sổ tay cdt chuong 12 nhiet dluc hoc

8/6/2019 s tay cdt Chuong 12 Nhiet Dluc Hoc

1/22

12Nhit ng lc hc

Michael J. Morani hc bang Ohio

12.1 C s ...................................................................1

12.2 Cn bng thuc tnh m rng ................. ........ ....3

12.3 Cc quan h thuc tnh v d liu ........ ......... ...10

12.4 Cc chu trnh cng sut ca cht kh v hi ... ..15

Mc d rt nhiu kha cnh v Nhit ng lc hc c ch t lu, hin nay cc nghin cu c c s khoa hc v l

lun n cc vn nng lng vn ng ca nhit: cc vt nng c kh nng to ra cng, mi ch bt u trong na u thk 19. Ngy nay phm vi nghin cu ln hn, gii quyt vn mt cch tng qut hn theo nng lng v entropy, v ccmi quan h trong thuc tnh ca vt cht. Hn th na, trong 25 nm qua Nhit ng lc hc k thut vt qua mt cuccch mng, cc thnh qu sau cuc cch mng ny c v hai mng: cc c s l thuyt v cc phng php u c ngdng. c bit, nh lut th hai ca nhit ng lc hc tr thnh mt cng c hiu qu phc v cho cng vic thit k vphn tch k thut.

12.1 C s

Nhit ng lc hc c in c lin quan mt thit ti cu trc v m ca vt cht. Lnh vc ny tp trung vo cc c tnhtng qut ca t hp lng ln cc phn t ch khng phi t cc phn t ring r. Cu trc vi m ca vt cht c nghincu trong l thuyt ng hc v c hc thng k (bao gm c nhit ng lc hc lng t). Trong chng ny, chng ta stip cn ti nhit ng lc hc theo hng c in.

Cc nh ngha v cc khi nim c bn

Nhit ng lc hc va l mt nhnh ca ngnh vt l va l mt ngnh khoa hc k thut. Cc nh khoa hc lun mongmun c c mt hiu bit c bn v tnh cht ho hc v vt l ca cc i lng vt cht c nh, bt bin v s dng ccnguyn l ca nhit ng lc hc m t cc thuc tnh ca vt cht. Cc nh k thut ng dng thng quan tm ti vicnghin cu cc h thng v s tng tc ca chng vi mi trng vt cht tn ti xung quanh chng nh th no. thuntin cho vic nghin cu, cc nh k thut m rng vn nhit ng lc hc ti vic nghin cu cc h thng m dngvt cht chy qua n.

H thng

Trong mt phn tch nhit ng lc hc, h thng l mt i tng c xem xt. Thng thng h thngl mt i

lng c th ca vt cht v/hoc mt min ngn cch vi nhng min khc bi mt b mt xc nh. B mt xc nh nyc gi l b mt iu khin hoc bin ca h thng. B mt iu khin ny c th chuyn ng hoc c nh. Mi thnhphn khc bn ngoi h thng gi l mi trng xung quanh. Mt h thng khi lng c nh c coi nh l mt khilng iu khin hoc h thng ng. Khi c mt dng chy mang khi lng i qua b mt iu khin, h thng c gi lmt th tch iu khin hoc h thng m. Mt h thng b cch ly l mt h thng ng v khng tng tc vi mi trngxung quanh n theo bt c hnh thc no.

Trng thi, thuc tnh

Cc c im ca mt h thng ti mt thi im no c gi l trng thi ca n. m t trng thi ca h thng mt thi im bt k, ta s dng cc thuc tnh ca h thng. Mt thuc tnh l i lng no m gi tr ca n ph thucvo trng thi,ch khng ph thuc vo qu trnh bin i ca h thng. Gi tr ca mt thuc tnh c xc nh theonguyn tc vn hnh hoc kim tra bng vt l.

Cc thuc tnh mrng ph thuc vo kch c hoc s m rng ca h thng. Th tch, khi lng, nng lng, entropy,v s thot nhit l cc v d v cc thuc tnh m rng. Mt thuc tnh m rng c tnh cng c theo ngha cc gi tr caton b h thng bng tng cc gi tr thnh phn. Cc thuc tnh c sn ca h thng c tnh cht c lp vi kch c hoc sm rng ca h thng. p sut v nhit l cc v d v loi thuc tnh m rng.

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S tay C in t

Qu trnh, Chu trnh

Hai trng thi c gi l ng nht khi v ch khi cc thuc tnh ca hai trng thi ny l ng nht. Khi c bt k mtthuc tnh no ca mt h thng thay i v gi tr s lm trng thi ny thay i, v h thng lc ny tri qua mt qu trnh.Khi mt h thng c mt trng thi ban u sau thc hin qua mt chui cc qu trnh v cui cng tr li trng thi banu ca n, tc l h thng ny thc hin chn mt chu trnh nhit ng lc hc.

Pha v nguyn cht

Khi nimpha c coi l mt i lng ca vt cht m c thnh phn ho hc v cu trc vt l ca n u ng nht.S ng nht trong cu trc vt l c ngha l vt cht hon ton th rn, hoc hon ton th lng, hoc hon ton thhi (cng gi l th kh). Mt h thng c th cha ng mt hoc nhiu pha. V d, mt h thng gm nc lng v hinc c hai pha. Mt nguyn chtl mt lng ca vt cht m thnh phn ho hc ca n l ng nht v khng bin i.Mt nguyn cht c th tn ti nhiu hn mt pha, tuy nhin thnh phn ho hc ca n phi lun khng i mi pha. Vd, khi nc lng v hi nc hp thnh mt h thng hai pha, h thng ny c coi l mt nguyn cht bi v mi pha ccng mt thnh phn ho hc. nh lut pha (xem Moran v Shapiro, 2000 c thm chi tit) ch ra bn cht ca cc pha llun cng tn ti cn bng ti mt v tr gi l v tr cn bng.

Trng thi cn bng

Trng thi cn bng c ngha l mt iu kin cn bng. Trong nhit ng lc hc, khi nim ny khng ch phn nh scn bng ca cc lc, m cn th hin s cn bng ca cc tc ng khc. Mi mt loi tc ng lin quan ti mt khacnh c bit ca trng thi cn bng nhit ng lc hc. Trng thi cn bng nhitlin qua ti nhit , trng thi cn bngc hc lin quan ti p sut, v trng thi cn bng pha lin quan ti cc nng lng ho hc ( thm chi tit xem Moran vShapiro, 2000). Trng thi cn bng ho hc cng c xy dng theo ho nng. c c trng thi cn bng hon ton,th mt vi trng thi cn bng cn phi tn ti ring r.

Nhit

Mt thang nhit c lp vi cc cht o nhit c gi l thang nhit nhit ng lc hc. Thang nhit Kelvin,l mt thang nhit ng lc hc, c th c suy ra t nh lut th hai ca nhit ng lc hc. Cc nh ngha ca nhit t nh lut hai ny c s dng cho ton b min nhit v a ra mt mi quan h gn kt quan trng gia mt vi nv o lng nhit bng thc nghim. c bit, cc nhit c o khi s dng mt nhit k kh th tch hng ngnhtvi cc nhit trong thang o nhit Kelvin trong min nhit m nhit biu hc kh c th c s dng.Trong thang o nhit theo Kelvin n v l kelvin (K).

Thang o nhit theo Celsius (cn gi l thang bch phn) s dng C, c cng ln nh kelvin. Do , s chnh

lch nhit l ng nht c hai thang o. Tuy nhin, im 0 trn thang C lch vi thang K l 273,15, im th ba canc (hnh 12.1b), c th hin bng mi quan h sau theo nhit Celsius v nhit Kelvin:

( ) ( ) 273.15T C T K = o (12.1)

C hai thang nhit khc cng thng c s dng trong k thut M. Thang Rankine, n v ca n l rankine (o

R), t l vi nhit Kelvin theo cng thc sau:

( ) 1.8 ( )T R T K =o (12.2)

Thang o theo Rankine cng mt thang o tuyt i trong Nhit ng lc hc vi mt gi tr khng tuyt i trng khpvi gi tr khng tuyt i ca thang o Kelvin. Trong cc mi quan h Nhit ng lc hc, nhit lun lun c tnh theothang o Kelvin hoc Rankine tr trng hp c bit no .

Mt khc c cng kch c nh thang Rankine l thang o nhit Fahrenheit, tuy nhin im 0 ca n c chnh

lch th hin theo quan h sau

( ) ( ) 459.67T F T R= o o (12.3)

Thay th phng trnh (12.1) v (12.2) vo phng trnh (12.3) ta thu c

( ) 1.8 ( ) 32T F T C = +o o (12.4)

Phng trnh ny th hin rng nhit Fahrenheit ca im ng bng(0o C) l 320 F v ca im bay hi (1000 C) l2120 F. 100 Celsius hoc Kelvin gia im ng bng v im bay hi tng ng vi 180 Fahrenheit hoc Rankine .

a ra mt tiu chun o c nhit m s a vo xem xt c trong l thuyt v trong thc t, thang o nhit theo quc t nm 1990 (ITS-90) c nh ngha theo cch m nhit o c trn n ph hp vi nhit nhit ng lchc, n v ca n l kelvin, v nm trong cc gii hn ca chnh xc o c c th t c. Preston-Thomas (1990) cth cung cp thm cc nghin cu v ITS-90 trong cc ti liu chuyn ngnh.

Qu trnh khng thun nghch

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Nhit ng lc hc

Mt qu trnh c gi l thun nghch khi ta c th loi b c nhng nh hng ca n v sau bng cch no khi phc li mt cch chnh xc cc trng thi ban u tng ng ca h thng v c mi trng xung quanh n. Mt qutrnh gi l khng thun nghch khi khng th khi phc c cc trng thi ban u ca h thng v c mi trng xungquanh n. C nhiu hiu ng trong sut mt qu trnh c tnh cht khng thun nghch. Bao gm: truyn nhit qua qua mtmin c chnh lch nhit hn ch; qu trnh gin n khng hn ch ca mt cht kh hoc lng lm gim p sut; phn ngho hc t pht; hn hp vt cht vi cc hp cht khc nhau hoc cc trng thi khc nhau; ma st (ma st trt cng nhma st trong dng chy ca cht lng); dng in chy qua mt in tr; s tr t ho v tr phn cc; v bin dng khngn hi,. Tnh khng thun nghch c s dng vi mc ch xc nh cc hiu ng nh trn.

