Drag crisis analysis of a high-altitude balloon in critical transition

Drag coefficient is one of the crucial parameters in the dynamic modeling of position control systems for high-altitude super-pressure balloons. Numerical simulations with Transition SST model are conducted to analyze the drag characteristics of a typical shape of super-pressure balloons. A series of the freestream Reynolds numbers in the range of 10³ to 10⁷ are considered, covering the subcritical, critical, and supercritical regimes of the flow transition. The relationship of the drag coefficient to the Reynolds number is obtained to present the drag crisis in the critical regime. The precipitous drop of the drag coefficient is observed as the Reynolds number increases. Accordingly, a fitted formula of the drag coefficient with respect to the Reynolds number is proposed, which is able to effectively predict the drag coefficient in the critical regime. Complex Flow phenomena at the critical Reynolds number are further analyzed by the flowfield and wall properties around the balloon. Flow transition is observed at the flat top area and the leeward side. Downstream of the transition, the flow separation occurs with the formation of a separation bubble. In the transition regions, substantial changes in pressure and skin friction coefficients are demonstrated.