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Calcul termic
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Calculul termic
3.1. consideraii preliminare
Prin calculul termic al motoarelor diesel navale se urmrete determinarea mrimilor de stare ale fluidului motor n evoluia sa n cadrul ciclului de funcionare. Cu ajutorul acestor mrimi se poate trasa diagrama indicat a ciclului de funcionare, pe baza creia se pot determina principalele mrimi caracteristice ale unui motor: parametrii indicai i efectivi, principalele dimensiuni constructive, puterea i economicitatea motorului, precum i forele care acioneaz asupra pieselor motorului.
Dup procedeul de calcul utilizat, se deosebesc metode analitice i metode grafice, bazate pe diagrame termodinamice.
n prezentul capitol este prezentat metoda analitic bazat pe determinarea variaiilor energiilor interne i ale entalpiilor fluidului motor pe parcursul ciclului de funcionare. Calculul se desfoar utiliznd urmtoarele ipoteze simplificatoare:
fluidul motor este alctuit dintr-un amestec de gaze semiideale, care respect ecuaia universal de stare a gazelor, pV = mRT;
ciclul de funcionare este format din evoluii cunoscute din punct de vedere termodinamic (transformri politropice, izocore, izobare);
n fiecare ciclu de funcionare arde complet cantitatea de un kilogram de combustibil diagrama indicat astfel obinut este similar cu cea real, pe baza acestei similitudini rezultnd i parametrii reali ai motorului;
arderea combustibilului se desfoar parial izocor, parial izobar;
comprimarea i destinderea reprezint transformri politropice cu exponeni constani;
modificarea compoziiei chimice a fluidului motor prin arderea combustibilului se realizeaz instantaneu la nceputul arderilor izocor i, respectiv, izobar;
procesul de admisie a fluidului proaspt lipsete din cadrul ciclului de funcionare, considerndu-se c admisia se realizeaz instantaneu la nceputul comprimrii;
evacuarea gazelor arse reprezint un proces izocor de cedare de cldur mediului nconjurtor.
Cu ajutorul acestor ipoteze simplificatoare, calculul termic se desfoar n urmtoarele etape:
alegerea parametrilor iniiali de calcul;
calculul procesului de admisie;
calculul procesului de comprimare;
calculul procesului de ardere izocor;
calculul procesului de ardere izobar;
calculul procesului de destindere;
determinarea parametrilor indicai, efectivi i constructivi ai motorului.
Alegerea parametrilor iniiali de calcul se face n funcie de caracteristicile tehnice ale motorului de referin i de proprietile fizico-chimice ale combustibilului utilizat. O parte nsemnat din parametrii iniiali de calcul nu este indicat ns n documentaia tehnic a motorului. De aceea, n funcie de caracteristicile de baz ale motorului (numr de timpi, turaie, tipul admisiei .a.), aceti parametri se adopt n funcie de valorile experimentale indicate n literatura de specialitate.
n cadrul calculelor proceselor ciclului de funcionare se urmrete determinarea mrimilor de stare (presiune, volum, temperatur) ale fluidului motor n punctele caracteristice ale ciclului, precum i a altor mrimi specifice proceselor respective.
n final, se determin parametrii indicai i efectivi, trasndu-se diagrama indicat a ciclului de funcionare. Trasarea se realizeaz pe baza similitudinii dintre ciclul teoretic n care se arde un kilogram de combustibil i ciclul real de funcionare.
3.2. ALEGEREA PARAMETRILOR INIIALI DE CALCUL
n cadrul calcului termic vor fi utilizai urmtorii parametri iniiali:
puterea efectiv (necesar a fi dezvoltat): Pec = 183,75 kW (250 CP);
numrul de timpi: ( = 4;
turaia nominal: n = 1500 rot/min;
numrul de cilindri: i = 6;
presiunea de supraalimentare: ps = 1,2105 Pa;
raportul curs/diametru: (d = 1,17 (205/175).
Calculul va fi efectuat n condiiile funcionrii motorului cu motorin cu puterea calorific inferioar Qi = 42000 kJ/kg (10145 kcal/kg) i urmtoarea compoziie procentual:
carbon: c = 85,7 (;
hidrogen: h = 13,3 (;
oxigen: o = 1 (.
Fiind un motor de propulsie naval, motorul de referin va funciona la presiunea atmosferic la nivelul mrii:
p0 = 1,01325(105 Pa (1 atm).
Temperatura mediului ambiant depinde de anotimp, de zona de navigaie, de momentul zilei, de condiiile de ventilaie ale compartimentului maini, etc. Se va considera valoarea medie:
T0 = 300 K (27(C).
Datorit rezistenelor gazodinamice ale sistemului de admisie, presiunea fluidului proaspt la intrarea n cilindru pa este mai mic dect presiunea avut iniial (ps). Raportul dintre cele dou presiuni (la intrarea n cilindru i cea iniial) reprezint coeficientul de scdere a presiunii de admisie (a, care, n cazul motoarelor supraalimentate, ia valori cuprinse n domeniul: (a = 0,880,96. Se adopt valoarea:
(a = 0,88.
Temperatura gazelor arse reziduale se adopt n intervalul Tr = 600900 K, urmnd ca ea s fie verificat la sfritul destinderii. Va fi utilizat valoarea:
Tr = 640 K.
Venind n contact cu piesele fierbini ale motorului, aerul furnizat de turbosuflant i mrete temperatura cu (T = 1020 grd. Se adopt valoarea:
(T = 10 K.
n interiorul rcitorului intermediar de aer se asigur o reducere a temperaturii fluidului proaspt. Aceast cdere de temperatur poate fi (Trc = 20100 grd. Se adopt:
(Trc = 20 K.
Pentru asigurarea unei arderi de bun calitate a combustibilului, introducerea aerului n cilindri se realizeaz n exces fa de cantitatea teoretic necesar asigurrii arderii complete. Valoarea coeficientului de exces de aer depinde de tipul motorului, n cazul motoarelor supraalimentate fiind ( = 1,72,2. Se adopt:
( = 2,2.
Cantitatea de gaze arse reziduale depinde de raportul de comprimare, de presiunea i temperatura lor, de particularitile sistemului de distribuie, de turaie.
n cazul motoarelor supraalimentate, coeficientul gazelor arse reziduale are valorile: (r = 0,010,04. Se utilizeaz valoarea:
(r = 0,04.
Din cantitatea de cldur dezvoltat prin arderea combustibilului, numai o anumit fraciune este utilizat pentru producerea de lucru mecanic exterior i pentru mrirea energiei interne a fluidului motor. Coeficienii de utilizare a cldurii n cele dou faze ale arderii nregistreaz valorile uzuale: (v = 0,750,85 i (p = 0,650,75. Pentru motoarele rapide, cu o bun formare a amestecului carburant i cu pierderi mici n fluidul de rcire, cu un ciclu apropiat de ciclul teoretic cu ardere izocor i cu o prelungire nsemnat a arderii n destindere, valoarea (v poate ajunge la 0,90, pe cnd a lui (p poate s se micoreze pn la 0,55 0,60. Se vor utiliza pentru cei doi parametri valorile:
(v = 0,90i(p = 0,55.
Coeficientul de rotunjire a diagramei indicate reprezint parametrul care ine seama de deosebirile dintre diagramele indicate real i teoretic ale ciclului de funcionare. Valorile sale uzuale sunt: (r = 0,960,99. Se adopt:
(r = 0,96.
Randamentul mecanic al unui motor diesel naval depinde, n primul rnd, de tipul i de construcia acestuia. El este influenat i de ali factori, cum ar fi: turaia i sarcina motorului; calitatea materialului de construcie al pieselor cu suprafee de frecare; calitatea uleiului de ungere i a procesului de lubrificaie. Pentru motoarele supraalimentate, n patru timpi, valorile experimentale ale acestui parametru sunt: (m = 0,800,90. Se va utiliza valoarea:
(m = 0,80.
Raportul dintre volumul maxim al camerei de ardere Va (corespunztor poziiei de p.m.e. a pistonului) i volumul minim al acesteia Vc (corespunztor poziiei de p.m.i. a pistonului) se numete raport de comprimare:
.
Alegerea valorii ( depinde de tipul motorului, de turaia lui, de felul formrii amestecului carburant, de particularitile constructive, precum i de o serie de ali factori.
Conform datelor experimentale, n cazul motoarelor cu aprindere prin comprimare, supraalimentate, raportul de comprimare ia valorile ( = 1216.
Se adopt valoarea:
( = 16.
Raportul dintre raza manivelei i lungimea bielei are o influen redus asupra proceselor termice din cilindru motor. Raportul (d = R / Lb ia valori cuprinse ntre 1/5,5 i 1/3. n cazul nostru, acest raport are valoarea:
(d = 0,249.
Avansul la injecie optim se stabilete pe cale experimental, cnd prototipul motorului se afl pe bancul de probe. Pentru motoarele navale, ( = 640 (RAC, la sarcin nominal. Se adopt valoarea:
( = 13 (RAC.
Durata total a arderii se consider drept suma algebric a avansului la injecie, a unghiului de ntrziere la autoaprinderea combustibilului i a unui unghi de corecie cu valori de: (( = -3.+3 (RAC. Se utilizeaz :
(( = + 3 (RAC.
Comprimarea ncrcturii proaspete n agregatul de supraalimentare reprezint un proces politropic al crui exponent ns , pentru suflante centrifugale, ia valori de 1,41,8.
Se utilizeaz:
ns = 1,8.
3.3. CALCULUL PROCESULUI DE ADMISIE
Procesul de admisie (admisia) reprezint procesul n decursul cruia fluidul proaspt ptrunde n cilindrul motorului. Procesul de admisie forat (supraalimentarea) are loc atunci cnd fluidul proaspt ptrunde n cilindru sub aciunea unei suflante care l comprim n prealabil, aciunea fiind i ea asociat cu deplasarea pistonului. n cazul supraalimentrii, naintea ptrunderii n sistemul de admisie, fluidul proaspt are presiunea (ps) i temperatura (Ts) care se stabilesc la ieirea din organul de refulare al suflantei.
Cantitatea de oxigen necesar arderii complete a unui kilogram de combustibil are valoarea:
0,10435 kmoli O2.
Cantitatea corespunztoare de aer este:
0,49692 kmoli aer,
rezultnd cantitatea real de aer utilizat pentru arderea cantitii de un kilogram de combustibil:
1,093234 kmoli aer.
n urma arderii combustibilului rezult urmtoarele produse:
bioxid de carbon:
0,071417 kmoli CO2;
vapori de ap:
0,0665 kmoli H2O;
oxigen:
0,125225 kmoli O2;
azot:
0,863655 kmoli N2.
Cantitatea total de gaze rezultate din arderea combustibilului este:
1,126797 kmoli g.a.,
unde j = CO2, H2O, O2, N2.
Gazele arse reziduale vor avea compoziia:
bioxid de carbon:
2,856610-3 kmoli CO2;
vapori de ap:
2,6610-3 kmoli H2O;
oxigen:
2,92191610-3 kmoli O2;
azot:
26,69478910-3 kmoli N2,
cantitatea total fiind:
35,1310-3 kmoli g.a.r.,
unde j = CO2, H2O, O2, N2.
n compoziia fluidului motor intr aerul i gazele arse reziduale. Utiliznd datele din tabelul 3.1 i avnd n vedere valoarea constantei universale a gazelor, ( = 8314,34 J/kmolgrd, rezult c masa fluidului are valoarea:
25,3869 kg,
unde j = CO2, H2O, O2, N2.
