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Internally insulated pipes for district-cooling systems
AppliedEnergy12(1982)99-115
INTERNALLY INSULATED PIPES FOR DISTRICTCOOLING S Y S T E M S
S. D. PROBERT,C. M. YEUNG and C. Y. CHU
School of Mechanical Engineering, Cranfield Institute of Technology, Cranfield, Bedford MK43 OAL (Great Britain)
SUMMARY
A method is presented whereby, for any set of prescribed conditions, an optimal thickness of a thermally insulating internal lining may be determined for pipes to be used for the conveyance of chilled water. The optimum investigated in this paper corresponds with the minimum total rate of energy dissipation costs as a result of refrigeration and pumping. The overall optimal design cannot be decided at this juncture without a knowledge of such unknowns as the capital cost of internally lining the pipe.
NOMENCLATURE
a, b a', b'
Cp D1, D 2
d
Coefficients indicating unit costs for refrigeration and pumping energy, respectively (arbitrary financial units per Ws expended). Effective cost of energy per Ws supplied respectively to the refrigerator and the pump, making due allowance that some of this energy reappears as heat in the flowing liquid (arbitrary financial units per Ws expended). See eqns (12) and (13). Specific heat of the considered pumped chilled water (J kg- 1 K - t). Internal diameters respectively of the considered flow channel and the structurally strong outer member of the pipeline (e.g. conventionally a metal pipe) (m). Thickness of the structurally strong outer member of the pipeline (m). d,~
Ehf,/~vd
2
=t
Steady-state rates of heat transfer into the flowing chilled water, and viscous dissipation within the water, respectively per unit length of pipeline (W m - 1). 99
Applied Energy 0306-2619/82/0012-0099/$02-75 Printed in Great Britain
© Applied Science Publishers Ltd, England, 1982
100 E;ot
S. D. PROBERT, C. M. YEUNG, C. Y. CHU
Steady-state rate of total energy expended per unit length of pipeline ( W ro - 1).
e
F(T,)
f hi,h2 he, hr ki kt L Nu
JDexp Pr
Equivalent roughness of the chilled water/insulating lining wetted interface--see eqn. (8) (m). Function of the temperature-dependent properties of the flowing chilled water. Dimensionless friction factor (0 < f ~ 1 (usually)). Average coefficients for the heat transfers respectively to the flowing chilled water from the insulant lining and to the effective outside surface of the pipeline from the ambient air (W m- 2 K - 1). Natural convection/conduction and radiation heat transfer coefficients respectively at the outside surface of the pipe ( W m - 2 K-~). Mean effective thermal conductivity of the insulant lining applied uniformly within the pipe (W m- 1 K - ~). Thermal conductivity of the chilled water (Wm-1 K - ~). Length of the considered, straight horizontal pipeline (m). Local Nusselt number for the heat flow to the moving chilled water from the pipe's insulating lining
I
==_hiD1
Steady-state total rate of financial expenditure resulting from the net energy loss (arbitrary financial units per metre of pipeline). Prandtl number for the flowing chilled water
=_C,~,] k, J Re
Reynolds number for the chilled water flowing through the pipeline
Too and T~ Temperatures respectively of the ambient air surrounding the pipeline and of the flowing chilled water (K). Temperature at the outside surface of the pipeline (K). L Radial thickness of the insulant liner t
f,
Mean speed of the chilled water flowing through the pipeline (m s - ~). Steady-state volumetric flow rate of the chilled water passing through the pipe (m 3 s- 1). Thermal expansion coefficient for the flowing chilled water (K- 1).
INTERNALLY INSULATED PIPES FOR DISTRICT-COOLING SYSTEMS
/h Pt
101
Proportion of viscous dissipation which is converted into heat in the flowing chilled water (0 < V< 1). Emissivity of the outside surface of the pipe (dimensionless). Overall efficiency of the pump and driver set (0 < r/p < 1). Overall performance index of compressor-chiller system. Dynamic viscosity of the flowing chilled water (N s m- 2). Density of the chilled water (kg m- 3).
Suffixes O(3
l opt
Of the ambient air. Of the chilled water. Optimal value of the parameter, corresponding to which the least total rate of financial expenditure occurs. DISTRICT COOLING
With the development of large-scale housing schemes, commercial complexes and airport facilities, district-cooling systems are becoming increasingly popular in those countries where air conditioning is deemed necessary. These systems employ centralised refrigeration plants. Such a centralised plant occupies only a relatively small amount of space and this very compactness can facilitate its operation and routine maintenance compared with personnel having to attend to a large number of air-conditioning plants, each serving an individual building. Large capacity-and hence more effficient--refrigeration machines can be used, and also advantage can be taken of the diversity in magnitude and phase of cooling loads that have to be met for different buildings. Consequently, less total plant capacity, and so smaller overall capital costs, are involved. To enhance still further the economic attractiveness of district-heating/cooling schemes, a developing trend is to combine the distribution systems--for example, chilled water for air conditioning would be conveyed in parallel conduits with those for high temperature water for heating. The combined system serving Hartford, Connecticut, USA, was the pioneer installation of this type. Consequently, proper insulation of the pipelines is essential. INTERNALLY INSULATED PIPELINES
For both district-cooling and district-heating systems, insulated pipeline costs represent significant fractions of the overall capital investments. Thus it is highly desirable that the design of each pipeline should be optimised. For example, the insulant thickness applied (whether externally or internally) to any pipe is dictated by, amongst several other parameters, the volumetric rate of flow of the nonambient temperature fluid being pumped through the pipeline (Probert et al.5).
102
s.D.
PROBERT, C. M. YEUNG, C. Y. CHU
But this is often ignored ! For large bore pipelines, it has been suggested that internal linings possess several advantages (e.g. fewer differential contraction/expansion loops being necessary) over the traditional external linings (Probert et al.5). However, as a preliminary stage in deciding which, for a prescribed set of applied conditions, is the most energy-conscious design for an internally insulated pipeline, an optimisation analysis concerning energy running costs needs to be undertaken.
ENERGY FLOWS
Consider a chilled liquid, at a temperature T~ (which is less than the temperature, T~, of the ambient environment) being pumped through a straight horizontal pipeline of length L and constant external diameter (D 2 + 2d)--see Fig. 1. The uniform wall thickness of the cylindrical pipe is d. The thicker the internally applied insulant for such a pipe, i.e. the greater the value of (D 2 - D I ) / 2 , the smaller will be
~ i~
~ i, _L_d
L
~
INTERNAL INSULANT LINING
A
'T
FLOWING CHILLED LIQUID AT TEMPERATURE TI
.-
•I
AMBIENT
Eht
ENVIRONMENT AT TEMPERATURE
T=
VIEW A - A
Fig. 1. Schematic sections through an internally-insulatedpipe with chilled liquid flowing. For the presented analysis,2d .~ D2 - Dt . the steady-state rate of heat leakage into the chilled liquid (/~,t per unit length of pipeline) whereas the steady-state rate of viscous dissipation (J~vdper unit length of pipeline) will become greater due to the narrower effective bore, D 1, for the flow. Neither of these energy fluxes is welcomed. Their conflicting trends lead to the existence of an optimal thickness (D 2 - D1o~,)/2 for the internal insulation liner corresponding to the minimum steady-state total rate of energy dissipation, Etot, per unit length of pipeline. To maintain the low temperature of the chilled liquid, and so compensate for heat gains, a refrigeration plant will be required. Also, an external pump is usually necessary to raise the pressure of the liquid to overcome the viscous dissipation within the chilled liquid. Unfortunately, some of this viscous loss is converted into heat within the flowing chilled liquid and thereby causes embarrassment because it
INTERNALLY INSULATED PIPES FOR DISTRICT-COOLING SYSTEMS
103
will involve a further expenditure of refrigerator power to compensate for it. Thus, the total rate of energy expenditure, Etot, per unit length of pipeline, becomes: • , _ (Rate of refrigerator power expended" / •Rate of pumping'~ Et°t - \ to compensate for heat gains J + \ power expended ]
(1)
the terms on the right-hand side each being per unit length of pipeline. The first term on the right-hand side of eqn. (1) equals (/~h~+ ~Evd)/r/,, where r/r is the overall performance index of the refrigeration plant and ~ the fraction of the viscous dissipation which is converted into heat in the liquid. The other term on the righthand side of this equation equals Eva/~/p, where % is the efficiency of the pump. Therefore:
E 'o, =-1
+
+
(2)
STEADY-STATE RADIAL HEAT LEAK INTO THE PIPELINE
This heat gain by the chilled liquid per unit length of pipeline is given (see Simonson 9) by: Eh, = - 2
2n(Too - Ti)
1
(3)
assuming that the wall thickness, d, of the pipe is negligible compared with D 2. The internal heat transfer coefficient, h I (at the liquid/insulant wetted interface) for fully developed turbulent flow, neglecting entrance effects, can be obtained using the Colburn 2 equation: Nu -- 0.023 Re °s Pr °33
(4)
which can be applied when 0.7 < Pr < 120 and Re > 104. With appropriate substitutions and simplifications, it can be shown (Probert et al. 5) that: h~ = 0.0278 I?°'SD~ - l"SF(Tt)
(5)
where '1"[11) ~ ' ' " =Pt0-8L0'66,'-'0"33 Kt ~p #t-0-47 • Substitution of h 1 from eqn. (5) into eqn. (3) reveals that:
/~ht--{71.8D°'S
2n(To~ - Tt) +lln(Da~
k,
\01/
(6)
+
2 }
104
s . D . PROBERT, C. M. YEUNG, C. Y. CHU
The temperature change of the flowing liquid along the length of the pipeline is very small (Probert et al. 5) so that Tt in this equation can be regarded as constant. Equation (6) may not be the sole heat transfer consideration, e.g. in present circumstances it is desirable to check that condensation does not occur on the external surface of the pipeline--see Appendix 1.
