New correlations for the standard EN 164 Federico Boldrin, Michele De arli, Giacomo Ruaro DFT Dipartimento di Fisica Tecnica, Università degli Studi di Padova, Italy orresponding email: michele.decarli@unipd.it SUMMARY The standard EN 164 is born as technical standard for designing and installing radiant floors for heating purposes. In the last years a revision of the standard took place in order to extend the existing calculation method for determining heat flow output also to other radiant systems (walls and ceilings) and operating conditions (heating and cooling). Nevertheless there are some aspects which have not so far been taken into account, like backward heat flows or how to determine, in cooling conditions, minimum surface temperature and related cooling capacity of the radiant system. In this paper the concepts for correctly consider those aspects are shown and the introduction of correlations and equations which can be integrated in the standard are presented. INTRODUTION The Standard EN 164 [1,, 3, 4] includes a simplified method for sizing radiant floors, by defining pipe spacing, pipe diameter and material type of insulation etc. Although it is a simplified method, its application has some limits, therefore it cannot always be applicable. The existing method has one limit, i.e. the determination of the downward heat flow, which is not directly specified and it is roughly estimated when defining the mass flow rate of the system. The new draft of standard makes possible to size not only radiant floors, but also radiant ceiling and walls, by defining different heat exchange coefficients on the surfaces (Table 1). It is also defined how to calculate the cooling heating capacity in steady state conditions, but it is not clear how to fix by calculations the limits of the cooling capacity, since a minimum surface temperature in cooling conditions has to be set. Table 1. Total heat exchange coefficients [W m - K -1 ] proposed in the draft of the standard heating cooling Wall 8 8 Floor 10.8 7 eiling 6 10.8 BAKWARDS EAT FLOW EVALUATION When sizing a radiant system, reference to the operative temperature has to be made. (i.e. both the radiant and convective heat exchanges with the surroundings are considered). Once calculated the heat loss due to external surfaces, thermal bridges, and the ventilation load, the heating specific capacity of the radiant system is the ratio between the calculated load and the area of the radiant system. The radiant system can be thought as a heat exchanger, having on
one side the water and on the other side a medium with infinite heat capacity (the room). The heating capacity is proportional to (Δϑ ) n, where n can be approximated to 1, since 1,00 < n < 1,05 and where Δϑ is the mean logarithmic temperature: ϑv ϑr ( ) Δϑ = ϑv ϑ1 / ln, (1) ϑr ϑ1 For calculating the heat exchange coefficient in EN 164 a simplified method, based on parameters reported in tables, is proposed, leading to the equation: mi K = B (a i ), () The resulting specific heating capacity of radiant systems is defined by the equation: m 1 (a i ) Δ i i i q = B ϑ, (3) The backwards heat flow can be roughly approximated considering the heat flowing in the adjacent space calculated through the following equation: ( ϑ ) q U w ϑ =, (4) The backwards thermal transmittance U may be calculated as inverse of the one dimension resistance of the whole structure from the conditioned room to the adjacent space R tot (or the inverse U tot -value), once known the upward resistance R 1 (or the inverse U 1 ), which can be calculated via the following equation (q 1 is calculated by equation 3): ( ϑ ) q1 U 1 w ϑ1 =, (5) The thermal transmittance from pipes level to the adjacent room can be calculated as follows: U 1 = R = R tot 1 R 1 1 = U tot 1 U1 1, (6) ASE STUDIES The models used in the analysis are EN164 method, Finite Element Method (FEM) and Finite Difference Method (FDM) for types A and B systems []. FEM can be considered as a reference method, since it allows to model the geometry of a circular pipe; FDM is also a correct method. Usually such models are based on a rectangular mesh and therefore there is the need to correctly model systems containing circular pipes. In heating case the pipe can be approximated by a square having length [6]: and internal resistance l = π r, (7) R = D ln[ r /( r d )]/( π k ), (8) p
