Influence of Heat Transfer on Gas Turbine Performance

In the current economic and environmental context dominated by the energy crisis and global warming due to the CO2 emissions produced by industry and road transportation, there is an urgent need to optimize the operation of thermal turbomachinery in general and of gas turbines in particular. This requires exact knowledge of their typical performance. The performance of gas turbines is usually calculated by assuming an adiabatic flow, and hence neglecting heat transfer. While this assumption is not accurate for high turbine inlet temperatures (above 800 K), it provides satisfactory results at the operating point of conventional machines because the amount of heat transferred is generally low (less than 0.5% of thermal energy available at the turbine inlet). Internal and external heat transfer are therefore neglected and their influence is not taken into account. However, current heating needs and the decentralized production of electrical energy involve micro Combined Heat and Power (CHP) using micro-gas turbines (20-250 kW). In aeronautics, the need for a power source with a high energy density also contributes to interest in the design of ultra-micro gas turbines. These ultra and micro machines, which operate on the same thermodynamic principles as large gas turbines, cannot be studied with the traditional adiabatic assumption, as has been underlined by many authors such as Ribaud (2004), Moreno (2006) and Verstraete et al. (2007). During operation, heat is transferred from the turbine to the outside, bearing oil, casing and compressor, thus heating the compressor and leading to a drop in turbine performance. Consequently, the performances reported on the maps developed under the adiabatic assumption are no longer accurate.


Introduction
In the current economic and environmental context dominated by the energy crisis and global warming due to the CO 2 emissions produced by industry and road transportation, there is an urgent need to optimize the operation of thermal turbomachinery in general and of gas turbines in particular.This requires exact knowledge of their typical performance.The performance of gas turbines is usually calculated by assuming an adiabatic flow, and hence neglecting heat transfer.While this assumption is not accurate for high turbine inlet temperatures (above 800 K), it provides satisfactory results at the operating point of conventional machines because the amount of heat transferred is generally low (less than 0.5% of thermal energy available at the turbine inlet).Internal and external heat transfer are therefore neglected and their influence is not taken into account.However, current heating needs and the decentralized production of electrical energy involve micro Combined Heat and Power (CHP) using micro-gas turbines (20-250 kW).In aeronautics, the need for a power source with a high energy density also contributes to interest in the design of ultra-micro gas turbines.These ultra and micro machines, which operate on the same thermodynamic principles as large gas turbines, cannot be studied with the traditional adiabatic assumption, as has been underlined by many authors such as Ribaud (2004), Moreno (2006) and Verstraete et al. (2007).During operation, heat is transferred from the turbine to the outside, bearing oil, casing and compressor, thus heating the compressor and leading to a drop in turbine performance.Consequently, the performances reported on the maps developed under the adiabatic assumption are no longer accurate.

This chapter presents: 
The influence of heat transfer on the performance at an adiabatic operating point of a gas turbine, and a method for determining the actual operating point knowing the amount of heat transfer.


A study of heat loss versus the geometry scale of the volute and some conclusions concerning the limits of validity of the adiabatic assumption.

Relocating an adiabatic operation point subjected to heat transfer on a gas turbine map 2.1 Introduction
The performance of a turbomachine is usually represented graphically with dimensionless coordinates obtained under the assumption of adiabaticity from an existing machine.These maps are employed by manufacturers and users to determine the overall performance in order to design a new machine or to use the same machine in different operating conditions.The results obtained are not always accurate, however, as this assumption is not valid in all circumstances.Under the influence of heat transfer, the supposedly adiabatic operating point may shift its position.The dimensionless coordinates change, making it necessary to find the actual values for a correct assessment of performance.
In order to simulate the movement of an adiabatic operating point subjected to heat transfer, we consider the single-shaft gas turbine with a simple cycle; the maps are shown in Fig. 13 (Pluviose 2005).

