Compressor isothermal

The actual compressor work is this latter quantity, divided by the compressor isothermal efficiency thus,... 

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. 

The turboexpander in combination with a compressor and a heat exchanger functions as a heat pump and is analyzed as follows In Fig. 29-44 consider the compressor and aftercooler as an isothermal compressor operating at To with an efficiency and assume the working fluid to be a perfect gas. Further, consider the removal of a quantity of heat by the tumoexpander at an average low temperature Ti-This requires that it dehver shaft work equal to Q. Now, make the reasonable assumption that one-tenth of the temperature drop in the expander is used for the temperature difference in the heat exchanger. If the expander efficiency is and this efficiency is mul-... 

The theoretical required (isothermal) compression work in the compressor, which is assumed to operate isothermally at To, is... 

Isothermal compression is presented here to represent the upper limits of cooling and horsepower savings. It is the equivalent of an infinite number of intercoolers and is not achievable in the practical types of compressors described in this book. For an isothermal process. 

The discussion of the last section is then useful in considering the evaporative cycles. We shall see that the effect of water injection downstream of the compressor (and possibly in the cold side of the heat exchanger) may lead towards the [CBTJiXr type of plant, with increased cold side effective specific heat and hence increased heat exchanger effectiveness. Water injection in the compressor may lead to a plant with isothermal compression. 

Figure 12-17A. Combined indicator cards from a two-stage compressor showing how cylinder water jackets and intercooler help bring compression line nearer to isothermal. (Used and adapted by permission Miller, H. H. Power, 1944. McGraw-Hill, Inc., New York. All rights reserved.)...

The gas compression in practically all commercial machines is polytropic. That is, it is not adiabatic or isothermal, but some form peculiar to the gas properties and the hydraulic design of the compressor. Actual machines may be rated on adiabatic performance and then related to polytropic conditions by the polytropic efficiency. Other performance rating procedures handle the calculations as polytropic. For reference, both methods are presented. 

A three-stage compressor is required to compress air from 140 kN/m2 and 283 K to 4000 kN/m2. Calculate fee ideal intermediate pressures, the work required per kilogram of gas, and fee isothermal efficiency of fee process. Assume the compression to be adiabatic and the interstage cooling to cool the air to the initial temperature. Show qualitatively, by means of temperature-entropy diagrams, fee effect of unequal work distribution and imperfect intercooling, on the performance of the compressor. 

A poly tropic compression is neither adiabatic nor isothermal, but specific to the physical properties of the gas and the design of the compressor. The polytropic coefficient n must therefore be determined experimentally. If the initial and final conditions for a given compression process are known, then n can be determined from a rearrangement of Equation B.23 ... 

If we compare the work required to compress a given gas to a given compression ratio by isothermal and isentropic processes, we see that the isothermal work is always less than the isentropic work. That is, less energy would be required if compressors could be made to operate under isothermal conditions. However, in most cases a compressor operates under more nearly adiabatic conditions (isentropic, if frictionless) because of the relatively short residence time of the gas in the compressor, which allows very little time for heat generated by compression to be transferred away. The temperature rise during an isentropic compression is determined by eliminating p from Eqs. (8-17) and (8-19) ... 

In reality, most compressor conditions are neither purely isothermal nor purely isentropic but somewhere in between. This can be accounted for in calculating the compression work by using the isentropic equation [Eq. (8-21)], but replacing the specific heat ratio k by a polytropic constant, y, where 1 < y < k. The value of y is a function of the compressor design as well as the properties of the gas. 

In the case of adiabatic flow we use Eqs. (9-1) and (9-3) to eliminate density and temperature from Eq. (9-15). This can be called the locally isentropic approach, because the friction loss is still included in the energy balance. Actual flow conditions are often somewhere between isothermal and adiabatic, in which case the flow behavior can be described by the isentropic equations, with the isentropic constant k replaced by a polytropic constant (or isentropic exponent ) y, where 1 < y < k, as is done for compressors. (The isothermal condition corresponds to y= 1, whereas truly isentropic flow corresponds to y = k.) This same approach can be used for some non-ideal gases by using a variable isentropic exponent for k (e.g., for steam, see Fig. C-l). 

A 12 in. ID gas pipeline carries methane (MW = 16) at a rate of 20,000 scfm. The gas enters the line at a pressure of 500psia, and a compressor station is located every 100 mi to boost the pressure back up to 500psia. The pipeline is isothermal at 70°F, and the compressors are adiabatic with an efficiency of 65%. What is the required horsepower for each compressor Assume ideal gas. 

The scope of coverage includes internal flows of Newtonian and non-Newtonian incompressible fluids, adiabatic and isothermal compressible flows (up to sonic or choking conditions), two-phase (gas-liquid, solid-liquid, and gas-solid) flows, external flows (e.g., drag), and flow in porous media. Applications include dimensional analysis and scale-up, piping systems with fittings for Newtonian and non-Newtonian fluids (for unknown driving force, unknown flow rate, unknown diameter, or most economical diameter), compressible pipe flows up to choked flow, flow measurement and control, pumps, compressors, fluid-particle separation methods (e.g.,... 

Although isothermal compression is desirable, in practice the heat of compression is never removed fast enough to make this possible. In actual compressors only a small fraction of the heat of compression is removed and the process is almost adiabatic. 

If an infinite number of intercoolers, compressors, reheaters, and turbines are added to a basic ideal Brayton cycle, the intercooling and multicompression processes approach an isothermal process. Similarly, the reheat and multiexpansion processes approach another isothermal process. This limiting Brayton cycle becomes an Ericsson cycle. 

The schematic Ericsson cycle is shown in Fig. 4.27. The p-v and T-s diagrams of the cycle are shown in Fig. 4.28. The cycle consists of two isothermal processes and two isobaric processes. The four processes of the Ericsson cycle are isothermal compression process 1-2 (compressor), isobaric compression heating process 2-3 (heater), isothermal expansion process 3-4 (turbine), and isobaric expansion cooling process 4-1 (cooler). 

Build the cycle as shown in Fig. 4.27. Assuming the compressor is isothermal, the heater is isobaric, the turbine is isothermal, and the cooler is isobaric. 

Build the ice cycle as shown in Fig. 4.41. Assume that the compressors and turbines are isothermal and isentropic. 

The compression work depends on the nature of the gas (Table 5.2). Real compressors work close to the isothermal limit (Figure 5.3). 

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