8.1.2. Floor heating calculations<br>

### 8.1.2. Floor heating calculations

The applied methodology of design and calculations of heating output of hydronic floor heating systems is consistent with that described in the EN 1264 standard. Issues that have not been dealt with in the standard mentioned, were solved on the basis of documents supplied by manufacturers of floor heating systems and other available source materials.

The program follows a number of optimising procedures and applies a number of calculation algorithms. A short description of the most important of them is presented below.

Distribution of heat loss among HZ’s in the room

If the user does not specify the contribution of individual HZ’s in the covering of heat losses of the entire room, the distribution is done automatically during calculations. The algorithm of distribution takes into account the heating capacities of individual HZ’s providing a high level of optimisation.

The distribution follows the following guidelines:

1. As far as possible a uniform output per square metre for all HZ’s in the room should be ensured to maintain the same average temperature of floor surface and provide favourable conditions of use.

2. In the peripheral zones output per square metre is increased in relation to occupied zones.

3. Check must be made to see whether each HZ is able to deliver the output assigned to it. If not, the distribution must be changed to match the values of assigned output to the heating capacities of individual HZ’s.

If it is not possible to distribute Qfh/Ffh in such way that all HZ’s are matched to the assigned values, then the heat loss is distributed in such way that the deficiency or excess of output acquired from individual HZ’s in relation to Qfh/Ffh assigned to them is uniform – all HZ’s will have, for instance, excess output. When some HZ’s in one room have excess output, while the output of other HZ’s in the same room is too low in relation to assigned output, the distribution of output is not optimised.

Determination of the available pipe spacing options for each HZ

The available pipe spacing options are determined for each HZ according to the following guidelines:

1. Permissible pipe spacing in OZ and PZ is specified in general data. These depend on the applied fastening system and the type and diameter of pipe.

2. Non-standard pipe spacing settings in HZ data (if specified).

3. For HZ’s with an integrated PZ all combinations of permissible spacing values for PZ and OZ are taken into consideration, provided that spacing in PZ is smaller than in OZ.

Calculation, for each pipe spacing, of temperature difference that provides the required heat output.

With the heating slab structure and floor covering and required heat flux density (output per square metre) known, the program calculates the mean temperature of the heating medium in the circuit that would provide the desired output. Then, with the supply temperature known, the program calculates the temperature drop (cooling down of the medium) in the circuit required to provide the mean temperature of the medium.

The following limiting factors are taken into account when determining the temperature drop that provides the required floor heating output at the specified pipe spacing:

1. Maximum and minimum temperature drops for OZ and PZ specified in the control circuit general data and, if necessary, amended in the HZ data.

2. For HZ’s that consist of a combination of uPZ/OZ (peripheral zone forming the beginning of the entire circuit) the Dt/Dq_max is equal to Dt/Dq_max_OZ + Dt/Dq_max_PZ. The value of Dt/Dq_min is determined in a similar way.

3. The maximum point temperature of the floor surface (tfs/qfs max) determined in accordance with the EN standard cannot be exceeded. The method of determining tfs/qfs max defined in the standard takes into account the difference in floor surface temperature above the pipe and in the middle of pipe spacing – the floor surface temperature curve resembles a sinusoid. The larger the pipe spacing and the lower the thermal resistance of the floor covering – the lesser is heat dissipation and the larger are differences in tfs/qfs. Under these conditions the mean tfs/qfs is much lower than tfs/qfs max, as the peak of the sine curve cannot exceed tfs/qfs max.

4. The return temperature must be higher than ti/qi of the room.

If the temperature difference that enables achieving the required mean temperature of the medium is not allowed for any of the reasons listed above, the best available Dt/Dq for the given pipe spacing will be selected. This will result in excess / deficiency of output from the HZ in relation to assigned Qfh/Ffh.

If the limitations described above cause that for the given pipe spacing the interval of permissible temperature differences is empty, that spacing is not available. This situation may be caused by non-compliance with the standard with regard to tfs/qfs_max or by return temperature being too low in relation to ti/qi. If this applies to all available pipe spacing options, the floor heating in the HZ will not be sized and the entire block of results for this HZ will be highlighted in yellow.

