THERMAL Fluid Machines Notes PDF

L01 - 28/02/23 - 08:30 A fluid machine is a device which operates an energy conversion by using a working fluid as a medium between the machine parts. 7 Motor machine: production of mechanical work by using energy stored in the fluid; Flui...

L01 - 28/02/23 - 08:30 A fluid machine is a device which operates an energy conversion by using a working fluid as a medium between the machine parts. 7 Motor machine: production of mechanical work by using energy stored in the fluid; Fluid machines - Operating machine: exploit of work provided by the surroundings in order to increase the fluid energy. ( nextical positionn melocty ) Prassure, , ß A compressor is an operating machine which aims to increase the pressure of the fluid, and also the ventilator is an operating machine which aims to increase the kinetic energy of the fluid. Primary energy sources: chemical energy of fuels (hydrocarbons), converted into thermal energy through a combustion process; - renewable energy: energy from wind, from tides (free fall of the sea), solar energy converted in electric or thermal energy, - energy from vegetation (bio-fuel); nuclear energy; - hydraulic potential energy. - The environmental impact of bio-fuel is far lower than that one of fossil fuel. Fluctuating: the availability is not continuous in time. s AE Non programmable: not possible to decide the right time of energy production. There are different ways of storing energy: batteries, water potential energy or hydrogen. V There is a technique in order to produce hydrogen (blue hydrogen) with methane and the segregation of CO2, which no produces CO2 emissions, so it’s almost an environmental sustainable source of energy. Fluid machines can either be: hydraulic machines: incompressible fluid (water, mineral oil), the heat exchange doesn’t affect the performances of the machine; · thermal machines: gas (compressible fluid: air, steam, combustion products in a gas turbine), the thermal phenomena affect the - performances of the machine. conside that this tuxtme fluit alweys changes profile is a fa t h e is Fluid machines can either be: Fluid 1 Lift turbo machines: continuous flow and momentum exchange (same principle of the lift effect - - - Do 7 on a wing profile) produced by the forces on the blades; - - - volumetric machines: pulsating flow which makes the machine work according to a cyclic - - working condition, where static actions (pressure) are enacting. ~ ~ -> Wave geing to strady steamen onrd gas traxoimes tuxbo compressor and Vahnethic canaptessor Pressure >. : , Thermodynamics review: System EnsnterectiSurroundings on System Specific Mass of Fluit : Boundary A system is closed when the study is concentrated on a specific mass and the boundary can not be crossed by the flow (closed boundary). Neglecting the losses in the fluid chamber, it is possible to apply the Lagrangian specification of fluid flow. - 7 Rings An open system is called control volume. Turbine symbol: I I 7 Eulerian specification of fluid flow. 7 2 System “state” (property): variable which can be measured with a value independent on the history of the system. Examples of property are: pressure (p), temperature (T), volume (V), mass (m), specific hentalpy (h), internal energy (U). Clapeyron plane: Thermodynamic cycle: Some quantities are not properties wixi D z because they depend on the process. A =B Process Steady-state system: 8) - = 0 8t Process v Properties: Additive property