Engineering task and calculation objective
The GGO module calculates the shell-side heat transfer coefficient and the pressure drop of shell-and-tube heat exchangers with longitudinal flow and no baffles. Such units are used when a low shell-side pressure drop is required, when vibration-prone bundles are to be avoided, or when the medium (e.g. condensate, clean gases) does not need cross-flow redirection.
The calculation is based on experimental investigations at the University of Karlsruhe, published at the GVC conference in 1994. Compared with simple annular-gap models, the approach takes into account the ratio of shell diameter to bundle length as well as the size and position of the inlet and outlet nozzles. In particular, it captures the local increase in heat transfer in the region of the inlet nozzle, where the medium impinges on the bundle in cross flow before aligning itself with the longitudinal flow.
The inputs are the mass flow or volume flow, the inlet and outlet temperatures with the fluid properties at the mean temperature (density, specific heat capacity, thermal conductivity, viscosity, Prandtl number) and the geometry: shell inside diameter, bundle diameter, tube outside diameter, number of tubes, bundle length and the inside diameters of the nozzles. The result feeds directly into the design of the heat exchanger by the k·A method.
Calculation workflow
- Define operating data and fluid properties: The mass flow or volume flow, the inlet pressure and the inlet and outlet temperatures are specified; at the mean temperature, density, specific heat capacity, thermal conductivity, dynamic or kinematic viscosity and the Prandtl number are evaluated. The liquid/gaseous indication controls the property handling.
- Capture the shell-side geometry: Shell inside diameter, diameter of the tube bundle, tube outside diameter, number of tubes and bundle length define the flow cross section; from these follow the free cross section and the hydraulic diameter of the intertube space.
- Determine the flow regime: From the flow rate, the free cross section and the fluid properties, the flow velocity and Reynolds number are formed; the correlation covers both laminar and turbulent longitudinal flow.
- Account for the nozzle influence: Via the inside diameters of the inlet and outlet nozzles and the diameter-to-bundle-length ratio, the method captures the cross flow at the inlet and the locally increased heat transfer it causes – an essential difference from pure annular-channel models.
- Output heat transfer and pressure drop: As results, the module delivers the mean shell-side heat transfer coefficient and the pressure drop, where applicable for several shell-side passes. Both values enter the overall thermal-hydraulic design of the unit.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Shell inside diameter | Di | m |
| Tube outside diameter | da | m |
| Number of tubes | nR | - |
| Bundle length | l | m |
| Inside nozzle diameter (inlet) | dN,i | m |
| Density | ρ | kg/m³ |
| Prandtl number | Pr | - |
| Kinematic viscosity | ν | m²/s |
| Thermal conductivity | λ | W/(m·K) |
| Inlet temperature | ϑe | °C |
| Outlet temperature | ϑa | °C |
| Mean temperature | ϑm | °C |
| Mass flow | m | kg/s |
| Volume flow | V | m³/s |
| Number of shell-side passes | nM | - |
| Specific heat capacity | cp | J/(kg·K) |
| Dynamic viscosity | η | mPa·s |
| Inlet pressure (abs.) | p | Pa |
| Inside nozzle diameter (outlet) | dN,o | m |
| Fluid liquid /gaseous? | 1 | - |
| Diameter of the tube bundle | DB | m |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Pressure drop | dp | Pa |
| Heat transfer coefficient | α | W/(m²·K) |
| Nusselt number | Nu | - |
| Hydraulic diameter | dh | m |
| Reynolds number | Re | - |
| Velocity (shell-side) | wM | m/s |
| Velocity (inlet nozzle) | wN,i | m/s |
| Relation of the Nu numbers | Nu/NuR | - |
| Void fraction | ϕ | - |
| Drag coefficient | ξ | - |
| Velocity (outlet nozzle) | wN,o | m/s |
| Drag coefficient (inlet nozzle) | ξN,i | - |
| Drag coefficient (outlet nozzle) | ξN,o | - |
Calculation options
Fluid liquid /gaseous?
liquid · 1
Frequently asked questions
When is a shell side without baffles chosen?
When the shell-side pressure drop must be minimized (vacuum condensers, large gas flows), when flow-induced tube vibrations from cross flow are to be avoided, or with very tight bundles in which baffles are difficult to manufacture. The price is a lower heat transfer coefficient than in cross-flow bundles with segmental baffles.
Why are the position and size of the nozzles relevant for the heat transfer?
At the inlet nozzle, the medium impinges on the bundle in cross flow and first has to turn into the longitudinal flow; this produces locally much higher heat transfer coefficients than in the developed longitudinal flow. For short bundles (small length-to-diameter ratio), this entrance effect strongly influences the mean value – exactly what the Karlsruhe correlation captures, while simple annular-gap approaches are too conservative here.
Which characteristic length underlies the Reynolds number?
The hydraulic diameter of the space between tubes and shell, formed as four times the free flow cross section divided by the wetted perimeter of the tube outside surfaces and the shell inside surface. It depends sensitively on the tube pitch, the number of tubes and the gap between bundle and shell – which is why the shell inside diameter and the bundle diameter are requested separately.
Is the bypass gap between bundle and shell taken into account?
Yes, via the separate input of shell inside diameter and bundle diameter. A large annular gap acts as a low-resistance bypass: part of the flow passes around the bundle, which reduces the effective heat transfer. The gap should therefore be kept small or sealed by design.