Adiabatic, insulated and non insulated gas turbine versions
In its simplest form, as shown in Fig. 4, a gas turbine consists of:  A centrifugal or axial air compressor;  A combustion chamber in which a mixture of air and fuel is burnt;  A centripetal or axial turbine;  A user device (alternator, pumps, etc.).Neglecting the kinetic and potential energy, the formulation of the first law of thermodynamics in an open system applied to turbomachinery (compressor and turbine) is written: In transient conditions: In steady conditions: dh: elementary variation of enthalpy; w: elementary work exchanged; q: elementary amount of heat exchanged with the surroundings; Δh: specific enthalpy variation; w: specific work exchanged by the fluid with the moving parts of the machine; q: heat exchanged by the fluid with its surroundings.In conventional machines, calculations are usually done by assuming that the gas turbine is adiabatic (q = 0).The adiabatic version of a gas turbine is one in which the heat exchanged by the fluid with surroundings in the turbomachine is exactly zero (compressor: q 12 ; turbine: q 34 ).This version cannot be obtained in practice because of the difference in temperature between the turbine inlet and the surroundings.In order to approximate this ideal configuration, experimenters introduce some thermal insulation.This leads to the concept of insulated and non-insulated gas turbines.In an insulated gas turbine, the fluid in the turbomachine is assumed not to exchange thermal energy with the surroundings.In practice, this is achieved by insulating the machines with very low thermally conductive materials.However, because of the external insulation, internal heat exchange (in particular from the turbine to the compressor) is increased and must be taken into account.The non insulated gas turbine is equivalent to one in which internal and external heat transfer coexist.

Characteristics of the nominal operating point of an adiabatic gas turbine (Pluviose, 2005)
The assumptions are:

Characteristics of the nominal operating point of a non-adiabatic gas turbine
As indicated in section 2.2, there are two non-adiabatic versions of the gas turbine: the insulated and the non-insulated version.

Influence of heat transfer on the adiabatic nominal operating point
In order to understand the influence of heat transfer on the nominal operating point, we assume that the turbine is cooled so that the heat losses account for 15% of the adiabatic work.
For the non-insulated version, 60% of these losses are considered to contribute to the heating of the compressor (Rautenberg & al. 1981).
In the insulated version, it is assumed that all the heat lost by the turbine is received by the air in the compressor.In this study, the amount of heat exchanged is assumed known.The internal work depends on the outlet temperature.In practice, during operation, the outlet temperature of the machine can be measured.But, here, we choose T i2 >T i2ad (compressor) and T i4is <T i4 <T i4ad (turbine).The comparison of the results in Table 1, Table 3 and Table 4, leads to the following comments:  Energy efficiency has dropped from 16.2 to 13.2% (Table 1 and Table 3), and from 16.2 to 12.8% (Table 1 and Table 4);  Net power of the gas turbine has decreased from 1 526 to 1 128 kW, or by 26% (Table 1 and Table 3); from 1526 to 1010 kW, or by 34% (Table 1 and Table 4); We can therefore conclude that if the gas turbine operates with heat transfer while maintaining the same parameters as under nominal adiabatic operation, there is a drop in performance.This significant drop in performance makes it necessary to determine the actual operating point, taking into account heat transfer and the needs of user devices.For example, in a power plant equipped with a gas turbine, meeting the needs of the consumer requires that the power be kept constant.This involves finding the new non-adiabatic operating point which fulfills this criterion (same power at constant rotational speed).

Search for the new operating point of the compressor
The gas turbine operates under adiabatic or non-adiabatic conditions at 8000 rpm.For this speed, the output power is plotted versus the compression ratio in the three configurations: adiabatic, insulated and non-insulated versions (Figure 5).For the selected power value, the new compression ratios in insulated and non-insulated operation can be deduced.Then drawing this pressure ratio on the compressor map (Fig. 6), the mass flow rate and the efficiency of this point are deduced.

Comments:
It can be seen on Figure 5 that for the same compression ratio, the net output power is low in the insulated version.The highest output power is obtained in the adiabatic version.For the same power, the compression ratio is low in the non-insulated version.The lowest value is obtained in the adiabatic version.

Search for the new operating point of the turbine
As the rotational speed is constant and imposed, the required power can be achieved only by means of the quantity of injected fuel which has a direct influence on T i3 (turbine inlet temperature).

Fig. 5. Output power of the gas turbine versus compression ratio in adiabatic, non-insulated and insulated version
Due to the turbine characteristics, for a pressure ratio above that shown in Fig. 3, the reduced mass flowing through the turbine is a constant which was calculated for the nominal operating point in adiabatic conditions (Pluviose, 2005).A reduced mass flow makes it possible to determine the new value of T i3 corresponding to the new pressure p i3 .

