Abstract
Research has been performed to determine the accuracy of neutrally buoyant and near-neutrally-buoyant bubbles used as flow tracers in an incompressible potential flowfield. Experimental and computational results are presented to evaluate the quantitative accuracy of neutrally buoyant bubbles using a commercially available helium bubble generation system. A two-dimensional experiment was conducted to determine actual bubble trajectories in the stagnation region of a NACA 0012 airfoil at 0° angle of attack. A computational scheme evaluating the equation of motion for a single bubble was also used to determine the factors which affect a bubble's trajectory. The theoretical and computational analysis have shown that neutrally buoyant bubbles will trace complex flow patterns faithfully in the flowfield of interest. Experimental analysis revealed that the use of bubbles generated by the commercially available system to trace flow patterns should be limited to qualitative measurements unless care is taken to ensure neutral buoyancy.
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Abbreviations
- a c :
-
centripetal acceleration
- c :
-
model chord
- c D :
-
bubble drag coefficient
- D :
-
bubble diameter
- g :
-
acceleration due to gravity
- g v :
-
acceleration due to gravity vector
- h :
-
trajectory deviation normalization parameter
- K :
-
nondimensional inertia parameter, \(\sigma D^2 U_\infty /18c\mu \)
- m f :
-
mass of fluid
- m p :
-
mass of bubble
- p :
-
static pressure
- r :
-
radial distance, bubble radius
- R :
-
gas constant
- Re :
-
free-stream Reynolds number, \(\rho cU_\infty /\mu \)
- Re p :
-
bubble slip Reynolds number, \((\rho DU_\infty /\mu )|v_p - v_f |\)
- S :
-
cross-sectional area of sphere
- T :
-
temperature
- t :
-
time
- u :
-
streamwise velocity component
- U ∞ :
-
free-stream velocity
- v f :
-
fluid velocity vector
- V p :
-
bubble velocity vector
- x p :
-
bubble position vector
- y b :
-
bubble trajectory y/c
- y s :
-
streamline y/c
- α :
-
model angle of attack
- γ :
-
bubble solution surface tension
- Γ :
-
potential vortex strength
- ϱ bfs :
-
bubble solution density
- ϱ :
-
fluid density
- σ :
-
bubble density
- Γ :
-
bubble wall thickness
- μ :
-
fluid viscosity
References
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Kerho, M.F., Bragg, M.B. Neutrally buoyant bubbles used as flow tracers in air. Experiments in Fluids 16, 393–400 (1994). https://doi.org/10.1007/BF00202064
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DOI: https://doi.org/10.1007/BF00202064