Quantitative liquid jet instability measurement system using asymmetric magnification and digital image processing

A new technique for measuring the growth of instabilities on the surface of liquid jets flowing into gas is demonstrated. A collimated beam of white light illuminates the jet from behind, forming a shadow image. A pair of cylindrical lenses are arranged to provide different magnifications in the streamwise and cross-stream directions. A number of streamwise diameters and one cross-stream diameter are thus captured with maximum resolution in a single image on a charge-coupled device (CCD) electronic camera. A short-duration spark is used to freeze the jet motion. A mask representing the theoretical edge-response of the imaging system is digitally convolved with the cross-stream gray scale data to obtain sub-pixel resolution of the jet edge profile. The method is demonstrated using the well-known capillary jet instability and a ratio of streamwise to cross-stream magnifications of 40. Well-resolved single images show the development of the instability from small perturbations through the formation of the first drop. The system forms an accurate automated method of measuring the development of liquid jet instabilities. It can readily be applied to practical problems including liquid jet atomization.List of symbols a undisturbed jet radius - k nondimensional wavenumber (= 2a/) - Q gas-to-liquid density ratio - r ₀ mean jet radius, from initial region of image - R Reynolds number (= 2Ua/) - U mean jet velocity - We Weber number - z streamwise coordinate, origin at jet orifice - temporal growth rate - _s measured spatial growth rate - nondimensional temporal growth rate - r absolute value of height of peaks or troughs relative to r ₀ - r ₁ height of first extremum in a particular record - instability wavelength - liquid viscosity - liquid density - surface tension of liquid-gas interface