Optimization of Geometric Parameters of Thermal Insulation of Pre-Insulated Double Pipes

energies

Article Optimization of Geometric Parameters of Thermal Insulation of Pre-Insulated Double Pipes

Dorota Anna Krawczyk * and Tomasz Janusz Teleszewski Department of HVAC Engineering, Bialystok University of Technology, 15-351 Bialystok, Poland; [email protected] * Correspondence: [email protected]; Tel.: +48-797-995-926

Received: 18 February 2019; Accepted: 11 March 2019; Published: 15 March 2019

Abstract: This paper presents the analysis of the heat conduction of pre-insulated double ducts and the optimization of the shape of thermal insulation by applying an elliptical shape. The shape of the cross-section of the thermal insulation is significantly affected by the thermal efficiency of double pre-insulated networks. The thickness of the insulation from the external side of the supply and return pipes affects the heat losses of the double pre-insulated pipes, while the distance between the supply and return pipes influences the heat flux exchanged between these ducts. An assumed elliptical shape with a ratio of the major axis to the minor half axis of an ellipse equaling 1.93 was compared to thermal circular insulation with the same cross-sectional area. All calculations were made using the boundary element method (BEM) using a proprietary computer program written in Fortran as part of the VIPSKILLS project.

Keywords: thermal insulation; double heating ducts; twin pipes; energy savings; pollutants emission; district heating; network

1. Introduction District heating networks and installations undoubtedly have an impact on the environment and the efficiency of primary energy use. The exemplary results of urban areas in Turin [1] show a significant reduction in NOx concentration as a result of the connection of residential heating systems to heating networks. Lower heat losses generated by heating networks also contribute to lower heat production at the source, and thus to a reduction in the level of pollutants entering the atmosphere. Currently, double pre-insulated in a common circular thermal insulation is most often used. Heating networks are the subject of many studies. Kudela et al. [2] presented a complex model of heat transfer in the elements of a heating network, which can be used to accurately control district heating networks. Bennet at al. [3] formulated a two-dimensional model of heat conduction in the cross-section of a pre-insulated conductor using the multipole method. Bøhm and Kristjansson [4] on the basis of calculated heat losses showed economic profitability of using pre-insulated double and triple pipes in relation to single pre-insulated pipes. In pre-insulated triple pipes, heat losses are about 45% lower than in single pre-insulated pipes [4]. Teleszewski and Zukowski [5] performed calculations for an aboveground pre-insulated network with Cassini oval shaped thermal insulation. The calculations were made for the outside temperature from −24 to 0 ◦C for the assumed Robin’s boundary condition. In the case of Cassini oval shape, average heat losses are smaller by about 14% than for pipes with circular thermal insulation [5]. Heijde et al. [6] based on the results of the analytical model calculation, showed that the heat losses in a typical heating network are independent of the flow of the heating medium. The second important facet of the paper [6] is the inclusion of heat exchange between the supply and return lines in double pre-insulated networks. The temperature fields and heat-lines in the cross-section of the circuit ducts were described in [7]. Paper [7] presents visualizations of heat

Energies 2019, 12, 1012; doi:10.3390/en12061012 www.mdpi.com/journal/energies Energies 2019, 12, 1012 2 of 11

flow lines and temperature fields for pre-insulated double ducts for different distances between the supply and return ducts. A free available tool [8] allows the decrease in temperature and heat losses in the pipes to be estimated. In ref. [9] a detailed two-dimensional FEM (Finite Element Method) model to calculate steady-state heat loss in district heating pipes was proposed. Based on measurement data, Danielewicz et al. [10] proposed a three-dimensional model for determining heat losses in a heating network. In the literature, non-circular shapes of thermal insulation, e.g., in the shape of an egg, were presented [11], where a greater thickness of thermal insulation was used for the supply pipe compared to the return pipe. The comparison of different systems of single, twin, and triple district heating networks indicates that an egg-shaped pipe reduces heat loss by 37% and the investment index by 12% compared to a single pipe system [11]. Modeling of the flow in district heat networks was discussed in many studies. Kontu et al. [12] on the basis of the hourly heat demand presented ways to manage heat networks depending on the type of customer segments. Neirotti et al. [13] presented variants of temperature decrease in heating networks, which can be reduced by 50 ◦C. Song and Cheing [14] showed that greater benefits can be obtained by managing one integrated heating network than managing several independent district heating networks. Yang et al. [15] presented a simulation model of a heating network with connections of various energy sources. Our previous work [7] presented an analysis of the influence of the distance between the supply and return lines on the heat losses in a typical double pre-insulated pipe with circular thermal insulation. The aim of this work is a numerical optimization of the cross-sectional shape of the thermal insulation of double pre-insulated pipes by applying elliptic thermal insulation. The calculations were performed as a part of the VIPSKILLS project using the boundary element method (BEM). The boundary element method is a non-grid method and is often used in thermal and flow calculations. Moreover ecological analyses were conducted to show the possibility of achieving a reduction of pollutants, for a district heating network supplied by a hard coal cogeneration plant.