C th chia qu trnh khng thun nghch thnh 2 lp, bn trongv bn ngoi. Qu trnh thun nghch bn trong xy rabn trong h thng, trong khi qu trnh thun nghch bn ngoi xy ra mi trng bn ngoi ca h thng, thng th lmi trng ngoi k st. Theo cch phn loi ny, ph thuc vo cc loi vng bin, s tn ti mt s tu chn khi phn loi(nh vic chn cc bin xc nh mi trng k st, tnh khng thun nghch u l bn trong). Tuy nhin, kt qu s l cth khi bit c s phn bit gia cc qu trnh khng thun nghch. Khi khng tn ti mt qu trnh khng thun nghchbn trong trong mt qu trnh, qu trnh ny s c gi l c tnh cht thun nghch bn trong. Ti mi trng thi trung gianca mt qu trnh c tnh thun nghch bn trong ca mt h thng kn, tt c cc thuc tnh l cng dng mi biu dinpha: nhit , p sut, th tch xc nh, v cc thuc tnh khc s khng thay i theo v tr.

Cc nh lut ca nhit ng lc hc

Cc bc u tin trong vic phn tch nhit ng lc hc l nh ngha cc h thng v nh ngha nhng mi quan htng tc ph hp vi mi trng xung quanh. Sau tp trung ti cc nh lut vt l lin quan trc tip ti chng v cc

mi quan h cho php din t s bin i ca h thng bng mt m hnh k thut, m hnh ny biu din bin i ca hthng theo mt cch n gin phc v cho mc ch phn tch, thm ch, khi b qua cc c im thc ca cc hthng trong thc t.

Thng s s dng mt trong 3 nh lut c bn hoc nhiu hn phn tch, mt cch trc tip hoc gin tip, nhitng lc hc ca cc th tch iu khin v cc h thng kn. Cc nh lut ny s c lp vi cc cht hoc hp cht c thtu thuc vo vn cn xem xt nh sau

Nguyn l bo ton khi lng,

Nguyn l bo ton nng lng,

nh lut th 2 ca nhit ng lc hc.

C th din t nh lut hai ny theo nng lng hoc entropy.

Cc nh lut nhit ng lc hc cn phi c b sung thm cc d liu thuc tnh nhit ng lc hc thch hp. i vi

mt s ng dng cn s dng thm mt phng trnh ng lng biu din nh lut Newton th hai v chuyn ng. D liucho cc thuc tnh truyn dn, cc h s truyn nhit, v cc h s ma st thng rt cn thit cho qu trnh phn tch trong kthut. Cc nguyn l ca kinh t k thut v d liu kinh t thch hp cng c th ng vai tr thch ng.

12.2 Cn bng thuc tnh m rng

Cc nh lut nhit ng lc hc c th c th hin qua s cn bng cc thuc tnh m rng cho khi lng, nnglng, entropy, v exergy. Cc ng dng k thut ni chung thng c phn tch trn mt c s th tch iu khin. Chnhv vy, y s trnh by cc cng thc th tch iu khin ca s cn bng khi nng lng, cn bng entropy v cn bngexergy. Chng s c th hin dng cn bng tng th vi gi thit dng chy l mt chiu. Cc phng trnh thay i vkhi lng, nng lng, v entropy s dng cc phng trnh vi phn v c th tm thy trong cc bi ging ca Bird v cccng s, 1960.

Cn bng khi lngi vi cc ng dng xut hin cc dng chy bn trong v dng chy bn ngoi i qua mt hoc nhiu cng, cn bng

thuc tnh m rng m t nguyn l bo ton khi lng c dng nh sau

i e

i e

dmm m

dt= & & (12.5)

y dm/dtbiu din tc thay i khi lng c cha ng trong th tch iu khin theo thi gian, im& th hin tc

dng chy c khi lng ti mt cng vo, v em& l tc dng chy c khi lng ti mt cng ra.

Mt dng chy chuyn ng qua mt phn ca b mt iu khin c din tch l dA s c tnh l tch ca thnh phnvn tc vung gc vi din tch , vn, vi vi phn din tch dA: vndA. Tc dng chy c khi lng i qua dA l

( )nv dA , y l t trng. T y ta c th tnh c tc ca dng chy c khi lng i qua mt cng c din tch

A bng cch tch phn trn ton b din tch nh sau

nA

m v dA= &

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S tay C in t

i vi dng chy mt chiu cc thuc tnh m rng l ng dng theo v tr trn ton b din tch A, v ta s thu cphng trnh cui cng l

vAm vA

v= =& (12.6)

vi l mt th tch ring (nghch o ca t khi) v ch s n t di vn tc lm r rng hn.

Cn bng nng lngNng lng l mt khi nim c bn ca nhit ng lc hc v cng l kha cnh quan trng nht khi phn tch k thut.

Nng lng c th c lu tr rt nhiu dng v m khc nhau: ng nng, th nng trng trng, v ni nng. Nnglng cng c th c chuyn i t dng ny sang dng khc v gia cc h thng. Nng lng c th c truyn bngcng, bng s truyn nhit, v bng s chy ca vt cht. Tng nng lng trong cc qu trnh chuyn i v truyn s cbo ton. Cn bng cc thuc tnh m rng biu din s nguyn l bo ton nng lng c dng nh sau

2 2( )

2 2i e

i i i e e e

i e

v vd U KE PE Q W m h gz m h gz

dt

+ += + + + + +

& & & & (12.7a)

vi U, KE, v PE tng ng biu din ni nng, ng nng, v th nng trng trng ca ton b th tch iu khin.

Pha bn phi ca phng trnh (12.7a) a ra lng nng lng truyn qua bin ca th tch iu khin. Nng lng cth truyn vo hoc thot ra cc th tch iu khin dng cng. Bi v cng c thc hin trn (hoc do) mt th tch iukhin khi dng vt cht i qua bin, nn phn chia tc sinh cng (cng sut) thnh hai loi thun tin cho cc mc chsau ny. Mt phn l tc cng sinh ra bi lc ca p sut dng chy do khi lng c dn n ti ng vo v b loib ng ra. Cc thnh phn ny thng c coi l cng dng chy, c nh lng thng qua cc i lng ln lt l

( )i i im p v& v ( ( )e e em p v ( )e e em p v& ), y p l p sut v v l th tch ring. Mt thnh phn na, c k hiu l W trong

phng trnh (12.7a), bao gm tt c cc hiu sut cng, m cc gi tr ca chng c lin quan ti cc trc quay, dch chuynca bin v cc hiu sut in. W c gi tr dngtrong qu trnh truyn nng lng tth tch iu khin.

Nng lng cng c th i vo v thot ra cc th tch iu khin cng vi cc dng chy ca vt cht. V c bn, i vi

dng chy mt chiu, tc m ti nng lng i vo ca vt cht u vo i l ( ( )2 / 2i i i im u v gz+ + ( )2 / 2i i i im u v gz+ +&

), y ba s hng trong ngoc n ln lt tng ng tnh ton cho ni nng ring, ng nng ring, v th nng ca lctrng trng ring ca vt cht chy qua cng i. Trong phng trnh (12.7a), tng ca ni nng ring v cng dng chyring ti mi ng vo v ng ra c th hin theo enthalpy ring h(= u + pv). Cui cng, Q l tc truyn nhit nng

v c gi tr dngtrong qu trnh truyn nng lng ti th tch iu khin.Bng cch lm dc cc s hng ca phng trnh (12.7a) lin quan ti dng chy c khi lng, ta c th thu c mt

cn bng tc nng lng cho cc h thng kn. V nguyn tc, c th tch phn cn bng tc nng lng h thng kntrong mt qu trnh gia hai trng thi thu c cn bng nng lng h thng kn:

2 1 2 1 2 1( ) ( ) ( )U U KE KE PE PE Q W + + = (12.7b)

y 1 v 2 th hin cc trng thi kt thc. Q v W ln lt l cc lngnhit nng c truyn v cng thc hin trongsut qu trnh.

Cn bng Entropy

Cc ng dng hin i ca nhit ng lc hc k thut th hin nh lut th 2 mt cn bng entropy hoc mt cn bngexergy. y xem xt ti cn bng entropy.

Nh l khi lng v nng lng, entropy c th c lu tr v truyn ti qua bin ca cc h thng. Tuy nhin, s khcnhau so vi khi lng v nng lng l, entropy khng c bo ton, nhng c th c to ra t cc qu trnh khngthun nghch trong cc h thng. Mt dng th tch iu khin ca cn bng thuc tnh m rng cho entropy l

j

i i e e gen

j i eJ

QdSm s m s S

dt T= + +

&&& & (12.8)

y dS/dt biu din tc bin i ca entropy theo thi gian trong th tch iu khin. Cc s hng i im s& v e em s& tng

ng s l cc tc ca entropy truyn ti v truyn ra khi th tch iu khin tng ng vi dng chy c khi lng. jQ&

biu din tc truyn nhit theo thi gian ti mt vng trn bin m y nhit tc thi l Tj, v /j jQ T& th hin tc

tng ng ca s truyn entropy. genS& l tc to ra entropy theo thi gian nh cc qu trnh khng thun nghch bn trong

th tch iu khin. Mt cn bng tc entropy cho cc h thng kn c th t c nh vic lm dc cc s hng trongphng trnh (12.8) lin quan ti cc tc dng chy c khi lng.

