Design Analysis of Micro Gas Turbines in Closed Cycles

Abstract

The problems faced by designers of micro-turbines are connected with a very small volume flow rate of working media which leads to small blade heights and a high rotor speed. In the case of gas turbines this limitation can be overcome by the application of a closed cycle with very low pressure at the compressor inlet (lower than atmospheric pressure). In this way we may apply a micro gas turbine unit of accepted efficiency to work in a similar range of temperatures and the same pressure ratios, but in the range of smaller pressure values and smaller mass flow rate. Thus, we can obtain a gas turbine of a very small output but of the efficiency typical of gas turbines with a much higher power. In this paper, the results of the thermodynamic calculations of the turbine cycles are discussed and the designed gas turbine flow parts are presented. Suggestions of the design solutions of micro gas turbines for different values of power output are proposed. This new approach to gas turbine arrangement makes it possible to build a gas turbine unit of a very small output and a high efficiency. The calculations of cycle and gas turbine design were performed for different cycle parameters and different working media (air, nitrogen, hydrogen, helium, xenon and carbon dioxide).

1. Introduction

Power plants with gas microturbines are intensively developed nowadays [1], including those operating in polygeneration systems [2,3]. It seems that microturbine technology will be frequently applied in distributed power generation [4,5]. This technology has greatly improved its efficiency thanks to the use of electric generators with rare earth magnets [6,7,8]. On the other hand, efforts are being made to improve the efficiency, durability and cost reduction of the energy systems based on fuel cells [9,10,11] or photovoltaic cells [12,13].

The development of technology has made it possible to develop Brayton closed cycles, in which various working media can be used [14]. The closed gas turbine cycle was patented in 1935 by J. Ackeret and C. Keller. The first closed cycle with 2 MW oil-fired gas turbine (AK-36) was built in Switzerland in 1939, followed by another six units built in Switzerland and Germany [15,16]. Gas power plants with a closed cycle and air as a working medium showed a very high reliability at that time. The most representative was the 50 MW helium plant installed in Oberhausen which operated from 1975 to 1987 in Germany [17,18]. Work on the progress of these power plants has been suspended due to the dynamic development of gas turbines in open cycles [19]. Currently, these technologies have become of interest again because of the possibility of their application in nuclear power plants [20,21] or in those power stations that use solar energy [22]. In the systems with nuclear reactors, closed cycles with air, CO₂ [23] or helium [24] are considered for application. Other working media, such as nitrogen or xenon, are also taken into account [25]. Supercritical CO₂ power plants are used which allow to obtain a very good efficiency at low temperatures at the turbine inlet [26,27].

In order to increase the efficiency, closed cycle power plants are modified [28]. The parameters of the working medium are optimized [29] and regenerators [30] and intercoolers [31] can sometimes be applied.

A scheme of a simple closed gas turbine cycle is shown in Figure 1a, [32]. The working medium is compressed in the compressor I and then heated in the high temperature heat exchanger IV. Next, hot gases expand in turbine II, which drives electric generator III. After expansion, the temperature of gases decreases in low temperature heat exchanger V and they return to the compressor inlet. In comparison to the simple open cycle, Figure 1b, the combustion chamber is replaced by an externally fired gas heater IV (source of upper temperature), while the gas cooling heat exchanger V replaces the atmosphere as the source of lower temperature.

The closed cycle presented in Figure 1a is the simplest possible. More complex cycles contain regeneration, intercooling and reheating systems. The advantages of power plants working in a closed cycle are given below [32]:

-

possibility of burning different kinds of fuel (due to an external combustion chamber),

-

possibility of using the high pressure of the medium (higher pressure means higher medium density, on the one hand leading to smaller dimensions for the same output, on the other hand enabling the building of high output units),

-

possibility of applying different gases as a working medium, in particular gases with better heat exchange parameters and a high value of specific heat c_p, remarkably reducing dimensions and increasing specific turbine output.

