Gogénération Par Turbine À Gaz

Modelling of waste heat recovery within

thermal machines

S. BOUDIGUES, G. DESCOMBES and Z. SERINYEL

Université P. et M. Curie, Laboratoire de mécanique physique, CNRS UMR 7068

2 place de la gare de ceinture 78210 Saint Cyr l’école France

Abstract: The current environmental context dictates to reduce the pollution emissions by improving thermal efficiency of the energetic units production. The authors present some examples of cogeneration applications using gas turbines and thermal engines. The on-going research concerns a detailed study of thermodynamic modelling cycles with energy recovery. These combined cycles with gas turbine and ICE can generate a potential increase about 10% of the energetic efficiency. They generate a technological complexity and the over-charge stays to estimate. In last, the authors insist on the necessary synergy between gas turbines and thermal engines.

Key words: gas turbine, internal combustion engine, combined cycle power, cogeneration, efficiency, energy recovery, thermodynamic cycles.

1

NOTATION

T Temperature

S Entropy

q Heat

ExExergy

AnAnergy

EnChemical energy

EcCogeneration efficiency

Efficiency

indices

c Carnot

exExergy

i Internal

1 INTRODUCTION

The energetic efficiency  of a thermal machine is given by relation (1) where and are the hot and cold entropic temperatures of the heat respective sources. The heat flux q is produced by the combustion reaction. iS is the entropy production due to the losses within each sub-block of the machine. So, the thermal efficiency th can be written as the produce of the Carnot efficiency c and the exergetic efficiency ex which depends of the level of losses given by the term of entropy production iS.

(1)

(2)

The exergy Ex of the heat flux q delivrated at the mean temperature of exchange is equivalent to the mechanical work w produced on the crankshaft of the engine. The anergy An represents the thermal energy which is losted as the intrinsic term on one hand and by the major entropy production iS due to the irreversibilities on the other hand.

(3)

(4)

The global energy balance (relation 5) shows that a fraction of these anergy An can be used partially for energy recovery applications.

(5)

2 ENERGY RECOVERY

The analysis of the energetic balance of a thermal engine show that 50% and more of the chemical energy is losted according to the application. A usual case of energy recovery concerns the simultaneous production of electrical energy and thermal energy. That is the case of the cogeneration applications as the production of steam and hot water on one hand and trigeneration with additional cold energy produced on an other hand.

Fig. 1 gives the comparative efficiency of energy recovery applications between gas turbines and thermal engines as a function of output of the machines. In a first approach, we can see that the thermal efficiency of a Diesel engine is better than the efficiency of a single gas turbine in the range of the low output power in particular at partial loads. This trend reverses for a range output power, which is higher than some MW and more.

Fig. 1 Comparative energy recovery applications

2.1 Gas turbine

Fig. 2 shows the diagram of a usual co generated gas turbine used in a power plant unit. The electrical power is equal to 1050 kW. We notes that the thermal losses are mostly concentred at the exhaust gas. The mass flow at the exhaust gas is 5.45 kg/s and the thermal recovery power is equal to 2175 kW when the exhaust gas are water-cooled form 500°C to 150°C. The mass flow of the hot water is equal to 95000 kg/h and the saturated steam production at 4 b is about 33000 kg/h. The overall efficiency of the power plant unit is then around 85%.

Fig. 2 Energy recovery within a gas turbine

2.2 Diesel engine

Figure 3 shows the case of a turbocharged Diesel engine with energy recovery to produce electrical energy and hot water to an urban city. The thermal efficiency of the engines is equal to 45%. Two engines 18 cylinders operate with heavy-duty fuel with a viscosity equal to 180 centistokes at 50°C, the percentage of sulphur is less than 1.5%. The electrical power is equal to 38.5MW. This cogeneration process allows obtaining a simultaneous thermal power equal to 30MW of hot pressurized water at 120°C and 1MW in water at low temperature. The overall efficiency of this power plant unit is around 80% and the saving of fuel compared with a non-cogeneration application is about 10000 tonnes equivalent petroleum.

Fig. 3Diagram of waste heat recovery on a thermal engine

2.3 Waste energy compared

We have seen that the major heat source of losses is concentred within a gas turbine on the exhaust gas unlike to an ICE, which imposes a more complicated technology to recover waste energy. Then, the levels of the temperature and the mass flow of the exhaust gas turbine can be adapted on the same machine as a function of the needs of the user with a simple branch circuit on the heat exchangers. The cogeneration efficiency Ec (relation 6) which is the ratio between recovery thermal energy Eth and mechanical work Em is higher in a gas turbine than within a thermal engines. This cogeneration efficiency, which can be evolved from 2 to 6, is distinctly higher than the cogeneration efficiency of an ICE which is about 0.5 to 2, but to the detriment for the gas turbine of its fuel consumption [6, 7].