Khi p dng cn bng entropy bt k mt dng no ca n, th mc ch s thng l tnh gi tr ca s hng pht sinhra entropy. Tuy nhin, gi tr c trng cho vic to ra entropy mt qu trnh cho trc ca mt h thng thng khng 4


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Nhit ng lc hc

ngha. ngha ny thng c xc nh thng qua vic so snh: s to ra entropy bn trong mt thnh phn c a ratrc s c so snh vi cc gi tr ca s to ra entropy ca cc thnh phn khc trong ton b mt h thng c to ra tcc thnh phn ny. iu ny cho php xy dng cc nguyn l v cc qu trnh khng thun nghch ca ton b h thngmt cch chnh xc.

Cc th tch iu khin ti trng thi n nh

Cc h thng trong thc t thng c l tng ho ti trng thi n nh, c ngha l tt c cc thuc tnh ca chng

khng thay i theo thi gian. i vi mt th tch iu khin ti trng thi n nh, tnh ng nht ca vt cht bn trongth tch iu khin thay i mt cch lin tc, nhng tng khi lng khng thay i. Ti trng thi n nh, phng trnhcn bng bin i khi lng (12.5) tr thnh

i e

i e

m m= & & (12.9a)

Ti trng thi n nh, phng trnh cn bng bin i nng lng (12.7a) tr thnh

2 2

02 2i e

i i i e e e

i e

v vQ W m h gz m h gz

= + + + + +

& & & & (12.9b)

Ti trng thi n nh, phng trnh cn bng bin i entropy (12.8) s l

0 j i i e e gen j i ej

Qm s m s S T= + +

&

&& & (12.9c)

Khi lng v nng lng l nhng i lng bo ton, tuy nhin entropy v tng qut l khng c bo ton. Phngtrnh (12.9a) ch ra rng tc tng ca dng chy c khi lng i ti th tch iu khin bng vi tc tng cng cadng chy c khi lng i ra khi th tch iu khin ny. Tng t, phng trnh (12.9b) pht biu rng tng cng tc ca nng lng truyn ti th tch iu khin bng vi tng cng tc ca nng lng truyn ra khi th tch iu khinny. Tuy nhin, phng trnh (12.9c) cho thy rng tc m ti entropy c truyn ra ngoi vt qu tc m ti entropy i vo, s khc nhau ca tc to ra entropy bn trong th tch iu khin v cc qu trnh khng thun nghch.

Nhiu ng dng c lin quan ti cc th tch iu khin m c mt ng vo n v mt ng ra n. Vi nhngtrng hp ny, cn bng s thay i khi lng, phng trnh (12.9a), tr thnh i em m=& & . Biu din tc dng chy ckhi lng chung bng m&, phng trnh (12.9b) v (12.9c) tng ng s l:

2 2

0 ( ) (2

i ei e i e

v vQ W m h h g z z = + + +

& & & (12.10a)

0 ( )i e genb

Qm s s S

T= + +

&&& (12.11a)

y i vi Tb n gin biu th nhit , hoc mt nhit trung bnh ph hp, trn bin ni m qu trnh truyn nhit xyra.

Khi cn bng s thay i nng lng v entropy c ng dng trong cc trng hp c bit cn c quan tm, lun

lun lm n gin thm. Gii hn truyn nhit Q&c gim i khi n khng c quan h ng k ti s truyn cc nng lng

khc qua bin. iu ny c th l kt qu ca mt hoc nhiu trng hp sau: (1) b mt bn ngoi ca th tch iu khin

c cch ly; (2) din tch b mt ngoi qu nh c th nh hng ti qu trnh truyn nhit ; (3) s chnh lch nhit gia th tch iu khin v mi trng xung quanh ca n nh c th b qua s truyn nhit; (4) cht kh hoc chtlng i qua th tch iu khin qu nhanh dn ti khng thi gian cho qu trnh truyn nhit xy ra mt cch ng k. Shng cng W& s khng cn trong phng trnh cn bng s bin i nng lng khi khng c cc trc quay, cc dch chuynca bin, hiu sut in,hoc cc c ch cng khc lin quan ti th tch iu khin ang cn c xem xt. Cc hiu ng cang nng v th nng thng c b qua so vi cc s hng khc ca cn bng s thay i nng lng.

Cc dng c bit ca phng trnh (12.10a) v (12.11a) c lit k trong bng 12.1 c th t c nh sau: Khi khngc qu trnh truyn nhit, phng trnh (12.11a) a ra nh sau

0gene iS

s sm

= &

&(12.11b)

Do vy, khi c mt qu trnh khng thun nghch bn trong mt th tch iu khin, entropy ring s tng theo cc dng

chy c khi lng t ng vo ti ng ra. Trong trng hp l tngm khng c cc qu trnh khng thunnghch bn trong, khi lng i qua th tch iu khin s khng thay i trong entropy ca n - tc l ng entropy.

Khi khng c qu trnh truyn nhit, phng trnh (12.10a) s l

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S tay C in t

2 2

( ) ( )2

i ei e i e

v vW m h h g z z

= + +

& & (12.10b)

Mt dng c bit c th p dng c, t nht mt cch gn ng, vi cc my bm, my nn v cc turbine t vic lmdc cc s hng th nng v ng nng trong phng trnh

( )i eW m h h= & & (12.10c)

Trong cc thit b van iu chnh, c th gim p sut mt cch ng k bng cch to ra mt cn tr trong mt ngdn m cht kh hoc cht lng chy qua n. i vi cc thit b ny W& = 0 v phng trnh (12.10c) s n gin hn nhiu

i eh h (12.10d)

iu ny c ngha l, lung ln v lung xung ca thit b van iu chnh, bng vi enthapy ring.

Bng 12.1 Cc phng trnh cn bng nng lng v Entropy cho cc th tch iu khin mt ng vo, mt ng ra titrng thi n nh v khng c s truyn nhit.

Phng trnh cn bng nng lng

2 2

( ) ( )

2

i ei e i e

v vW m h h g z z

= + +

& & (12.10b)

Cc my nn, my bm, v turbinea

( )i eW m h h= & & (12.10c)

Van chnh

i eh h (12.10d)

My khuych tnb, vi phun

2 2( )e i i ev v h h= + (12.10e)

Phng trnh cn bng Entropy

0gene iS

s sm

= &

&(12.11b)

a i vi mt cht kh l tng vi hng s cp, phng trnh (1') ca bng 12.4 cho php phng trnh (12.10c) trthnh

( ) p i eW mc T T = & & (12.10c')

Cng sut to ra trong qu trnh ng entropy c th t c t phng trnh (5') ca bng 12.4 nh sau:

( 1) /1 ( / ) ( )k k p i e iW mc T p p s c = =

& & (12.10c'')

y cp = kR/(k-1).b i vi mt cht kh l tng vi hng s cp, phng trnh (1') ca bng 12.4 cho php phng trnh (12.10e) c

vit li nh sau:

2

12 ( )e p i ev v c T T = + (12.10e')

C th tnh c vn tc u ra trong mt qu trnh ng entropy bng cch s dng phng trnh (5') ca bng 12.4nh sau:

( )2 ( 1) /1 2 1 ( / )k k

e p i e iv v c T p p s c = + = (12.10e'')

y /( 1)pc kR k = .

Mt vi phun l mt ng chy c din tch mt ct ngang bin i m vn tc ca cht kh hoc cht lng tng

theo hng dng chy. my khuych tn, cht kh hoc cht lng s gim tc theo hng dng chy. i vi nhng thit bny, W 0=& . Ni chung l c th b qua s thay i th nng v qu trnh truyn nhit. Lc ny phng trnh (12.10b) cdng n gin hn nh sau

6


7/22

Nhit ng lc hc

2 2

02

i ei e

v vh h

= +

Ta c vn tc thot ra

2 2( )e i i ev v h h= + (12.10e)

Cc dng trng thi n nh ca cc phng trnh cn bng s bin i khi lng, nng lng, v entropy c th c

ng dng cho cc th tch iu khin c nhiu ng vo v/hoc ng ra, v d, cc trng hp lin quan ti cc my phthi nng phc hi, thit b cp nc nng, v thit b trao i nhit chy ngc v chy cho. Vic phn tch chuyn tip (cngi l khng n nh) c th c dn ti cc phng trnh (12.5), (12.7a), v (12.8). Cc minh ho ca tt c cc ng dngny c cung cp bi Moran v Shapiro (2000).

Cn bng exergy

Exergy cung cp mt s la chn s dng entropy cho vic ng dng nh lut th hai. Khi cc khi nim exergy c sdng cng vi cc nguyn l ca kinh t k thut, cc kt qu thu c s thuc lnh vc kinh t nhit hc. Kinh t nhit hccho php xc nh c cc ngun chi ph thc t: cc chi ph u t vn, chi ph bo qun v vn hnh, v cc chi ph linquan ti vic ph hu v hao ph exergy. S ti u cc h thng c th t c bng vic nh gi cn thn cc ngun chiph ny. Mc ch ca nhit kinh t hc l mong mungim thiu nht chi ph nh s tr gip ca exergy. Cc nh nghincu Moran (1989), Bejan v cc cng s (1996), Moran v Tsatsaronis (2000) v Moran cng Shapiro (2000) l nhng ngi

cung cp cc kin thc trong phn tch exergy v nhit kinh t hc. phn ny s trnh by cc kha cnh ni bt nht vExergy.

nh ngha exergy

Mt thun tin cho vic thc hin cng tn ti bt k khi no hai h thng ti cc trng thi khc nhau c mi quan hvi nhau, bi v, v nguyn tc, cng c th c sinh ra t hai h thng v c th tin ti cn bng. Khi mt trong hai hthng l mt h thng c l tng ho ph hp l mt mi trngv h thng cn li l mt h thng cn xem xt,exergy l cng hu ch theo l thuyt ln nht (cng trc quay hoc cng in) c th t c do h thng ang xt v mitrng tng tc vi nhau tin ti cn bng, qu trnh truyn nhit xy ra ch trong mi trng ny. (nh mt s la chn,exergy l cng hu dng l thuyt b nht c yu cu nh dng mt i lng ca vt cht t cc cht c mt trongmi trng v mang vt cht ti mt trng thi ring.). Exergy l mt i lng o s bt u mt trng thi ca h thngt mi trng, v do vy n l thuc tnh ca s tng tc gia h thng v mi trng vi nhau. Khi xc nh c mitrng, exergy c th c gn cho mt gi tr theo cc gi tr ca cc thuc tnh ch cho h thng, do vy exergy c th c

coi nh l mt thuc tnh m rng ca h thng. C th ph hu exergy nh l entropy, ni chung l exergy khng c boton.