VISCOUS DISSIPATION IN THE COLD LIQUID
For the flow of a liquid through a straight unobstructed horizontal pipeline, the rate of viscous losses per unit length of the pipeline, as derived from the DarcyWeisbach equation (see Jeppson 4 and Schlichting a) can be given by: 8fp,~ "a
E~d- n2O~
(7)
The friction factor,f, for turbulent rough flows (Re > 4 x l0 3) may be deduced (see Schlichting s) from Nikuradse's modified version of von Kfirmfin's friction factor equation, namely:
.1.+0.8691n where e is the equivalent roughness of the surface over which the chilled liquid flows. So, substituting for f into eqn. (7) reveals that: E~d = 8 [PI?3"~'l'139 + 0"869 In
D~-s
(9)
ENERGY-CONSCIOUS DESIGN
Normally it is the financial expenditure which decides the choice of design. Ifa and b are the unit costs (i.e. financial costs per Ws) for energy supplied to the refrigeration plant and the pump set, respectively, then the total rate of financial expenditure Pexp, per unit length of pipeline on energy running costs can be seen from eqn. (2) to be: pexp = a ~r
(Eh, + ~Eo~) + b
Eo~
(10)
~p
By rearrangement this becomes: eexp
a ( b +a~'~ = ~r JEh, "~F-~vd \r/t, r/, /
(11)
INTERNALLY INSULATED PIPES FOR DISTRICT-COOLING SYSTEMS
105
To simplify, let us define a t =
b'
E
a
(12)
b =
__
rip
ay +
- -
rl r
b =
- -
rip
+
(13)
a' 7
So, we can express eqn. (1 l) in the more compact form: • Pexp =
a ' Eht + b' Eva "
(14)
"
Substituting the expressions for/~ht and/~d from eqns (3) and (9), respectively gives:
• 2na'(T~ - T~) P~P=J'71"8D~'8 + 1 1n{D2~ + ( 2 )} (12°'SF(T,) k i \Dx) D~+8b'{P'(/3"]~l.139+O.8691n(~-)} -2 D~-5
(15)
So, in order to deduce the geometry appropriate to the minimum rate of financial expenditure (due solely to the running costs incurred as a result of energy losses) for chosen values of I? and DE, the deduced value of dPexp/dD 1 would be set equal to zero. The corresponding value of D 1 is the optimal diameter of the flow channel provided that d2Pexp/dD 2 > 0. Applying this procedure to eqn. (15) reveals that the optimal condition is:
b'Pt p3
--,-~,71"8D°~" 8, 1 / D 2 \ 2 -]2 f po.sFCT. ~ + -ki ln iDa°") -+ D2h21 5+
1.738
,, 9+08691n( ) 57'41D°:"8' } D5 I?O8F(T, ) 'o,,
)
(16)
This equation is solved numerically by computer. MINIMISATION OF ENERGY RUNNING COSTS FOR THE CHILLED WATER FLOW
It has been shown (Probert et al. 6) that, in general, 7 can be expressed by: y=l -ill
(17)
106
S. D. PROBERT, C. M. YEUNG, C. Y. CHU
Consider the chilled water flow at a temperature, Tz, of 5 °C. Under this condition: f l = l - 4 x 1 0 - S K -1 T~ = 278 K Thus, from eqn. (17): 7 = 0.9961 This, almost unity value for y, indicates that the Joule-Kelvin effect in this instance is negligible. The ratio b'/a' can be obtained by dividing b' from eqn. (13) by a' from eqn. (12), i.e.
a'
+~
(18)
Typical values of qp, b/a and r/r are given in Appendices 2, 3 and 4, respectively. Consider as an example, the configuration in which an electrically driven compressor-chiller system and centrifugal pump are used for cooling and pumping the water, respectively. In the range of hydraulic horsepower between 100 and 500, it is reasonable to assume an average overall pumping efficiency, qp, of 0.75 (see Appendix 2). With an electrically-driven centrifugal compressor-chiller system at normal operating conditions for air-conditioning, 7, can be taken as 4.25 (see Appendix 4). As electricity can be used to drive both the compressor and the water pump, b/a would then equal unity. So, substituting these values into eqn. (18) reveals: b' -a -' = 6 . 7 For other types of refrigeration machines, pumps and drivers, the appropriate values of the ratio of b'/a' can be deduced in a similar way.
NUMERICAL PREDICTIONS
Let us consider a typical district-cooling mains pipeline having D 2 = 0 . 4 m , conveying 5 °C water (for which p, = 1000 kg m - a, Cp = 4205 J k g - 1 K - 1, kl = 0 . 5 7 8 W m - X K -x and p t = 1.528 x 1 0 - 3 N s m -2) at a steady rate o f 0 . 2 m 3 s - t . The heat transfer coefficient for the outside surface of the pipe is assumed to be 1 0 W m - 2 K - x. The insulant liner is typically taken to have a mean effective thermal conductivity, k~, of 0.035 W m - 1 K - t and it is assumed that it presents to the chilled water a smooth surface of equivalent roughness e = 2.1 ;an (which can be achieved readily with plastic linings). The ambient temperature, Too, is taken to be 25 °C.
INTERNALLY INSULATED PIPES FOR DISTRICT-COOLING SYSTEMS
~?0
~
107
~
,
~
\
\
x
Eht
xx
022
02z.
026 028 030 032 03l, 036 INTERNAL[~AHETEROF INSULANTLINING D,.Ira I
038
Fig. 2. These curves are graphical representations ofeqn. (! 5) for Pc~, (in arbitrary units per metre) and of its components a'Eht and b'~:,a for chilled water flows with a' and b' in arbitrary financial units. For these predictions, it is assumed that F ' = 0 . 2 m 3 s -1, h 2 = 1 0 W m - 2 K -1, T I = 5 ° C , T~0=25°C, D 2 = 0.4 m,/q = 0.035 W m - t K - s, e = 2. l/Jm and b'a' = 1. It can be seen that Dt optchanges successively from 0.318m to 0.344m, 0.354 m and 0.358m as b' increases from I to 3, 5 and 7, respectively, a|| in arbitrary financial units per Ws expended.
