# Plane mixing layers from parallel and non-parallel merging of two streams

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## Abstract

Two types of mixing layers produced from two streams merging at 0° and 18° have been investigated. Each type of mixing layer was produced with velocity ratios 0.7, 0.8 and 0.9 and measurements were taken at six streamwise locations. The boundary layers were untripped and initially turbulent in all cases. Both types of mixing layers were found to attain a self-similar state for velocity ratios 0.7 and 0.8 but failed for 0.9 within the measurement domain. It appears that the mixing layer flow becomes self-similar earlier when merging at 18° than at 0°. With increasing velocity ratio, the development distance was increased and the splitter wake played a dominant role in the development of the mixing layers. The mixing layers from non-parallel merging streams (18°) were found to have higher growth in the near-field than those from parallel merging streams (0°). Both types of mixing layers were found to decrease in growth with increasing velocity ratio, though they spread more at the high-speed side.

## Keywords

Reynolds Stress Velocity Ratio Free Shear Layer Streamwise Pressure Gradient Streamwise Velocity Profile## List of symbols

*α*angle of merging

*δ*mixing layer thickness (=

*y*_{0.1}–*y*_{0.9})*η*similarity variable [=(

*y*–*y*_{0.5})/*δ*]*λ*modified velocity ratio [=(1−

*r*)/(1+*r*)]*r*velocity ratio (=

*u*_{2}/*u*_{1})*Re*_{θ}Reynolds number based on

*θ*(=*u*_{o}*θ*/*ν*)*θ*momentum thickness of the mixing layer

*u,v*mean velocities in

*x*and*y*directions, respectively*u′(t)*fluctuating component of the streamwise velocity

*u*^{⋆}non-dimensional velocity [=(

*u*−*u*_{2})/(*u*_{1}−*u*_{2})]*u*_{c}mixing layer convection velocity [=(

*u*_{1}+*u*_{2})/2]*u*_{e}free-stream velocity (at 470 mm upstream)

*u*_{o}shear velocity (=

*u*_{1}−*u*_{2})*u*_{1},*u*_{2}mean velocities of high and low speed streams, respectively

- \(\overline {u'^2 } \)
Reynolds streamwise normal stress

- \(\overline {v'^2 } \)
Reynolds cross-stream normal stress

- \(\overline {w'^2 } \)
Reynolds spanwise normal stress

- \(\overline {u'v'} \)
Reynolds primary shear stress

*x, y*streamwise and cross-stream directions, respectively

*x*_{o}virtual origin of the mixing layer

*y*_{0.1}isovel for

*u*^{⋆}=0.1; similarly for*y*_{0.05},*y*_{0.5},*y*_{0.9}and*y*_{0.95}- ()
_{max} max maximum value at given

*x*location

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