In the present study, the structure of normal (or inverted) Bunsen flame tips under the influence of a monodisperse dilute water spray and external heat loss is investigated using large activation energy asymptotics. We consider two flame structures: normal and inverted Bunsen flames, and two spray modes: completely and partially prevaporized burnings. In this way, a complete parametric study of flame tip intensification or extinction (opening) can be conducted. Five parameters are used in the analysis. Three are the droplet size, amount of liquid-water loading (which indicates internal heat loss for inert spray), and the external heat loss. The other two are the stretch and Lewis number (Le). Stretch is negative for a normal Bunsen flame but positive for an inverted Bunsen flame. Stretch strengthens (or weakens) the burning intensity of the Le > 1 (or Le < 1) normal Bunsen flame but decreases (or increases) the burning intensity of the Le > 1 (or Le 1) inverted Bunsen flame. Burning intensity of the flame tip weakens when the water spray has a smaller droplet size or a larger amount of liquid loading, or when the curved flame experiences a larger amount external heart loss. For a rich methane-air normal Bunsen flame with Le > 1 ora lean methane-air inverted Bunsen flame with Le 1, closed-tip solutions are obtained. Conversely, stretch weakens the burning intensity of a rich methane-air inverted Bunsen flame with Le > 1, or a lean methane-air normal Bunsen flame with Le < 1, eventually leading to tip opening. Moreover, the opening becomes wider when the droplet size decreases, liquid loading increases, or external beat loss enlarges.