Unified Length Scale of Spray Structure by Unlike Impinging Jets

Abstract

In bi-propellant thrusters, impinging type injectors are widely used to deliver propellants to a combustion chamber. By impinging the jet streams of fuel and oxidizer, the spray spreads while the two liquids mix. To design the injectors, several correlations related to injection conditions have been proposed (e.g., Rupe factor), and practically utilized over the last half-century. However, the physical meanings of the past correlations are not well understood, because the essential scale of the spray structure is elusive. In this paper, we derive the global length scale of the spray produced by impinging injectors of unlike doublet, fuel-oxidizer-fuel triplet, and oxidizer-fuel-oxidizer triplet in a consistent manner. The unified length scale is found representing the spray width ratio of oxidizer to fuel evidenced by comprehensive cold-flow tests including several past studies, covering various parameters such as injector types, nozzle diameters, physical properties of working liquids, and injection velocities. Finally, we clearly provide the physical meaning based on practical correlations in a phenomenological sense.

Direct Formulation of Bipropellant Thruster Performance for Quantitative Cold-Flow Diagnostic

“…Combustion tests were performed for cases 1, 3, and 4 using the propellant combination of NTO/MMH (η 1480∕880 1.6) to obtain c from the Fig. 5 Unlike-doublet spray impinging dyed-water and water jets [15]. Fig.…”

“…2b. The validity of stream tube model was convinced in past studies [15,17] as an appropriate structure representing practical thrusters. At the upstream surface (left side) of the combustion chamber in Fig.…”

“…Irrespective of the liquid species and injection conditions, the physical meaning of Λ was clearly identified as a global length scale of the impinging spray [14,15]:…”

“…In recent years, authors [14,15] first identified the global scale of the unlike-impinging spray, succeeded in the direct formulation of characteristic velocity c as the function of injection conditions in bipropellant thrusters by extending the idea of the stream-tube approach [16], and confirmed the validity by comprehensive combustion tests. Afterward, the direct formulation of I sp was proposed [17] by combining the c prediction methodology with the nozzle performance prediction method.…”

Unsteady Stream-Tube Model for Pulse Performance of Bipropellant Thrusters

“…Following on from those studies, the present authors clarified a non-dimensional number governing the non-uniform mixture ratio occurring inside a thrust chamber, successfully formulating 𝑐 * and 𝐼 sp for any mixture ratio as a direct function of injection conditions during steady operation [31,32]. As a next step, it was hoped that a physics-based theoretical model useful for predicting pulse performance could be established.…”