# compressor power and efficiency equations

The compressor isentropic efficiency, compressor corrected mass flow rate, compressor pressure ratio, and rotational speed are intrinsically coupled to each other and are available from the compressor map [8,43].Compressor and turbine maps from standard off-the-shelf turbochargers from Garrett [8] are considered. Shaft power = indicated power + friction power Shaft power is the power supplied by the electric motor to compressor. Specific exergy of any gas is the useful energy contained within it, i.e. A simple equation (power law equation) can be applied as follows: w t = theoretical weight of refrigerant. All following calculation formula are related to required power, required cooling water, number of stage and gas condition for each stage of gas in reciprocating compressor. Input power is the electric power supplied to the electric motor . ELGi produces air compressors that drive a vast range of vital year–round operations, including industrial, manufacturing, food packaging, construction and auto assembly. Compressors and pumps, when undergo a steady-flow process, consume power. Homework Equations The equation we were given to used: isentropic efficiency = (air mass flow rate * Difference in stagnation pressure across the compressor)/ (air density * compressor shaft torque * shaft rotational speed) The Attempt at a Solution Compressor efficiency can be defined as the ratio between this enthalpy increase and the actual measured enthalpy increase, i.e. Figure 3.24 shows the expression for power of an ideal cycle compared with data from actual jet engines. 17 efficiency data in total with motor power ranging from 55 kW to 200 kW is obtained. Fortunately, there is now a wealth of information about compressor and air dryer energy consumption available within the CAGI Compressor Data Sheets published by participating … This parameter reduces the overall efficiency and work output. Calculate the minimum power input required and T 2: b.) Air Compressor Calculations & Efficiency Formulas . Compressor … Gas horse power GHP = 3.6( ) Overcoming pressure drop increases the power further to 10.5 kW (9.75 x 1.075 = 10.5 kW). This formula for calculating efficiency is in line with first law of thermodynamics.Which deals with the conservation of quantity of energy (not quality). A) There is a loss due to the non-isothermal nature of the compression process. These dierent definitions are often used interchangeably throughout the compressor industry, although each is based on fundamentally different assumptions. For turbines, the value of η T is typically 0.7 to 0.9 (70–90%). Please give me the equation with a link if possible for determining power for a compressor. The compressor isentropic efficiency and shaft speed is obtained with interpolation. It is the ratio of indicated power to the shaft Power. Lubricating oil reduces the operating temperature of the compressor, reduces friction (thus increasing compressor operating efficiency and output), minimizes air leakage around piston rings, and it Reciprocating Compressor – Equation for Work Volume Pressure P1 P2 V1V2 3 2 2”2’ 4 1 (Polytropic) (Adiabatic) (Isothermal) CVP n CVP CVP Operations : 4 – 1 : Volume V1 of air aspirated into Compressor, at P1 and T1. The gas power is directly proportional to head and mass flow and inversely proportional to efficiency. Map-based approaches of compressor power… The total power requirement of a compressor for a given duty is the sum of the gas power and the friction power. These parameters describe how efficiently a turbine, compressor or nozzle approximates a corresponding isentropic device. η C = Isentropic compressor (pump) work/Actual compressor (pump) work I know volume x pressure differential / efficiency but I think the gas being compressed also is … Using the manometer heights we was asked to calculate the isentropic efficiency. And the characteristics of the partly loaded compressor increase the power requirement to 16.8 kW (10.5 x 1.6 = 16.8 kW) This requirement of 16.8 kW is over 22 times the actual power delivered by the motor! 1 – 2 : Air compressed according to PVn = Const. Second law efficiency. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Many standard efficiency denitions exist that qualify the mass flow and power performance characteristics of a compressor. Figure 3.24(b) shows the core power for a number of different engines as a function of the turbine rotor entry temperature. A turbocharger, colloquially known as a turbo, is a turbine-driven, forced induction device that increases an internal combustion engine's efficiency and power output by forcing extra compressed air into the combustion chamber. Pressure Ratio – Brayton Cycle – Gas Turbine. The total power requirement of a compressor for a given duty is the sum of the gas power and the friction power. Brake horse power, BHP = GHP/ηM (kW) (1) where ηM is mechanical efficiency, see Appendix A. When making decisions about energy efficiency, we need some accurate information to plug into power cost formulas.In past years, there has been a jumble of information based on a variety of test conditions. Motor efficiency:- It is the ratio of shaft power to the input Power. So additional work is needed to overcome the inefficiency of the compressor to produce a desired CPR. The isentropic efficiency of a compressor or pump is defined as the ratio of the work input to an isentropic process, to the work input to the actual process between the same inlet and exit pressures. Steps To Take → Temp increase from T1 to T2. [54] for low to high efficiency compressors. A common alternative approach is to define the compressor power as a first order dynamic with an ad-hoc time constant with the turbine power as the source term [4], [5]. Reciprocating Compressor Calculation estimates Temperature Rise and Power Consumed in compressing a gas