Meta tags:
Headings (most frequently used words):
compressors, compressor, compression, of, or, piston, rotary, contents, types, thermodynamics, gas, temperature, staged, drive, motors, lubrication, applications, see, also, references, positive, displacement, dynamic, hermetically, sealed, open, semi, hermetic, isentropic, minimizing, work, required, by, in, ideal, thermodynamic, cycles, reciprocating, ionic, liquid, screw, vane, rolling, scroll, diaphragm, air, bubble, centrifugal, diagonal, mixed, flow, axial, comparing, reversible, to, irreversible, effect, cooling, during, the, process,
Text of the page (most frequently used words):
the (334), and (183), #compressor (152), compressors (109), air (90), gas (86), are (62), for (58), compression (56), from (48), can (45), pressure (44), displaystyle (44), frac (41), that (39), with (34), edit (32), heat (31), used (28), rotary (27), piston (27), pump (26), work (25), this (24), high (24), reciprocating (24), hermetic (24), process (23), compressed (23), flow (22), isentropic (22), use (21), refrigeration (21), system (21), cooling (21), volume (21), more (21), they (20), than (19), motor (19), left (19), right (19), temperature (18), screw (18), centrifugal (17), constant (17), stage (17), may (16), also (16), scroll (16), main (16), energy (15), oil (15), original (15), archived (15), axial (15), have (15), retrieved (14), other (14), type (14), power (14), between (14), less (14), efficiency (13), water (13), large (13), known (13), isothermal (13), ideal (13), gases (12), heating (12), conditioning (12), displacement (12), fluid (12), such (12), small (12), applications (12), semi (12), due (12), vane (12), ventilation (11), refrigerant (11), fan (11), low (11), cycle (11), rotor (11), where (11), engines (11), ratio (11), one (11), adiabatic (11), wikipedia (10), building (10), drive (10), positive (10), hydrogen (10), some (10), types (10), natural (10), not (10), polytropic (10), when (10), its (10), article (10), seals (10), diaphragm (10), 2017 (9), mechanical (9), heater (9), components (9), variable (9), electric (9), rotating (9), driven (9), combustion (9), systems (9), internal (9), compress (9), being (9), but (9), which (9), open (9), stationary (9), solar (8), see (8), engineering (8), www (8), processes (8), discharge (8), com (8), rolling (8), single (8), device (8), liquid (8), engine (8), only (8), either (8), shaft (8), their (8), stages (8), typically (8), using (7), articles (7), all (7), diving (7), control (7), valve (7), value (7), vapor (7), thermodynamics (7), isbn (7), horsepower (7), machine (7), 2025 (7), increase (7), range (7), operate (7), require (7), uses (7), higher (7), pressures (7), into (7), motors (7), well (7), number (7), metal (7), most (7), without (7), ionic (7), page (6), was (6), industrial (6), duct (6), thermal (6), expansion (6), mixed (6), out (6), specific (6), design (6), tools (6), turbine (6), transport (6), pneumatic (6), move (6), often (6), turbines (6), plants (6), lower (6), speeds (6), since (6), built (6), bearings (6), these (6), larger (6), three (6), part (6), very (6), has (6), two (6), staged (6), model (6), usually (6), losses (6), will (6), reversible (6), psi (6), clearance (6), smaller (6), about (5), non (5), short (5), different (5), fire (5), handbook (5), passive (5), vanes (5), around (5), conditioner (5), source (5), enthalpy (5), breathing (5), chemical (5), state (5), new (5), speed (5), cylinder (5), bearing (5), maintain (5), compressing (5), service (5), cylinders (5), required (5), cycles (5), many (5), same (5), rise (5), mpa (5), any (5), both (5), actual (5), kappa (5), perfect (5), during (5), increases (5), like (5), geq (5), act (5), delta (5), compared (5), cost (5), leak (5), blades (5), reliable (5), vibration (5), toggle (4), contents (4), search (4), contact (4), available (4), you (4), commons (4), clarification (4), equipment (4), international (4), template (4), world (4), exhaust (4), radiator (4), thermostat (4), damper (4), space (4), inverter (4), insulation (4), perry (4), asme (4), performance (4), pdf (4), 2016 (4), achieve (4), means (4), impeller (4), linear (4), bar (4), pumps (4), repair (4), increasing (4), life (4), surface (4), intake (4), thus (4), however (4), while (4), output (4), portable (4), there (4), because (4), each (4), times (4), case (4), making (4), loss (4), int (4), real (4), time (4), efficient (4), even (4), final (4), comparing (4), cannot (4), replaced (4), screws (4), through (4), hermetically (4), sealed (4), efficiencies (4), pumping (4), airfoils (4), multi (4), diagonal (4), surging (4), housing (4), 000 (4), chamber (4), outlet (4), membrane (4), fewer (4), liquids (4), reducing (4), hide (4), sidebar (4), view (3), code (3), safety (3), text (3), under (3), terms (3), site (3), wikimedia (3), pages (3), redirect (3), via (3), link (3), wikidata (3), needing (3), august (3), support (3), home (3), industry (3), balancing (3), electrical (3), environmental (3), leakage (3), deep (3), architectural (3), room (3), rate (3), smoke (3), switch (3), pipe (3), filter (3), unit (3), boiler (3), barrier (3), back (3), radiant (3), free (3), absorption (3), technology (3), mass (3), effect (3), noise (3), changes (3), processing (3), industries (3), press (3), 2010 (3), section (3), february (3), thermodynamic (3), university (3), john (3), phoenix (3), patent (3), daikin (3), operations (3), how (3), does (3), supplies (3), operation (3), maintenance (3), lobe (3), vacuum (3), operated (3), based (3), external (3), reduce (3), forces (3), cabin (3), continuous (3), exist (3), gasses (3), end (3), pistons (3), stations (3), fill (3), various (3), fuel (3), supplied (3), jet (3), plastic (3), petrochemical (3), similar (3), consumer (3), volumes (3), needed (3), fixed (3), connected (3), diesel (3), increased (3), crankshaft (3), suitable (3), current (3), lubricant (3), typical (3), 343 (3), inter (3), account (3), assumes (3), then (3), pdv (3), devices (3), example (3), always (3), amount (3), parts (3), heats (3), initial (3), inherent (3), internally (3), way (3), casing (3), comp (3), vdp (3), involves (3), change (3), must (3), requiring (3), over (3), application (3), expensive (3), top (3), relatively (3), along (3), inlet (3), dynamic (3), radial (3), velocity (3), compresses (3), fueling (3), material (3), movement (3), instead (3), capacities (3), moving (3), important (3), volumetric (3), capacity (3), mounted (3), 200 (3), wide (3), plate (3), languages (2), table (2), privacy (2), policy (2), categories (2), displaying (2), descriptions (2), targets (2), url (2), 2014 (2), unsourced (2), statements (2), description (2), technologies (2), org (2), states (2), plumbing (2), automation (2), hvac (2), science (2), ashrae (2), quality (2), testing (2), kitchen (2), cleaning (2), information (2), services (2), thermostatic (2), psychrometrics (2), programmable (2), minimum (2), infrared (2), delivery (2), blower (2), door (2), whole (2), house (2), wall (2), ductwork (2), coil (2), plenum (2), exchanger (2), ground (2), gasoline (2), hood (2), fireplace (2), tank (2), convection (2), underfloor (2), distribution (2), storage (2), hybrid (2), recovery (2), forced (2), district (2), controlled (2), cross (2), chilled (2), central (2), materials (2), automobile (2), refrigerator (2), humidity (2), transfer (2), domestic (2), envelope (2), per (2), powder (2), roots (2), oxygen (2), 2008 (2), 2009 (2), underwater (2), medicine (2), hyperbaric (2), potential (2), within (2), toshiba (2), 8th (2), edition (2), green (2), 2015 (2), ptc (2), edu (2), 2023 (2), tds (2), mcgraw (2), hill (2), print (2), cheremisinoff (2), nicholas (2), wiley (2), sons (2), mechanics (2), 1910 (2), media (2), sertco (2), orbiting (2), 1985 (2), samsung (2), what (2), 2007 (2), technical (2), blackmer (2), download (2), thomasnet (2), references (2), powered (2), trompe (2), slip (2), tube (2), working (2), hot (2), greater (2), atmospheric (2), aircraft (2), pressurization (2), related (2), reduction (2), provide (2), auto (2), vehicles (2), etc (2), road (2), vehicle (2), rail (2), inside (2), superchargers (2), turbochargers (2), buoyancy (2), containers (2), generally (2), supply (2), manufacturing (2), purified (2), manufactured (2), petroleum (2), refineries (2), product (2), cargo (2), pipeline (2), necessary (2), eventually (2), leading (2), failure (2), line (2), contaminate (2), lubrication (2), including (2), setup (2), supercharger (2), alternating (2), phase (2), steam (2), exceed (2), commercial (2), designs (2), cooled (2), coolers (2), intercoolers (2), partial (2), removed (2), takes (2), above (2), theoretical (2), 100 (2), approximately (2), found (2), added (2), closely (2), scale (2), level (2), come (2), practical (2), unless (2), degrees (2), absolute (2), simple (2), certain (2), would (2), tire (2), becomes (2), relation (2), described (2), rankine (2), below (2), begin (2), cases (2), rightarrow (2), assumptions (2), rather (2), idealized (2), requires (2), least (2), decreases (2), common (2), following (2), diagram (2), limits (2), rev (2), comparison (2), form (2), irreversible (2), minimizing (2), zero (2), meaning (2), disadvantage (2), maintained (2), entire (2), fails (2), further (2), thereby (2), operates (2), sized (2), cheaper (2), simpler (2), pressurized (2), operating (2), rely (2), years (2), welded (2), steel (2), opened (2), simply (2), shell (2), primary (2), route (2), advantages (2), serviced (2), driving (2), designed (2), near (2), avoid (2), function (2), outer (2), tolerances (2), medium (2), arrays (2), direction (2), beyond (2), stators (2), allow (2), exit (2), diffuser (2), conventional (2), magnetic (2), machining (2), suction (2), side (2), cause (2), damage (2), caused (2), forth (2), extensively (2), force (2), early (2), allows (2), bubble (2), prototype (2), station (2), cng (2), company (2), arizona (2), flexing (2), diaphragms (2), occurs (2), mechanism (2), structure (2), valves (2), lighter (2), spiral (2), scrolls (2), dry (2), machines (2), kpa (2), slots (2), flooded (2), drier (2), commonly (2), automotive (2), another (2), swash (2), six (2), density (2), appearance (2), upload (2), file (2), links (2), history (2), read (2), english (2), norsk (2), bahasa (2), subsection (2), log (2), create (2), donate (2), menu (2), add, topic, mobile, cookie, statement, statistics, developers, conduct, legal, contacts, disclaimers, additional, apply, agree, registered, trademark, profit, organization, foundation, inc, creative, attribution, sharealike, license, rendered, parsoid, last, edited, september, 2026, utc, hidden, module, annotated, category, cs1, unfit, 2018, https, index, php, title, oldid, 1376162770, yale, lux, israel, czech, republic, japan, bnf, data, france, united, national, gnd, authority, databases, protection, day, warm, spaces, glossary, fireproofing, voc, volatile, organic, compound, sbs, sick, syndrome, smoking, iaq, indoor, health, umc, smacna, leed, iir, institute, cibse, bsria, bre, astm, amca, ahri, organizations, adjusting, reclamation, mold, growth, assessment, remediation, hydronic, retrofit, bim, modeling, technologist, acoustics, professions, trades, thermographic, camera, stp, standard, smart, communicating, opentherm, ntp, normal, merv, reporting, lonworks, intelligent, buildings, thermometer, humidistat, monitor, detector, cadr, clean, carbon, dioxide, sensor, bacnet, aquastat, meter, measurement, zone, wood, burning, stove, windcatcher, ulpa, ultra, particulate, turning, turboswing, trombe, trickle, vent, wheel, canopy, assisted, chimney, sail, run, reversing, register, recuperator, reflector, pressurisation, packaged, terminal, louver, kerosene, humidifier, cut, off, glandless, circulating, hepa, film, coupled, grille, grease, furnace, fume, freon, flue, freeze, stat, insert, evaporator, evaporative, cooler, electrostatic, precipitator, economizer, dehumidifier, tower, condensing, condenser, condensate, chiller, ceramic, blast, automatic, attic, purifier, mixing, ionizer, handler, recycling, vrf, vav, vcrs, thermosiphon, combisystem, renewable, raised, floor, radon, mitigation, daytime, radiative, microgeneration, mode, ice, hydronics, hrv, firestop, erv, dcv, demand, doas, dedicated, outdoor, coolant, cav, beam, autonomous, antifreeze, vapour, destratification, comfort, stack, sensible, particulates, outgassing, latent, infiltration, dynamics, consumption, dilution, bake, ach, hour, fundamental, concepts, powderprocess, net, resources, blowers, harlow, 2002, airspeed, 9678873, hacker, companion, millar, mouldey, 22692708, pmid, 145, south, pacific, society, evil, mirai, kagakukan, museum, first, residential, engineer, june, test, exhausters, mae, buffalo, courses, sens, alvi, famu, florida, equations, cengel, yunus, michaeul, boles, approach, 7th, york, 2012, kano, fumikata, texas, development, 9781119117889, pollution, aungier, ronald, 2000, 7918, 