Cc m hnh c nhiu mc ring thay i c ng dng trong vic din t mi trng c s dng nh giexergy. Cc m hnh ca mi trng thng l mt vi thnh phn ca cc mi trng xung quanh h thng, cc thuc tnhm rng ca mi pha m lun ng dng v khng thay i ng k l mt kt qu ca mt qu trnh no ang c xemxt. Mi trng c coi l hp bi cc cht thng gp tn ti nhiu trong p sut kh quyn, cc i dng, v v tri t.Cc cht cc dng n nh ca chng nh l chng tn ti trong t nhin, v khng th sinh cng t cc tng tc - vt lhoc ho hc - gia cc phn ca mi trng. Mc d cc thuc tnh m rng ca mi trng ny c gi thit l khngthay i, cc thuc tnh m rng ny vn c th thay i do nguyn nhn ca s tng tc vi cc h thng khc. Th nngv ng nng c xc nh tng i so vi cc to trong mi trng, tt c cc thnh phn khc c cp s cxem xt vi chng. D dng thy, nhit T 0 v p sut p0 ca mi trng thng l cc gi tr bao quanh, nh l 1 atm v25o C (77o F). Tuy nhin, cc thuc tnh ny c th c xc nh khc i ph thuc vo ng dng.

Khi mt h thng l cn bng vi mi trng, trng thi ca h thng lc c gi l trng thi bt ng. Ti trngthi cht ny, cc iu kin v cn bng c hc, nhit, v ho hc gia h thng vi mi trng c tho mn nh sau: psut, nhit , v cc th nng ho hc ca h thng tng ng s ging nh ca mi trng. Thm vo , h thng khngchuyn ng hoc chnh lch so vi cc to trong mi trng. Theo cc iu kin ny, s khng th c mt s thay i tpht no bn trong h thng hoc trong mi trng, hoc l khng c mt s tng tc no gia chng. Gi tr ca exergybng khng. C th nh ngha mt loi cn bng khc gia h thng v mi trng. y l mt dng cn bng c hn chm y ch c cc iu kin cn bng c hc v nhit hc phi c tho mn. Trng thi ny ca h thng c gi l btng hon ton (restricted dead state). trng thi ny, lng vt cht c nh cn xem xt c coi ng kn trong mt binkhng cho php dng chy c khi lng i qua, ti vn tc bng khng v cao so vi cc to ca mi trng, v tinhit T0 v p sut p0.

Truyn Exergy v ph hu exergy

Exergy c th c truyn theo ba cch: exergy truyn cng vi cng, exergy truyn cng vi qu trnh truyn nhit, v

exergy truyn lin quan ti qu trnh i vo v i ra ca vt cht qua mt th tch iu khin.Tt c cc qu trnh truynexergy ny c tnh ton so vi mi trng m dng xc nh exergy. Exergy cng b ph hu bi cc qu trnh khngthun nghch bn trong h thng hoc th tch iu khin. Cc phng trnh cn bng exergy c th c vit rt nhiudng, ph thuc vo h thng l kn hay l th tch iu khin cn xem xt v vic quan tm ti trng thi n nh ca n hay

7


8/22

S tay C in t

l s hot ng trong giai on chuyn tip. Do vai tr quan trng ca chng trong mt min ln ng dng, cn bng tc exergy cho cc th tch iu khin ti trng thi n nh c biu din theo mt trong hai phng trnh sau, phng trnh(12.12a) v (12.12b).

,0 q j i e D

j i e

E W E E E = + & & & & & (12.12a)

00 1j i i e e D

j i ij

TQ W m e m e E

T

= + & & && &

(12.12b)

W& c cng tnh cht nh trong phng trnh (12.7a): tc loi tr cng dng chy. jQ& l tc theo thi gian ca s

truyn nhit trn bin ca th tch iu khin ni m nhit tc thi l Tj. Tc lin quan ti s truyn exergy l

0

,1q j j

j

TE Q

T

=

&& (12.13)

Vi cc phng trnh cn bng tc th tch iu khin khc, ch s di i v e ln lt l cc ng vo v ng ra.Cc tc truyn exergy ti th tch iu khin ng vo v ng ra ln lt l i i iE m e=& & v e e eE m e=& & . Cui cng, DE& tnh ton cho tc theo thi gian ca qu trnh ph hu exergy nguyn nhn do cc qu trnh khng thun nghch bn trongth tch iu khin. Tc ca qu trnh ph hu exergy c lin quan ti tc pht sinh entropy nh sau

0 D genE T S = && (12.14)

Cc s hng truyn exergy ring ei, ec c th c th hin theo bn thnh phn: exergy vt l ePH, ng nng eKN, thnng ePT, v exergy ho hc eCH:

PH KN PT CH e e e e e= + + + (12.15a)

Ba thnh phn u tin c tnh ton nh sau:

0 0 0( ) ( )PHe h h T s s= (12.15b)

21

2KNe v= (12.15c)

PTe gz= (12.15d)

phng trnh (12.15b), h0 v s0 ln lt l enthalpy ring v entropy ring ti trng thi bt ng hon ton (restricteddead state). phng trnh (12.15c) v (12.15d), v v z tng ng l vn tc v cao so vi cc to trong mi trng.

nh gi exergy ho hc (cc thnh phn exergy lin quan ti s tham gia cc thnh phn ho hc ca mt h thngtrong mi trng). Mt trong cc m hnh ca mi trng c th c cung cp da vo cc ng dng; xem thm cc ti liuca Moran (1989) v Kotas (1995). Phn tch exergy c th thc hin c d dng bng cch ng dng mt mi trngchun v s dng mt bng cc exergy ho hc chun tng ng. Cc exergy ho hc tiu chun c xy dng da trncc gi tr tiu chun, v d ca nhit tiu chun T 0 v p sut tiu chun p0 ca mi trng, 298,15 K (25o C) v 1 atm.Cc mi trng tiu chun cng bao gm mt tp hp cc cht tham gia vi cc tiu chun phn nh cng gn cng tt vcc thuc tnh ho hc ca mi trng t nhin. D liu exergy ho hc tiu chun c cung cp bi Szargut v cc cng s(1988), Bejan v cc cng s (1996), v Moran cng Shapiro (2000).

Cc nguyn tc nng cao hiu sut nhit ng lc hc

nng cao hiu sut nhit ng lc hc, chng ta cn phi khc phc ngay lp tc s thiu hiu qu lin quan ti s phhu exergy v s hao tn exergy. Cc nguyn nhn chnh gy ra s ph hu exergy l phn ng ho hc, s truyn nhit, hpcht, v ma st, bao gm c s bay hi t do ca cc cht kh v cht lng. gii quyt cc vn ny mt cch hiu qu, takhng ch cn hiu r cc nguyn nhn chnh gy ra s khng hiu qu, m cn cn xc nh c gi tr ca chng, t nhtcng phi xc nh c gi tr tng i. Thay i thit k nng cao hiu sut cn phi c thc hin mt cch sngsut, tuy nhin, vn s c th khc i khi ta tnh ton chi ph c lin quan ti cc ngun khc nhau gy ra s khng hiuqu. Th d, chi ph trn 1 n v ca cng sut in hoc cng sut c hc c yu cu cung cp cho vic t ph huexergy gim p lc ni chung s cao hn chi ph cho 1 n v nhin liu c yu cu cung cp cho ph hu exergy bi vb tn hao trong qu trnh t chy hoc qu trnh truyn nhit.

Phn ng ho hc l mt nguyn nhn ni bt gy ra s khng hiu qu ca nhit ng lc hc. Do , ni chung trongthc t thng lm gim vic hiu qu ca qu trnh t chy. Tuy nhin, trong nhiu ng dng thng khng th trnh khivic s dng cc thit b t chy nh cc ni un. Lc ny, khng th hy vng lm gim ng k nh hng trong qu trnht chy khng thun nghch bng cc phng php truyn thng n gin c, i vi phn chnh ca s ph hu exergyc to ra bi s t chy l mt chui vn thng thy ca s hot ng khng ng b cc thit b. Mc d vy, c th

8


9/22

Nhit ng lc hc

gim s ph hu exergy trong cc h thng t chy thc t bng cch gim thiu vic s dng kh tha v bng vic lmnng trc cc cht phn ng. Trong hu ht cc trng hp ch mt phn nh ca s ph hu exergy trong mt bung t lc th c khc phc bng cc phng php ny. iu ny dn ti, sau khi xem xt cc la chn trn lm gim s phhu exergy lin quan ti s t chy, nng cao tnh hiu qu ca nhit ng lc hc nn tp trung vo cc thnh phn caton b h thng m d dng hn cho vic tnh ton ti chi ph. Thm vo , c th trnh mt vi hin tng ph hu exergyv hao tn nng lng, m mt vi trng hp khc khng lm c nh vy. Nn tp trung vo cc hiu qu m ta cth trnh.

S truyn nhit trong thc t rt kh t tnh hiu qu cao. Do vy, phi trnh s dng qu trnh truyn nhit khi khngcn thit hoc khi qu tn km. Mt s hng dn nh sau:

Khi nhit cng cao hn nhit T m ti mt qu trnh truyn nhit xy ra, trng hp ny T>T o, y Tol nhit ca mi trng, lc ny qu trnh truyn nhit c gi tr hn, ln hn mc yu cu trnh truynnhit ra xung quanh, truyn ti nc mt, hoc ti cc lung ng bng. Nn trnh khi qu trnh truyn nhit quaTo.