As detailed methods two commercial software have been used: STRAUSS for FEM and EAT for FDM. The water inside pipes has been considered in turbulent flow (inner convection resistance negligible) and the same water temperature has been used in the different cases. Pipe material is PE-X (k = 0.35 W m -1 K -1 ). Thermal conductivity of the concrete layer where pipes are embedded has been set to 1. W m -1 K -1. The structural slab below the systems is 00 mm thick and two values for the thermal conductivity have been fixed: 0.67 W m -1 K -1 and 1. W m -1 K -1. Type A Simulations have been carried out by considering the data reported in Table 1. For both the conditioned and the adjacent rooms the same temperature (0 ) has been used. Pipes have 0 mm external diameter and mm thick. Pipe distances have been varied from 50 mm to 375 mm. As for the concrete layer and the position of the pipe within it, data can be seen in Table. Two values of floor covering materials have been simulated (0.015 m K W -1 and 0.0 m K W -1 thermal resistance respectively). The insulation layer is 30 mm thick and thermal conductivity is 0.04 W m -1 K -1. Table. Thickness of the concrete layer and position of the pipe within it Thickness of the concrete layer [mm] Position of the pipe above the insulation [mm] 60 0 10 30 80 0 0 40 Type B Simulations have been carried out by using the same boundary conditions of Type A. Two circular pipes have been considered: 0 mm external diameter ( mm thick) and 10 mm external diameter (1.7 mm thick). Pipes are directly in contact with thermal insulation and distances between pipes have been varied from 50 mm to 450 mm. Three floor covering materials have been simulated (0.015 m K W -1, 0.15 m K W -1 and 0.0 m K W -1 thermal resistances). The concrete layer above pipes is 60 mm. The insulation layer is 30 mm or 40 mm thick and thermal conductivity is 0.04 W m -1 K -1. The additional conductive element above pipes is 0.5 mm thick with 5 W m -1 K -1 thermal conductivity. Two dimensions have been considered: continuous covering (L = T) or 10 mm distance between each device (L = T 0.01 m). RESULTS AND DISUSSION Since simulations have been performed under the same conditions and with fixed temperature, in order to generalize the results reference has to be made in each simulation to the results of the FEM method q ref, thus defining the heat flow ratio Ξ: Type A Ξ = q / q ref, (9) Results for the conditioned room heat flow ratio Ξ 1 and the adjacent room heat flow ratio Ξ are reported in Table 3. As it can be seen, FDM gives the same results as FEM. Existing method is also accurate regarding heat flux from pipes to the conditioned room. The adjacent
room heat flow calculated via equation (4) is not accurate and precision decreases as the pipes spacing enlarges (Figure 1). The heat flowing in the adjacent room Ξ is dependent most of all on the covering material R λ,b. Tile covering (0.015 m K W -1 ) and 0 mm wood covering (0.15 m K W -1 ) are the two extreme cases, i.e. for each pipes distance and resistance of covering layer, the value is always between the curves represented in Figure 1. It is therefore possible to consider the pipes spacing and the floor covering resistance as parameters for correcting the values of Ξ through the equation (coefficients are reported in Table 4): q [ λ, B λ, B λ B ] b d f ( ϑ ϑ )( a R T ) + ( c R T ) + ( e R ) =, (10) U w, At the end the proposed equation gives the results reported in the last column of Table 3. The error is slightly higher when pipe distance is great, but the result is on the safety side. Table 3. onditioned room heat flux ratio Ξ 1 and adjacent room heat flux ratio Ξ for Type A Ξ 1 Ξ FDM EN 164 FDM equation (4) equation (10) Mean value 0.99 0.99 1.00 1.56 1.00 St. dev. 0.01 0.04 0.01 0.54 0.05 Table 4. oefficients for evaluating the heat flux in the adjacent room to be used in eq. (10) a b c d e f 4.686 10 - -7.6348 10-1 -1.1165-1.9091 10-1 1.0490-1.3619 10 - Type B Results for the conditioned room heat flow ratio Ξ 1 and for the adjacent room heat flow ratio Ξ are reported in Table 5. Also in this case FDM gives the same results as FEM. Existing method is accurate regarding heat flux from pipes to the upper room. The heat flow in the adjacent room calculated via equation (4) is not accurate and precision decreases as the pipes spacing enlarges (Figure ). The heat flow ratio Ξ is depending most of all by the pipes spacing T and external diameter D of the pipe, but it does not depend on insulation layer thickness. It is possible to write the following equation for determining the heat flux towards the adjacent room (coefficients are reported in Table 6): q = U [ ] b 3 d f h ( ϑ )( a D T ) + ( c D T ) + ( e D T ) + ( g D ) ϑ, (11) w In this way for each pipes spacing the curve is always between the curves reported in the diagram of Figure. The proposed equation gives the results reported in the last column of Table 5. The error is slightly higher when pipe distance is great, but also heat flow in the conditioned room is not very accurate in these cases.