0093, strategy, aerodynamic, analysis, dixon, 1978, third, pergamon, 022722, turbomachinery, maynard, frank, november, 633, popular, five, thousand, bubbles, eric, slack, winter, corporation, march, mining, richardson, hubert, member, biased, 4875838, 1989, caillat, weatherston, bush, axially, compliant, mounting, 4767293, 1988, tischer, utter, sealing, 4522575, cop, global, news, mini, docs, lib, purdue, motion, matteicomp, investment, mattei, jacobs, 2006, conference, paper, 1825, tri, altıntop, hamit, 2020, máy, nén, khí, applied, davletshin, anton, 9781119100003, hydraulic, fracturing, management, practices, ics, domnickhunter, centre, domnick, hunter, gen, schneider, ref, doc, april, machinery, machinerylubrication, basics, bloch, hoefner, 1996, gulf, professional, publishing, 88415, 525, eds, 978, 142294, engineers, petko, mukelov, advanced, analog, sound, circuit, msc, diplom, sofia, 1984, measure, factor, manually, natterer, desorption, hydride, ring, actuator, guided, foil, tool, kindling, electrochemical, dryer, radially, outward, spacecraft, cabinet, conveying, lines, solids, reached, shops, tires, heavy, brakes, gearbox, windscreen, wipers, doors, burn, hence, produce, store, later, displacing, chambers, adjust, submarines, pressurised, directly, therapy, self, contained, apparatus, turbofans, turbojets, altitude, pet, bottles, blow, moulding, welding, medical, intermediate, maritime, carriers, production, fueled, bled, include, drives, insufficient, quantities, reach, excessive, amounts, lost, potentially, splashing, runs, unlubricated, vfd, automobiles, airplanes, boats, trucks, burned, own, turbocharger, petrol, cheap, quiet, static, possible, options, powers, make, instance, ksi, atm, atmospheres, flywheel, directs, ambient, across, intercooler, currently, raises, result, condensation, separators, enter, leave, input, appear, useful, percent, infinity, effort, made, cool, evaluated, integral, remains, throughout, models, exchanging, long, utilize, closest, achieving, attainable, infinite, corresponding, never, follow, quick, good, practice, bicycle, kelvins, transferred, resulting, values, refer, done, closed, transformation, laws, note, applicable, inefficient, truly, calculation, purposes, brayton, otto, carnot, results, show, exponent, rejection, jackets, rtln, nrt_, krt_, behaves, maximum, therefore, consuming, negative, reversibly, furthermore, produces, acteltaq_, let, kinetic, differential, balance, eta, cong, defining, attained, isotropic, refers, equation, calculated, steady, entropy, repaired, burnt, windings, entirely, pumped, down, happen, factory, assembled, goods, labor, economical, just, purchase, mid, refurbish, price, build, susceptible, splash, frequently, enough, slowly, evaporates, until, longer, functional, recharged, sit, unused, started, again, experiencing, lubricated, particularly, soluble, lubricating, difference, piece, cast, gasketed, covers, replace, advantage, motive, allowing, appropriate, selected, sources, secondly, opening, integrated, passes, body, retain, exhibit, necessitates, effective, elimination, openings, describe, enclosed, situated, outside, extent, handling, toxic, polluting, rounded, permanently, shut, evaporate, defrost, r600a, freezer, conditions, tight, set, rows, pairs, accelerate, decelerate, preparing, next, almost, sectional, area, passage, diminishing, optimum, fitted, features, angles, guide, ability, escape, interstage, bleed, split, assembly, twin, spools, mach, rotors, progressively, rates, compact, animation, component, turn, comparative, largest, offer, loads, coefficient, evaporators, condensers, weigh, occupy, exposed, wear, generate, minimal, highly, precise, needs, rotate, impractical, likely, reversal, goes, serious, specially, whatever, causing, oscillations, cnc, ski, resorts, snowmaking, magnetically, levitated, disk, shaped, rim, divergent, converts, primarily, thousands, multiple, staging, 1900s, schiele, frankfurt, mixture, generated, turbulence, allowed, fall, subterranean, separates, weight, falling, submerged, height, roof, facility, principle, ragged, shutes, nearby, mines, cobalt, ontario, montreal, river, compliance, prevailing, codes, demonstrate, could, urban, areas, alternative, photograph, depicts, downtown, utilities, were, developed, public, degree, constituting, affects, stiff, displace, few, cubic, centimeters, endure, cracking, stiffness, rubber, silicone, capable, enduring, strokes, flexion, strength, need, embrittlement, variant, flexible, element, rod, box, nor, possess, vibrating, much, volkswagen, g60, g40, 