Performance Enhancement of Double Pipe Heat Exchangers by Enforced Turbulence on Single Surface. Hussain H. Al-Kayiem1, Laheeb N. Al-Habeeb2 1. Ass. Prof. Dr., Dept. of Mech. Eng., Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 31750 Tronoh, Perak, MALAYSIA. E-mail:
[email protected] 2. Assistant Lecturer, Mech. Eng. Dept., University of Al-Mustansiryah, Baghdad,Iraq. Abstract – Results are presented from Theoretical analysis for pressure drop and heat transfer in annular flow having repeated turbulators. The annular flow represents the outer part of counter flow in a double-pipe heat exchanger. The modeling enables estimation of the friction factor, Nusselt number and Stanton number. The mathematical modeling is based on the law of the wall similarity to correlate both friction factor and heat transfer coefficient. The regime of hot water inside the inner pipe is investigated within a Reynolds number range from 10000 to 72000. The annular cold flow is ranging 26000 to 200000 Reynolds number. Four different types of promoter installations were tested. The results are verified by comparing with experiments. They are in good agreement. The results have shown enhancement in the heat transfer coefficient combined with increase in the friction factor. The performance index has shown highest enhancement of about 1.8 at pitch to diameter ratio equal 10 and promoter height to hydraulic diameter equal 0.0595 when the promoters are attached to inner surface of the outer pipe. Key words: Heat exchangers, heat transfer enhancement, ribbing, friction, Counter flow.
INTRODUCTION In many mechanical systems, as example, refineries, power plants, reactors, solar thermal systems…etc, it is obvious that heat exchangers are an important part of the system. The improvement of such systems requires continuous improvement of the individual units, one of which is the heat exchangers. In recent years, the need to augment or intensify heat transfer has had engineers urgently searching for new methods and techniques. It is only recently that comprehensive experiments have been performed and reported which more clearly defines the conditions of augmentative technique for improving the heat transfer. These techniques may be broadly classified as follows: Augmentative stimulation is continuously supplied. Turbulence promotion. Extended heat transfer surfaces.(e.g. finned tubes)
Enhanced heat transfer surfaces.
Typical examples of the first technique are fluid additives, electrostatic fields, and fluid or surface vibration. Some examples of the second technique are coiled wires, inlet vortex generator, twisted tapes, displaced promoters (ribs) and spirally grooved tubes. The fourth technique is achieved by using rough surfaces through which it is possible to achieve the two-fold objective of maximum heat transfer and minimum pressure drop. An early study of the effect of roughness on friction and velocity distribution was performed experimentally by Nikuaradse [1] in 1933. The other experimental work on roughening by sand and its effect on friction and heat transfer was reported by Nummer [2] in 1958 whom came up with the conclusion that the laminar sub layer was the same in both rough and smooth conditions. In 1963, Dipprey and Sabersky[3] presented experimental results and correlated the friction and heat transfer in smooth and rough tubes at various roughness to diameter, various Reynolds numbers and various Prandtl numbers. The flow over sets of artificial roughness consisting of square slots normal to the flow direction was carried out by Harry and Sabersky [4] in 1966. In the same year, Sheriff and Gumley [5] investigated experimentally the friction and heat transfer of surfaces roughened by means of wire warpping at constant pitch-to-diameter ratio. They found that heat resistance from the wall to the roughness tip has a minimum value at roughness Reynolds number, e+ ~35, and this produces an optimum heat transfer surface. One year after that, Sutherland [6], established the performance of turbulent boundary layer promoter and he found that the maximum improvement in heat transfer performance occurs at e+ ≥ 40. Since 1970 till recently, Webb conducted a series of experiments on the repeated-rib and has come out with many correlations relating the geometries of the ribs to the heat transfer and friction factor. The early publication is carried out by Webb et al. [7] in circular tubes having
