TOPLOTNE OPERACIJE KONDUKCIJA – prenos toplote kroz čvrsto stanje KONVEKCIJA – prenos toplote sa fluida na zid ili sa zida na fluid u zavisnosti od temperature. PROLAZ toplote K – karakterističan za razmenjivače toplote.
NESTACIONARNO PROVOĐENJE TOPLOTE (UNSTEAY STATE HEAT TRANSFER) This means the rate of heat transfer transfer is not constant constant with time as temperature difference between source and sink
is changing over time. “Heat Equation” is important partial differential equation which describes the distribution of heat (or variation in temperature) in a given region over time. For a function u(x,y,z,t)
*θ(x,y,z,t)+ of three spatial variables (x,y,z) an the time
̇
variable t, the heat equation is:
(For U variation is just a positive constant)
̇
Diferencijalna jenačina provođenja toplote - izvor ili ponor toplote (egzoterman ili endoterman proces) iliti generisanje toplote,
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* + * + ** + * + ̇
brojilac (demonitaor – brojilac, numerator – imenilac) – predstavlja zapreminski toplotni kapacitet, čije su jedinice
,
α – termička difuznost,
:::
,
- toplotna provoljivost za čvrste materije (thermal
conductivity – obeležavaju je sa k inače
),
c – specifični toplotni kapacitet
za ravan zid – brzina promene temperature de
biti veda ako je θ
θ
vede
θ
θ
- trodimenzionalno nestacionarno
provođenje toplote
za
θ
θ
θ
θ
θ
- dvodimenzionalno
– jednodimenzionalno
proces je stacionaran
- nema generisanja toplote u sistemu.
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STACIONARNI:
̇ ̇ ̇
NESTACIONARNI:
Dvodimenzionalno stacionarno:
RAZMENJIVAČI TOPLOTE (HEAT EXCHANGERS) Su aparati u kojima se obezbeđuje razmena toplote između 2 fluia. Oko 80% termičke energije se troši u procesima hemijske procesne industrije (petrohemije, bazne industrije)
Koriste za grejanje ili hlađenje jenog ili rugog fluia i za rekuperaciju “otpane” toplote. Neophodni su za procese destilacije – dovodi se toplota a bi se tečna faza isparila i na vrhu estilacione kolone se ponovo kondenzovala u npr Libigovom kondenzatoru. ISPARAVANJE – sve komponente u smeši su isparljive
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Razmenjivač toplote obija naziv prema procesnom fluidu. Ako procesni fluid hladi onda imamo hladnjak.
KLASIFIKACIJA: Prema načinu ostvarivanja kontakta fluia pri razmeni toplote
Prema kompaktnost površine za toplotnu razmenu
Prema konstruktivnim karakteristikama Prema konfiguraciji tokova fluida Prema broju fluia koji učestvuju u toplotnoj razmeni
(1, 2, 3 ili više, ko regeneratora nije neobično a se jedan fluid u jednoj fazi procesa zagreva toplotom koju je sam predao u drugoj fazi procesa) Prema mehanizmu prenosa toplote PREMA NAČINU OSTVARIVANJA KONTAKTA
DIREKTNI KONTAKT
Neophono je a se fluii nakon hlađenja ili grejanja mogu razdvojiti Retko se koristi i fluidi su u direktnom kontaktu. INDIREKTNI KONTAKT
REKUPERATORI (RECUPERATOR)
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Termički izolovani. Najčešde se koriste u inustriji The term recuperator refers as well to liquid-liquid counterflow heat exchangers used for heat recovery in counterflow chemical and refinery industries and in closed processes such as ammonia-water or LiBr-water absorption refrigeration cycles. Donja slika pokazuje tri osnovne konfiguracije, svi su suprotnostrujni,
R
(R
H
E
)
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Preko površine za toplotnu razmenu prvo stuji topliji flui (hlai se) a površina akumulira toplotu. Potom se preko tako zagrejane površine pušta hlaniji fluia i on prima toplotu. The flow through the heat exchanger is cyclical and periodically changes direction. It is similar to a countercurrent heat exchanger. However, a regenerator mixes the two fluid flows while a countercurrent exchanger maintains them separated. The temperature profile remains at a nearly constant temperature, and this includes the fluid entering and exiting each end. In regenerative heat exchangers, the fluid on either side of the heat exchanger is nearly always the same fluid. The fluid is cycled through the heat exchanger, often reaching high temperatures. The fluid may go through an external processing step, and then it is flowed back through the heat exchanger in the opposite direction for further processing. Usually the application will use this process cyclically or repetitively. Thus, in regenerative heat exchangers, a fluid incoming to a process is heated using the energy contained in the fluid exiting this
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reclaimed nearly in a thermodynamically reversible way. This type of heat exchanger can have a thermal efficiency of over 90%, transferring almost all the relative heat energy from one flow direction to the other. Only a small amount of extra heat energy needs to be added at the hot end, and dissipated at the cold end, even to maintain very high or very low temperatures.
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RAZMENJIVAČI SA FLUIIZOVANIM SLOJEM (FLUIISE BE HEAT EXCHANGER) Fluiizovan sloj je sloj nasutih čvrstih čestica koje ispoljavaju karakteristike fluida. Koriste se ko raa sa tečnim fluiima kaa je potrebno
smanjiti proces taloženja naslaga i prljavštine iz tečnih fluida (proces se naziva Fouling ili Scaling) u cevima
razmenjivača iliti “onečišdenje” ono što obeležavaju sa Rf .
