3.1. Response characteristics for assisting flow ðRi ¼ −1Þ

In this section, the response characteristics for assisting flow are presented. Figure 2 shows the resulting nondimensional mean flow and thermal profiles at Ri <sup>¼</sup> <sup>−</sup><sup>1</sup> <sup>ð</sup>Gr <sup>¼</sup> <sup>−</sup>4×104 Þ, illustrating how the relatively narrow wake of the upstream semicylinder reattaches at the forebody of the downstream semicylinder. Here, the near wake of the latter is clearly shorter and narrower and an increase in the longitudinal velocity component is observed at the central part of the channel ðY ¼ 0Þ toward the downstream direction. The third strip illustrates how for the cooling process, the flow pattern is slightly asymmetric and the peak vorticity values are particularly large.

Figure 3 shows typical instantaneous flow and thermal patterns for Ri ¼ −1, illustrating how small amplitude flow oscillation takes place within the gap, while Kármán vortices of relatively small size are shed from the rear face of the downstream semicylinder. The third strip shows how the interaction between the shear layers generated at the surface of both semicylinders and the channel walls increases toward the downstream direction and reaches a peak at a location of X≈7.

time τ ¼ 0. Transient calculations are performed up to 500 nondimensional time units. In order to make comparisons with experimental results obtained on what are effectively unbounded

> D ð =2

−D=2

In Eq. (10), u is the vertical component of the velocity field specified on the upstream boundary and uD is the average longitudinal velocity based on the diameter of the semicylinder. The accuracy of the numerical algorithm was tested by comparing results of the mean Nusselt number against available analytical [2] and numerical results [35] for the standard case of a symmetrically confined isothermal circular cylinder in a plane channel. Details about the numerical solution, validation of the algorithm and the grid employed can be found elsewhere [36, 37].

The numerical results presented in this work correspond in all cases to ReD ¼ 200, Pr ¼ 7, BR ¼ 0:2, and σ ¼ L=D ¼ 3. In this section, results are presented for the mean and instantaneous flow and thermal characteristics under varying thermal buoyancy. For clarity, only a portion of the computational domain is shown. The images display (from left to right) the nondimensional longitudinal and transverse velocity components with superimposed streamlines, the nondimensional vorticity field and the temperature field with superimposed velocity profiles. The color scales below each image map the velocity, vorticity and temperature contours, with red/yellow coloration representing positive vorticity or counterclockwise fluid

In this section, the response characteristics for assisting flow are presented. Figure 2 shows the

how the relatively narrow wake of the upstream semicylinder reattaches at the forebody of the downstream semicylinder. Here, the near wake of the latter is clearly shorter and narrower and an increase in the longitudinal velocity component is observed at the central part of the channel ðY ¼ 0Þ toward the downstream direction. The third strip illustrates how for the cooling process, the flow pattern is slightly asymmetric and the peak vorticity values are particularly large.

Figure 3 shows typical instantaneous flow and thermal patterns for Ri ¼ −1, illustrating how small amplitude flow oscillation takes place within the gap, while Kármán vortices of relatively small size are shed from the rear face of the downstream semicylinder. The third strip shows how the interaction between the shear layers generated at the surface of both semicylinders and the channel walls increases toward the downstream direction and reaches a peak at a location of

resulting nondimensional mean flow and thermal profiles at Ri <sup>¼</sup> <sup>−</sup><sup>1</sup> <sup>ð</sup>Gr <sup>¼</sup> <sup>−</sup>4×104

rotation and the green regions reflecting a lack of rotational motion.

3.1. Response characteristics for assisting flow ðRi ¼ −1Þ

uðyÞdy: (10)

Þ, illustrating

domains, Chen et al. [35] defined a Reynolds number, ReD ¼ uDD=ν, where

3. Results and discussion

226 Heat Exchangers– Design, Experiment and Simulation

X≈7.

uD <sup>¼</sup> <sup>1</sup> D

Figure 2. Nondimensional mean flow values at ReD <sup>¼</sup> 200, BR <sup>¼</sup> <sup>0</sup>:2, <sup>σ</sup> <sup>¼</sup> 3 and Ri <sup>¼</sup> <sup>−</sup><sup>1</sup> <sup>ð</sup>Gr <sup>¼</sup> <sup>−</sup>4×10<sup>4</sup>Þ. From left to right: U and V velocity, Ω vorticity and θ temperature fields, respectively.

Figure 3. Nondimensional near wake patterns of instantaneous velocity, vorticity and temperature contours at ReD ¼ 200, BR <sup>¼</sup> <sup>0</sup>:2, <sup>σ</sup> <sup>¼</sup> <sup>3</sup>, and Ri <sup>¼</sup> <sup>−</sup><sup>1</sup> <sup>ð</sup>Gr <sup>¼</sup> <sup>−</sup>4×104 Þ. From left to right: U and V velocity, Ω vorticity and θ temperature fields, respectively.

Figure 4 shows the time variations of the nondimensional longitudinal and transverse velocity components at the symmetry plane and selected positions inside the channel. Clearly, the velocity fluctuations depict a harmonic behavior after a short induction time of <sup>τ</sup>e100. The inset of the top and bottom left images illustrates how the recirculation zone within the gap depicts small amplitude oscillations at a location of ðX, YÞ¼ð1:5, 0Þ, while the maximum amplitude of the velocity fluctuations is reached at a downstream position of ðX, YÞ¼ð4:5, 0Þ.

Figure 4. Time variations of the nondimensional longitudinal and transverse velocity components as a function of the nondimensional time at Ri <sup>¼</sup> <sup>−</sup><sup>1</sup> <sup>ð</sup>Gr <sup>¼</sup> <sup>−</sup>4×10<sup>4</sup>Þ. The extracted data is obtained at the symmetry plane and several <sup>X</sup> positions.