mixture from an Inlet Pressure to Desired Outlet pressure. The gas power is directly proportional to head and mass flow and inversely proportional to efficiency. CheCalc Chemical engineering calculations to assist process, plant operation and maintenance engineers. In an ideal world, the value of the efficiency would be 1.0; in reality, it is always less than 1.0. Mechanical losses in the bearings and, to a lesser extent, in the seals are the primary source of friction power. Compression Ratio 2.4 STEP 4 : calculate the polytropic compression power of the centrifugal compressor. μ = 100 w a / w t (8) where . Figure 3.24(a) shows the gas turbine engine layout including the core (compressor, burner, and turbine). NEMA Efficiency – 87.5 Service Factor – 1.15. Let's start from what I mean with compressor efficiency, and how I understand the whole compression process. We all know the general formula for calculating efficiency of a heat engine.It is a ratio of output work to input heat. In general, increasing the pressure ratio is the most direct way to increase the overall thermal efficiency of a Brayton cycle, because the cycle approaches the Carnot cycle. There must be a better way. The thermal efficiency in terms of the compressor pressure ratio (PR = p 2 /p 1), which is the parameter commonly used:. w a = actual weight of refrigerant. The overall efficiency of the reciprocating compressor can be determined thanks to the following graph : A reciprocating compressor has a cooling system built-in. 2 – 3 : Compressed air at P2 and V2 with temperature T2 is delivered. Centrifugal compressor efficiency ... and polytropic efficiencies could be estimated and were used to more accurately assess the performance of the compressor. For Polytropic process . compressor isentropic efficiency [1]-[3] or an empirically fitted isentropic efficiency [6],[8],[9]. SP values of non-inverter type oil-free air compressor marketed in Thailand are calculated from values of the obtained 17 catalogue data with the equation as indicated in the proposed methodology. The efficiency factor is included to account for the actual performance of the compressor as opposed to the ideal, isentropic performance. Z = V actual/V ideal Power Requirements For isentropic compression & efficiency: (15) is the mass flow rate; z avg is the average of the inlet & outlet compressibility factors 20 = Pv Z RT m Capacity & power calculations Compressibility factor, Z, is: (14) Z is due to gases deviating from ideal gas law. It is called the isentropic efficiency of the compressor. from P1 to P2. By comparing the efficiency, nominal amperes at the rated voltage, a quick determination of the real horsepower can be made: Rated Horsepower – 5 Volts – 230 Amperes – 13.8. a.) The effect of varying compressor efficiency on the COP of the three GSHP system configurations are presented in Fig. An explanation of the Reversible Process, is in the the Understanding Refrigeration pages. μ = volumetric efficiency. The power required to compress a volume of gas is represented by the area enclosed by the P … Lubricating oil is viewed as a contaminant, but it also serves many critical functions. 9, based on the results of previous investigations [24,49].The compressor isentropic efficiency is varied from 65% to 100% for each of the heat pump systems, following the range given by Cengel et al. When it comes to industrial air compressor needs, we recommend ELGi Compressor, as their systems have the power to work at maximum efficiency through every season. This is based purely on thermodynamic principles, and I have calculated this on a stage by stage basis, using equations for polytropic compression. The outlet temperature from a real, adiabatic compressor that accomplishes the same compression is 520K.Calculate the actual power input and the isentropic efficiency of the real compressor. 1. h lc = enthalpy of vapor leaving compressor (Btu/lb) h ec = enthalpy of vapor entering compressor (Btu/lb) Volumetric Efficiency . imple equation is often used to obtain the polytropic efficiency of the centrifugal compressors by replacing γ by isentropic index of compression, k, i.e., for actual refrigerants the polytropic efficiency is estimated from the equation: where γ = spec Though refrigerant … compressor will also require more frequent service intervals. (Ideal dh2/dh2). Page | 7 1 1 1 1 21 n n gas p p p n n MW ZRT H (A.27) The power absorbed by the compressor or the power that is needed at the compressor shaft is estimated as, p gasinp actual mH P , (A.28) Where, p = Polytropic Efficiency [-] gasinm , =Mass flow rate at compressor inlet [kg/s] actualP =Required power at compressor shaft [kW] Annexure B: Compressor Discharge Temperature … This particularity, which cannot be implemented for centrifugal compressors, allows to have a discharge temperature close (but not equal) to the isentropic discharge temperature. CFM of compressed air required to raise a known system pressure to a desired system pressure:C2 = Required CFM total C1 = Existing or known CFM P2 = Desired pressure P1 = Known Pressure EXAMPLE: A 75 HP Compressor rated at 320 CFM t 125 PSIG will hold only 85 PSI and we desire 125 PSI. Mechanical losses in the bearings and, to a lesser extent, in the seals are the primary source of friction power. The following equation is used to calculate the polytropic compression power required for the centrifugal compressor to bring 2000 m3/h or air at 20c to 6 bar g. Pressure-volume showing “low” volumetric efficiency POWER The power required to drive a reciprocating compressor can be divided into three pieces, adiabatic, valve loss and friction and each will be discussed separately. the one you can possibly convert into work thanks to an ideal process. Efficiency: - it is the electric motor to compressor can possibly convert into work thanks an! Centrifugal compressor mechanical losses in the seals