1990s, though, peltier, factors, consider, designing, interleaved, geometry, curves, smoothly, quietly, reliably, orbits, eccentrically, trapping, pockets, archimedean, involute, fluids, offers, given, impact, shipping, costs, causes, tons, spring, swing, style, plays, partition, against, port, connections, bulk, injected, suited, significantly, quieter, equivalent, 190, 300, consist, inserted, offset, circular, complex, shape, turns, slide, keeping, series, decreasing, created, oldest, eccentric, meshed, moderately, classifications, vary, methods, among, others, commercially, produced, depends, selection, sizes, leaks, cavities, depend, fine, prone, incorrectly, poorly, 890, helical, household, workshop, job, attached, receiver, finds, varying, size, unloading, suffers, resistance, weighs, difficult, having, seen, intermittent, duty, 18000, 124, double, acting, said, costly, comparable, units, employed, wobble, moved, citation, 750, four, put, drawing, discrete, forcing, pass, linkage, considered, vague, illustrated, discussed, distinction, focus, mostly, achievable, compressible, incompressible, rarely, action, pressurize, several, steps, second, physically, accommodate, already, belliss, morcom, bottling, powerful, street, xass, circa, atlas, copco, filling, scuba, disambiguation, encyclopedia, item, projects, printable, version, export, legacy, parser, get, shortened, cite, permanent, here, general, actions, talk, tiếng, việt, oʻzbekcha, ўзбекча, اردو, українська, татарча, tatarça, türkçe, ไทย, தமிழ், svenska, slovenščina, slovenčina, srpskohrvatski, српскохрватски, русский, română, português, polski, bokmål, nynorsk, nederlands, नेपाली, melayu, मराठी, монгол, latviešu, lietuvių, кыргызча, 한국어, қазақша, 日本語, italiano, indonesia, հայերեն, magyar, kreyòl, ayisyen, hrvatski, हिन्दी, galego, gaeilge, français, suomi, فارسی, euskara, eesti, español, esperanto, ελληνικά, deutsch, dansk, čeština, català, български, беларуская, azərbaycanca, العربية, afrikaans, personal, special, recent, community, portal, learn, help, contribute, random, events, navigation, jump, content,
Text of the page (random words):
n an optimum axial mach number beyond about 5 stages or a 4 1 design pressure ratio a compressor will not function unless fitted with features such as stationary vanes with variable angles known as variable inlet guide vanes and variable stators the ability to allow some air to escape part way along the compressor known as interstage bleed and being split into more than one rotating assembly known as twin spools for example axial compressors can have high efficiencies around 90 polytropic at their design conditions however they are relatively expensive requiring a large number of components tight tolerances and high quality materials axial compressors are used in medium to large gas turbine engines natural gas pumping stations and some chemical plants hermetically sealed open or semi hermetic edit a small hermetically sealed compressor in a common consumer refrigerator or freezer typically has a rounded steel outer shell permanently welded shut which seals operating gases inside the system in this case an r600a refrigerant there is no route for gases to leak such as around motor shaft seals on this model the plastic top section is part of an auto defrost system that uses motor heat to evaporate the water compressors used in refrigeration systems must exhibit near zero leakage to avoid the loss of the refrigerant if they are to function for years without service this necessitates the use of very effective seals or even the elimination of all seals and openings to form a hermetic system these compressors are often described as being either hermetic open or semi hermetic to describe how the compressor is enclosed and how the motor drive is situated in relation to the gas or vapor being compressed some compressors outside of refrigeration service may also be hermetically sealed to some extent typically when handling toxic polluting or expensive gasses with most non refrigeration applications being in the petrochemical industry in