3.2. Response characteristics for isothermal flow ðRi ¼ 0Þ

Figure 5 shows the nondimensional mean flow values for an isothermal flow ðRi ¼ 0Þ. In the absence of buoyancy, the mean flow solution is symmetric. Although the recirculation zone of the upstream semicylinder still occupies the total space within the gap, its width is now larger than the semicylinder diameter. In addition, the length of the near wake of the downstream semicylinder extends to X≈4:5 and a slight decrease in vorticity strength takes place.

Figure 6 shows typical instantaneous patterns of velocity and vorticity illustrating how vortex shedding takes place at the rear of the downstream semicylinder. The third strip illustrates how in the absence of buoyancy, the interaction between the shear layers generated by the upstream semicylinder and the confining walls reduces.

Figure 7 shows the time variations of the nondimensional longitudinal and transverse velocity components at the symmetry plane and selected positions inside the channel. This image shows how after an induction time of <sup>τ</sup>e120, flow oscillation within the gap and downstream of the lower semicylinder depict a nice harmonic behavior. Here, the amplitude of the oscillations reaches a peak at a location of ðX, YÞ¼ð5:5, 0Þ and decreases toward the downstream direction.

Figure 5. Nondimensional mean flow values for the unheated semicylinders at ReD ¼ 200, BR ¼ 0:2, σ ¼ 3, and Ri ¼ 0. From left to right: U and V velocity and Ω vorticity fields, respectively.

3.2. Response characteristics for isothermal flow ðRi ¼ 0Þ

228 Heat Exchangers– Design, Experiment and Simulation

upstream semicylinder and the confining walls reduces.

takes place.

positions.

direction.

Figure 5 shows the nondimensional mean flow values for an isothermal flow ðRi ¼ 0Þ. In the absence of buoyancy, the mean flow solution is symmetric. Although the recirculation zone of the upstream semicylinder still occupies the total space within the gap, its width is now larger than the semicylinder diameter. In addition, the length of the near wake of the downstream semicylinder extends to X≈4:5 and a slight decrease in vorticity strength

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>

Figure 6 shows typical instantaneous patterns of velocity and vorticity illustrating how vortex shedding takes place at the rear of the downstream semicylinder. The third strip illustrates how in the absence of buoyancy, the interaction between the shear layers generated by the

Figure 7 shows the time variations of the nondimensional longitudinal and transverse velocity components at the symmetry plane and selected positions inside the channel. This image shows how after an induction time of <sup>τ</sup>e120, flow oscillation within the gap and downstream of the lower semicylinder depict a nice harmonic behavior. Here, the amplitude of the oscillations reaches a peak at a location of ðX, YÞ¼ð5:5, 0Þ and decreases toward the downstream

Figure 6. Nondimensional near-wake patterns of instantaneous velocity and vorticity contours for the unheated semicylinders at ReD ¼ 200, BR ¼ 0:2, σ ¼ 3, and Ri ¼ 0. From left to right: U and V velocity and Ω vorticity fields, respectively.

Figure 7. Time variations of the nondimensional longitudinal and transverse velocity components as a function of the nondimensional time at ReD ¼ 200, BR ¼ 0:2, σ ¼ 3, and Ri ¼ 0. The extracted data is obtained at the symmetry plane and several X positions.