example: extensive: additive properties such mass (m), volume (V), …; I intensive: non-additive properties such specific quantities, - me mas pressure, temperature, etc. m m1 me ms = + + First law of thermodynamics - closed system ts V System Q, L: interactions / actions (non-properties). & + L = AE = Ez - Es : Energy (extensive property) 1 S 1 tz L ↓ Macroscopic forms of energy Internal energy: v = (ad m - - E = U + Ec + Eg + E W c: absolute velocity 2 we magnitude Kinetic energy: (edm L I Potential energy from Ec = (E) centrifugal forces 7 8 W2 w: relative velocity ŞezŞmEedme ; Gravitational energy: 2 magnitude Eg egtm Eg - = 8 = ) Height ( Ew ) I ( ew ) I & (inertial frame of reference) 1 , Energy from centrifugal forces: Ea = ewdm e W - W y - S -u (n = w. 2 ( 2 Both the kinetic and the gravitational energy depend on the chosen reference frame. s a + b = Au + 1Ec + 1Eg + AEm q + l = Au + Alc , g , w 1 PROPRIETà FISICHE E chiriche Homogeneous system: U = m. U E , = m. b... unifotme in tulto Il Swo Haleme. L ↳y - Infinitesimal process: the two states are infinitely close one another. t -> t + dt W d) A + d = dE - Fake differentials because they depend on the process antae L02 - 02/03/23 - 13:00 The mechanical energy in closed systems conserves. Starting from the Newton’s law it’s possible to demonstrate this principle. tmmny E = ma = mac de = - nda + dec + drg + den + e Specific Viscous dissipation per unit volume mass (non negative: dl > 0) W (19 + al = da dec deg de dlw + du wd + dy + W = + - => d = - ndv + bl + deg + dba+ den ę Result of 1 Low of thernobyne is s5 Q Ff heat per unit mass Fg L work Infinitesimal process t t ft da dL JU JEgg w } CONSERVATION OF MECHANICAL ENERGY EMME CLOSED SYSTEMS Newton's law È mai F È I momentum Ch'g.ms IL pdr dEagwtdlw visTous dissipation pressure spetne per unit mass NON NEGATIVE ALWI da dL JU JEgg w I dL pdr deagwtdlwdQ JU ptr.tw  1st da JLW SU pdr AUXILIARY EQUATION znt Lessou avw 2 03 FIRST LAW OF THERMODYNAMICS FLY FOR A CLOSED SYSTEM Quantita mnita di per masse propriete leniforml in ogres parte , Del system siseema Homogeneous. L AUTO Ect deg DEW Finite Evolution 4 E LA IL JU DECISE Ew INFINITESIMAL EVOLUTION C te f CONSERVATION OF MECHANICAL ENERGY CHE USED SYSTEM Newton's law È m.I.me fJL p.dr JEcxLEgtJEw JLw I Pressure I specific tg PER UNIT Dissipation Mass volume NON NEGATIVE IL 0 JQTIL JU iJEC JEg JEwjdls da p.dr Jurpar JEc LEg Jlw JEw.tw dlw 20 Non I JLw Reversible process dlwso irreverside =O -negative  not tepend by The Process b LA JIN JU PIN 1 AUXILIARY EQUATION NFPROperties TROPERIES Enthalpy h U per Jhs SU pirandp Japan th rip LA DIW Ih NIP 12 Auxiliary Equation convention Sign Beating machines sign convention { a + s = a E } Q 0 if delivered to the system so it done on Motor machines convention sign Gan it tone the L o by system on the surradings  I tea Q L di OEC ) gu zeal JU JU Jtag w sea Jls plu JE giu blu ) Thermodynamic cycle p Il N Ist Law Thexmodymennc WRITing Q L E En 0 Q L CcycLe ) ftp.fsl L 21 02 = Qiu - Qout OVERALL TO OVERALL HEAT DELIVERED NEST TO THE SYSTEM REJECTED Deving the cyct BY THE SYSTEM M CYCLE Efficiency =EQI  SECOND LAW OF THERMODYNAMICS FOR CLOSED SYSTEMS seys QFL , Clausius inequality f IO cbeadery O reversible process 80 inversible internal irreversibility inside the a hp only system sia , The effect present inside the system that genre irreversibility. Property entropy () $ is da 1dm T 14 Dependomlu passo flat o E The state aud not by