The graphs in Fig. 2 show values for the total financial c o s t , Pexp, of the energy expended and its corresponding costs of heat extraction, a'Eh,, and viscous dissipation, b'Eva, components, all per metre length of the pipeline. Four representative cases are illustrated with the value of a' maintained constant at unity and b' increased successively from unity to 3, 5 or 7, all in arbitrary financial units per Ws expended. It can be seen that, in each case, there exists a clearly identifiable optimal diameter, Dlo~,, which increases with the value of b'/a' as expected. Corresponding predictions have been performed to obtain DI°~, for various flow rates, 17, for several values of the pipe's internal diameter, D2, with the ratio b'/a' assumed to be unity for the purpose of this investigation. The results are presented in Fig. 3. It can be seen that incremental changes in Dx.~ become smaller for unit changes in D 2 as D 2 increases for a particular flow rate, I?, resulting in thicker insulant linings (i.e. greater values of/opt)" The rates of financial expenditure, Peep, for different flow rates, I7, and at different optimal insulant thicknesses are presented in Fig. 4. Obviously, Pc~p decreases with increasing topt. However, as seen from Fig. 4, the savings achieved by increasing/opt by an increment will become smaller at larger values of/opt. However, in practice, the
E ~
(5
~=O,m~sec' v=o 2m)sec' =0 1mssec
z V : 0 O Z m3
sec~
~'= 0002mlsec1 /
01
0
02
03 0~ 0S 06 ~TSIDEDIAMETEROF NSULAt~TD~
07
0B
,(m)
Fig. 3. A family of design curves for selecting D~,,p, for various values of the pipe's internal diameter (D2). It is assumed that k / = 0 . 0 3 5 W m - 1 K -~, h 2 = 1 0 W - 2 K -1, e = 2 . 1 / t m , T~=5°C, To~ =25°C, b'/a' = 1 and d<~ (D 2 - Dlop,)/2.
S0
OOS
i,0 OO3
i '°
!"
i
OO2
z 001 • I00
Z00
OPTIMAL THICKNESSOF INTERNALINSULANT
ml
300
LININGtopt .{mmI
Fig. 4. This Figure should be read in conjunction with Fig. 3. For.a particular pipe diameter, D2, and flow rate, V, of chilled water, Dlopt is first read from Fig. 3. From this value of Dlopt, to~ = (D 2 - Dlop,)/2 can be calculated, and hence from Fig 4 the corresponding value. of PezP • • , determined. It can be seen that the thicker the lining chosen, for a given flow rate, the lower will be P., p- Also , P , p changes . dramatically at . low . values of to_ so that a small increase of to_t In this region results m a considerable reduction of Pexp"
/
• ~'o
2'o
;o
~oo
TEMPERATUREOF AMBIENT A~R T~ * l'C i
Fig. 5. The optimal thickness, /opt, of insulant is plotted against temperature, T~, of the ambient air. The conditions applying are I;"= 0.2m3s -1, D 2 = 0 . 4 m , k ~ = 0 . 0 3 5 W m - l K - l , e=2.1y.m, h 2 = 1 0 W m - 2 K -~, b'/a'=l and TI = 5°C.
INTERNALLY INSULATED PIPES FOR DISTRICT-COOLING SYSTEMS
109
E
~ 005(
i0~'
00~0
0035
_'o0~
0'02
0!0]
0!0~
0!05
0'06
0!07
0'08
0'09
0!10
THERMAL CONDUCTIVITY OF INTERNAL INSULANTLINING.k~, (WmIKI)
Fig. 6.
The variation of topt with changes in k~ is shown, the other applied conditions being as for Fig. 5, except that T~ = 25 °C.
00(
)
~ 00~
O0?
OO2 Fig. 7.
I
2
3
The variation of top' with changes in b'/a', the other applied conditions being as for Fig. 5, except that T o is chosen to be 25°C.
110
s.D.
"~ 0.0~
PROBERT, C. M. YEUNG, C. Y. CHU
~
.....
BEHAVIOUROf THEORETICAL
~ O.o;
~ o~
10
15
20
25
TEMPERAIURE OF WATER, Tt , ('C)
Fig. 8.
The variation of top' with changes in Tt, the other applied conditions being as for Fig. 5, except that T o is chosen as fixed at 25 °C.
required increase in capital expenditure for thicker liners needs also to be accounted for in a judicious choice of top,. A typical sensitivity analysis for /opt t o changes of the independent variables (based on the representative conditions of l>=0.2m3s -1, D 2 = 0 . 4 m , ki= 0 . 0 3 5 W m - I K -1, e = 2 . 1 p m , h 2 = 1 0 W m - 2 K -l, b'/a'=l, TI=5°C and Too = 25 °C), has been performed and the results are presented in Figs 5 to 9. The sensitivity of the optimal thickness,/opt, of the insulant lining to changes in any of its independent variables is defined as the ratio of the percentage change in/opt to the corresponding percentage change in the independent variable. From the presented analysis it can be deduced that the sensitivities of topt to changes of (/, To~, kl, b'/a', T t
00~2I NOTE topt FOR ZERO ROUrHNESSIS Of THEORETICAL SIrNIFIEANEE ONLY
00~0
0O38
0 O36
00]~
0001
0028 0
Fig. 9.
!
b
~0 2O EO~UIVALENY ROUSHNESS OF INSULATING LINING WETTED SURFACE, e, { ~O~m}
The variation of/opt with changes in e, the other applied conditions being as for Fig. 5, except that Too is chosen to be equal to 25 °C.
INTERNALLY INSULATED PIPES FOR DISTRICT-COOLING SYSTEMS
111
and e are - 1.981, +0.468, +0.1993, -0-1194, -0-0915, and -0.0041, respectively over the ranges of variables considered. The parameter, toot, is practically unaffected by changes in h 2.
CONCLUSIONS
An optimal thickness of the applied internal insulant lining always exists for which the minimum rate of financial expenditure upon energy occurs when a fluid at a temperature other than ambient is pumped through a pipeline. For a given flow rate of the liquid, a bigger diameter pipeline will result in a thicker optimal insulant liner and smaller total energy losses. However, larger pipelines and thicker insulation layers require greater capital investments and so, in practice, a compromise choice would invariably be made. For chilled water flows in an internally insulated pipeline of fixed outside diameter (D 2 + 2d), under the conditions studied, too t is most dependent upon the water flow rate, f', and then in sequence of decreasing sensitivity upon (i) the ambient temperature (see Fig. 5), (ii) the effective thermal conductivity of the applied insulant liner (see Fig. 6), (iii) the ratio of effective unit costs of energy used for pumping and for chilling the water (see Fig. 7), (iv) the temperature of the pumped water (see Fig. 8), and (v) the equivalent surface roughness of the flow channel (see Fig. 9). For a particular value of D 2, the greater the flow rate, the bigger will be the effective bore, D~o,. Each insulated pipe should preferably be used at its specified volumetric throughput so that energy losses are minimised. (This applies irrespective of whether it is internally or externally insulated.) In appraising the sensitivity of/opt to changes of each variable, the limits of the variables need to be considered. For example, e could increase from 1-5/an for drawn brass tubing to 2000 #m for concrete tubing--i.e, more than a thousand-fold rise. (Such surfaces might be used as thin sleeves to protect the thick insulant liners.) Thus although top t exhibits such a low sensitivity to changes in the surface roughness of the flow channel, such large variations among the commercially available linings might make surface roughness an influential parameter with respect to the design. The temperature, T~, of the chilled water is unlikely to vary by more than 2 °C in a well-insulated pipeline. Thus, although changes in both T~ and T o (the temperature of the ambient air) affect the radial heat leak, T~ is the parameter more likely to be susceptible to changes and so the more influential variable. The effective thermal conductivity, k i, of the applied insulant is an important factor affecting the rate of heat gain, but/opt is relatively insensitive to changes in k i. Nevertheless, it is important to design the insulant lining properly; the effective thermal conductivity of the insulant increasing significantly if moisture penetrates into it.
