The sampling error in the measurement of particle concentration is studied both theoretically and experimentally for the case that the sampling velocity is lower than the main-flow velocity. When the velocity ratio (ratio of the sampling velocity to the main-flow velocity) is larger than 0.5, the sampling efficiency is well predicted by the theory in which the end point of the critical trajectory is assumed, as usual, to coinside with the probe-inlet edge. On the other hand, the efficiencies for the velocity ratio between 0.2 and 0.5 are predicted by a modified theory in which the end point of the critical trajectory is assumed to coinside with the stagnation point of gas flow in the probe. In this range of the velocity ratio, returning flow entrains the particles which collide with the probe-inside wall between the inlet and the stagnation point.
When the velocity ratio is smaller than 0.2, even the particles deposited in the inmost recesses of the probe are reentrained.
The theoretical calculations show that the sampling efficiencies increase with increasing the gravitational parameter for the downward flow, while the efficiencies decrease with increasing the parameter for the upward flow. It is also found that the efficiency becomes larger when the flow Reynolds number increases and/or the particle-Reynolds number decreases.
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