Tabelul 3.1: Masele moleculare ale componentelor fluidului motor
ComponentaMasa molecular
(u.a.m.)
Aer28,850334
Bioxid de carbon44,0095
Vapori de ap18,0153
Bioxid de sulf64,0628
Oxigen31,9988
Azot28,0134
Constanta caracteristic a fluidului motor este:
288,173465 J/kggrd.
Temperatura aerului la ieirea din suflanta agregatului de supraalimentare are valoarea:
387,646152 K.
Prin urmare, la intrarea n cilindru, aerul va avea temperatura:
355,646152 K.
Pentru determinarea temperaturii fluidului motor (amestecul de fluid proaspt i gaze arse reziduale) la sfritul procesului de admisie, se utilizeaz dou metode. O prim metod se bazeaz pe valoarea entalpiei fluidului motor Iama, determinat cu ajutorul relaiei:
,
unde indicele j are, pe rnd, semnificaiile: CO2, H2O, O2, N2. Pentru aceast determinare, entalpiile specifice i se determin prin interpolare, cu ajutorul valorilor din nomograme. Pentru Taer = 355,646152 K i Tr = 890 K, vom avea:
kJ/kmol;
kJ/kmol;
kJ/kmol;
kJ/kmol;
kJ/kmol.
Se poate determina astfel entalpia fluidului motor n procesul de admisie:
Iama = 9712,481823 kJ/kmol.
Adoptnd temperaturile arbitrare T1 = 374 K i T2 = 384 K se determin entalpiile corespunztoare:
9575,100700 kJ/kmol
9831,200611 kJ/kmol
Cu ajutorul acestor valori, se reprezint grafic funcia Iam = f(T), considerat ca avnd o variaie liniar. Pe baza construciei grafice din figura 3.1, rezult valoarea temperaturii fluidului motor la sfritul admisiei: Ta(gr) ( 379,3 K.
Valoarea exact a temperaturii va fi:
379,364356
Fig. 3.1 Determinarea grafic a lui TaPe baza componenei fluidului motor, se poate obine valoarea analitic a temperaturii fluidului motor la sfritul admisiei:
376,198223 K.
ntre cele dou valori obinute exist o eroare procentual care nu depete limita admisibil de dou procente:
0,84 %
Presiunea fluidului motor pe parcursul procesului de admisie are valoarea:
2,314105 Pa.
Drept urmare, la sfritul admisiei, fluidul motor va ocupa volumul:
11,893701 m3.
n sfrit, coeficientul de umplere are valoarea:
0,96
Valorile obinute se ncadreaz n limitele experimentale indicate n literatura de specialitate. Astfel, n cazul motoarelor supraalimentate, pa = (1,0563,85)105 Pa, iar temperatura ia valori in intervalul 300400 K. La rndul su, coeficientul de umplere nregistreaz valorile uzuale: (v = 0,800,96.
3.4. CALCULUL PROCESULUI DE COMPRIMARE
Procesul de comprimare ndeplinete trei funciuni:
1. sporete randamentul termic;
2. permite aprinderea combustibilului, fapt fundamental pentru m.a.c.;
3. genereaz micri organizate ale fluidului motor n camera de ardere.
Pentru determinarea exponentului mediu politropic al procesului de comprimare, se calculeaz iniial expresiile cldurilor specifice medii molare ale fluidului motor, utiliznd expresiile cldurilor specifice ale componentelor (indicate n tabelul 3.2) i compoziia fluidului motor.
Tabelul 3.2: Coeficienii cldurii medii molare
cj = aj + bjT *
SubstanaIntervalul: 278Tc [K]**Intervalul: 273Tmax [K]***
ajbjajbj
Aer19,672,5110-3--
Benzin101,98219,4610-3--
CO227,6211,7210-338,503,3510-3
CO19,253,3510-320,922,0910-3
H2O23,015,4410-323,855,0210-3
SO230,9711,7210-330,9711,7210-3
H220,091,2610-318,832,0910-3
O219,254,6010-323,021,6710-3
N219,672,5110-321,341,6710-3
Observaii:* cj n kJ/kmolgrd;
** limita superioar Tc a intervalului corespunde temperaturii fluidului motor la sfritul comprimrii;
*** limita superioar Tmax a intervalului corespunde temperaturii maxime a fluidului motor n timpul arderii.
Rezult:
20,491374 kJ/kmolgrd
2,65618010-3 kJ/kmolgrd2.
Prin urmare, ecuaia de determinare va avea expresia:
Conform literaturii de specialitate, exponentul mediu politropic al comprimrii ia valori n intervalul nc = 1,321,38. Atribuind succesiv, diverse valori exponentului nc , se calculeaz valorile celor doi membri ai ecuaiei de determinare. Cu ajutorul acestor valori, n figura 3.2 sunt reprezentate grafic variaiile celor doi membri ai ecuaiei n funcie de exponentul politropic nc. La intersecia celor dou curbe rezult valoarea aproximativ nc ( 1,361.
Fig. 3.2 Determinarea grafic a lui ncPentru creterea preciziei se utilizeaz metoda iterativ ce urmrete obinerea diferenei absolute minime dintre cei doi membri. Rezultatele sunt prezentate n tabelul urmtor 3.3.
Rezult astfel valoarea exact a exponentului mediu politropic al comprimrii:
1,3611591163
Ca urmare, la sfritul comprimrii, mrimile de stare ale fluidului motor au valorile:
presiunea:
68,124094105 Pa;
volumul:
0,991141 m3;
temperatura:
922,938760 K.
Temperatura la sfritul comprimrii trebuie s asigure o autoaprindere sigur a combustibilului. De aceea, la m.a.c.-uri, ea trebuie s fie cu 200300 grade mai mare dect temperatura de autoaprindere a combustibilului. Uzual, aceste valori sunt Tc = 700950 K. Presiunea la sfritul comprimrii ia valori cuprinse n domeniile pc = (5075)105 Pa. Se observ ca valorile obinute din calcule se ncadreaz n aceste intervale.
Tabelul 3.3: Valorile membrilor ecuaiei de determinare a exponentului mediu
politropic al comprimriinc
[kJ/kmolgrd]
[kJ/kmolgrd]MS - MD
1,3624,019204423,935065520,084138925
1,3723,370036823,99656858-0,62653182
1,36123,952669323,941147280,011521972
1,36223,886501723,94724417-0,06074252
1,361123,94603623,941756290,004279713
1,361223,939406423,94236545-0,00295902
1,3611523,942720823,942060850,000659905
1,3611623,942057823,94212177-6,395210-5
1,36115923,942124123,942115678,4325110-6
1,3611623,942057823,94212177-6,395210-5
1,361159123,942117523,942116281,1940910-6
1,361159223,942110823,94211689-6,044310-6
1,3611591123,942116823,942116344,7024810-7
3.5. CALCULUL PROCESULUI DE ARDERE IZOCOR
Dintre toate procesele termice din cilindrul motorului, procesul de ardere are cel mai nalt grad de complexitate. Indicii energetici ai motorului, cei de economicitate i de durabilitate, de funcionare linitit i de adaptabilitate la sarcin, depind ntr-o msur larg, uneori hotrtoare, de procesul de ardere.
Prin ardere se nelege o reacie chimic, produs prin oxidarea substanelor combustibile. Etapele arderii sunt:
1. apariia flcrii sau aprinderea;
2. dezvoltarea flcrii sau propagarea.
Conform ipotezelor simplificatoare prezentate n 3.1., n cadrul calculului termic se consider c procesul de ardere se desfoar iniial izocor i apoi izobar. n cadrul arderii izocore, se consider, de asemenea convenional, c este ars cantitatea de combustibil gv injectat n cilindru pe durata de ntrziere la autoaprindere (aa, injecia decurgnd dup o lege liniar.
n momentul declanrii injeciei de combustibil, fluidul motor ocup volumul:
1,094423 m3.
Acest moment fiind situat n cadrul procesului de comprimare, presiunea i temperatura fluidului motor vor avea valorile:
59,525518105 Pa;
890,481859 K.
Pentru calculul ntrzierii la autoaprindere, se utilizeaz presiunea n momentul injeciei, exprimat n uniti ST:
pinj = 60,699362 kgf/cm2Rezult:0,0015606 s
Conform datelor experimentale, la motoarele navale acest parametru are valorile aa=0,0010,005 s. Prin urmare valoarea obinut se ncadreaz n intervalul indicat. Ei i corespunde unghiul de rotaie:
9,363708 (RAC.
Duratei totale a arderii i va corespunde unghiul:
22,363708 (RAC,
rezultnd cantitatea de combustibil care arde izocor (n ipoteza arderii cantitii gtot = 1 kg combustibil pe ciclu):
0,418701 kg.
n urma arderii acestei cantiti de combustibil rezult urmtoarele produse:
bioxid de carbon:
2,99022310-2 kmoli CO2;
vapori de ap:
2,78436210-2 kmoli H2O;
oxigen:
0,133708 kmoli O2;
azot:
0,667369 kmoli N2,
cantitatea total fiind:
0,858824 kmoli g.a.
Drept urmare, pe parcursul arderii izocore, fluidul motor are compoziia urmtoare:
bioxid de carbon:
3,27589010-2 kmoli CO2;
vapori de ap:
3,05036210-2 kmoli H2O;
oxigen:
00,136630 kmoli O2;
azot:
0,694064 kmoli N2.
Cantitatea total de gaze care formeaz fluidul motor va fi:
0,893957 kmoli g.a.
Masa fluidului are valoarea:
25,806363 kg,
iar constanta sa caracteristic va fi:
288,016925 J/kggrd
n continuare se determin energiile interne specifice ale componentelor fluidului motor pentru temperatura Tc = 922,938760 K. Prin interpolare liniar se obin valorile:
bioxid de carbon:
30942,670039 kJ/kmol
vapori de ap:
25172,635698 kJ/kmol
oxigen:
21283,130063 kJ/kmol
azot:
19934,472959 kJ/kmol
Pe baza acestor valori, rezult energia intern a fluidului motor n starea c:
18525,246108 kJ
Ca urmare a arderii izocore a combustibilului, energia intern a fluidului motor ajunge la valoarea:
34531,937979 kJ
Pentru determinarea temperaturii Ty , se adopt temperaturile arbitrare T1 = 1581 K i T2 = 1591 K. Utiliznd energiile interne specifice ale componentelor din tabele i nomograme, rezult energiile interne ale fluidului motor pentru cele dou temperaturi:
34387,123712 kJ
34639,933437 kJ
Pe baza ipotezei simplificatoare, conform creia energia intern variaz liniar n funcie de temperatur, n figura 3.3 este reprezentat grafic aceast variaie. Corespunztor energiei interne , rezult temperatura Ty ( 1587 K. Valoarea exact a acestei emperaturi este:
1586,728192 K
Fig. 3.3 Determinarea grafic a lui TyDeoarece procesul decurge izocor:
Vy = Vc = 0,991141 m3
i presiunea fluidului motor la sfritul arderii izocore va fi:
118,990299105 Pa
Se realizeaz astfel un raport de cretere a presiunii:
1,746669
n literatura de specialitate sunt indicate valorile uzuale pe care le nregistreaz parametrii caracteristici ai arderii izocore. Astfel, ntrzierea la autoaprindere a combustibilului ia valori situate n jurul a 0,0010,005 s. n cazul arderii mixte, cantitatea de combustibil ars izocor reprezint, de obicei, 1040 % din cantitatea total (gv = 0,10,4 kg), iar temperatura n starea y este Ty = 10001500 K. n cazul arderii violente, temperatura poate atinge valori mai ridicate, pn la 1800 K. n sfrit, presiunea maxim de ardere nregistreaz valori n intervalul py = pz = (80140)105 Pa.
