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The Grind > mutiphase > Flashcards

mutiphase Flashcards

1
Q

Quanti gradi di libertà ha un sistema?

A

I need the balance for energy, mechanics and chemical for a system with m phases and r species. I also write the Gibbs eq. and get:
eq = M+(M-1)(r+2)
unk: M(r+2)

so since eq <= unk:
M<=r+2

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2
Q

cosa sono x, xv, eps e come sono legati?

A

x is the mass quality (gamma_g/gamma)
xv is the volume quality (Q_g/Q)
eps is the void fraction (omega_g/omega)

(1-x)/x = rho_l/rho_g * (i-xv)/xv = s * rho_l/rho_g * (1-eps)/eps

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3
Q

what are rho_b, rho_actual, rho_m

A

rho_b = gamma/Q
rho_actual = M/V = rho_geps + rho_l(1-eps)
rho_m = rho_gx^2/eps + rho_l(1-x)^2/(1-eps)

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4
Q

slip-ratio model

A

s = cost* (rho_g/rho_l)^a (mu_l/mu_g)^b ((1-x)/x)^c

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5
Q

drift-flux model

A

The slippage is locally calculated and then integrated:
u_g-u_l = j_g/eps - j_l/(1-eps) …
… J_g = C_0 * eps * J + J_drift

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6
Q

Patterns?

A

churn (L_c = D) :
inertia = buoyancy
u_c = sqrt((gdelta_rhoL_c)/rho_l)

bubbly (L_c«D) :
buoyancy = surface tension = inertia
L_c = sqrt(sigma/(gdelta_rho))
u_c = sqrt4((gdelta_rho*sigma)/(rho_l^2)

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7
Q

two phase mass balance

A

gamma(z) - gamma(z+dz) = 0
d(gamma)/dz = 0
d(gamma_l)/dz = d(gamma_g)/dz = 0 if no boiling or condensation

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8
Q

two phase momentum balance

A

(gamma_gu_g+gamma_lu_l)_z - (gamma_gu_g+gamma_lu_l)_z+dz = NFM

NFM = G^2d(x^2/epsv_g + (1-x)^2/(1-eps)v_l)/dzomega*dz

-dp/dz = G^2dv_m/dz + rho_actgsin(theta) + tau_wS/omega

…we need something for tau_w

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9
Q

pressure drop for homogeneous flow

A

f = 2tau_w/(G^2v)
Re = G*D/mu

Blausius correlation: f = A/Re^n
n = 0.2 for turbulent, 1 for laminar

-(dp/dz)_f = 2fG^2*v/D

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10
Q

homogeneous flow model

A

Re_tp = GD/mu_b
f_tp = A/Re_tp^n = 2tau_w/(G^2*v_b)

owens: mu_b = mu_l
cicchitti: mu_b = xmu_g + (1-x)mu_l
mcAdams: 1/mu_b = x/mu_g + (1-x)/mu_l
and
v_b = xv_g + (1-x)*v_l

We use mcAdams so:
Re_tp = GD(x/mu_g + (1-x)/mu_l)=
=GD/mu_l * (1 + xmu_lg/mu_g)

so:
f_tp = A/(Re_lo^n * (1 + x*mu_lg/mu_g)^n)

so:
-(dp/dz)_f,tp = 2 * f_lo * G^2 v_l/D * (1+xv_gl/v_l)/(1+x*mu_lg/mu_g)^n

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11
Q

liquid only vs liquid alone

A

-liquid ONLY means that the liquid flows with a flowrate equal to the total flow rate
-liquid ALONE means that the liquid flows alone with his superficial velocity

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12
Q

Descrbe the separated flow model

A

G°_g = gamma_g/omega = x * G (gas alone)
-(dp/dz)_g = 2f_gG°_g^2 * v_g/D
same for liquid so that:
Phi_g = -(dp/dz) / -(dp/dz)_g = fn (X)
X = sqrt( -(dp/dz)_l / -(dp/dz)_g )

Chisolm says:
Phi_g^2 = 1 + cost*X + X^2

so X_tt = f_l/f_g * (G°_l/G°_g)^2 * rho_g/rho_l =((1-x)/x)^(1-n/2) * sqrt(rho_l/rho_g) * (mu_l/mu_g)^n/2

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13
Q

why is 3 mm the limit between macro and micro pipes?

A

Because of the capillary length:
L_c = sqrt(sigma/(g*delta_rho)) = 3 mm

conf = L_c / D;
Bond = 1/conf^2

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14
Q

What are stable states?

A

in stable states the iosothermal compressibility:
k_T = -1/v(dv/dp)_T>0 so
(dp/dv)_T <0: these are the stable states
Thery are actually metastable (stable under small perturbations)

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15
Q

Bubble equilibrium curve

A

we start from thermodynamic equilibrium:
T_g = T_l
(p_g-p_l) * r^2pi = sigma2rpi
= >p_g = p_l + 2sigma / r
(dp/dT)_vpc = h_lg / (T_satv_lg)

3 hp: - small dp, dT
- v_lg = v_g
- far from T_crit
= > (p_g-p_l)/(T_g - T_sat) = h_lg/(T_satv_g)
2sigma/r = h_lg * (T_g-T_sat) / (T_sat*v_g)

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16
Q

Bubble nucleation

A

Bubble nucleation is related to the wall superheating: graph.

