Applied Thermal Engineering 29 (2009) 2579–2582

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Applied Thermal Engineering

journal homepage: www.elsevier .com/locate /apthermeng

Short communication

Possible ways of regulation for branched heating systems

Vladimir Mijakovski *

Faculty of Technical Sciences, University ‘‘Sv. Kliment Ohridski”, 7000 Bitola, Ivo Lola Ribar bb, Macedonia

a r t i c l e i n f o a b s t r a c t

Article history:Received 28 September 2006Accepted 8 March 2008Available online 18 March 2008

Keywords:RegulabilityCirculationHeating systemComputer programme

1359-4311/$ - see front matter � 2008 Elsevier Ltd. Adoi:10.1016/j.applthermaleng.2008.03.023

* Tel.: +389 47 207748; fax: +389 47 203370.E-mail address: vladimir.mijakovski@uklo.edu.mk

Hydraulic imbalance of circulational heating systems can be considered as their main disadvantage.Methodology presented in this article is used to determine regulability of existing circulational heatingsystem in a factory. Four computer programmes are created based on presented mathematical model.Results from calculations are checked and later applied on one of the branches of the above mentionedheating system enabling its proper operation.

� 2008 Elsevier Ltd. All rights reserved.

1. Introduction

Main disadvantage of circulation network systems is hydraulicimbalance because it is a consequence of the uneven pressure dropin every closed circuit [1]. Even though the system was initiallyproperly designed, it did not work in practice.

A calculation of the pressure drop in every section in a branch ofthe network is presented in the article. Calculations are based uponthe developed mathematical model and derived computer pro-grammes. Basically this article shows a solution to a practical prob-lem in reference with regulability of the supply lines with greatlength.

2. Mathematical model

Opening/closing on one of the valves in any circuit causeschanges on the engaged specific energy of the pump and re-distri-bution of the flow towards the consumers.

Flow through the pipeline is determined with the followingequation

m � D2vn � p4� q � cpDtw ¼ Q ðkWÞ ð1Þ

For a known value of heat energy transferred through the pipeline,diameter of the pipe equals

Dvn;i ¼0:88 � K0:25

q � p2 � c2p � Dt2 �

Q 2i

Ri

! 15:25

ðmÞ ð2Þ

ll rights reserved.

Pressure drop in each circuit is determined by

Dp¼ k � LDvnþX

n

� ��q � m

2

2¼ k � L

DvnþX

n

� ��q � 8

D4vn �p2

�q2m ðPaÞ or

Dp¼ k � LDvnþX

n

� �� 8q �D4

vn �p2 � c2p �Dt2

w

�Q 2 ðPaÞ

ð3Þ

During fluid transport through parallel pipelines, the total flowequals the sum of separate flows through all sections and heatingunits, while the pressure drop in any closed circuit is also equal

qm;0 ¼ qm;i19 þ qm;j19; qm;i18 ¼ qm;i17 þ qm;j17; � � � qm;i2 ¼ qm;j2 þ qm;i1¼j1 ð4ÞDpRK�i19�j19�SK ¼ DpRK�i19�i18�j18�SK ¼ � � � ¼ DpRK�i19�i18�...i1�j1�SK ð5Þ

The value of additional local resistance coefficient for every valve(V1, V2, . . . Vi) is determined by these Eqs. (4) and (5). These valuesenable proper heat distribution for every heating unit.

nm;i ¼X1

i�1

ki �L

Dvn;iþX

ni

� ��D4

vn;j

D4vn;i

� Q2i

Q 2j

ð6Þ

Heating capacity of one section in the system equals:

Qi ¼Dpi � D4

vn;i � p2 � q � c2p � Dt2

i

8 � ki � LiDvn;iþP

ni

� �0@

1A

12

ð7Þ

Qi ¼ Qi�1 þ Q j; i ¼ j ð8Þ

where

ki ¼ 0:11 � KDvn;iþ 68�m

mi �Dvn;i

� �0:25� coefficient of friction for the

branch i;mi ¼ 4�Q i

D2vn;i �p�q�cp;i �Dt

(m/s) – velocity of the hot water in the branch i;

Nomenclature

cp specific heat under constant pressure (J/kg K)p pressure (Pa)qv volume flow rate (m3/s)t temperature (�C)v velocity (m/s)D diameter (m)K absolute roughness of pipe’s inner wall (m)L length (m)R singular pressure drop (Pa/m0)Q heat energy (W) or (kW)

Subscripts1,2. . . branch/heating unit numbervn internal (diameter) of the pipew water

Abbreviationsi sectionj heating unitRK distributerSK collectorV valve

Greek symbolsk coefficient of friction (–)q density (kg/m3)m kinematic viscosity (m2/s)p pi = 3.14159n coefficient of local resistance (–)D difference, ratio (–)P

sum, total (–)

2580 V. Mijakovski / Applied Thermal Engineering 29 (2009) 2579–2582

Ri – singular pressure drop. According to [2], R = (50–100) Pa/m0

– for small facilities; R = (100–200) Pa/m0 – for large facilities.