2. A Simplified Calculation Model for Determining Energy Losses of a Double Thermal Network The diagram of a double pre-insulated pipe is shown in Figure1. In the simplified model, the thermal resistance of the wall of the supply and return pipe as well as the thermal resistance of the outer casing of the double-duct insulation were neglected. A constant thermal conductivity coefficient k of the thermal insulation was assumed. The following boundary conditions of the Dirichlet were assumed on the duct wall: the temperature on the wall of the TS supply duct, the temperature at the wall of the return duct TR, and the temperature at the surface of the insulation wall from the outer side T0. The unit heat loss in the pre-insulated twin pipes consists of heat losses through the supply qS and return qR ducts: q = qS + qR [W/m], (1)

The heat flow in the return tube qR is composed of two heat flows: the heat flux qR2 from the return duct to the thermal insulation with a positive sign and the heat flow qR1 from the supply duct to the return duct with a negative sign:

qR = qR2 − qR1 [W/m], (2)

The unit heat fluxes were calculated from the differential thermal equation, which was solved by the boundary element method: ∂2T ∂2T k + = 0, (3) ∂x2 ∂y2 The algorithm for determining the heat-line by the boundary elements method can be found in [16], whereas the method of calculating the heat flux density values and temperature fields is presented in [17,18]. Verification of the method was performed by comparing the heat flux results of calculations of the boundary element method with the known results of the multipole method presented in the Energies 2019, 12, 1012 3 of 11 Energies 2019, 12, x FOR PEER REVIEW 3 of 11 literatureliterature [3]. [3]. The The calculations calculations were were made made for for a twin pipe with assumed boundary conditions from ref. [3]. [3]. For For the the boundary consisting consisting of 3000 elements, the relative error was not greater thanthan 0.001%.0.001%.

Figure 1. Geometry and boundary conditions. 3. Pre-Insulated Double Pipes with Circular Insulation 3. Pre-Insulated Double Pipes with Circular Insulation In a pre-insulated twin pipe, circular insulations are commonly used. This section presents the In a pre-insulated twin pipe, circular insulations are commonly used. This section presents the results of the simulation of heat conduction in a typical double pre-insulated pipe for different distances results of the simulation of heat conduction in a typical double pre-insulated pipe for different between the supply and return conduits. The boundary conditions, circular insulation parameters, distances between the supply and return conduits. The boundary conditions, circular insulation and dimensions of the twin pipe are shown in Table1. parameters, and dimensions of the twin pipe are shown in Table 1.