David - Anderson: he considers a linear temperature profile near the wall so that the heat exchange is the same so that:
T_g = T_l
= > T_sat + 2sigmaT_satv_g/(r * h_lg) = T_s - q’‘_s /k_lz

so you get:
T_s-T_sat = 2sigmaT_satv_g/ (r_ch_lg) + q’‘_s/k_lr_c
r_c = sqrt(8sigmaT_satv_gq’‘_s/(h_lgk_l)

17
Q

Yukiyama’s curve

A

Onet of Nucleate Boiling
Critical Heat Flux
Leidenfrost Point
Natural convection: q’‘_s == deltaT_ssat^n
n = 6/5 laminar horizontal
n = 5/4 laminar vertical
n = 3/2 turbulent
Nucleate Boiling: q’‘_s == deltaT_ssat^3
isolated bubbles or hydrojets
Partial Film Boiling
unstable situation with film and columns
Film boiling
vapour blanket

18
Q

Boiler operating point

A

q’‘_s fixed = > always stable
q’‘_s from heating fluid = > with electrical analogy it’s an inclined line

19
Q

boiling stability

A

Audiutori studied it: let’s consider a stable situation and a small perturbation with T_s not a function of positon.
Write the energy balance and use taylor expansion from stable state in dT_s.

You get
dT_s/dt = A/C*deltaT_ssat * (dq’‘_s,in/dT_s - dq’‘_s,out/dT_s)

Since the first two terms should be different in sign to esnure stability than the third one is always negative.

You can also talk about stability and histeresis here

20
Q

Rohsenow model

A

It’s a semiempirical model to describe nucleate boiling.
Bubbles behave like a pump for the fluid so it’s single-phase forced convection:
L_c = sqrt(sigma/(gdeltaRho))
t_c = E_evap/Q_supplied = rho_lh_lgL_c/q’‘_s
u_c = L_c/t_c = q’‘_s/(h_lgrho_l)

Re = q’’s * L_c / (h_lgrho_l * mu_l)
St = Nu/(RePr) = h_lg/ ( C_p,l*deltaT_ssat)

Rohsenow says:
1/St = cost * Re^m * Pr^n
m = 1/3 ; Pr = 1 (or 1.7 for organic fluids)
so:
q’‘_s = mu_lh_lg/L_c(C_p,ldeltaT_ssat / (Ch_lg*Pr^n)^(1/m)

It’s also important to say that pressure has a high influence on bubble formation ( higher pressure, easier bubbles)

21
Q

Influence factor model

A

We use correlations for q’‘_s and deltaT_ssat
- F(pr) = pr^a/(1-pr)^b
- F(MM) = A/MM^a
- F(R) = (Ra/Ra_0)^(2/15) * (e_th/e_th_0)^0.5

Gorenflo says:
alfa/alfa_ref = F_q(q’‘_s/q’‘_s,ref) * F_p(pr/pr_0) * F_prop(P0/P0_ref) * F_w

where pr_0 = 0.1 bar; q’‘_s,ref = 20 kW/m^2
P0_ref is a fictitious fluid (=1 at pr_0, q_ref)

we are missing correlations between phenomena

22
Q

Kutateladze

A

Model for CHF. Supposing then lots of bubbles. Jets are going to transport energy. To find u_jet we compare inertia, buoyancy and surface tension.
L_c = sqrt(sigma/(gdeltaRho))
u_jet = (gdeltaRho*sigma/rho_g^2)^0.25

from q’‘_s = rho_gu_jeth_lg
q’‘_s/(rho_gh_lggdeltaRhosigma)^0.25 = cost = 0.16 (for horiz. plates)

23
Q

Zuber model

A

Zuber model is based on hydrodynamic instabilites. Considering vapur jets there are two instabilites. The Railegh-Taylor instabilites due to a lighter phase (gas) below the heavier one. This create vapour jets. Then we have two fluids moving in different directions next to each other and this creates Kelvin-Helmoltz instabilites so that jets are cut and create a vapour blanket.
A single jet of diameter D_j is heated by:
A=(D_j2)^2 while A_j = d_j^2/4pi
q’‘_s * A = gamma_jeth_lg = rho_gu_jA_jh_lg

from helmoltz instability:
L_c = sqrt(Nsigma/(gdeltaRho))

from inertia and capillary forces:
u_j = sqrt(sigma/(rho_g*L_c))

so
q’‘_s = pi/16h_lg * rho_g^0.5 (gdeltaRhosigma/N)^0.25
The most critical is for N = 3.

24
Q

what is the heat transfer in film boiling

A

It’s dominated by radiative and natural convection of vapour.

The radiative one is:
q’‘_s,rad = epssigma(T_s^4 - T_sat^4) = alfa * deltaT_ssat
eps depends on surface (gray body)
we add a 075 due to photon absorption

The natural convection gives:
u_c = sqrt(gdeltaRhoL_c/rho_g) from inertia and buoyancy balance

so Reynolds squared became Grashoff
Re^2 = Gr = rho_ggdeltaRhoL_c^3/mu^2
Ra = GrPr = rho_ggdeltaRhoL_c^3Cp/(mu*k_g)

Nu = C*Ra^n, n=1/4 for laminar

25
Q

bulk velocity, bulk enthalpy, bulk temperature and thermodynamic quality

A

.

26
Q

subcooled flow boiling model

A
27
Q

saturated flow boiling model

A
28
Q

shah model

A
29
Q

upper and lower bound for CHF

A
30
Q

post CHF

A
31
Q

subcooled flow boiling models

A

.

32
Q

saturated flow boiling

A

.

33
Q

CHF

A

.

34
Q

post CHF

A

.

The Grind (6 decks)

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