Variants of the basic cycle

Free turbines

Most designs used for gas turbine sets use two turbines, one to drive the compressor and a free turbine. The free turbine drives the load and it is not connected directly to the compressor. It may also run at a different speed to the compressor.

Fig.4 shows such a layout with turbines in parallel configuration. Fig.5 shows the layout with series configuration.

Fig.4. Parallel turbines

Fig.5. Series turbines

Improving an air standard cycle

Intercooling

If the air is compressed in stages and cooled between each stage, then the work of compression is reduced. The layout is shown on Fig.6.

Let the compression process be divided into two stages. Air, after being compressed in the first stage, is cooled to initial temperature in a heat exchanger, called an intercooler, and then compressed further in the second stage.

Fig.6. Two stage compression

Reheating

The reverse theory of intercooling applies. If several stages of expansion are used and the gas reheated between stages, the power output is increased. The layout is shown on Fig.7.

I n each Brayton cycle with more than one turbine, we have chosen the pressures so that the pressure ratio for each turbine is roughly the same as for all the rest of them. The same is true for the compressors. Why do we take this approach? There are two reasons. First, in keeping with our overall goal of improving cycle efficiency, we want the mean temperature of heat addition to be as high as possible and the mean temperature of heat rejection to be as low as possible. It turns out (and this can be shown with a math) that we achieve this by keeping the pressure ratios of the turbines even.

The other reason is a purely pragmatic design consideration. If we are going to order turbines, larger ones tend to be more expensive than smaller ones (both in initial cost and in overhead for physical space and maintenance). The same will tend to be true of compressors.

Fig.7. Reheating

Regeneration (exhaust heat exchangers)

Regenerators or air heaters are applied in gas-turbine plants to preheat the air for combustion with exhaust gas. This results in less fuel being burned in order to produce the same temperature prior to the turbine and so makes the cycle more efficient. The layout of such a plant is shown on Fig.8.

It is possible to heat up the air before it enters the combustion chamber by use of an exhaust gas heat exchanger if only the gas leaving the turbine is hotter than the gas leaving the compressor.

Fig.8. Plant layout

HOMEWORK PROBLEM:

A simple ideal Brayton cycle with air as the working fluid has a pressure ratio r_p (_к). The air enters the compressor at Т₁ (Т_н - inlet temperature) and р₁ (р_н - inlet pressure). After constant pressure heating, the temperature is Т₃ (Т_г ).

Working fluid - 1 kg of air: k = 1.4; R=287 J/kg K; cp = 1.005 kJ/kg K.

Air-standard assumptions: Assumptions that the compression and expansion processes are adiabatic (insulated) and reversible (isentropic), that there is no pressure drop during the heat addition process, and that the pressure leaving the turbine is equal to the pressure entering the compressor. The combustion process is replaced by a heat addition process from the external source. The exhaust process is replaced by a heat rejection process that restores the working fluid to its initial state.

1. Calculate the following:

- the air temperature, density (volume) and pressure at the compressor and turbine exits,

- change of internal energy, enthalpy, entropy in processes,

- the heat in the processes,

- the work in the processes,

- change of internal energy, enthalpy, entropy in cycle,

- the net work output,

- the cycle thermal efficiency.

2. Show cycle on T-s and p-v diagrams (Temperature-Entropy and Pressure-Volume Diagrams).

3. Draw cycle efficiency as a function of pressure ratio; the net work output as a function of pressure ratio.

4. Improve cycle efficiency (cycle operates between the same high and low temperature limits) using the following variants:

• Brayton cycle with a regenerative heat exchanger,

• Brayton cycle with an intercooling,

• Brayton cycle with an intercooling and regeneration,

• Brayton cycle with a reheating,

• Brayton cycle with a reheating and regeneration,

• Brayton cycle with an intercooling, a reheating and a regeneration.

Our purpose to examine several improvements that can be made to the simple air-standard cycle which increase its efficiency and work.

Notice. To draw cycle on p-v diagram you have to take two additional points on a line representing compression process (1-2 or н-к) and two points for expansions process (3-4 or г-т). You arbitrarily choose points belong to pressure interval p₁  p₂, using relation between parameters in adiabatic process you can determine volume corresponding pressure of additional points(x_1, x_2, x_3, x₄).

To draw cycle on T-s diagram take two additional points for processes 2-3 (к-г) and 4-1 (т-н). Know temperatures of chosen points find change of entropy and plot processes 2-3(к-г) and 4-1 (т-н) according to 4 points.

Functional relations w=f(r_p) and η_t=f(r_p) are drawn according to 3 values of pressure ratio: pressure ratio given for calculation, optimal pressure ratio and additional arbitrarily chosen value (if r_p>r_{p opt} additional r_{p ad}< r_{p opt}; if r_p<r_{p opt} additional r_{p ad}> r_{p opt}).

ANALYSIS OF BASIC IDEAL BRAYTON CYCLE:

This cycle consist of such processes:

• Adiabatic compression in compressor (H-K);

• Isobaric heat addition to the system in combustion chamber (K-Г);

• Adiabatic expansion in turbine (Г-T);

• Isobaric heat rejection (T-H);

Fig.9. A basic gas turbine plant

1- filter; 2- compressor of low pressure; 3- compressor of high pressure; 4- combustion chamber; 5- turbine of high pressure; 6- turbine of low pressure; 7- pump; 8- cock;

Determination of air parameters at main points:

• Parameters at point H (1):

The T_н and р_н are known, volume at point H (1) ν_н (or ρ_н) can be determined from ideal gas equation of state:

; ; ;

• Parameters at point K (2):

; ; ; ;

• Parameters at point Г (3):

T_г – is given; p_г=p_к ; ; ;

• Parameters at point T (4):

р_т=p_н; T_т= T_г/r_P^(k-1)/k; ; ;

Determination of change of energy parameters in processes:

• 

• 

• 

• 

where ,

Determination of work and heat in processes:

q_H-K=0; w_com = w_H-K = c_р (T_к –T_н);

q_K-Г=q₁=c_р (T_г – T_к); w_K-Г=0;

q_Г-T=0; w_exp= w_Г-T = c_р (T_г- T_т);

q_T-H=q₂= c_р(T_н - T_т); w_T-H=0;

Determination of net work and thermal efficiency of the cycle:

; .

w_cycle= w_exp- w_c= η_th q₁;

w_exp – expansion work;

w_com – compression work.

Determination of optimal parameters:

; ; w_{cycle max}= η_{th опт} q_1опт.

Plot the p-v and T-s diagrams.