressures will lead to auto-ignition of the mixture, resulting in premature and uncontrollable combustion which is destructive for the engine. High compression ratios also result in higher friction losses.

Further, it is impossible to prevent heat from the hot cylinder contents escaping to the cylinder walls. In other words, the cylinder process is not adiabatic. The cylinder walls must be kept at a relatively low temperature in order to avoid deterioration of the lubricating oil.

Lubrication is essential for facilitating proper movement of the pistons inside the cylinders. It is therefore unavoidable that heat flows from the hot cylinder contents to the relatively cold cylinder walls. Less heat in the cylinder contents means that the cylinder pressure is lower and consequently the process efficiency is lower than in the theoretical case. The ratio of wall area to combustion chamber volume increases with the cylinder bore. That is why large-bore engines have relatively lower heat losses to the cylinder wall than small-bore engines. This is slightly counteracted by the lower running speed of large-bore engines. A lower running speed means the hot cylinder contents are inside the engine for a longer time, and therefore more time is available for heat transfer.

Friction between moving and fixed engine parts is another reason that real engine efficiency deviates from that of the idealised process. Pistons move inside the cylinders, and friction between the piston and the cylinder wall is the major cause of friction loss. Other friction losses occur in the crankshaft and camshaft bearings. The good news is that friction losses relatively decrease for a higher load of the engine. The same applies for heat losses to the cylinder walls. These are the major reasons that highly loaded turbocharged engines have a better fuel efficiency than low-loaded, naturally aspirated engines.

Further efficiency losses are caused by incomplete fuel combustion and by pressure drop in the intake over the throttle valve that controls the engine’s output. Also, in reality the medium property k has a value lower than the 1.4 of standard air. In the case of fuel-rich mixtures, the k value can be as low as 1.32, which drastically reduces the attainable fuel efficiency.

Turbocharging to improve performance

Modern engines in cogeneration and on-site power production applications are almost always equipped with turbocharging, which drastically increases an engine’s power output. It also helps to reduce the investment costs per kW of output, since less material is needed for achieving a given output. Turbocharging consists of an expansion turbine in the engine exhaust that drives a compressor in the intake part of the engine. This compressor increases the pressure of the intake air or, in many cases, the intake mixture of air and fuel gas. Since the compressor increases not only the pressure of the air or mixture but also the temperature, a cooler is needed to bring the temperature of the intake flow back to a lower value. Without a low intake temperature, the density of the mixture entering the cylinders is too low and the benefit of the turbocharger is diminished. And a high intake mixture means that destructive knocking combustion easily occurs and that the engine’s NOx production will be unnecessarily high.

The cooler downstream of the turbocharger’s compressor is generally called the aftercooler or intercooler. In today’s cogeneration applications the intercooler is often split into high-temperature and low-temperature sections. The desired intake temperature for the cylinders can be around 30à‚°C while the temperature downstream of the compressor can be close to 200à‚°C. Cooling the hot air flow to 30à‚°C in one step would mean that the full intercooler heat would be available at a relatively low temperature, while in most cogeneration installations the desired outgoing water temperature is between 75à‚°C-95à‚°C. With a two-stage intercooler, much of the heat can be captured at this desirable level.

Energy balance at nominal output

Figure 2 (p 31) gives the energy flows of a modern high-performance gas engine. There are three temperature levels at which the heat is made available. The exhaust heat can be used for producing steam. The high-temperature (HT) heat can be used for sanitary water applications and radiator heating. The low-temperature (LT) heat can be used for space heating such as under-floor heating, and for product drying.

Figure 2: Example of the energy balance of a reciprocating engine running at nominal output
Figure 2: Example of the energy balance of a reciprocating engine running at nominal output

Engines’ energy balance is always based on the lower heating value of the fuel applied. Fuels’ higher heating value includes the energy that can be recovered by cooling of the combustion end products, i.e., the exhaust gas, to the starting conditions including the heat released by condensing the water vapour in the exhaust gas. The temperatures of an engine process will never be so low that condensation occurs inside the engine. Therefore, the energy flow given in Figure 2 is based on the lower heating value of the fuel. As an example, the lower heating value of methane is 50 MJ/kg and the higher heating value is about 10% higher, for a starting condition of 15à‚°C.

