**5.2. Graphical illustration of the results of analysis by Yakhot, Arad and Ben-dor (1999)**

The velocity profiles in pulsating flow at selected instants within one complete period are shown below. Flow in a duct is compared to flow between parallel plates for different aspect ratios and frequencies.

**Figure 7.** Sketch of the rectangular duct used by Yakhot, Arad and Ben-dor (1999) in their numerical studies.

due to the effects of viscosity.

of the duct. On the axis, the phase shift is 90o

112 Wind Tunnel Designs and Their Diverse Engineering Applications

side walls. This is clearly due to the effects of viscosity.

For low pulsating frequencies, *h* =1 , flow in a duct of square cross-sectional area, the ve‐ locity distribution is in phase, that is in lock step, with the driving pressure gradient. This was true at low and at high aspect ratios. This result is the same as what happens in the case of flow between parallel plates. When one compares the amplitudes of the in‐ duced velocity, one finds that the amplitude of flow between flat plates is larger than that in a square duct. This is due to the fact that, in a duct the fluid experiences friction of four sides, whereas in the case of flow between parallel plates, it experiences flow on‐ ly from two sides. When the aspect ratio is increased to a/h = 10, the velocity in the duct differs only with the velocity between parallel plates near the side walls. This is clearly

For moderately pulsating frequencies, *αh* =8 , the velocity distribution of the flow in a duct of square cross- sectional area differs considerably from that obtained at low frequencies. The shapes of the velocity profiles are different; results indicate that, at certain instants of time during a complete cycle, the profiles reach maximum values near the wall of the pipe rather than on its axis of symmetry. This is Richardson's "annular effect". The induced ve‐ locity is no longer in phase, that is in lock step, with the driving pressure gradient. Rather, the velocity is shifted with respect to the driving pressure and the magnitude of the shift de‐ pends on how far away points in the flow space are from the wall. Near the wall, the in‐ duced velocity on the axis of the duct lags behind that in the regions that are near the walls

This result is the same as what happens in the case of flow between parallel plates. When one compares the amplitudes of the induced velocity, one finds that the amplitude of flow between flat plates is larger than that in a square duct. This is due to the fact that, in a duct the fluid experiences friction of four sides, whereas in the case of flow between parallel plates, it experiences flow only from two sides. When the aspect ratio is increased to a/h = 10, the velocity in the duct differs only with the velocity between parallel plates near the

. This was true at low and at high aspect ratios.

**Figure 8.** Velocity profiles in pulsating flow at different instants of one period. (a) Pressure gradient variation with time. (b) Duct flow, a/*h* =1, α *h =1*: solid line, *x*/*a* = 0.5; dashed, *x*/*a* = 0.25; dot-dashed, *x*/*a* = 0.1. (c) Flow between two parallel plates.

**Figure 9.** Velocity profiles in pulsating flow at different instants of one period. (a) Pressure gradient variation with time. (b) Duct flow, a/*h* =10, α *h=1*: solid line, *x*/*a* = 0.5; dot, *x*/*a* = 0.1; dashed, *x*/*a* = 0.025; dot-dashed, *x*/*a* = 0.01. (c) Flow between two parallel plates.

**Figure 10.** Velocity profiles in pulsating flow at different instants of one period. (a) Pressure gradient variation with time. (b) Duct flow, a/*h* =1, α *h=8*: solid line, *x*/*a* = 0.5; dashed, *x*/*a* = 0.25; dot-dashed, *x*/*a* = 0.1. (c) Flow between two parallel plates.

A Method of Evaluating the Presence of Fan-Blade-Rotation Induced Unsteadiness in Wind Tunnel Experiments http://dx.doi.org/10.5772/54144 115

**Figure 11.** Velocity profiles in pulsating flow at different instants of one period. (a) Pressure gradient variation with time. (b) Duct flow, a/*h* =10, α *h=8*: solid line, *x*/*a* = 0.5; dashed, *x*/*a* = 0.025; dot-dashed, *x*/*a* = 0.01. (c) Flow between two parallel plates.
