Longitudinal flow spiral recuperators in building ventilation systems

Energy and Buildings 40 (2008) 1883–1888

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Longitudinal flow spiral recuperators in building ventilation systems Mariusz Adamski * Technical University of Białystok, Department of Heat Engineering, ul. Wiejska 45E, PL-15-351 Białystok, Poland

A R T I C L E I N F O

A B S T R A C T

Article history: Received 18 September 2007 Received in revised form 30 March 2008 Accepted 20 April 2008

Capital expenditure and exploitation costs of ventilation systems with longitudinal counterflow spiral recuperators are minimized taking into consideration the results of measurements and calculations together with the well-known effectiveness–NTU method. It was estimated that ventilation system with longitudinal flow spiral recuperators refunds the capital expenditure within 2 or 3 years. Due to their advantages, spiral recuperators with the longitudinal counter current flow should be widely utilized for ventilation systems in winter and cool recuperation in summer. ß 2008 Elsevier B.V. All rights reserved.

Keywords: Spiral recuperator Ventilation system

1. Introduction The increasing emphasis to use energy efficiently motives to analyze the performance and operational strategies of heating, ventilating and air conditioning (HVAC) systems in buildings. Improvements in efficiency of HVAC systems could be instrumental in maintaining existing power-plant generation capacity and avoiding further dependency on fuels. HVAC systems in commercial, industrial and residential buildings consume approximately one-half of the total energy in these buildings [1]. The European building sector is responsible for about 40% of the total primary energy consumption [2]. Heat recovery equipments find an extensive literature (for instance [3–7]). A survey of the previous work related to the HVAC systems indicates that efforts have been made in computer simulations and experimental works [8–11]. The aim of heat recovery ventilation is to provide fresh air in the way in which thermal comfort as well as energy saving are maintained, using a recuperator with heat recovery from removed air. In particular, heat recovery should be used in buildings of public utility (banks, offices, cinemas, etc.), gastronomic institutions, swimming-pools and water parks, halls and sport objects, hospitals and clinics, industrial institutions and halls, shops, market-halls and supermarkets, in one-family and multifamily buildings. The ventilation stations with heat recovery consist of:

* Tel.: +48 85 746 96 33; fax: +48 85 746 95 59. E-mail address: [email protected]. 0378-7788/$ – see front matter ß 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2008.04.008

 the longitudinal spiral recuperator;  two ventilators;  two filters;  electric switch-board and controller; and supplementary:      

the reheater of air; the cooler of air; bedewing cabins and humidifiers; the silencers of noise; the recirculation of air; the by-pass of heat exchanger.

Heat recovery from the exhaust air is a simple process. The main cost items are investment and running costs. As far as the running costs are concerned, they are essentially two: the cost of heating energy (here assumed the district heating system), or alternatively electrical energy for cooling equipment and the cost of electrical energy for fans of heat recovery system. Investment costs and year round savings can be evaluated during the useful life of the heat recovery system. Two methods were utilized: the present worth (PW) and the payback period. The former is a reliable evaluation procedure for alternative investments, whereas the latter is a rough one, but well understood by engineers. Longitudinal flow spiral-tube heat exchanger is made of metal sheets, which are wound at constant intervals between subsequent windings [12]. In comparison with cross-flow ventilation heat exchangers, they obtain greater efficiency e for the same value of the parameter NTU. Furthermore, longitudinal counterflow spiral recuperators have more uniform thermal field in each transverse

