Yuav ua li cas xam lub sij hawm yuav tsum tau rau lub PFA rhaub kom ncav cuag 90% ntawm Setpoint Thaum cov kua muaj ib tug Prandtl tus naj npawb ntawm 500?

High Prandtl cov kua dej (Pr=500, cov txiaj ntsig zoo rau cov roj viscosity siab, glycerin lossis polymer melts) muaj cov thermal diffusivity qis dua piv rau lub zog diffusivity. Thaum tshav kub kub kis tau tus mob thaum sov-up yog feem ntau yog conduction, tsis convection. Lub sij hawm los tsa cov kua dej li no mus rau 90% ntawm qhov teeb tsa yog teem los ntawm lub sij hawm thermal diffusion tas li, tsis yog watt ntom ntawm PFA lub rhaub. Rau lub tank ntawm tus yam ntxwv ntev L (piv txwv li . 0.5 m), lub sij hawm thermal diffusion yog τ_diff=L² / , qhov twg yog qhov thermal diffusivity (m² / s). Rau Pr=500, yog tias peb xav tias thermal diffusivity a=n/Pr, qhov twg n yog ib txwm rau roj (50 cSt=5e-5 m^2/s) ces yog=5e-5/500=1e-7 m^2/s. Rau L=0.5 m, τ_diff=(0.5) 2 / 1e-7=0.25 / 1e-7=2.5e6 vib nas this=694 teev. Qhov ntawd yog 29 hnub, tsis muaj tseeb tiag. Kev suav yields ib qho kev pom tseem ceeb uas rau cov kua dej Pr siab heev, cov cua sov sib xws xav tau kev quab yuam convection los yog ncua sij hawm ntev heev. Lawv xav tau cov twj recirculation los yog ob peb lub tshuab cua sov kom txo tau qhov zoo thermal diffusion ntev.

Txoj hauv kev los suav cov sij hawm sov-
The 90% setpoint time for a batch of fluid heated by an immersed PFA heater has two parts: (1) the time to heat the boundary layer near the heater and (2) the heat diffusion time for the bulk fluid. For low-Pr fluids (water, Pr$\approx$7) the bulk mixing (natural convection) prevails and the time is determined by the strength of the heater. High-Pr fluids (Pr>100) yog tus cwj pwm los ntawm qhov tsis muaj zog lossis tsis muaj qhov cuam tshuam thiab kev ua haujlwm txwv kev hloov hluav taws xob.

Qhov kub nkag qhov tob yog muab los ntawm Fourier tooj Fo=$\\alpha \\times t/L^2$ Rau cov kua dej pib ntawm T0 nrog lub rhaub ntawm Twall, qhov kub ntawm qhov deb x mus txog 90% ntawm (Twall – T0) ntawm Fo ≈ 0.5 (semi-infinite slab). Rau ib lub tank ntawm 0.5 m, =1e-7 m2/s L=0.5 m Fo=0.2 → t=Fo × L2 =0.2 × 0.25 1e-7=500,000 s=5.8 hnub no tseem ntev heev.

Txoj kev coj ua:

Xam cov thermal diffusivity ntawm cov kua:=k / (ρ × c_p) qhov twg k yog cov thermal conductivity (W/m·K), ρ qhov ceev, c_p cov cua sov tshwj xeeb.

3) kwv yees tus yam ntxwv diffusion ntev L=tank txoj kab uas hla los yog ib nrab ntawm qhov tsawg tshaj plaws dimension.

Lub sijhawm ua haujlwm: t_cond=0.2 × L² / .

Muab piv rau lub sijhawm yog cov kua dej sib tov zoo: t_mix=m * c_p * delta_T / P qhov twg m yog huab hwm coj, P yog lub zog cua sov.

Lub sij hawm tiag tiag yog qhov siab tshaj plaws ntawm t_cond thiab t_mix, piv txwv li qhov siab tshaj plaws ntawm qhov diffusion thiab lub sijhawm sib xyaw, vim tias cov kua dej tsis tuaj yeem ua kom sov sai dua li diffusion.