The main disadvantage of the closed gas turbine cycle is the necessity of introducing additional heat exchangers, especially the high temperature exchanger IV, which is large in size, heavy and costly (compared with a typical combustion chamber). The low temperature cooler V also increases the dimensions of the whole power plant. Gas turbines can be used in closed cycles with high-temperature gas-cooled reactors (HTGR) and in this form they constitute a competitive alternative to light water nuclear power plants.

As a rule, the main advantage of the closed cycle is the possibility of using the high pressure of the working medium and increasing the output of the power unit. The interpretation of the thermodynamic processes for different power outputs is presented in Figure 2. We propose a reverse situation: a closed cycle with a very low value of pressure at the compressor inlet (lower than the atmospheric pressure). In this way we may apply a gas turbine unit of a relatively high efficiency in the same range of temperatures and the same pressure ratios but in the range of smaller pressure values and a smaller mass flow rate. Thus, we can obtain a gas turbine of a very small output but of the efficiency typical of gas turbines of much higher power.

The most important innovation is that instead of a classical approach to closed gas turbines, a new feature of a closed cycle was shown and applied to design a micro gas turbine of a higher efficiency than the typical engines of the same power. These types of power plants have not been discussed in literature so far.

By applying the proposed method, the micro gas turbines can achieve an efficiency which is higher than that of typical open cycle turbines. For example, the performed analyses have clearly proved that it is possible to design a 10 kW gas micro turbine of a relatively high efficiency of about 31.2% (which is a very competitive value).

2. Modelling

The design analysis was carried out for the turbine closed cycle with a regenerator. The schema of the cycle and its interpretation in a temperature-entropy diagram are shown in Figure 3a and Figure 4, respectively, while the open cycle with a regenerator is presented in Figure 3b.

The classical approach to designing gas turbine plants usually leads to a situation where the decrease in the assumed output results in lower values of volume flow rate, lower diameters, lower blade heights, a drop in the efficiency and an increase in the rotor speed. These relations are illustrated by the comparison of the examples of micro turbines of 50 kW, 35 kW and 10 kW.

The flow parts of the compressors (Figure 5) and the turbines (Figure 6) have been designed by CFD (Computational Fluid Dynamics) codes while the heat exchangers (regenerators) and the combustion chambers have been calculated with the use of standard thermodynamics relations, occasionally applying the iteration method. The symbols and subscripts used in the paper are presented in

Table 1. List of symbols.

Symbol	Description	Unit
D	diameter	[m]
i	enthalpy of unit mass	[kJ/kg]
l	blade height	[m]
m	mass flow rate	[kg/s]
Ma	Mach number	[-]
n	rotational speed	[rpm]
N	power	[kW]
p	pressure	[Pa]
Re	Reynolds number	[-]
Q	heat flux	[kW]
s	entropy of unit mass	[kJ/kg·K]
T	temperature	[°C]
V	volumetric flow rate	[m3/s]
η	efficiency	[-]
α1	angle of absolute velocity vector at nozzle exit	[°]
α2	angle of absolute velocity vector at blade exit	[°]
β1	angle of relative velocity vector at nozzle exit	[°]
β2	angle of relative velocity vector at blade exit	[°]
Δ	gradient	[-]
П	compressor pressure ratio	[-]
σ	regenerator efficiency	[-]

and

Table 2. List of used subscripts.

Symbol	Description
G	generator
K	compressor
el	electrical
m	mechanical
n	leakage
R	regenerator
T	turbine
D	delivered
1, 2, …	numbers on diagrams

.

Calculations were made with the use of standard formulae (the indices refer to the points marked in the diagram, Figure 1 and Figure 3):

-

heat delivered to the working media (heater IV):

$$q_1=\left(i_0-i_6\right),$$

(1)

-

heat rejected with the water cooling the heater (V):

$$q_2=\left(i_4-i_1\right),$$

(2)

-

turbine work obtained by CFD calculations,

-

compressor work obtained by CFD calculations.