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Nomenclature a1, a2, a3, a4, n coefficients A heat transfer area (m2) AC area of the duct cross-section (m2) c specific heat at constant pressure (J/(kg K)) ch, cc, ce unit cost of heat energy, of cool energy, of electrical energy, respectively (zł/Wh) C ¼ mc ¼ rAC vc heat capacity flow rate (W/K) D, L, Lo diameter, length, length of the tested exchanger, respectively (m) DH hydraulic diameter of channel (m) degree-days for cooling (8C day) DDC DDH degree-days for heating (8C day) E˙ wasted energy on pressure drops in channels of the recuperator (W) j the month number K cost (zł) DK W additional costs considering pressure drops in channels of the recuperator (zł) Ld(j) the number of heating days in the j-month of the year number of exploitation days ND NTU number of transfer units Dp pressure drops (Pa) PP payback period (years) Q˙ heat flow rate (W) t temperature (8C) mean exterior temperature in the j-month of the te(j) year (8C) U overall heat transfer coefficient (W/(m2 K)) v mean velocity in channels of the longitudinal flow spiral recuperator (m/s) V ¼ AC v volumetric flow rate (m3/s) V h ¼ 3600AC v volumetric flow rate (m3/h)

Although there are many previous studies on optimum heat exchanger size [11,13–26], all of these are not directly related to the basic idea of the present study. 2. Formulation of the problem The wasted energy rate in ventilation systems with heat recovery (Figs. 1 and 2) is as follows: 1 Q˙ outflow þ ðE˙ 1 þ E˙ 2 Þ

h

(1)

or in dimensionless form: NE ¼

Q˙ outflow þ ð1=hÞðE˙ 1 þ E˙ 2 Þ : Q˙ max

(2)

For the ventilation systems without heat recovery Q˙ outflow ¼ Q˙ max , E˙ 1 ¼ E˙ 2 ¼ 0 and we obtain NE = 1. For the ventilation systems with an ideal heat recuperator Q˙ outflow ¼ 0, E˙ 1 ¼ E˙ 2 ¼ 0 and NE = 0. Moreover, for the most frequently used cross-flow recuperators could be taken Q˙ outflow  0:5Q˙ max , ð1=hÞðE˙ 1 þ E˙ 2 Þ  0:25Q˙ max so NE  0.75. The energy losses rate (1) has got to complement to keep appropriate thermal conditions in the ventilated zone. The cost rate of the wasted energy rate for the heat recovery is as follows: ch Q˙ outflow þ

ce ˙ ðE1 þ E˙ 2 Þ

h

(3)

and for the chill recovery: ce cc Q˙ outflow þ ðE˙ 1 þ E˙ 2 Þ:

h

(4)

The above functions ((3) and (4)) could be normalized to the form: Nh ¼

ch Q˙ outflow þ ðce =hÞðE˙ 1 þ E˙ 2 Þ ch Q˙ max

(5)

cc Q˙ outflow þ ðce =hÞðE˙ 1 þ E˙ 2 Þ : cc Q˙ max

(6)

or Nc ¼

Greek symbols e

h u r w

effectiveness fan efficiency wetted perimeter of the duct cross-section (m) mean density of air in ducts (kg/m3) dimensionless parameter

Subscripts 1, 2 cooled, heated air i, o inlet, outlet min, max, opt minimum, maximum, optimum outflow wasted R, W exchanger, ventilator

sections of the air stream. As a result, they are more resistant to outdropping moisture from air-cooled stream and the effect of frosting practically does not occur. In order to drain condensed water vapour effectively, they should be installed almost horizontally or vertically so that the condensate flows to the waste pipe.

Fig. 1. Scheme of heat recovery system with the longitudinal flow spiral recuperator.

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There exist many parameters in a thermo economical manner. The service life for the longitudinal flow spiral recuperators is claimed between 20 and 24 years [12]. The actual heat transfer rate Q˙ is defined as Q˙ ¼ C 1 ðt 1;i  t 1;o Þ ¼ C 2 ðt 2;o  t 2;i Þ

(13)

and maximum possible heat transfer rate Q˙ max is determined as Q˙ max ¼ C min ðt 1;i  t 2;i Þ:

(14)

The maximum possible heat transfer rate Q˙ max depends upon the smaller value of the two heat capacity flow rates C1, C2: C min ¼ minðC 1 ; C 2 Þ

(15)

and upon the difference between values of the temperature exhausted air and of the outside air temperature. In the ventilation heat recovery systems the exhausted air volume is approximately equal to the fresh air supplied volume. For the balanced counterflow heat exchangers [25]: C min ¼ C 1 ¼ C 2 ¼ C:

Fig. 2. Sankey diagram for the heat recovery system.