Non-insulated gas turbine
The characteristics of the new operating points are summarized in table 5 (see calculations in the appendix).
Comparing the results of Table 1 to The compression ratio has increased from 7 to 7.17 with a relative deviation of 2.4%;  The turbine inlet temperature has risen from 973 to 1 041 K.The maximum is 1100 K;  The energy efficiency has decreased to 16.2 à 15.6% (the relative deviation is 3.7%).

Insulated gas turbine
In order to simplify calculations, we consider that all the heat lost by the turbine is fully received by the compressor q m (kg.s -1 ) When the results of tables 1 and 6 are compared, it can be seen that:  The mass flow rate has decreased from 20 to 19.5 kg.s -1 .The relative deviation is 2.5%;  The compression ratio has increased from 7 to 7.22.The relative increase is 3.14%;  The turbine inlet temperature has increased from 973 to 1 088 K.The limit is 1 100 K;  The energy efficiency has dropped from 16.2 to 14.9% (the relative deviation is 8.02%).Overall in the two operating configurations, the operating area on the compressor map has slightly narrowed.However, the temperature increase can be a problem, as this value has a direct influence on the turbine life span.Comparing tables 7 and 8, we can see that at iso speed and iso net power produced, the efficiency of the gas turbine is better in the non-insulated version.

Comparison with experimental results
The analysis and the results presented above for the nominal operating point were extended to the other points of the working area.
Figure 8 shows the experimental results obtained by Moreno (2006) on a small gas turbine (75 kW).
The tests were carried out in two versions: an insulated version at 39 000 rpm and a noninsulated one at 40 000 rpm.It may be noted that the speeds are not identical because of the practical difficulties of measurement in testing.But the relative difference of 2.5% between these two speeds can be considered negligible.
Figure 9 shows that, as in the case of our study, iso-speed, iso net power produced by the gas turbine, and energy efficiency are better in the insulated than in the non-insulated version.
Fig. 7. Energy efficiency versus net power produced (Moreno, 2006) This study not only confirms the decrease in performance due to heat losses, but also that this drop in performance is proportionally greater with the internal heat transfer.
Compared with the gas turbine studied here (1500 kW), it can be seen that the energy efficiency of the gas turbine used by Moreno (75 kW) is very low: 8% vs 16% at nominal power.This can be attributed to the size of the machine: it is a small machine with a nominal power about approximately twenty times smaller.Heat losses could be the cause of the drop in performance.

Heat transfer and geometric scale of gas turbines
As already mentioned in the introduction, the results of the performance calculations carried out in conventional turbomachines remain satisfactory at the full load operating point.In addition, the literature indicates that the impact of heat transfer on the performance of small turbomachines is negative.In these circumstances, it is important to know the characteristic size of the machines in which the assumption of adiabaticity is no longer valid.This study of heat transfer limited only to the volute of machines studied is conducted in similar operating conditions.It therefore calls on the notion of similarity.

The similarity of turbomachines: a summary
Similarity makes it possible, when a physical phenomenon for given operating conditions is known, to predict the same phenomenon for other conditions through laws involving dependent and independent dimensionless variables.Similarity generally focuses on two aspects: the geometric aspect that is relative to a family of geometrically similar machines, and the functional aspect that deals with a family of machines with similar operation.These two aspects are simultaneously taken into account.
For adiabatic machines, the dimensionless independent variables used to characterize the similar operating points are (Pluviose, 2005):  dimensionless mass flow rate  dimensionless speed.For adiabatic machines, the dimensionless independent variables used to characterize the similar operating points are ( Pluviose, 2005) q m : mass flow rate (kg.s -1 ); T i1 : turbomachine inlet temperature(K); p i3 : turbomachine inlet pressure (p a ); R : external radius of the rotor a (m); r : specific perfect gas constant (J.kg -1 ).
A study of similarity in non-adiabatic turbomachines operating with compressible fluid, conducted by Diango (2010) led to the generalization of Rateau's theorem.The author shows that these two dimensionless variables are also valid when operating with heat transfer.
From the foregoing and for a judicious comparison of heat exchange in different volutes, it is generally assumed that the fluid flows are similar.This leads to the following assumptions:  Inlet parameters are the same (pressure and temperature);  Reynolds numbers are equal;  The inlet dimensionless velocities are identical;  The mass flow rate is the same in the volutes.In the heat transfer equations, only the mass flow rate and the inlet conditions are involved.For two machines a and b, the first and last assumptions imply: q ma : mass flow rate of machine a (kg.s -1 ); q mb : mass flow rate of machine b (kg.s -1 ); p i1 : inlet pressure (p a ); T i1 : inlet temperature (K); R a : external radius of the rotor of machine a (m); R b : external radius of the rotor of machine b (m); r: specific perfect gas constant (J.kg -1 ).Due to the complex geometry of the casing (volute) of turbomachines and the difficulties of calculating heat transfer coefficients, a numerical approach has been adopted.The outer shape is a logarithmic spiral.In the volute, the fluid does not exchange mechanical energy with the surroundings, so:

