DRLL
Heat transfer and pressure drop of liquids and gases flowing through tubes are depending, next to the physical properties of the medium and the type of flow, mainly on the structure and type of the heat transferring surface.
To improve the heat transfer corrugated tubes are quite suitable, as on one hand they guarantee a spacious helical secondary flow an on the other hand an excitation and increase of turbulence.
Select your corrugated tubes by means of using the ComboBox in the input mask.
Click the input field and select at tube type. The geometrical dimensions and the empirical parameters for calculating the heat transfer and the pressure drop are automatically transferred to the input mask..
The equations published for heat transfer are only valid in the turbulent area starting from Re = 4000. If the Reynolds number is less, the following message is shown:
In general, a result at Re < 4000 does not make much sense. By default, e.g., when the module is called up from another module like e.g. WTS, this result is discarded.
For calculating the pressure drop, two methods are published:
Equations for z with especially adjusted parameters for each tube type. These equations are valid for laminar and turbulent flow.
For some tube types, these parameters are not available. You will receive a notification in the input mask:
In this case, generalized equations that are only valid for turbulent flow 2000 < Re < 100000 are used for z. For laminar flow these equations are not valid, but you may see the results anyhow, knowing that the results are uncertain:
At the moment, data for several tube types from HDE GmbH, Menden are available. The specific data of these tubes are saved in the file DRLL.TAB in the program directory.
If you have your own measured results for heat transfer and pressure drop, you may adjust your results to the equations stated below. You can enter the parameters you receive into the DRLL.tab and extend the number of tubes by your own tubes. The data are structured line wise, separated by a comma without a space.
You must not change the order of the data:
Tube description, da, s, dh, h, j, f1, e1, e2, f2, a0, a1, a2, a3, Rek
With:
|
da |
Outside diameter of the tube |
|
s |
Wall thickness |
|
dh |
Hydraulic diameter |
|
h |
Depth of corrugation |
|
j |
Angle of corrugation |
|
f1, e1, e2 |
Adjustment parameters for heat transfer equation |
|
f2 |
Adjustment parameters , laminar friction factor |
|
a0, a1, a2, a3 |
Adjustment parameter, pressure drop factor |
|
Rek |
Critical Reynold number (turnover from laminar to turbulent flow) |
Parameters f1, e1 and e2 for calculating the Nu number must be given!.
Parameters a0, a1, a2, a3 and Rek for calculating the pressure drop factor are optional. If these parameters are missing, the pressure drop is calculated using a general equation.
Sample entry with parameters a0, a1, a2, a3 and Rek for pressure drop calculation:
DR 20x0.8 - 45°/0.8,20,0.8,18.07,0.8,45,0.03,0.8,0.4,180,2.45423,-2.18752,0.447768,-0.0341115,1000
Sample entry without parameters a0, a1, a2, a3 and Rek for pressure drop calculation
DR 20x0.8 - 45°/1.2,20,0.8,17.5,1.2,45,0.0325,0.8,0.4,,,,,,
Equation for heat transfer:
With hydraulic diameter dh
Pressure drop Dp and pressure drop factor VDT for turbulent flow
With:
|
Nu |
Nußelt number |
|
Re |
Reynolds number |
|
Pr |
Prandtl number |
|
f1, e1, e2 |
Adpation parameters, heat transfer equation |
|
dh |
Hydraulic diameter, mm |
|
h |
Depth of corrugation, mm |
|
da |
Tube outside diameter (nominal diameter), mm |
|
s |
Wall thickness, mm |
|
Δp |
Pressure drop, Pa |
|
L |
Tube length, mm |
|
u |
Velocity, m/s |
|
a0, a1, a2, a3 |
Adjustment parameters, Pressure drop factors |
|
|
|
|
ςDT |
Pressure drop factor for corrugated tube at turbulent flow |
|
α |
Heat transfer coefficient, W/(m²·K) |
|
φ |
Angöle of corrugation, ° |
|
λ |
Thermal conductivity of medium, W/(m·K) |
|
ρ |
Density of medium, kg/m³ |