The flow parts of the turbine and the compressor have been calculated using ANSYS software. The examples of the distribution of the calculated parameters in flow channels (velocity lines and pressure) are presented in Figure 5 and Figure 6 for the compressor stage and the turbine stage, respectively. The numerical mesh for the compressor flow channel consisted of about 54,000 nodes and 48,600 elements. The example of a mesh at 50% blade span is shown in Figure 7a. Numerical meshes for the turbine nozzles and the rotor blades are shown in Figure 7b,c, respectively. Numerical stationary calculations have been performed assuming the multiple reference method (MRF method), the k-ω shear stress transport (SST) turbulence model and the circumferential symmetry. Air as a working medium has been treated as a viscous and compressible gas.

The energy efficiency is defined as the ratio of the net electric power obtained related to the heat flux supplied to the system and given by the equation:

$${\eta }_{el}=\frac{N_{el}}{{\dot{Q}}_D}.$$

(3)

Depending on the variant, the net electric power is the power N_T obtained in the turbine, diminished by the power N_K consumed to drive the compressor and by the losses in the system (generator efficiency η_G, mechanical efficiency η_m, leakage losses).

The effectiveness of the regenerator is defined as the ratio of the actual temperature increase in the exchanger to the maximum possible increase and is determined by the formula:

$${\sigma }_R=\frac{\Delta T_{\mathit{real}}}{\Delta T_{\max }}=\frac{T_{2^{\prime }}-T_2}{T_4-T_2}.$$

(4)

The assumed values of the efficiences or the losses of particular engine elements are presented in

Table 3. Assumptions for the design analysis of turbine variants.

Description	Unit	Value
compressor efficiency	[-]	from CFD calculations of particular variant
turbine efficiency	[-]	from CFD calculations of particular variant
mechanical efficiency	[-]	0.980
leakage losses	[-]	0.02
generator efficiency	[-]	0.900
sum of pressure losses	[-]	0.06

[32,33,34]. The chosen numbers can be considered as good average values but not the highest.

The calculations have been performed for temperature T₃ in front of the turbine equal to T₃ = 850 °C (within the range typical of gas turbines of very small output). The parameters of the working media have been determined using REFPROP [35] media library.

3. Results and Discussion

The gas turbine units and the whole power plants of 10 kW, 35 kW and 50 kW were designed. In Figure 8 the example of the turbine power plant is shown, while the main parameters of the particular variants are presented in

Table 4. The main parameters of the gas turbine sets.

Description	Unit	Value
Ne	[kW]	50.0	35.0	10.0
П	[-]	2.6	2.4	2.2
p1	[MPa]	0.1000	0.1000	0.1000
T3	[°C]	850.00	850.00	850.00
ηREG	[-]	0.87	0.87	0.88
mpow	[kg/s]	0.5181	0.4722	0.1681
ηel	[-]	0.31259	0.26911	0.23665
n	[rpm]	55,000	65,000	120,000
D1K	[m]	0.0790	0.0673	0.0367
D2K	[m]	0.1437	0.1223	0.0667
ηK	[-]	0.83	0.78	0.75
Maw2	[-]	0.29	0.33	0.32
Mac2	[-]	0.74	0.73	0.73
Rec3	[-]	326,161.41	327,239.87	335,282.76
α1	[°]	90.00	90.00	90.00
β1	[°]	30.00	30.00	30.00
β2	[°]	44.01	45.12	41.53
α2	[°]	15.51	15.98	12.92
l1K	[m]	0.0159	0.0139	0.0750
l2K	[m]	0.0085	0.0070	0.0043
DT	[m]	0.1477	0.1151	0.0688
l1T	[m]	0.0170	0.0164	0.0120
l2T	[m]	0.0180	0.1720	0.0124
ηT	[-]	0.83	0.79	0.76
Mac1	[-]	0.71	0.73	0.74
Maw2	[-]	0.74	0.79	0.79
α1	[°]	17.50	17.00	11.00
β1	[°]	83.32	70.79	85.11
β2	[°]	21.78	21.26	14.73
α2	[°]	87.04	73.96	89.93

and in Figure 9, the compressor rotors and Figure 10, the turbine discs.