Table 1. Boundary conditions, circular insulation parameters, and dimensions of a twin pipe. Table 1. Boundary conditions, circular insulation parameters, and dimensions of a twin pipe. Description Symbol Value Unit Description Symbol Value Unit Diameter of the supply and return pipes d 0.09 m DiameterDiameter of the of thermal supply insulation and return pipes D d0.25 0.09 m m DiameterThe distance of thermal between insulation the supply and return pipes s D0–0.07 0.25 m m Thermal conductivity coefficient of thermal insulation made The distance between the supply and return pipes k 0.0265s 0–0.07 W/(m ·K) m of polyurethane foam Thermal conductivity coefficient of thermal insulation made of The temperature of the outer surface of thermal insulation, T k 8 0.0265 ◦C W/(m·K) polyurethaneadopted as foam the constant temperature of the ground o The Thetemperature wall temperature of the outer of the surface supply pipeof thermal is equal insulation, to the adopted as ◦ TS To90 8 C °C the constanttemperature temperature of the flowing of the liquid ground The wall temperature of the return pipe is equal to the ◦ The wall temperature of the supply pipe is equal to the temperatureTR of 50–90 C temperature of the heating medium TS 90 °C the flowing liquid The wall temperature of the return pipe is equal to the temperature of TR 50–90 °C the heatingFigure 2medium shows the dependence of the heat flow unit qR1 transferred from the supply pipe to the return pipe. As the temperature difference ∆T increases between the supply and return pipes at Figure 2 shows the dependence of the heat flow unit qR1 transferred from the supply pipe to the a constant supply pipe temperature, the heat flux qR1 increases. With the increase in the distance s return pipe. As the temperature difference ΔT increases between the supply and return pipes at a between the supply and return pipes, the heat flow qR1 decreases. For example, for s = 0.02 m the constant supply pipe temperature, the heat flux qR1 increases. With the increase in the distance s heat flux qR1 exchanged between the supply and return pipes is five times higher than in the case of s between= 0.04 m the for supply a given and temperature return pipes, difference the heat∆ Tflow= 20 qR◦1 C.decreases. This example For example, shows howfor s important= 0.02 m the it heat is to fluxmaintain qR1 exchanged a sufficiently between large distancethe supply between and return the supply pipes andis five return times pipes higher ina than common in the insulation. case of s = 0.04 m for a given temperature difference ΔT = 20 °C. This example shows how important it is to maintain a sufficiently large distance between the supply and return pipes in a common insulation.

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Figure 2. Unit heat flux transferred from the supply pipe to the return pipe as a function of the Figure 2. 2. UnitUnit heat heat ﬂux flux transferred transferred from from the the supply supply pipe pipe to the to return the return pipe as pipe a function as a function of the distance of the distance between the conductors at different return temperatures (qR1 = f(s,TR)). distancebetween between the conductors the conductors at different at different return temperatures return temperatures (qR1 = f (s,T (qR1)). = f(s,TR)).

Figure 33 showsshows thethe dependence of the heat flux flux on the qqS supplysupply as as a afunction function of of the the distance distance s Figure 3 shows the dependence of the heat flux on the qSS supply as a function of the distance s betweens between the the pipes pipes and and the the temperature temperature difference difference ΔT∆. TThe. The heat heat flow flow qS qincreasesincreases both both in the in the case case of between the pipes and the temperature difference ΔT. The heat flow qS increasesS both in the case of decreasing distance s and increasing distance s, which is respectively related to the impact of the decreasingof decreasing distance distance s and s and increasing increasing distance distance s, swhich, which is is respectively respectively related related to to the the impact impact of of the return duct and the decreasing thickness of the insulation layer from the outside of the supply pipe. return duct and the decreasing thickness of of the insulation layer layer from from the the outside outside of of the the supply supply pipe. pipe. The trend of changes in the unit heat flux is close to the trend of the supply heat flux presented in ref. The trend of of changes changes in in the the unit unit heat heat flux flux is isclose close to tothe the trend trend of the of the supply supply heat heat flux flux presented presented in ref. in [11]. [11].ref. [ 11].

Figure 3. TheThe dependence dependence of of the the unit unit heat heat ﬂux flux of the of supply the supply pipe as pipe a function as a function of the distance of the distancebetween Figurethe pipes 3. atThe different dependence return temperaturesof the unit heat (q = fluxf (s, of T the)). supply pipe as a function of the distance between the pipes at different return temperaturesS (qRS = f(s, TR)). between the pipes at different return temperatures (qS = f(s, TR)).

Figure 4 shows the dependence of heat flux qR of the return pipe as a function of the distance s Figure 4 shows the dependence of heat flux qR of the return pipe as a function of the distance s between the pipes and the temperature difference ΔT. Heat losses in the return duct increase with between the pipes and the temperature difference ΔT. Heat losses in the return duct increase with

