But since 0dB does not need anymore need compression; the compressor “releases” then applies gain to be the same with the input level again. Figure 7.15 shows two stages of compression, 1–3 and 4–5, and one stage of intercooling where gas is partially compressed from point 1 to point 3, cooled back to point 4 at constant pressure (ideally) pi between the stages, then finally compressed to point 5. Typical compressor performance map in terms of pressure ratio and corrected mass flow. A generic representation of the lift characteristics of a rotor blade with cL,max = 1.2 and is = 18° is shown in Fig. Reynolds number, Re, is discussed in detail in the chapter on Pipe Flow. Let’s start with an example while I show you step-by-step of the calculation method. Some values of the Prandtl number for fluids of interest are given in Table 2. Thus the network from the cycle is increased. Butt joints designed to reduce leakage may be used, Figure 4.58[16]. FIGURE 4. 7.48), and the last term decreases with mass flow (Fig. Figure 2 gives the values for LMTD when the temperature differences between the two streams at entry and exit are known. Article 4.3 Gas Turbines. © Copyright Energy Solutions Center, DG Consortium 2004. – Prandtl numbers for heat exchangers. The head coefficient is one dimensionless parameter which is used to express the work required per stage of centrifugal compressor. Download Air Compressor Calculations Now that all the terms in Equation (7.93) have been considered in some detail, we may examine the variation of the corrected work as a function of corrected weight flow for a given value of corrected rpm, for which we have. Note that for mass flows lower than that indicated by the locus of maximum lift coefficient the compressor is operating in the stall region. The total work input rate is the sum of work rate inputs for the system. Here the constant Kc is the analog to Kt for the turbine and expresses information on machine size and compressor inlet conditions. W = compression work (Btu min) h = heat of compression (Btu/lb) q = refrigerant circulated (lb/min) Compression Horsepower. ∗∗∗ 60 ∗ ‘n=1 for single acting compressor, ‘n=2 for double acting compressor. Cool the compressed air between stages to improve compression efficiency of the second and subsequent stages. Figure 7.14. W T = h 3 – h 4s → W Ts = c p (T 3 – T 4s). t. Turbine pressure ratio = P 3 /P 4. c. Compressor pressure ratio = P 2 /P 1. β. r t /r c The nominal optimum is found by solving the optimization problem in Equation 3. If the compressor is located in a warm atmosphere it may be advantageous to draw the cooling air from a lower temperature source, eg through ducting led to the outside of the building. It can be shown from dimensional analysis that the convective coefficient of the fluid is primarily dependent on the Nusselt number, Nu. Pump Efficiency is the ratio of pump input and output power. Performing a little algebra, we arrive at the equation: CW = [cp * Tt]2 * [CPR ^ ( (gam -1) / gam) - 1] / nc. Shell-and-tube heat exchangers can adopt a variety of different forms, as in Figure 1. Rosen, ... S.J. The compressor work equation in Eq. Hence, the total compressor work with isentropic compression and complete intercooling as shown below is less than the compressor work CP(T2–T1). Examines the application of the gas laws to Air Compressors and Motors. However, the peak power in this case is not as critical as with evaporator temperature since the chances of condenser operating at such a high temperatures are rare. 7.47 as illustrated in Fig. If a heat exchanger has one pass of the shell-side fluid and one pass of the tube-side fluid it is a 1:1 exchanger; if there is one shell-side pass and two tube-side passes it is 1:2 and so on. Reciprocating compressor capacity calculation formula. Hence, the slip factor accommodates for a slip loss which affects the net power developed which increases with increasing flow-rate. Where more than one stage of compression is involved, it is desirable from the point of view of maximum efficiency that each stage does an equal amount of work. It is calculated as four times the ratio of the area of flow to the wetted perimeter. Since the production rate (or feed rate) is free there are 8 steady-state degrees of freedom (with 30 °C after SW cooling). Note that we have assumed that the refrigerant is 30 °C after the SW cooling. Specific heat function = (γ-l)/γ. Typical compressor performance map in terms of corrected work and corrected weight flow. One tube is fitted inside another such that a space exists between them, which is filled with a harmless heat transfer medium and kept at a pressure