The highest efficiency, equal to about 32%, was obtained for 50 kW turbine, while the lowest (about 23.6%) for 10 kW unit. The 50 kW turbine has the highest diameter, the longest blades and the lowest rotor speed (55,000 rpm), while the 10 kW turbine has the lowest diameter, the smallest blades and the highest rotor speed (120,000 rpm). Thus, the dimensions and the operating parameters vary remarkably for the turbines of different output (Table 4 and Figure 9 and Figure 10). The calculations and the designs have confirmed a well-known statement that the lower the turbine power the more difficult it is to build a turbine of good efficiency.

The situation described above illustrates a typical approach to the designing of gas turbines, however, thanks to the application of a closed cycle with a very low value of pressure at the compressor inlet (lower than the atmospheric pressure), it is possible to obtain a gas turbine of a very small output but with the efficiency typical of gas turbines of much higher power. We may choose a micro gas turbine unit of an accepted design and efficiency to work in the same range of temperatures and the same pressure ratios, but with smaller pressure values and a smaller mass flow rate. Let us consider the gas turbine unit of 50 kW presented above. Applying this engine in a closed cycle and changing the value of pressure at the compressor inlet, it is possible to obtain lower output with the same efficiency. The results are shown in Table 4 and the interpretations of the cycles are presented in Figure 11.

As a result of the calculations, we may conclude that it is enough to apply a highly efficient gas turbine in a closed cycle and reduce the pressure at the compressor inlet in order to obtain a power plant of a smaller output but the same high efficiency. In the presented example of the 50 kW turbine with a reduction of pressure in front of the compressor from 0.1 MPa to 0.07 MPa or to 0.02 MPa allows us to receive 35 kW and 10 kW, respectively. All the variants have the same efficiency (31.26%), identical rotor speed (55,000 rpm), the same pressure ratio (2.6) and the same upper temperature (T₃ = 850 °C) (Table 4). It seems that the proposed method enables us to obtain a gas turbine of a very small output but high efficiency and a relatively small rotor speed. Thus, a new feature of a closed gas turbine cycle was shown and applied to design a micro turbine of a relatively high efficiency. This conclusion is one of the most important innovations that has not been described in literature so far.

Closed gas turbine cycles make it possible to apply different working media, especially the gases with better heat exchange parameters and a high value of specific heat c_p, thus remarkably reducing the dimensions and, at the same time, increasing specific turbine output. The calculations of the closed cycles have been performed for six different fluids: air, nitrogen, helium, carbon dioxide, hydrogen and xenon and for various values of the temperature in front of the turbine (800–1000 °C, the range typical of gas turbines of very small output). The parameters of the working media have been determined using REFPROP [35] media library. In Figure 12 the overall efficiency of the cycles with a regenerator and the upper temperature T₃ = 850 °C are presented as the function of the compressor pressure ratio. The engine efficiency reaches over 36% for air, nitrogen and hydrogen. It is slightly smaller for helium and xenon and about 2% lower for carbon dioxide. The optimum pressure ratio varies from less than 2 for helium and xenon to about 3.7 for carbon dioxide.

4. Conclusions

The authors have presented the results of the design analysis of micro turbines proving that it is possible to increase the efficiency of gas turbines of small output. By the application of a closed cycle with a very low value of pressure at the compressor inlet a gas turbine of a very small output is obtained which has the efficiency typical of gas turbines of a much higher power. We may choose a well-designed micro gas turbine unit of high efficiency and apply it to work in the same range of temperatures and the same pressure ratios but with smaller pressure values and a smaller mass flow rate. Thus, a gas turbine of a very small output can operate with the efficiency typical of gas turbines of a much higher power. In the presented example the efficiency of the 10 kW turbine has increased from 23.6% to 31.2%.

The performed analyses have clearly proved that applying closed gas turbine cycles is possible when we use different working media. The cycle and the gas turbine design calculations were performed for different cycle parameters and different working media (air, nitrogen, hydrogen, helium, xenon and carbon dioxide). Their better heat exchange parameters and a higher value of specific heat c_p can reduce the engine dimensions and increase the specific turbine output.