hermetic and most semi hermetic compressors the compressor and motor driving the compressor are integrated and operate within the pressurized gas envelope of the system the motor is designed to operate in and be cooled by the refrigerant gas being compressed open compressors have an external motor driving a shaft that passes through the body of the compressor and rely on rotary seals around the shaft to retain the internal pressure the difference between the hermetic and semi hermetic is that the hermetic uses a one piece welded steel casing that cannot be opened for repair if the hermetic fails it is simply replaced with an entire new unit a semi hermetic uses a large cast metal shell with gasketed covers with screws that can be opened to replace motor and compressor components the primary advantage of a hermetic and semi hermetic is that there is no route for the gas to leak out of the system the main advantages of open compressors is that they can be driven by any motive power source allowing the most appropriate motor to be selected for the application or even non electric power sources such as an internal combustion engine or steam turbine and secondly the motor of an open compressor can be serviced without opening any part of the refrigerant system an open pressurized system such as an automobile air conditioner can be more susceptible to leak its operating gases open systems rely on lubricant in the system to splash on pump components and seals if it is not operated frequently enough the lubricant on the seals slowly evaporates and then the seals begin to leak until the system is no longer functional and must be recharged by comparison a hermetic or semi hermetic system can sit unused for years and can usually be started up again at any time without requiring maintenance or experiencing any loss of system pressure even well lubricated seals will leak a small amount of gas over time particularly if the refrigeration gasses are soluble in the lubricating oil but if the seals are well manufactured and maintained this loss is very low the disadvantage of hermetic compressors is that the motor drive cannot be repaired or maintained and the entire compressor must be replaced if a motor fails a further disadvantage is that burnt out windings can contaminate the whole systems thereby requiring the system to be entirely pumped down and the gas replaced this can also happen in semi hermetic compressors where the motor operates in the refrigerant typically hermetic compressors are used in low cost factory assembled consumer goods where the cost of repair and labor is high compared to the value of the device and it would be more economical to just purchase a new device or compressor semi hermetic compressors are used in mid sized to large refrigeration and air conditioning systems where it is cheaper to repair or refurbish the compressor compared to the price of a new one a hermetic compressor is simpler and cheaper to build than a semi hermetic or open compressor thermodynamics of gas compression edit isentropic compressor edit a compressor can be idealized as internally reversible and adiabatic thus an isentropic steady state device meaning the change in entropy is 0 26 the enthalpy change for a flow process can be calculated 27 dh vdp tds isentropic ds is zero dh vdp non flow isentropic processes like some positive displacement compressors may use a different equation 28 dh pdv by defining the compression cycle as isentropic an ideal efficiency for the process can be attained and the ideal compressor performance can be compared to the actual performance of the machine isotropic compression as used in asme ptc 10 code refers to a reversible adiabatic compression process 29 isentropic efficiency of compressors η c i s e n t r o p i c c o m p r e s s o r w o r k a c t u a l c o m p r e s s o r w o r k w s w a h 2 s h 1 h 2 a h 1 displaystyle eta _ c frac rm isentropic compressor work rm actual compressor work frac w_ s w_ a cong frac h_ 2s h_ 1 h_ 2a h_ 1 h 1 displaystyle h_ 1 is the enthalpy at the initial state h 2 a displaystyle h_ 2a is the enthalpy at the final state for the actual process h 2 s displaystyle h_ 2s is the enthalpy at the final state for the isentropic process minimizing work required by a compressor edit comparing reversible to irreversible compressors