112
S. D. PROBERT, C. M. YEUNG, C. Y. CHU
When determining the optimal geometry of the internally-insulated pipe, it is the ratio b'/a', rather than the individual unit costs, a or b, of the fuels used for chilling and pumping the water that is more important. It should also be noted that the ratio b/a (and hence b'/a') is less susceptible (as indicated by percentage changes) to inflation than are either unit fuel costs a or b alone. So, the deductions in terms of b/a are likely to have significance for a longer period, and hence the nondimensional approach has been used in this analysis. The pipeline's external heat transfer coefficient has little effect on the value of topt because the rate of heat gain is dictated primarily by the thermal conductivity of the insulant, ki. The presented analysis has been restricted to energy 'running costs'. It could, however, be expanded to include the energy costs of the pipe and insulant (as would be involved in its materials, manufacture and installation). Thereby, it is feasible to extend the present approach to predict a more comprehensive energy conscious design, but further cost data for lining processes would be needed to permit this to Occur.
APPENDIX 1 : PREVENTION OF CONDENSATION ON THE EXTERNAL SURFACES OF PIPELINES CONVEYING CHILLED LIQUIDS
If the temperature of the external surface drops below the dew point of the ambient air, condensation will occur on that surface. This is undesirable from a corrosion point of view and could irreversibly damage components of the system. The temperature difference between the pipeline's outer surface and the ambient air depends on the amount of heat that is transmitted to it through the air. For horizontal pipes in still air, the total heat absorbed by a unit length of pipe is given (IHVE Guide 3) by:
Eh, = nD2hz(Ts - Too)
(19)
where h 2 is the overall outside surface heat transfer coefficient, which involves both a radiative and combined convective/conductive component, namely h, and hc, respectively. Thus: hE = hr q- hc (20) where: ( Ts - Too']°'2s hc _ 1 . 3 2 \ - ~ -]
(21)
for combined natural convection and conduction through the air, and h, = 5.67 x 10-8e(T 2 + T2)(T~ + Too) where e is the emissivity of pipe's outside surface.
(22)
INTERNALLY INSULATED PIPES FOR DISTRICT-COOLING SYSTEMS
113
The thickness o f insulation, t, to avoid c o n d e n s a t i o n in an internally insulated large d i a m e t e r pipe can be p r e d i c t e d to a r e a s o n a b l e accuracy by assuming T Stakes a value o f l °C higher t h a n dew p o i n t in a m b i e n t air. Then: (
/~h, T ~ ) } _
(23)
In general, for a h o r i z o n t a l pipe in still air, the surface heat transfer coefficient is between 5 a n d 1 0 W m -2 K -1 ( I H V E Guide3). So, t h r o u g h o u t the presented analysis, a value o f 1 0 W m z K - 1 has been assumed. It can be seen f r o m Fig. 10 that, except for very thin insulant liners, c o n d e n s a t i o n is unlikely to occur in general with the thicknesses o f insulant liner r e c o m m e n d e d by the o p t i m i s i n g analysis presented in the m a i n text. In o b t a i n i n g h c f r o m eqn. (21), c o n v e c t i o n u n d e r n a t u r a l circulation has been assumed. However, forced circulation (due to a d r a u g h t ) will reduce the possibility o f m o i s t u r e c o n d e n s a t i o n on cold surfaces a n d thus help to avoid the p r o b l e m .
V=02 mJs~cI ~=o.02m3sec 1 ~=O002n?se( ~
100 200 )90 OPTIMAL THICKNESSOF rNTERNALINSULANTLJNING,topt,lmm)
Fig. 10. The temperature difference (T~ - T~) between the ambient air and the outside surface of the pipe is plotted against the insulant's optimal thickness, top' for various flow rates of the chilled water at 5 °C. Note that the value of (To~- Ts) rises dramatically for low values of topt, which could lead to condensation on the outside surface of the pipeline. The other applied conditions are as for Fig. 5 except that T~ is chosen to be equal to 25 °C.
114
s . D . PROBERT, C. M. YEUNG, C. Y. CHU APPENDIX
2
TABLE 1 OVERALL EFFICIENCIESOF COMMONLYAVAILABLETYPES OF PUMPS (Data compiled from the Pumping Manual ( A n o n ) ) ) The efficiency of each pump is determined by its design, pumping speed and operating conditions
Type
Hydraulic horsepower
Approximate overall efficiency rlp (per cent)
Electric, motor-driven centrifugal pump
10 --* 100 100 ~ 500
55 ~ 70 70 --, 80
Diesel-driven centrifugal pump
10 --* 100 100 ~ 500
30 ~ 45 45 ~ 50
Direct acting steam pump
10 ~ 100 100 --, 500
20 --, 30 30 --, 35
Turbine-driven centrifugal pump
10 --, 100 100 --*500
10 -, 30 30 ~ 40
APPENDIX 3 TABLE 2 COSTS OF VARIOUSENERGYSUPPLIES Average data for energy supplies at demand point in the UK: July 1980. (Prices vary with delivery distance, amount of that fuel consumed regularly, and for coal and wood with their calorific values)
Conventional commercial unit of supply
Energy form
Electricity Fuel oil (3500 s) Natural gas Coal Wood
APPENDIX
kWh Gallon Commercial Therm Ton Ton
4:
Net available heat (Therms/unit) 0.0341 1.68 ~ 0.92 256 150
Average retail price (£/MWh) as at 1/7/80 24 9.8 8.8 5.9 4.8
Ratio of unit costs of electricity to other fuel 1.00 2.45 2.73 4.06 5.00
COOLING ABILITY AND POWER CONSUMPTION OF A REFRIGERATOR
The cooling powers achieved by various types of refrigerator depend mainly on their coefficients of performance, which, in turn, are dictated by the operating conditions, e.g. the evaporating and condensing temperatures (see Table 3). To obtain the total power expended by a refrigeration system, the type of driver (if any) and its efficiency have to be considered. For an induction electric motor, an average efficiency of 0.85 can be taken. The performance indices of the compressor
INTERNALLY INSULATED PIPES FOR DISTRICT-COOLINGSYSTEMS
115
TABLE 3 COMPARISON OF THE PERFORMANCE INDICES OF TYPICAL EXAMPLES OF DIFFERENT TYPES OF REFRIGERATION MACHINE
The data have been evaluated for evaporator and condenser temperatures of 3 °C and 35 °C, respectively,and have been compiled from IHVE Guide Section B14, 1970.a
Type of refrigerator
Performance index = Cooling power (in k W) per k W of power input
Screw compressor Centrifugal compressor Reciprocating compressor Absorption machine
5.26 5.00 4.55 2.33
systems as stated in Table 3 should then be multiplied by this factor, 0.85, to o b t a i n the values of the overall p e r f o r m a n c e index, r/,, of the compressor-chiller system. This leads to values of 4.47, 4.25 a n d 3.87 for the chilling system with screw compressor, centrifugal compressor a n d reciprocating compressor, respectively.
ACKNOWLEDGEMENTS The a u t h o r s wish to t h a n k the Science a n d E n g i n e e r i n g Council for s u p p o r t of this project. In particular, a debt is owed to the late D r Jack Butterworth for his interest a n d guidance.
REFERENCES 1. A~ON.,Pumping Manual (6th edn). The Trade and Technical Press Ltd, Morden, Surrey, England, 1979. 2. A. P. COLBUR~,A method ofcorrelating forced convection heat transfer data and a comparison with fluid friction, Trans. Am. Inst. Chem. Engineers, 29 (1933), pp. 174-210. 3. IHVE, Institution of Heating and Ventilating Engineers, London. Guide Book C, Section B14, p. 7; Section C-3, pp. 1-7, 1970. 4. R. W. Jl~vPSON,Analysis offlow inpipe networks, Ch. 3, Ann Arbor Science, Michigan, USA, 1976. 5. S. D. PROBERT,C. Y. CHU and C. M. YEUNG,Thermal insulation lining for pipelines? 4th National Conference. District Heating Association, Torquay, England, 1981. 6. S. D. PROnERT,C. Y. CHU and C. M. YEU~G,A possible alternative approach to the thermal insulation of pipelines, Applied Energy, II (1982), pp. 15-34. 7. S. D. PROBERT,C. M. YEtmGand C. Y. CHu, Optimising the performance of internally insulated pipelines for conveying super-heatod steam, Applied Energy, in press. 8. H. SCHLICHTING,Boundary-layer Theory (7th edn). Ch. 20 (translated by J. Kestin). McGraw-Hill, New York, USA, 1976. 9. J. R. SIMOr4SON,Engineering heat transfer, p. 27. McGraw-Hill Publishing Co. Ltd, London, 1967.