(6)

3 COMBINED CYCLES

A series of co generated cycles, which are derived of the basis Joule cycle can be modelled and have a real possibility of industrial application. All the results of modelling program which are presented use systematically the thermodynamic balances [1] to [6].

3.1 Gas turbine

The first simulation concerns the evolutive range of waste heat recovery as a function of the ratio of the thermal energy recovered on the exhaust gas which is taken on the turbine circuit. (Fig. 4). The entropic diagram illustrates the case without derivation and with derivation toward the inlet of the combustion chamber (Fig. 5).

Fig. 4

Fig.5

Fig.5

Fig. 6

Fig. 6

The performances of the machine can be evolved as a function of the mass flow, which is by-passed in the exchanger (Fig. 6). The outlet temperature is a function as the level of the exhaust gas by-passed at the exchanger. The outlet temperature is maximum at 900K when non derivation is realised. It is a linear decreasing function of the ratio by passed and the thermal energy is also maximum when there is no derivation. The results of the calculus give a potential increase of the thermal efficiency about 20% from 0.4 to 0.482. The ratio of the recovery thermal energy and mechanical work increases to 40% when the levels of gas temperature evolve from 500 to 90?K.

3.2 Cycle dépressurisé

Le cycle dépressurisé est réalisé sans compression préalable, l’énergie thermique étant fournie à la pression ambiante. La détente des gaz chauds est réalisée jusqu’à un niveau de pression inférieur à la pression atmosphérique et une énergie thermique peut ensuite être prélevée avant la recompression des gaz refroidis qui permet de retrouver la pression ambiante P0. Un gain sensible de rendement peut être obtenu par une compression refroidie qui peut également alimenter un circuit extérieur en énergie thermique (Fig.7).

Ce cycle dépressurisé concerne en particulier les machines dont les niveaux de puissance sont modérés et l’on observe que le niveau de pression en fin de détente d’un tel cycle est par définition inférieur à celui d’une détente classique. Il en résulte une réduction de la masse volumique qui pénalise a priori la puissance et le rendement de la machine. Cet inconvénient est atténué en augmentant la dimension des aubages qui permet de retrouver les débits nécessaires tout en diminuant les pertes générées par les épaisseurs de couches limites sur la paroi des ailettes. Le régime de rotation peut ainsi être diminué par un facteur 3 qui permet de retrouver un niveau convenable de performances (Boudigues et Descombes 2001).

La figure 8 illustre le concept appliqué à un moteur atmosphérique. La turbine à géométrie variable et le compresseur fonctionnent à puissance constante. Le calcul est réalisé avec une température d’échappement de 1200K en amont de la turbine et de 980K à l’échappement où règne une pression égale à 0,69b. Une récupération d’énergie thermique à l’échappement de la turbine peut être envisagée et la production d’énergie mécanique additionnelle produite sur le rotor évolue progressivement de 2 à 8% de l’énergie produite sur le vilebrequin en fonction de la charge (Descombes 2002).

Fig.7

Fig. 8 Cycle dépressurisé

(Boudigues et Descombes 2002)

3.3 Cycle à sur-détente

Le cycle à sur-détente qui fait l’objet de brevets déposés par l’Onéra (Boudigues 1985) comporte une compression suivie d’un apport de chaleur à pression constante (figure 9). Les gaz de combustion sont détendus à un niveau de pression inférieure à la pression ambiante fixé par les caractéristiques de la turbine et du compresseur. Ils sont ensuite refroidis par un échangeur et ramenés en fin de cycle à la pression ambiante par une recompression qui peut être refroidie.

Ce cycle à sur-détente peut améliorer la puissance de l’unité de production d’énergie ainsi que son rendement par un choix de taux de détente optimal qui est fonction des niveaux de températures et des rapports de pression de la machine. La sur-détente en-dessous de la pression ambiante Po est suivie d’un échange de chaleur entre l’échappement de la turbine et l’air de suralimentation en sortie du compresseur. Un radiateur refroidit les gaz sous-détendus avant d’être recomprimés pour retrouver la pression ambiante Po.

Fig. 9 Cycle à sur-détente (Boudigues 1985)

3.4 Résultas comparés de modélisation

L’objectif des cycles dépressurisé et à sur-détente est d’augmenter les taux de suralimentation tout en améliorant les rendements. On augmente pour cela les hauteurs d’aubes de compresseur et de turbine qui permettent de diminuer les niveaux de vitesses angulaires de rotation. Un calcul comparatif des cycles dépressurisé, à sur détente et à échangeur est illustré par le tableau 1 avec la prise en compte des pertes par frottements aérodynamiques et mécaniques, la variation des chaleurs massiques Cp et le calcul exact de la richesse. Pour une puissance de 50 kW et une efficacité des échangeurs égale à 0,85, on mentionne les valeurs de l’enthalpie de compression optimale, du débit m, du rendement , de la richesse r et de la vitesse angulaire de rotation de la turbine de puissance.