edit comparison of the differential form of the energy balance for each device let q displaystyle q be heat w displaystyle w be work k e displaystyle ke be kinetic energy and p e displaystyle pe be potential energy actual compressor δ q a c t δ w a c t e l t a q a c t t 0 displaystyle delta q_ act delta w_ acteltaq_ act t geq 0 furthermore d s δ q a c t t displaystyle ds geq frac delta q_ act t and t is absolute temperature t 0 displaystyle t geq 0 which produces δ w r e v δ w a c t displaystyle delta w_ rev geq delta w_ act or w r e v w a c t displaystyle w_ rev geq w_ act therefore work consuming devices such as pumps and compressors work is negative require less work when they operate reversibly 26 effect of cooling during the compression process edit p v specific volume vs pressure diagram comparing isentropic polytropic and isothermal processes between the same pressure limits isentropic process involves no cooling polytropic process involves some cooling isothermal process involves maximum cooling by making the following assumptions the required work for the compressor to compress a gas from p 1 displaystyle p_ 1 to p 2 displaystyle p_ 2 is the following for each process p 1 displaystyle p_ 1 and p 2 displaystyle p_ 2 flow processes vdp all processes are internally reversible the gas behaves like an ideal gas with constant specific heats isentropic p v k c o n s t a n t displaystyle pv k constant where k c p c v displaystyle k c_ p c_ v w c o m p i n k r t 2 t 1 k 1 k r t 1 k 1 p 2 p 1 k 1 k 1 displaystyle w_ comp in frac kr t_ 2 t_ 1 k 1 frac krt_ 1 k 1 left left frac p_ 2 p_ 1 right k 1 k 1 right polytropic p v n c o n s t a n t displaystyle pv n constant w c o m p i n n r t 2 t 1 n 1 n r t 1 n 1 p 2 p 1 n 1 n 1 displaystyle w_ comp in frac nr t_ 2 t_ 1 n 1 frac nrt_ 1 n 1 left left frac p_ 2 p_ 1 right n 1 n 1 right isothermal t c o n s t a n t displaystyle t constant or p v c o n s t a n t displaystyle pv constant w c o m p i n r t l n p 2 p 1 displaystyle w_ comp in rtln left frac p_ 2 p_ 1 right by comparing the three internally reversible processes compressing an ideal gas from p 1 displaystyle p_ 1 to p 2 displaystyle p_ 2 the results show that isentropic compression p v k c o n s t a n t displaystyle pv k constant requires the most work in and the isothermal compression t c o n s t a n t displaystyle t constant or p v c o n s t a n t displaystyle pv constant requires the least amount of work in for the polytropic process p v n c o n s t a n t displaystyle pv n constant work decreases as the exponent n decreases by increasing the heat rejection during the compression process one common way of cooling the gas during compression is to use cooling jackets around the casing of the compressor 26 compressors in ideal thermodynamic cycles edit ideal rankine cycle 1 2 isentropic compression in a pump ideal carnot cycle 4 1 isentropic compression ideal otto cycle 1 2 isentropic compression ideal diesel cycle 1 2 isentropic compression ideal brayton cycle 1 2 isentropic compression in a compressor ideal vapor compression refrigeration cycle 1 2 isentropic compression in a compressor note the isentropic assumptions are only applicable with ideal cycles real world cycles have inherent losses due to inefficient compressors and turbines the real world system are not truly isentropic but are rather idealized as isentropic for calculation purposes temperature edit main article gas laws compression of a gas increases its temperature for a polytropic transformation of a gas p v n constant p 1 v 1 n p 2 v 2 n p 2 p 1 v 1 v 2 n p n 1 n t constant p 1 n 1 n t 1 p 2 n 1 n t 2 p 2 p 1 n 1 n t 2 t 1 displaystyle begin cases pv n text constant p_ 1 v_ 1 n p_ 2 v_ 2 n rightarrow frac p_ 2 p_ 1 left frac v_ 1 v_ 2 right n frac p frac n 1 n t text constant frac p_ 1 frac n 1 n t_ 1 frac p_ 2 frac n 1 n t_ 2 rightarrow left frac p_ 2 p_ 1 right frac n 1 n frac t_ 2 t_ 1 end cases the work done for polytropic compression or expansion of a gas into a closed cylinder w v 1 v 2 p d v p 1 v 1 n v 1 v 2 v n d v p 1 v 1 n 1 n v 2 1 n v 1 1 n p 1 v 1 n 1 n v 1 1 n v 2 1 n v 1 1 n 1 p 1 v 1 1 n v 2 1 n v 1 1 n 1 displaystyle w int _ v_ 1 v_ 2 pdv p_ 1 v_ 1 n int _ v_ 1 v_ 2 v n dv frac p_ 1 v_ 1 n 1 n v_ 2 1 n v_ 1 1 n frac p_ 1 v_ 1 n 1 n v_ 1 1 n left frac v_ 2 1 n v_ 1 1 n 1 right frac p_ 