Contrary to general belief, the real conversion from fuel energy to energy at the shaft of a modern engine can be close to 48%. This is generally called the shaft efficiency. Many engineering textbooks and papers still mention a maximum shaft efficiency of 35%, which was traditionally the case for a typical naturally aspirated (no turbo) passenger car engine. In the example of Figure 2, the shaft efficiency of the engine is 45.7%. Some 30% of the fuel energy is available in the exhaust gas at 400à‚°C. The available HT heat equals the 6.1% from the first-stage intercooler plus the 6.5% from the jacket water. The available LT heat equals the 3.8% from the second-stage intercooler plus the 4.9% from the lube oil cooler. The total sum of mechanical and heat energy released by the engine is therefore 97.1% of the fuel energy. Loss due to incomplete combustion equals 1.6%. The remaining 1.3% is caused by heat flowing from the engine block to the surroundings. An engine block has a temperature of around 85à‚°C while its surroundings are generally much cooler.

Application of this engine in a cogeneration installation does not mean that the total fuel efficiency will by definition be 100 – (1.6 + 1.3) = 97.1%. That entirely depends on the temperature level at which the heat is used and on the housing of the cogeneration installation. (This will be explained in an article in a forthcoming issue of COSPP. )

Energy balance at different loads

The energy balance shown in Figure 2 applies only to a fully loaded engine, in other words to an engine running at its nominal load. In cogeneration and on-site power applications, the engine’s output often has to be adapted to demand. As mentioned earlier, running an engine at a reduced output increases the relative effect of friction and internal heat loss. It was the Englishman Peter William Willans (1851-1892), the famous steam engine manufacturer, who found that the relationship between many machines’ fuel consumption and shaft output is a close-to-straight line with an offset. The reason for this offset is that, at zero shaft output of a running engine, fuel is still needed to create work to compensate for friction losses and to provide the energy for the heat losses from the cylinder contents to the cylinder walls. The so-called Willans line also applies to reciprocating engines. Fuel consumption at zero shaft output of the engine is about 10% of the fuel consumption at 100% shaft output. That means that the Willans line of that engine is fully known, since one can draw a straight line when two of its points are known.

Thus, we can easily find the shaft efficiency of the engine as a function of its shaft output, since the fuel consumption at every output point is now known. Figure 3 (p 32) gives this shaft efficiency as a function of shaft power. An interesting observation is that the shaft efficiency declines only slightly with load in the higher range, because the effect of internal friction and heat loss is still very low in this output region. However, for loads below 50%, the effect of internal losses becomes more severe. The nice thing about a rather flat efficiency line in the higher shaft output region is that the engine power output can vary according to demand without severe consequences for fuel efficiency. Engines which have lower shaft efficiency at nominal output will have a less flat efficiency curve in the upper output range.

Figure 3: Shaft efficiency depending on shaft power
Figure 3: Shaft efficiency depending on shaft power

If the shaft output of a given engine decreases because of a lower load, the losses caused by convection from the engine block and by incomplete combustion stay close to the same in an absolute sense. The temperature of the engine block is thermostatically controlled so the temperature difference between the block and its surroundings is independent of the relative shaft output. Also, the heat to the coolant and to the lubricating oil will not decrease drastically with decreasing shaft output. However, the power transferred from the exhaust to the intake system by the turbocharger will substantially decrease with the shaft power so that the intercooler heat will also decrease rapidly with the load. Below some 30% of nominal shaft power, the turbocharger has hardly any effect on the system so that the engine will act like a naturally aspirated engine.

The heat released in the exhaust is most severely affected by shaft power reductions. This is a good thing, since in cogeneration installations, heat demand variations often determine the set-point of the shaft power. So, if an installation’s heat production can be varied without serious consequences for shaft efficiency, economic operation can be more easily guaranteed.

It is therefore very important in most cases that the owner chooses a cogeneration installation with high shaft efficiency at nominal output. Electrical and mechanical energy generally have a higher economic value than heat. Moreover, a high-efficiency engine can more easily vary its heat output without negative consequences for its shaft efficiency.

Dr Jacob Klimstra is Managing Editor of COSPP

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