Emmanuel Hitimana, Engineer, Research

Roughness can be understood as a surface texture or height variation with respect to a perfectly flat or smooth surface. Tube and heat exchanger users are keenly interested in surface roughness because it affects pressure drop and heat transfer, which then impacts the thermal performance and cost of operating a heat exchanger.

Figure 1 shows a 3D surface texture and the roughness profile of the highlighted (red line) area in a bare (unfinished or uncoated), unused tube.

Microscope scan of SS-304 bare tube
Figure 1. Microscope scan of SS-304 bare tube: (a) 3D surface texture and (b) roughness profile

To assess the full extent of the roughness impact, we have to account for both heat transfer enhancement and pressure losses. In this regard, heat transfer efficiency is often computed as a function of the Nusselt number and the friction factor [1]. Correlations that predict both Nusselt number and friction factor require a sandgrain roughness (εr).

Current roughness models are based on Nikuradse's work from 1933 [2]. In his experiments, Nikuradse artificially roughened pipes with uniform size sand grains and measured pressure drop. Interpreting roughness in this manner does not accurately characterize the 3D physical features of roughness (i.e., spacing, waviness, shape, etc.) [3]. The actual roughness depends on the surface material and the manufacturing process. Nevertheless, following Nikuradse's lead, Colebrook [4] developed a friction factor correlation, which Moody later used to formulate the Moody diagram [5]. Since then, the Moody diagram has been used to estimate εr values; however, the Moody diagram can be understood to be a hydraulic (not physical) scale [6].

Physical roughness is often measured using a stylus-type profilometer or perthometer. However, a perthometer measures only 2D or line roughness. The length the stylus can traverse (typically within a few tens of millimeters) and mechanical wear can further hinder the resolution of a perthometer.

In recent years, HTRI acquired a high-resolution 3D laser-scanning microscope for local characterization and measurement of roughness for a wide range of surfaces. Because of the need to measure roughness over an extended area, HTRI just added a new interferometry-based 3D microscope (Figure 2) to existing characterization instruments.

HTRI 3D interferometry-based microscope scanning SS-304 tube sample
Figure 2: HTRI 3D interferometry-based microscope scanning SS-304 tube sample

These microscopes allow measurement of several surface roughness parameters. Translating measured roughness parameters into an equivalent sandgrain roughness for use in predicting pressure drop and heat transfer coefficient remains challenging. Results presented in Figure 3 show that predicted pressure drop and heat transfer coefficients can differ if correlations use different measured roughness parameters of the same tube alloy (SS-304). Here, the measured maximum and average roughness parameters, shown in Figure 4, were used.

Predicted pressure and heat transfer coefficient change
Figure 3: Predicted pressure and heat transfer coefficient change using average and maximum roughness parameters measured using microscope shown in Figure 2
Illustration of average roughness and maximum peak to valley roughness
Figure 4: Illustration of (a) average roughness, Sa , and (b) maximum peak to valley roughness, Sz

HTRI is currently measuring the change in pressure drop and heat transfer coefficients for different heat exchanger tube alloys. Insights learned from measured data trends may provide guidance on how to better use measured roughness parameters in pressure drop and heat transfer coefficient correlations.

Nomenclature

h, Heat transfer coefficient, W/m2 K

Re, Reynolds number

Sa, Average roughness, µm

Sz, Maximum peak-to-valley roughness, um

Tbulk, Bulk temperature, °C

Twall, Wall temperature, °C

ΔP, Pressure drop, Pa

εr, Equivalent sandgain roughness, µm

References

  1. E. R. G. Eckert and R. M. Drake Jr., Analysis of Heat and Mass Transfer, Hemisphere Publishing, New York, NY, USA (1987).
  2. J. Nikuradse, Strömungsgesetze in Rauhen Rohren, VDI-Verlag, Berlin, Germany (1933).
  3. J. B. Taylor, A. L. Carrano, and S. G. Kandlikar, Characterization of the effect of surface roughness and texture on fluid flow—past, present, and future, Intl. J. Thermal Sci. 45(10), 962 – 968 (2006).
  4. C. F. Colebrook, Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws, J. Inst. Civil Eng. 11(4), 133 – 156 (1939).
  5. L. F. Moody, Friction factors for pipe flow, Trans. ASME 66(8), 671 – 684 (1944).
  6. K. A. Flack, Moving beyond Mood, J. Fluid Mech. 842, 1 – 4 (2018).