the process Il Goff REVERSIBLE CYCLE pe o IRREVERSIBLE CYCLE pelo Alternative form Tts da Sla Reversible Adiabati process is Isoentropic ,  lst 2nd LT Tts Jupp dux egs Tts th Ndp aud Tds equations FUNDAMENTAL ERS FOR OPEN SYSTEMS CONTROL VOLUME CONSERVATION OF MASS CONTINUITY EQUATION mess imside the system at Thre a givare -( system tester a ) closea. Cs Smesso Zet closed mCS is coseaNP in a Pluitflow ; system we dont cousider conutrol nuclear reaction. Volum cousidering the Intexual between : e traffic ness aut flaw frar b The syspem ( morlt - necs initielmoss) ) ( mor ics + due final men outflow (test)= -dunz that Jma h I mos from the system Smau dm dm misuta bi ena caxte quautité ti fluito , che attraversa mell emite di tempo una sezione Ji are a A. î iportata ) Mass flow rates Miff Miff mass censide Smau Matt Matt bomutxal reluve inf ma ma Mds II ni naso IYI ( let t t È Im ; f UNSTEADY b zo u t l e t ) uscite ingresso EH III STEADY STATE FLOW O D 0 o o ma mia * boundaries Multiple Steady iI Min è Mont -state  1 D Flow one dimensional Coxtisponnting Valenna Tvi è \ C 1 Bondezy , 2 ME uniform intensive Bäsuntaxy r I properties are -timansianal it æfter over the surface boudary I JXEG.tt tu Aika SME fatta a mess flow rate Mestre fatta la : b I suzface  I 7 03 ^ Continuity equation Steady state flow 1 inlet tant'let 7 miasmi * 19 few fac 114 Low Thermuodymerkcs. FIRST L I FOR OPEN SYSTEMS Jhe cux suspeme euly å monung Fluid poxts Js elements i : Iuternal powers i S the O pert exchage with moring salid. iii dqi JL betwee CS t test : JEcsjdt ftt.IE - es Make ous a the distinction intexnal between thermrodynemic work L work ( Theenical work Li ii - - ) JE I JE { = SI ] å CU mi mia o 20 st 2= a5s5 k I I cousider Ecu M E ME energy Ir CV t pt FE TERM TERM : T Jon [ Js demosinate 't we This equation -  First Law of Thermodynamics for open systems LI internal power exchanged with moving III E solid parts da 1dL decs I 7 ii Fai CS CV II 0 Is I presentcouse tha mi mi 0 la trlantion the wall consudenting " Mediante ll locetion work to D 12 Ø etteced ) I 12 bisplecneo ME MEboudery ay Work Done loy of surface forces s 14 is mees flust At wall the elocity Jo flerit ovex the of The flest system. uppex fenit , at the beel A - In flard hos - c IE FEET boecause E7 so Adisiens î woodneeendltleldddtdder " - mm mmmmm 2.01 assssartedd Thermodymamic Work acting outlet ~ Due to the forces that at the Baretarys Bourtaxy they provoke a 12 Litt as bisplacement t.ie octing of loxes i looving element The Forces Pushing The fluid in inside C Veluue iI.i.i.. î of ( Re ) 2 l ; § dL Litt paAadxa Pattada weneglete b viscosity the [ Litta Path o Foxces acting In the evaluation 2 forces ecting coxtispouding corrisperding of Forcas so Path , The Imlet Wall locations but * neglet Tongertle we.. force X , Bontexles. Is Effect of foxces excerted loy element ( piseou the mooring to Jyseem. olates, )  Specific Volume ( IL Litt Pari dms PaEdma [ If we evoluate The Coxtispanding £? JEat Marte Ma Per Powex back to fixs law of thermotynamic box syseem going a & I Li ieri nera Ie NII NII I E Ut Ea w I g b 7 infu per Egg Ma Ysthaw man L 7 ma h Eag ma h Eagw I CONTROL VOLUME FORMULATION ID FLOW 1 INLET 1OUTLETT flow 7 steady state 0 UUSTADY TERMS be the ins Mz flow vate will same b twitöesnitöppera in hteag.ws h Eag w L Li um ire the F because is.L.T. power dissipate in to heat I viscosity ixklevent megligible 1 is if it is  Dividet by in : beh Ec Egg Eg Ew Ew Q Li Heat pex