La technologie du cycle à simple échangeur est la plus simple, mais sa consommation et sa pollution sont les plus fortes et sa vitesse angulaire de rotation demeure prohibitive pour une puissance de 56 KW. Les performances du cycle à sur détente sont les meilleures, mais elles semblent réservées aux puissances supérieures à 100 KW. Le cycle dépressurisé est bien adapté aux puissances modérées de l’ordre de 50 kW.

Type de cycle /

Enthalpie de compression optimale

(kJ/kg) / Débit
(g/s) / Rendement / Richesse / Vitesse de rotation (rpm)
Echangeur / 218 / 229 / 0,409 / 0,0127 / 64000
Dépressurisé / 225 / 194 / 0,414 / 0,0147 / 31000
Sur-détente / 222 / 193 / 0,431 / 0,0143 / 46000

Tableau 1 Performances comparées des cycles thermodynamiques cogénérés

3.2 Over expansion cycle

The over expansion cycle consists in a preliminary compression and a heat transfer given by a combustion chamber at constant pressure. Fig. 9 shows the entropic diagram of this ideal over expansion cycle. The over expansion depressurises the compressible flow in three steps. The power produced by the expansion from the point C to D is used to give the power compression The gas is then compressed until ambient pressure. The, the expansion continue to the point E which is at a low pressure under the ambient pressure until a level fixed by the turbine and compressor characteristics. The expansion is ended from the point E to F to produce the power

An exchanger extracts thermal energy at constant pressure from the exhaust gas to the compressor. Then, a radiator extracts thermal energy to a exterior cogeneration circuit. (Fig. 9). This over expansion cycle can be improved the power and the efficiency of the machine for an optimum over expansion ratio as a function of the level of temperature and ratio pressure.

Fig. 9 Over expansion cycle

3.3 Depressurized cycle

The depressurised cycle is a specific application of the over expansion cycle. Fig. ? shows the entropic diagram of this deprusserized cycle which is compared to a basic cycle. It is made without preliminary compression and the heat transfer is given at constant pressure. The under expansion is realized to a low pressure under the ambient pressure. A thermal energy can be extracted to a cogeneration application at constant pressure and a cooling compression can be operated until atmospheric pressure.

1 dessin de cycle.

The depressurised cycle concerns in particular the low powers of the machines. For a maximum temperature of the cycle which is fixed by the technology material, the level of the pressure at the end of the expansion is of course low compared to a classic cycle with exchanger. The density is also low and imposes to use a larger geometry of turbine and compressor. This increasing of the geometry machine is better to decrease the losses within the blades and therefore the rotating speed is reduced by a factor 3. In return, the global efficiency is less convenient that a classic machine.

Fig. 6 shows the calculated performances of these cycles. The efficiency of the exchangers and the radiators are equal to 0.9 and the range of pressure losses evolves from 2 to 7% as a function of the studied case.

The modelling is led with an efficiency of the exchanger equal to 0.9 and the losses of pressure progress from 2 to 7% in accordance with the studied application. Fig. ? shows the improvement of the overall efficiency unit as a function of the studied cycle. Dotted lines concern a gas turbine without cooling blades where the temperature is not higher than 1300K. The ratio pressure is about 2 to 4 and the mass flow rate is not higher than 2 kg/s.

4. ICE and gas turbine

Figure 3 concerns the over-expansion cycle within the exhaust gas of a thermal engine. The level of temperature at the exhaust gas of the engine is fixed at 1000K and the cycle of the power unit is an over expansion cycle. The ratio energy between thermal energy recovered and work production is illustrated as a function of the temperature and the calculation shows that an additional recovery can be obtained. The optimal point is a function of the level of temperature, ratio pressure and the number of the exchangers and the calculus shows a potential thermal energy recovery from 10 to 20% of mechanical power (figure 8).

Fig. 10 Over-expansion cycle

CONCLUSION

This cycle can be used in the automotive applications. Nevertheless, the range of the mass flow rate and the enthalpy rate is very variable and constitutes a severe difficulty.

In SI engines, the reduce of the cubic capacity of the engine can be obtained with a high supercharging and lean burn with a conventional turbocharging or a depressurised cycle with cogeneration applications to produce cold energy and electricity energy. The actual and major problem is the wide range of transient functioning conditions and very variables evolutions within these small thermal machines.

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