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Figure4 shows the dependence of heat ﬂux qR of the return pipe as a function of the distance s betweenEnergies the 2019 pipes, 12, x FOR and PEER the REVIEW temperature difference ∆T. Heat losses in the return duct increase 5 of 11 with Energies 2019, 12, x FOR PEER REVIEW 5 of 11 the increase of the distance s and the temperature difference ∆T. In the case of very small distances the increase of the distance s and the temperature difference ΔT. In the case of very small distances s s betweenthe increase the return of the distance and supply s and pipesthe temperature (s > 0), the difference return Δ pipeT. In isthe “reheated” case of very viasmall the distances supply s pipe. between the return and supply pipes (s > 0), the return pipe is “reheated” via the supply pipe. Therefore,between negative the return heat and ﬂux supplyqR results pipes for (s >s >0), 0. the In return the case pipe of largeis “reheated” values of via s, the heat supply losses pipe. increase Therefore, negative heat flux qR results for s > 0. In the case of large values of s, heat losses increase Therefore, negative heat flux qR results for s > 0. In the case of large values of s, heat losses increase rapidly,rapidly, which which is associated is associated with with the the smaller smaller thicknessthickness of of the the insulation insulation layer layer from from the outside the outside of the of the rapidly, which is associated with the smaller thickness of the insulation layer from the outside of the returnreturn pipe. pipe. The The trend trend of changesof changes in in the the feed feed streamstream as as a a function function of ofthe the distance distance between between the pipes the pipes is is return pipe. The trend of changes in the feed stream as a function of the distance between the pipes is consistentconsistent with with the the results results obtained obtained [11 [11].]. consistent with the results obtained [11].

FigureFigure 4. The 4. dependenceThe dependence of the of unit the unit heat heat ﬂux flux of the of return the return pipe pipe as a asfunction a function of the of distance the distance between Figure 4. The dependence of the unit heat flux of the return pipe as a function of the distance the pipesbetween at different the pipes returnat different temperatures return temperatures (qR = f (s, ( TqR )).= f(s, TR)). between the pipes at different return temperatures (qR = f(s, TR)).

FigureFigure5 shows 5 shows the the percentage percentage ratio ratio of of the the unit unit heatheat ﬂuxflux qqR1R (transferred1 (transferred from from the supply the supply pipe to pipe to Figure 5 shows the percentage ratio of the unit heat flux qR1 (transferred from the supply pipe to the returnthe return pipe) pipe) to theto the unit unit heat heat losses lossesq qdepending depending on on the the distance distance between between the thepipes pipes for different for different the return pipe) to the unit heat losses q depending on the distance between the pipes for different supplysupply temperatures. temperatures. With With decreasing decreasing distance between between the the pipes, pipes, the % theqR1 %/q qratio/q increases,ratio increases, e.g., in e.g., supply temperatures. With decreasing distance between the pipes, the %qR1/q ratioR1 increases, e.g., in the case of distance s = 0.004 m and ΔT = 40 °C,◦ the heat flow transferred from the supply to the in thethe case case of of distance distances s= = 0.0040.004 m and Δ∆TT == 40 40 °C,C, the the heat heat flow ﬂow transferred transferred from from the supply the supply to the to the return pipe constitutes 50% of the total heat loss. returnreturn pipe pipe constitutes constitutes 50% 50% of of the the total total heat heatloss. loss.

Figure 5. Percentage ratio of heat flux unit qR1 (transferred from the supply pipe to the return pipe) to FigureFigure 5. Percentage 5. Percentage ratio ratio of of heat heat ﬂux flux unitunit qqRR1 1(transferred(transferred from from the supply the supply pipe to pipe the toreturn the pipe) return to pipe) unit heat losses q depending on the distance between the pipes for different supply temperatures to unitunit heat heat losses losses q q depending depending on the distance between between the the pipes pipes for for different different supply supply temperatures temperatures (%qR1/q = f(s, TR)). (%qR(1%q/qR=1/qf =(s, f(s, T RT)).R)).

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Analyzing the heat losses in the presented example in the supply and return pipes, it appears that the most optimal solution for the distance s between the supply and return pipes is a distance of 0.01 < ss << 0.03 0.03 m, m ,because because the the lowest lowest heat heat losses losses from from the the supply supply pipe pipe qqSS occuroccur in in this this range range (Figure (Figure 33);); at the same time the heat ﬂuxflux from thethe supplysupply pipepipe toto thethe returnreturn qqRR1 isis small (Figure 2 2).). TheThe gradientgradient of the heat flux ﬂux increase from the return pipepipe qqRR in this range is also small (Figure4 4).).

