# Air Heater

Under construction.

## Performance

The following performance calculations are available on airheater instances:

 Calculation Reference Output Tags X Factor ASME PTC 4.1, S 7.07 .xFactor.use Gas Side Efficiency ASME PTC 4.1, S 7.01 .gasEfficiency.use Air Temperature Rise .c1.dT.use Gas Temperature Drop ASME PTC 4.1, S 7.12 .c2.dT.use Gas Side Pressure Drop ASME PTC 4.1, S 7.14 .c2.dP.use Air Side Pressure Drop ASME PTC 4.1, S 7.15 .c1.dP.use

## Calculations

Air Heater Inlet Temp

Air Heater inlet tempearture.

$$T_{1in} = \frac{\dot{M}_{PA} \times T_{PAin} + \dot{M}_{SA} \times T_{SAin}}{\dot{M}_{PA} + \dot{M}_{SA}}$$

Where

• $\dot{M}_{PA}$ = PA in mass flow $(\frac{kg}{s})$
• $T_{PAin}$ = PA in temperature $(^{0}C)$
• $\dot{M}_{SA}$ = SA in mass flow $(\frac{kg}{s})$
• $T_{SAin}$ = SA in temperature $(^{0}C)$

In CAS Terms:

$$T1in = \frac{(ob.c1PAin.massFlow.use * PAin + ob.c1SAin.massFlow.use * SAin)}{(ob.c1PAin.massFlow.use + ob.c1SAin.massFlow.use)}$$

Air Heater Outlet Temp

Air Heater outlet tempearture.

$$T_{1out} = \frac{\dot{M}_{PA} \times T_{PAout} + \dot{M}_{SA} \times T_{SAout}}{\dot{M}_{PA} + \dot{M}_{SA}}$$

Where

• $\dot{M}_{PA}$ = PA out mass flow $(\frac{kg}{s})$
• $T_{PAout}$ = PA out temperature $(^{0}C)$
• $\dot{M}_{SA}$ = SA out mass flow $(\frac{kg}{s})$
• $T_{SAout}$ = SA out temperature $(^{0}C)$

In CAS Terms:

$$T1out = \frac{(ob.c1PAout.massFlow.use * PAout + ob.c1SAout.massFlow.use * SAout)}{(ob.c1PAout.massFlow.use + ob.c1SAout.massFlow.use)}$$

Gas Side Efficiency

The Gas Side Efficiency describes the heat transfer inside the air heater and is defined as the ratio of gas temperature drop, corrected for no leakage, to temperature head. It describes the utilisation of the gas side temperature head, which is defined by the temperature of gas entering air heater and temperature of air entering air heater, corrected for no leakage.

The Gas Side Efficiency is defined as:

$$\eta _{G} = 100 \times \frac{t_{Gin} - t_{Gout(NL)}}{t_{Gin} - t_{Ain}}$$

Where:
• $\eta _{G}$ = gas side efficiency (%)
• $t_{Gin}$ = air heater gas inlet temperature $(^{0}C)$
• $t_{Gout(NL)}$ = air heater gas outlet temperature corrected for no leakage $(^{0}C)$
• $t_{Ain}$ = the air heater air inlet temperature $(^{0}C)$

In CAS terms:

$$airheater.gasEfficiency.use = 100 \times \frac{(ah.c2in.prop.temp.use - ah.c2out.prop.temp.undiluted)}{(ah.c2in.prop.temp.use - ah.c1in.prop.temp.use)}$$

Air Leakage

The air heater leakage represents the amount of higher pressure Primary/Secondary Air leaking into the lower pressure gas stream due to gaps in the seals between air and gas sections:

$$A_{(L)} = 100 \times \frac{W_{Gout} - W_{Gin}}{W_{Gin}}$$

Where:
• $A_{(L)}$ = air heater leakage (%)
• $W_{Gout}$ = mass flow of air heater outlet wet gas per kg of As Fired Fuel (kg/kg Fuel)
• $W_{Gin}$ = mass flow of air heater inlet wet gas per kg of As Fired Fuel (kg/kg Fuel)

In CAS terms:

$$ah.leakage.use = \frac{ah.c2out.massFlow.use - ah.c2in.massFlow.use}{ah.c2in.massFlow.use}$$

$$ah.leakage.percentage = 100 \times \frac{ah.c2out.massFlow.use - ah.c2in.massFlow.use}{ah.c2in.massFlow.use}$$

Note that the air heater leakage is best determined from the $O_{2}/CO_{2}$ content of the Air heater of the inlet and outlet gas streams. In the absence of these measurements the leakage must be determined by air heater leakage test and used as an input to the performance calculations.

