B. Isentropic compression. Now, the pressure rises from P1 to P2 from 2-3. The P-V diagram is a plot of the pressure of the gas versus the volume of the gas trapped in the compression chamber. Reciprocating Compressor Calculation estimates Temperature Rise and Power Consumed in compressing a gas mixture from an Inlet Pressure to Desired Outlet pressure. = P2V2 + 2.3 P2V2 log (V1/V2) - P1V1 —————————————(1), We know that for an isothermal process PV = constant, Since P1V1 = P2V2 , Therefore V1/V2 = P2/P1, = 2.3 P2V2 log (r) ( where r - compression ratio = P2/P1). 1. Compressors and Expanders Compressors Depending on application, compressors are manufactured as positive-displacement, dynamic, or thermal type ( Fig. 79 0 obj <> endobj However, this formula tends to work best for large reciprocating air compressor systems. The Work Done And The Power Required For Compressing The Refrigerant A). - Area 1-1’-2-2. The head developed by the compressor is expressed in following compressor equations.... Adiabatic compressor head equation The same principles are applied to the compression of other gasses. All Rights Reserved. This means those compressors can only operate half the time which reduces your ability to get the job done. 0 Thus this process takes maximum energy input as no heat loss takes place through the cylinder walls. The mass flow per unit time ṁ is often used to compute the work done/time or indicated power. Therefore the work done by the compressor is : W = 2.3 m R T1 log(r) ( where m is mass of air delivered by the compressor per cycle). With : Pis=Power (kW) Tsuct=Temperature inlet compre… None … Therefore equation (4) can be re-written as: which means that the work done is equal to the heat required for raising the temperature from T1 to T2 at a constant pressure. The compression follows the path 1-2-3”-4-1. CALCULATION FORMULA. = Area 3-4-1’-3. Now let us discuss the work done by the compressor when it follows the law PVn = constant. Then the pressure ratio of the compressor is P 2 /P 1. Above calculation is correct for ideal case. P = compression power (hp) W = compression work (Btu min) Alternatively. Therefore the work done by the compressor is, W = γ/(γ-1) m R (T2- T1) ———————————(4), R = cp - cv and γ = cp / cv (where R- gas constant, cp -specific heat capacity at constant pressure, cv - specific heat capacity at constant volume respectively). L���0�L�MP�ܑ`[���t٩$s�ؙ/Ad��($��^f`��X=#M��L�> ��l This is very similar to polytropic compression except the polytropic index n is replaced by γ. The volume of air delivered being 3”-4. Now let us consider the following for a single stage single acting reciprocating compressor without clearance volume. In this diagram, the path 2-3 represents the polytropic compression and the path 2-3’ represents the isothermal compression and the path 2-3” represents the isentropic compression. Here P i will remain same for all stages. %%EOF . Let P1, V1, T1 be the Pressure, volume and Temperature of the fluid before compression, P2, V2, T2 be the pressure, volume and temperature of the fluid after compression, and r be the compression ratio = P2/P1. In a single stage, single acting reciprocating air compressor, without clearance volume, the work-done is minimum during. Identifying the maximum consumption of an air compressor system is critical when sizing an air receiver tank. W = m cp (T2 - T1) which means that the work done is equal to the heat required for raising the temperature from T1 to T2 at a constant pressure. + Area 2-3-3.-2. Reciprocating Compressor – Efficiency Isothermal work done / cycle = Area of P – V Diagram = P1V1 loge(P2/P1) Isothermal Power = P1V1 loge(P2/P1) N 60 X 1000 kW Indicated Power : Power obtained from the actual indicator card taken during a test on the compressor. Head = Compressor head, m (ft) Power = Compressor power, kW (HP) R = Universal gas constant, 848 kg-m/(kmol-K) or (1545 ft-lb f /(lbmol-°R)) P S = Standard condition pressure, kPa (psia) P 1 = Suction pressure, kPa (psia) P 2 = Discharge pressure, kPa (psia) T S = Standard condition temperature, K (°R) T 1 = Suction temperature, K (°R) P = c / (42.4 COP) (2b) where. A reciprocating compressor is a positive displacement machine in that a volume of gas is drawn into a compressor cylinder’s compression chamber where it is trapped, compressed and pushed out. compressor. The piston starts doing to and fro motion inside the cylinder. Use only this equation for finding out the dimensions of the cylinder. 