Energy balance on a mesh volume
Variations in kinetic and potential energy are generally negligible compared to the enthalpy.Equation ( 5) becomes: In steady state, equation ( 7) becomes: w1, 2 q  : Heat exchanged through the walls; in1,2 h : Total specific enthalpy at inlet of the mesh volume (J.kg -1 ); out1,2 h : Total specific enthalpy at outlet of control volume (J.kg -1 ); • k w : Mechanical power exchanged by the fluid with surroundings (W); It is assumed in a first approximation that the specific heat of the burnt gas at constant pressure (cpf) does not vary in the mesh volume and that the inlet temperature of gas in the upstream guide is identical to the outlet of the volume vi.Knowing that: out1 out2 mm m q= q + q in Noted henceforth as: The expression (8) becomes :   eq burnt gas a p q hST T   (10) S : Heat exchange surface (m 2 ); eq h : Equivalent convective heat transfer coefficient (W.m -2 .K -1 ); burnt gas T : Average temperature of the burnt gas in the control volume (K); a T : Average ambient temperature (K)

Heat exchange surface
The mesh volume is considered as a tube in which fluid flows.The elementary exchange surface is the area of the contour of the tube, not including the passage through the upstream guide.It is equal to the perimeter multiplied by the elementary length of the spiral.
The equation of the outer profile of the logarithmic spiral volute ranging from 0 to 2 is given by equation ( 11), following Moreno (2006): external radius of the volute at = 0 ;  and 2 (m).
 are known, we can write the following relationships, from Moreno (2006), which describe the outer shape of the volute: a and b: constant real numbers (m) The arc length of the spiral at the position is given by equations ( 15) and ( 16), from Berger & Gostiaux (1992): The flow section has a trapezoidal shape whose dimensions must be calculated in order to estimate the perimeter.
To determine the large base b (i), of the trapezium, the equation used is: The angle generated by the height and the lateral side (Figure 9, Figure 10) is expressed by:  l tn : turbine nozzle width.The length of the lateral side (L l ) Hence the perimeter is: The heat exchange surface of the mesh volume is then: www.intechopen.com Advances in Gas Turbine Technology 228

Forced convection inside the volute
The heat transfer coefficient is given by equation ( 22 µ burnt gas : dynamic viscosity of burnt gas;

Free convection outside the volute
The Nusselt number is given by the Morgan correlation (Padet 2005) from the Rayleigh number (Ra).
h amb : coefficient of heat exchange with ambient air; h nc : coefficient of heat exchange by natural convection; h rad : coefficient of heat exchange by radiation.
The coefficient of heat exchange by radiation is given by equation ( 29): The equation of the model of mass flow in the volume is (30): q m : the mass flow at position ; q m0 : the mass flow at position 0.

Numerical results of modeling
Calculations are started from a nominal operating point of a turbine of a turbocharger whose dimensions are known (see Table 9).Geometric similarity requires that the linear dimensions of the similar volutes be multiplied by the same factor.Four other turbines have therefore been considered.The main dimensions and corresponding mass flow are recorded in table 10, which also shows the numerical results of the modeling.Q w : Thermal power lost through the walls of the volute; Q wdim : dimensionless thermal power lost through the walls of the volute.Figures 13 and 14 give the modeling results.Figure 13 shows the evolution of the heat exchange surface versus the inlet radius.The greater the volute, the smaller the surface to volume ratio.Small turbomachines therefore have a higher surface to volume ratio.The necessity of taking into account heat transfer in small turbomachines is largely confirmed by Figure 14: the heat losses in the volute are relatively greater.
In this study, when the inlet radius is halved, the surface to volume ratio doubles and the heat losses are multiplied by about 2.5