INTERNALLY INSULATED PIPES FOR DISTRICTCOOLING S Y S T E M S
S. D. PROBERT,C. M. YEUNG and C. Y. CHU
School of Mechanical Engineering, Cranfield Institute of Technology, Cranfield, Bedford MK43 OAL (Great Britain)
SUMMARY
A method is presented whereby, for any set of prescribed conditions, an optimal thickness of a thermally insulating internal lining may be determined for pipes to be used for the conveyance of chilled water. The optimum investigated in this paper corresponds with the minimum total rate of energy dissipation costs as a result of refrigeration and pumping. The overall optimal design cannot be decided at this juncture without a knowledge of such unknowns as the capital cost of internally lining the pipe.
NOMENCLATURE
a, b a', b'
Cp D1, D 2
d
Coefficients indicating unit costs for refrigeration and pumping energy, respectively (arbitrary financial units per Ws expended). Effective cost of energy per Ws supplied respectively to the refrigerator and the pump, making due allowance that some of this energy reappears as heat in the flowing liquid (arbitrary financial units per Ws expended). See eqns (12) and (13). Specific heat of the considered pumped chilled water (J kg- 1 K - t). Internal diameters respectively of the considered flow channel and the structurally strong outer member of the pipeline (e.g. conventionally a metal pipe) (m). Thickness of the structurally strong outer member of the pipeline (m). d,~
Ehf,/~vd
2
=t
Steady-state rates of heat transfer into the flowing chilled water, and viscous dissipation within the water, respectively per unit length of pipeline (W m - 1). 99
Applied Energy 0306-2619/82/0012-0099/$02-75 Printed in Great Britain
© Applied Science Publishers Ltd, England, 1982
100 E;ot
S. D. PROBERT, C. M. YEUNG, C. Y. CHU
Steady-state rate of total energy expended per unit length of pipeline ( W ro - 1).
e
F(T,)
f hi,h2 he, hr ki kt L Nu
JDexp Pr
Equivalent roughness of the chilled water/insulating lining wetted interface--see eqn. (8) (m). Function of the temperature-dependent properties of the flowing chilled water. Dimensionless friction factor (0 < f ~ 1 (usually)). Average coefficients for the heat transfers respectively to the flowing chilled water from the insulant lining and to the effective outside surface of the pipeline from the ambient air (W m- 2 K - 1). Natural convection/conduction and radiation heat transfer coefficients respectively at the outside surface of the pipe ( W m - 2 K-~). Mean effective thermal conductivity of the insulant lining applied uniformly within the pipe (W m- 1 K - ~). Thermal conductivity of the chilled water (Wm-1 K - ~). Length of the considered, straight horizontal pipeline (m). Local Nusselt number for the heat flow to the moving chilled water from the pipe's insulating lining
I
==_hiD1
Steady-state total rate of financial expenditure resulting from the net energy loss (arbitrary financial units per metre of pipeline). Prandtl number for the flowing chilled water
=_C,~,] k, J Re
Reynolds number for the chilled water flowing through the pipeline
Too and T~ Temperatures respectively of the ambient air surrounding the pipeline and of the flowing chilled water (K). Temperature at the outside surface of the pipeline (K). L Radial thickness of the insulant liner t
f,
Mean speed of the chilled water flowing through the pipeline (m s - ~). Steady-state volumetric flow rate of the chilled water passing through the pipe (m 3 s- 1). Thermal expansion coefficient for the flowing chilled water (K- 1).
INTERNALLY INSULATED PIPES FOR DISTRICT-COOLING SYSTEMS
/h Pt
101
Proportion of viscous dissipation which is converted into heat in the flowing chilled water (0 < V< 1). Emissivity of the outside surface of the pipe (dimensionless). Overall efficiency of the pump and driver set (0 < r/p < 1). Overall performance index of compressor-chiller system. Dynamic viscosity of the flowing chilled water (N s m- 2). Density of the chilled water (kg m- 3).
Suffixes O(3
l opt
Of the ambient air. Of the chilled water. Optimal value of the parameter, corresponding to which the least total rate of financial expenditure occurs. DISTRICT COOLING
With the development of large-scale housing schemes, commercial complexes and airport facilities, district-cooling systems are becoming increasingly popular in those countries where air conditioning is deemed necessary. These systems employ centralised refrigeration plants. Such a centralised plant occupies only a relatively small amount of space and this very compactness can facilitate its operation and routine maintenance compared with personnel having to attend to a large number of air-conditioning plants, each serving an individual building. Large capacity-and hence more effficient--refrigeration machines can be used, and also advantage can be taken of the diversity in magnitude and phase of cooling loads that have to be met for different buildings. Consequently, less total plant capacity, and so smaller overall capital costs, are involved. To enhance still further the economic attractiveness of district-heating/cooling schemes, a developing trend is to combine the distribution systems--for example, chilled water for air conditioning would be conveyed in parallel conduits with those for high temperature water for heating. The combined system serving Hartford, Connecticut, USA, was the pioneer installation of this type. Consequently, proper insulation of the pipelines is essential. INTERNALLY INSULATED PIPELINES
For both district-cooling and district-heating systems, insulated pipeline costs represent significant fractions of the overall capital investments. Thus it is highly desirable that the design of each pipeline should be optimised. For example, the insulant thickness applied (whether externally or internally) to any pipe is dictated by, amongst several other parameters, the volumetric rate of flow of the nonambient temperature fluid being pumped through the pipeline (Probert et al.5).
102
s.D.
PROBERT, C. M. YEUNG, C. Y. CHU
But this is often ignored ! For large bore pipelines, it has been suggested that internal linings possess several advantages (e.g. fewer differential contraction/expansion loops being necessary) over the traditional external linings (Probert et al.5). However, as a preliminary stage in deciding which, for a prescribed set of applied conditions, is the most energy-conscious design for an internally insulated pipeline, an optimisation analysis concerning energy running costs needs to be undertaken.
ENERGY FLOWS
Consider a chilled liquid, at a temperature T~ (which is less than the temperature, T~, of the ambient environment) being pumped through a straight horizontal pipeline of length L and constant external diameter (D 2 + 2d)--see Fig. 1. The uniform wall thickness of the cylindrical pipe is d. The thicker the internally applied insulant for such a pipe, i.e. the greater the value of (D 2 - D I ) / 2 , the smaller will be
~ i~
~ i, _L_d
L
~
INTERNAL INSULANT LINING
A
'T
FLOWING CHILLED LIQUID AT TEMPERATURE TI
.-
•I
AMBIENT
Eht
ENVIRONMENT AT TEMPERATURE
T=
VIEW A - A
Fig. 1. Schematic sections through an internally-insulatedpipe with chilled liquid flowing. For the presented analysis,2d .~ D2 - Dt . the steady-state rate of heat leakage into the chilled liquid (/~,t per unit length of pipeline) whereas the steady-state rate of viscous dissipation (J~vdper unit length of pipeline) will become greater due to the narrower effective bore, D 1, for the flow. Neither of these energy fluxes is welcomed. Their conflicting trends lead to the existence of an optimal thickness (D 2 - D1o~,)/2 for the internal insulation liner corresponding to the minimum steady-state total rate of energy dissipation, Etot, per unit length of pipeline. To maintain the low temperature of the chilled liquid, and so compensate for heat gains, a refrigeration plant will be required. Also, an external pump is usually necessary to raise the pressure of the liquid to overcome the viscous dissipation within the chilled liquid. Unfortunately, some of this viscous loss is converted into heat within the flowing chilled liquid and thereby causes embarrassment because it
INTERNALLY INSULATED PIPES FOR DISTRICT-COOLING SYSTEMS
103
will involve a further expenditure of refrigerator power to compensate for it. Thus, the total rate of energy expenditure, Etot, per unit length of pipeline, becomes: • , _ (Rate of refrigerator power expended" / •Rate of pumping'~ Et°t - \ to compensate for heat gains J + \ power expended ]
(1)
the terms on the right-hand side each being per unit length of pipeline. The first term on the right-hand side of eqn. (1) equals (/~h~+ ~Evd)/r/,, where r/r is the overall performance index of the refrigeration plant and ~ the fraction of the viscous dissipation which is converted into heat in the liquid. The other term on the righthand side of this equation equals Eva/~/p, where % is the efficiency of the pump. Therefore:
E 'o, =-1
+
+
(2)
STEADY-STATE RADIAL HEAT LEAK INTO THE PIPELINE
This heat gain by the chilled liquid per unit length of pipeline is given (see Simonson 9) by: Eh, = - 2
2n(Too - Ti)
1
(3)
assuming that the wall thickness, d, of the pipe is negligible compared with D 2. The internal heat transfer coefficient, h I (at the liquid/insulant wetted interface) for fully developed turbulent flow, neglecting entrance effects, can be obtained using the Colburn 2 equation: Nu -- 0.023 Re °s Pr °33
(4)
which can be applied when 0.7 < Pr < 120 and Re > 104. With appropriate substitutions and simplifications, it can be shown (Probert et al. 5) that: h~ = 0.0278 I?°'SD~ - l"SF(Tt)
(5)
where '1"[11) ~ ' ' " =Pt0-8L0'66,'-'0"33 Kt ~p #t-0-47 • Substitution of h 1 from eqn. (5) into eqn. (3) reveals that:
/~ht--{71.8D°'S
2n(To~ - Tt) +lln(Da~
k,
\01/
(6)
+
2 }
104
s . D . PROBERT, C. M. YEUNG, C. Y. CHU
The temperature change of the flowing liquid along the length of the pipeline is very small (Probert et al. 5) so that Tt in this equation can be regarded as constant. Equation (6) may not be the sole heat transfer consideration, e.g. in present circumstances it is desirable to check that condensation does not occur on the external surface of the pipeline--see Appendix 1.