4. Optimization of the Shape of Thermal Insulation One of of the the methods methods of improving of improving the energy the energy efficiency efficiency of pre-insulated of pre-insulated double heating double networks heating networksis to modify is to the modify shape the of shape thermal of insulation.thermal insulation. In paper In [ 3paper] a solution [3] a solution for thermal for thermal insulation insulation in the inshape the ofshape an egg of an was egg proposed, was proposed, where thewhere supply the supply pipe was pipe insulated was insulated with a thicker with a layerthicker of thermallayer of thermalinsulation insulation than the than return the pipe. return This pipe. solution This significantlysolution significantly reduced heatreduced losses heat compared losses compared to standard to standardcircular insulations. circular insulations. Thermal insulations Thermal of insulations circular pre-insulated of circular double pre-insulated ducts are double characterized ducts are by characterizeduneven insulation by uneven thickness insulation around thickness the supply around and the return supply ducts. and Figure return6 ducts.shows Figure an example 6 shows of an a viewexample of a of pre-insulated a view of a pre-insulated double-insulated double-insulated pipe with circular pipe with insulation. circular The insulation. thickness The of thickness the thermal of theinsulation thermal above insulation the return above and the under return the and supply under cord the issupply thinner cord than is thethinner thickness than ofthe the thickness insulation of theon theinsulation left and on right the left of the and pipes. right of A the small pipes. distance A small between distance the between supply the and supply return and lines return can cause lines canheat cause transfer heat between transfer thebetween supply the and supply return and pipes. return In orderpipes. toIn improveorder to theimprove distribution the distribution of uniform of uniformthermal insulationthermal insulation thickness thickness between between the supply the and supply return and pipes, return an pipes, elliptical an elliptical shape for shape the thermal for the thermalinsulation insulation was proposed. was proposed. Equal areas Equal of areascircular of and circular elliptical and ellipticalthermal insulation thermal insulation were assumed were assumedfor the calculations. for the calculations. The ratio The of the ratio major of the axis major of the axis ellipse of the (a ellipse= 0.17361 (a = m) 0.17361 to the m) minor to the half minor axis halfof the axis ellipse of the (b = ellipse 0.09 m) (b is = equal 0.09 to m)a/b is = equal 1.93. Theto a/b main = 1.93. parameters The main affecting parameters the energy-efficient affecting the energy-efficientoperation of heating operation networks of heating are heat networks losses and are the heat exchange losses ofand heat the exchange exchange between of heat the exchange supply betweenand return the pipes. supply and return pipes.

Figure 6. View of pre-insulated double pipes.

Figure 77 comparescompares thethe unitunit heatheat losseslosses forfor circularcircular andand ellipticelliptic insulationinsulation asas aa functionfunction ofof thethe distance between between the the supply supply and and return return pipes. pipes. A Avariant variant with with circuit circuit isolation isolation was was analyzed analyzed in [7]. in [ In7]. theIn the case case of small of small distances distances between between the thesupply supply and andreturn return pipes pipes (s < 0.01 (s < 0.01m), the m), unit the heat unit losses heat losses both inboth the in case the caseof circular of circular andand elliptic elliptic thermal thermal insulation insulation are are similar similar and and the the differences differences between between these heat losses do not exceed 2%. With the increase in the distance between the supply and return pipes for s > 0.02 0.02 m, m, the the differences differences in in unit unit heat heat losses losses between between the the circular circular and elliptical thermal insulation become larger,larger, whichwhich is is associated associated with with a smaller a smaller insulation insulation thickness thickness over over the supply the supply pipe andpipe under and underthe return the pipereturn in pipe the case in the of thecase circular of the thermalcircular insulationthermal insulation compared compared to the elliptic to the thermal elliptic insulation. thermal insulation. For example, for the spacing of the supply and return pipes given by the manufacturer of twin pipes (s = 0.025 m, TS/TR = 90 °C/50 °C), the unit heat losses for circular thermal insulation are

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Energies 2019, 12, x FOR PEER REVIEW 7 of 11 Energies 2019, 12, x FOR PEER REVIEW 7 of 11 For example, for the spacing of the supply and return pipes given by the manufacturer of twin pipes 10.23% higher than the unit heat losses for elliptical insulation, while in the case of spacing equal to s 10.23%(s = 0.025 higher m, T than/T = the 90 unit◦C/50 heat◦C), losses the unit for elliptical heat losses insulation, for circular while thermal in the insulation case of spacing are 10.23% equal higher to s = 0.05 m, unit heatS R losses for circular insulation are 33.7% higher than in the case of elliptical thermal =than 0.05 the m, unitunit heatheat losseslosses forfor ellipticalcircular insulation insulation, are while 33.7% in thehigher case than of spacing in the case equal of toellipticals = 0.05 thermal m, unit insulation. insulation.heat losses for circular insulation are 33.7% higher than in the case of elliptical thermal insulation.