Air heater leakage can be calculated from O2 quantities

$$A_{(L)} = \frac{(O_{2out} - O_{2in}) \times 0.9 \times 100 \%}{21 - O_{2out}}$$

In CAS Terms:

$$ob.ah.leakage.use = (ob.ah.gasout.prop.mix.o2.use - ob.blr.econ.c2out.prop.mix.o2) * 0.9 * 100 / (21 - ob.ah.gasout.prop.mix.o2.use)$$

X-Ratio

The X-Ratio is ratio of the temperature difference of air passing through the heater to the difference of gas passing through the air heater. This term describes the thermal performance of the air heater.

X-Ratio is defined as:

$$\chi _{R} = \frac{t_{Gin} - t_{Gout(NL)}}{t_{Aout} - t_{Ain}}$$

Where:
• $\chi _{R}$ = X-Ratio (unitless)
• $t_{Gin}$ = air heater gas inlet temperature $(^{0}C)$
• $t_{Gout(NL)}$ = air heater gas outlet temperature corrected for no leakage $(^{0}C)$
• $t_{Aout}$ = the air heater air outlet temperature $(^{0}C)$
• $t_{Ain}$ = the air heater air inlet temperature $(^{0}C)$

In CAS terms:

$$ah.xratio.use = \frac{ah.c2in.prop.temp.use - ah.c2out.prop.temp.undiluted}{ah.c1out.prop.temp.use - ah.c2in.prop.temp.use}$$

Gas Side Temerature Drop

$$\Delta T_{GAS} = T_{GAS_{IN}} - T_{GAS_{OUT}}$$

Where:

• $T_{GAS_{IN}}$ = gas inlet temperature $(^{0}C)$
• $T_{GAS_{OUT}}$ = gas outlet temperature $(^{0}C)$

In CAS Terms:

$$ob.c2.dT.use = ob.c2in.prop.temp.use - ob.c2out.prop.temp.use$$

Gas Side Pressure Drop

$$\Delta P_{GAS} = P_{GAS_{IN}} - P_{GAS_{OUT}}$$

Where:

• $P_{GAS_{IN}}$ = gas inlet pressure $(kPa)$
• $P_{GAS_{OUT}}$ = gas outlet pressure $(kPa)$

In CAS Terms:

$$ob.c2.dP.use = ob.c2in.prop.press.use - ob.c2out.prop.press.use$$

Air Side Pressure Drop

$$\Delta P_{AIR} = P_{AIR_{IN}} - P_{AIR_{OUT}}$$

Where:

• $P_{AIR_{IN}}$ = gas inlet pressure $(kPa)$
• $P_{AIR_{OUT}}$ = gas outlet pressure $(kPa)$

In CAS Terms:

$$ob.c1.dP.use = ob.c1PAin.prop.press.use - ob.c1PAout.prop.press.use$$

Gas Outlet Temperature No Leakage

To determine the gas outlet temperature corrected for no leakage:

$$t_{Gout(NL)} = \frac{A_{(L)} \times c_{pA} \times (t_{Gout} - t_{Ain})}{100 \times c_{pG}}$$

Where:
• $A_{(L)}$ = air heater leakage (%)
• $t_{Gout}$ = air heater gas outlet temperature $(^{0}C)$
• $c_{pA}$ = mean specific heat between gas out temperature and air inlet temperature (kJ/kg.K)
• $c_{pG}$ = mean specific heat between air heater gas outlet temperature $(t_{Gout})$ and air heater gas outlet temperature corrected for no leakage $(t_{Gout(NL)})$ (kJ/kg.K)

In CAS terms:

$$c2out.prop.temp.undiluted = \frac{ah.leakage.use}{ah.c2in.massFlow.use} \times \frac{ah.cpair.dontknow \times (ah.c2out.prop.temp.use - ah.c1in.prop.temp.use)}{ah.cpgas.dontknow}$$

This may be calculated in the Boiler ASME Efficiency calculation.

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