VISCOUS DISSIPATION IN THE COLD LIQUID
For the flow of a liquid through a straight unobstructed horizontal pipeline, the rate of viscous losses per unit length of the pipeline, as derived from the DarcyWeisbach equation (see Jeppson 4 and Schlichting a) can be given by: 8fp,~ "a
E~d- n2O~
(7)
The friction factor,f, for turbulent rough flows (Re > 4 x l0 3) may be deduced (see Schlichting s) from Nikuradse's modified version of von Kfirmfin's friction factor equation, namely:
.1.+0.8691n where e is the equivalent roughness of the surface over which the chilled liquid flows. So, substituting for f into eqn. (7) reveals that: E~d = 8 [PI?3"~'l'139 + 0"869 In
D~-s
(9)
ENERGY-CONSCIOUS DESIGN
Normally it is the financial expenditure which decides the choice of design. Ifa and b are the unit costs (i.e. financial costs per Ws) for energy supplied to the refrigeration plant and the pump set, respectively, then the total rate of financial expenditure Pexp, per unit length of pipeline on energy running costs can be seen from eqn. (2) to be: pexp = a ~r
(Eh, + ~Eo~) + b
Eo~
(10)
~p
By rearrangement this becomes: eexp
a ( b +a~'~ = ~r JEh, "~F-~vd \r/t, r/, /
(11)
INTERNALLY INSULATED PIPES FOR DISTRICT-COOLING SYSTEMS
105
To simplify, let us define a t =
b'
E
a
(12)
b =
__
rip
ay +
- -
rl r
b =
- -
rip
+
(13)
a' 7
So, we can express eqn. (1 l) in the more compact form: • Pexp =
a ' Eht + b' Eva "
(14)
"
Substituting the expressions for/~ht and/~d from eqns (3) and (9), respectively gives:
• 2na'(T~ - T~) P~P=J'71"8D~'8 + 1 1n{D2~ + ( 2 )} (12°'SF(T,) k i \Dx) D~+8b'{P'(/3"]~l.139+O.8691n(~-)} -2 D~-5
(15)
So, in order to deduce the geometry appropriate to the minimum rate of financial expenditure (due solely to the running costs incurred as a result of energy losses) for chosen values of I? and DE, the deduced value of dPexp/dD 1 would be set equal to zero. The corresponding value of D 1 is the optimal diameter of the flow channel provided that d2Pexp/dD 2 > 0. Applying this procedure to eqn. (15) reveals that the optimal condition is:
b'Pt p3
--,-~,71"8D°~" 8, 1 / D 2 \ 2 -]2 f po.sFCT. ~ + -ki ln iDa°") -+ D2h21 5+
1.738
,, 9+08691n( ) 57'41D°:"8' } D5 I?O8F(T, ) 'o,,
)
(16)
This equation is solved numerically by computer. MINIMISATION OF ENERGY RUNNING COSTS FOR THE CHILLED WATER FLOW
It has been shown (Probert et al. 6) that, in general, 7 can be expressed by: y=l -ill
(17)
106
S. D. PROBERT, C. M. YEUNG, C. Y. CHU
Consider the chilled water flow at a temperature, Tz, of 5 °C. Under this condition: f l = l - 4 x 1 0 - S K -1 T~ = 278 K Thus, from eqn. (17): 7 = 0.9961 This, almost unity value for y, indicates that the Joule-Kelvin effect in this instance is negligible. The ratio b'/a' can be obtained by dividing b' from eqn. (13) by a' from eqn. (12), i.e.
a'
+~
(18)
Typical values of qp, b/a and r/r are given in Appendices 2, 3 and 4, respectively. Consider as an example, the configuration in which an electrically driven compressor-chiller system and centrifugal pump are used for cooling and pumping the water, respectively. In the range of hydraulic horsepower between 100 and 500, it is reasonable to assume an average overall pumping efficiency, qp, of 0.75 (see Appendix 2). With an electrically-driven centrifugal compressor-chiller system at normal operating conditions for air-conditioning, 7, can be taken as 4.25 (see Appendix 4). As electricity can be used to drive both the compressor and the water pump, b/a would then equal unity. So, substituting these values into eqn. (18) reveals: b' -a -' = 6 . 7 For other types of refrigeration machines, pumps and drivers, the appropriate values of the ratio of b'/a' can be deduced in a similar way.
NUMERICAL PREDICTIONS
Let us consider a typical district-cooling mains pipeline having D 2 = 0 . 4 m , conveying 5 °C water (for which p, = 1000 kg m - a, Cp = 4205 J k g - 1 K - 1, kl = 0 . 5 7 8 W m - X K -x and p t = 1.528 x 1 0 - 3 N s m -2) at a steady rate o f 0 . 2 m 3 s - t . The heat transfer coefficient for the outside surface of the pipe is assumed to be 1 0 W m - 2 K - x. The insulant liner is typically taken to have a mean effective thermal conductivity, k~, of 0.035 W m - 1 K - t and it is assumed that it presents to the chilled water a smooth surface of equivalent roughness e = 2.1 ;an (which can be achieved readily with plastic linings). The ambient temperature, Too, is taken to be 25 °C.
INTERNALLY INSULATED PIPES FOR DISTRICT-COOLING SYSTEMS
~?0
~
107
~
,
~
\
\
x
Eht
xx
022
02z.
026 028 030 032 03l, 036 INTERNAL[~AHETEROF INSULANTLINING D,.Ira I
038
Fig. 2. These curves are graphical representations ofeqn. (! 5) for Pc~, (in arbitrary units per metre) and of its components a'Eht and b'~:,a for chilled water flows with a' and b' in arbitrary financial units. For these predictions, it is assumed that F ' = 0 . 2 m 3 s -1, h 2 = 1 0 W m - 2 K -1, T I = 5 ° C , T~0=25°C, D 2 = 0.4 m,/q = 0.035 W m - t K - s, e = 2. l/Jm and b'a' = 1. It can be seen that Dt optchanges successively from 0.318m to 0.344m, 0.354 m and 0.358m as b' increases from I to 3, 5 and 7, respectively, a|| in arbitrary financial units per Ws expended.