Based on the mathematical model described with Eqs. (1)–(8),four computer programmes are created. They are named: ‘‘DIMEN-ZII”, ‘‘PARAMETRI”, ‘‘MOKNOST” and ‘‘OTPOR”, respectively. Theseprogrammes are written in Microsoft C#.net computer languagewith user interface in Macedonian language. User interface of theprogramme ‘‘DIMENZII”is shown on Fig. 1.

First computer programme ‘‘OTPOR”, calculates values for addi-tional coefficient of local resistance of the valves in front of theheating units. This data enables proper distribution of flow throughthe heating units. If the values for the additional local resistanceare much greater than the maximum allowed value (the maximumvalue in the literature is 100), the system cannot be regulated [3,4].

Fig. 1. User interface of the comp

Computer programme ‘‘MOKNOST” is used to determine theheating power for each heating unit. With these data, regulabilityor non-regulability of the system can be determined.

3. Verification of the model on a existing heating system

Branch (2/2) of the heating system in the Cable Factory ‘‘Nego-tino”, Macedonia is used for verification of the model (Fig. 2).Water (110/70 �C) is used as heating media.

With the usage of ‘‘PARAMETRI”, key characteristics of thebranch 2/2 are calculated. These are shown in Table 1.

With comparison of values presented in Table 1 and recom-mended values for velocity and mass flow according to [5], it isobvious that the heating installation is properly designed. Yet, itis slightly over-dimensioned because the velocity of the heating

uter programme ‘‘DIMENZII”.

Fig. 2. Branch 2/2 heating system, Cable factory ‘‘Negotino”-Macedonia. i, section; j, heating unit; V, valve; RK, distributer; SK, collector.

Table 1Result of the calculation performed by ‘‘PARAMETRI”

i Dvn (mm) L (m) Q (kW)P

n (–) m(m/s) Dp (Pa)

1 100.8 60 665 9 0.51 34082 100.8 10 630 0.5 0.49 3963 100.8 10 595 0.5 0.46 3534 100.8 10 560 0.5 0.43 3135 100.8 10 525 0.5 0.41 2766 100.8 16 490 2.5 0.38 5037 100.8 10 455 0.5 0.35 2088 100.8 10 420 0.5 0.32 1779 100.8 10 385 0.5 0.30 14910 70.3 10 350 0.5 0.56 76611 70.3 16 315 2.5 0.50 120012 70.3 10 280 0.5 0.44 49213 70.3 10 245 0.5 0.39 37814 70.3 10 210 0.5 0.33 27915 54.5 10 175 0.5 0.46 71216 54.5 10 140 0.5 0.37 45817 43.1 16 105 2.5 0.44 154218 43.1 10 70 0.5 0.30 38819 43.1 10 35 1.0 0.15 105P

Dp = 12103 Pa.

Fig. 3. Left sub-branch with heating units in the Cable Factory ‘‘Negotino” -Macedonia.

V. Mijakovski / Applied Thermal Engineering 29 (2009) 2579–2582 2581

medium (0.15 � 0.56 m/s) is in the lower part of the recommendedvelocities interval. The same applies for the singular pressure dropR.

‘‘MOKNOST” computer programme is used for calculation of thevalues for distributed heating capacities in every heating unitrelated to flow parameters of the system in branch 2/2, shown inTable 2.

The installation is not regulable. There is no even distribution ofheat energy on the heating units. Data presented in Table 2 showsthat the branch is not regulable due to uneven distribution of heatenergy on heating units.

Table 2Heating capacity in every section of branch 2/2 calculated by computer programme‘‘MOKNOST”

J 1 2 3 4 5 6 7 8 9 10Q (kW) 0.9 1.1 2.0 5.0 6.4 9.5 11.3 14.2 18.6 29.4

J 11 12 13 14 15 16 17 18 19Q (kW) 37.6 39.7 43.1 47.8 60.2 67.7 77.3 89.3 103.9

Table 3Values for additional coefficient of local resistance for every section of the branch 2/2at heating unit entrance (valves) as calculated by the programme ‘‘OTPOR”

Vi 1 2 3 4 5 6 7 8 9 10Pni 6 26 37 131 168 183 203 229 292 332

Vi 11 12 13 14 15 16 17 18 19Pni 340 349 360 387 401 418 436 457 637

Additional local resistance coefficient values are calculated withcomputer programme ‘‘OTPOR”. These values are necessary in or-der to enable proper operation of each heating unit connected onthe branch.

Data in Table 3 shows that the system is not regulable. Valuesfor additional local resistance coefficient required for proper oper-ation of the system cannot be achieved by any valve on the market.

