APPLICATION OF A NOVEL THERMO-ECOLOGICAL PERFORMANCE CRITERION : EFFECTIVE ECOLOGICAL POWER DENSITY ( EFECPOD ) TO A JOULE-BRAYTON CYCLE ( JBC ) TURBINE

This study presents an application of a new performance analysis criterion named as Effective Ecological Power Density (EFECPOD) to a Joule-Brayton cycle (JBC) turbine. The turbine performance is expressed a single value by the proposed criterion using effective efficiency, effective power, cycle temperature ratio and volume. NOx formation and turbine dimensions are considered by the cycle temperature ratio and turbine volume, respectively. The turbine volume is also related to production cost of the heat engine. Therefore, the proposed criterion is essential for multi purpose optimization. Furthermore, this criterion can be developed and applied to the other gas cycle and heat engines. Also, the influences of engine design parameters such as cycle temperature ratio, pressure ratio, turbine speed, and equivalence ratio on the EFECPOD have been examined based on FiniteTime Thermodynamics Modelling (FTTM). In order to obtain realistic results, temperature-dependent specific heats for working fluid have been used and heat transfer and exhaust output losses have been taken into consideration. The results presented could be an essential tool for JBC turbine designers.

modeling.Mahto and Pal [13] performed thermodynamic and thermo-economic analysis of simple combined cycle power plant with gas turbine blade cooling by means of fogging.Fernández-Villacé and Paniagua [14] developed a methodology to evaluate exergetic effectiveness, propulsive efficiency, total loss and subcomponent losses of a combined cycle engine.Pantaleo et al. [15] proposed a thermo-economic assessment of a small scale micro-gas turbine fuelled with solid biomass and natural gas in Italy.Singh and Kaushik [16] presented an evaluation and thermoeconomic optimization for a Brayton-Rankine-Kalina combined triple power cycle using Specific Exergy Costing methodology.Goodarzi et al. [17] modified regenerative Brayton and inverse Brayton cycle partially by passing the airflow entering the regenerator.The results showed that higher power output with reasonable thermal efficiency can be generated by adjusting the bypass mass flow ratio.Al-Sulaiman and Atif [18] thermodynamically performed a comparison study for different supercritical carbon dioxide Brayton cycles integrated with a solar power tower.Le Roux et al. [19] defined the first law and second law efficiencies of a stainless steel closed-tube open rectangular cavity solar receiver for a small-scale solar thermal Brayton cycle.Dutta et al. [20] proposed a solid sorption based Brayton cycle using R134a, CO2, R507a, propane, R32 and R410a with activated carbon as sorbent.
This study reports a new performance analysis criterion named as EFECPOD includes the effective efficiency, effective power, cycle temperature ratio and turbine volume.In the literature, there is not any criterion covers effective efficiency, effective power, maximum combustion temperatures and turbine dimensions altogether, based on finite time thermodynamics.Furthermore, a comprehensive comparison for the design parameters such as pressure ratio, turbine speed, turbine diameter, turbine length, heat transfer coefficient, equivalence ratio has been presented.The results could be used by real turbine designers to optimize the JBC gas turbines in terms of dimensions, performance and NOx emissions.

Figure 1. P-v diagram for the irreversible Diesel-Miller cycle
This study presents a comprehensive analysis for JBC which is depicted in Figure 1.A numerical simulation of EFECPOD is carried out based on FTTM.In the analysis, pressure ratio (  ) , residual gas fraction (RGF), turbine speed ( N ), inlet temperature ( 1 T ), inlet pressure ( 1 P ), combustion chamber wall temperature ( W T ), mass flow rate of the air ( m ), heat transfer coefficient ( tr h ), turbine bore ( b ) and length ( L ) are defined as follow; 4, 5%, 3000 rpm, 300 K, 100 kPa, 400 K, 1 kW/m2K, 0.5 m, 1 respectively, at the standard conditions.
In the present model, the evaluated criteria called effective ecological power density, effective power and effective efficiency could be stated as follow: Where, the total heat addition   in Q at constant pressure (2-3) and the total heat rejection   out Q at constant volume (4-1) could be written as below:  is isentropic efficiency for the compression process,  is pressure ratio and it may be expressed as: Where f Q is the total heat potential of the injected fuel and it is given as below: Where u H is lower heat value (LHV).f m is time-dependent fuel mass and it can be expressed as follows: Where f m is fuel mass per cycle (kg).
, fc Q is heat released by combustion; ht Q is the heat loss by heat transfer into cylinder wall and they are given as below: Where, c  is combustion efficiency.It can be written as below [21-24]:  is equivalence ratio and it can be written as below: Where, a m is air mass per cycle (kg), V T is total turbine volume, sur A is surface area where heat transfer is carried out, st F is stoichiometric fuel-air ratio [25] and they are given as follow: (12.01 1.008 16 14.01 ) 28.85 Where b and L are turbine bore (inner diameter) and turbine length, 4 v is specific volume of the state point 4 in which the specific volume of cycle is the maximum.T m is the total mass of the working fluid and it can be expresses as follows: Where rg m is mass residual gas (kg) per cycle, which is given as: Where a  and rg  are the densities of the air and residual gas in the turbine, they can be obtained from functions below: 11 ( , ) Where mix T is average temperature of air-steam mixture.They are given as below: a R and rg R are gas constants of air and residual gas.Their values are taken as 0.287 kJ/kg.K The compression ratio ( r ) is given as: Where N and RGF are the turbine speed and the residual gas fraction, V a and V rg are volumes of air and residual gas, f stands for function.The functional expressions are obtained by using EES software [26] Where subscript "1" stands for the condition before the compression process (state point 1).