The graphs in Fig. 2 show values for the total financial c o s t , Pexp, of the energy expended and its corresponding costs of heat extraction, a'Eh,, and viscous dissipation, b'Eva, components, all per metre length of the pipeline. Four representative cases are illustrated with the value of a' maintained constant at unity and b' increased successively from unity to 3, 5 or 7, all in arbitrary financial units per Ws expended. It can be seen that, in each case, there exists a clearly identifiable optimal diameter, Dlo~,, which increases with the value of b'/a' as expected. Corresponding predictions have been performed to obtain DI°~, for various flow rates, 17, for several values of the pipe's internal diameter, D2, with the ratio b'/a' assumed to be unity for the purpose of this investigation. The results are presented in Fig. 3. It can be seen that incremental changes in Dx.~ become smaller for unit changes in D 2 as D 2 increases for a particular flow rate, I?, resulting in thicker insulant linings (i.e. greater values of/opt)" The rates of financial expenditure, Peep, for different flow rates, I7, and at different optimal insulant thicknesses are presented in Fig. 4. Obviously, Pc~p decreases with increasing topt. However, as seen from Fig. 4, the savings achieved by increasing/opt by an increment will become smaller at larger values of/opt. However, in practice, the
E ~
(5
~=O,m~sec' v=o 2m)sec' =0 1mssec
z V : 0 O Z m3
sec~
~'= 0002mlsec1 /
01
0
02
03 0~ 0S 06 ~TSIDEDIAMETEROF NSULAt~TD~
07
0B
,(m)
Fig. 3. A family of design curves for selecting D~,,p, for various values of the pipe's internal diameter (D2). It is assumed that k / = 0 . 0 3 5 W m - 1 K -~, h 2 = 1 0 W - 2 K -1, e = 2 . 1 / t m , T~=5°C, To~ =25°C, b'/a' = 1 and d<~ (D 2 - Dlop,)/2.
S0
OOS
i,0 OO3
i '°
!"
i
OO2
z 001 • I00
Z00
OPTIMAL THICKNESSOF INTERNALINSULANT
ml
300
LININGtopt .{mmI
Fig. 4. This Figure should be read in conjunction with Fig. 3. For.a particular pipe diameter, D2, and flow rate, V, of chilled water, Dlopt is first read from Fig. 3. From this value of Dlopt, to~ = (D 2 - Dlop,)/2 can be calculated, and hence from Fig 4 the corresponding value. of PezP • • , determined. It can be seen that the thicker the lining chosen, for a given flow rate, the lower will be P., p- Also , P , p changes . dramatically at . low . values of to_ so that a small increase of to_t In this region results m a considerable reduction of Pexp"
/
• ~'o
2'o
;o
~oo
TEMPERATUREOF AMBIENT A~R T~ * l'C i
Fig. 5. The optimal thickness, /opt, of insulant is plotted against temperature, T~, of the ambient air. The conditions applying are I;"= 0.2m3s -1, D 2 = 0 . 4 m , k ~ = 0 . 0 3 5 W m - l K - l , e=2.1y.m, h 2 = 1 0 W m - 2 K -~, b'/a'=l and TI = 5°C.
INTERNALLY INSULATED PIPES FOR DISTRICT-COOLING SYSTEMS
109
E
~ 005(
i0~'
00~0
0035
_'o0~
0'02
0!0]
0!0~
0!05
0'06
0!07
0'08
0'09
0!10
THERMAL CONDUCTIVITY OF INTERNAL INSULANTLINING.k~, (WmIKI)
Fig. 6.
The variation of topt with changes in k~ is shown, the other applied conditions being as for Fig. 5, except that T~ = 25 °C.
00(
)
~ 00~
O0?
OO2 Fig. 7.
I
2
3
The variation of top' with changes in b'/a', the other applied conditions being as for Fig. 5, except that T o is chosen to be 25°C.
110
s.D.
"~ 0.0~
PROBERT, C. M. YEUNG, C. Y. CHU
~
.....
BEHAVIOUROf THEORETICAL
~ O.o;
~ o~
10
15
20
25
TEMPERAIURE OF WATER, Tt , ('C)
Fig. 8.
The variation of top' with changes in Tt, the other applied conditions being as for Fig. 5, except that T o is chosen as fixed at 25 °C.
required increase in capital expenditure for thicker liners needs also to be accounted for in a judicious choice of top,. A typical sensitivity analysis for /opt t o changes of the independent variables (based on the representative conditions of l>=0.2m3s -1, D 2 = 0 . 4 m , ki= 0 . 0 3 5 W m - I K -1, e = 2 . 1 p m , h 2 = 1 0 W m - 2 K -l, b'/a'=l, TI=5°C and Too = 25 °C), has been performed and the results are presented in Figs 5 to 9. The sensitivity of the optimal thickness,/opt, of the insulant lining to changes in any of its independent variables is defined as the ratio of the percentage change in/opt to the corresponding percentage change in the independent variable. From the presented analysis it can be deduced that the sensitivities of topt to changes of (/, To~, kl, b'/a', T t
00~2I NOTE topt FOR ZERO ROUrHNESSIS Of THEORETICAL SIrNIFIEANEE ONLY
00~0
0O38
0 O36
00]~
0001
0028 0
Fig. 9.
!
b
~0 2O EO~UIVALENY ROUSHNESS OF INSULATING LINING WETTED SURFACE, e, { ~O~m}
The variation of/opt with changes in e, the other applied conditions being as for Fig. 5, except that Too is chosen to be equal to 25 °C.
INTERNALLY INSULATED PIPES FOR DISTRICT-COOLING SYSTEMS
111
and e are - 1.981, +0.468, +0.1993, -0-1194, -0-0915, and -0.0041, respectively over the ranges of variables considered. The parameter, toot, is practically unaffected by changes in h 2.
CONCLUSIONS
An optimal thickness of the applied internal insulant lining always exists for which the minimum rate of financial expenditure upon energy occurs when a fluid at a temperature other than ambient is pumped through a pipeline. For a given flow rate of the liquid, a bigger diameter pipeline will result in a thicker optimal insulant liner and smaller total energy losses. However, larger pipelines and thicker insulation layers require greater capital investments and so, in practice, a compromise choice would invariably be made. For chilled water flows in an internally insulated pipeline of fixed outside diameter (D 2 + 2d), under the conditions studied, too t is most dependent upon the water flow rate, f', and then in sequence of decreasing sensitivity upon (i) the ambient temperature (see Fig. 5), (ii) the effective thermal conductivity of the applied insulant liner (see Fig. 6), (iii) the ratio of effective unit costs of energy used for pumping and for chilling the water (see Fig. 7), (iv) the temperature of the pumped water (see Fig. 8), and (v) the equivalent surface roughness of the flow channel (see Fig. 9). For a particular value of D 2, the greater the flow rate, the bigger will be the effective bore, D~o,. Each insulated pipe should preferably be used at its specified volumetric throughput so that energy losses are minimised. (This applies irrespective of whether it is internally or externally insulated.) In appraising the sensitivity of/opt to changes of each variable, the limits of the variables need to be considered. For example, e could increase from 1-5/an for drawn brass tubing to 2000 #m for concrete tubing--i.e, more than a thousand-fold rise. (Such surfaces might be used as thin sleeves to protect the thick insulant liners.) Thus although top t exhibits such a low sensitivity to changes in the surface roughness of the flow channel, such large variations among the commercially available linings might make surface roughness an influential parameter with respect to the design. The temperature, T~, of the chilled water is unlikely to vary by more than 2 °C in a well-insulated pipeline. Thus, although changes in both T~ and T o (the temperature of the ambient air) affect the radial heat leak, T~ is the parameter more likely to be susceptible to changes and so the more influential variable. The effective thermal conductivity, k i, of the applied insulant is an important factor affecting the rate of heat gain, but/opt is relatively insensitive to changes in k i. Nevertheless, it is important to design the insulant lining properly; the effective thermal conductivity of the insulant increasing significantly if moisture penetrates into it.
112
S. D. PROBERT, C. M. YEUNG, C. Y. CHU
When determining the optimal geometry of the internally-insulated pipe, it is the ratio b'/a', rather than the individual unit costs, a or b, of the fuels used for chilling and pumping the water that is more important. It should also be noted that the ratio b/a (and hence b'/a') is less susceptible (as indicated by percentage changes) to inflation than are either unit fuel costs a or b alone. So, the deductions in terms of b/a are likely to have significance for a longer period, and hence the nondimensional approach has been used in this analysis. The pipeline's external heat transfer coefficient has little effect on the value of topt because the rate of heat gain is dictated primarily by the thermal conductivity of the insulant, ki. The presented analysis has been restricted to energy 'running costs'. It could, however, be expanded to include the energy costs of the pipe and insulant (as would be involved in its materials, manufacture and installation). Thereby, it is feasible to extend the present approach to predict a more comprehensive energy conscious design, but further cost data for lining processes would be needed to permit this to Occur.
