Stochastic rocket dynamics under random nozzle side loads: Ornstein-Uhlenbeck boundary layer separation and its coarse grained connection to side loading and rocket response

TL;DR

This paper models the stochastic dynamics of rocket response to altitude-dependent side loads caused by boundary layer separation, using Ornstein-Uhlenbeck processes to connect boundary layer behavior with overall rocket motion, validated against high-fidelity simulations.

Contribution

It introduces a novel analytical framework linking boundary layer separation dynamics to rocket response via OU processes, providing insights for response mitigation.

Findings

Model accurately predicts altitude-dependent response statistics.

Separation line behavior aligns with experimental side load distributions.

Analytical models suggest effective response reduction strategies.

Abstract

A long-standing, though ill-understood problem in rocket dynamics, rocket response to random, altitude-dependent nozzle side-loads, is investigated. Side loads arise during low altitude flight due to random, asymmetric, shock-induced separation of in-nozzle boundary layers. In this paper, stochastic evolution of the in-nozzle boundary layer separation line, an essential feature underlying side load generation, is connected to random, altitude-dependent rotational and translational rocket response via a set of simple analytical models. Separation line motion, extant on a fast boundary layer time scale, is modeled as an Ornstein-Uhlenbeck process. Pitch and yaw responses, taking place on a long, rocket dynamics time scale, are shown to likewise evolve as OU processes. Stochastic, altitude-dependent rocket translational motion follows from linear, asymptotic versions of the full nonlinear equations of motion; the model is valid in the practical limit where random pitch, yaw, and roll rates all remain small. Computed altitudedependent rotational and translational velocity and displacement statistics are compared against those obtained using recently reported high fidelity simulations [Srivastava, Tkacik, and Keanini, J. Applied Phys., 108, 044911 (2010)]; in every case, reasonable agreement is observed. As an important prelude, evidence indicating the physical consistency of the model introduced in the above article is first presented: it is shown that the study's separation line model allows direct derivation of experimentally observed side load amplitude and direction densities. Finally, it is found that the analytical models proposed in this paper allow straightforward identification of practical approaches for: i) reducing pitch/yaw response to side loads, and ii) enhancing pitch/yaw damping once side loads cease.