3.6. CALCULUL PROCESULUI DE ARDERE IZOBAR
n cadrul acestui proces, este ars cantitatea de combustibil (n condiiile arderii cantitii gtot=1kg combustibil pe ciclu):
0,581298 kg
Ca urmare, n compoziia fluidului motor intr gazele rezultate din arderea unui kilogram de combustibil i gazele arse reziduale:
bioxid de carbon:
7,42733310-2 kmoli CO2 vapori de ap:
6,91610-2 kmoli H2O
oxigen:
7,59698310-2 kmoli O2 azot:
0,694064 kmoli N2O
Cantitatea total de gaze arse este:
0,913467 kmoli g.a.
Masa i constanta caracteristic ale fluidului motor vor avea, aadar, valorile:
26,388721 kg,
287,807845 J/kggrd
Corespunztor temperaturii Ty = 1586,728192 K, pe baza valorilor indicate n tabele i nomograme, prin interpolare liniar, rezult entalpiile specifice ale componentelor:
bioxid de carbon:
76190,280648 kJ/kmol
vapori de ap:
62309,104462 kJ/kmol
oxigen:
52391,887603 kJ/kmol
azot:
50099,504609 kJ/kmol
Pe baza acestor valori, rezult entalpia fluidului motor n starea y:
48720,695953 kJ
Entalpia fluidului motor va crete n decursul arderii izobare pn la valoarea:
67239,622310 kJ
Se adopt n continuare temperaturile arbitrare T1 = 2103 K i T2= 2113 K, pentru care entalpia fluidului motor nregistreaz urmtoarele valori:
67047,802063 kJ
67406,466490 kJ
Pe baza ipotezei simplificatoare conform creia entalpia fluidului motor variaz liniar cu temperatura, n figura 3.4 este reprezentat grafic dependena Iam = f(T). Corespunztor entalpiei Iamz , rezult c pe cale grafic temperatura Tz ( 2108,5 K.
Valoarea exact a acestui parametru este:
2108,348181 K
Fig. 3.4 Determinarea grafic a lui TzPresiunea fluidului motor meninndu-se constant:
118,990299105 Pa,
volumul ocupat n aceast stare este:
1,345710 m3
Rezult astfel i raportul de destindere prealabil:
1,3577373.7. CALCULUL PROCESULUI DE DESTINDERE
Procesul de destindere reprezint partea din ciclul motor n care se produce fraciunea principal din lucrul mecanic disponibil. O parte din energia acumulat prin ardere de ctre fluidul motor este cedat n timpul destinderii sub form de lucru mecanic al pistonului. n destindere, compoziia i masa fluidului motor rmn practic invariabile.
Utiliznd expresiile cldurilor specifice ale componentelor (indicate n tabelul 3.2), rezult coeficienii cldurii specifice medii molare a fluidului motor n decursul acestui proces:
23,065021 kJ/kmolgrd
2,06023310-3 kJ/kmolgrd2
Prin urmare, ecuaia de bilan energetic al procesului are expresia:
Atribuind diverse valori exponentului mediu politropic al destinderii, se obin variate valori pentru cei doi membri ai ecuaiei. n figura 3.5 sunt reprezentate grafic aceste variaii n funcie de exponentul mediu nd. La intersecia celor dou curbe rezult valoarea aproximativ a exponentului: nd ( 1,279.
Fig. 3.5 Determinarea grafic a lui nd Pentru determinarea valorii exacte, n urmtorul tabel sunt calculate iterativ valorile membrilor ecuaiei care conduc la stabilirea diferenei absolut minime:
Tabelul 3.4: Valorile membrilor ecuaiei de determinare a exponentului mediu
politropic al destinderii nd
[kJ/kmolgrd]
[kJ/kmolgrd]MS - MD
1,2730,7938518529,820502950,973348898
1,2829,6940714329,76851637-0,07444494
1,27929,8005017929,77366420,026837595
1,279229,7791547329,772633730,006520994
1,279329,7684926629,77211867-0,00362601
1,2792629,7727565729,772324680,000431889
1,2792729,7716904829,77227318-0,0005827
1,27926429,7723301229,772304082,6044810-5
1,27926529,7722235229,77229893-7,541410-5
1,279264229,772308829,772303055,7529310-6
1,279264329,7722981429,77230253-4,39310-6
1,2792642529,7723034729,772302796,7996610-7
Rezult astfel valoarea exponentului mediu politropic al destinderii:
1,2792642581
Prin urmare, mrimile de stare ale fluidului motor la sfritul destinderii au valorile:
volumul :
Vb = Va = 11,893701 m3 presiunea:
7,32589105 Pa
temperatura:
1147,245414 K
Pot fi acum calculate raportul de destindere:
8,838230
i raportul de scdere a presiunii:
3,165897
n finalul acestei etape a calcului termic se verific temperatura gazelor arse reziduale adoptat iniial:
892,067087 K
Eroarea de alegere a acestui parametru:
0,231718 %
Valorile uzuale ale presiunii i temperaturii la sfritul destinderii sunt pb = (28)105 Pa i, respectiv, Tb = 9001300 K.
3.8. DETERMINAREA PARAMETRILOR INDICAI, EFECTIVI I CONSTRUCTIVI
Cunoscndu-se mrimile de stare ale fluidului motor n punctele caracteristice ale ciclului de funcionare, se poate trece la determinarea valorilor parametrilor indicai i efectivi ai ciclului de funcionare, precum i a principalelor dimensiuni constructive ale motorului.
Lucrul mecanic indicat dezvoltat ntr-un cilindru pe parcursul unui ciclu de funcionare n care arde un kilogram de combustibil are valoarea:
1,928214107 J
Prin urmare, presiunea medie indicat a ciclului de funcionare este:
1,782617106 Pa
Randamentul indicat va fi:
0,456844,
iar consumul specific indicat de combustibil:
0,185515 kg/kWh
Pentru motoarele n patru timpi, supraalimentate, pentru presiunea medie indicat sunt menionate valorile uzuale: pi = (1025)105 Pa. Randamentul indicat nregistreaz valorile: (i = 0,420,50, iar consumul specific indicat de combustibil ci variaz ntre 160 i 195 g/kWh. Prin urmare, valorile obinute corespund limitelor uzuale indicate n literatura de specialitate.
La rndul lor, parametrii efectivi vor avea valorile:
presiunea medie efectiv:
1,604355106 Pa
randamentul efectiv:
0,411160
consumul specific efectiv de combustibil:
0,206127 kg/kWh (0,1515 kg/CPh)
Limitele uzuale indicate n literatura de specialitate, pentru motoarele n patru timpi, supraalimentate sunt: pe = (7,520)105 Pa; (e = 0,300,40; ce = 215285 g/kWh. Se observ c presiunea medie efectiv se ncadreaz n intervalul de mai sus, dar pentru randamentul efectiv i consumul specific efectiv de combustibil s-au obinut valori superioare din punct de vedere funcional, acest lucru explicndu-se prin caracterul pur teoretic al calculului termic.
Pentru dezvoltarea puterii Pec, impus prin tema de proiectare, este necesar ca n fiecare cilindru s se realizeze lucrul mecanic indicat:
20532,708333 J
Drept urmare, coeficientul de similitudine dintre ciclul real de funcionare i cel ipotetic n care arde un kilogram de combustibil va fi:
0,001056
Rezult astfel volumele reale ocupate de fluidul motor n punctele caracteristice ale ciclului de funcionare:
0,012565 m3
0,001047 m3
0,001421 m3Pentru trasarea diagramei indicate a ciclului de funcionare este necesar determinarea curbelor de comprimare i de destindere. Presiunile corespunztoare diferitelor valori Vj ale volumului ocupat de fluidul motor se calculeaz cu relaiile:
- pentru comprimare:
- pentru destindere:
Rezultatele calculelor efectuate sunt centralizate n urmtorul tabel:
Tabelul 3.5: Variaiile presiunii n cadrul proceselor de comprimare i de destindere
Vj [m3]pjc [MPa]pjd [MPa]Vj [m3]pjc [MPa]pjd [MPa]
0,0010476,812409130,00620,605266461,80850359
0,00125,658997550,00660,555889001,66949252
0,00142111,899030000,0070,513103381,54843872
0,00183,258751798,799069530,00740,475724041,44218399
0,00222,479853516,806888620,00780,442828011,34825799
0,00261,975481765,497144700,00820,413686861,26470240
0,0031,625847604,577555020,00860,387718651,18994605
0,00341,371167173,900279750,0090,364453301,12271469
0,00381,178528403,382994630,00920,353711511,09158717
0,00421,028433772,976440460,00940,343507271,06196465
0,00460,908654782,649447600,00960,333803081,03374462
0,0050,811163472,381389300,00980,324564771,00683349
0,00540,730488422,158105050,010,315761130,98114565
0,00580,662782161,969570790,0125650,231400000,73258874
n figura 3.6 este reprezentat la scar diagrama indicat, caroiajul fiind realizat din dreptunghiuri a cror arie este A0 = 13,872 mm2. Prin planimetrarea diagramei indicate, rezult aria A = n0A0 = 25513,872 = 3537,36 mm2. Reprezentarea fiind fcut la scri kp = 6,2210-2 MPa/mm i kv = 9,2110-5 m3/mm, rezult lucrul mecanic indicat:
20264,19124 J
Valoarea analitic a acestui parametru este:
20371,12714 J
Erorile de determinare n cadrul metodelor grafice au valori reduse:
0,549 %
Pot fi acum determinate principalele dimensiuni constructive ale motorului. Valorile acestor dimensiuni sunt urmtoarele:
diametrul cilindrului:
232,959324 mm
cursa pistonului:
270,232816 mm raza manivelei:
135,116408 mm
lungimea bielei:
542,636178 mm
cilindreea unitar:
11,518294 dm3
cilindreea total:
184,292707 dm3Se remarc valorile extrem de apropiate de cele indicate n cartea tehnic a motorului. Eroarea de determinare are o valoare nesemnificativ:
1,90 %
Aceeai precizie ridicat a determinrilor se constat i n cazul puterii efective, a crei valoare este:
2463,925 kW
Utiliznd lucrul mecanic indicat, puterea efectiv are valoarea:
2395,644551 kW
Calculnd densitatea aerului de admisie:
2,547260 kg/m3
puterea efectiv se poate determina i cu ajutorul relaiei:
2685,621760 kW
Puterea indicat a motorului are valoarea:
2737,694444 kW
Indicii de performan ai motorului au, la rndul lor, valorile:
- puterea pe cilindru:
153,99531 kW/cil
- puterea specific de arie a pistonului:
3612,912320 kW/m2
- puterea specific volumic:
13369,628318 kW/m3
- indicele de baleiaj:
232,959324 m/min
- gradul de solicitare a motorului:
7,225824106 N/ms
n sfrit, utiliznd datele din tabelul 3.6, se verific dimensiunile de gabarit ale motorului:
Tabelul 3.6: Coeficienii dimensiunilor de gabarit
CoeficientulMAC semirapide
n patru timpiMAC lente
n doi timpi
CL2,02,92,43,7
CH6,08,55,67,5
CE2,02,51,01,2
CB4,36,33,45,0
Lungimea:
Lmot = CLDcalci = 2,1232,95932416 = 7827,433286 mm
nlimea de la axa de rotaie:
H = CHS = 7,2270,232816 = 1945,676275 mm
Adncimea de la axa de rotaie:
E = CES = 2,2270,232816 = 594,512195 mm
Limea:
B = CBS = 5,1270,232816 = 1378,187361 mm
Fig. 3.6 Diagrama indicat a ciclului de funcionare
2
_1054985528.unknown
_1055012433.unknown
_1055576184.unknown
_1055584916.unknown
_1892378709.unknown
_1892382103.unknown
_1892382260.unknown
_1892382315.unknown
_1892382011.unknown
_1055585605.unknown
_1055616364.xlsDiagram2
66940.320273566200067047.802063621967406.466490152567239.62231
66976.069178315867047.802063621967406.466490152567239.6223167047.802063621967406.466490152567239.62231
67011.9356209688
67047.8020636219
67083.6685062749
67119.534948928
67155.4013915811
67191.2678342341
67227.1342768872
67263.0007195403
67298.8671621933
67334.7336048464
67370.6000474995
67406.4664901525
67442.3329328056
Iam2
Iam1
Iam"z"
Tz
Iam = f(T)
Tz [K]
Iam [kJ]
pj,nc,nd
0.00104711776.812409130.00620.605266461.80850359
0.00125.658997550.00660.555889001.66949252
0.001421711311.899030000.0070.513103381.54843872
0.00183.258751798.799069530.00740.475724041.44218399
0.00222.479853516.806888620.00780.442828011.34825799
0.00261.975481765.497144700.00820.413686861.26470240
0.0031.625847604.577555020.00860.387718651.18994605
0.00341.371167173.900279750.0090.364453301.12271469
0.00381.178528403.382994630.00920.353711511.09158717
0.00421.028433772.976440460.00940.343507271.06196465
0.00460.908654782.649447600.00960.333803081.03374462
0.0050.811163472.381389300.00980.324564771.00683349
0.00540.730488422.158105050.010.315761130.98114565
0.00580.662782161.969570790.01256541190.231400000.73258874
Ms-Md
1.3624.019204444423.93506551940.0841389251.2730.793851851929.82050295430.9733488975
1.3723.370036756823.9965685781-0.62653182141.2829.694071428629.7685163676-0.074444939
1.36123.952669252123.94114728030.01152197181.27929.800501792129.77366419710.0268375951
1.36223.886501657523.9472441725-0.06074251511.279229.779154727829.77263373360.0065209942
1.361123.946036001123.9417562880.00427971311.279329.768492660229.7721186702-0.00362601
1.361223.93940642323.942365447-0.0029590241.2792629.772756570929.77232468210.0004318889
1.3611523.942720753123.94206084860.00065990461.2792729.771690478729.7722731774-0.0005826987
1.3611623.942057813723.9421217652-0.00006395151.27926429.772330124929.77230408010.0000260448
1.36115923.94212410623.94211567350.00000843251.27926529.772223515329.7722989296-0.0000754143
1.3611623.942057813723.9421217652-0.00006395151.279264229.772308802929.772303050.0000057529
1.361159123.942117476823.94211628270.00000119411.279264329.772298141929.7723025349-0.000004393
1.361159223.942110847523.9421168918-0.00000604431.2792642529.772303472429.77230279250.00000068
1.3611591123.942116813823.94211634360.00000047021.2792642629.772302406329.772302741-0.0000003346
Date
Rrond =8314.3400000000231400
0.04000000000.0125654119
20.49137418681.3611591163
0.002656180411899029.998
376.19822354580.0014217113
e =12.00000000001.2792642581
23.0650213900
0.0020602330
2108.3481815600
1.3577379169
Presiunea se va introduce n Pascal
Presiunea se va introduce n Pascal
Date pt. diagrama
0.001047117711.899029997611.899029997606.8124091296
0.001047117711.211.899029997606.8124091296
0.001047117710.511.89902999760.00016.8124091296
0.00104711779.511.89902999760.00026.8124091296
0.00104711778.511.89902999760.00036.8124091296
0.0010471177811.89902999760.00046.8124091296
0.00104711777.511.89902999760.00056.8124091296
0.0010471177711.89902999760.00066.8124091296
0.00104711776.812409129611.89902999760.00076.8124091296
0.001056.786967551811.89902999760.00086.8124091296
0.001086.531647383811.89902999760.00096.8124091296
0.00116.37053270611.89902999760.0016.8124091296
0.001155.996507230911.89902999760.00116.8124091296
0.00125.658997545311.89902999760.00126.8124091296
0.001255.353130523711.89902999760.00136.8124091296
0.00135.074844596811.89902999760.00146.8124091296
0.001315.022187089611.89902999760.00156.8124091296
0.001324.970470204911.89902999760.00166.8124091296
0.001334.919670203811.8990299976
0.001344.86976411911.8990299976
0.001354.820729724211.8990299976
0.001364.772545504611.8990299976
0.001374.725190629811.8990299976
0.001384.678644926611.8990299976
0.001394.632888853911.8990299976
0.00144.587903478611.8990299976
0.00142171134.492800448511.8990299976
0.0014254.478692810711.8639110763
0.0014284.465890500211.8320358179
0.001434.457390847311.8108703024
0.001444.415310302411.7060470469
0.001454.373914135511.6028699236
0.001484.253676857111.3028513022
0.00154.176664181711.1104202739
0.00163.825410144610.2299695969
0.001653.66849158449.835089234
0.00173.52241182399.4665704826
0.00183.25875179198.7990695266
0.00222.47985350946.8068886211
0.00261.97548176335.4971447015
0.0031.62584760284.5775550224
0.00341.37116717333.9002797544
0.00381.17852839973.3829946315
0.00421.02843376592.9764404644
0.00460.90865478092.6494476046
0.0050.81116347492.3813892957
0.00540.73048842312.1581050519
0.00580.66278215591.9695707928
0.00620.60526645981.8085035866
0.00660.55588900141.6694925159
0.0070.51310338421.5484387247
0.00740.47572404281.4421839902
0.00780.4428280061.3482579852
0.00820.41368685821.2647023958
0.00860.38771865221.1899460542
0.0090.36445330221.1227146904
0.00920.35371151071.0915871668
0.00940.34350726861.0619646477
0.00960.33380307791.0337446168
0.00980.32456476541.0068334852
0.010.31576112750.9811456508
0.01050.29547222090.9217789158
0.0110.27734263240.8685229532
0.01150.26105934580.8205119403
0.0120.24636578270.7770335041
0.01256541190.23140.7325887375
0.01256541190.250.7325887375
0.01256541190.30.7325887375
0.01256541190.40.7325887375
0.01256541190.50.7325887375
0.01256541190.60.7325887375
0.01256541190.70.7325887375
0.01256541190.750.7325887375
0.01256541190.73258873750.7325887375
Diagrama indicata
11.211.30285130226.81240912960.26105934580.820511940311.899029997611.8990299976
10.511.11042027396.81240912960.24636578270.777033504111.211.8990299976
9.510.22996959696.81240912960.23140.732588737511.8990299976
8.59.8350892346.81240912960.250.732588737511.8990299976
89.46657048266.81240912960.30.732588737511.8990299976
7.58.79906952666.81240912960.40.732588737511.8990299976
76.80688862116.81240912960.50.732588737511.8990299976
6.81240912965.49714470156.81240912960.60.732588737511.8990299976
6.78696755184.57755502246.81240912960.70.732588737511.8990299976
6.53164738383.90027975446.81240912960.750.732588737511.8990299976
6.3705327063.38299463156.81240912960.73258873750.732588737511.8990299976
5.99650723092.97644046446.812409129611.8990299976
5.65899754532.64944760466.812409129611.8990299976
5.35313052372.38138929576.812409129611.8990299976
5.07484459682.15810505196.812409129611.8990299976
5.02218708961.96957079286.812409129611.8990299976
4.97047020491.80850358666.812409129611.8990299976
4.91967020381.66949251596.812409129611.8990299976
4.8697641191.548438724711.8990299976
4.82072972421.442183990211.8990299976
4.77254550461.348257985211.8990299976
4.72519062981.264702395811.8990299976
4.67864492661.189946054211.8990299976
4.63288885391.122714690411.8990299976
4.58790347861.091587166811.8990299976
4.49280044851.061964647711.8990299976
4.47869281071.033744616811.8990299976
4.46589050021.006833485211.8639110763
4.45739084730.981145650811.8320358179
4.41531030240.921778915811.8108703024
4.37391413550.868522953211.7060470469
4.25367685710.820511940311.6028699236
4.176664181711.3028513022
3.8254101446
3.6684915844
3.5224118239
3.2587517919
2.4798535094
1.9754817633
1.6258476028
1.3711671733
1.1785283997
1.0284337659
0.9086547809
0.8111634749
0.7304884231
0.6627821559
0.6052664598
0.5558890014
0.5131033842
0.4757240428
0.442828006
0.4136868582
0.3877186522
0.3644533022
0.3537115107
0.3435072686
0.3338030779
0.3245647654
0.3157611275
0.2954722209
0.2773426324
0.2610593458
pc
c
y
z
a
b
Scara:kp = 6,25 x 10-2 MPa/mmkv = 8,1 x 10-5 m3/mm
Comprimare
Destindere
pc
Inceput comprimare
Final destindere
Ardere1
Ardere2
V [m3]
p [MPa]
Foaie4
3749575.1007003909575.1007003909831.2006119209712.48182354379.360
3759600.71069154509575.10070039509831.20061192509712.48182354379.369600
3769626.320682691009575.100700391009831.200611921009712.48182354379.369650
3779651.930673851509575.100700391509831.200611921509712.48182354379.369700
3789677.540665002009575.100700392009831.200611922009712.48182354379.369712.48182354
3799703.150656162509575.100700392509831.200611922509712.48182354
3809728.760647313009575.100700393009831.200611923009712.48182354
3819754.370638463509575.100700393509831.200611923509712.48182354
3829779.980629623749575.100700393849831.20061192379.369712.48182354
3839805.59062077
3849831.20061192
1.3227.0216050023.7037819715
1.3326.2027684823.7594658486
1.3425.4320988223.8165507532
1.3524.7054674323.8750719355
1.3624.0192044423.9350655328
1.3723.3700367623.9965685917
1.3822.7550357924.0596190909
1.361159110.00000000
1.3611591115.00000000
1.3611591123.94211630
158134387.12371
158234412.40468
158334437.68566
158434462.96663
158534488.2476
158634513.52857
158734538.80955
158834564.09052
158934589.37149
159034614.65247
159134639.93344
15810
158115000
158134387.123712
15910
159115000
159134639.933437
034387.123712
70034387.123712
158134387.123712
034639.933437034531.9379791586.7281920
80034639.93343775034531.9379791586.72819215000
159134639.9334371586.72819234531.9379791586.72819234531.937979
210066940.32027
210166976.06918
210267011.93562
210367047.80206
210467083.66851
210567119.53495
210667155.40139
210767191.26783
210867227.13428
210967263.00072
211067298.86716
211167334.73360
211267370.60005
211367406.46649
211467442.33293
21030.00000
210367047.80206
21130
211367406.46649067047.80206
210367047.80206
2108.3481810