1
T and 1 P are in-cylinder temperature and pressure at the beginning of compression process.The fuel used in the model is octane and its chemical formula is given as C8H18 [25].
Where , , ,     are atomic numbers of carbon, hydrogen, oxygen, nitrogen in fuel, respectively. is molar fuel-air ratio [25]: Where me T and W T are mean combustion temperature and cylinder wall temperature.
The equations for reversible adiabatic processes (1-2s) and (3-4s) are respectively as follows: Where,    is named as pressure ratio.For irreversible conditions, 2 T and 4 T could be written as below: Where

C
 and E  are isentropic efficiencies for the compression and expansion processes, respectively.

RESULTS AND DISCUSSION
In this study, a new performance anlysis criterion named as EFECPOD and FTTM have been applied to a JBC gas turbine.
Figure 2 show the effects of pressure ratio on the EFECPOD with respect to equivalence ratio.There are optimum points of the equivalence ratio for the EFECPOD at the constant turbine speed and air mass flow rate.The equivalence ratios give the maximum EFECPOD and effective efficiency increase to a particular value and then start to decrease with increasing equivalence ratio.The maximum values of EE and EFECPOD increase with increasing pressure ratio owing to high temperatures and pressures in the combustion chamber.Also, the turbine volume decreases with increasing pressure ratio to provide constant air mass flow rate and turbine speed.Therefore, higher performance can be obtained at the lower turbine volume.
Figures 3 and 4 show the influence of turbine speed on the EE and EFECPOD for constant pressure ratio-air mass per cycle and constant pressure ratio-mass flow rate of the air introduced into the compressor.Total intake air and injected fuel per second enhance with increasing engine speed, therefore, turbine performance increases at the constant cycle air mass conditions.At this condition, the EE and EFECPOD increase since the turbine volume and maximum combustion temperatures increase with increasing turbine speed.However, the turbine volume which is needed to provide constant air mass flow rate abates with increasing turbine speed.

EFECPOD
of the length and diameter are related to turbine dimensions, their changes affect the performance reversely, since the heat transfer area decreases with the diameter increment and the length reduction.Increasing heat transfer area causes to performance retrogression as higher heat transfer loss is occurred.Figure 7 demonstrates the effects of heat transfer coefficient on the EE and EFECPOD at constant mass flow rate and pressure ratio.As expected, the turbine performance abates with increasing heat transfer coefficient since total heat transfer loss raises.
Figure 8 demonstrates the effects of pressure ratio, equivalence ratio and turbine speed together.It is clear that turbine speed and pressure ratio positively affect the performance parameters.However, there is an optimum point for the equivalence ratio which gives the maximum EFECPOD values.It is approximately 0.8 for the EFECPOD.The turbine performance decreases at higher values of equivalence ratio due to lower combustion  Figure 9.The variation of the EFECPOD with respect to  at constant N and m for different  efficiency and higher heat transfer and exhaust losses.As can be seen in the figures, the turbine volume is considerably affected by equivalence ratio and pressure ratio.The turbine volume increases with increasing turbine speed and equivalence ratio; decreasing pressure ratio.The maximum turbine volumes are obtained with 4 of the pressure ratio and 1.1 of the equivalence ratio.At the different  conditions, the maximum combustion temperatures increase and the turbine volumes decreases with increasing pressure ratio.The EFECPOD increases with increasing turbine speed because intake air mass enhances with increasing turbine speed.Another substantial point is that NOx formation is very sensitive the combustion temperatures, thus, it can be said that NOx increases with increasing pressure ratio and turbine speed at the constant  and air m conditions.Figure 9 demonstrates the effects of equivalence ratio on the turbine performance with respect to changing pressure ratio at constant turbine speed and the mass flow rate of the air.It is obvious that the EFECPOD raise with the enhancing pressure ratio.As similar to previous figures, the optimum points of the equivalence ratios which give the maximum EFECPOD are observed.The maximum value of the EFECPOD increases to a specified value of the equivalence ratio which is 0.8 and then start to decrease.However, the maximum volume is seen at 1.1 of the equivalence ratio.

CONCLUSION
A new performance analysis criterion has been developed and applied to a gas turbine cycle.The effects of the engine design and operating parameters on the performance parameters and energy losses of a gas turbine have been investigated by using the presented analysis criterion.A comprehensive parametrical study has been performed based on numerical examples.In the parametrical studies, the effects of pressure ratio (  ), turbine speed (N), turbine diameter ( b ), turbine length ( L ), equivalence ratio ( ) and heat transfer coefficient ( tr h ) on the performance have been examined.The results showed that the determined performance parameter called effective ecological power density (EFECPOD) increases with pressure ratio, turbine speed, turbine diameter; decrease with turbine height ( L ), heat transfer coefficient ( tr h ).The EFECPOD increases up to a particular value and then begin to decrease with increasing equivalence ratio.

1 T
are the ambient temperature and the temperature at the beginning of the compression. is cycle temperature ratio and it is stated as below:

Figure 2 .Figure 3 .
Figure 2. The variation of EFECPOD with respect to

Figure 4 .Figure 5 .Figure 6 .Figure 7 .Figure 8 .
Figure 4.The variation of EFECPOD with respect The results are scientifically valuable and therefore, they can be assessed by JBC turbine designers.
u H lower heat value of the fuel (kJ/kg) ICE Internal combustion engines