Nhit thp hn nhit T m ti mt qu trnh truyn nhit xy ra, trng hp ny T


10/22

S tay C in t

12.3 Cc quan h thuc tnh v d liu

Nhit ng lc hc k thut phn loi thnh mt lng ln cc thuc tnh nhit ng lc hc v mi quan h trong ccthuc tnh ny. Bng 12.2 lit k mt vi thuc tnh thng c s dng. Trong thc nghim lun c th thy c ccthuc tnh: p sut, nhit , v th tch ring. Ni nng ring, entropy ring, v enthalpy ring l cc thuc tnh m khng ddng c th thy c trong phng th nghim. Cc gi tr ca cc thuc tnh trn c th c tnh ton t cc d liu thnghim ca cc thuc sau qu trnh o c, t y cng c th suy ra c cc quan h thuc tnh thch hp bng vic s

dng cc nguyn l nhit ng lc hc.D liu thuc tnh c cng b trong cc ti liu ca Hc vin Quc gia v tiu chun v cng ngh (trc y l cctiu chun ca M), hoc ca cc nhm chuyn gia nh l Hi c kh M (ASME), Hi k thut nhit, ng bng v iu hokhng kh ca M (ASHRAE), v hi ho hc M, v ca cc tp on nh Dupont v Dow ho hc. Cc s tay v cc tuyntp tham kho v thuc tnh c lit k trong chng ny c th d dng truy cp vo d liu gc. Cng c th lyc cc d liu thuc tnh t rt nhiu cc c s d liu trc tuyn thng mi. Phn mm my tnh gip phn nng cao tnhsn c s dng cho mc ch ny.

B mt P-v-T

Mt lng ln d liu v p sut, th tch ring v nhit c tch lu i vi cc cht kh v cht lng quan trngtrong cng nghip. Cc d liu ny c th c biu din dng p = f(v,T), c gi l mtphng trnh trng thi. Cth biu din cc phng trnh trng thi dng th, bng, v dng gii tch. Hnh 12.1(a) th hin mi quan h b mtp-v-Tca nc. Hnh 12.1(b) th hin hnh chiu ca b mt p-v-Tln mt phng p sut-nhit , c gi l biu pha.

Hnh chiu ln trn mt phngp-v c th hin hnh 12.1(c).Hnh 12.1(a) c 3 vng c nh du l c, lng, v kh m y hp cht ch tn ti mt pha. Gia cc vng pha

ring c cc vng hai pha, m y hai pha s cng tn ti trng thi cn bng. ng thng chia cc vng n pha cchra khi cc vng hai pha l cc ng bo ho. Mt trng thi bt k c biu din bng mt im trn mt ng bo hol mt trng thi bo ho.

Hnh 12.1 B mt th tch-nhit p sut ring v cc hnh chiu ca nc (khng co gin v t l)

ng chia cch pha lng vi vng hai pha lng-kh l ng lng c bo ho. Trng thi ny c biu din l flmt trng thi lng c bo ho. ng hi c bo ho chia cch vng hi vi vng hai pha kh-lng. Trng thi nyc k hiu lg- mt trng thi hi c bo ho. ng lng c bo ho v ng hi c bo ho gp nhau ti mtim ti hn. Ti im ti hn ny, p sut l p sut ti hn pc, v nhit l nhit ti hn Tc, 3 pha c th cng tn ti trng thi cn bng trn ng nh du l ng bc 3. ng bc 3 ny chiu xung biu pha thnh mt im: im bi3.10


11/22

Nhit ng lc hc

Khi mt pha thay i trong khi p sut qu trnh lm nng v lm mt khng thay i th nhit vn khng i trongc hai pha. Do , trong vng hai pha lng-kh, ng p sut khng i cng l ng nhit khng i. i vi mt psut c xc nh trc, nhit tng ng vi n c gi l nhit bo ho. i vi mt nhit xc nh, p suttng ng vi n c gi l p sut bo ho. Vng pha bn phi ca ng hi c bo ho c gi l vng hi qunhitv hi tn ti ti mt nhit ln hn nhit bo ho cho p sut ca n. Vng bn tri ca ng lng c boho l vng lng b nn v cht lng ti mt p sut cao hn p sut bo ho cho nhit ca n.

Khi pha lng v pha kh cng tn ti trng thi cn bng, th c hai pha (pha lng v pha kh) s c bo ho. Th tch

tng cng ca s trn pha ny l V = Vf + Vg, hoc c th vit khc l mv = mfvf + mgvg, y m v v ln lt l khi lngv th tch ring. Chia tt c cho khi lng tng cng ca hai pha m ta c thnh phn khi lngca pha kh trong hai pha,mg/m, c k hiu lx, gi l quality, th tch ring v xut hin trong lng pha ny l:

(1 )f g f fg v x v xv v xv= + = + (12.16a)

y vfg = vg - vf. Tng t ta c th biu din cho ni nng, enthalpy v entropy:

(1 ) f g f fg u x u xu u xu= + = + (12.16b)

(1 ) f g f fg h x h xh h xh= + = + (12.16c)

(1 ) f g f fg s x s xs s xs= + = + (12.16d)

Cc d liu nhit ng lc hc (Thermodynamic Data Retrieval)S biu din dng bng ca p sut, th tch ring, v nhit c sn cho cc cht kh v cht lng quan trng trong

thc t. Cc bng ny thng lit k cc thuc tnh hu dng cho mc ch phn tch nhit ng lc hc, nh l ni nng,enthalpy v entropy. Hng lot cc bng v hi c a vo trong phn tham kho ca chng ny. Phn mm my tnhcng l mt cng c c sn phc v vic tra cu cc thuc tnh cho mt di ln cc loi cht ho hc, v d, cc bng kh caASME (1993) v Bornakke cng Sonntag (1996). Ngy cng nhiu cc ti liu cng vi a my tnh cung cp d liu v ccthuc tnh nhit ng lc hc ca nc, cc cht lm lnh, v mt vi cht kh c m hnh l tng ho - xem thm ti liuca Moran v Shapiro (2000).

bng 12.3 trnh by mt v d v d liu dng bng v cht khthng gp trong thc t. Dng ca cc bng ny v sdng chng nh th no c th hin rt n gin vi ngi s dng. y, mc nhin coi rng ngi s dng bit cchni suy tuyn tnh.

Cc d liu v ni nng ring, enthalpy ring v entropy ring c xc nh theo cc d liu bt k v theo cc cht khc

nhau. Tham kho bng 12.3a, c th tm c cc d liu ni nng ring, enthalpy ring v entropy ring ca nc tng ngvi nc lng c bo ho ti nhit 0,01oC (32,02oF), nhit bi 3. Gi tr ca mi thuc tnh ny c t bng khngti trng thi ny. Khi ch tnh ton n s khc nhau trong mt thuc tnh ring c bit, d liu s xo b. Khi thay ithnh phn ho hc trong qu trnh, cn a ra lu c bit. Lc ny s tip cn vn khi thnh phn ho hc thay i dophn ng ho hc s c xem xt trong cc ti liu ca Moran v Shapiro (2000).

D liu nc lng (xem bng 12.3d) cho thy rng ti mt nhit c nh s thay i th tch ring, ni nng ring, ventropy ring theo p sut khng ln. S thay i ca enthalpy ring theo p sut ti nhit cho trc ln hn mt cht vp sut xut hin tng minh trong nh ngha v enthalpy. S bin thin v, u, s v h c th hin mt cch tng qut bngcc d liu lng v l c s cho vic thit lp cc phng trnh nh gi thuc tnh d liu trng thi lng t d liu lngc bo ho:

( , ) ( )fv T p v T (12.17a)

( , ) ( )fu T p u T (12.17b)

[ ]( , ) ( ) ( ) f f sat h T p h T v p p T + (12.17c)

( , ) ( )fs T p s T (12.17d)

Ch s difth hin trng thi lng c bo ho ti nhit T, v psat l p sut bo ho tng ng. S hng c gchchn trong phng trnh (12.17c) c th b qua, a vo h(T,p) hf (T).

Cc biu din dng th ca cc d liu thuc tnh cng thng c s dng. Chng bao gm cc biu v p-Tvp-v trn hnh 12.1, biu T-s ca hnh 12.2, biu h-s (Mollier) ca 12.3 v biu p-h ca hnh 12.4. Cc th v nn c c xem xt tip theo s dng h s nn c l mt to trong mt vect.

th nn c

Hnh 12.5 minh ho th v nn suy rng ca mi quan h p-v-Ts dng cho mt lot cc cht kh thng gp. th ny, h s nn c,Z, c v ngc li vi p sutgim,pR, nhit gim, TR v th tch ringgim,

'

Rv , y

11


12/22

S tay C in t

pvZ

RT= (12.18)

Trong cng thc ny v l th tch ring trong mt phn t gam (v d, m3/kmol) v R l hng s kh chung(v d 8314N.m/kmol.K). Cc thuc tnh ny c biu din n gin hn nh sau:

,, ,( / ) R R Rc c c c

P T vP T v

P T RT p= = = (12.19)

ypc v Tc ln lt l p sut v nhit ti hn. Cc gi tr capc v Tc c th t c t l thuyt-xem thm cc ti liuchuyn ngnh, v d, Moran v Shapiro (2000). th ng nhit c n gin trn hnh 12.5 biu din cc ng cong thhin gn ng nht v cc d liu ca mt vi cht kh. Vi 30 cht kh trong th ny, s sai lch ca gi tr quan st cso vi cc gi tr trn th ny nhiu nht l 5% v i vi cc vng rng hn th sai lch ny nh hn.

Cc phng trnh gii tch ca trng thi

Xem xt th ng nhit trn hnh 12.5, thy rng s thay i ca h s nn c c th c th hin dng mtphng trnh tin cy c, t nht cho cc khong gia s tc thi ca p v T. C th vit hai biu din ny theo mt biu dinl thuyt c bn. H s nn c c th biu din theo mt khai trin dng chui v hn ca p sut,

2 3 1 ( ) ( ) ( ) ....Z B T p C T p D T p= + + + + (12.20a)

v dng khc l mt chui theo 1/ v ,

2 3

( ) ( ) ( )1 ...