repeated-rib roughness to test the correlation over a wide range of pitch to height, p/e and height to diameter, e/D. Three types of fluids were tested to investigate the effect of Prandtl number. In 1980, Gee and Webb [8] presented experimental information for single-phase convection in circular tube containing two dimensional rib roughening. They have examined the heat and friction for air flow with three helix angles. With 49o angle, they obtained reduction in the heat exchanger surface area by 25% and increase in the conductance by 27%. In 1986, Webb and Blanco [9] studied enhancement of heat transfer between a counter current drained water film and air flowing in vertical tube by using transverse wire placed in the air boundary layer. The second known researcher in the field of repeated rib roughening is Han who published his first finding in 1978 with others [10]. They have studied experimentally and theoretically the effect of rib shape, the angle of attack, α and pitch-to-height ratio on friction factor and heat transfer in parallel plate geometry. In 1984 and in 1985, Han [11] and Han et al. [12] respectively performed an experimental study of fully developed turbulent air flow in square ducts with two opposite rib roughened wall. They determined the friction and heat transfer under various p/e, e/D, and the α with Reynolds number varied from 7000 to 9000. In 1988, Han and Park [13] investigated the combined effect α and the channel aspect ratio on the distribution of the local heat transfer coefficient for Reynolds number from 10000 to 60000. In addition to that, in the same year, Han [14] reported the contribution of p/e. Other results were reported by Han et al [15] and Han and Zhang [16] in 1989 and then Han and Zhang [17] in 1992 about the combined effect of the flow channel aspect ratio and the rib configuration as well as Reynolds number. They have obtained an empirical correlation used to design the turbine airfoil cooling passage. From the above and some other works, e.g. Park et al. [18] and Liou and Hwang [19] both in 1992, semi empirical correlations have been verified and used in the design of heat transfer equipment and the turbine cooling passages. The present paper presents further addition to the field of heat transfer enhancement by rib-roughening technique. It presents the analytical part of research work to enhance the performance of industrial Double Pipe Heat Exchanger (DPHE). The paper presents how the previous findings and correlations are used to apply to ribbed annular flow of the DPHE. OBJECTIVE AND METHODOLOGY The main objective of the present paper is to present the performance enhancement of a counter flow DPHE by the use of artificial surface roughening. The roughening was done by using regular turbulence promoter to enhance the heat transfer performance. Also, the study involved the effect of the promoters on the friction factor which combines the heat transfer enhancement.
The investigation methodology adopted in the study is mainly experimental in addition to analytical and numerical approaches. Here, only the analytical and numerical techniques are discussed. The correlations recommended by Han and Webb were adopted and applied after suitable manipulation to suit the annular flow of the DPHE. Four arrangements inside the annulus have been analyzed under various Reynolds numbers. ANALYTICAL MODELING The outlines of the DPHE under investigation, which is manufactured and commercialized, are shown in Fig.1.
2000
Fig. 1 The outlines of the DPHE (dimensions in mm) The analysis is based on evaluation of the heat transfer and pressure drop changes in the case of promoter roughening, so called ribbing case, compared to the non ribbed case. The ribs have height, e and repeated inside the annulus in regular manner with separating distances, so called pitch, p as shown in Fig.2.
Fig.2 Repeated ribs on the inner surface of outer pipe and on the outer surface of the inner pipe. I. Friction Factor in Non-Ribbed Annulus Cases, f: In fully developed flow in closed conduits, either laminar or turbulent, the pressure drop varies with inertia force parameters, shear force parameters and the surface conditions as:
p u m , , D, , L
1
where, ε is the absolute roughness of the conduit surface having dimensions of length. μ and ρ are the fluid viscosity and density, respectively and um is the mean velocity. Using dimensional analysis and adopting the hydraulic diameter criteria, Dh instead of the pipe diameter, D, getting the known Darcy Weisbach equation from which the friction factor, f in the annular flow is:
f
p 4 L u m2 D 2 h
2
4 d o2 d i2 4 Dh do di d o d i
3
The functional relationship of equation 2 has taken a large effort from many investigators. As long as ε /Dh < 0.001, the friction factor is function of Re only. According to [20], the widely used among those correlations are the following:
Blasius correlation:
f 0.0791 Re 0.25
0.32
4 10 Re 10 5 4
6