In temperate and cold climate countries the problems with the cold recovery usually do not occur. The inclusive construction and exploitation cost in technical lifetime of the recuperator is as follows:   ce K R þ DK W1 þ DK W2 þ 24ND ch Q˙ outflow þ ðE˙ 1 þ E˙ 2 Þ : (7)

h

The length of the heat exchanger affects the effectiveness e, which is an important performance indicator. On the other hand, the initial and operational cost of the heat exchanger mainly depends on the size of the heat exchanger. Optimum heat exchanger size for heat recovery can be determined by fixing the length assuming that the cross-section area is predetermined. Then the values of the flow velocities, the heat transfer coefficients and the overall heat transfer coefficient remain the same. The optimum length Lopt of the spiral recuperator could be determined using two opposite criteria [27,28]:  minimum heat transfer losses: Q˙ outflow ¼ Q˙ max  Q˙ ¼ ð1  eÞQ˙ max

K R þ DK W1 þ DK W2 þ 24ND ½ch Q˙ outflow þ ðce =hÞðE˙ 1 þ E˙ 2 Þ : 24N D ch Q˙ max

E˙ 1 or 2 ¼ AC v D p1 or 2 ¼ a1 or 2 AC v1þn : (8)

e¼ (9)

NTU ¼

 for energy losses: 1

(10)

 for cost of energy losses:

’¼

ce =ch

h

;

(11)

 and for the inclusive construction and exploitation costs in technical lifetime of the recuperator: K þ DKW1 þ DKW2 ce ’¼ R : þ hch 24ND ch ðE˙ 1 þ E˙ 2 Þ

NTU NTU þ 1

(19)

where NTU = UA/C. Because A = uL and DH = (4AC/u) we obtain

where dimensionless parameter w takes values:

’¼ ; h

(18)

Taking into consideration balanced counterflow heat exchangers, the effectiveness e could be described by the formula [25]:

Let us define the general function as þ ’ðE˙ 1 þ E˙ 2 Þ Q˙ N ¼ outflow Q˙ max

(17)

 minimum pressure drops in the channels of the recuperator D p1 or 2 ¼ a1 or 2 vn which induce energy losses:

or in dimensionless form: Nc ¼

(16)

(20)

Taking into consideration the above equations ((17)–(20)) the general function N (Eq. (9)) could be transformed into the sum of two components NDT and NDp multiplied by the coefficient w as follows: N ¼ N DT þ ’ N D p

(21)

where N DT ¼

(12)

If we consider energy losses, the parameter w takes values ranging from 1.3 to 2.5 practically. In case of cost of energy losses the parameter w is ranging from 3 to 5 and for the inclusive construction and exploitation costs from 102 to 104.

4U L: DH vrc

1 1 Q˙ outflow ¼ ¼1e ¼ NTU þ 1 ð4U=ðDH vrcÞÞL þ 1 Q˙ max

(22)

ða1 þ a2 Þvn L E˙ 1 þ E˙ 2 ¼ ˙ c rðt1;i  t 2;i Þ Lo Qmax

(23)

and ND p ¼

where a1  a2, n are determined experimentally (Fig. 3) for the tested longitudinal flow spiral recuperator. The effectiveness e was

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where U is calculated from Eq. (26). It is possible to obtain Lopt  0 for very great values of the parameter w. Then the recuperator is needless. From condition: Lopt > 0

(29)

we find that 4ULo ðt 1;i  t 2;i Þ >1 DH ’ða1 þ a2 Þv1þn

(30)

and N min < 1

Fig. 3. Pressure drop Dp (Pa) versus the mean velocity v (m/s) in channels of the tested longitudinal flow spiral recuperator type WS.

