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Calculation of local two phase heat transfer coefficient kc_2ph for (horizontal/vertical) boiling or (horizontal) condensation for an overall flow regime.

Restriction

• circular cross sectional area
• no subcooled boiling
• film condensation

Geometry

Calculation

Boiling in a horizontal pipe (target = Modelica.Fluid.Dissipation.Utilities.Types.TwoPhaseHeatTransferTarget.BoilHor):

The local two phase heat transfer coefficient kc_2ph during boiling in a horizontal straight pipe for an overall regime is calculated according to [Gungor/Winterton 1986, p.354, eq. 2] :

kc_2ph = E_fc*E_fc_hor*kc_fc+S_nb+S_nb_hor*kc_nb

with

Bo=qdot_A/(mdot_A*dh_lv)	as boiling number [-],
dh_lv	as evaporation enthalpy [J/kg],
E_fc=f(Bo,Fr_l,X_tt)	as forced convection enhancement factor [-],
E_fc_hor =f(Fr_l)	as forced convection enhancement factor for horizontal straight pipes [-],
Fr_l	as Froude number assuming total mass flow rate flowing as liquid [-],
kc_2ph	as local two phase heat transfer coefficient [W/(m2K)],
kc_fc	as heat transfer coefficient considering forced convection [W/(m2K)],
kc_nb	as heat transfer coefficient considering nucleate boiling [W/(m2K)],
mdot_A	as total mass flow rate density [kg/(m2s)],
qdot_A	as heat flow rate density [W/m2],
Re_l	as Reynolds number assuming liquid mass flow rate flowing alone [-],
S_nb =f(E_fc,Re_l)	as suppression factor of nucleate boiling [-],
S_nb_hor =f(Fr_l)	as suppression factor of nucleate boiling for horizontal straight pipes [-],
x_flow	as mass flow rate quality [-],
X_tt = f(x_flow)	as Martinelli parameter [-].

Boiling in a vertical pipe (target = Modelica.Fluid.Dissipation.Utilities.Types.TwoPhaseHeatTransferTarget.BoilVer):

The local two phase heat transfer coefficient kc_2ph during boiling in a vertical straight pipe for an overall regime is calculated out of the correlations for boiling in a horizontal straight pipe, where the horizontal correction factors E_fc_hor,S_nb_hor are unity.

Please note that the correlations named above are not valid for subcooled boiling due to a different driving temperature for nucleate boiling and forced convection. At subcooled boiling there is no enhancement factor (no vapour generation) but the suppression factor remains effective.

Condensation in a horizontal pipe (target = Modelica.Fluid.Dissipation.Utilities.Types.TwoPhaseHeatTransferTarget.CondHor):

The local two phase heat transfer coefficient kc_2ph during condensation in a horizontal straight pipe for an overall regime is calculated according to [Shah 1979, p.548, eq. 8] :

kc_2ph = kc_1ph*[(1 - x_flow)^0.8 + 3.8*x_flow^0.76*(1 - x_flow)^0.04/p_red^0.38]

where the convective heat transfer coefficient kc_1ph assuming the total mass flow rate is flowing as liquid according to [Shah 1979, p.548, eq. 5] :

kc_1ph = 0.023*Re_l^0.8*Pr_l^0.4*lambda_l/d_hyd

with

d_hyd	as hydraulic diameter [m],
kc_2ph	as local two phase heat transfer coefficient [W/(m2K)],
kc_1ph	as convective heat transfer coefficient assuming total mass flow rate is flowing as liquid [W/(m2K)],
lambda_l	as thermal conductivity of fluid [W/(mK)],
pressure	as thermodynamic pressure of fluid [Pa],
p_crit	as critical pressure of fluid [Pa],
p_red = pressure/p_crit	as reduced pressure [-],
Pr_l	as Prandtl number assuming [-],
Re_l	as Reynolds number assuming total mass flow rate is flowing as liquid [-],
x_flow	as mass flow rate quality [-],

Verification

The local two phase heat transfer coefficient kc_2ph during for horizontal and vertical boiling as well as for horizontal condensation is shown for a straight pipe in the figures below.

Boiling in a horizontal pipe (target = Modelica.Fluid.Dissipation.Utilities.Types.TwoPhaseHeatTransferTarget.BoilVer):

Here the validation of the two phase heat transfer coefficient is shown for boiling in a horizontal straight pipe.

The two phase heat transfer coefficient (kc_2ph) w.r.t. Gungor/Winterton is shown in dependence of the mass flow rate quality (x_flow) for different mass flow rate densities (mdot_A). The validation has been done with measurement results from Kattan/Thome for R134a as medium.

The two phase heat transfer coefficient increases with increasing mass flow rate quality up to a maximum value. After that there is a rapid decrease of (kc_2ph) with increasing (x_flow). This can be explained with a partial dryout of the pipe wall for a high mass flow rate quality.

Condensation in a horizontal pipe (target = Modelica.Fluid.Dissipation.Utilities.Types.TwoPhaseHeatTransferTarget.CondHor):

Here the validation of the two phase heat transfer coefficient is shown for condensation in a horizontal straight pipe.

The two phase heat transfer coefficient (kc_2ph) w.r.t. Shah is shown in dependence of the mass flow rate quality (x_flow) for different mass flow rate densities (mdot_A). The validation has been done with measurement results from Dobson/Chato for R134a as medium.

References

Bejan,A.:

Heat transfer handbook. Wiley, 2003.

M.K. Dobson and J.C. Chato:

Condensation in smooth horizontal tubes. Journal of HeatTransfer, Vol.120, p.193-213, 1998.

Gungor, K.E. and R.H.S. Winterton:

A general correlation for flow boiling in tubes and annuli, Int.J. Heat Mass Transfer, Vol.29, p.351-358, 1986.

N. Kattan and J.R. Thome:

Flow boiling in horizontal pipes: Part 2 - new heat transfer data for five refrigerants.. Journal of Heat Transfer, Vol.120. p.148-155, 1998.

Shah, M.M.:

A general correlation for heat transfer during film condensation inside pipes. Int. J. Heat Mass Transfer, Vol.22, p.547-556, 1979.