4. Solution of the problem

One of the possible solutions of the problem is to place the mainsupply line for hot water for branch 2/2 after section i10. That willmean ‘conditional’ separation of branch 2/2 onto two sub-branches: left and right (Figs. 3 and 4).

Calculations of dimensional parameters, velocity, distribution ofheat energy in every heating unit and additional coefficient of localresistance for every section at heating unit entrance (valve) are

Fig. 4. Right sub-branch of the heating installation in the Cable Factory ‘‘Negotino”– Macedonia.

Table 5Values for heat energy distribution for every heating unit of the newly ‘formed’ leftsub-branch

J 1 2 3 4 5 6 7 8 9Q (kW) 11.9 13.2 17.5 31.7 36.3 44.8 47.1 50.9 61.7

Table 6Values for local resistance coefficient for every section (valve) of the newly‘composed’ left sub-branch

Vi 1 2 3 4 5 6 7 8 9Pni 2 8 33 40 50 52 55 64 68

Table 7Key data as a result of calculation, for each section of the newly ‘created’ right sub-branch

n Dvn (mm) L (m) Q (kW)P

n (–) m(m/s) Dp (Pa)

1 100.8 5 350 1.0 0.27 882 100.8 16 315 2.5 0.24 2103 100.8 10 280 0.5 0.22 804 100.8 10 245 0.5 0.19 615 100.8 10 210 0.5 0.16 456 70.3 10 175 0.5 0.28 1957 70.3 10 140 0.5 0.22 1258 54.5 16 105 2.5 0.28 4799 54.5 10 70 0.5 0.19 117

10 54.5 10 35 0.5 0.10 33P

Dp = 1433 Pa.

Table 4Dimensions, total heat energy in main line, velocity and pressure drop in everysection of the newly ‘formed’ left sub-branch

i Dvn (mm) L (m) Q (kW)P

n (–) m(m/s) Dp (Pa)

1 100.8 5 315 1.0 0.24 722 100.8 16 280 2.5 0.22 1663 100.8 10 245 0.5 0.19 614 100.8 10 210 0.5 0.16 455 70.3 10 175 0.5 0.28 1956 70.3 10 140 0.5 0.22 1257 54.5 16 105 0.5 0.28 4798 54.5 10 70 0.5 0.19 1179 54.5 10 35 0.5 0.1 33P

Dp = 1293 Pa.

Table 8Values for heating energy distributed on each heating unit in the newly ‘created’ rightsub-branch

j 1 2 3 4 5 6 7 8 9 10Q (kW) 11 12.1 16.1 29.2 33.4 41.2 43.4 46.9 51.8 64.9

Table 9Values for the additional local resistance coefficient for each valve in the newly‘created’ right sub-branch

Vi 1 2 3 4 5 6 7 8 9 10Pni 2 8 33 40 50 52 55 60 71 75

2582 V. Mijakovski / Applied Thermal Engineering 29 (2009) 2579–2582

performed for both sub-branches. Obtained results for the left sub-branch are presented in Tables 4–6.

From data in Tables 5 and 6, it is obvious that the left sub-branch is regulable.

Calculations of same parameters are performed for the rightsub-branch and obtained results are shown in Tables 7–9.

Values in Tables 8 and 9 indicate that with newly proposedparameters (Table 7), right sub-branch of 2/2 is regulable.

The suggested solution solves the problem, meaning that a fullregulability of the circulational heating system is achieved, en-abling equal and complete heating of the working premises withheating units connected to this branch.

5. Conclusion

In the first part of this article a review of the present situation ofheating system defined with ‘as built’ values represents check ofthe developed computer programmes is given. It is clear that thecurrent system (as built) cannot be regulated. Heating units atthe end of each line are not working, they are ‘cold’. All of the men-tioned above imposed a necessity to seek for a solution that will al-low regulation, by small scale adaptation and small investmentcosts. Proposed adaption was sucessfully applied on the heatingsystem described in this article, resulting in its higher efficiency,even distribution of heat and proper heating of production facility.

Same solution was later applied on other similar heating sys-tems which furthermore verified and justified its usage.

References

[1] J. Sokolov, Toplifikacija i toplotne mreze, Gradevinska knjiga, Beograd, 1985.[2] Reknagel, Šprenger, Šramek, Ceperkovic, Grejanje i klimatizacija 95, Interklima,

Vrnjacka Banja, 1995.[3] V. Mijakovski, K. Popovski, Energy savings of a water pump with VFD in air

conditioning systems, in: Proceedings, XII Conference, Society of thermalEngineers of Serbia and Montenegro, Sokobanja, SCG, 2005.

[4] V. Mijakovski, I. Mijakovski, Prednost primene metoda jednakih promena uodnosu na metod afinosti kod centrifugalnih pumpi, 19 kongres o procesnojindustriji-Procesing 2006, Beograd, Srbija, 2006.

[5] VDI 2073:1999–07, Hydraulische Schaltungen in Heiz- und Raumluft-technischen Anlagen.