(31)

If we put an arbitrary taken Lopt into Eq. (27), we can compute the velocity corresponding to the optimal length of recuperator for the considered parameter w values. The payback period value PP is calculated for the selected city in Poland as the function of the flow velocity through the longitudinal flow spiral recuperator as follows: K R þ DK W1 þ DK W2 : K 1  DK W

estimated as linear function of the mean velocity in channels of the spiral recuperator (Fig. 4):

PP ¼

e ¼ a3  a4 v:

The saved value of the heat energy within a year is described by

(24)

K 1 ¼ 24ecrVðcc DDC þ ch DDH Þ

From Eq. (22) we obtain 1e¼

(33)

and for the buildings without cooling systems

1 ; ð4U=ðDH vrcÞÞL þ 1

(25)

hence U¼

(32)

K 1 ¼ 24ecrVch DDH

(34)

or

DH vrc e DH vrc a3  a4 v : ¼ 4 4 1  ða3  a4 vÞ 1e

(26)

K 1 ¼ 24crAC ða3  a4 vÞvch

12 X ðt 1;i  t e ð jÞÞ Ldð jÞ:

(35)

j¼1

The component NDT expresses the non-exchanged heat in the recuperator. The component NDp expresses the electrical energy losses, which are induced by pressure drops in channels of the recuperator. The general function N(L) reaches its extreme value, if an equation (@N(L)/@L) = 0 is satisfied. Hence the optimum length of recuperator is sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! DH Lo ðt 1;i  t 2;i Þ DH v  Lopt ¼ rc (27) 4U 4U ’ða1 þ a2 Þvn1 and N min ¼ NðLopt Þ ¼ 1 

The additional exploitation costs within a year DKW induced by pressure drops in channels of the recuperator is described by

DK W ¼ 24 ¼ 24

1

 !2 1þn 0:5

DH ’ða1 þ a2 Þv 4ULo ðt 1;i  t 2;i Þ

h

ce

h

j¼1

ða1 þ a2 ÞAC v1þn

12 X Ldð jÞ

(36)

j¼1

and Eq. (32) takes the form: PP ¼



12 X ce ˙ ðE1 þ E˙ 2 Þ Ldð jÞ

K R þ DK W1 þ DK W2

0

1:

B C P12 C 24AC vB @crða3  a4 vÞch j¼1 ðt 1;i  t e ð jÞÞ Ldð jÞ A P 12 n  ðce =hÞða1 þ a2 Þv j¼1 Ldð jÞ

(28)

We find the heat recovery in individual months or days of the year advisable if the denominator in (37) is positive. Then we obtain crða3  a4 vÞch ðt 1;i  t e ð jÞÞ >

ce

h

ða1 þ a2 Þvn

0

(37 )

or t 1;i  t e ð jÞ >

ce

ða1 þ a2 Þvn

hch crða3  a4 vÞ

:

(38)

This borderline temperature condition limits the advisability of heat recovery. 3. Results and discussion Fig. 4. Efficiency e versus the mean velocity v (m/s) in channels of the tested longitudinal flow spiral recuperator.

The data assumed for computation of the longitudinal flow spiral recuperators were as follows: a1 = a2 = 65.048, a3 = 0.9965,

M. Adamski / Energy and Buildings 40 (2008) 1883–1888

Fig. 5. Relative variation of the investment and exploitation costs N(L)/N(Lopt) versus the dimensionless length of the recuperator L* = L/Lopt for w = (ce/cc)/h.

a4 = 0.0372, n = 1.3642, ce = 0.3747  103 zł/Wh, ch = 0.1070  103 zł/Wh, temperature exhausted air t1,i = 20 8C, c = 1011 J/ (kg K), r = 1.252 kg/m3. The degree-days for heating DDH, the number of heating days during the j-month of the year Ld(j) and mean exterior temperature te(j) were assumed for Warsaw climatic data in accordance with polish norm [29]. The tested exchanger has constant length Lo = 1.35 m. Taking into consideration the thickness of the aluminium walls 0.00015 m, the width of the channels 0.003 m and the diameter of the poor centre 0.05 m, the areas of the duct cross-section AC have been calculated as follows from condition: AC ¼

p D2  0:052 0:003  0:00015 2

4

0:003

¼ 0:373ðD2  0:0025Þ:

(39)

1887

Fig. 7. The calculated optimum outside diameters D (mm) of the spiral recuperators versus volumetric air flow rate V (m3/h).