B T C T D T Z

v v v= + + + + (12.20b)

Cc phng trnh trng thi trn c bit n nh l cc khai trin virial, v cc h s , , ...B C D vB, C, D, ... c gil cc h s virial. Trong thc t, c th tnh ton cc h s virial bng cch s dng cc cng thc ca c hc thng k csuy ra t vic xem xt cc trng lc xung quanh cc phn t. T y cc h s u tin c tnh ton cho cc cht kh baogm cc phn t n gin mt cch tng i. V nguyn tc cng c th tm c cc h s ny bng cch iu chnh dliup-v-Tkhp bn trong mt phm vi c quan tm c bit. Ch c cc h s u tin l c th c tm thy mt cchchnh xc bng cch ny, tuy nhin kt qu s l mt phng trnh c xp xch ph hp ti cc trng thi tc thi.

Hn 100 phng trnh trng thi c xy dng v pht trin nhm miu t mt cch chnh xc ng x p-v-Tca cccht v trnh tnh phc tp c sn trong n mt dng chui virial y . Ni chung, cc phng trnh ny t th hin cctnh cht mang ngha vt l c bn v th hin cc tnh cht thin v tnh thc nghim nhiu hn. Hu ht chng c phttrin cho cc cht kh, nhng cng c mt s din t v cc ng x p-v-T ca pha lng, t nht l v mt nh nh tnh.

Bng 12.3 D liu bng hi mu

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Nhit ng lc hc

Hnh 12.2 Biu nhit -entropy ca nc. (Ti liu ngun: Jones, J.B, v Dugan, R.E. 1996.Nhit ng lc hc k thut,Prentice Hall, Englewood Cliffs, NJ, da vo d liu v cc cng thc cung cp t cc bng hi Haar, L., Gallagher, J.S., v

Kell, G.S. 1984. NBS/NRC. Hemisphere, Washington, D.C)

Hnh 12.3 Biu Enthalpy-entropy (Mollier) ca nc. (Ti liu ngun:Jones, J.B, v Dugan, R.E. 1996.Nhit ng lchc k thut, Prentice Hall, Englewood Cliffs, NJ, da vo d liu v cc cng thc cung cp t cc bng hi Haar, L.,

Gallagher, J.S., v Kell, G.S. 1984. NBS/NRC. Hemisphere, Washington, D.C)

Mi phng trnh trng thi ch c s dng cho mt s trng thi c bit. Phm vi ng dng ca chng thng cquyt nh bi gia s ca p sut, hoc t trng, m y mong mun cc phng trnh th hin c ng x p-v-Tmt cchchnh xc. c c thm thng tin v phng trnh trng thi, hy xem Reid v Sherwood (1966) v Reid cng cc cngs (1987).

M hnh cht kh l tng

Xem xt k th nn c suy rng, Hnh 12.5, thy rng khi pR nh, v vi nhiu trng thi m khi TR l ln, hs nn cZc gi tr gn ti 1. Ni cch khc, khi cc p sut thp hn so vi pc, v i vi nhiu trng hp c nhit cao hn Tc, h s nn c c gi tr tin ti 1. Bn trong khong gii hn ch ra trn, c th gi s chnh xc chpnhn c lZ = 1-i.e.,

pv RT pv RT = = (12.21a)

Cc dng khc ca phng trnh ny thng c s dng l

,pV nRT pV mRT = = (12.21b)

13


14/22

S tay C in t

cc phng trnh trn, / ,n m M v Mv= = , v hng s kh ringl / R R M = , y Ml trng lng ca phn t.

Hnh 12.4 Biu p sut-enthalpy ca nc. (Ti liu ngun: Jones, J.B, v Dugan, R.E. 1996.Nhit ng lc hc k thut,Prentice Hall, Englewood Cliffs, NJ, da vo d liu v cc cng thc cung cp t cc bng hi Haar, L., Gallagher, J.S., v

Kell, G.S. 1984. NBS/NRC. Hemisphere, Washington, D.C)

Hnh 12.5 th nn c suy rng ( '/ , / , / R c R c R c cT T T p p p v vp RT = = = ) i vi 10Rp . (Ti liu ngun: Obert, E.F.1960. Cc khi nim ca Nhit ng lc hc. McGraw Hill, New York)

Bng 12.4 Cc cng thc v kh l tng cho ,h u v s

Nhit ring thay i Nhit ring hng b

2

1

2 1( ) ( ) ( )

T

pT

h T h T c T dT =

(1)2 1 2 1

( ) ( ) ( )ph T h T c T T = (1')

14


15/22

Nhit ng lc hc

2

1

2

2 2 1 1

1

( )( , ) ( , ) ln

T p

T

c T ps T p s T p dT R

T p =

(2)a2 2

2 2 1 1

1 1

( , ) ( , ) ln lnpT p

s T p s T p c RT p

= (2')

2

12 1

( ) ( ) ( )T

vT

u T u T c T dT = 3) (3) 2 1 2 1( ) ( ) ( )vu T u T c T T = (3')

2

1

2

2 2 1 1

1

( )( , ) ( , ) ln

Tv

T

c T vs T v s T v dT R

T v

= +

2 1s s=

(4)2 2

2 2 1 1

1 1

( , ) ( , ) ln lnvT v

s T v s T v c R

T v

= +

2 1s s=

(4')

2 2

1 1

( )

( )r

r

p T p

p T p=

(5) ( 1) /2 2

1 1

k k

T p

T p

=

(5')

2 2

1 1

( )

( )r

r

v T v

v T v=

(6) ( 1)2 2

1 1

k

T v

T v

=

(6')

a c th s dng,0 0 2

2 2 1 1 2 1

1

( , ) ( , ) ( ) ( ) lnp

s T p s T p s T s T Rp

= .

b cp v cv l cc gi tr trung bnh trn khong nhit t T1 n T2.

C th thy rng ( )/ Tu v trit tiu vi mt cht kh m phng trnh trng thi ca n c dng chnh xc l phngtrnh (12.21), v do ni nng ring ch ph thuc vo nhit . Kt lun ny c cng c thm bng cc quan st thcnghim bt u t cng ca Joule, ngi ch ra rng ni nng ca cht kh t trng thp ph thuc chnh vo nhit .

Cc vn xem xt trn cho php m hnh ho mt cht kh thc no vi mt m hnh l tngca n: (1) Phngtrnh trng thi c th hin bi phng trnh (12.21) v (2) ni nng, enthalpy, v nhit ring (bng 12.2) l cc hm chph thuc vo nhit . Cht kh thc tip cn ti cc m hnh ny vi mt gii hn l p sut gim chm. Ti cc trng thikhc, s ng x thc ca cht kh c th v cn bn khng ging vi nhng g c d on. Do vy, nn thn trng khi lmvic vi m hnh cht kh l tng.

D liu nhit ring cho cc cht kh c th t c bng vic o trc tip. Khi ngoi suy ti p sut khng, s tm cnhit ring ca cht kh l tng. Cng c th tnh ton c nhit ring ca cht kh l tng bng vic s dng cc m hnh

phn t ca vt cht cng vi cc d liu t o c bng knh quang ph. Mi quan h nhit ring ca cht kh l tngthng hu dng v c dng nh sau:

( ) ( )p vc T c T R= + (12.22a)

,1 1P v

kR Rc c

k k= =

(12.22b)

y k = cp/cv.

i vi cc qu trnh ca mt cht kh l tng gia trng thi 1 v 2, Bng 12.4 a ra cc biu thc tnh ton s thayi v enthalpy ring, h , entropy ring, s v ni nng ring, u . Cng c th cung cp cc mi quan h ny cho cc qutrnh ca mt cht kh l tng gia cc trng thi m c cng mt entropy ring: s2=s1. Mi quan h ca thuc tnh v dliu s dng trong cc biu thc ca bng 12.4: h, u, cp, cv, pr, vr, vso tnh c t cc ti liu chuyn ngnh-v d ca Moranv Shapiro (2000).

12.4 Cc chu trnh cng sut ca cht kh v hi

Cc h thng nng lng kh v hi to ra cc nng lng c hc v nng lng in t cc ngun nng lng gc l: hohc, mt tri, hoc ht nhn. cc h thng nng lng hi, cht lng, thng l nc, s tri qua mt giai on thay i phat lng sang hi, v ngc li. Trong cc h thng nng lng kh, cht lng lm vic gi li mt cht kh i qua, mc dthnh phn ho hc thng thay i do vic to ra qu trnh t chy nhin liu.

Cc qu trnh din ra trong cc h thng cng sut thng phc tp, do vy thng pht trin cc m hnh nhit ng lchc l tng ho d x l phn tch.Phn tch tiu chun khca cc h thng nng lng kh c xem xt trong phnny l mt v d ng ch . Ph thuc vo cp ca s l tng ho, cc m hnh l tng ny c th ch cung cp ccthng tin nh tnh v s hot ng ca cc h thng tht tng ng. Cc thng tin ny thng c ch trong vic o cc thayi ca cc tham s vn hnh chnh m c th nh hng ti s hot ng thc t. Cc m hnh nhit ng lc hc c s

cng c th cung cp cc phng php t c, t nht l xp x, cc c im thun tin v khng thun tin m chng sc s dng nng cao hiu qu hot ng ca h thng nhit ng lc hc.