2. h�b```�e��g@��(�����ç3֊SO?``�{&����-x���u5�V!J P = compression power (hp) c = capacity (Btu/min) COP = coefficient of performance. Therefore the equation (3) can be re-written as: (or) The equation (2) can be re-written as: or V2/V1 = (P1/P2)1/n or V1/V2 = (P2/P1)1/n, since, for a polytropic process PVn = constant. Work done during discharge W 3 = Area C 1 DA'C 1 '. W 3 = p 2 v 2. Find the Temperature at the end of the Compression and Calculate per pound of Air, the Compressor Work input and the heat rejected during Compression. The air will be delivered when sufficient pressure has been reached so that the valves can be opened. 122 0 obj <>stream Answer: Option A The compression may be isothermal, isentropic, or polytropic compression. The compressors used for compressing air are called air compressors. C. Polytropic compression. Reciprocating Compressor INTRODUCTION TO COMPRESSOR: Compressors are work-absorbing devices that are used for increasing the pressure of the fluid ( Air, oil, Refrigerant ) at the expense of work done on fluid. Actually I already referred book of reciprocating compressor. POWER REQUIRED. A rotary screw compressor is designed to run 100% of the time so you can get your job done without needing to wait. With a single-acting reciprocating compressor, here is how it works: When you start the motor, it turns the crankshaft using a belt, you can see attached to the motor. P i = 2.5875 . From the above diagram it is clear that the air is drawn in by the cylinder during the suction stroke (1-2). Some of them are the reciprocating compressor, rotary compressor, etc., Each have their own advantages and disadvantages. Now let us discuss the PV and TS diagrams of a single acting, single stage reciprocating compressor without clearance volume. On a pressure versus volume graph of a reciprocating compressor the area enclosed represents the work done by the reciprocating compressor. Calculating Maximum Air Consumption. CheCalc Chemical engineering calculations to assist process, plant operation and maintenance engineers. Now the piston after reaching at BDC, starts moving upward (i.e. What is the correct formula for net work done of reciprocating engine? The reciprocating compressor is probably the most versatile of all the types and is only out performed by rotary types when large volumes at low pressures are required. Isothermal power = W (isothermal compression ) Nw / 60 watts, Polytropic power = W (polytropic compression) Nw / 60 watts, Isentropic power = W ( Isentropic compression) Nw / 60 watts, Wireless Energy Management System Explained: Configuration, Components Used, and Benefits. The reciprocating compressor is either powered by electric motor, diesel/gas engines. P 2 /P 1 = (V 1 /V 2) n... Polytropic compression P 2 /P 1 = (V 1 /V 2) γ... Adiabatic compression. 13-2 ). An Air Compressor takes in Air at 14 psi and at 20 degrees C. It is compressed in accord to the law and delivers it to receiver at 140psi. MECH402 ENERGY SUSTAINABLE DESIGN 3 Figure 3.1: Cylinder and Piston Mechanism and P-V Diagram of a Reciprocating Compressor The work done for compression is given by the cyclic integral of pdV. The above area can be further split as follows: W= Area 1’-4-3’-3.’ + Area 2-3’-3.'-2. 1. Reciprocating Compressors Compression Ratios - posted in Industrial Professionals: Hi, I am new to this forum and have a quick question. Now let us discuss each in detail in the following paragraphs. As power is On, the electric motor starts rotating and also rotates the crankshaft attached to it. 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. The other types are covered briefly.