Downward heat flow ratio for Type A 3.5 3.0 R λ,b = 0.15 m K W -1 R λ,b = 0.0 m K W -1.5.0 1.5 1.0 0.5 0.0 0 50 100 150 00 50 300 350 400 Pipe spacing [mm] Figure 1. Values of Ξ in the case of existing method based on equation (4) for Type A. Downward heat flow ratio for Type B 7.0 6.0 5.0 D = 10 mm D = 0 mm Poli. ( ) Poli. ( ) 4.0 3.0.0 1.0 0.0 0 100 00 300 400 500 Pipe spacing [mm] Figure. Values of Ξ in the case of existing method based on equation (4) for Type B Table 5. onditioned room heat flux ratio Ξ 1 and adjacent room heat flux ratio Ξ for Type B Ξ 1 Ξ FDM EN 164 FDM equation (4) equation (10) Mean value 1.01 0.9 0.99.1 0.98 St. dev. 0.00 0.13 0.00 1.9 0.10
Table 6. oefficients for evaluating the adjacent room heat flux to be used in eq. (11) a b c d e f g h -39.146 0.68386 149.60 0.9054-61.77 1.1118 17.617 0.5847 MINIMUM TEMPERATURE IN OOLING ONDITION ANALYSIS The existing EN 164 takes into account the heat output from the radiant floor and it fixes a surface temperature which cannot be exceeded. For radiant floor 9 for the occupancy space, 35 for outside area. For radiant ceiling the surface temperature is related to the radiant asymmetry, but it is usually better not to exceed 35. For radiant walls the maximum allowed temperature is related to the risk of burning, i.e. about 40. Maximum surface temperature is the average surface temperature, i.e. the maximum surface temperature above or below the pipe in the section where water temperature is equal to: ϑ = ϑ + Δϑ, (1) w 1 When calculating the thermal output of a radiant floor in cooling conditions, the minimum allowable surface temperature must be taken into account. Such temperature for a radiant floor is 19, while for the other radiant systems the dew point temperature is the reference temperature. It must be underlined that such surface temperature is above the section where the supply water temperature occurs. The question is how to consider in a proper way the minimum temperature, once it is known the maximum output of the radiant system, since the cooling capacity has to be determined in the section where water temperature is equal to: ϑ w = ϑ Δϑ, (13) 1 The idea is to evaluate, for the maximum heating capacity, the average temperature of the surface and determine the difference between such temperature and the maximum surface temperature. Therefore the following equation can be written: Δ ϑ = ϑ ϑ + q / α ), (14) surf,max ( 1 At the same time for the cooling capacity a similar equation can be calculated: ase studies Δϑ = ( ϑi q / α ) ϑ, (15) surf, min Detailed simulations have been carried out for different systems with FDM, since the accuracy of the method has been previously demonstrated. The analysis has been carried out with the reference limit temperatures reported in Table 7. Simulations have been carried out by considering for the heat transfer coefficients the data reported in Table 1. The water inside pipes has been considered in turbulent flow (i.e. convective inner resistance negligible). Pipes have 0 mm external diameter and mm thick. Material is PE-X (k = 0.35 W m -1 K -1 ). Table 7. Surface temperature limits [ ] considered in this work heating ooling Wall 40 19 Floor 35 19 eiling 9 19
Type A Internal resistance due to water convection in the pipe has been considered negligible Pipe distances have been varied from 50 mm to 300 mm. The concrete layer is 60 mm thick and the position of the pipe within it has been set above insulation layer or in the centre of the concrete layer. Three values of floor covering materials have been simulated: 0 m K W -1, 0.015 m K W -1 and 0.0 m K W -1 thermal resistance respectively. Thermal conductivity of the concrete layer where pipes are embedded has been set to 1. W m -1 K -1. The insulation layer is 30 mm thick and thermal conductivity is 0.04 W m -1 K -1. The structural slab is 00 mm thick with 0.9 W m -1 K -1 thermal conductivity. Type B In this case pipes are directly in contact with thermal insulation and distances between pipes have been varied from 50 mm to 300 mm. Four floor covering materials have been simulated, having thermal resistances 0 m K W -1, 0.015 m K W -1, 0.15 m K W -1 and 0.0 m K W -1. The concrete layer above pipes is 70 mm thick and thermal conductivity has been set to 1. W m -1 K -1. The insulation layer is 30 mm thick and thermal conductivity is 0.04 W m -1 K -1. The structural slab is 00 mm thick with 0.67 W m -1 K -1 thermal conductivity. The additional conductive element above pipes is 0.5 mm thick and its thermal conductivity is 5 W m -1 K -1. The dimension of the conductive covering equal to the pipes spacing (L = T). Results and discussion The two temperature differences given by equations (1) and (13) have the same value only when the overall heat transfer coefficient is the same for heating and cooling and if the following condition is valid: ϑ 1 ϑsurf,min = ϑsurf,max ϑ1, (16) Since equation (16) cannot be