The expansion process

Three principal hypotheses have been proposed to account for the decreased expansion observed if the reactive material is more finely ground or present in quantities above the pessimum  

These hypotheses are not mutually exclusive, though the general slowness of pozzolanic reactions renders (3) unlikely. The evidence is insuHicient to determine their relative importance, which could probably be assessed from a combination of expansion data, pore solution analyses and SEM of polished sections with accompanying X-ray microanalyses made in parallel on a series of mortars of suitable ages and compositions. 

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So far we have seen that a periodic function can be expanded in a discrete basis set of frequencies and a non-periodic function can be expanded in a continuous basis set of frequencies. The expansion process can be viewed as expressing a function in a different basis. These basis sets are the collections of solutions to a differential equation called the wave equation. These sets of solutions are useful because they are complete sets. 

The expansion process consists of three steps creating small discontinuities or cells in a fluid or plastic phase causing these cells to grow to a desired volume and stabilizing this cellular stmcture by physical or chemical means. 

Prom the onset of creaming to the end of the rise during the expansion process, the gas must be retained completely in the form of bubbles, which ultimately result in the closed-ceU stmcture. Addition of surfactants faciUtates the production of very small uniform bubbles necessary for a fine-cell stmcture. 

The Intercooled Regenerative Reheat Cycle The Carnot cycle is the optimum cycle between two temperatures, and all cycles try to approach this optimum. Maximum thermal efficiency is achieved by approaching the isothermal compression and expansion of the Carnot cycle or by intercoohng in compression and reheating in the expansion process. The intercooled regenerative reheat cycle approaches this optimum cycle in a practical fashion. This cycle achieves the maximum efficiency and work output of any of the cycles described to this point. With the insertion of an intercooler in the compressor, the pressure ratio for maximum efficiency moves to a much higher ratio, as indicated in Fig. 29-36. 

Any work developed by the turboexpander is at the expense of the enthalpy of the process stream, and the latter is correspondingly cooleci. A low inlet temperature means a correspondingly lower outlet temperature, and the lower the temperature range, the more effective the expansion process becomes. 

Most ethylene plants operate continuously with the expander functioning at or near design point. However, by using inlet guide vanes, the expander can still provide optimum performance at off-design conditions. Also, the expansion process generates power, which is used by the compressor. The ethylene enters the expanders at approximately 26 bar (377 psia) and exits at approximately 6 bar (87 psia). The expanders generate over 2,000 hp for gas compression. 

At the instant a pressure vessel ruptures, pressure at the contact surface is given by Eq. (6.3.22). The further development of pressure at the contact surface can only be evaluated numerically. However, the actual p-V process can be adequately approximated by the dashed curve in Figure 6.12. In this process, the constant-pressure segment represents irreversible expansion against an equilibrium counterpressure P3 until the gas reaches a volume V3. This is followed by an isentropic expansion to the end-state pressure Pq. For this process, the point (p, V3) is not on the isentrope which emanates from point (p, V,), since the first phase of the expansion process is irreversible. Adamczyk calculates point (p, V3) from the conservation of energy law and finds... 

Most rigid polyurethane foams have a closed cell structure. Closed cells form when the plastic cell walls remain intact during the expansion process and are not ruptured by the increasing cell pressure. Depending on the blowing process a small fraction (5-10%) of the cells remain open. Closed cell structures provide rigidity and obstruct gaseous or fluid diffusional processes. 

There is no way to use the expansion process to raise or lower a weight in the surroundings, so there can be no work. 

What are the disadvantages of a Rankine cycle in the expansion process ... 

An ideal Otto Cycle with air as the working fluid has a compression ratio of 9. At the beginning of the compression process, the air is at 290 K and 90kPa. The peak temperature in the cycle is 1800 K. Determine (a) the pressure and temperature at the end of the expansion process (power stroke), (b) the heat per unit mass added in kJ/kg during the combustion process, (c) net work, (d) thermal efficiency of the cycle, and (e) mean effective pressure in kPa. 

To solve this problem, we build the cycle as shown in Fig. 3.14. Then, (1) assume isobaric for the precooling process 7-8, isentropic for the compression process 8-9, isentropic for the compression process 9-10, isobaric for the heating process 10-11, isentropic for the expansion process 11-12, and isochoric for the cooling process 12-13 (2) input pq= 14.7 psia. 

An ideal Diesel engine receives air at 103.4 kPa and 27°C. Heat added to the air is 1016.6 kJ/kg, and the compression ratio of the engine is 13. Determine (a) the work added during the compression process, (b) the cut-off ratio, (c) the work done during the expansion process, (d) the heat removed from the air during the cooling process, (e) the MEP (mean effective pressure), and (f) the thermal efficiency of the cycle. 

Find the pressure and temperature of each state of an ideal Atkinson cycle with a compression ratio of 16. The heat addition to the combustion chamber is 800 Btu/lbm, the atmospheric air is at 14.7 psia and 60°F, and the cylinder contains 0.02 Ibm of air. Determine the maximum temperature, maximum pressure, heat supplied, heat removed, work added during the compression processes, work produced during the expansion process, net work produced, MEP, and cycle efficiency. 

COMMENTS. (1) The turbine work produced is very small. It does not pay to install an expansion device to produce a small amount of work. The expansion process can be achieved by a simple throttling valve. (2) The compressor handles the refrigerant as a mixture of saturated liquid and saturated vapor. It is not practical. Therefore, the compression process should be moved out of the mixture region to the superheated region. 

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