POGO Instability Research Articles

Adaptive control design for active Pogo suppression of large strap-on liquid launch vehicles

In order to better solve the problem of Pogo stability considering parameter uncertainty and time-variation in the large launch vehicle, the model-reference adaptive control based on the dimensionality reduction model (MRAC-DRM) is proposed. Firstly, the state space Pogo model with an active controller is established for control system design by the improved Rubin method. Secondly, a greatly reduced dimensional model of the Pogo control system is derived from the eigenvalue transformation theory, which preserves the features of Pogo instability and is appropriate for control design. Then, the reference model and adaptive control law are designed by the model-reference adaptive control method based on the reduced dimensional model. Finally, two examples with different types of propulsion systems are used to demonstrate the effectiveness of the proposed MRAC-DRM. Simulation results demonstrate that the proposed method not only has excellent adaptability to the Pogo systems with parameter uncertainty and time-variation but also is insensitive to the initial value of feedback gain.

Dynamic Model-Based Identification of Cavitation Compliance and Mass Flow Gain Factor in Rocket Engine Turbopump Inducers

Abstract Cavitation dynamics continue to pose a significant risk in the development and operation of launch vehicle (LV) propulsion systems. In addition to generating unsteady loads that can directly damage turbopump hardware, cavitation dynamics often couple with LV fluid feed systems, producing system wide POGO instability that can cause catastrophic failures. Despite its importance, the current understanding of cavitation dynamics, and especially pump transfer matrices, is limited. Given the relatively sparse amount of inducer transfer matrix data available, there is a critical need for more in-depth characterization of the cavitation dynamics in turbopump inducers to avoid POGO instability. This paper defines and validates a new reduced-order approach to infer key parameters such as cavitation compliance, K, and mass flow gain factor, M, from simple, single sensor unsteady pressure measurements during inducer inlet pressure ramps. The utility of this approach is demonstrated for a range of inducer geometries reported in the literature. The results are in agreement with experimental data and the paper provides a new capability supporting the assessment of LV POGO instability.

Верифікація гідродинамічної моделі кавітуючих насосів РРД за теоретичними та експериментальними передавальними матрицями насосів

Cavities at the pump inlet may lead to inadmissible cavitation self-oscillations in the feed system of liquid-propellant rocket engines (LPREs) and to POGO instability if the oscillation frequency of the liquid is close to that of the rocket structure. Because of this, it is important to prevent both cavitation and POGO oscillations as early as at the engine and rocket design stage. This calls for a reliable mathematical model of the dynamics of LPRE cavitating pumps. In this paper, a hydrodynamic model of LPRE cavitating pumps is verified using theoretical and experimental transfer matrices of cavitating pumps. The experimental transfer matrix was borrowed from Brennen, Meissner, Lo, and Hoffman’s work because it features the least spread of values among the matrices reported in the literature. The theoretical matrix was borrowed from Pilpenko and Kvasha’s work where is was constructed for a cavitating pump as a distributed-parameter system. Four versions of the hydrodynamic model of LPRE cavitating pumps are verified, and six possible model coefficients are considered. Only one coefficient, namely, the liquid inertance at the cavity location, takes a physically meaningless negative value, which makes its use impossible. The verification results show that a four-coefficient model of cavitating pipe dynamics adequately describes cavitation effects in LPRE pumps over the frequency range up to 200 Hz. The four coefficients are the cavitation elasticity, the cavitation resistance, the cavity-caused disturbance transfer delay time, and the cavity time constant or the cavitation resistance distribution coefficient.

Pogo Accumulator Optimization Based on Multiphysics of Liquid Rockets and Neural Networks

In this study, a numerical analysis of pogo instability in liquid propulsion rockets was conducted and an optimization of the pogo suppressor was attempted. Pogo analysis was carried out using numerical results obtained via the major models for fuselage structure, feedline, and propulsion systems. In the structural system, the fuselage vibration modes were obtained and the relevant meta-model was constructed using the modal superposition method. To obtain accurate results for the hydraulic transmission line modeling, cavitation effects were also taken into account. Thus, a numerical analysis was performed on a pump inducer to provide the quantitative information of the cavitation volume in the liquid-oxygen feedline. By employing the rocket combustion equations, it was confirmed that the dynamic response was fed back to the longitudinal characteristics of the fuselage structure. In addition, an accumulator was installed to suppress pogo instability. For design optimization, an artificial neural network was suggested by performing Latin hypercube sampling. The sampling verifies the convergence by the learning process. Finally, a multi-objective optimization for the pogo accumulator was achieved with the present meta-model.

