Adopting molecular tagging velocimetry for high-resolution measurements of oscillating grid turbulence
Authors: Ramesh Bhaarath , Klewicki Joseph C. , Philip Jimmy 
Published: March 2024

Single-component molecular tagging velocimetry (1c-MTV) experiments are conducted in an oscillating grid turbulence facility to systematically clarify the trade-offs between maximizing measurement dynamic range and minimizing measurement uncertainty. The primary aim is to obtain reliable turbulence data with the maximum possible vector resolution ($$\varDelta {x}_{1}$$

Δ

x
1

). Four optical magnifications ($$M{_{0}}$$

M

0

=0.11, 0.22, 0.45, 1.11) with four interframe time delay ($$\varDelta {t}$$

Δ
t

) values, for each optical magnification case, ranging from 3 to 10 ms, are investigated. The grid oscillates with a frequency (f) of 3.2 and 4.1 Hz, and a single fixed stroke length (S) of 55 mm. The measurement quality is quantified using three important turbulence descriptors — the second-order transverse velocity correlation function $$(\langle {g(r)}\rangle )$$

(
⟨

g
(
r
)

⟩
)

, the second-order transverse velocity structure function $$([\Delta {_{g}u}]^2)$$

(

[
Δ

g

u

]

2

)

, and the turbulence energy dissipation rate ($$\langle \epsilon \rangle$$

⟨
ϵ
⟩

). Other descriptors such as the longitudinal integral length scale (l) and the longitudinal Taylor microscale ($${\lambda }$$
λ
) are also used to compare with reference values reported in literature. The degree of agreement with the reference values from literature, and insensitivity of the descriptor estimates to different MTV design parameters are used to determine the most robust means of obtaining high-resolution turbulence data from 1c-MTV. The experimental design parameters are contextualized using the Kolmogorov length ($${\eta }$$
η
), time ($${\tau _{\eta }}$$

τ
η

), and velocity ($${u_{\eta }}$$

u
η

) scales that are based on the most reliable $$\langle {\epsilon }\rangle$$

⟨
ϵ
⟩

estimates from the current experiments. The pixel-displacement corresponding to $${u_{\eta }}$$

u
η

$$({\varDelta {x}{_{2}}{_{\eta }}})$$

(

Δ
x

2

η

)

describes the interdependencies between $${M_{0}}$$

M
0

and $$\varDelta {t}$$

Δ
t

. The data set with $${M_{0}}=0.45$$

M
0

=
0.45

($${\eta =}18{\varDelta {x}_{1}}$$

η
=

18

Δ

x
1

for f=3.2 Hz, and $${\eta =}13{\varDelta {x}_{1}}$$

η
=

13

Δ

x
1

for f=4.1 Hz) represents the most reliable and the highest resolution case. This conclusion was deduced by taking the performance of all the turbulence descriptors into account. As far as the interframe time delay is concerned, $$\varDelta {t} \ge$$

Δ
t
≥

4 ms ($${\varDelta {x}{_{2}}{_{\eta }}}\ge 0.5 \text {pixels}$$

Δ
x

2

η

≥
0.5
pixels

) works well for all $${{M}_{0}}$$

M
0

. To the authors’ knowledge, the present study documents the first instance of a series of 1c-MTV experiments conducted for a systematic clarification of the nature of balancing the available dynamic range and the measurement uncertainty. Additionally, since the study involves turbulent flow with negligible mean-flow, it serves as an adequate representation of 1c-MTV performance in a three-dimensional flow.