Adiabatic compression work

This chapter establishes the basis for the Second Law of Thermodynamics. It is not critical that you read this chapter to be able to understand the more practical chapters on compression that follow. But, for those readers who have technical training, wouldn t it be lovely to actually understand the basis for the Second Law of Thermodynamics. Wouldn t it be grand to really see the beauty and simplicity of the basis for the adiabatic compression work equation ... 

The percent of adiabatic compression work that was being wasted across the partially plugged in-line filter basket was then... 

For mnltistage compressors of JX, number of stages with adiabatic-compression in each stage, equal division of work between stages, and intercoohng to the irit e temperature, the following formulas ai e helpful ... 

The thermal efficiency of the process (QE) should be compared with a thermodynamically ideal Carnot cycle, which can be done by comparing the respective indicator diagrams. These show the variation of temperamre, volume and pressure in the combustion chamber during the operating cycle. In the Carnot cycle one mole of gas is subjected to alternate isothermal and adiabatic compression or expansion at two temperatures. By die first law of thermodynamics the isothermal work done on (compression) or by the gas (expansion) is accompanied by the absorption or evolution of heat (Figure 2.2). 

For theoretical cycle work performed in an adiabatic compression cycle (nonideal fluid) ... 

Compression efficiency is the ratio of the work required to adiabatically compress a gas to the work actually done within the compressor cylinder as shown by indicator cards. Figures 12-12 and 12-16. The heat generated during compression adds to the work that must be done in the cylinder. Valves may vary from 50-95% efficient depending on cylinder design and the ratio of compression. Compression efficiency (or sometimes termed volumetric efficiency) is affected by several details of the systems ... 

Horsepower is the work done in a cylinder on the gas by the piston connected to the driver during the complete compression cycle. The theoretical horsepower is that required to isen-tropically (adiabatically) compress a gas through a specified pressure range. The indicated horsepower is the actual work of compression developed in the compressor cylinder(s) as determined from an indicator card. Brake horsepower (bhp) is the actual horsepower input at the crankshaft of the compressor drive. It does not include the losses in the driver itself, but is rather the actual net horsepower that the driver must deliver to the compressor crankshaft. 

Adiabatic expansion of the air in the engine causes a maximum temperature drop of the exhaust. Adiabatic compression causes a maximum temperature rise of the compressed air. These effects combine to cause the greatest work loss of any compressed-air system, when pressurized air must be cooled back to atmospheric temperature. The energy analysis parallels the one just made for the polytropic system. This shows that net areas on both PV and TS graphs measure the work lost. 

The working substance being initially at the temperature T2 of the refrigerator, we place the cylinder on the non-conducting stand, and compress the working substance reversibly until the temperature rises to Ti. By the conditions imposed, this is an adiabatic compression, and will be represented by a continuous curve on the indicator diagram, say AB (Fig. 8). 

Much work has been done on the adiabatic compression ignition of NPN vapor mixed with various gases by both NOL (Ref 2) and Brit Imp Chem Inds (Ref 4). A table of compression ratios and resultant temps from the detons of NPN vapor saturated gas mixts is presented below... 

An adiabatic compression of the fluid returns the volume to V. Since work is added to the system and heat is not allowed to escape, the temperature increases to the initial temperature 92. 

The work for a real adiabatic compression can also be calculated from the difference between the total enthalpy of the outlet and inlet flows ... 

The compression work cannot be evaluated from Eq. (8-15) using Eq. (8-17) unless the operating condition or temperature is specified. We will consider two cases isothermal compression and adiabatic compression. 

So far only reversible adiabatic compression of an ideal gas has been considered. For the irreversible adiabatic compression of an actual gas, the shaft work W required to compress the gas from state 1 to state 2 can be obtained from equation 6.7, which in this case becomes... 

Step IV. A reversible adiabatic compression in which the temperature of the working substance increases to t2 and the substance is returned to its initial state. 