2108.34818167239.62231067406.46649
211367406.46649
067239.62231
2108.34818167239.62231
Foaie4
9575.10070038569575.10070038569831.20061192479712.481823540
9600.71069153959575.10070038569831.20061192479712.481823549600
9626.32068269349575.10070038569831.20061192479712.481823549650
9651.93067384739575.10070038569831.20061192479712.481823549700
9677.54066500129575.10070038569831.20061192479712.481823549712.48182354
9703.15065615519575.10070038569831.20061192479712.48182354
9728.7606473099575.10070038569831.20061192479712.48182354
9754.3706384639575.10070038569831.20061192479712.48182354
9779.98062961699575.10070038569831.20061192479712.48182354
9805.5906207708
9831.2006119247
Iam2
Iam1
Iam = f(T)
Iam"a"
Ta
c
Ta [K]
Iam [kJ]
27.02160523.70378197150
26.202768484823.759465848615
25.432098823523.816550753223.9421163
24.705467428623.8750719355
24.019204444423.9350655328
23.370036756823.9965685917
22.755035789524.0596190909
MS=f(nc)
MD=f(nc)
S
D
nc
MS;MD [kJ/kmol*grd]
Uam2
Uam1
Uam"y"
Ty
Ty [K]
Uam [kJ]
1581
1581
1591
0
0
0
1586.728192
1582
1581
1591
700
800
750
1586.728192
1583
1581
1591
1581
1591
1586.728192
1586.728192
1584
1585
1586
1587
1588
1589
1590
1591
34387.12371
0
0
34387.123712
34639.933437
34531.937979
0
34412.40468
15000
15000
34387.123712
34639.933437
34531.937979
15000
34437.68566
34387.123712
34639.933437
34387.123712
34639.933437
34531.937979
34531.937979
34462.96663
34488.2476
34513.52857
34538.80955
34564.09052
34589.37149
34614.65247
34639.93344
Iam2
Iam1
Iam"z"
Tz
Iam = f(T)
Tz [K]
Iam [kJ]
_1055616701.xlsDiagram3
34387.123710034387.12371234639.93343734531.9379790
34412.40468150001500034387.12371234639.93343734531.93797915000
34437.6856634387.12371234639.93343734387.12371234639.93343734531.93797934531.937979
34462.96663
34488.2476
34513.52857
34538.80955
34564.09052
34589.37149
34614.65247
34639.93344
Uam2
Uam1
Uam"y"
Ty
Uam = f(T)
Ty [K]
Uam [kJ]
pj,nc,nd
0.00104711776.812409130.00620.605266461.80850359
0.00125.658997550.00660.555889001.66949252
0.001421711311.899030000.0070.513103381.54843872
0.00183.258751798.799069530.00740.475724041.44218399
0.00222.479853516.806888620.00780.442828011.34825799
0.00261.975481765.497144700.00820.413686861.26470240
0.0031.625847604.577555020.00860.387718651.18994605
0.00341.371167173.900279750.0090.364453301.12271469
0.00381.178528403.382994630.00920.353711511.09158717
0.00421.028433772.976440460.00940.343507271.06196465
0.00460.908654782.649447600.00960.333803081.03374462
0.0050.811163472.381389300.00980.324564771.00683349
0.00540.730488422.158105050.010.315761130.98114565
0.00580.662782161.969570790.01256541190.231400000.73258874
Ms-Md
1.3624.019204444423.93506551940.0841389251.2730.793851851929.82050295430.9733488975
1.3723.370036756823.9965685781-0.62653182141.2829.694071428629.7685163676-0.074444939
1.36123.952669252123.94114728030.01152197181.27929.800501792129.77366419710.0268375951
1.36223.886501657523.9472441725-0.06074251511.279229.779154727829.77263373360.0065209942
1.361123.946036001123.9417562880.00427971311.279329.768492660229.7721186702-0.00362601
1.361223.93940642323.942365447-0.0029590241.2792629.772756570929.77232468210.0004318889
1.3611523.942720753123.94206084860.00065990461.2792729.771690478729.7722731774-0.0005826987
1.3611623.942057813723.9421217652-0.00006395151.27926429.772330124929.77230408010.0000260448
1.36115923.94212410623.94211567350.00000843251.27926529.772223515329.7722989296-0.0000754143
1.3611623.942057813723.9421217652-0.00006395151.279264229.772308802929.772303050.0000057529
1.361159123.942117476823.94211628270.00000119411.279264329.772298141929.7723025349-0.000004393
1.361159223.942110847523.9421168918-0.00000604431.2792642529.772303472429.77230279250.00000068
1.3611591123.942116813823.94211634360.00000047021.2792642629.772302406329.772302741-0.0000003346
Date
Rrond =8314.3400000000231400
0.04000000000.0125654119
20.49137418681.3611591163
0.002656180411899029.998
376.19822354580.0014217113
e =12.00000000001.2792642581
23.0650213900
0.0020602330
2108.3481815600
1.3577379169
Presiunea se va introduce n Pascal
Presiunea se va introduce n Pascal
Date pt. diagrama
0.001047117711.899029997611.899029997606.8124091296
0.001047117711.211.899029997606.8124091296
0.001047117710.511.89902999760.00016.8124091296
0.00104711779.511.89902999760.00026.8124091296
0.00104711778.511.89902999760.00036.8124091296
0.0010471177811.89902999760.00046.8124091296
0.00104711777.511.89902999760.00056.8124091296
0.0010471177711.89902999760.00066.8124091296
0.00104711776.812409129611.89902999760.00076.8124091296
0.001056.786967551811.89902999760.00086.8124091296
0.001086.531647383811.89902999760.00096.8124091296
0.00116.37053270611.89902999760.0016.8124091296
0.001155.996507230911.89902999760.00116.8124091296
0.00125.658997545311.89902999760.00126.8124091296
0.001255.353130523711.89902999760.00136.8124091296
0.00135.074844596811.89902999760.00146.8124091296
0.001315.022187089611.89902999760.00156.8124091296
0.001324.970470204911.89902999760.00166.8124091296
0.001334.919670203811.8990299976
0.001344.86976411911.8990299976
0.001354.820729724211.8990299976
0.001364.772545504611.8990299976
0.001374.725190629811.8990299976
0.001384.678644926611.8990299976
0.001394.632888853911.8990299976
0.00144.587903478611.8990299976
0.00142171134.492800448511.8990299976
0.0014254.478692810711.8639110763
0.0014284.465890500211.8320358179
0.001434.457390847311.8108703024
0.001444.415310302411.7060470469
0.001454.373914135511.6028699236
0.001484.253676857111.3028513022
0.00154.176664181711.1104202739
0.00163.825410144610.2299695969
0.001653.66849158449.835089234
0.00173.52241182399.4665704826
0.00183.25875179198.7990695266
0.00222.47985350946.8068886211
0.00261.97548176335.4971447015
0.0031.62584760284.5775550224
0.00341.37116717333.9002797544
0.00381.17852839973.3829946315
0.00421.02843376592.9764404644
0.00460.90865478092.6494476046
0.0050.81116347492.3813892957
0.00540.73048842312.1581050519
0.00580.66278215591.9695707928
0.00620.60526645981.8085035866
0.00660.55588900141.6694925159
0.0070.51310338421.5484387247
0.00740.47572404281.4421839902
0.00780.4428280061.3482579852
0.00820.41368685821.2647023958
0.00860.38771865221.1899460542
0.0090.36445330221.1227146904
0.00920.35371151071.0915871668
0.00940.34350726861.0619646477
0.00960.33380307791.0337446168
0.00980.32456476541.0068334852
0.010.31576112750.9811456508
0.01050.29547222090.9217789158
0.0110.27734263240.8685229532
0.01150.26105934580.8205119403
0.0120.24636578270.7770335041
0.01256541190.23140.7325887375
0.01256541190.250.7325887375
0.01256541190.30.7325887375
0.01256541190.40.7325887375
0.01256541190.50.7325887375
0.01256541190.60.7325887375
0.01256541190.70.7325887375
0.01256541190.750.7325887375
0.01256541190.73258873750.7325887375
Diagrama indicata
11.211.30285130226.81240912960.26105934580.820511940311.899029997611.8990299976
10.511.11042027396.81240912960.24636578270.777033504111.211.8990299976
9.510.22996959696.81240912960.23140.732588737511.8990299976
8.59.8350892346.81240912960.250.732588737511.8990299976
89.46657048266.81240912960.30.732588737511.8990299976
7.58.79906952666.81240912960.40.732588737511.8990299976
76.80688862116.81240912960.50.732588737511.8990299976
6.81240912965.49714470156.81240912960.60.732588737511.8990299976
6.78696755184.57755502246.81240912960.70.732588737511.8990299976
6.53164738383.90027975446.81240912960.750.732588737511.8990299976
6.3705327063.38299463156.81240912960.73258873750.732588737511.8990299976
5.99650723092.97644046446.812409129611.8990299976
5.65899754532.64944760466.812409129611.8990299976
5.35313052372.38138929576.812409129611.8990299976
5.07484459682.15810505196.812409129611.8990299976
5.02218708961.96957079286.812409129611.8990299976
4.97047020491.80850358666.812409129611.8990299976
4.91967020381.66949251596.812409129611.8990299976
4.8697641191.548438724711.8990299976
4.82072972421.442183990211.8990299976
4.77254550461.348257985211.8990299976
4.72519062981.264702395811.8990299976
4.67864492661.189946054211.8990299976
4.63288885391.122714690411.8990299976
4.58790347861.091587166811.8990299976
4.49280044851.061964647711.8990299976
4.47869281071.033744616811.8990299976
4.46589050021.006833485211.8639110763
4.45739084730.981145650811.8320358179
4.41531030240.921778915811.8108703024
4.37391413550.868522953211.7060470469
4.25367685710.820511940311.6028699236
4.176664181711.3028513022
3.8254101446
3.6684915844
3.5224118239
3.2587517919
2.4798535094
1.9754817633
1.6258476028
1.3711671733
1.1785283997
1.0284337659
0.9086547809
0.8111634749
0.7304884231
0.6627821559
0.6052664598
0.5558890014
0.5131033842
0.4757240428
0.442828006
0.4136868582
0.3877186522
0.3644533022
0.3537115107
0.3435072686
0.3338030779
0.3245647654
0.3157611275
0.2954722209
0.2773426324
0.2610593458
pc
c
y
z
a
b
Scara:kp = 6,25 x 10-2 MPa/mmkv = 8,1 x 10-5 m3/mm
Comprimare
Destindere
pc
Inceput comprimare
Final destindere
Ardere1
Ardere2
V [m3]
p [MPa]
Foaie4
3749575.1007003909575.1007003909831.2006119209712.48182354379.360
3759600.71069154509575.10070039509831.20061192509712.48182354379.369600
3769626.320682691009575.100700391009831.200611921009712.48182354379.369650
3779651.930673851509575.100700391509831.200611921509712.48182354379.369700
3789677.540665002009575.100700392009831.200611922009712.48182354379.369712.48182354
3799703.150656162509575.100700392509831.200611922509712.48182354
3809728.760647313009575.100700393009831.200611923009712.48182354
3819754.370638463509575.100700393509831.200611923509712.48182354
3829779.980629623749575.100700393849831.20061192379.369712.48182354