II. The Convective Heat Transfer at Non-Ribbed Annulus Cases, St: The coefficient of convective heat transfer, h is a function of many variables such as the geometry of the flow passage, the surface roughness, the flow direction and velocity, temperatures of the fluid and the surface and the fluid properties (density, viscosity, heat capacity and the thermal conductivity). The differential equations of convection are of the most difficult class. The empirical treatment is not entirely satisfactory, but yields adequate results. Accordingly, treatment of the above set of variables by dimensional analysis method has led to number of correlations in the form of:
Nu NuRe, Pr
7
for heating for cooling
The equation is used in the present annulus flow by using Dh instead of D. The physical properties were evaluated at the mean bulk temperature. Accordingly,
8
Nu Re Pr
III. The Friction Factor of Ribbed Annulus Cases, fr: By combining the velocity defect law for pipe flow with the law of the wall, Nikuradse [1], developed the “friction similarity law” for sand grain roughness. This can assumed to hold for the entire cross section of the flow. To satisfy the ribbed annulus flow, again, replace the diameter by the annulus hydraulic diameter and the average surface roughness, ε by the rib height, e ; the approximation could apply for the annulus flow. The Roughness function, Re + is obtained as:
Re e
2 fr
0.5
2e 3.75 2.5 ln D h
9
where, the roughness Reynolds number, e+ is:
Drew, Koo and McAdams correlation:
f 0.0014 0.125 Re
0.4 n 0 .3
4 10 3 Re 10 5 4
hi D 0.023 Re 0.8 Pr n k
and the exponent, n has values of:
St
where, the hydraulic diameter for the annulus is:
Nu
6
For fully developed turbulent flow in pipes with ε /D < 0.001, the following correlation is recommended by Dittus and Boelter as mentioned by [9]:
e f e Re r Dh 2
0.5
10
Ref. [10] correlated the friction data for turbulent flow between parallel plates with repeated-rib roughness by taking into account the geometrically non similar roughness parameters of p/e, rib shape, φ and the angle of attack as:
Re e
where
e m 4.9 35 n 0.35 0.57 10 o p o 90 ( e ) 45
m = -0.4 m=0 n = -0.13
n 0.53 o 90
if if if
e+ < 35 e+ ≥ 35 p/e < 10
if
p/e ≥ 10
0.71
(11)
Equations, 9, 10, and 11 were solved iteratively within the full computational program of the analysis procedure. Values of fr corresponding to the four ribbing cases were evaluated at different Re for each case.
the inner surface of the outer pipe or to the outer surface of the inner pipe. Two different pitches have been selected for each surface. The regular roughening is tested for four different cases as shown in Fig.2 and table1.
IIV. Heat Transfer of Ribbed Annulus Case, Str: From the heat and momentum transfer analogy, the temperature distribution between rough wall and distance ym can be resolved into two regions. Based on that, Ha et al. [10] and Webb et al. [7] have proposed a formula that applies the above analogy for the region from the base to the height of the rib, e and from e to ym as:
fr 1 2St Re He e , Pr 0.5 fr 2
12 Fig. 3 The investigated ribbing configurations.
which is called” Heat Transfer Similarity Law”. Table 1 The investigated cases of repeated ribbing.
If He+, Re+ and fr are known, then Stanton number in the ribbed flow could be evaluated as:
He
Re 2 f r 2
0.5
13
If fr is calculated as in Paragraph III above, then, Re+ calculated by equation 11. For evaluation of He+, based on the heat transfer similarity law, two correlations are available from the literature. Webb [7] developed a successful heat transfer similarity relationship for turbulent flow with repeated rib-roughness by taking into account the non-similar geometry of the promoters in the form:
Pr
He 4.5 e
0.28
14
0.57
On the other hand, Han[10] suggested another correlation to evaluate H+, as following
He
8 e / 35
/ 45
p/e
Case 1
0.0595
10
Case 2
0.107
10
Case 3
0.0595
15
Case4
0.107
15
The results of the friction factor and the heat transfer coefficient, f for non ribbed case are compared with experimental results obtained by [21] for the same DPHE. The experimental results are obtained by using equations 2 and 3. A Sample of the friction factor comparison is shown in Fig.5.as (log f ~ log Re). At higher Reynolds numbers, the agreement of the friction factor becomes closer.
0.100
i
15
o j
where: i =1 when e+ < 35 ; j = 0.5 when α < 45o ;
e/Dh
1. The Friction Factor:
i = 0.28 when e+ ≥ 35 j = -0.45 when α ≥ 45
The set of equations is converted to a computer program using Quick Basic Language. The obtained results are presented in non-dimensional, normalized format.
f
St r
fr
Annulus
0.010
0.001 10000
1000000
Re
DISCUSSION OF RESULTS Blasius
The recent paper takes into account one type of hot and cold fluid flow in the heat exchanger. The hot fluid flows in the inner pipe while the coolant flows in the annulus. The promoters selected for this analysis were attached to
100000
McAdms
Experimental
Fig. 4 Friction factor verses Reynolds number for nonribbed annulus, as log f ~ log Re.
