On the measurement of particle concentration near a stagnation point

Conclusions

• (1) This work has evaluated the particle number density measured by a single particle counting instrument, based on either the particle mean velocity or on the particle residence time in the measuring volume.

• (2a) In regions where the mean velocity of a size class is near zero the number density should be based on the residence time of the particle, Eq. (3).

• (2b) Equation (3) can be used for two-dimensional flow and removes the need to measure the magnitude of the velocity vector, as is the case with the definition of Eq. (1), provided that V(d _i ) — and hence A(d _i ) — is known. A twochannel laser-Doppler anemometer, however, permits the direct, “on-line” measurement of V(d _i ) and A(d _i ).

• (3) In regions where the mean velocity of all size classes is non-zero, there is little difference in the values of the Sauter mean diameter returned by the two equations.

• (4) In instruments which do not have the facility for measuring the residence time, it is suggested that the Sauter mean diameter should be evaluated directly from the measured value of n _i .

• (5) For instruments based on laser-Doppler anemometry, the correction for the effect of frequency shifting on the cross-sectional area, A(d _i ) and volume, V(d _i ), of the anemometer is of the order of 25% for small particles and for N _f /N ₀ = 1.4.

• (6) Further work is required to establish the theoretical foundation of Eq. (3) in relation to the work of Buchhave et al. (1979). The accuracy with which C(d _i ) can be measured is determined by the tolerances on A(d _i ), V(d _i ) and z _p .Further experimental work is also required to determine the accuracy with which these quantities are known.