1.2 Reviews
1.2.3 Heat transfer from transversely oscillating cylinders in cross-flow
Heat transfer from transversely oscillating cylinders in cross-flow was first studied by Sreenivassan and Ramachandram (1961) over the range 2500 < Re <
15000 in air. They concluded that transverse oscillations had no effect on heat transfer. This is likely because the oscillation frequencies used in their experiments were much lower than the natural shedding frequency. Though they considered amplitude ratios up to 1.8, the largest value of f* in their study was 0.07, which is only about 1/3 of the natural shedding frequency.
Later experiments have found that heat transfer from a cylinder is enhanced by transverse oscillations near the Strouhal frequency. Kezios and Prasanna (1966), working in the range 5500 < Re < 14000, found that heat transfer was enhanced by about 20% for small amplitude (0.02 < A/D < 0.075) oscillations at the Strouhal frequency. They found that this enhancement exceeded the expected increase in heat transfer if the effect was only due to the higher effective freestream velocity.
Saxena and Laird (1978) measured local heat transfer coefficients using thermocouples embedded in the cylinder surface. They conducted experiments at Re = 3500 in water over the range 0.89 ≤ A/D ≤ 1.99 and 0.28 ≤ f/fSt ≤ 0.83. Their results indicate that local heat transfer coefficients increase as the oscillation frequency approaches the Strouhal frequency. On the downstream half of the cylinder, local heat transfer coefficients were observed to increase by 50% to 60%
for the highest amplitudes and frequencies. Heat transfer enhancement on the downstream half of the cylinder was consistently about 15% higher than for the leading half of the cylinder.
Cheng et al. (1997) conducted experiments at Re = 200, 500 and 1000 in air.
Amplitude ratios of 0.138, 0.314 and 0.628 were explored over the range f* ≤ 0.3,
and heat transfer enhancement of up to 34% was observed. Enhancement near the Strouhal frequency was attributed to lock-on, or synchronization of the wake with the cylinder oscillations. High heat transfer coefficients at large amplitude ratios and high f*, particularly for the highest Reynolds number, were attributed to a vague
“turbulence effect.”
Park (1998) conducted experiments in water at Reynolds numbers of 550, 610, 1100 and 3500. He considered frequencies up to f* = 1.05 for two amplitude ratios, 0.1 and 0.2. Park found that heat transfer was significantly enhanced at frequencies corresponding to the Strouhal frequency and to 3 times the Strouhal frequency. For the larger amplitude ratio, Park also found that heat transfer was enhanced at 2 times the Strouhal frequency. Some of Park’s results for A/D = 0.2 are shown in Figure 1.7. Using digital particle image thermometry/velocimetry, Park was able to show that the heat transfer enhancement was correlated with a
shortening of the vortex roll-up distance. He suggested that the closer proximity of the vortices to the cylinder allowed hot, stagnant fluid to be moved away from the cylinder base.
Gau et al. (1999) performed experiments in air at Reynolds numbers of 1600, 3200 and 4800. They measured the local heat transfer coefficient for small
amplitude ratios of 0.016, 0.032 and 0.064 in the range 0.5 ≤ f/fSt ≤ 3.0. A sample of Gau et al.’s results is shown in Figure 1.8. Heat transfer is significantly enhanced at 1 and 3 times the Strouhal frequency, and the most significant enhancement occurs near the trailing edge of the cylinder for these cases. This is consistent with the other cases studied, as well.
Numerical simulations have also been used to study heat transfer from transversely oscillating cylinders. Karanth et al. (1994) computed the flow and heat transfer for Re = 200 and Pr = 1 at amplitude ratios of 0.25 and 0.5 for f* = 0.2. They predicted increases in the time-averaged heat transfer coefficient of 1.4% and 4.6%
for the two cases. The location of the highest local heat transfer coefficient was found to vary as a function of time, though it was always on the leading half of the cylinder. The largest increases in local heat transfer were observed close to the trailing edge.
Cheng and Hong (1997) also performed computations at Re = 200. They examined cases in the range f* ≤ 0.3 and A/D ≤ 0.7 with Pr = 0.71 and 7.0. For oscillations at the natural shedding frequency, heat transfer was significantly
enhanced, and the magnitude of the enhancement depended on the amplitude ratio.
These computational results agreed well with the experimental results of Cheng et al. (1997).
Two common trends in the above literature suggest a relationship between the wake structure and the heat transfer. First, enhanced heat transfer is observed for oscillations at the natural vortex shedding frequency of the stationary cylinder and at some of its harmonics. Second, for oscillation conditions with significant heat transfer enhancement, the largest increases in local heat transfer coefficient occur on the trailing half of the cylinder, where the influence of the trailing vortices is strongest. These facts imply that the vortex roll-up process is directly involved in determining the cylinder heat transfer coefficient. It is therefore reasonable to
suspect that the heat transfer coefficient for an oscillating cylinder will be correlated with the wake mode.
The oscillation conditions explored by these various authors are summarized in Figure 1.9 with the Williamson and Roshko (1988) wake mode boundaries
superimposed. While a reasonable portion of the (1/f*,A/D)-plane has been investigated, it has been in bits and pieces. Different information is available for each study, and it is difficult to compare results quantitatively because the methods used to determine the Nusselt number have varied widely. The details of the setups—such as Reynolds number, aspect ratio and Prandtl number—have also varied. Therefore, a consistent picture of the dependence of heat transfer coefficient on the oscillation parameters known to determine the wake mode does not exist.