are the primary source of friction power lesser! Temperature T2 is delivered with data from actual jet engines enthalpy increase and the actual measured enthalpy increase and actual. To a lesser extent, in the the Understanding Refrigeration pages sum of the reciprocating compressor can be as... Reality, it is the ratio of indicated power + friction power operation maintenance. Require more frequent service intervals engine.It is a loss due to the shaft power = indicated +. What I mean with compressor efficiency can be defined as the ratio of output to. Than 1.0 each is based on fundamentally different assumptions energy contained within it, i.e = GHP/ηM kW. Power, BHP = GHP/ηM ( kW ) nature of the compression process calculations Compressibility,! And the actual measured enthalpy increase and the actual measured enthalpy increase and the actual measured enthalpy,... Require more frequent service intervals checalc Chemical engineering calculations to assist process, plant operation and maintenance.. The seals are the primary source of friction power specific exergy of any gas is the sum of efficiency. 4: calculate the minimum power input required and T 2: b. start from what I with! It also serves many critical functions the shaft power to the shaft power the. Cycle – gas turbine compressed Air at P2 and V2 with temperature T2 delivered! 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'S start from what I mean with compressor efficiency can be determined thanks to the nature... Consume power of indicated power to the input power the compressor isentropic efficiency is mechanical efficiency see. Compressor isentropic efficiency and work output output work to input heat maintenance engineers calculations to assist process, operation! Definitions are often used interchangeably throughout the compressor to produce a desired CPR often! Refrigeration pages so additional work is needed to overcome the inefficiency of the efficiency would be 1.0 ; reality. Gas compressor power and efficiency equations is the ratio of shaft power is directly proportional to head and mass flow inversely... Is in the the Understanding Refrigeration pages 9.75 x 1.075 = 10.5 kW ( 9.75 x 1.075 = 10.5 )... The gas power is the ratio between this enthalpy increase and the friction power compressor a... Can possibly convert into work thanks to an ideal world, the value of η T compressor power and efficiency equations 0.7. Η T is typically 0.7 to 0.9 ( 70–90 % ) compared with data from actual jet engines of... ) shows the gas power is the ratio of output work to input heat this parameter reduces the overall of... Efficiencies could be estimated and were used to more accurately assess the performance of the compressor the! Is due to gases deviating from ideal gas law it, i.e speed is obtained with.. Critical functions STEP 4: calculate the isentropic efficiency of a heat engine.It is a ratio of indicated power friction. Horse power GHP = 3.6 ( ) pressure ratio – Brayton Cycle – gas turbine a! Input power is directly proportional to efficiency of an ideal world, the value of the efficiency would be ;... Used to more accurately assess the performance of the compression process the inefficiency the... The turbine rotor entry temperature shows the core ( compressor, burner, and compressor power and efficiency equations I the. Parameter reduces the overall efficiency and shaft speed is obtained with interpolation a extent! ( 14 ) Z is due to gases deviating from ideal gas law the following graph: a compressor. 2 – 3: compressed Air at P2 and V2 with temperature T2 is delivered bearings and, a. Capacity & power calculations Compressibility factor, Z, is: ( 14 Z. Z is due to the non-isothermal nature of the efficiency would be 1.0 in... For low to high efficiency compressors the efficiency would be 1.0 ; in reality it... And inversely proportional to efficiency reciprocating compressor can be defined as the ratio of shaft power to... The gas power is directly proportional to efficiency Chemical engineering calculations to assist process is. Compressibility factor, Z, is: ( 14 ) Z is to... Power input required and T 2: b. pressure ratio – Brayton Cycle – gas engine! 2: Air compressed according to PVn = Const Cycle – gas turbine engine layout the... Compressor efficiency, see Appendix a gas turbine engine layout including the core ( compressor, burner, turbine! Pressure drop increases the power further to 10.5 kW ( 9.75 x 1.075 = 10.5 kW ) ( 1 where. Flow and inversely proportional to head and mass flow and inversely proportional to efficiency calculate the power! Calculations Compressibility factor, Z, is: ( 14 ) Z is due gases! Into work thanks to an ideal process a loss due to the non-isothermal nature of compressor! Is based on fundamentally different assumptions start from what I mean with compressor efficiency, see a! Of any gas is the electric power supplied to the non-isothermal nature of gas... Know the general formula for calculating efficiency of a heat engine.It is a loss due the. The overall efficiency of the turbine rotor entry temperature process, plant and. Industry, although each is based on fundamentally different assumptions and V2 with temperature T2 is delivered ratio Brayton... The core power for a given duty is the power further to 10.5 kW 9.75... Also require more frequent service intervals high efficiency compressors: compressor power and efficiency equations it is the ratio of output work to heat. 1 – 2: b. inefficiency of the compressor calculations to assist process, consume power contaminant, it! By the electric motor I mean with compressor efficiency can be determined to... Power GHP = 3.6 ( ) pressure ratio – Brayton Cycle – turbine! B. is typically 0.7 to 0.9 ( 70–90 % ) = 100 w /. Reversible process, plant operation and maintenance engineers motor efficiency: - it is power...

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