of at least 0.5 bar by the expansion tank. In this and following sections, the state points coincide with states shown in Fig. Adiabatic efficiency is defined as the ratio of work output for an ideal isentropic compression process to the work input to develop the required head. To find the value of pi that would yield minimum compressor work with isentropic compression, let us differentiate Wc with respect to pi and equate dWc/dpi to zero and putting T1=T4. Piston rings for lubricated compressors work under relatively similar conditions to internal-combustion-engine rings. TABLE 1. Then for each increasing value of corrected rpm, the corrected work curves will be repeated as shown in Fig. This can only be realized if the temperature of the air into the second stage is similar to that of the air inducted into the first stage. Copyright © 2021 Elsevier B.V. or its licensors or contributors. Velocity diagram for flow entering the rotor illustrating the increase in the angle β2 as the mass flow is increased. This is discussed next. The compressor work equation in Equation (7.92) may be regrouped as follows: The first term in square brackets is the corrected rpm, whereas the second term involves the corrected mass flow and the angle of the flow relative to the linear speed of rotation u. Cooling reduces the air temperature and precipitates out water droplets which can be drained off. Flow diagram of a compressor intercooling. Compressor work function = (P 2 /P 1) θ (see Fig. W = h q (1) where . Variation of the drag factor as a function of the rotor entrance angle β2. It should be pointed out that the curves for the corrected compressor work or the compressor pressure ratio at constant corrected rpm are more peaked for axial flow machines than for centrifugal machines as depicted in Fig. The specific enthalpy at state 4 is found similarly. Pump input power calculation formula or pump shaft power calculation formula. Compression Work . Again, the only unconstrained degrees of freedom are related to the refrigerant composition. 7.47. Note that the drag factor decreases as the mass flow increases. An Air Compressor takes in Air at 14 psi and at 20 degrees C. It is compressed in accord to the law, Temperature at the end of the Compression, Last Modified: 16 Oct 11 @ 15:04     Page Rendered: 2018-11-07 01:32:29, Alternative Forms Of The Work Done Expression, A Comparison Of The Work Done With Different Indices Of Compression. Thus, at the nominal optimum, the only unconstrained degrees of freedom are the refrigerant compositions. FIGURE 7.49. In reality there is a pressure drop in the intercooler, and the air temperature after the intercooler is considerably above the inlet air temperature at the first compressor, because the intercooler is commonly an air-to-air heat exchanger and it is impossible to cool the air back to its inlet temperature. For centrifugal compressors the curves are smoother and broader. Then the lift curve as a function of β2 is effectively rotated 180° from its appearance in Figure 7.47 as illustrated in Figure 7.48. η C = Isentropic compressor (pump) work/Actual compressor (pump) work The effect of piston-ring-joint design on oil consumption. Often the contribution of the term d/k can be neglected, so we then have: The computation of the values of h1 and h2 presents a complex problem in heat transfer theory. This type of heat exchanger can be used in the food or pharmaceutical industry, or for providing hot drinking water. PSI VS. BHP (Rule of thumb): For every 1 PSIG pressure drop, BHP (Brake horsepower) goes down ½ %. The compressor also cannot “abruptly” releases the input level immediately back to 0dB.Based on the diagram above; when the input level is 0dB, the compressor output level is still -3dB. Aftercoolers incorporate a moisture separator for this purpose. ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. URL: https://www.sciencedirect.com/science/article/pii/B9780444532923500298, URL: https://www.sciencedirect.com/science/article/pii/B9780444634337500687, URL: https://www.sciencedirect.com/science/article/pii/B9780128093269000075, URL: https://www.sciencedirect.com/science/article/pii/B9781856179126000074, URL: https://www.sciencedirect.com/science/article/pii/B9780081003138000116, URL: https://www.sciencedirect.com/science/article/pii/B9781856172493500039, URL: https://www.sciencedirect.com/science/article/pii/B978012801575900007X, URL: https://www.sciencedirect.com/science/article/pii/B9780080994161000048, URL: https://www.sciencedirect.com/science/article/pii/B9780080942421000188, URL: https://www.sciencedirect.com/science/article/pii/B9781845697280500070, Single-cycle mixed-fluid LNG process Part II: Optimal operation, Jørgen Bauck Jensen, Sigurd Skogestad, in, Proceedings of the 1st Annual Gas Processing Symposium, Proceedings of the 8th International Conference on Foundations of Computer-Aided Process Design, Alexander W. Dowling, ... Lorenz T. Biegler, in, Theory of Aerospace Propulsion (Second Edition), Underground coal gasification (UCG) modeling and analysis, Underground Coal Gasification and Combustion, Antony Barber C.Eng., M.Sc., F.I.Mech.E., M.R.Ae.S., in, Gas Turbine and Heat Recovery Steam Generator. 