예비설계 단계 우주발사체의 공급/추진계 모델을 이용한 포고 불안정성 예측

예비설계 단계 우주발사체의 공급/추진계 모델을 이용한 포고 불안정성 예측

Effects of Damping Ratio and Critical Coupling Strength on Pogo Instability

Limitations of the classical critical damping ratio method are discussed and a new method based on critical coupling strength for pogo stability is proposed in this paper. First, the effects of the damping ratio on pogo stability are investigated in detail. When the structural damping ratio is less than the propulsion system damping ratio, increasing the structural damping ratio will increase pogo stability monotonically. However, when the structural damping ratio is greater than the propulsion system damping ratio, the effect of the structural damping ratio on pogo stability is complex and nonmonotonic. So, applicability of the critical damping ratio method is limited. Then, a critical coupling strength method for pogo stability is proposed, considering the effect of coupling strength on pogo stability is always monotonic. Furthermore, a stability margin is defined based on the critical coupling strength. Compared to the critical damping ratio method, the critical coupling strength method is always applicable. Finally, through analyzing the effects of the physical parameters (such as equivalent stiffness, combustion resistance, and structural damping ratio) on pogo stability of a certain type of Chinese liquid rocket, the limited applicability of the critical damping ratio method and the validity of the critical coupling strength method are demonstrated.

Analysis on Stability of POGO and Parameters of Propulsion System in Liquid Rocket

To explore effective methods of avoiding POGO instability, this paper starts with a thorough study on influence of parameters on natural frequency of propulsion system in liquid rocket. By adopting the method of critical damping ratio, stability of coupled structure-propulsion system is analyzed. The results show that installing an accumulator in suction line can effectively decrease natural frequency of propulsion system, which can improve the stability of coupled system. When cavitation and inertance of accumulator increases or installation position gets closer to top of pump, the influence of accumulator on the natural frequency becomes more significant.

0438 キャビテーション発生時のインデューサの動特性計測(OS4-7 流体機械の研究開発とそれに関連した複雑流動現象,OS4 流体機械の研究開発とそれに関連した複雑流動現象)

In the liquid propellant rockets, POGO instability can occur through the fluctuation of propellant supply to the engine, the thrust fluctuation, and structural vibration. For the prediction of this instability, it is required to provide unsteady characteristics of the pump represented as the transfer matrices correlating the upstream and downstream pressure and flow rate fluctuations. In the present study, the flow rate fluctuation is evaluated from the fluctuation of pressure difference at different locations assuming that the fluctuation is caused by the inertia of the flow rate fluctuation. The present paper describes the results of experiments performed in some situations. For the validation, transfer functions obtained by experiments are compared with Rubin's result.

액체추진 로켓의 포고 불안정성 해석과 제어에 관한 연구

Pogo is the instability resulting from the interaction between rocket structure and propulsion system of liquid propellant rocket. The coupling of structure and propulsion system can lead to severe problem in rocket. For the analysis of pogo, a time-invariant linearized mathematical model is developed for a selected flight time. Propulsion system is modeled using element representations for each components. Rocket structure is modeled using FEM. Form the results of modal analysis of structure, the behavior of structure can be represented. System equations for coupling structure and propulsion system are composed. The stability in obtained by the eigen solution of system matrix. The optimization of the design variables such as size, place of accumulator for suppressing pogo instability in carried out. This article of study can be used to determine the degree of stability, and guide the design of pogo suppression system.

Unsteady Flow in Cavitating Turbopumps

Unsteady flow in a cavitating axial inducer pump is analyzed with the help of a simple two-dimensional cascade model. This problem was motivated by a desire to study the effect of unsteady cavitation on the so-called POGO instability in the operation of liquid rocket engines. Here, an important feature is a closed loop coupling between several different modes of oscillation, one of which is due to the basic unsteady characteristics of the cavitation itself. The approaching and leaving flow velocities up- and downstream of the inducer oscillate, and the cavity-blade system participates dynamically with the basic pulsating flow. In the present work, attention is focused on finding a transfer matrix that relates the set of upstream variables to those downstream. This quantity, which is essentially equivalent to cavitation compliance in the quasi-static analyses, is found to be complex and frequency dependent. It represents the primary effect of the fluctuating cavity in the system. The analysis is based on a linearized free streamline theory.

The Dynamic Behavior and Compliance of a Stream of Cavitating Bubbles

The role played by turbopump cavitation in the POGO instability of liquid rockets motivates the present study on the dynamic response of streams of cavitating bubbles to imposed pressure fluctuations. Both quasistatic and more general linearized dynamic analyses are made of the perturbations to a cavitating flow through a region of reduced pressure in which the bubbles first grow and then collapse. The results when coupled with typical bubble number density distribution functions yield compliances which compare favorably with the existing measurements. Since the fluids involved are frequently cryogenic, a careful examination was made of the thermal effects both on the mean flow and on the perturbations. As a result the discrepancy between theory and experiment for particular engines could be qualitatively ascribed to reductions in the compliance caused either by these thermal effects or by relatively high reduced frequencies.

Theoretical, quasi-static analysis of cavitation compliance in turbopumps.

The serious POGO instability experienced by many liquid propellant rockets results from a closed loop interaction between the first longitudinal structural mode of vibration and the dynamics of the propulsion system. One of the most important features in the latter is the cavitation compliance of the turbopumps. This report presents calculations of the blade cavitation compliance obtained from free streamline cascade theory and demonstrates the various influences of angle of attack, blade angle, blade thickness and cavitation number. Discrepancies between calculated and experimentally derived values are discussed.