Conclusion
Internal and external heat transfer induces a drop in the performance of gas turbines.This study shows that the performance of small turbomachines evaluated with the assumption of adiabaticity is not accurate.For a given operating point, the mass flow and the compression ratio recorded on the maps and the calculated performance do not correspond to the actual characteristics when the machine operates with heat transfer.
The assumption that heat losses represent 15% of the work of adiabatic turbines, of which 60% is received by the compressor (non-insulated), leads to overestimating the power by 35% and the energy efficiency by 23% Insulation of the turbine, although it seems to be a solution to maintain the operating characteristics of adiabatic turbines, leads in fact to increasing the drop in performance.
For the insulated version, the net power is overestimated by 51% and efficiency by 26.6%.In the absence of an adiabatic gas turbine (ideal machine), which provides the best performance, we must avoid insulating the turbine in order not to decrease performance still further.
To maintain the level of performance, and in particular the net power produced by the gas turbines, despite heat transfer, adjustments are needed.They consist mainly in increasing the fuel flow, resulting in an increase in the turbine inlet temperature.In the case of our study, the fuel flow increase is 3.5% in the non-insulated version and 8.5% in the insulated version.The turbine inlet temperature increase is 6.4% in the insulated version and 11.8% in the non-insulated version.
Finally, this study confirms that the assumption of adiabaticity is not valid in turbochargers, micro and ultra-micro gas turbines.Compared to the available thermal energy at the turbine inlet, heat losses increase with the surface to volume ratio which decreases in small-sized machines.The quality of operation of small turbomachinery cannot be characterized with isentropic efficiency which has no physical meaning because of the relative importance of heat transfer.
The proposal of a new performance indicator and the development of new maps available for any type of thermal turbomachines will therefore be the subject of our forthcoming investigations.

Acknowledgment
The authors would like to acknowledge the French Cooperation EGIDE for funding this study.
Power of the gas turbine: P GT

Search for new turbine inlet temperature
The variation in the expansion ratio of the turbine versus the reduced mass flow (Figure 3) shows that when the expansion ratio is greater than two (2), the reduced mass flow remains constant (Pluviose M., 2005).This reduced flow constant calculated in adiabatic conditions enables the new turbine inlet temperature (T i3 ) corresponding to the new pressure (p i3 ) to be determined by the following equations.

Fig. 6 .
Fig. 6.Adiabatic compressor map with operating points in the three configurations

Fig. 11 .:
Fig. 11.Mesh volume of the turbine voluteThe first law of thermodynamics can be written in any time by the following equation:

Fig. 12 .
Fig. 12.The width of the upper volute versus the unrolled spiral viscosity of the air; T a : air temperature.The coefficient of external heat exchange is the combination of a coefficient by natural convection and exchange by radiation defined by equation 28.

Fig. 13 .
Fig. 13.Ratio of heat exchange surface (S) and the volume (V) of the volute versus the inlet radius Thermal power lost in the exhaust Q exh =Q -P -P -P =10253-66-1042-1526.2=7618.8kWech CC ml th l TAG Q

Table 1 .
Characteristics of the operating point of an adiabatic gas turbineThe energy balance at the operating point is shown in Table2(see the detailed calculations in the appendix).

Table 2 .
Energy balance at the operating point of the adiabatic gas turbine

Table 3 and
Table4summarize the new performances calculated for the adiabatic gas turbine used in insulated and non-insulated versions at the adiabatic operating point.

Table 4 .
Characteristics of nominal operating point in insulated version

Table 5 .
Characteristics of the new operating point in the non-insulated version

Table 6 .
Characteristics of the new operating point in the insulated version

Table 7 .
Energy balance of the new operating point (non-insulated gas turbine)

Table 8 .
Energy balance of the new operating point (insulated gas turbine) )

Table 10 .
Heat loss through the volutes of different sizes www.intechopen.com ). T i2 = 622.68K, Q 12 = 1042 kW (thermal power received by the compressor) Power of the gas turbine: P GT Thermal power received by the compressor: Q 12