For the external diameter D = 0.3 m of the tested longitudinal flow spiral recuperator, for example, we obtain AC = 0.0326 m2. The hydraulic diameter of the channels has been calculated using the formula: D = 2  0.003 = 0.006 m. The fan efficiency h has been computed from the following equation:

h ¼ 0:6112ðAC vÞ0:1459 :

(40)

The tested exchanger has been computed (for results see Fig. 5). Values of parameter KR/Vh (zł h/m3) for the spiral recuperators type WS are shown in Fig. 6. If we put the length Lo = 1.35 m of the tested exchanger into Eq. (27), we can compute the velocity corresponding to the optimal length of recuperator for the considered parameter (w) values. It has been computed about 2.5 m/s for the parameter w = (ce/cc)/h (minimum cost of energy losses). The calculated diameters D of recuperators correspond to volumetric flow rate for range velocities 2–3 m/s are shown in Fig. 7. The exemplary results of the computation of the payback period are shown in Fig. 8. And finally, we obtain the borderline temperature condition (38) for average, exemplary value v ¼ 3 m=s and fan efficiency h = 0.5 as follows: 0:3747 0:5  0:1070 ð65:048 þ 65:048Þ31:3642  1011  1:252ð0:9965  0:0372  3Þ

t 1;i  t e ð jÞ >

¼ 3:6  C:

Fig. 6. Values of parameter KR/Vh (zł h/m3) for the spiral recuperators type WS.

(41)

Fig. 8. Payback period versus the flow velocity in channels longitudinal flow spiral recuperators for heat recovery (climatic data: city Warszawa).

1888

M. Adamski / Energy and Buildings 40 (2008) 1883–1888

When the temperatures difference t1,i  te(j) is greater than 8 8C, the heating system of the buildings are utilized. Then the heat recovery systems are always favourable. 4. Conclusions The aim of heat recovery ventilation is to provide fresh air in the way in which the thermal comfort as well as energy saving are maintained, using a recuperator with heat recovery from removed air. In particular, heat recovery should be used in offices, gastronomic institutions, and industrial institutions. For the sake of calculations were assumed current prices of energy and cost of the longitudinal flow spiral recuperator. The length of the heat exchanger affects the effectiveness, which is an important performance indicator. On the other hand, the initial and operational cost of the heat exchanger mainly depends on the size of the heat exchanger itself. The effectiveness– NTU method is a simple method and is used together with the economic parameter method based on the general function N for the optimization task. Optimization of heat recuperator size for heat recovery applications is extremely significant in order to get maximum savings from these systems. Payback period is the function of flow velocity through longitudinal flow spiral recuperators. It takes minimum values for velocity in channels of the spiral recuperators about speed 3.5 m/s in all results of calculations. Ventilation system with spiral recuperators refunds the capital expenditure within 2 or 3 years. If the heating system of the buildings are utilized, then the heat recovery systems are always favourable. Acknowledgement This study has been made within the frame of the Project No. W/ IIS´/21/06. References [1] Iowa Energy Center 1992 Annual Report, IEC, Ames, IA, 1992. [2] H. Tommerup, S. Svendsen, Energy savings in Danish residential building stock, Energy and Buildings 38 (2006) 618–626. [3] K.L. Bowlen, Energy recovery from exhaust air, ASHRAE Journal (1974) 49–56. [4] ASHRAE, Air-to-air energy recovery, in: ASHRAE Systems and Equipment Handbook, 1992 (Chapter 44). [5] D.A. Reay, Heat Recovery Systems, Spon, London, 1979. [6] G. Brooks, D.A. Reay, Comparative merits of heat recovery equipment, Heat Recovery Systems (1982) 31–36.

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