Figure 7. Comparison of the unit heat losses of a twin pipe for thermal circular and elliptic insulation Figure 7. ComparisonComparison of of the the unit unit heat heat losses losses of of a a twin twin pipe pipe for for thermal thermal circular and elliptic insulation as a function of the distance between the supply and return pipes. as a function of the distance between the supply and return pipes.

FigureFigure 88 showsshows thethe unitunit heatheat flowflow exchangedexchanged betweenbetween thethe supplysupply andand returnreturn pipespipes asas aa functionfunction ofof the the distance distance between between these these pipes. pipes. For For the the same same distances distances between between the thesupply supply and and return return pipes, pipes, the unitthe unitheat heatflux values flux values for both for circular both circular and elliptic and elliptic thermal thermal insulation insulation are similar are to similar each other. to each Both other. in theBoth case in the of case circular of circular and elliptic and elliptic insulation, insulation, as the as thedistance distance between between the the supply supply and and return return pipes pipes increases,increases, the the unit unit heat heat flux flux qR1 decreases,decreases, whereas whereas in in the the case case of of elliptical elliptical insulation insulation there there is is a a greater greater increases, the unit heat flux qR11 decreases, whereas in the case of elliptical insulation there is a greater possibilitypossibility of of increasing the the distance ss,,, andand reducingreducing the the unit unit heat heat flux. flux.flux. ForFor example,example, doublingdoubling thethe distancedistance between between the the supply supply and and return return pipes pipes from from s == 0.0250.025 mm toto ss == 0.050.05 0.05 mm m resultsresults results inin in aa reductionreduction ofof aboutabout four four times times of of the the unit heat flux flux exchanged between the supply and return pipes.

FigureFigure 8. ComparisonComparison of of the the unit unit heat heat ﬂux flux exchanged exchanged between between the supply the supply and return and returnpipes for pipes thermal for Figure 8. Comparison of the unit heat flux exchanged between the supply and return pipes for thermalcircular andcircular elliptic and insulation elliptic insulation as a function as a offunction the distance of thebetween distance the between supply the and supply return and pipes. return thermal circular and elliptic insulation as a function of the distance between the supply and return pipes. pipes.

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FigureEnergies9a,d 2019 shows, 12, x FOR temperature PEER REVIEW fields with heat-lines for circular insulation (Figure9a,b) 8 ofand 11 elliptical insulation (Figure9c,d) for distance s = 0.02 m and s = 0.07 m (T /T = 90 ◦C/50 ◦C). The results Figure 9a,d shows temperature fields with heat-lines for circularS insulationR (Figure 9a,b) and are consistentelliptical with insulation the results (Figure of 9c,d) calculations for distance for circulars = 0.02 m thermal and s = insulation 0.07 m (TS/T [1R]. = The 90 °C/50 influence °C). The of the unit heatresults flux areqR 1consistentin elliptic with thermal the results insulation of calculations is similar for circular to that ofthermal the unit insulation heat flux [1]. TheqR1 influencefor circular insulation.of the For unit the heat same flux distances qR1 in elliptics, in thethermal case ofinsulation elliptical is thermalsimilar to isolation, that of the the unit temperature heat flux q gradientR1 for over thecircular supply insulation. and return For pipes theis same much distances smaller thans, inin the the case case of of circular elliptical thermal thermal insulation isolation, which the is relatedtemperature to the additional gradient ellipticalover the supply thermal and insulation return pipes in theseis much places. smaller than in the case of circular thermal insulation which is related to the additional elliptical thermal insulation in these places. a) b)

c) d)

Figure 9.FigureComparison 9. Comparison of temperature of temperature ﬁelds and fields heat-lines and heat-lines for circular for circular (a,c) and (a,c elliptical) and elliptical (b,d) thermal (b,d) insulationthermal for selected insulation distances for selected between distances the supplybetween and the returnsupply pipes: and returns = 0.02 pipes: m (sa ,=b 0.02), s = m 0.06 (a,b m), s ( c=,d ). 0.06 m (c,d). Below, an assessment of the ecological effect of optimizing the shape of the thermal insulation Below, an assessment of the ecological effect of optimizing the shape of the thermal insulation was carried out by determining the reduction of pollutant emissions into the air before and after the was carried out by determining the reduction of pollutant emissions into the air before and after the application of elliptical thermal insulation. The reduction of annual emissions of pollutants emitted application of elliptical thermal insulation. The reduction of annual emissions of pollutants emitted into theinto air the resulting air resulting from from combustion combustion can can be be determineddetermined using using the the following following general general formula formula in ref. in ref. [19]:[19]: ∆Em = (Ec − Ee) × Ef [W/m], (4) ΔEm = (Ec − Ee) × Ef [W/m], (4) where E and E are the energy consumption for the heat loss of a twin pipe with circular insulation wherec Ec eand Ee are the energy consumption for the heat loss of a twin pipe with circular insulation and ellipticaland elliptical insulation insulation respectively: respectively:

