Additional Thermal Energy Required

 None of the candidate locations can provide enough thermal energy without supplemental firing of the thermal fluid. In the case of the Rankine cycle, it is the closed steam loop, for Brayton, the air/fuel mixture. 

In a ground based application, the Brayton cycle is defined by the appropriate entry Pressure and Temperature, with turbine stages added post combustor to extract every possible bit of energy from the working fluid. In this case, the working fluid is external to the engine, combustion is direct and air (containing oxygen) is added to fuel (a Methane mix) and the exit temperature of the combustor is the design parameter for the system. When the working fluid has passed through the final turbine stage, post heating must be added to the exhaust in order to give the exhaust flume enough thermal energy to rise up the stack and travel away from populated areas before dispersing. 

If a Stirling engine is inserted into the exhaust stream pre-combustor, there will not be enough energy in the exhaust fluid in order for the flume to rise. The only location the Stirling engine may be considered is at the secondary application point to utilize the remaining available thermal energy. 

The results of the comparisons for the three nodes in the Rankine cycle, supplemental firing in the Brayton cycle and direct firing are presented in this section below. A Compressed Natural Gas mixture with a HHV of 54,600BTU is used as a comparable fuel.

By considering the thermal energy available to each application and comparing against the required minimum temperature for the Stirling engine to operate efficiently, a calculation was performed to evaluate the amount of supplemental firing, and thus mass fuel flow, required.

TREQUIRED
TAMB
TAVAILABLE
ΔTREQUIRED α FUEL REQUIRED

The Rankine cycle, is a closed system, therefore thermal energy is added back into the working fluid by reheating the fluid passing it through a reheater or boiler. The Brayton cycle is an open loop and thermal energy is added downstream of the receiver directly into the exhaust stream. The latter principal is also the method employed when considering direct firing of the engine.

mfuel
mair
mheated air

mdotair = CpΔT                                                                                            mdot hot air = CpΔT

 By the 1st Law:

                               Q + mair Cp Tair inlet  –  mair Cp Tair exit  =  0

Q  =  (mfuel / mair) HVfuel

then

ΔT  =  Te  –  Ti  =  {(mf / ma ) HV} / Cpair

Nationally, consumer process for natural gas can vary between $0.55 and $1.23 per therm as determined by the supplier.

 

$’s / thousand cubic feet

Therms / thousand cubic feet

BTU / thousand cubic feet

ft3 / 10,000 BTU

$’s / 10,000 BTU

5.87

10

1,000,000

10

0.0587

Source: EIA – Natural Gas Prices 2008

If a Stirling Engine with a working fluid of Helium and a hot side temperature of 540oC runs at 1800 RPM, the electrical energy output will be 25kW.

RANKINE CYCLE
NODE   Tinitial     (K)   Tfinal        (K)   ΔT   mdot working fluid   (kg/s)   Δh air        (kJ/kg)   mdot fuel (kg/s)   Qdot     (kJ/kg)
                             
8   594.9   813   218.1   372.2   743.0   5.1   276,561.3
12   610.3   813   202.7   60.5   690.6   0.8   41,780.0
14   318.8   813   494.2   311.7   1683.7   9.6   524,806.2
                             
BRAYTON CYCLE
    498   813   315   58.4   316.1   0.3   18,460.4
                             
DIRECT FIRE
                             
    298   813   515   58.4   516.8   0.6   30,181.3

 

 The Solar Stirling or Dish Stirling System

The sun, with a heat rate of 440 Btu/ft2, and a twelve foot diameter parabolic mirrored dish focused to a receiver at approximately seven feet away from the center of the dish, provides the necessary 425oC to start the Stirling cycle. When discussing dish/Stirling technology, small variances in dimensions equate to large differences in the field. Over a distance of eight inches around the focal point, flux can decrease from 1200 W/m2 to 75 W/m2. The opposite is also true.

Photo voltaic is available to the consumer at approximately $6.40 / Watt; the proposed cost of a 3kW dish/Stirling system from INFINIA will be in the range of $13,500 – $15,400. (SOLO Kleinmotoren pricing of ~$40-50,000 U.S. for a 10kW dish/Stirling system.) At $14,000, this is equivalent to pricing available to the consumer at $4.67 / Watt. The dish/Stirling system can only operate 9 hours per day on average.

 

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~ by frazerthompson on May 5, 2009.

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