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Pokretljivost
fluidizovanog
sloja
daje
ovakvim
razmenjivačima ve izrazite prenosti u onosu na klasične razmenjivače tipa cev-u-cev. 1) “krstarede kretanje” elemenata sloja sprečava taloženje naslaga i smanjuje koroiranje cevi, i 2) Koeficijent prelaza toplote α u sloju je skoro uplo vedi nego ko klasičnih razmenjivača Cena im je u rangu cena klasičnih razmenjivača.
KOMPAKTOST POVRŠINE ZA TOPLOTNU RAZMENU
Cilj je a se što veda površina za razmenu toplote smesti u aparat – kompaktni, a manje nekompaktni Kompaktnost
PREMA KONSTRUKTIVNIM KARAKTERISTIKAMA: CEVNI (REKUPERATORI) cev u cevi sa zmijastim cevima
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pločasti
REGENERATORI PREMA KONFIGURACIJI TOKOVA FLUIDA
SA JEDNIM PROLAZOM FLUIDA istostrujni suprotnostrujni unakrsnostrujni SA VIŠE PROLAZA FLUIA
sa istaknutim površinama
cevni
pločasti sa cevnim snopom i omotačem pločasti
PREMA MEHANIZMU PRENOSA TOPLOTE
konvekcija u jednofaznom fluidu sa 2 strane
površine za toplotnu razmenu
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sa fluida na zid ili obrnuto, q – toplotni flux, – thermal diffusivity [In the study of transport phenomena (heat transfer, mass transfer and fluid dynamics), flux is defined as the amount that flows through a unit area per unit time. Generally that definition is the definition for flux density. Flux in this definition is a vector. Generally , in particular in the field of electromagnetism and mathematics, flux is usually the integral of a vector quantity, flux density, over a finite surface.] Grejanje fluida:
| |
Dolazi o prelaza toplote strujanjem fluia už zia koji može biti ravan ili cilinričan
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w – brzina strujanja fluia. Za oređivanje α koristi se
teorija sličnosti ili kolburnov pristup TEORIJA SLIČNOSTI NUSELTOV KRITERIJUM (Nusselt - gives a measure of the ratio of the total heat transfer to conductive heat transfer.):
Odnosi se na prinudno strujanje Za turbulentno: Pogonska sila za strujanje fluida je razlika pritisaka
(ostvaruje se pomodu pumpi i kompresora) REJNOLDSOV BROJ (is a dimensionless number that gives a 2 measure of the ratio of inertial forces /L
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- toplotna provodljivost (k - thermal conductivity) [W/(m K)]; α - termička ifuznost - thermal iffusivity, α 2 = λ / (ρcp), [ m /s] GRASHOFOV BROJ – –daje odnos sile potiska (buoyancy) prema viskoznim silama koje deluju na flui. (često se
koristi ko izučavanja prirone konvekcije)
-1
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– se
promenom a
manje
najviše.
menjaju sa - hiraulički
prečnik
c, m, n su empirijske konstante. Zbog razlike u temperaturama dolazi do deformacije strujnog polja pa se uvodi
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oređuje se grafički ili analitički
u cevima. Termo-hiraulični
proračun = pa pritiska u razmenjivaču toplote usle gubitaka iz bernulijeve jenačine:
– koeficijent použnog trenja.
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̇ ̇ ⏟̇ ⏟ ̇ * + Cancel Anytime.
– Faning (Fanning friction factor) se oređuje grafički ili analitički JENAČINA ENERGETSKOG BILANSA RAZMENJIVAČA TOPLOTE
- toplotni kapacitet
Index t – topliji, h – hladniji fluid.
RASPOELA TEMPERATURA U REKUPERATORIMA
Fluidi tokom razmene toplote ne menjaju agregatno
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Ukoliko tokom razmene toplote dolazi do fazne transformacje:
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Termički proračun razmene toplote Hiraulički proračun razmene toplote Kod termičkog proračuna cilj nam je da odredimo
i za to koristimo 2 metode: a) Metodu srednje logaritamske razlike temperatura b) metodu prenosnih jedinica.
U razmenjivaču je uvek izobarski proces p=const METOA SRENJE LOGARITAMSE RAZLIKE TEMPERATURA: Assume:
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PROTIVSTRUJNI - menja se už aparata – pogonska sila. Odnosi se na jedan presek a ne neke srednje vrednosti. Dakle kao ili na krajevima razmenjivača
̇ ̇ ̇ ̇ ̇
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Log mean temperature difference - The log mean temperature difference (also known by its acronym
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relatively small range. However, if the specific heat changes, the LMTD approach will no longer be accurate. * A particular case where the LMTD is not applicable are condensers and reboilers, where the latent heat associated to phase change makes the hypothesis invalid (nije linearna promena temperature). * It has also been assumed that the heat transfer 2 coeffficient (K=[W/(m ·K)]) is constant, and not a
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̇
ISTOSTRUJNI
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efikasnost rekuperatora broj prenosnih jedinica
–
treba pokazati
ODNOS TOPLOTNIH KAPACITETA
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̇ ̇
Na kraju beskonačnog razmenjivača izjenačavaju se temperature
.
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BROJ PRENOSNIH JEDINICA – broj jedinica za prenos toplote NTU (Number of Transfer Units)
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