Adiabatic compression efficiency

Similar to volumetric efficiency, isentropic (adiabatic) efficiency T is the ratio of the work required for isentropic compression of the gas to work input to the compressor shaft. The adiabatic efficiency is less than one mainly due to pressure drop through the valve ports and other restricted passages and the heating of the gas during compression. 

The adiabatic efficiency is a function of the pressure ratio, and thus, dependent on the thermodynamic state of the gas undergoing compression. ... 

Adiabatic Efficiency. The ratio of theoretical adiabatic horsepower to actual brake horsepower required at the compressor shaft is adiabatic efficiency. It is equal to compression efficiency X mechanical efficiency. ... 

Calculate the compression ratio, Pd/Ps = P2/P1 = Pc-From Table 12-9B for the compressor frame selected, select polytropic efficiency, Cp, and using Figure 12-65A, determine adiabatic efficiency, e d. 

Where Zg is average gas compressibility factor, R = 1,544, T is temperature (R), Pj is inlet pressure (psia), P2 is outlet pressure (psia), k is adiabatic exponent and Ep is adiabatic efficiency, and... 

Saturated steam at 175 kPa is compressed adiabatically in a centrifugal compressor to 650 kPa at the rate of 1.5 kg s 1. The compressor efficiency is 75 percent What is the power requirement of the compressor and what arc the enthalpy and entropy of the steam in its final state ... 

Solution Saturated steam at 100 kPa is compressed adiabatically to 300 kPa with a compressor efficiency of 0.75. From the results of Example 7.8, we have ... 

Adiabatic efficiencies typically are in the range from 70% to 90%. They tend to increase with increasing flow rate and compression ratio. That means that larger compressors tend to be more efficient than smaller ones. 

The effect of increasing tlie compression ratio, defined as tlie ratio of the volumes at the begimiing and end of tlie compression stroke, is to increase the efficiency of tlie engine, i.e., to increase the work produced per imit quantity of fuel. We demonstrate this for an idealized cycle, called the air-standard Otto cycle, shown in Fig. 8.9. It consists of two adiabatic and two constant-volume steps, which comprise a heat-engine cycle for which air is tlie working fluid. In step DA, sufficient heat is absorbed by tlie air at constant volmiie to raise its temperature and pressure to the values resulting from combustion in an actual Otto engine. Then the air is expanded adiabatically and reversibly (step AB), cooled at constant volume (step BC), and finally compressed adiabatically and reversibly to the initial state at D. 

The maximum possible performance of a heat engine set by that given by a reversible heat engine operating on a Carnot cycle, which involves four reversible processes (i) reversible isothermal heat addition, Qh, (ii) reversible adiabatic expansion (work), W, (iii) reversible isothermal heat rejection, Ql, and (iv) reversible adiabatic compression. Thermal efficiency of the heat engine is given by... 

Starting at point (1), the fluid is compressed without heat loss (adiabatically) or mechanical loss to point (2). The absolute temperature rises from to T2 during this compression. The fluid expands at constant temperature without losses to point (3) as it takes heat Q ) from a reservoir at temperature (T ), It then expands without heat or mechanical loss to point (4) as the temperature of the fluid drops to Tj. The fluid is compressed adiabatically back to point (1) at constant temperature as it rejects heat (Qj) to a second reservoir having a constant temperature (Tj). From points (2) to (3) and (3) to (4), work equal to Q2 is delivered to an external system, but from (4) to (1) and (1) to (2), work equal to Qi is taken from an external system. The net work done is Q2 - 2i) and the efficiency of the process (e ) is ... 

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). 

It follows that the efficiency of the Carnot engine is entirely determined by the temperatures of the two isothermal processes. The Otto cycle, being a real process, does not have ideal isothermal or adiabatic expansion and contraction of the gas phase due to the finite thermal losses of the combustion chamber and resistance to the movement of the piston, and because the product gases are not at tlrermodynamic equilibrium. Furthermore the heat of combustion is mainly evolved during a short time, after the gas has been compressed by the piston. This gives rise to an additional increase in temperature which is not accompanied by a large change in volume due to the constraint applied by tire piston. The efficiency, QE, expressed as a function of the compression ratio (r) can only be assumed therefore to be an approximation to the ideal gas Carnot cycle. 

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 ... 

Cg,. = compression efficiency, the product of adiabatic and reversible efficiencies, which vary with the cylinder and valve design, piston speed, and fraction values range from 0.70-0.88 usually. 

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. 

The polytropic process is mathematically easier to handle than the adiabatic approach for the following (1) determination of the discharge temperature (see later discussion under Temperature Rise During Compression ) and (2) advantage of the polytropic efficiency ... 

Adiabatic Head Developed per Single-Stage Wheel. The head developed hy a single stage of compression, consisting of an impeller and diffuser, depends upon the design, efficiency, and capacity and is related to its speed. 

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. 

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