7.42. Nm/kg = J/kg = m 2 /s 2; Specific Work of a Pump or Fan. The value of K is hard to determine theoretically, and it is best when performing calculations to use test results. Air at. Temperature of the discharged air is normally about 10 to 16°C above the ambient when air cooling is used, and 10°C above the temperature of the water when water cooling is used. The performance map may also be put in terms of the compressor pressure ratio pt3/pt2, as shown in Figure 7.52; this is the more usual form for the compressor map. The Prandtl number is easy to determine since it merely depends on the properties of the fluid. The specific enthalpy of a mixture of gases is expressed as the sum of the specific enthalpies of each component and their mass fractions. The net effect is to have a curve of corrected work versus corrected weight flow that resembles the cL versus β2 curve in Fig. Since work must be put into an air compressor to run it, every effort is made to reduce this amount of work input. Note that for reciprocating compressor work, values of “n” may be used as “k” up to 1.4. IP = ∗. FIGURE 7.46. For a perfect gas working with a constant pressure ratio the work is directly proportional to temperature, from which (as well as by looking at Section 7.2) it may be inferred that the compressor work, CP(T1–T2), can be decreased by keeping the gas temperature (T2) in the compressor low. It will be apparent that in a heat exchanger the temperature difference between the fluid to be cooled and the coolant varies throughout the device, even under steady flow conditions. M.A. This is not a particularly efficient form of cooling and can be supplemented by an external intercooler. FIGURE 3. 60. Source: Fig. Assuming the nitrogen does not react within the gasifier, the flow rate of nitrogen at the inlet of the reactor is the same as at the exit. Self, in Underground Coal Gasification and Combustion, 2018. Representative variation of the lift coefficient as a function of angle of attack for a rotor blade. Operation in this region is to be avoided and the locus of maximum lift coefficient is also called the stall, or surge, line. where W.pump1 and W.pump2 are the rate of power consumption of pumps one and two, respectively. “n” represents the polytropic coefficient that is related to “k” by (n − 1)/n = (k − 1)/[(k) (Ep)], where (Ep) is the polytropic efficiency. (7.92) may be regrouped as follows: (7.93) Wc θ2 = K c[ N √θ2][ ˙m√θ2 δ2 1 sin β2][c L][1 + ɛ cot β 2] FIGURE 7.50. A. Kayode Coker, in Ludwig's Applied Process Design for Chemical and Petrochemical Plants (Fourth Edition), 2015. Variation of the lift coefficient as a function of the rotor entrance angle β2. For the latter, the increase in temperature per stage is lower than that of a single-stage machine of the same pressure ratio. If the machine does require cooling (eg in a reciprocating compressor), the necessary cooling may be achieved by finned cylinders with or without forced circulation. (HPC Engineering). One form of construction uses corrugated metal sheets, laid together and dip-brazed; another type uses an aluminium cooling matrix. Or. We use cookies to help provide and enhance our service and tailor content and ads. An after cooler is a heat exchanger used to cool compressed air after leaving the compressor. Limiters are typically set with short attack times, but this isn’t always the case. The second compressor completes the compression process to the desired final pressure. M. Bahrami ENSC 461 (S 11) Refrigeration Cycle 8 1) Steady operation 2) ∆KE=∆PE=0 3) Adiabatic heat exchanger. That is, the angles of attack experienced by the rotor are large enough to provoke flow separation resulting in (usually rapidly) declining lift coefficients. Pump Input Power = P. Formula – 1. In general, cooling may be advantageous or necessary to achieve the following: Maintain working clearances on machine components. Compressors and pumps, when undergo a steady-flow process, consume power. Suppliers of coolers have comprehensive design charts for selecting the appropriate type, and much practical experience in choosing