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examples of passive augmentation are surface roughness, displaced promoters, and vortex generators. Surface roughness--introduced through knurling or threading or formed by repeated r i b s - - p r o m o t e s augmentation through the disturbance of the sublayer that is close to the surface. These methods are used to improve heat-transfer coefficients inside tubes [2] or outside tubes or rods [3]. Displaced promoters include inserts that alter flow mechanics near the surface by disturbing the core flow. Examples are baffles [4] and mixing elements [5]. Vortex flow can be created through coiled wires [6], stationary propellers [7], or twisted tapes [8]. Active augmentation, which has also been studied extensively, requires the addition of external
Address correspondence to Professor T. S. Ravigururajan, Department of Mechanical Engineering, Wichita State University, Wichita, KS 67260-0035. E-mail: ravi@
INTRODUCTION Thermal system performance and efficiency can be vastly improved, thereby reducing the size of heat exchangers. The augmentation (or enhancement) of heat transfer has become an important factor in achieving these goals [1]. The performance of heat exchangers, for single-phase flows in particular, can be improved by many active and passive augmentation techniques. The former uses surface modification or an additional device incorporated into the equipment. The existing boundary layer is disturbed and the heat-transfer performance is improved, usually with an increase in the flow friction and pressure drop. Typical
Experimental Thermal and Fluid Science 1996; 13:55-70
© Elsevier Science Inc., 1996 655 Avenue of the Americas, New York, NY 10010
0894-1777/96/$15.00 PII S0894-1777(96)00014-3
Department of Mechanical Engineering Wichita State University Wichita, Kansas 67260 USA
• General correlations are developed and verified for friction factor and heat-transfer coefficient for single-phase turbulent flow in internally augmented tubes. Data from frequently referred investigations were gathered for a wide range of tube parameters with e/d, 0.01 to 0.2; p / d , 0.1 to 7.0; a/90, 0.3 to 1.0, and flow parameters Re, 5000 to 250,000 and Pr, 0.66 to 37.6. The data were applied to a linear model to obtain normalized correlations that were then modified to approach smooth tube correlation as the roughness variables became very small. A shape function was included in the friction correlation to account for different rib profiles. These correlations were then verified by independent experiments. Different types of commercial fibbed tubes were tested with water as working fluid under heating conditions. Five wire coil inserts were tested in another apparatus using air under cooling conditions. The parameters tested were Re = 5000-60,000, e / d = 0.023-0.127, p / d = 0.17-1.12, and a/90 = 0.34-0.91. The results proved that the correlations can be successfully applied to a wide range of roughness types and Prandtl number. The present correlations are superior, for this large database, to those presented by other investigators. The friction factor correlation predicts 96% of the database to within + 50% and 77% of the database to within + 20%. Corresponding prediction figures for the heat-transfer correlation are 99 and 69%. Keywords: heat-transfer enhancement, correlations, augmented tubes,
A. E. Bergles
Department of Mechanical Engineering Aeronautical Engineering and Mechanics Renssalaer Polytechnic Institute Troy, New York 12180, USA
wire coils
56 T.S. Ravigururajan and A. E. Bergles power to bring about the desired flow modification. Examples include heat-transfer surface vibration [9], fluid vibration [10], and electrostatic field introduction [11]. Of the several methods discussed above, the most popular and successful technique has been augmentation through surface roughness. This is mainly because of its effectiveness in enhancing the heat transfer and its simplicity in application. Transverse or helical repeated ribs* are an especially attractive way of creating the surface roughness. Ribs are found in several configurations, depending on the manufacturing technique (machining, forming, or insert). Figure 1 presents sketches of the various types of ribbed tubes along with the important geometrical parameters involved. Tubes with transverse ribs of rectangular profile shape are fabricated in segments, each of which is machined from a smooth pipe on a lathe. These segments are fitted over a long mandrel and brazed together to obtain any desired length. But this method of fabrication is suitable only for laboratory testing. Production on a large scale may be carried out through rolling or indenting, which produces ribs having a smooth profile. High production rates usually dictate helical ribs; a feed is given to the tube to form the desired helix angle. Here the roughness height, pitch, helix angle, and to a large extent, the profile shapes are controlled by the roller design, the feed rate, and the pressure applied * Ribbed tubes are also commonly referred to as "spirally fluted," "convoluted," "corrugated," "spiral," "helically fluted," "spirally grooved," "spirally indented," "roped," or "enhanced." during the process. Another simple method of introducing roughness in a tube is to insert wire coils, in which case the roughness height equals the wire diameter. The various investigations carried out on these augmented tubes are listed in Ref. [1], and patents describing the fabrication methods are included in [12]. Ribbed tubes are sometimes considered in the design of shell-and-tube heat exchangers. The applications include single-phase tubeside augmentation of flooded chillers for air conditioners [13], surface condensers for desalting plants [14], and surface condensers for power plants [15]. The size of these heat exchangers can be reduced considerably by use of augmented tubes instead of smooth tubes; alternatively, the heat duty of a fixed area heat exchanger can be increased. This has important potential applications in large systems such as those used in thermal, geothermal, and ocean thermal energy conversion (OTEC) power plants, which require very large heat exchangers. BACKGROUND In spite of the increasing use of these augmented tubes, there are no truly general correlations available for quantitative assessment of pressure drop and heat transfer. In one of the early studies on ribbed tubes, Kalinin et al. [16] proposed correlations for pressure drop and heat transfer. However, the correlations are valid only for transverse ribs within specific ranges of e/d and p/d. Many of the studies found in the literature have tried to extend the studies of Nikuradse [17] on friction with sand-grain roughness and the heat-transfer-momentum-