Maximum specific work

The isentropic temperature rise for maximum specific work (J , ) is obtained by differentiating Eq. (3.11) with respect to x and equating the differential to zero, giving... 

The Hawthorne and Davis approach thus aids considerably our understanding of a/s plant performance. The main point brought out by their graphical construction is that the maximum efficiency for the simple [CHT]i cycle occurs at high pressure ratio (above that for maximum specific work) whereas the maximum efficiency for the recuperative cycle [CHTX]i occurs at low pressure ratio (below that for maximum specific work). This is a fundamental point in gas turbine design. 

Rufli s calculations (Fig. 7.7a, b), indicated that the optimum pressure ratio for a CCGT plant is relatively low compared with that of a simple gas turbine (CBT) plant. In both cases, the optimum pressure ratio increa.ses with maximum temperature. Davidson and Keeley [6] have given a comparative plot of the efficiencies of the two plants (Fig. 7.9), showing that the optimum pressure ratio for a CCGT plant is about the same as that giving maximum specific work for a CBT plant. 

We may define the stage efficiency, n,. as the ratio of the actual specific work extracted from the stage, w (J/kg), to the maximum specific work that is possible to extract, w ax (J/kg) ... 

Here Wnuxs is the maximum specific work that the blade can extract. Note that less than... 

The maximum specific work, Wm B, available for the moving blades to extract is the sum of the specific kinetic energy of the gas leaving the nozzle blades and the isentropic specific enthalpy drop across the moving blades ... 

For a given firing temperature there is an optimum pressure ratio for achieving the maximum specific work which is different from the optimum thermal-efficiency pressure ratio. 

A reversible recuperative a/s cycle, with the maximum possible heat transfer from the exhaust gas, qj = Cp(74 — 7y), is illustrated in the T,s diagram of Fig. 3.2, where 7y = 72. This heat is transferred to the compressor delivery air, raising its temperature to 7x = 74, before entering the heater. The net specific work output is the same as that... 

Calculation of the specific work and the arbitrary overall efficiency may now be made parallel to the method used for the a/s cycle. The maximum and minimum temperatures are specified, together with compressor and turbine efficiencies. A compressor pressure ratio (r) is selected, and with the pressure loss coefficients specified, the corresponding turbine pressure ratio is obtained. With the compressor exit temperature T2 known and Tt, specified, the temperature change in combustion is also known, and the fuel-air ratio / may then be obtained. Approximate mean values of specific heats are then obtained from Fig. 3.12. Either they may be employed directly, or n and n may be obtained and used. 

Fig. 4.11. Calculation of efficiency of simple CBT plants—single-.step cooled ICBTlica uncooled [CBT ]ii—a.s a function of specific work with pressure ratio (r) and maximum temperature as parameters and with r)p< = t), = 0.9. 7hi = 1073 K (after Ref. 5 ).

Fig. 3.16 showed carpet plots of efficiency and specific work for several dry cycles, including the recuperative [CBTX] cycle, the intercooled [CICBTX] cycle, the reheated [CBTBTX] cycle and the intercooled reheated [CICBTBTX] cycle. These are replotted in Fig. 6.17. The ratio of maximum to minimum temperature is 5 1 (i.e. T nx 1500 K) the polytropic efficiencies are 0.90 (compressor), 0.88 (turbine) the recuperator effectiveness is 0.75. The fuel assumed was methane and real gas effects were included, but no allowance was made for turbine cooling.

For the ISTIG cycle, Fig. 6.18 shows thermal efficiency plotted against specific work for varying overall pressure ratios and two maximum temperatures of 1250 and 1500°C. Peak efficiency is obtained at high pressure ratios (about 36 and 45, respectively), before the specific work begins to drop sharply. Note that the pressure ratios of the LP and HP compressors were optimised within these calculations. 