A hypothetical cycle for achieving reversible work, typically consisting of a sequence of operations (1) isothermal expansion of an ideal gas at a temperature T2 (2) adiabatic expansion from T2 to Ti (3) isothermal compression at temperature Ti and (4) adiabatic compression from Ti to T2. This cycle represents the action of an ideal heat engine, one exhibiting maximum thermal efficiency. Inferences drawn from thermodynamic consideration of Carnot cycles have advanced our understanding about the thermodynamics of chemical systems. See Carnot s Theorem Efficiency Thermodynamics... 

Compression of hydrogen consumes energy depending on the thermodynamic process. The ideal isothermal compression requires the least amount of energy (just compression work) and the adiabatic process requires the maximum amount of energy. The compression energy W depends on the initial pressure p and the final pressure pf, the initial volume V and the adiabatic coefficient y ... 

Figure 5.3 Work for isothermal (solid line) and adiabatic (dotted line) compression of hydrogen from an initial pressure ofpj = 1 bar on the left axis. Compression work as a percentage of the higher heating value (39.4 kWh l ) of hydrogen on the right axis.

It is reported in Refs 42 67 that moderate quantities of waxy materials incorporated with such expl materials as HMX, RDX and PETN do not appreciably affect their initiation sensitivity, but do inhibit propagation to expin. Ref 67 further states that no relationship between the specific and latent heats of the desensitizers and its ability to desensitize could be found, and concludes that the desensitizer cannot be regarded merely as a thermal sink. This is somewhat in conflict with results of work in Ref 91, where it is reported that it has been established firmly that the sensitivity of the RDX compositions decreases with increasing specific heats of the additives, and a solid desensitizer functions primarily by absorbing heat from local regions of initiation including any hot spots which arise from adiabatic compression of occluded gas ... 

Figure 4.3 Reversible Camot cycle, showing steps (1) reversible isothermal expansion at th (2) reversible adiabatic expansion and cooling from th to tc (3) reversible isothermal compression at tc (4) reversible adiabatic compression and heating back to the original starting point. The total area of the Camot cycle, P dV, is the net useful work w performed in the cyclic process (see text).

The area enclosed by the solid line is the total or actual compression work. The area enclosed by the dotted line is ideal or useful compression work. The areas between the dotted line and the solid line represent compression work lost to heat. The area inside the dotted line, divided by the area inside the solid line, is called adiabatic compressor efficiency. 

So far, we have limited our discussion to adiabatic compression efficiency. This sort of inefficiency downgrades work to heat. For a given compression ratio, the temperature rise of the gas as it flows through the compressor may be excessive, thus indicating a low adiabatic compression efficiency. Both centrifugal and reciprocating compressors suffer from this common problem, which is the subject of Chap. 30. 

Unfortunately, valve disablers have a detrimental effect on the adiabatic compressor efficiency. This means that, even though no gas may be moving through the crank end of a cylinder, the piston is still doing work on the gas inside the crank end of the cylinder. If you would like proof, place your hand on the valve cap on such a disabled cylinder. The high temperature you will feel is wasted compression work going to useless heat. I have measured in the field that, after a cylinder end is completely disabled, it is still converting 20 percent of the former compression work to heat. 

Which is more efficient—my beat-up, old centrifugal compressor, or my brand-new reciprocating compressor Both machines are working in parallel, but which has a better adiabatic compression efficiency ... 

In Fig. 8, step I is an isothermal expansion, step II is an adiabatic expansion, step III is an isothermal compression, and step IV is an adiabatic compression. Note that zero heat is transferred in the adiabatic expansion and compression (steps II and IV) that we have added to complete the cycle, and that the work terms in these two steps exactly cancel, being equal to TC Cv dT in the expansion and Th Cv dT in the compression. (The work in an adiabatic... 

The appropriate energy balance can be written W = AH — Q. Since Q is negative (heat transfer is out of the system), the work of non-adiabatic compression is greater than for adiabatic compression. Note that in order to have the same change in state of the air, i.e., the same AH, the irreversibilities of operation would have to be quite different for the two cases. 

In the adiabatic compression, (d) in Fig. 29, work is applied again to raise the pressure and temperature of the gas till the initial state. 

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