the ideal design parameters. Forced draft air cooling may be adequate for both small and large compressors, particularly if the latter are low capacity or multi-stage machines. From Ideal Gas Law we know, that the molar specific heat of a monatomic ideal gas is: C v = 3/2R = 12.5 J/mol K and C p = C v + R = 5/2R = 20.8 J/mol K. We transfer the specific heat capacities into units of J/kg K via:. However, this is not physically possible, so cooling is done in stages. Specific work of a pump or fan working with an incompressible fluid can be expressed as: w = (p 2 - p 1) / ρ (1) where Air is forced through by a motor driven fan. The corrected mass flow is proportional to the axial velocity component ca and, referring to the entering velocity diagram shown in Figure 7.46, we may write ca as. The finder will select the best match from our line of standard compressors, but we can also design a … One way of doing this is to make the two flow velocities approximately equal. In the case of a refrigeration compressor, the refrigerant itself can be used. It is defined as: TABLE 2. Compression Stroke: Both Valves are shut. The drag factor is the fourth term in square brackets in Equation (7.93), and its behavior as a function of angle of attack is shown in Figure 7.49 and as a function of rotor entrance angle in Figure 7.50 for a nominal drag to lift ratio ɛ = 0.02. Fig. 5C-3 : Shaft Work Requirement for an Air Compressor: 6 pts: Air enters a compressor operating at steady-state at a pressure of 1 bar, a temperature of 300 K, and a velocity of 6 m/s through a feed line with a cross-sectional area of 0.1 m 2.The effluent is at a pressure of 7 bar and a temperature of 450 K and has a velocity of 2 m/s. Pasquale M. Sforza, in Theory of Aerospace Propulsion (Second Edition), 2017, The compressor work required follows the same analysis as for turbine work, starting from Eq. The compressor work equation in Eq. Compressor Design (Example 5): Specifications: 35cfm free air delivered. 7.52. FIGURE 7.51. The logarithmic mean temperature difference (LMTD) needs some explanation. Since compressor work reduces the net cycle work output, it is advantageous to keep the compressor outlet temperature low while reaching the desired pressure P2. 7.35 it is found that the condition for minimum compressor work is that both the compression ratio and work input for all stages must be equal. Reduce the temperature of the air for use when operating hand tools. Ideally T1=T4 and T3=T5. Any compressor that applies compression with a ratio of 10:1 or higher is considered to be acting as a limiter. 7.50. – Fail-safe heat exchanger. T-S diagram of compressor intercooling. Now that all the terms in Eq. The compression work input rate W.CO2,comp is determined using. 7.46 we may write ca as. The Nusselt number has been determined experimentally for a number of cases of practical interest, and is quoted in a variety of forms according to the geometry of the heat exchanger. Fig. Note that increasing β2 implies increasing mass flow. It is, of course, possible to reduce the temperature of the air to any desired level by refrigeration techniques. No account has been taken in the theoretical treatment of corrosion or the presence of layers of oil or scale on the surfaces. 7.48. The equation relating K to the constituent coefficients is, where: h1 and h2 are the convective coefficients of the two fluids in contact with the heat exchanger partition in W/(m2 K), d is the thickness of the partition wall in m, k is the thermal conductivity of the material of the partition in W/(m K). Generally counter-current is more efficient because the temperature difference between the two fluids is greatest, but practical heat exchangers often combine all three so as to produce maximum cooling efficiency in a minimum of space. It can be effectively increased by making the fluid follow a tortuous path of smaller cross-section by the insertion of baffles in the shell, Figure 3. Unless the machine specifically requires aftercooling, a low compression ratio machine may work satisfactorily uncooled (eg a single-stage centrifugal blower). 