Calculation method

Overview

Automatic pipe sizing selects for each route of the heat network the smallest pipe type from a given pipe selection that satisfies the sizing criterion. The basis is the consumer loads aggregated along the network, optionally reduced by the simultaneity factor, together with the pressure-loss calculation according to Darcy-Weisbach with the Colebrook friction coefficient. This page documents the calculation model; the operation of the dialog is described in Running pipe sizing.

Opening

The method is run via the Network > Size pipes … dialog, see Running pipe sizing.

Load aggregation along the network

For each energy plant the supply paths to all consumers are determined via a shortest-path search (Dijkstra) in the network graph. Each route $j$ receives as its nominal power the sum of the loads of all consumers supplied via it:

$$\dot{Q}_j = \sum_{i \,\in\, \text{downstream consumers}} \dot{Q}_i$$

Depending on the setting, the consumer load $\dot{Q}_i$ is the connection load or the maximum heating power from the building demand (for heat pumps, divided by the COP). With several energy plants, the maximum of the loads from the individual supply scenarios is applied to each route, see Multiple energy plants.

Simultaneity factor

If simultaneity is activated for the network, the nominal power of each route is multiplied by the simultaneity factor achieved for it. The target simultaneity function depending on the number of downstream buildings $n$ follows Winter et al. (Euroheat & Power, 2001):

$$f(n) = \min\!\left(1,\; a + \frac{b}{1 + \left(n/c\right)^{d}}\right)$$

with $a = 0.4497$, $b = 0.5512$, $c = 53.84$ and $d = 1.7627$. Details on calculating and adjusting simultaneity can be found under Simultaneity.

Mass flux

From the route load, the specific heat capacity $c_p$ of the fluid and the nominal temperature difference $\Delta T$ between supply and return at the transfer stations, the nominal mass flux results:

$$\dot{m}_j = \frac{\dot{Q}_j}{c_p \cdot \Delta T}$$

Pressure gradient according to Darcy-Weisbach

For each pipe type of the pipe selection the pressure loss per pipe length is calculated at the nominal mass flux:

$$\frac{\Delta p}{L} = \frac{\lambda}{d_i} \cdot \frac{\rho}{2}\, v^2 \qquad \text{with} \qquad v = \frac{\dot{m}}{\rho \cdot A}, \quad Re = \frac{v \cdot d_i}{\nu}$$

Here $d_i$ is the inner diameter in [m], $A$ the cross-sectional area in [m²], $\rho$ the density in [kg/m³] and $\nu$ the kinematic viscosity in [m²/s]. The friction coefficient $\lambda$ is determined depending on the flow regime:

• laminar ($Re < 2300$): $\lambda = 64/Re$
• turbulent ($Re > 10000$): implicit Colebrook-White equation, solved iteratively:

$$\frac{1}{\sqrt{\lambda}} = -2 \log_{10}\!\left(\frac{k/d_i}{3.7} + \frac{2.51}{Re\,\sqrt{\lambda}}\right)$$

• transition range ($2300 \le Re \le 10000$): linear interpolation between the two values

The pipe roughness $k$ comes from the pipe database of the respective pipe type.

Pipe selection

For each route the pipe type with the smallest inner diameter is chosen from the list of available pipes that satisfies all criteria:

1. Pressure gradient below the limit: $\Delta p / L < (\Delta p / L)_{max}$ (default: 150 Pa/m)
2. optional: flow velocity below the velocity limit of the corresponding nominal diameter (DN)

Routes locked for sizing are skipped and keep their currently assigned pipe type, see Locking sizing. If no pipe of the selection satisfies the criteria, the largest available pipe is assigned as a fallback option; the affected routes are listed in a warning message after completion.

Velocity limits per nominal diameter

Optionally, a maximum flow velocity per DN can additionally be specified. The default values are based on ÖKL leaflet 67 (corresponds to about 200 Pa/m) and range from 0.5 m/s at DN 20 to 4.8 m/s at DN 1000. Alternatively, the limits can be calculated from the set maximum pressure gradient: for each DN the velocity is determined iteratively from

$$v = \sqrt{\frac{(\Delta p / L)_{max} \cdot d_i \cdot 2}{\lambda(Re, k/d_i) \cdot \rho}}$$

(fixed-point iteration with a maximum of 20 steps, convergence bound $10^{-6}$ m/s). The inner diameters of standard steel pipes according to EN 10220/DIN 2448 and a roughness of $k = 0.01$ mm (recommendation of the Planungshandbuch Fernwärme) are used. The DN of a database pipe is derived from its outer diameter.

Maximum pump head method

As an alternative to the maximum pressure gradient criterion, the pipes can be sized against a given pump head. Here the pipes are first pre-assigned according to the maximum pressure gradient and then corrected so that the total pressure loss along each supply path stays within the available head: bottleneck routes are enlarged, oversized routes reduced, as far as the head allows. The pressure losses of the fittings are included in this.

Fluid material properties

The kinematic viscosity is evaluated temperature-dependently from the characteristic curve of the network fluid at the set fluid temperature. Density and specific heat capacity are parameters of the fluid from the database, see Fluids and further databases.

Related topics

• Running pipe sizing
• Simultaneity
• Fittings (pipe fittings)