Truyn nhit v cng trong cc qu trnh thun nghch bn trong15


16/22

S tay C in t

Cc biu thc biu din cng v s truyn nhit bn trong cc qu trnh thun nghch rt c ch cho vic din t s hotng nhit ng lc hc ca cc chu trnh kh v hi. Cc trng hp ring quan trng s c xem xt nh sau. i vi mtcht kh l mt h thng, cng gin n sinh ra t cc lc m h thng tc dng di chuyn ti bin ca n s ngc li vitnh tr khng ca mi trng xung quanh:

2 2

1 1W F dx pAdx= =

y lc bng tch ca din tch di chuyn v p sut tc dng bi h thng y. Ch rng Adx l s thay i ca tng thtch h thng,

2

1W p dV =

Biu thc ny biu din cng p dng cho c hai qu trnh ni gin n v qu trnh gin n pht ng. Tuy nhin, i vimt qu trnh ngc bn trong thp khng ch bao gm p sut ti bin di ng m cn c p sut qua h thng. Hn th na,i vi mt qu trnh ngc bn trong, th tch bng mv, y th tch ring v c mt gi tr n xuyn sut h thng ti mtthi im c a ra. Do vy, cng ca qu trnh gin n bn trong (hoc nn) trn mt n v khi lng h thng l

2

1intrev

Wpdv

m = (12.23)

Khi biu din mt qu trnh ca mt h thng kn bng mt ng cong lin tc trn th p sut theo th tch ring,din tch bn di ng cong chnh l ln ca cng cho mt n v khi lng h thng: din tch a-b-c'-d' ca hnh 12.6.

i vi cc th tch iu khin mt ng vo, mt ng ra khng c mt trong cc qu trnh khng thun nghch ni,cc biu thc sau s a ra cng c to ra cho mt n v khi lng:

2 2

int

( )2

ei e

i ei

rev

v vWv dp g z z

m

= + +

&

&(12.24a)

y tch phn c tnh t ng vo n ng ra (xem Moran v Shapiro (2000) thm). Nu khng c mt thay i ngk no ca ng nng v th nng t ng vo ti ng ra, phng trnh (12.24a) s l

1int

( 0)e

rev

Wv dp ke pe

m

= = =

&

&(12.24b)

Hnh 12.6 Cc qu trnh ngc bn trong trn mt phngp-v

Th tch ring gn nh khng i trong nhiu ng dng cho cht lng. Lc ny phng trnh (12.24b) s tr thnh

int

( ) ( )e irev

Wv p p v consta nt

m

= =

&

&(12.24c)

Khi xem xt cc trng thi kch thc mt n v khi lng khng c cc qu trnh khng thun nghch t ng voti ng ra, v din t chng bng mt ng cong lin tc biu din qua th p sut vi th tch ring, nh c th hin

trn Hnh 12.6, ln ca tch phn vdp trong phng trnh (12.24a) v (12.24b) c biu din bi din tch a-b-c-d saung cong.

i vi mt qu trnh thun nghch bn trong ca mt h thng kn gia trng thi 1 v trng thi 2, s truyn nhit chomt n v khi lng h thng l

16


17/22

Nhit ng lc hc

2

1intrev

QT ds

m = (12.25)

i vi th tch iu khin mt ng vo, mt ng ra khng c mt cc qu trnh khng thun nghch bn trong, biuthc sau y ch ra truyn nhit cho mi n v khi lng t ng vo i n ng ra e:

1int

e

rev

QT ds

m

=

&

& (12.26)

Khi mt qu trnh no nh vy c biu din bi mt ng cong lin tc qua th ca nhit vi entropy ring, dintch di ng cong chnh l ln ca nhit truyn cho mt n v khi lng.

Cc qu trnh nhiu hng

Mt qu trnh thun nghch bn trong c din t bi biu thc pvn = hng s c gi l mt qu trnh a hngv n ls m a hng. Trong cc ng dng hin nay n c th tnh c bng cch lm thch hp cc d liu th tch p sut ring.Mc d c th p dng biu thc ny khi xem xt mt cht kh thc, ni chung trong thc t vn thng s dng m hnhcht kh l tng v m hnh thc t vi nhau. Bng 12.5 cung cp mt vi biu thc c th p dng cho cc qu trnh nhiu

hng v cc dng ring ca chng khi xy dng m hnh cht kh l tng v chng. Cc biu thc cho pdv v vdp ln

lt p dng tnh ton cc phng trnh (12.23) v (12.24).Bng 12.5 Qu trnh a hng: Constn apv =

Tng qut Kh l tngb

2 2

1 1

n

p v

p v

=

0n = : p sut hng

n = : th tch ring hng

(1)

/( 1)

2 2 2

1 1 1

n n n

p v T

p v T

= =

0n = : p sut hng

n = : th tch ring hng1n = : nhit hng

n k= : entropy hng khi k bng hng

(1')

1n =2

2

1 11

1

lnv

pdv p vv

=2

2

1 11

1

lnp

vdp p vp

=

(2)

(3)

1n =2

2

11

lnv

pdv RT v

=2

2

11

lnp

vdp RT p

=

(2')

(3')

1n 2

2 2 1 1

1

( 1) /

1 1 2

1

1

11

n n

p v p vpdv

n

p v p

n p

=

=

2

2 2 1 11

( 1) /

1 1 2

1

( )1

11

n n

nvdp p v p v

n

np v p

n p

=

=

(4)

(5)

1n 2

2 1

1

( 1) /

1 2

1

( )

1

11

n n

R T T pdv

n

RT p

n p

=

=

2

2 11

( 1) /

1 2

1

( )1

11

n n

nRvdp T T

n

nRT p

n p

=

=

(4')

(5')

a i vi cc qu trnh nhiu hng ca cc h thng kn y th tch thay i ch trong ch cng, phng trnh (2),(4), v (2'), (4') c th ng dng vi phng trnh (12.23) tnh ton cng. Khi mi n v khi lng i qua mt th tchiu khin mt ng vo, mt ng ra ti trng thi n nh s thc hin mt qu trnh nhiu hng, phng trnh (3), (5),v (3'), (5') c th ng dng vi phng trnh (12.24a) v (12.24b) tnh ton cng sut. Cng nn ch rng, ni chung,

2 2

1 1

vdp n pdv = .

17


18/22

S tay C in t

Cc chu trnh Rankine v Brayton

Vi cc m hnh n gin nht v cc my cng sut turbine kh v cng sut hi thng c biu din ln lt theo bnthnh phn dng chui, dng hnh thi, chu trnh Rankine v chu trnh Brayton c th hin di dng biu trong bng12.6. Cc m hnh l tng nhit ng lc hc ca cc chu trnh ny c to thnh t 4 qu trnh thun nghch bn trong:hai qu trnh ng entropy c k tip vi hai qu trnh c p sut khng i. Bng 12.6 cung cp cc biu thuc tnh cacc chu trnh tht v cc chu trnh l tng tng ng ca chng. Mi mt chu trnh tht c nh du l 1-2-3-4-1; chutrnh l tng ca n l 1-2s-3-4s-1. n gin, khng th hin p sut thay i trn cc thit b un nhit, cc ni ngng,v cc thit b trao i nhit. Lin quan ti phng trnh (12.26) i vi cc chu trnh l tng, nhit c thm vo mt nv khi lng chy c th hin bi din tch di ng ng p t trng thi 2s ti trng thi 3: din tch a-2s-3-b-a. Nhiti ra l din tch di ng ng p t trng thi 4s n trng thi 1: din tch a-1-4s-b-a.

Bng 12.6 Cc chu trnh Rankine v BraytonChu trnh Rankine Chu trnh Brayton

din tch khp kn 1-2s-3-4s-1 biu din nhit li c thm vo mi n v khi lng dng chy. i vi mt chu trnh

cng sut no , nhit li thm vo bng vi cng li thc hin.Cc biu thc cho cc qu trnh truyn nng lng chnh tc c th hin trn cc biu trong bng 12.6 v c thhin t cc phng trnh (1) n phng trnh (4) ca bng. C th t c chng bng vic n gin phng trnh (12.10a)vi cc gi s b qua s hao tn nhit v b qua s thay i v ng nng v th nng t ng vo n ng ra ca tngthnh phn. Tt c cc i lng u l dng theo cc hng mi tn trn hnh.

Hiu sut nhit ca mt chu trnh cng sut c nh ngha l t s ca cng (net work) c ch vi nng lng tng cngc thm vo bi qu trnh truyn nhit. S dng cc biu thc (1)-(3) ca bng 12.6, hiu sut nhit s l

3 4 2 1

3 2

4 1

3 2

( ) ( )

1

h h h h

h h

h h

h h

=

=

(12.27)

t c hiu sut nhit ca mt chu trnh l tng, h 2s, thay th h2 bng h4s, thay th h4 trong phng trnh (12.27).Thng th cc nh gi v chu trnh theo cc iu kin vn hnh cho thy rng hiu sut nhit c xu th tng khi nhit

trung bnh ca nhit thm vo tng v/ hoc ca nhit i ra gim. Trong chu trnh Rankine, nhit thm vo c th t c

18


19/22

Nhit ng lc hc

mt nhit cao bng cch cp qu nhit u tin cho cht kh i vo turbin v/hoc vn hnh ti mt p sut hi pht cao.Trong chu trnh Brayton vic tng t s p sut nn p2/p1 s lm tng nhit trung bnh ca nhit i vo. Do cc vt liu ccc gii hn v nhit v p sut, trng thi ca cht lng lm vic ti ng vo ca turbin phi kim tra cc gii hn thct. Nhit ng vo ca turbine trong chu trnh, v d, c iu khin bng vic cung cp mt lng kh vt mc yucu cho bung t. Trong mt chu trnh Rankine c s dng nc lm cht lng lm vic, thng t c mt nhit thpca nhit i ra bng cch vn hnh thit b ngng ti mt p sut thp di 1 atm. gim s xi mn v bo mn do chtlng ri trn cc cnh ca turbine hi chu trnh Rankine, c th bo qun t nht 90% lng hi ng ra ca turbine: x 4 >0,9.

T s cng tr li, bwr, l t s ca cng c yu cu bi bm hoc my nn vi cng pht sinh bi turbine:

2 1

3 4

h hbwr

h h

=

(12.28)

V mt cht kh c th tch ring ln gin n trong mt turbine s dng chu trnh Rankine v mt cht lng c th tchring thp hn nhiu c bm, t s cng tr li ni v mt bn cht rt thp trong cc my cng sut hi-trong nhiutrng hp n c t 1-2%. Tuy nhin, trong chu trnh Brayton, c turbine v my nn cha mt cht kh c th tch ringcao, v t s cng tr li s ln hn nhiu, thng th 40% hoc hn.

nh hng ca ma st v cc qu trnh khng thun nghch khc i vi cc dng chy i qua turbine, cc my nn, vbm thng c nh gi qua mt hiu sut ng entropy thch hp. Tham kho thm bng 12.6 v kha cnh ny, hiu sutturbine ng entropy l

3 4

3 4

t

s

h hh h

=

(12.29a)

Hiu sut ca my nn ng entropy l

2 1

2 1

sc

h h

h h

=

(12.29b)

Vi hiu sut my bm ng entropy, m c cng mt dng nh phng trnh (12.29b), t s ca n thng c xp xbng phng trnh (12.24c) l 2 1 1sh h v p , y p l p sut truyn qua bm.