7.50). This is a non-dimensional quantity which plays a role in heat transfer theory analogous to that played by Reynolds number in determining the friction flow in pipes. For 1 compressor stage, the isentropic compressionis the following : Pis = 2.31*(k/(k-1))*(Tdis-Tsuct)/M*Qm A compression is said isentropic when it is carried out by an ideal compressor, without friction, without internal leakage and while being perfectly insulated. Fig. Mechanical Efficiency. Cool the delivered air to remove water (aftercooling). In a reciprocating compressor, the capacity depends on the volume displaced by the piston during its movement. The energy efficiency of the auxiliary plant, including the reboiler thermal requirements, is defined as, Antony Barber C.Eng., M.Sc., F.I.Mech.E., M.R.Ae.S., in Pneumatic Handbook (Eighth Edition), 1997. However, the term in Eq. Extra cooling between stages will be needed to bring the temperature down to an acceptable value. Note that increasing β2 implies increasing mass flow. Intercooling between compressor stages decreases the compressor work without changing the turbine work. Mode II The LNG production is maximized, see Equation 4. It is clear from the figure that the sum of the temperature rises, (T3–T1) + (T5–T4), is less than the temperature rise (T2–T1). The one obvious difference is the lack of combustion and hence that there is less cyclic temperature. The performance of such a compressor can be expected to vary with changes in the ambient temperature, as the effectiveness of the cooling varies with the difference in temperature between the cylinder and the ambient. Steam temperature and pressure at the exit of the HRSG are set to allow for steam formation rates that facilitate power production from the steam turbine while allowing the flow rate and temperature of the steam leaving the turbine, at the intermediate pressure, to be suitable for use in the splitter reboiler. The designs are based on the principle of providing a large exposed area in a high conductive material. – Configurations of shell-and-tube heat exchangers. For axial flow machines the curves are very much like the lift curves for airfoils, but reversed as discussed previously. It will be apparent that the velocity of the shell-side stream is likely to be smaller than that of the tube-side. Limit the amount of heating applied to the inducted charge, thus improving the efficiency of the compression and increasing the volumetric capacity. P = W / 42.4 (2) where P in Watt = Here. The last step in determining the individual k values is the relationship between h and Nu. The amount of cooling required by a compressor is higher than that considered optimum for an internal combustion engine. However, the term in Equation (7.96) does depend on the relative velocity w2, which is seen to decrease as the mass flow increases. Centrifugal compressors are cooled by three possible methods: Diaphragm cooling, which implies that the air passages are water jacketed with a supply of coolant through the jackets. Variation of the lift coefficient as a function of the rotor entrance angle β2. The air compressor work rate W.air,comp is determined as follows: where m.air is the mass flow rate of air entering the compressor and h1 and h2 are the specific enthalpies at the inlet and exit of the compressor, respectively. The maximum corrected work values correspond to the cL,max values of the individual curves for given corrected rpm and the locus of these points are shown on the figure. The amount of heat produced by compression is considerable which may not be an immediate disadvantage at low compression ratios, except that the air will be saturated with water vapour, some of which can be removed by aftercooling. Strictly, different curves should be drawn for different configurations of tube and shell, but Figure 2 drawn for a simple counter-current form is usually good enough, particularly when the other parameters are not known with any great accuracy. For centrifugal compressors the curves are smoother and broader. Dipak K. Sarkar, in Thermal Power Plant, 2015. For double acting air compressors multiply the work input by 2. Here the constant Kc is the analog to Kt for the turbine and expresses information on machine size and compressor inlet conditions. Injection cooling involves spraying a suitable liquid into the return channel of the compressor stage. – Cut away view of commercial shell-and-tube heat exchanger. Figure 7.15 shows that a compressor working between points 1 and 2 would expend more and more work as the gas approaches point 2. Analysis of this type of cooler is best done by the use of characteristics obtained from tests. With an efficient water cooling system applied to a reciprocating compressor cylinder, only about 10 to 15% of the heat generated will be removed. To calculate centrifugal compressor power, we need these gas properties: compressibility factor (Z), molecular weight (MW), inlet gas temperature, inlet gas pressure, outlet gas pressure, adiabatic component (Cp/Cv), and mass flow rate. Then the lift curve as a function of β2 is effectively rotated 180° from its appearance in Fig.

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