* Piv txwv suav rau Roj, Pr=500
Parameter, Tus nqi, Chav FluidHeavy roj (ISO VG 220)
Kub nce ΔT 20℃rau 80℃(60 degree)
Tank loj (lub voos xwmfab) 0.5 m ntawm txhua sab
Qhov hnyav 125 l
Qhov hnyav 110 kg (ρ{1}} kg / m3
Cov cua kub tshwj xeeb cp 2,000 J / kg K
Thermal conductivity k 0.14 W / (m·K)
Thermal diffusivity alpha 0.14/(880*2000)=7.95e-8 ~ 8e-8 m2/sec
Prandtl number Pr=ν/ , ν=4e-5 m²/s → 4e-5/8e-8=500
Conduction lub sij hawm t_cond 0.2 × (0.5)² / 8e-8=0.05 / 8e-8=625,000 s=7.2 hnub
Lub zog hluav taws xob (xws li 3 kW) 3 kW lossis 3000 W
Lub sij hawm sib xyaw t Mix (110 × 2000 × 60) / 3000=13,200,000 / 3000=4,400 s=1.2 teev
Qhov tseeb 90% ntawm lub sijhawm: 7.2 hnub (diffusion-limited)
Tsis muaj kev rov ua dua tshiab, yog li cov roj uas nyob ze lub tshuab rhaub kom sov li 80℃hauv ib teev, tab sis nws yuav siv sij hawm ntau tshaj li ib lub lim tiam kom sov cov roj ntawm phab ntsa ntawm lub tank. Cov cua sov hauv cheeb tsam ntawm lub rhaub (teev, degradation ntawm PFA) tuaj yeem tshwm sim thaum tos kom sov ntau - nce.

Siab -Pr Fluid Mitigation Strategies
Strategy Effective L (m) Tshiab t_cond Tus nqi ntawm kev siv
Natural convection (tsis muaj) 0.5 7.2 hnub $0
Nruab lub twj tso kua mis recirculation (1 m3 / hr) N / A (mixed) 1.2 teev (mix-limited) $1,500
Ntau lub tshuab cua sov (3 lub tshuab cua sov, qhov chaw) 0.25 (ib nrab nrug) 1.8 hnub $ 2,000 (2 lub tshuab cua sov ntxiv)
Txhim kho cov ntawv sib tov zoo li qub 0.3 2.6 hnub $800
Extended finned rhaub 0.4 4.6 hnub $300
Agitate nrog mechanical stirrer (100 RPM) N / A (sib xyaw) 1.2 teev (mix-limited) $2,500 (lub cev muaj zog + ncej)
For Pr>100, tib txoj kev siv tau yog recirculation lossis mechanical stirring. Tsis sib tov lub sij hawm sov so yog hnub los yog lub lis piam. Lub tshuab cua sov PFA yuav dhau los ua kom sov thiab ua tsis tiav vim qhov ntsuas (yog tias dej raws) lossis oxidation (yog tias muaj roj). Loj lub twj tso kua mis recirculation rau qhov tsawg kawg nkaus ntawm 1 ntim khoom ib teev rau Pr=500.

Hauv -Testing site
Hauv ib lub tuam txhab kws tshuaj, siab -viscosity glycerin (Pr≈600, 50–90 degree) tau ua kom sov hauv 200-L tank nrog ib lub rhaub 6-kW PFA, tsis muaj kev rov ua dua. Lub glycerin nyob ze ntawm lub rhaub yog 90℃tom qab 24 teev tab sis tag nrho cov kub tsuas yog 55 degree. Cov cua sov saum npoo mus txog 150 degree, uas ua rau glycerin rau polymerise thiab stink. Cov nroj tsuag ntxiv ib lub twj tso kua mis rov (2 m³ / h). Tom qab 3 teev qhov kub ntawm tag nrho lub tank yog 88-92℃thiab cua sov saum npoo yog<110°C. Polymerisation was ceased." Heater replacement Weeks of downtime 5,000pumpsaveda 1,000pumpsaveda

Xaus: Diffusion Time Dominates rau Fluids Pr= 500
Rau qhov siab -Prandtl- cov kua dej (Pr=500) lub sijhawm rau lub tshuab cua sov PFA kom ncav cuag 90% ntawm qhov teeb tsa yog tswj los ntawm thermal diffusion es tsis yog lub tshuab cua sov. Yog hais tias lub tank yog 0.5 m thiab tsis muaj kev sib tov tshwm sim, lub sij hawm conduction yog 100 × ntev tshaj li lub sij hawm sib tov, 5-10 hnub. Thaum tsis muaj kev quab yuam los yog kev sib tsoo tshuab, lub tshuab cua sov yuav overheat hauv zos, ua rau cov nplai, fouling lossis PFA deterioration. Rau ib qho txheej txheem kua dej nrog Pr> 100, engineers yuav tsum tau qhia txog cov twj tso kua mis los yog cov agitators. Kev suav: t_90%=0.2*L^2/alpha. Yog tias t_90% > lub sijhawm ua haujlwm tau zoo, ntxiv kev sib xyaw. Sib tov lossis tos hnub Pr=500. Nws yog qhov kev txiav txim siab pom tseeb.