Determination of pipe feed spacing and calculation of pipe feed output

For each HZ with pipe feeds running across it, the area occupied by pipe feeds and their output are calculated. The area occupied by the pipe feeds depends on the pipe spacing adopted. If automatic determination of pipe spacing is enabled, the spacing is determined according to the following rules:

1. For non-insulated pipe feeds, the pipe spacing is equal to that of the main circuit in the HZ. This means that pipe feeds will occupy different areas depending on the current pipe spacing in the circuit. This solution may be treated as a simulation of the main circuit by pipe feeds, so that the floor temperature in the area where pipe feeds run does not differ much from tfs/qfs in the area of the main circuit.

2. For insulated pipe feeds the minimum pipe spacing is adopted. These pipe feeds are in practice excluded from heating and the area occupied by them is minimised.

! These fragments of pipe feeds are treated as insulated, which have the “I” (insulated) option specified in the pipe feed data table. Pipe feeds with the “P” (in conduit) option are not treated as insulated. According to available manufacturers’ data, putting a pipe feeds into a conduit (casing) does not change significantly its heat output (low insulating power is compensated by increased heat exchange area).

To calculate the output of pipe feeds, their pipe spacing and average operating parameters (mean temperature of heating medium) of the control circuit to which the pipe feeds are assigned are taken into account.

Selection of pipe spacing optimised with regard to heat output and flow

The execution of the steps described above results in a list of available pipe spacing options and in the temperature drop and other heat calculation results for each of these spacing options. The pipe spacing selected is the best in terms of heat output and is hydraulically matched. The selection is based on the following criteria:

1. That spacing is selected, which ensures the attaining of the required output (excess Qfh/Ffh is equal to zero or the value set in advanced options of calculations). During optimisation the program tries to select a pipe spacing with an output within “Matching” range. If there is no such spacing, that spacing is selected, which ensures an output within “Moderately unmatched” range.

2. If there are several spacing options that meet the above criterion, that spacing is selected, which ensures the widest possibilities for changing the floor covering, meaning that adaptation to a floor covering with a different thermal resistance may be done by adjusting the flow rate.

3. Those spacing options that lead to non-compliance with the standard with regard to tfs/qfs max or to a return temperature being too low in relation to ti/qi, will not be listed and will not be made available to the user.

The structure of the system is optimised in terms of flow conditions. This means that hydraulic parameters of pipe spacing options are taken into account when optimum options are selected (optimisation is done with regard to heat output – see above). The hydraulic parameters obtained are provided as results, and if the selected pipe spacing is correct in terms of heat output, but not correct with regard to flow conditions, then one of the many available methods of correcting hydraulic results must be applied (see section 9.8).

Determination of optimum supply temperature for each control circuit

The optimisation algorithm uses defined temperature ranges fit for each room. The temperature is assumed fit for the room when it is possible to attain the required output of floor heating in that room (total output of all HZ’s in the room). Depending on current data (type and number of HZ’s, required output of floor heating, permissible pipe spacing, temperature drops, etc.) the range of fitting temperatures may vary. In specific case there may be no fitting temperature, which indicates that it will not be possible to attain the required output of floor heating with the existing set of data.

For each temperature within the range between tsmin/qs min and tsmax/qs max the pipe spacing optimised in heat output and flow terms for the HZ is sized, the quality of the solution is computed, temperature quality graph is plotted and temperature is selected from the highest quality range.

“Minimise ts/qs” optimisation

After heat and flow optimisation the graph is corrected. In this case the lower the supply temperature the better: the graph is modified, and if there are several high quality ranges, then the lowest temperature that meets the quality requirements is selected.

“Minimise cost” optimisation

After heat and flow optimisation the graph is corrected. In this case the total length of pipes and the number and sizes of manifolds are taken into account. The temperature selected should ensure the lowest possible number of manifolds with the lowest possible number of ports and the shortest possible length of piping. The heat and flow graph is modified using the calculated cost and the corrected graph is used to select the supply temperature.