3839805.59062077
3849831.20061192
1.3227.0216050023.7037819715
1.3326.2027684823.7594658486
1.3425.4320988223.8165507532
1.3524.7054674323.8750719355
1.3624.0192044423.9350655328
1.3723.3700367623.9965685917
1.3822.7550357924.0596190909
1.361159110.00000000
1.3611591115.00000000
1.3611591123.94211630
158134387.12371
158234412.40468
158334437.68566
158434462.96663
158534488.2476
158634513.52857
158734538.80955
158834564.09052
158934589.37149
159034614.65247
159134639.93344
15810
158115000
158134387.123712
15910
159115000
159134639.933437
034387.123712
70034387.123712
158134387.123712
034639.933437034531.9379791586.7281920
80034639.93343775034531.9379791586.72819215000
159134639.9334371586.72819234531.9379791586.72819234531.937979
210066940.32027
210166976.06918
210267011.93562
210367047.80206
210467083.66851
210567119.53495
210667155.40139
210767191.26783
210867227.13428
210967263.00072
211067298.86716
211167334.73360
211267370.60005
211367406.46649
211467442.33293
21030.00000
210367047.80206
21130
211367406.46649067047.80206
210367047.80206
2108.3481810
2108.34818167239.62231067406.46649
211367406.46649
067239.62231
2108.34818167239.62231
Foaie4
Iam2
Iam1
Iam = f(T)
Iam"a"
Ta
c
Ta [K]
Iam [kJ]
MS=f(nc)
MD=f(nc)
S
D
nc
MS;MD [kJ/kmol*grd]
Uam2
Uam1
Uam"y"
Ty
Uam = f(T)
Ty [K]
Uam [kJ]
Iam2
Iam1
Iam"z"
Tz
Iam = f(T)
Tz [K]
Iam [kJ]
_1055618422.xlsDiagram1
31.978230769229.8736346620
30.793851851929.820502810829.772302
29.694071428629.7685162251
28.67013793129.7176502187
27.714466666729.6678806371
26.820451612929.6191838469
25.982312529.5715367239
MS = f(nd)
MD = f(nd)
nd
MS;MD [kJ/kmol*grd]
pj,nc,nd
0.00104711776.812409130.00620.605266461.80850359
0.00125.658997550.00660.555889001.66949252
0.001421711311.899030000.0070.513103381.54843872
0.00183.258751798.799069530.00740.475724041.44218399
0.00222.479853516.806888620.00780.442828011.34825799
0.00261.975481765.497144700.00820.413686861.26470240
0.0031.625847604.577555020.00860.387718651.18994605
0.00341.371167173.900279750.0090.364453301.12271469
0.00381.178528403.382994630.00920.353711511.09158717
0.00421.028433772.976440460.00940.343507271.06196465
0.00460.908654782.649447600.00960.333803081.03374462
0.0050.811163472.381389300.00980.324564771.00683349
0.00540.730488422.158105050.010.315761130.98114565
0.00580.662782161.969570790.01256541190.231400000.73258874
Ms-Md
1.3624.019204444423.93506551940.0841389251.2730.793851851929.82050295430.9733488975
1.3723.370036756823.9965685781-0.62653182141.2829.694071428629.7685163676-0.074444939
1.36123.952669252123.94114728030.01152197181.27929.800501792129.77366419710.0268375951
1.36223.886501657523.9472441725-0.06074251511.279229.779154727829.77263373360.0065209942
1.361123.946036001123.9417562880.00427971311.279329.768492660229.7721186702-0.00362601
1.361223.93940642323.942365447-0.0029590241.2792629.772756570929.77232468210.0004318889
1.3611523.942720753123.94206084860.00065990461.2792729.771690478729.7722731774-0.0005826987
1.3611623.942057813723.9421217652-0.00006395151.27926429.772330124929.77230408010.0000260448
1.36115923.94212410623.94211567350.00000843251.27926529.772223515329.7722989296-0.0000754143
1.3611623.942057813723.9421217652-0.00006395151.279264229.772308802929.772303050.0000057529
1.361159123.942117476823.94211628270.00000119411.279264329.772298141929.7723025349-0.000004393
1.361159223.942110847523.9421168918-0.00000604431.2792642529.772303472429.77230279250.00000068
1.3611591123.942116813823.94211634360.00000047021.2792642629.772302406329.772302741-0.0000003346
Date
Rrond =8314.3400000000231400
0.04000000000.0125654119
20.49137418681.3611591163
0.002656180411899029.998
376.19822354580.0014217113
e =12.00000000001.2792642581
23.0650213900
0.0020602330
2108.3481815600
1.3577379169
Presiunea se va introduce n Pascal
Presiunea se va introduce n Pascal
Date pt. diagrama
0.001047117711.899029997611.899029997606.8124091296
0.001047117711.211.899029997606.8124091296
0.001047117710.511.89902999760.00016.8124091296
0.00104711779.511.89902999760.00026.8124091296
0.00104711778.511.89902999760.00036.8124091296
0.0010471177811.89902999760.00046.8124091296
0.00104711777.511.89902999760.00056.8124091296
0.0010471177711.89902999760.00066.8124091296
0.00104711776.812409129611.89902999760.00076.8124091296
0.001056.786967551811.89902999760.00086.8124091296
0.001086.531647383811.89902999760.00096.8124091296
0.00116.37053270611.89902999760.0016.8124091296
0.001155.996507230911.89902999760.00116.8124091296
0.00125.658997545311.89902999760.00126.8124091296
0.001255.353130523711.89902999760.00136.8124091296
0.00135.074844596811.89902999760.00146.8124091296
0.001315.022187089611.89902999760.00156.8124091296
0.001324.970470204911.89902999760.00166.8124091296
0.001334.919670203811.8990299976
0.001344.86976411911.8990299976
0.001354.820729724211.8990299976
0.001364.772545504611.8990299976
0.001374.725190629811.8990299976
0.001384.678644926611.8990299976
0.001394.632888853911.8990299976
0.00144.587903478611.8990299976
0.00142171134.492800448511.8990299976
0.0014254.478692810711.8639110763
0.0014284.465890500211.8320358179
0.001434.457390847311.8108703024
0.001444.415310302411.7060470469
0.001454.373914135511.6028699236
0.001484.253676857111.3028513022
0.00154.176664181711.1104202739
0.00163.825410144610.2299695969
0.001653.66849158449.835089234
0.00173.52241182399.4665704826
0.00183.25875179198.7990695266
0.00222.47985350946.8068886211
0.00261.97548176335.4971447015
0.0031.62584760284.5775550224
0.00341.37116717333.9002797544
0.00381.17852839973.3829946315
0.00421.02843376592.9764404644
0.00460.90865478092.6494476046
0.0050.81116347492.3813892957
0.00540.73048842312.1581050519
0.00580.66278215591.9695707928
0.00620.60526645981.8085035866
0.00660.55588900141.6694925159
0.0070.51310338421.5484387247
0.00740.47572404281.4421839902
0.00780.4428280061.3482579852
0.00820.41368685821.2647023958
0.00860.38771865221.1899460542
0.0090.36445330221.1227146904
0.00920.35371151071.0915871668
0.00940.34350726861.0619646477
0.00960.33380307791.0337446168
0.00980.32456476541.0068334852
0.010.31576112750.9811456508
0.01050.29547222090.9217789158
0.0110.27734263240.8685229532
0.01150.26105934580.8205119403
0.0120.24636578270.7770335041
0.01256541190.23140.7325887375
0.01256541190.250.7325887375
0.01256541190.30.7325887375
0.01256541190.40.7325887375
0.01256541190.50.7325887375
0.01256541190.60.7325887375
0.01256541190.70.7325887375
0.01256541190.750.7325887375
0.01256541190.73258873750.7325887375
Diagrama indicata
11.211.30285130226.81240912960.26105934580.820511940311.899029997611.8990299976
10.511.11042027396.81240912960.24636578270.777033504111.211.8990299976
9.510.22996959696.81240912960.23140.732588737511.8990299976
8.59.8350892346.81240912960.250.732588737511.8990299976
89.46657048266.81240912960.30.732588737511.8990299976
7.58.79906952666.81240912960.40.732588737511.8990299976
76.80688862116.81240912960.50.732588737511.8990299976
6.81240912965.49714470156.81240912960.60.732588737511.8990299976
6.78696755184.57755502246.81240912960.70.732588737511.8990299976
6.53164738383.90027975446.81240912960.750.732588737511.8990299976
6.3705327063.38299463156.81240912960.73258873750.732588737511.8990299976
5.99650723092.97644046446.812409129611.8990299976
5.65899754532.64944760466.812409129611.8990299976
5.35313052372.38138929576.812409129611.8990299976
5.07484459682.15810505196.812409129611.8990299976
5.02218708961.96957079286.812409129611.8990299976
4.97047020491.80850358666.812409129611.8990299976
4.91967020381.66949251596.812409129611.8990299976
4.8697641191.548438724711.8990299976
4.82072972421.442183990211.8990299976
4.77254550461.348257985211.8990299976
4.72519062981.264702395811.8990299976
4.67864492661.189946054211.8990299976
4.63288885391.122714690411.8990299976
4.58790347861.091587166811.8990299976
4.49280044851.061964647711.8990299976
4.47869281071.033744616811.8990299976
4.46589050021.006833485211.8639110763
4.45739084730.981145650811.8320358179
4.41531030240.921778915811.8108703024
4.37391413550.868522953211.7060470469
4.25367685710.820511940311.6028699236
4.176664181711.3028513022
3.8254101446
3.6684915844
3.5224118239
3.2587517919
2.4798535094
1.9754817633
1.6258476028
1.3711671733
1.1785283997
1.0284337659
0.9086547809
0.8111634749
0.7304884231
0.6627821559
0.6052664598
0.5558890014
0.5131033842
0.4757240428
0.442828006
0.4136868582
0.3877186522
0.3644533022
0.3537115107
0.3435072686
0.3338030779
0.3245647654
0.3157611275
0.2954722209
0.2773426324
0.2610593458
pc
c
y
z
a
b
Scara:kp = 6,25 x 10-2 MPa/mmkv = 8,1 x 10-5 m3/mm
Comprimare
Destindere
pc
Inceput comprimare
Final destindere
Ardere1
Ardere2
V [m3]
p [MPa]
Foaie4
3749575.1007003909575.1007003909831.2006119209712.48182354379.360
3759600.71069154509575.10070039509831.20061192509712.48182354379.369600
3769626.320682691009575.100700391009831.200611921009712.48182354379.369650
3779651.930673851509575.100700391509831.200611921509712.48182354379.369700
3789677.540665002009575.100700392009831.200611922009712.48182354379.369712.48182354
3799703.150656162509575.100700392509831.200611922509712.48182354
3809728.760647313009575.100700393009831.200611923009712.48182354
3819754.370638463509575.100700393509831.200611923509712.48182354
3829779.980629623749575.100700393849831.20061192379.369712.48182354
3839805.59062077
3849831.20061192
1.3227.0216050023.7037819715
1.3326.2027684823.7594658486
1.3425.4320988223.8165507532
1.3524.7054674323.8750719355
1.3624.0192044423.9350655328
1.3723.3700367623.9965685917
1.3822.7550357924.0596190909
