Submerged combustion methods and systems including a melter equipped with an exhaust passage through the ceiling or the sidewall having an aggregate hydraulic diameter. Submerged combustion burners configured to create turbulent conditions in substantially all of the material being melted, and produce ejected portions of melted material. An exhaust structure including a liquid-cooled exhaust structure defining a liquid-cooled exhaust chamber having a cross-sectional area greater than that of the exhaust stack but less than the melter. The exhaust passage and liquid-cooled exhaust structure configured to maintain temperature and pressure of the exhaust, and exhaust velocity through the exhaust passage and the exhaust structure, at values sufficient to prevent the ejected material portions of melted material from being propelled out of the exhaust structure as solidified material, and maintain any molten materials contacting the first interior surface molten so that it flows down the first interior surface into the melter.