Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.HelicalPipe Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.HelicalPipe

Extends from Modelica.Icons.Information (Icon for general information packages).

Package Content

Name Description
Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.HelicalPipe.kc_laminar kc_laminar  
Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.HelicalPipe.kc_overall kc_overall  
Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.HelicalPipe.kc_turbulent kc_turbulent  

Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.HelicalPipe.kc_laminar Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.HelicalPipe.kc_laminar

Calculation of the mean convective heat transfer coefficient kc for a helical pipe in the laminar flow regime.

Functions kc_laminar and kc_laminar_KC

There are basically three differences:

Restriction

The critical Reynolds number Re_crit in a helical pipe depends on its mean curvature diameter d_coil. The smaller the mean curvature diameter of the helical pipe, the earlier the turbulent regime will start due to vortexes out of higher centrifugal forces.

Geometry

helicalPipe

Calculation

The mean convective heat transfer coefficient kc for helical pipes is calculated through the corresponding Nusselt number Nu according to [VDI 2002, p. Gc 2, eq. 5] :

Nu = 3.66 + 0.08*[1 + 0.8*(d_hyd/d_coil)^0.9]*Re^m*Pr^(1/3)

with the exponent m for the Reynolds number

m = 0.5 + 0.2903*(d_hyd/d_coil)^0.194

and the resulting mean convective heat transfer coefficient kc

kc =  Nu * lambda / d_hyd

with

d_mean as mean diameter of helical pipe [m],
d_coil = f(geometry) as mean curvature diameter of helical pipe [m],
d_hyd as hydraulic diameter of the helical pipe [m],
h as slope of helical pipe [m],
kc as mean convective heat transfer coefficient [W/(m2K)],
lambda as heat conductivity of fluid [W/(mK)],
L as total length of helical pipe [m],
Nu = kc*d_hyd/lambda as mean Nusselt number [-],
Pr = eta*cp/lambda as Prandtl number [-],
Re = rho*v*d_hyd/eta as Reynolds number [-],
Re_crit = f(geometry) as critical Reynolds number [-].

Verification

The mean Nusselt number Nu representing the mean convective heat transfer coefficient kc is shown below for different numbers of turns n_nt at constant total length of the helical pipe.

kc_laminar

The convective heat transfer of a helical pipe is enhanced compared to a straight pipe due to occurring turbulences resulting out of centrifugal forces. The higher the number of turns, the better is the convective heat transfer for the same length of a pipe.

Note that the ratio of hydraulic diameter to total length of helical pipe d_hyd/L has no remarkable influence on the coefficient of heat transfer kc.

References

GNIELINSKI, V.:
Heat transfer and pressure drop in helically coiled tubes.. In 8th International Heat Transfer Conference, volume 6, pages 2847-2854, Washington,1986. Hemisphere.

Extends from Modelica.Icons.Information (Icon for general information packages).

Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.HelicalPipe.kc_overall Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.HelicalPipe.kc_overall

Calculation of the mean convective heat transfer coefficient kc of a helical pipe in a hydrodynamically developed laminar and turbulent flow regime.

Functions kc_overall and kc_overall_KC

There are basically three differences:

Geometry and Calculation

This heat transfer function enables a calculation of heat transfer coefficient for laminar and turbulent flow regime. The geometry, constant and fluid parameters of the function are the same as for kc_laminar and kc_turbulent.

The calculation conditions for laminar and turbulent flow is equal to the calculation in kc_laminar and kc_turbulent. A smooth transition between both functions is carried out between 2200 ≤ Re ≤ 30000 (see figure below).

Verification

The mean Nusselt number Nu representing the mean convective heat transfer coefficient kc is shown below for different numbers of turns n_nt at constant total length of the helical pipe.

kc_overall

The convective heat transfer of a helical pipe is enhanced compared to a straight pipe due to occurring turbulences resulting out of centrifugal forces. The higher the number of turns, the better is the convective heat transfer for the same length of a pipe.

Note that the ratio of hydraulic diameter to total length of helical pipe d_hyd/L has no remarkable influence on the coefficient of heat transfer kc.

References

GNIELINSKI, V.:
Heat transfer and pressure drop in helically coiled tubes.. In 8th International Heat Transfer Conference, volume 6, pages 2847?2854, Washington,1986. Hemisphere.

Extends from Modelica.Icons.Information (Icon for general information packages).

Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.HelicalPipe.kc_turbulent Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.HelicalPipe.kc_turbulent

Calculation of the mean convective heat transfer coefficient kc of a helical pipe for turbulent flow regime.

Functions kc_turbulent and kc_turbulent_KC

There are basically three differences:

The critical Reynolds number Re_crit in a helical pipe depends on its mean curvature diameter. The smaller the mean curvature diameter of the helical pipe d_mean, the earlier the turbulent regime will start due to vortexes out of higher centrifugal forces.

Geometry

helicalPipe

Calculation

The mean convective heat transfer coefficient kc for helical pipes is calculated through the corresponding Nusselt number Nu according to [VDI 2002, p. Ga 2, eq. 6]:

Nu = (zeta_TOT/8)*Re*Pr/{1 + 12.7*(zeta_TOT/8)^0.5*[Pr^(2/3)-1]},

where the influence of the pressure loss on the heat transfer calculation is considered through

zeta_TOT = 0.3164*Re^(-0.25) + 0.03*(d_hyd/d_coil)^(0.5) and

and the resulting mean convective heat transfer coefficient kc

kc =  Nu * lambda / d_hyd

with

d_mean as mean diameter of helical pipe [m],
d_coil = f(geometry) as mean curvature diameter of helical pipe [m],
d_hyd as hydraulic diameter of the helical pipe [m],
h as slope of helical pipe [m],
kc as mean convective heat transfer coefficient [W/(m2K)],
lambda as heat conductivity of fluid [W/(mK)],
L as total length of helical pipe [m],
Nu = kc*d_hyd/lambda as mean Nusselt number [-],
Pr = eta*cp/lambda as Prandtl number [-],
Re = rho*v*d_hyd/eta as Reynolds number [-],
Re_crit = f(geometry) as critical Reynolds number [-].

Verification

The mean Nusselt number Nu representing the mean convective heat transfer coefficient kc is shown below for different numbers of turns n_nt at constant total length of the helical pipe.

kc_turbulent

The convective heat transfer of a helical pipe is enhanced compared to a straight pipe due to occurring turbulences resulting out of centrifugal forces. The higher the number of turns, the better is the convective heat transfer for the same length of a pipe.

Note that the ratio of hydraulic diameter to total length of helical pipe d_hyd/L has no remarkable influence on the coefficient of heat transfer kc.

References

GNIELINSKI, V.:
Heat transfer and pressure drop in helically coiled tubes.. In 8th International Heat Transfer Conference, volume 6, pages 2847?2854, Washington,1986. Hemisphere.

Extends from Modelica.Icons.Information (Icon for general information packages).

Automatically generated Thu Oct 1 16:07:59 2020.