Flow over a Heated Cylinder

The cylinder is placed in an incoming air stream and will acquire certain temperature depending on the heat source power and the air stream velocity and temperature. The geometry model is shown in Figure 1.

Based on experimental data for the average coefficient of heat transfer from a heated circular cylinder to air flowing over it (see Ref. 12), the corresponding Nusselt number can be determined from the following formula:

where constants C and n are taken from the Table 1 below.

Here, the Nusselt number, NuD = (h∙D)/k (where h is the heat transfer coefficient averaged over the cylinder, and k is fluid thermal conductivity), the Reynolds number, ReD = (U∙D)/μ (where U is the incoming stream velocity, and μ is fluid dynamic viscosity), and the Prandtl number, Pr = μ∙Cp/k (where μ is fluid dynamic viscosity, Cp is fluid specific heat at constant pressure, and k is fluid thermal conductivity) are based on the cylinder diameter D and on the fluid properties taken at the near-wall flow layer. According to Ref. 12, Pr = 0.72 for the entire range of ReD.

To validate the Flow Simulation predictions, the air properties have been specified to provide Pr = 0.72: k = 0.0251375 W/(m∙K), μ = 1.8∙10-5 Pa∙s, specific heat at constant pressure Cp = 1005.5 J/(kg∙K). Then, the incoming stream velocity, U, has been specified to obtain ReD = 1, 10, 100, 103, 104, 5∙104, 105, 2∙105, and 3∙105 for a cylinder diameter of D = 0.1 m (see Figure 1).

This validation approach consists of specifying the heat generation source inside the cylinder with a power determined from the desired steady-state cylinder temperature and the average heat transfer coefficient, h = (NuD∙k)/D. NuD is determined from the specified ReD using the empirical formula presented above. The final cylinder surface temperature, that is also required for specifying the heat source power Q (see Table 2) is assumed to be 10°C higher than the incoming air temperature. The initial cylinder temperature and the incoming air temperature are equal to 293.15 K. The cylinder material is aluminum. Here, the heat conduction in the solid is calculated simultaneously with the flow calculation, i.e., the conjugate heat transfer problem is solved.

As a result of the calculation, the cylinder surface has acquired a steady-state temperature differing from the theoretical one corresponding to the heat generation source specified inside the cylinder. Multiplying the theoretical value of the Nusselt number by the ratio of the obtained temperature difference (between the incoming air temperature and the cylinder surface temperature) to the specified temperature difference, we have determined the predicted Nusselt number versus the specified Reynolds number. The values obtained by solving the steady-state and time dependent problems at result resolution level 5 are presented in Figure 2 together with the experimental data taken from Ref. 12.

From Figure 2, it is seen that the predictions made with Flow Simulation, both in the time-dependent approach and in the steady-state one, are excellent within the whole ReD range under consideration.