Cc my cng sut turbine kh n gin khc vi m hnh chu trnh Brayton nhiu kha cnh quan trng. Khi vn hnhthc, thng cp vo thit b nn tha kh, y chng s c nn vi mt p sut cao hn, sau nhin liu s c cp

v qu trnh t chy xy ra; cui cng s t chy ca hn hp trn xy ra v cht kh gin n trong turbine, sau chngc x ra mi trng bn ngoi. Do vy, b trao i nhit nhit thp c th hin bi mt ng thng m nt trnbiu chu trnh Brayton bng 12.6 khng phi l mt thnh phn trong thc t, tuy nhin n c dng ch tnh tonchnh thc qu trnh lm mt trong mi trng xung quanh ca khi nng c x ra t turbine.

Mt l tng ho khc thng c ng dng ca cc my cng sut turbine kh l phn tch kh tiu chun. Mt phntch kh tiu chun lin quan ti hai gi s quan trng: (1) Qu trnh t chy s pht sinh ra nhit gy ra nh hng cho hthng thay vo vic truyn nhit t mt ngun bn ngoi, nh c th hin bi biu chu trnh Brayton ca bng 12.6. (2)Cht hot ng trong ton b chu trnh l cht kh, v l mt cht kh l tng. Trong phn tch kh tiu chun lnh, t snhit ring k cho kh c coi l hng. Phng trnh (1) n (6) ca bng 12.4 ni chung p dng phn tch kh tiu chun.Phng trnh (1') ti (6') ca bng 12.4 p dng phn tch kh tiu chun lnh, t y c th c c biu thc sau tnhton cng sut ca turbine t bng 12.1 (Phng trnh (10c'')):

( 1) /3

4 51 ( / )

1

k k

t

kRTW m p p

k

=

& & (12.30)

C th vit mt biu thc cng sut tng t v dng cho mt my nn.

Cc chu trnh Otto, Diesel v chu trnh kp

Mc d hu ht cc turbine kh l cc ng c t trong, chng cng thng c tn l cc ng c t trong kh hi lloi c s dng nhiu trong t, xe ti v xe khch. C hai nguyn l c bn ca cc ng c t trong kh hi l ng cnh la bng tia la in v ng c nh la bng qu trnh nn. ng c nh la bng tia la in , mt hn hp canhin liu v kh s c nh la bng mt cng tc la in. mt ng cnh la bng qu trnh nn, kh s c nnti mt p sut cao v nhit m qu trnh nn xy ra mt cch t pht khi nhin liu c dn vo.

mt ng c t trong bn k, piston ca n thc hin 4 k phn bit bn trong mt xi lanh cho hai vng quay ca tayquay. Hnh 12.7 v mt biu p sut-dch chuyn. Vi van vo m, piston s thc hin mt k np ko kh np sch votrong xi lanh. Tip theo, lc ny c hai van u ng, piston s tri qua k nn v s gia tng nhit v p sut ca kh np.

Sau qu trnh chy s bt u, kt qu s to ra mt hn hp kh c p sut cao, nhit cao. Tip theo k nn l k n, k ny hn hp kh gin n v sinh cng ln piston. Tip theo piston s thc hin mt k x m y s thi sch cc kh bchy ra ngoi xi lanh qua van x m. Cc ng c nh hn vn hnh trong hai chu trnh. cc ng c hai k, cc qu trnhvo, nn, gin n v thi c thc hin cho mt vng quay ca tay quay. Mc d cc ng c t trong thc hin cc chu

19


20/22

S tay C in t

trnh c hc, chng khng thc hin mt chu trnh nhit ng lc hc no c, v vt cht c to ra thnh mt hp cht vsau li c chuyn sang thnh mt hp cht khc.

Mt tham s c s dng din t hot ng ca cc ng c t trong kh hi l p sut hiu dng trung bnh, hocmep.

Hnh 12.7 Biu p sut-dch chuyn cho mt ng c t trong kh hi

p sut hiu dng trung bnh l mt p sut hng s theo l thuyt m khi n tc dng ln piston trong thi gian k cngsut, s to ra cng mt cng li ging nh trong mt chu trnh, tc l:

net work for onecyclemep

displacement volume= (12.31)

y th tch di chuyn l th tch m piston s qut ra ngoi v n s di chuyn t tm im cht trn n tm im chtdi. i vi hai ng c c cng th tch dch chuyn nh nhau, ng c no c p sut hiu dng trung bnh cao hn s tora c nhiu cng li hn, v khi chy cng mt tc , n s c cng sut ln hn.

Cc nghin cu chi tit v s hot ng ca cc ng c t trong kh hi c th xem xt v nh gi c nhiu cim, bao gm qu trnh t chy xy ra trong xi lanh v cc nh hng ca cc qu trnh khng thun nghch lin quan tima st v gradient p sut v nhit . Nhit truyn gia cc cht kh trong xi lanh, thnh xi lanh v cng cn thit np vx cc sn phm ca qu trnh chy cng c th c xem xt n. Do tn ti nhng vn phc tp ny, vic m hnh chnhxc cc ng c t trong kh hi thng c m phng trn my tnh.

tin hnh phn tch nhit ng lc hc c sca cc ng c t trong, cn c qu trnh n gin ho. Mt th tc mcho php cc ng c c nghin cu mt cch nh tnh p dng cho vic phn tch kh tiu chun c cc thnh phnsau y: (1) mt lng khng i cc kh c m hnh thnh mt kh l tng ca h thng; (2) qu trnh chy c thayth bng mt qu trnh truyn nhit t mt ngun bn ngoi v c biu din bng cc qu trnh nhit ng lc hc c bn;(3) S khng c cc qu trnh x v dn vo nh l trong mt ng c tht: chu trnh ny c hon thnh bng mt qu trnhtruyn nhit vi hng s th tch; (4) Tt c cc qu trnh u c tnh thun nghch bn trong.

Cc qu trnh c ng dng trong cc phn tch kh tiu chun ca cc ng c t trong c chn biu din cc skin xy ra bn trong ng c n gin v th hin ging vi cc c trng ca cc biu p sut-dch chuyn quan stc. Thm vo qu trnh truyn nhit th tch hng c ni trc , k nn v t nht mt phn ca k cng sut

thng c coi l ng entropy. S thm nhit thng c xem xt khi xy ra trong mt th tch hng, ti mt p suthng, hoc ti mt th tch hng l kt qu sau ln lt qu trnh p sut hng, qu trnh do, cc chu trnh Otto, Diesel, vkp c th hin trong bng 12.7.

Gim s cn bng nng lng ca h thng kn, phng trnh 12.7b, a ra cc biu thc tnh cng v kh nng nhittrong mi trng hp nh trong bng 12.7:

3412 41

1 2 3 4 1 4, ,

WW Qu u u u u u

m m m= = = (12.32)

Bng 12.7 cung cp thm cc biu thc cho cng, truyn nhit, v hiu sut nhit xc nh cho tng trng hp ring. Tt ccc biu thc tnh cng v nhit gn vi cc thut ng du ring ca phng trnh (12.7). Phng trnh (1) n (6) ca bng12.4 thng p dng cho phn tch kh tiu chun. Trong phn tch kh lnh tiu chun, t s nhit ring k cho cht khthng c coi l hng s. Phng trnh (1') n (6') ca bng 12.4 p dng cho phn tch kh lnh tiu chun, nh l

phng trnh (4') ca bng 12.5, vi n = kcho cc qu trnh ng entropy ca cc chu trnh ny.

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Nhit ng lc hc

Tham kho bng 12.7, t s ca cc th tch ring v1/v2 l t s nn, r. i vi chu trnh Diesel, t s v3/v2 l t s gii hn, rc.Hnh 12.8 th hin s thay i ca hiu sut nhit theo t s nn cho mt chu trnh Otto v cc chu trnh Diesel c t s giihn ca 2 v 3. Cc ng cong ny c xc nh trn mt c s v kh tiu chun lnh vi k = 4 c s dng biu thc sau:

1

111 ( )

( 1)

k

c

k

c

rconstant k

k rr

=

(12.33)

y chu trnh Otto tng ng vi rc = 1.

Bng 12.7 Cc chu trnh Otto, Diesel v Dual

(a) Chu trnh Otto (b) Chu trnh Diesel (c) Chu trnh Dual

Hnh 12.8 Hiu sut nhit ca cc chu trnh Otto v Diesel kh lnh tiu chun, k = 1,4

Vi tt c cc qu trnh thun nghch bn trong, cc din tch trn cc biu p-v v T-s ca bng 12.7 tng ng c thc gii thch nh l cng v truyn nhit. Lin quan ti phng trnh (12.23) v tham kho cc biu p-v, cc din tchdi qu trnh 3-4 ca chu trnh Otto, qu trnh 2-3-4 ca chu trnh Diesel, v qu trnh x-3-4 ca chu trnh Dual biu dincng thc hin bi cht kh trong giai on ca k cng sut, cho mt n v khi lng. i vi mi chu trnh, din tchpha di qu trnh ng entropy 1-2 biu din cng thc hin trn cht kh trong giai on k nn, cho mt n v khilng. Din tch ng kn ca mi chu trnh biu din cng li thc hin cho mt n v khi lng. Cng vi phng trnh

(12.25) v tham kho cc biu T-s, cc din tch di qu trnh 2-3 ca cc chu trnh Otto v Diesel v di qu trnh 2-3ca chu trnh Dual biu din nhit c thm vo mt n v khi lng. Din tch ng kn ca mi chu trnh biu dinnhit li c thm vo, n bng vi cng li thc hin, cho tng n v khi lng.

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S tay C in t

Tham kho

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