The field of regular ribbed flow is studied widely by Webb [7], [22], and Han [10] and [11]. For the case of regularly ribbed roughening, Han recommended a correlations given by combining equations 9, 10 and 11 for the friction factor fr for the flow between parallel plates. The method was adopted in this study by exchanging the hydraulic diameter using equation 3 for the case of the annulus of the DPHE. The results for the four ribbing cases are shown in Fig.5. One of the tasted cases, namely case 2, is compared with experimental results of ref. [21]. The experimental and calculated results are in good agreement over the test range of Re. The friction factor for all ribbing arrangements approaches negligible change over the tested range of Re. The friction evaluation is less affected by the inertia change of the flow in the ribbing case compared to that in non-ribbed flow case. The expected reason is that the ribs cause high turbulence near the surface at low Re. This high turbulence contributes on the pressure drop larger than affecting the inertia increment. By referring to fig.4, it is clear that there is noticeable difference in f value at low Re and high Re, which is in contrast to the case of ribbed annulus flow. This is applied on both, experimental and calculated results. This agreed with the published results by Webb and Han for ribbed circular and rectangular cross sectional conduits.
another correlation as given by equations13 and 15. The results for the four ribbing cases are presented in fig 6(a to d) in form of log Str ~ log Re. Fig. 6b is showing the results of case 2, where, e/Dh equal to 0.107 at p/e equal to 10. The ribs are installed on the outer surface of the inner pipe.
0.01
Str
The maximum deviation of f calculated is about 6% in case of McAdams correlation and 3% in case of Blasius correlation.
0.001 10000
100000
1000000
Re Webb
Han
a. Case 1 0.01
fr
Str
1.00
0.10
0.001 10000
0.01 10000
100000 fr(3)
fr(2)
Webb
fr(1)
Han
fr(2)exp
b. Case 2 Fig.5 Friction factor verses Reynolds number for four cases of ribbed annulus, as log f ~ log Re. 2. The Heat Transfer: The indicator usually used for the heat transfer performance is the Stanton number; St. For the evaluation of the heat transfer by Stanton number in the ribbed annulus cases, Str, Webb stated correlation as presented in equations 13 and 14. Han, on other side, has suggested
1000000
Re
1000000
Re fr(4)
100000
Exp.
3. Rib Configuration Contribution: 0.01
Str
Taking into consideration the rib geometries, the trends of the results in the recent analysis are matching the experimental observations reported by Webb and Han. The combined effect of the ribbing on the pressure drop and heat transfer was studied by evaluating the performance index [(Str/St) / (fr/f)]1/3. The results are summarized in table 2. The values of the index are ranged over the Re range mentioning the lowest enhancement to the largest enhancement. 0.001 10000
100000
1000000
Re Webb
Table 2 Performance index of the rib-roughening annulus.
case Han
c. Case 3
1 2 3 4
configuration
Performance enhancement range
p/e
e/Dh
lowest
highest
10 10 15 15
0.0595 0.107 0.0595 0.107
1.3 1.25 1.25 1.14
1.8 1.65 1.71 1.56
0.01
Str
CONCLUSION
0.001 10000
100000
1000000
Re
Webb
Han
Performance of counter flow DPHE is investigated under enforced turbulence by the use of rib-roughening technique. Four types of regular ribbing in the annulus flow of the DPHE are modeled and analyzed. The analysis is carried out under rage of Reynolds number from 26000 to 200000. The results are compared with experimental results and they are all in good agreement. The results demonstrate many findings obtained by previous experimental researches. Based on the performance index criteria, the best performance of the exchanger was obtained when the ribs are installed on the inner surface of the outer pipe with p/e = 10 and e/d = 0.0595.
d. Case 4
ACKNOWLEDGMENT
Fig. 6 Stanton number verses Reynolds number for four different cases of ribbed annulus.
The authors acknowledge Universiti Teknologi PETRONAS for sponsoring the publication of the work.
The calculated Str results compared with the experimental Str results obtained by [21]. They are in good agreement with maximum deviation 4% in case of Webb correlation and about 7% incase of Han correlation. In the lower range of Re, about 2.7 x 104, the experimental values of Str are higher than the calculated results. In the high range of Re, 2 x 105, the calculated values are higher than the experimental results. Han correlation resulted in lower values than Webb correlation in entire tested cases under all conditions of Re. Also, the results obtained by Han correlation are lower than the experimental results over the entire range of tested Re.
REFERENCES [1] Nikuradse, J., “Laws for Flow in Rough Pipes”, VDI Forsch.361, series B, 4 NACA YM, 1950. [2] Nummer, W., “Heat Transfer and Pressure Drop in Rough Pipes”, VDI Forsch. 455 B, English trans. Lib. 1 Trans. 786, 1959. [3] Dipprey, D. F. and Sabersky, R. H., “Heat and Momentum Transfer in Smooth and Rough Tubes at Various Prandtl Number”, Int. J. Heat Mass Transfer, Vol.6, pp. 329-353, 1963.