unit mass D In Li way final form in a compect J operative rachine.. Q Li Oh OEgg W OP n CONVENTION Matox Machina Q Li ah Okay w M M Faxe attenzione lu quauto quel s sta cousiderando ientalpia statica se simale considete lentalpie totale ho Jove -h+V 1 ; se c viferlance ad alloxe la total entalpy sere ADIABATKCA saxe cospanee se Li DEgin trascatabili. , Differential form refexs to a CV wkich is infinitesimal o da dli th Jtag w IVa system.rr infinitesival closed If along flow sixectionas which e moove Cs e Ima Qu aw Quantitie inside a z integrol bifferent fron each other Qcs Facs timeover ) not demostrate. : In steady state flow Qov Facs  ftp frtp since all the property i every time dont chage PiV We can say integral dlw used box a gliver S r ILw su 2 ovex the ie close syser s time 1 ti 2nd AUXILIARY E OVATION CLOSED SYSTEM te 12 tw Ih frsp thuck 4 I t t towain ) charging the texms from time tomein to " stice Steady state flow po Ilw hih ftp ErtpIQ subrtacting the equatione of steaty -state That ha he find Lw frdp wes up Q Li he hstOEc g w Li tw trap 049 W IMPORTANt OF CONSERVATION MECH ENERGY Li ftp.OEGg.WTLW FOR OPEN SYSTEMS STEADY STATE 1 D 1 inlet 1 outlet î Generalized Bernoulli equation , no work exchange but only internal  I Li 0 4 1 9172 7 Luso inertial f a r 0 7 Ew 0 b frame of reference 4 71 7 0 e psconst Ls spacific volume ( flows liquis ) 0 1.9 cost 7 Eg 2nd LAW OF THERMODYNAMICS OPEN SYSTEM STEADY STATE FLOW È cs fdmasfi.fi ihIi.s formulation CS how it was foud at ss.m fixst is integrate 1 1 : ( 1 E 1,7 1 l 55 no tima to jependart 05 12 o 1,2  Reference to a infinitasimal coutral Volume : 15 1214 Integton No becanse system o the , 1 It self infimitesime state is an steaty ) Iva system 7 03 Quantité 2, noto b CONSERVATION OF MOMENTUM NEWTON'S LAW pMoMantum cs F II I è'm all body and LEI p flux texn romenture IELEMental i , È mici Cv Ifpetuotinati L to the suna exstennt to oll the part E Steady state flow R in E 4 c flow deflect bu profile î wing exchage of Force Exomple how to the equationtion of marage The cansetuetion of Momenturn b Example Turbojet engine cld orberIm to trive the commpressol i at fixst approxinetien L loss is meglected men to lucreose the BURNER Nozze. flow relocity increase 0 p gym The In the some pressute COMPRESSOR Tme. papa - T ( p Pouer Q) e =viLi ~ IE * Mcompr Li e Mturb lit ine a fixsapptox Cohmp Jlnse Aix Mcompa Mturls Tuxbalm frual oud Aix since unfuel ze mAiv Li So Li e m comrp = mm Tertlo 5 t Work pex mamit mass is the ben hp ideal gas o this Cptt o Cp heat capacity constant pressure comprassor 3 FLT Li ah de µg µW 0 2 o IEg gas is megli respect if. other energy 1915 - HEc is useral negligible , respact the 4 4,0 ah Cp T Ta h. neglgible becouse the Q , mic high Q in denar wexp 33 O.  same txop of tempatatente between Zand 3 ond 4-7 lout pressute drop is lower Pf is higher Li Ta Ta , Pernw E Cp Thew there is Thrust the engine so sa ore so we spent fluit in to dotain accelletatione of flow. Lie lit TI Ta Ta releture velocity s wi We gang È ab Ambient axhas velocity that batt a is ie mull volume of outsite the anglne o mo black - speet of Air craft frome of verefece velocity = FO In the engine.K. ? The frae - of referece is w̅ w̅ o w̅ it Lsme the aiz the moving agaist see still inextiole becouse the is mooing at a engine eugine , costout speed se Q Pa Po Penu ladding cured Qmexave Is a so D inextial foxces ) cuped casidering ) Momentum equation È mi E È bothe section t ond 9 î weigh W 0