Effect of Triangular Roughness Elements on Pressure Drop and Laminar- Turbulent Transition in Microchannels and Minichannels

Roughness elements affect internal flows in different ways. One effect is a transition from laminar to turbulent flow at a lower Reynolds number than the predicted Re=2300. Initial work at RIT in the subject area was performed by Schmitt and Kandlikar (2005) and Kandlikar et al. (2005), and this study is an extension of these efforts. The channel used in this study is rectangular, with varying separation between walls that have machined roughness elements. The roughness elements are saw-tooth in structure, with element heights of 107 and 117 μm for two pitches of 405 μm and 815 μm respectively. The resulting hydraulic diameters and Reynolds numbers based on the constricted flow area range from 424 μm to 2016 μm and 210 to 2400 respectively. Pressure measurements are taken at sixteen locations along the flow length of 88.9 mm to determine the local pressure gradients. The results for friction factors and transition to turbulent flow are obtained and compared with the data reported by Schmitt and Kandlikar (2005). The roughness elements cause an early transition to turbulent flow, and the friction factors in the laminar region are predicted accurately using the hydraulic diameter based on the constricted flow area. INTRODUCTION Work in the area of roughness effects on frictional factors in internal flows was pioneered by Colebrook, Nikuradse, and Moody. Their work was limited to relative roughness values of less than 0.05, a value which may be exceeded in microfluidics applications where smaller hydraulic diameters are encountered. Peiyi and Little (1983) noticed an early transition to turbulent flow in microminiature refrigerators. Their channels were etched on glass and silicon with Dh from 45.46 to 83.07μm. Wu and Little (1984) fabricated microchannels with the same process of Dh around 150μm, and found unusually high frictional factors. They found these to contribute to low critical Reynolds numbers from ~400900. Schmitt and Kandlikar (2005) performed work in this area using rectangular minichannels of hydraulic diameters ranging from 325μm to 1819μm with air and water as the working fluids. They found early turbulent transition and FdRa irregular pressure drops when compared to conventional values. Also shown was that the laminar friction factor could be calculated by using the constricted hydraulic diameter, Dh,cf. They also found a relationship between the critical Reynolds number and the relative roughness (ε/Dh,cf). Kandlikar, et al (2006) reports laminar-to-turbulent transitions at far lower values than the accepted value of Re=2300. It was shown, citing work by Schmitt and Kandlikar et al. (2005) that increasing relative roughness values resulted in decreasing critical Reynolds numbers. They give the relation governing the transition Reynolds number in Equation (1). Also resulting from this work is a modified Moody Diagram, based on constricted hydraulic diameter determining the friction factor. This is shown in Fig. 2. (1) Recently, Kandlikar et al. (2005) proposed new roughness parameters of interest to roughness effects in microfluidics as shown in Fig. 1. First, RP is proposed as the maximum peak height from the mean line. Next, RSm is defined as the mean separation of profile irregularities. This is also defined in this paper as the pitch of the roughness elements. Finally, FP is defined as the distance of the floor profile from the mean line. This is the average of roughness heights that low below the mean profile line, or the average of these heights. These values are established to correct for the assumption that different roughness profiles with equal values of Ra, average roughness, may have different effects on flows with variations in other 0 < ε/Dh,cf < 0.08 Ret,cf = 2300 – 18,750(ε/Dh,cf) 0.08 < ε/Dh,cf < 0.15 Ret,cf = 800 – 3,270(ε/Dh,cf – 0.08) Figure 1 – Illustration of Roughness parameters Sm1 Sm2 Sm3 Rp1 Rp2 Rp3 Main Profile Mean Line Floor Profile Mean Line 1 Copyright © 2006 by ASME Figure 2 – Modified Moody Diagram, based on Dh,cf, Kandlikar et al (2005) profile characteristics. Rawool et al. (2005) performed numerical CFD-ACE+ simulation of sawtooth roughness elements, similar in nature to those used in this experiment. In the simulation, serpentine channels were examined. They found that differing pitches of identical triangular roughness elements led to variations in pressure drop, and velocity profiles. Pressure drop decreases with an increase in the pitch of the elements. A diagram of this discrepancy can be found in Fig. 3.