Engineering task and calculation objective
The RIES module calculates the heat transfer in falling films on horizontal tubes according to the progress report by Mitrovic (VDI Reihe 3 No. 211, VDI-Verlag 1990). In horizontal tube bundles irrigated with liquid from above, a thin liquid film forms on each tube; from the liquid load, fluid properties and bundle geometry, the module determines the Nusselt number and from it the heat transfer coefficient of the film.
Having to calculate this heat transfer is typical for the design of horizontal-tube falling film evaporators and irrigated coolers: in seawater desalination (MED evaporators), the sugar industry, refrigeration plants (flooded or sprayed evaporators) and waste heat recovery. Falling film units operate with a small liquid inventory, small driving temperature differences and without hydrostatic boiling point elevation — advantages that presuppose an accurate prediction of the film heat transfer.
The correlation works with the governing dimensionless numbers of film flow: the film Reynolds number formed from the liquid load, the Prandtl number, the Kapitza number (surface tension effect) and the Galileo number; a correction factor captures the tube arrangement in the bundle via the tube pitch and the number of rows in the flow direction.
Standard and calculation basis: Mitrovic, Jovan / “Wärmeübergang in Rieselfilmen an waagrechten Rohren"; Fortschr.-Bericht VDI Reihe 3 Nr. 211; Düsseldorf: VDI-Verlag 1990
Calculation workflow
- Define the bundle geometry: The inputs are the tube outside diameter, tube length, number of tubes per row, number of tube rows in the flow direction and the longitudinal tube pitch; from these follow the total tube count and the total tube surface area.
- Determine the liquid load: From the mass or volume flow of the liquid fed to the bundle and the wetted tube length follows the liquid load (irrigation density) — the liquid flow per unit length of tube, the central operating parameter of the falling film.
- Fluid properties at the mean state: At the mean temperature (from inlet and outlet temperature) and the given pressure, density, viscosity, thermal conductivity, heat capacity, surface tension and, if applicable, the enthalpy of vaporization are evaluated.
- Dimensionless numbers of the film flow: From the liquid load and fluid properties, the film Reynolds number, Prandtl number, Kapitza number and Galileo number are formed; they characterize the flow regime (laminar, wavy, turbulent) and the influence of surface tension and gravity.
- Nusselt number and bundle correction: The Mitrovic correlation with its exponents m and n yields the Nusselt number of the single-tube film; a correction factor accounts for the mutual interaction of the tube rows (impact of the draining film on the tubes below).
- Heat transfer coefficient and heat flux: The heat transfer coefficient of the falling film follows from the Nusselt number; together with the tube surface area and the driving temperature difference, this gives the transferable heat flux.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Inlet temperature | T1 | °C |
| Outlet temperature | T2 | °C |
| Mean temperature | Tm | °C |
| Pressure (abs.) | p | Pa |
| Mass flow | ṁ | kg/s |
| Volume flow | V̇ | m³/s |
| Number of tubes per row | NR | - |
| Number of tube rows in flow direction | NRow | - |
| Total number of tubes | Ntotal | - |
| Longitudinal tube pitch | sl | m |
| Tube length | l | m |
| Tube outside diameter | da | m |
| Total tube surface | A | m² |
| Density | ρ | kg/m³ |
| Specific heat capacity | cp | J/(kg·K) |
| Dynamic viscosity | η | mPa·s |
| Kinematic viscosity | ν | m²/s |
| Thermal conductivity | λ | W/(m·K) |
| Prandtl number | Pr | - |
| Heat of evaporation | Δhv | J/kg |
| Surface tension | σ | mN/m |
| Heat flux | q̇ | W/m² |
| Reynolds number | Re | - |
| Kapitza number | Ka | - |
Frequently asked questions
What is the liquid load and why is it so important?
The liquid load (irrigation density) is the liquid mass flow per unit length of tube (defined per one side or both sides — pay attention to the definition convention). It determines the film thickness and the film Reynolds number and thus directly the heat transfer. Too little irrigation causes the film to break up, leaving dry patches — there the heat transfer collapses and deposits and local overheating threaten; too much irrigation thickens the film and can degrade the heat transfer again.
What is the Kapitza number for?
The Kapitza number links the surface tension, viscosity and density of the fluid and describes the film's tendency to form waves. Wavy films mix the film surface toward the wall and improve the heat transfer considerably compared with the smooth laminar Nusselt solution. It is a pure fluid-property number and clearly distinguishes, for example, water from viscous solutions.
Why does the heat transfer depend on the number of tube rows?
The film drains from the upper tube as droplets, columns or a sheet onto the tubes below. Impact and redistribution disturb the film development and can change the heat transfer of the lower rows relative to the single tube; in addition, the film loading grows downward if liquid evaporates or additional liquid is collected. The module's correction factor captures this row effect via pitch and row count.
Does the correlation also apply to evaporating films?
The Mitrovic correlation primarily describes the convective heat transfer in the non-boiling falling film or one evaporating at the film surface — the typical operating range of horizontal-tube evaporators at small wall superheats. If nucleate boiling sets in within the film (higher heat fluxes), the heat transfer rises above the convective value and must be assessed with boiling correlations; the calculated heat flux helps to classify this transition.