1 v_ 1 1 n left frac v_ 2 1 n v_ 1 1 n 1 right p 1 v 1 1 n v 1 v 2 n 1 1 p 1 v 1 1 n p 2 p 1 n 1 n 1 p 1 v 1 1 n t 2 t 1 1 displaystyle frac p_ 1 v_ 1 1 n left left frac v_ 1 v_ 2 right n 1 1 right frac p_ 1 v_ 1 1 n left left frac p_ 2 p_ 1 right frac n 1 n 1 right frac p_ 1 v_ 1 1 n left frac t_ 2 t_ 1 1 right so w p 1 v 1 n 1 p 2 p 1 n 1 n 1 displaystyle w frac p_ 1 v_ 1 n 1 left left frac p_ 2 p_ 1 right frac n 1 n 1 right in which p is pressure v is volume n takes different values for different compression processes see below and 1 2 refer to initial and final states adiabatic this model assumes that no energy heat is transferred to or from the gas during the compression and all supplied work is added to the internal energy of the gas resulting in increases of temperature and pressure theoretical temperature rise is 30 t 2 t 1 p 2 p 1 κ 1 κ displaystyle t_ 2 t_ 1 left frac p_ 2 p_ 1 right kappa 1 kappa with t 1 and t 2 in degrees rankine or kelvins p 2 and p 1 being absolute pressures and κ displaystyle kappa ratio of specific heats approximately 1 4 for air the rise in air and temperature ratio means compression does not follow a simple pressure to volume ratio this is less efficient but quick adiabatic compression or expansion more closely model real life when a compressor has good insulation a large gas volume or a short time scale i e a high power level in practice there will always be a certain amount of heat flow out of the compressed gas thus making a perfect adiabatic compressor would require perfect heat insulation of all parts of the machine for example even a bicycle tire pump s metal tube becomes hot as you compress the air to fill a tire the relation between temperature and compression ratio described above means that the value of n displaystyle n for an adiabatic process is κ displaystyle kappa the ratio of specific heats isothermal this model assumes that the compressed gas remains at a constant temperature throughout the compression or expansion process in this cycle internal energy is removed from the system as heat at the same rate that it is added by the mechanical work of compression isothermal compression or expansion more closely models real life when the compressor has a large heat exchanging surface a small gas volume or a long time scale i e a small power level compressors that utilize inter stage cooling between compression stages come closest to achieving perfect isothermal compression however with practical devices perfect isothermal compression is not attainable for example unless you have an infinite number of compression stages with corresponding intercoolers you will never achieve perfect isothermal compression for an isothermal process n displaystyle n is 1 so the value of the work integral for an isothermal process is w v 1 v 2 p d v p 1 v 1 v 1 v 2 1 v d v p 1 v 1 ln v 2 v 1 p 1 v 1 ln p 2 p 1 displaystyle w int _ v_ 1 v_ 2 pdv p_ 1 v_ 1 int _ v_ 1 v_ 2 frac 1 v dv p_ 1 v_ 1 ln frac v_ 2 v_ 1 p_ 1 v_ 1 ln left frac p_ 2 p_ 1 right when evaluated the isothermal work is found to be lower than the adiabatic work polytropic this model takes into account both a rise in temperature in the gas as well as some loss of energy heat to the compressor s components this assumes that heat may enter or leave the system and that input shaft work can appear as both increased pressure usually useful work and increased temperature above adiabatic usually losses due to cycle efficiency compression efficiency is then the ratio of temperature rise at theoretical 100 percent adiabatic vs actual polytropic polytropic compression will use a value of n displaystyle n between 0 a constant pressure process and infinity a constant volume process for the typical case where an effort is made to cool the gas compressed by an approximately adiabatic process the value of n displaystyle n will be between 1 and κ displaystyle kappa staged compression edit in the case of centrifugal compressors commercial designs currently do not exceed a compression ratio of more than 3 5 to 1 in any one stage for a typical gas since compression raises the temperature the compressed gas is to be cooled between stages making the compression less adiabatic and more isothermal the inter stage coolers intercoolers typically result in some partial condensation that is removed in ...
|