achieved and the heat transfer coefficients are not always the same for heating and cooling conditions, the error Λ can be calculated as follows: Λ = Δϑ Δ, (17) ϑ Results of Λ for a set of simulations are reported in Figure 3 for type A and in Figure 4 for Type B. The overall thermal resistance from pipes level to conditioned room R tot as well as the pipes spacing are the factors that mostly influence the results. The hypothesis of a linear relationship between Λ and pipes space T leads to the following equation: Λ = a R T + c R, (18) b tot where the coefficients are reported in Table 8 for the different cases. In this case the minimum temperature can be directly calculated, once known the maximum allowable heating output for all configurations of radiant systems: b tot ( q / α Λ ϑ + ϑ ϑ ϑ ) qv α surf,max 1 surf,min + 1 =, (19)
where q V means the cooling output in the section of the supply temperature (i.e. in the section where the water enters in the room). Equation (19) can be solved for the different systems, leading to: q V ( q Λ p) = α / α, (0) where p = for a radiant floor, p = 13 for a radiant wall and p = 8 for a radiant ceiling. Once known the heat flow q V, the calculation of the supply water temperature is possible, since K c is known: ϑ = ϑ 1 q / K, (1) V V From the supply water temperature, once fixed the maximum temperature difference between supply and return, it is possible to evaluate the maximum cooling output of the system q. 0.0-0. -0.4-0.6-0.8-1.0-1. -1.4-1.6 TYPE A - ENTRE OF TE ONRETE LAYER T[mm] 0 5 10 15 0 5 30 R λ Rlb = 0 R λ Rlb = 0,015 R λb Rlb = 0, Figure 3. Values of Λ [ ] for Type A (floor) 0.0 TYPE B T[mm] 0 5 10 15 0 5 30-0.1-0. -0.3-0.4-0.5-0.6 R λb Rb = 0 R λb Rb = 0.015 R λb Rb = 0.15 R λb Rb = 0. -0.7 Figure 4. Values of Λ [ ] for Type B (floor)
Table 8. oefficients to be used in equation (18) a B c A 30 mm above insulation -0.88-0.501 0.066 Floor A 0 mm above insulation -0.61-0.597 0.458 B -0.34-0.68 0.06 A 30 mm above insulation -3.56-0.41 0.67 Wall A 0 mm above insulation -.61-0.50 0.35 B -1.18-0.590 0.11 A 30 mm above insulation -1.87-0.33 0.140 eiling A 0 mm above insulation -1.5-0.373 0.144 B -0.78-0.398 0.086 ONLUSIONS When pipes are approximated thorough equations () and (3) the use of FDM leads to no error and the accuracy can be assumed to be the same as FEM. As for hating flow behind the pipes, both for type A and B, correlation for determining the correct values are proposed and seem to be accurate (error less than % in the worst case for type B). Also modification for taking into account minimum temperature of supply water temperature in cooling conditions, starting by the value (calculated or measured) of the maximum allowable heating output, has been proposed and it seems to be accurate enough (on cooling heat flux less than %). SYMBOLS α a i B D d k k p l L m i q ref r R R λ, B T U 1 U Δϑ ϑ V ϑ R ϑ w ϑ 1 ϑ overall heat flow coefficient from surface to space multiplication factors which depend on thermal and geometrical characteristics of the radiant system coefficient characteristic of the radiant system external diameter of the pipe thickness of the pipe thermal conductivity thermal conductivity of the pipe equivalent length of the square approximating the pipe for FDM simulations length of conductive layer above pipes for type B radiant systems exponential factors which depend on thermal and geometrical characteristics of the radiant system reference heat flow from FEM in the considered simulations external radius of the pipe equivalent internal resistance of the pipes for FDM simulations resistance of the covering layer distance between pipes thermal transmittance from pipes level to conditioned space thermal transmittance from pipes level to backwards mean logarithmic temperature supply temperature of the water return temperature of the water mean temperature of the water temperature of conditioned room temperature of backwards room
ϑ suf,max maximum average surface temperature ϑ suf,min minimum surface temperature at supply point Δ ϑ difference between surface average and maximum/minimum surface temperature Ξ heat flow ratio Λ error when considering Δϑ in heating and cooling case cooling case heating case REFERENES 1. EN. 1997. EN 164-1997 Part 1, Floor heating Systems and components. Definitions and symbols.. EN. 1997. EN 164-1997 Part, Floor heating Systems and components. Determination of the thermal output. 3. EN. 1997. EN 164-1997 Part 3, Floor heating Systems and components. Dimensioning. 4. EN. 1997. EN 164-1997 Part 4, Floor heating Systems and components. Installation. 5. ENT130WG9. 006. pren 164-006 Part 5, eating and cooling surfaces integrated in floors, ceilings and walls - Determination of heating output and cooling output. 6. Blomberg, T. 1999. eat A P-program for heat transfer in two dimensions. Manual with brief theory and examples. Lund Group for omputational Building Physics, Sweden.