1.361159110.00000000
1.3611591115.00000000
1.3611591123.94211630
158134387.12371
158234412.40468
158334437.68566
158434462.96663
158534488.2476
158634513.52857
158734538.80955
158834564.09052
158934589.37149
159034614.65247
159134639.93344
15810
158115000
158134387.123712
15910
159115000
159134639.933437
034387.123712
70034387.123712
158134387.123712
034639.933437034531.9379791586.7281920
80034639.93343775034531.9379791586.72819215000
159134639.9334371586.72819234531.9379791586.72819234531.937979
210066940.32027
210166976.06918
210267011.93562
210367047.80206
210467083.66851
210567119.53495
210667155.40139
210767191.26783
210867227.13428
210967263.00072
211067298.86716
211167334.73360
211267370.60005
211367406.46649
211467442.33293
21030.00000
210367047.80206
21130
211367406.46649067047.80206
210367047.80206
2108.3481810
2108.34818167239.62231067406.46649
211367406.46649
067239.62231
2108.34818167239.62231
1.2631.978230769229.873634662
1.2730.793851851929.8205028108
1.2829.694071428629.7685162251
1.2928.67013793129.7176502187
1.327.714466666729.6678806371
1.3126.820451612929.6191838469
1.3225.982312529.5715367239
1.2792640
1.27926429.772302
Foaie4
00000
00000
00000
00000
00000
0000
0000
0000
0000
0
0
Iam2
Iam1
Iam = f(T)
Iam"a"
Ta
c
Ta [K]
Iam [kJ]
000
000
000
00
00
00
00
MS=f(nc)
MD=f(nc)
S
D
nc
MS;MD [kJ/kmol*grd]
0000000
0000000
0
0
0
0
0
0
0
0
0
0
0
0
0
Uam2
Uam1
Uam"y"
Ty
Uam = f(T)
Ty [K]
Uam [kJ]
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Iam2
Iam1
Iam"z"
Tz
Iam = f(T)
Tz [K]
Iam [kJ]
MS = f(nd)
MD = f(nd)
nd
MS;MD [kJ/kmol*grd]
_1055589934.xlsDiagram1
27.02160523.70378197150
26.202768484823.759465848615
25.432098823523.816550753223.9421163
24.705467428623.8750719355
24.019204444423.9350655328
23.370036756823.9965685917
22.755035789524.0596190909
MS=f(nc)
MD=f(nc)
S
D
nc
MS;MD [kJ/kmol*grd]
pj,nc,nd
0.00104711776.812409130.00620.605266461.80850359
0.00125.658997550.00660.555889001.66949252
0.001421711311.899030000.0070.513103381.54843872
0.00183.258751798.799069530.00740.475724041.44218399
0.00222.479853516.806888620.00780.442828011.34825799
0.00261.975481765.497144700.00820.413686861.26470240
0.0031.625847604.577555020.00860.387718651.18994605
0.00341.371167173.900279750.0090.364453301.12271469
0.00381.178528403.382994630.00920.353711511.09158717
0.00421.028433772.976440460.00940.343507271.06196465
0.00460.908654782.649447600.00960.333803081.03374462
0.0050.811163472.381389300.00980.324564771.00683349
0.00540.730488422.158105050.010.315761130.98114565
0.00580.662782161.969570790.01256541190.231400000.73258874
Ms-Md
1.3624.019204444423.93506551940.0841389251.2730.793851851929.82050295430.9733488975
1.3723.370036756823.9965685781-0.62653182141.2829.694071428629.7685163676-0.074444939
1.36123.952669252123.94114728030.01152197181.27929.800501792129.77366419710.0268375951
1.36223.886501657523.9472441725-0.06074251511.279229.779154727829.77263373360.0065209942
1.361123.946036001123.9417562880.00427971311.279329.768492660229.7721186702-0.00362601
1.361223.93940642323.942365447-0.0029590241.2792629.772756570929.77232468210.0004318889
1.3611523.942720753123.94206084860.00065990461.2792729.771690478729.7722731774-0.0005826987
1.3611623.942057813723.9421217652-0.00006395151.27926429.772330124929.77230408010.0000260448
1.36115923.94212410623.94211567350.00000843251.27926529.772223515329.7722989296-0.0000754143
1.3611623.942057813723.9421217652-0.00006395151.279264229.772308802929.772303050.0000057529
1.361159123.942117476823.94211628270.00000119411.279264329.772298141929.7723025349-0.000004393
1.361159223.942110847523.9421168918-0.00000604431.2792642529.772303472429.77230279250.00000068
1.3611591123.942116813823.94211634360.00000047021.2792642629.772302406329.772302741-0.0000003346
Date
Rrond =8314.3400000000231400
0.04000000000.0125654119
20.49137418681.3611591163
0.002656180411899029.998
376.19822354580.0014217113
e =12.00000000001.2792642581
23.0650213900
0.0020602330
2108.3481815600
1.3577379169
Presiunea se va introduce n Pascal
Presiunea se va introduce n Pascal
Date pt. diagrama
0.001047117711.899029997611.899029997606.8124091296
0.001047117711.211.899029997606.8124091296
0.001047117710.511.89902999760.00016.8124091296
0.00104711779.511.89902999760.00026.8124091296
0.00104711778.511.89902999760.00036.8124091296
0.0010471177811.89902999760.00046.8124091296
0.00104711777.511.89902999760.00056.8124091296
0.0010471177711.89902999760.00066.8124091296
0.00104711776.812409129611.89902999760.00076.8124091296
0.001056.786967551811.89902999760.00086.8124091296
0.001086.531647383811.89902999760.00096.8124091296
0.00116.37053270611.89902999760.0016.8124091296
0.001155.996507230911.89902999760.00116.8124091296
0.00125.658997545311.89902999760.00126.8124091296
0.001255.353130523711.89902999760.00136.8124091296
0.00135.074844596811.89902999760.00146.8124091296
0.001315.022187089611.89902999760.00156.8124091296
0.001324.970470204911.89902999760.00166.8124091296
0.001334.919670203811.8990299976
0.001344.86976411911.8990299976
0.001354.820729724211.8990299976
0.001364.772545504611.8990299976
0.001374.725190629811.8990299976
0.001384.678644926611.8990299976
0.001394.632888853911.8990299976
0.00144.587903478611.8990299976
0.00142171134.492800448511.8990299976
0.0014254.478692810711.8639110763
0.0014284.465890500211.8320358179
0.001434.457390847311.8108703024
0.001444.415310302411.7060470469
0.001454.373914135511.6028699236
0.001484.253676857111.3028513022
0.00154.176664181711.1104202739
0.00163.825410144610.2299695969
0.001653.66849158449.835089234
0.00173.52241182399.4665704826
0.00183.25875179198.7990695266
0.00222.47985350946.8068886211
0.00261.97548176335.4971447015
0.0031.62584760284.5775550224
0.00341.37116717333.9002797544
0.00381.17852839973.3829946315
0.00421.02843376592.9764404644
0.00460.90865478092.6494476046
0.0050.81116347492.3813892957
0.00540.73048842312.1581050519
0.00580.66278215591.9695707928
0.00620.60526645981.8085035866
0.00660.55588900141.6694925159
0.0070.51310338421.5484387247
0.00740.47572404281.4421839902
0.00780.4428280061.3482579852
0.00820.41368685821.2647023958
0.00860.38771865221.1899460542
0.0090.36445330221.1227146904
0.00920.35371151071.0915871668
0.00940.34350726861.0619646477
0.00960.33380307791.0337446168
0.00980.32456476541.0068334852
0.010.31576112750.9811456508
0.01050.29547222090.9217789158
0.0110.27734263240.8685229532
0.01150.26105934580.8205119403
0.0120.24636578270.7770335041
0.01256541190.23140.7325887375
0.01256541190.250.7325887375
0.01256541190.30.7325887375
0.01256541190.40.7325887375
0.01256541190.50.7325887375
0.01256541190.60.7325887375
0.01256541190.70.7325887375
0.01256541190.750.7325887375
0.01256541190.73258873750.7325887375
Diagrama indicata
11.211.30285130226.81240912960.26105934580.820511940311.899029997611.8990299976
10.511.11042027396.81240912960.24636578270.777033504111.211.8990299976
9.510.22996959696.81240912960.23140.732588737511.8990299976
8.59.8350892346.81240912960.250.732588737511.8990299976
89.46657048266.81240912960.30.732588737511.8990299976
7.58.79906952666.81240912960.40.732588737511.8990299976
76.80688862116.81240912960.50.732588737511.8990299976
6.81240912965.49714470156.81240912960.60.732588737511.8990299976
6.78696755184.57755502246.81240912960.70.732588737511.8990299976
6.53164738383.90027975446.81240912960.750.732588737511.8990299976
6.3705327063.38299463156.81240912960.73258873750.732588737511.8990299976
5.99650723092.97644046446.812409129611.8990299976
5.65899754532.64944760466.812409129611.8990299976
5.35313052372.38138929576.812409129611.8990299976
5.07484459682.15810505196.812409129611.8990299976
5.02218708961.96957079286.812409129611.8990299976
4.97047020491.80850358666.812409129611.8990299976
4.91967020381.66949251596.812409129611.8990299976
4.8697641191.548438724711.8990299976
4.82072972421.442183990211.8990299976
4.77254550461.348257985211.8990299976
4.72519062981.264702395811.8990299976
4.67864492661.189946054211.8990299976
4.63288885391.122714690411.8990299976
4.58790347861.091587166811.8990299976
4.49280044851.061964647711.8990299976
4.47869281071.033744616811.8990299976
4.46589050021.006833485211.8639110763
4.45739084730.981145650811.8320358179
4.41531030240.921778915811.8108703024
4.37391413550.868522953211.7060470469
4.25367685710.820511940311.6028699236
4.176664181711.3028513022
3.8254101446
3.6684915844
3.5224118239
3.2587517919
2.4798535094
1.9754817633
1.6258476028
1.3711671733
1.1785283997
1.0284337659
0.9086547809
0.8111634749
0.7304884231
0.6627821559
0.6052664598
0.5558890014
0.5131033842
0.4757240428
0.442828006
0.4136868582
0.3877186522
0.3644533022
0.3537115107
0.3435072686
0.3338030779
0.3245647654
0.3157611275
0.2954722209
0.2773426324
0.2610593458
pc
c
y
z
a
b
Scara:kp = 6,25 x 10-2 MPa/mmkv = 8,1 x 10-5 m3/mm
Comprimare
Destindere
pc
Inceput comprimare
Final destindere
Ardere1
Ardere2
V [m3]
p [MPa]
Foaie4
3749575.1007003909575.1007003909831.2006119209712.48182354379.360
3759600.71069154509575.10070039509831.20061192509712.48182354379.369600
3769626.320682691009575.100700391009831.200611921009712.48182354379.369650
3779651.930673851509575.100700391509831.200611921509712.48182354379.369700
3789677.540665002009575.100700392009831.200611922009712.48182354379.369712.48182354
3799703.150656162509575.100700392509831.200611922509712.48182354
3809728.760647313009575.100700393009831.200611923009712.48182354
3819754.370638463509575.100700393509831.200611923509712.48182354
3829779.980629623749575.100700393849831.20061192379.369712.48182354
3839805.59062077