Macchi et al. provided a similar comprehensive study of the more complex RWI cycles as illustrated in Fig. 6.19, which shows similar carpet plots of thermal efficiency against specific work for maximum temperatures of 1250 and 1500°C, for surface intercoolers. The division of pressure ratio between LP and HP compressors is again optimised within these calculations, leading to an LP pressure ratio less than that in the HP. For the RWI cycle at 1250°C the optimisation appears to lead to a higher optimum overall pressure ratio (about 20) than that obtained by Horlock [5], who assumed LP and HP pressure ratios to be same in his study of the simplest RWI (EGT) cycle. His estimate of optimum pressure ratio... 

Maximum Allowable Working Pressure (MAWP) the maximum pressure pounds per square inch gauge permissible at the top of a completed vessel in its operating position for a specific designated temperature corresponding to the MAWP pressure. This pressure is calculated in accordance with the ASME code (Par. UG-98) [1] for all parts or elements of the vessel using closest next larger to calculated value nominal thickness (closest standard for steel... 

MAWP = maximum allowable working pressure of a pressure vessel, psi gauge (or psi absolute if so specifically noted)... 

A high level of poly(3HB) accumulation is also obtained if the cells are grown under carbon substrate limitation, and the cultivation in the second fermenter is also carried out under carbon limitation. In this case, a substrate flow rate (F2) below that corresponding to the maximum specific poly(3HB) formation rate should be chosen [114]. This cultivation strategy is especially convenient when using toxic substrates like acetic acid. Low substrate concentrations are more conveniently maintained in continuous cultivation than in fed-batch cultivation. The only additional equipment needed is a system to ensure constant working volumes and flow rates. 

An Instron Testing System (Model 1122), fitted with a 10 cm six-wire grid (Ottawa Texture measuring system, OTMS cell) was used to determine rheological properties. A loading rate of 50 mm/min and a chart speed of 500 mm/min resulted in a well defined force-deformation curve. Force at the bioyield point and the area under the curve were calculated. These values were then converted into maximum stress, work and specific work values ... 

The conversion of the reaction at the specific temperature, pressure and initial gas compositions is governed by its thermodynamic equilibrium. According to Equation (2.16), the maximum available work of the fuel cell can be determined by the Nemst potential, which represents the electrical potential of the reaction. 

Thermodynamic Work of Adhesion. One other important aspect of surface energetics (71, 72) is the use of surface free energy to calculate the maximum reversible work of adhesion, Wad, which has been correlated to the adhesive strength (41, 44) and should not be equated to the strength of an adhesive joint (6). Since neither wetting nor adhesion is controlled purely by thermodynamic factors, we should use the maximum reversible work of adhesion, Wad on the basis of an idealistic approach. When all other variables are equal, we can use Wad to compare the effectiveness of adhesives for a specific substrate. 

Magnesium oxide of high surface area can be produced by the thermal decomposition of various magnesium compounds. In the early work of Gregg and Packer (1955), a maximum specific area of about 200 m2g 1 was obtained by the calcination of Mg (OH) 2 at 380°C. This temperature was a little below the temperature required for the complete decomposition of the Mg(OH)2 under these experimental conditions. 

From several points of view (for example, in battery technology), it is extremely important to have solutions of maximum specific conductivity. Basically, the specific conductivity increases proportionally to the concentration of ions. On this simplistic ground, it would seem important to have as high a concentration as possible up to the solubility limits. However (see the work of Haymet described in Chapter 3), increasing concentration leads to an inaease of ionic association which decreases the concentration of conducting entities. Also, as... 

Table I gives the maximum allowable working pressure, in psig, ba.sed on an allowable stress ol 15,000 psi. fo correct for the specific material and temperature,...

Hence, combining equation (13.47) with equations (13.87) to (13.89) gives the maximum available specific work as... 

DESIGN WORKING PRESSURE - The maximum allowable working pressure for which a specific part of a system is designed. 

In this section, we assume that the legs are already determined and given. We want to generate driver schedules by combiiung legs. An acceptable schedule must meet specific work rules, which specify the minimum number of hours that a driver must be paid for a day s work (usuaUy 8 hours) and the maximum length of a workday (usually 10 hours). In addition, a driver must return to his or her domicile every day and a workday must incorporate breaks of specified duration at specified times. For example, a lunch break must last 1 hour and be scheduled between 11 00 am and 2 00 pm. 

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