Ec = qc × L × t [GJ], (5) Ec = qc × L × t [GJ], (5)

Ee = qe × L × t [GJ], (6) Ee = qe × L × t [GJ], (6) where qc and qe are unit heat losses for a pipe with circular and elliptical insulation respectively, L is where qthec and lengthqe are of the unit pipe, heat while losses t is forthe atime. pipe with circular and elliptical insulation respectively, L is the length of the pipe, while t is the time. Emission factors Ef used to calculate the emission of pollutants into the air of substances such as nitrogen oxides (NOX), carbon monoxide (CO), non-methane volatile organic compounds (NMVOC), Energies 2019, 12, 1012 9 of 11

sulphur oxides (SOX), total suspended particles (TSP), particulate matter (PM10 and PM2.5) for objects which are combined heat and power (CHP) plants powered with a hard coal, adopted in accordance with the guidelines of the European Environment Agency [19]. Standard twin pipes with circular thermal insulation (D = 0.25 m, d = 0.09 m, s(1) = 0.025 m) and twin pipes with elliptic thermal insulation (a = 0.17361 m, b = 0.09 m, s(1) = 0.025 m) were assumed for calculations. The length of conductors is equal to L = 1000 m, the constant thermal conductivity of thermal insulation k = 0.0265 W/(m·K), ◦ ◦ and network parameters TS/TR = 90 C/50 C were assumed. The unit heat losses for the pipe with round and elliptic insulation were determined from Figure7 and amounted to qc = 24 W/m and qe = 21.54 W/m, respectively. The values of energy used for heat losses during the year calculated from Equations (5) and (6) equal 756.2 GJ and 678.83 GJ for circular and elliptical thermal insulation, respectively. As an example a network with a length of 1000 m was considered. Emission factors Ef, the annual emissions of pollutants resulting from a combustion of hard coal in CHPs [19], and the reduction of annual pollutants emitted into the air as a result of the use of elliptical thermal insulation instead of circular insulation are shown in Table2. The ecological effect of the optimization of the thermal insulation by changing the shape of the cross-section from circular to elliptical (s(1) = 0.025 m) is a decrease of annual emissions of pollutants emitted into the air by about 10%. Combined heat and power plants powered with hard coal are characterized by high emission of sulphur oxides and nitrogen oxides. The use of the elliptical shape as an alternative to the standard circular thermal insulation enables the limitation of the annual sulphur oxides and nitrogen oxides emissions from the combined heat and power plants powered with hard coal for the assumed parameters of the pre-insulated network with a length of 1000 m by values of 63,436 g/year and 16,169 g/year, respectively.

Table 2. The results of calculations for the reduction of pollutant emissions into the air as a result of the optimization of the cross-section shape of the thermal insulation.

Pollutant Ef [g/GJ] Ec × Ef [g/year] Ee × Ef [g/year] ∆Em [g/year]

NOx 209 158,045 141,876 16,169 CO 8.7 6579 5906 673 NMVOC 1 756 679 77 SOx 820 620,080 556,644 63,436 TSP 11.4 8621 7739 882 PM10 7.7 5823 5227 596 PM2.5 3.4 2571 2308 263

Moreover, an ecological effect assessment was carried out for three different distances (s(1) = 0.025 m, s(2) = 0.03 m and s(3) = 0.035 m) between the supply and return ducts in a circular thermal isolation by determining the reduction of pollutant emissions from the CHPs. The parameters ◦ ◦ of pre-insulated pipes from Table1 and TS/TR = 90 C/50 C, L = 1000 m were assumed for calculations. In order to determine the reduction of annual emissions of pollutants emitted into the air, Equations (4)–(6) were used, which in the above-mentioned conditions take the following form:

∆Em = (Es(i+1) − Es(i)) × Ef [W/m], (7)

Es(i) = qs(i) × L × t [GJ], (8)

Es(i+1) = qs(i+1) × L × t [GJ], (9) where Es(i) and Es(i+1) are the energy consumption for the heat loss of a twin pipe in circular thermal isolation with distances s(i+1) and s(i+1), respectively, and qs(i) and qs(i+1) are unit heat losses for a double pipe in circular thermal isolation with distances s(i) and s(i+1), respectively. The results of the calculation of the annual emission of pollutants emitted into the air for a distance s(1) = 0.025 m can be found in Table2( EcEf). The value of energy used for heat losses Energies 2019, 12, 1012 10 of 11 during the year calculated on the basis of Equations (8) and (9) equals 805.04 GJ and 863.37 GJ for s(2) = 0.03 m and s(3) = 0.035 m, respectively. Table3 presents emission factors Ef and annual emissions of pollutants emitted into the air for two distances between the supply and return pipes s(2) = 0.03 m and s(3) = 0.035 m in common circular thermal insulation. The increase in the distance between the supply and return ducts from s(1) = 0.025 m (Table2) to s(2) = 0.03 m (Table3) increases the annual emission of pollutants emitted into the air by 6.46%, while the increase in the distance from s(2) = 0.03 m (Table3) to s(3) = 0.035 m (Table3) generates an increase in annual emissions of pollutants emitted into the air by 7.25%. The increase in the distance between the pipes by 0.01 m (from s(1) to s(3)) for the tested section of the pre-insulated double network results in an increase in the annual emission of sulphur oxides and nitrogen oxides from the combined heat and power plants by 87,884 g/year and 22,399 g/year, respectively. The above example illustrates the importance of the proper spacing of the supply and return ducts inside the thermal insulation. Too large a distance between the supply and return ducts causes an increase in heat losses, and thus contributes to the increase of emissions to the air emitted by heat sources.

Table 3. The results of calculations for the reduction of pollutant emissions into the air as a result of a

change in the distance between the supply and return pipes from s(2) = 0.03 to s(3) = 0.035 for circular thermal insulation.

Pollutant Ef [g/GJ] Es(2) × Ef [g/year] Es(3) × Ef [g/year] ∆Em [g/year]

NOx 209 168,253 180,444 12,191 CO 8.7 7004 7511 507 NMVOC 1 805 863 58 SOx 820 660,133 707,964 47,831 TSP 11.4 9177 9842 665 PM10 7.7 6199 6648 449 PM2.5 3.4 2737 2935 198

5. Conclusions Currently worldwide there is a trend of “energy-saving” in heat transport. This trend is determined by the increase in the prices of energy carriers and the ecological effects. This paper presents optimizations of the cross-sectional shape of the thermal insulation of double pre-insulated ducts by using an elliptical cross-section. Numerical simulations showed that a change in the shape of the cross-sectional thermal insulation of pre-insulated double-ducts can significantly reduce heat losses with the same cross-sectional area as in circular insulation. The distance between the supply and return ducts has a significant impact on the heat losses outside the pre-insulated duct and the heat exchange between the supply and return ducts. Too large a distance between the supply and return pipes results in a short distance between the pipes and the surface, that generates significant heat losses. On the other hand, too short a distance between the supply and return lines increases the heat transfer between the pipes. The use of elliptical thermal insulation allows larger distances between the return and supply ducts, as well as a sufficiently large distance of the pipes to the isolation surface, to be maintained. The results of analysis showed also a better ecological effect of using elliptical thermal insulation instead of standard circular thermal insulation.

Author Contributions: D.A.K. proposed the research methodology and aims, as well as organizing the draft of the manuscript; T.J.T. conducted simulations and prepared figures, D.A.K. and T.J.T. analyzed the simulation results, wrote the manuscript, and agreed the submission. Funding: The costs of development of e-lab used as a tool in this analysis as the publishing of the manuscript were covered by funds of the VIPSKILLS project (Virtual and Intensive Course Developing Practical Skills of Future Engineers) 2016-1-PL01-197 KA203-026152 Strategic Partnerships Erasmus +. Acknowledgments: This scientific project was implemented under S/WBIS scientific research at Bialystok University of Technology. Energies 2019, 12, 1012 11 of 11

Conﬂicts of Interest: The authors declare no conﬂict of interest.

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