3849831.20061192
1.3227.0216050023.7037819715
1.3326.2027684823.7594658486
1.3425.4320988223.8165507532
1.3524.7054674323.8750719355
1.3624.0192044423.9350655328
1.3723.3700367623.9965685917
1.3822.7550357924.0596190909
1.361159110.00000000
1.3611591115.00000000
1.3611591123.94211630
Foaie4
Iam2
Iam1
Iam = f(T)
Iam"a"
Ta
c
Ta [K]
Iam [kJ]
MS=f(nc)
MD=f(nc)
S
D
nc
MS;MD [kJ/kmol*grd]
_1055585402.xlsDiagram2
9575.10070038569575.10070038569831.20061192479712.481823540
9600.71069153959575.10070038569831.20061192479712.481823549600
9626.32068269349575.10070038569831.20061192479712.481823549650
9651.93067384739575.10070038569831.20061192479712.481823549700
9677.54066500129575.10070038569831.20061192479712.481823549712.48182354
9703.15065615519575.10070038569831.20061192479712.48182354
9728.7606473099575.10070038569831.20061192479712.48182354
9754.3706384639575.10070038569831.20061192479712.48182354
9779.98062961699575.10070038569831.20061192479712.48182354
9805.5906207708
9831.2006119247
Iam2
Iam1
Iam = f(T)
Iam"a"
Ta
Ta [K]
Iam [kJ]
pj,nc,nd
Vj [m3]pjc [MPa]pjd [MPa]Vj [m3]pjc [MPa]pjd [MPa]
0.00104711776.812409130.00620.605266461.80850359
0.00125.658997550.00660.555889001.66949252
0.001421711311.899030000.0070.513103381.54843872
0.00183.258751798.799069530.00740.475724041.44218399
0.00222.479853516.806888620.00780.442828011.34825799
0.00261.975481765.497144700.00820.413686861.26470240
0.0031.625847604.577555020.00860.387718651.18994605
0.00341.371167173.900279750.0090.364453301.12271469
0.00381.178528403.382994630.00920.353711511.09158717
0.00421.028433772.976440460.00940.343507271.06196465
0.00460.908654782.649447600.00960.333803081.03374462
0.0050.811163472.381389300.00980.324564771.00683349
0.00540.730488422.158105050.010.315761130.98114565
0.00580.662782161.969570790.01256541190.231400000.73258874
ncMsMdMs-MdndMsMdMs-Md
1.3624.019204444423.93506551940.0841389251.2730.793851851929.82050295430.9733488975
1.3723.370036756823.9965685781-0.62653182141.2829.694071428629.7685163676-0.074444939
1.36123.952669252123.94114728030.01152197181.27929.800501792129.77366419710.0268375951
1.36223.886501657523.9472441725-0.06074251511.279229.779154727829.77263373360.0065209942
1.361123.946036001123.9417562880.00427971311.279329.768492660229.7721186702-0.00362601
1.361223.93940642323.942365447-0.0029590241.2792629.772756570929.77232468210.0004318889
1.3611523.942720753123.94206084860.00065990461.2792729.771690478729.7722731774-0.0005826987
1.3611623.942057813723.9421217652-0.00006395151.27926429.772330124929.77230408010.0000260448
1.36115923.94212410623.94211567350.00000843251.27926529.772223515329.7722989296-0.0000754143
1.3611623.942057813723.9421217652-0.00006395151.279264229.772308802929.772303050.0000057529
1.361159123.942117476823.94211628270.00000119411.279264329.772298141929.7723025349-0.000004393
1.361159223.942110847523.9421168918-0.00000604431.2792642529.772303472429.77230279250.00000068
1.3611591123.942116813823.94211634360.00000047021.2792642629.772302406329.772302741-0.0000003346
Date
Rrond =8314.3400000000pa =231400
gr =0.0400000000V'a =0.0125654119
aam =20.4913741868nc =1.3611591163
bam =0.0026561804pz =11899029.998
Ta =376.1982235458V'z =0.0014217113
e =12.0000000000nd =1.2792642581
a'am =23.0650213900
b'am =0.0020602330
Tz =2108.3481815600
r =1.3577379169
Presiunea se va introduce n Pascal
Presiunea se va introduce n Pascal
Date pt. diagrama
0.001047117711.899029997611.899029997606.8124091296
0.001047117711.211.899029997606.8124091296
0.001047117710.511.89902999760.00016.8124091296
0.00104711779.511.89902999760.00026.8124091296
0.00104711778.511.89902999760.00036.8124091296
0.0010471177811.89902999760.00046.8124091296
0.00104711777.511.89902999760.00056.8124091296
0.0010471177711.89902999760.00066.8124091296
0.00104711776.812409129611.89902999760.00076.8124091296
0.001056.786967551811.89902999760.00086.8124091296
0.001086.531647383811.89902999760.00096.8124091296
0.00116.37053270611.89902999760.0016.8124091296
0.001155.996507230911.89902999760.00116.8124091296
0.00125.658997545311.89902999760.00126.8124091296
0.001255.353130523711.89902999760.00136.8124091296
0.00135.074844596811.89902999760.00146.8124091296
0.001315.022187089611.89902999760.00156.8124091296
0.001324.970470204911.89902999760.00166.8124091296
0.001334.919670203811.8990299976
0.001344.86976411911.8990299976
0.001354.820729724211.8990299976
0.001364.772545504611.8990299976
0.001374.725190629811.8990299976
0.001384.678644926611.8990299976
0.001394.632888853911.8990299976
0.00144.587903478611.8990299976
0.00142171134.492800448511.8990299976
0.0014254.478692810711.8639110763
0.0014284.465890500211.8320358179
0.001434.457390847311.8108703024
0.001444.415310302411.7060470469
0.001454.373914135511.6028699236
0.001484.253676857111.3028513022
0.00154.176664181711.1104202739
0.00163.825410144610.2299695969
0.001653.66849158449.835089234
0.00173.52241182399.4665704826
0.00183.25875179198.7990695266
0.00222.47985350946.8068886211
0.00261.97548176335.4971447015
0.0031.62584760284.5775550224
0.00341.37116717333.9002797544
0.00381.17852839973.3829946315
0.00421.02843376592.9764404644
0.00460.90865478092.6494476046
0.0050.81116347492.3813892957
0.00540.73048842312.1581050519
0.00580.66278215591.9695707928
0.00620.60526645981.8085035866
0.00660.55588900141.6694925159
0.0070.51310338421.5484387247
0.00740.47572404281.4421839902
0.00780.4428280061.3482579852
0.00820.41368685821.2647023958
0.00860.38771865221.1899460542
0.0090.36445330221.1227146904
0.00920.35371151071.0915871668
0.00940.34350726861.0619646477
0.00960.33380307791.0337446168
0.00980.32456476541.0068334852
0.010.31576112750.9811456508
0.01050.29547222090.9217789158
0.0110.27734263240.8685229532
0.01150.26105934580.8205119403
0.0120.24636578270.7770335041
0.01256541190.23140.7325887375
0.01256541190.250.7325887375
0.01256541190.30.7325887375
0.01256541190.40.7325887375
0.01256541190.50.7325887375
0.01256541190.60.7325887375
0.01256541190.70.7325887375
0.01256541190.750.7325887375
0.01256541190.73258873750.7325887375
Diagrama indicata
11.211.30285130226.81240912960.26105934580.820511940311.899029997611.8990299976
10.511.11042027396.81240912960.24636578270.777033504111.211.8990299976
9.510.22996959696.81240912960.23140.732588737511.8990299976
8.59.8350892346.81240912960.250.732588737511.8990299976
89.46657048266.81240912960.30.732588737511.8990299976
7.58.79906952666.81240912960.40.732588737511.8990299976
76.80688862116.81240912960.50.732588737511.8990299976
6.81240912965.49714470156.81240912960.60.732588737511.8990299976
6.78696755184.57755502246.81240912960.70.732588737511.8990299976
6.53164738383.90027975446.81240912960.750.732588737511.8990299976
6.3705327063.38299463156.81240912960.73258873750.732588737511.8990299976
5.99650723092.97644046446.812409129611.8990299976
5.65899754532.64944760466.812409129611.8990299976
5.35313052372.38138929576.812409129611.8990299976
5.07484459682.15810505196.812409129611.8990299976
5.02218708961.96957079286.812409129611.8990299976
4.97047020491.80850358666.812409129611.8990299976
4.91967020381.66949251596.812409129611.8990299976
4.8697641191.548438724711.8990299976
4.82072972421.442183990211.8990299976
4.77254550461.348257985211.8990299976
4.72519062981.264702395811.8990299976
4.67864492661.189946054211.8990299976
4.63288885391.122714690411.8990299976
4.58790347861.091587166811.8990299976
4.49280044851.061964647711.8990299976
4.47869281071.033744616811.8990299976
4.46589050021.006833485211.8639110763
4.45739084730.981145650811.8320358179
4.41531030240.921778915811.8108703024
4.37391413550.868522953211.7060470469
4.25367685710.820511940311.6028699236
4.176664181711.3028513022
3.8254101446
3.6684915844
3.5224118239
3.2587517919
2.4798535094
1.9754817633
1.6258476028
1.3711671733
1.1785283997
1.0284337659
0.9086547809
0.8111634749
0.7304884231
0.6627821559
0.6052664598
0.5558890014
0.5131033842
0.4757240428
0.442828006
0.4136868582
0.3877186522
0.3644533022
0.3537115107
0.3435072686
0.3338030779
0.3245647654
0.3157611275
0.2954722209
0.2773426324
0.2610593458
pc
c
y
z
a
b
Scara:kp = 6,25 x 10-2 MPa/mmkv = 8,1 x 10-5 m3/mm
Comprimare
Destindere
pc
Inceput comprimare
Final destindere
Ardere1
Ardere2
V [m3]
p [MPa]
Foaie4
3749575.1007003909575.1007003909831.2006119209712.48182354379.360
3759600.71069154509575.10070039509831.20061192509712.48182354379.369600
3769626.320682691009575.100700391009831.200611921009712.48182354379.369650
3779651.930673851509575.100700391509831.200611921509712.48182354379.369700
3789677.540665002009575.100700392009831.200611922009712.48182354379.369712.48182354
3799703.150656162509575.100700392509831.200611922509712.48182354
3809728.760647313009575.100700393009831.200611923009712.48182354
3819754.370638463509575.100700393509831.200611923509712.48182354
3829779.980629623749575.100700393849831.20061192379.369712.48182354
3839805.59062077
3849831.20061192
Foaie4
00000
00000
00000
00000
00000
0000
0000
0000
0000
0
0
Iam2
Iam1
Iam = f(T)
Iam"a"
Ta
c
Ta [K]
Iam [kJ]
_1055576599.unknown
_1055584382.unknown
_1055584531.unknown
_1055576641.unknown
_1055576492.unknown
_1055576554.unknown
_1055576439.unknown
_1055026403.unknown
_1055026709.unknown
_1055026823.unknown
_1055575937.unknown
_1055576155.unknown
_1055026883.unknown
_1055026905.unknown
_1055151835.unknown
_1055026893.unknown
_1055026869.unknown
_1055026755.unknown
_1055026792.unknown
_1055026729.unknown
_1055026569.unknown
_1055026590.unknown
_1055026656.unknown
_1055026579.unknown
_1055026475.unknown
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