APPENDIX 1 : PREVENTION OF CONDENSATION ON THE EXTERNAL SURFACES OF PIPELINES CONVEYING CHILLED LIQUIDS
If the temperature of the external surface drops below the dew point of the ambient air, condensation will occur on that surface. This is undesirable from a corrosion point of view and could irreversibly damage components of the system. The temperature difference between the pipeline's outer surface and the ambient air depends on the amount of heat that is transmitted to it through the air. For horizontal pipes in still air, the total heat absorbed by a unit length of pipe is given (IHVE Guide 3) by:
Eh, = nD2hz(Ts - Too)
(19)
where h 2 is the overall outside surface heat transfer coefficient, which involves both a radiative and combined convective/conductive component, namely h, and hc, respectively. Thus: hE = hr q- hc (20) where: ( Ts - Too']°'2s hc _ 1 . 3 2 \ - ~ -]
(21)
for combined natural convection and conduction through the air, and h, = 5.67 x 10-8e(T 2 + T2)(T~ + Too) where e is the emissivity of pipe's outside surface.
(22)
INTERNALLY INSULATED PIPES FOR DISTRICT-COOLING SYSTEMS
113
The thickness o f insulation, t, to avoid c o n d e n s a t i o n in an internally insulated large d i a m e t e r pipe can be p r e d i c t e d to a r e a s o n a b l e accuracy by assuming T Stakes a value o f l °C higher t h a n dew p o i n t in a m b i e n t air. Then: (
/~h, T ~ ) } _
(23)
In general, for a h o r i z o n t a l pipe in still air, the surface heat transfer coefficient is between 5 a n d 1 0 W m -2 K -1 ( I H V E Guide3). So, t h r o u g h o u t the presented analysis, a value o f 1 0 W m z K - 1 has been assumed. It can be seen f r o m Fig. 10 that, except for very thin insulant liners, c o n d e n s a t i o n is unlikely to occur in general with the thicknesses o f insulant liner r e c o m m e n d e d by the o p t i m i s i n g analysis presented in the m a i n text. In o b t a i n i n g h c f r o m eqn. (21), c o n v e c t i o n u n d e r n a t u r a l circulation has been assumed. However, forced circulation (due to a d r a u g h t ) will reduce the possibility o f m o i s t u r e c o n d e n s a t i o n on cold surfaces a n d thus help to avoid the p r o b l e m .
V=02 mJs~cI ~=o.02m3sec 1 ~=O002n?se( ~
100 200 )90 OPTIMAL THICKNESSOF rNTERNALINSULANTLJNING,topt,lmm)
Fig. 10. The temperature difference (T~ - T~) between the ambient air and the outside surface of the pipe is plotted against the insulant's optimal thickness, top' for various flow rates of the chilled water at 5 °C. Note that the value of (To~- Ts) rises dramatically for low values of topt, which could lead to condensation on the outside surface of the pipeline. The other applied conditions are as for Fig. 5 except that T~ is chosen to be equal to 25 °C.
114
s . D . PROBERT, C. M. YEUNG, C. Y. CHU APPENDIX
2
TABLE 1 OVERALL EFFICIENCIESOF COMMONLYAVAILABLETYPES OF PUMPS (Data compiled from the Pumping Manual ( A n o n ) ) ) The efficiency of each pump is determined by its design, pumping speed and operating conditions
Type
Hydraulic horsepower
Approximate overall efficiency rlp (per cent)
Electric, motor-driven centrifugal pump
10 --* 100 100 ~ 500
55 ~ 70 70 --, 80
Diesel-driven centrifugal pump
10 --* 100 100 ~ 500
30 ~ 45 45 ~ 50
Direct acting steam pump
10 ~ 100 100 --, 500
20 --, 30 30 --, 35
Turbine-driven centrifugal pump
10 --, 100 100 --*500
10 -, 30 30 ~ 40
APPENDIX 3 TABLE 2 COSTS OF VARIOUSENERGYSUPPLIES Average data for energy supplies at demand point in the UK: July 1980. (Prices vary with delivery distance, amount of that fuel consumed regularly, and for coal and wood with their calorific values)
Conventional commercial unit of supply
Energy form
Electricity Fuel oil (3500 s) Natural gas Coal Wood
APPENDIX
kWh Gallon Commercial Therm Ton Ton
4:
Net available heat (Therms/unit) 0.0341 1.68 ~ 0.92 256 150
Average retail price (£/MWh) as at 1/7/80 24 9.8 8.8 5.9 4.8
Ratio of unit costs of electricity to other fuel 1.00 2.45 2.73 4.06 5.00
COOLING ABILITY AND POWER CONSUMPTION OF A REFRIGERATOR
The cooling powers achieved by various types of refrigerator depend mainly on their coefficients of performance, which, in turn, are dictated by the operating conditions, e.g. the evaporating and condensing temperatures (see Table 3). To obtain the total power expended by a refrigeration system, the type of driver (if any) and its efficiency have to be considered. For an induction electric motor, an average efficiency of 0.85 can be taken. The performance indices of the compressor
INTERNALLY INSULATED PIPES FOR DISTRICT-COOLINGSYSTEMS
115
TABLE 3 COMPARISON OF THE PERFORMANCE INDICES OF TYPICAL EXAMPLES OF DIFFERENT TYPES OF REFRIGERATION MACHINE
The data have been evaluated for evaporator and condenser temperatures of 3 °C and 35 °C, respectively,and have been compiled from IHVE Guide Section B14, 1970.a
Type of refrigerator
Performance index = Cooling power (in k W) per k W of power input
Screw compressor Centrifugal compressor Reciprocating compressor Absorption machine
5.26 5.00 4.55 2.33
systems as stated in Table 3 should then be multiplied by this factor, 0.85, to o b t a i n the values of the overall p e r f o r m a n c e index, r/,, of the compressor-chiller system. This leads to values of 4.47, 4.25 a n d 3.87 for the chilling system with screw compressor, centrifugal compressor a n d reciprocating compressor, respectively.
ACKNOWLEDGEMENTS The a u t h o r s wish to t h a n k the Science a n d E n g i n e e r i n g Council for s u p p o r t of this project. In particular, a debt is owed to the late D r Jack Butterworth for his interest a n d guidance.
REFERENCES 1. A~ON.,Pumping Manual (6th edn). The Trade and Technical Press Ltd, Morden, Surrey, England, 1979. 2. A. P. COLBUR~,A method ofcorrelating forced convection heat transfer data and a comparison with fluid friction, Trans. Am. Inst. Chem. Engineers, 29 (1933), pp. 174-210. 3. IHVE, Institution of Heating and Ventilating Engineers, London. Guide Book C, Section B14, p. 7; Section C-3, pp. 1-7, 1970. 4. R. W. Jl~vPSON,Analysis offlow inpipe networks, Ch. 3, Ann Arbor Science, Michigan, USA, 1976. 5. S. D. PROBERT,C. Y. CHU and C. M. YEUNG,Thermal insulation lining for pipelines? 4th National Conference. District Heating Association, Torquay, England, 1981. 6. S. D. PROnERT,C. Y. CHU and C. M. YEU~G,A possible alternative approach to the thermal insulation of pipelines, Applied Energy, II (1982), pp. 15-34. 7. S. D. PROBERT,C. M. YEtmGand C. Y. CHu, Optimising the performance of internally insulated pipelines for conveying super-heatod steam, Applied Energy, in press. 8. H. SCHLICHTING,Boundary-layer Theory (7th edn). Ch. 20 (translated by J. Kestin). McGraw-Hill, New York, USA, 1976. 9. J. R. SIMOr4SON,Engineering heat transfer, p. 27. McGraw-Hill Publishing Co. Ltd, London, 1967.