[4] Harry, W. T. and Sabersky, R. H., “Experimentes on the Flow Over a Rough Surfaces”, Int. J. Heat Mass Transfer, Vol. 9, pp. 729-738, 1966. [5] Sheriff, N. and Gumley, P., “Heat Transfer and Friction in Tubes with Repeate-Rib roughness”, Int. J Heat Mass Transfer, Vol. 14, pp.601-617, 1967. [6] Sutherland, W. A., “Improved Heat Transfer Performance with Boundary-Layer Turbulence Promoters”, Int. J. Heat Mass Transfer, Vol. 10, pp. 15891320, 1967. [7] Webb, R. L., Eckert, E. R. G. And Goldstein, R. J., “Heat Transfer and Friction in Tubes with Repeated-Rib Roughness”, Int. J. Heat Mass Transfer, Vol. 14, pp. 601617, 1971. [8] Gee , D. L. and Webb, R. L., “Forced Convection Heat Transfer in Helically Rib-Roughened Tubes”, Int. J. Heat Mass Transfer, Vol. 23, pp. 1127-1136, 1980. [9] Webb, R.L. and Perez-Blanco, H., “Enhancement of Combined Heat and Mass Transfer in a Vertical Tube Heat and Mass Exchanger”, ASME Journal of Heat Transfer, Vol. 108, pp. 70-75, 1989. [10] Han, J. C., Glicksman, L. R. And Rohsenow, W. M., ” An Investigation of Heat Transfer and Friction Factor for Rib-Roughened Surfaces”, Int. J. Heat Mass Transfer, Vol. 21, pp.1143-1156,1978. [11] Han, J. C., “Heat Transfer and Friction Factor Channels with Two Opposite Rib-Roughened Walls”, ASME Journal of Heat Transfer, Vol. 106, pp. 774-781, 1984. [12] Han, J. C., Park, J. S. And Lei, C. K., “Heat Transfer Enhancement in Channels with Turbulence Promoters”, ASME Journal of Engineering for Gas Turbine and Power, Vol. 107, pp.628-635, 1985. [13] Han, J. C. and Park, J. S., “Developing Heat Transfer in Rectangular Channels with Rib Turbulators”, Int. J. Heat Mass Transfer, Vol. 31, pp.183-195, 1988. [14] Han, J. C., “Heat Transfer and Friction Characteristics in Rectangular Channels with Rib Turbulators”, ASME Journal of Heat Transfer, Vol. 110,pp.321-328, 1988. [15] Han, J. C., Park, J. S. And Lei, C.K., “ Augment heat Transfer in Rectangular Channels of Narrow aspect ratios with rib Turbulators”, Int. J. Heat Mass Transfer, Vol. 32, pp. 1619-1630,1989. [16] Han, J. C. and Zhag, P., ” Pressure Loss Distribution in Three-Pass Rectangular Channels with Rib Turbulator”, ASME Journal of Turbomachinary, Vol. 111, pp. 515-521, 1989.
[17] Han, J. C. and Zhag, Y. M., ”High Performance Heat Transfer Fucts with Parallel Broken and V-Shaped Broken Ribs”, Int. J. Heat Mass Transfer, Vol.35, pp.513-523, 1992. [18] Park, J S., Han, J. C. Huang, Y. And OU, S., ” Heat Transfer Performance Comparisons of five different rectangular channels with Parallel Angled Ribs”. Int. J. Heat Mass Transfer, Vol. 35, pp. 2891-2902, 1992. [19] Liou, T. M. and Hwang, J. J., “Turbulent Heat Transfer Augumentation and Friction factor in Periodic Developed Channel Flows”, ASME Journal of Heat Transfer, Vol. 114, pp.56-64, 1992. [20] Kakac, S. and Paykoc, E., “Basic Relationships for Heat Exchangers”, Two-Phase Flow Heat Exchanger Thermal Hydraulic Design, Eds. Kakac, S. Berbles, A.E. and Fernandes, E. O., Cooperation with NATO Scientific Affairs Division Applied Sciencer, Vol. 143, pp. 29-80, 1988. [21] Al-Habib, L. N.,’ Performance Enhancement of Double Pipe Heat Exchanger by Regular Roughing in Counter Flow” MSC Dissertation, Mech. Eng. Dept., ALMustansirya Univ., (1999)
