Suppress Pressure Oscillations Research Articles

Experimental and theoretical studies on thermoacoustic limit cycle oscillation in a simplified solid rocket motor using flat flame burner

Combustion instability is a common phenomenon in solid rocket motors. Coupling between pressure and heat release rate produces pressure oscillation, which seriously affects the operation and safety of the motors. It is necessary to investigate this mechanism in order to prevent or at least suppress pressure oscillations. A segmented combustor is designed, and a movable flat flame burner is used as the heating source. A stability map is plotted by moving the flat flame burner along the combustor and changing the equivalence ratio. The experimental results are predicted by employing the low-order thermoacoustic network model. When the heat source position is fixed, it is shown that the combustion changes from stable to very unstable and then returns to a stable state, with the increase of equivalence ratio from 0.9 to 1.5. The pressure oscillation is the strongest in the rich combustion region (equivalence ratio is 1.2–1.3), with the amplitude of about 122 dB. The pressure oscillation is strongest and the amplitude is about 125 dB, when the heat source is close to the nozzle exit. The calculation results by thermoacoustic network model agree well with the experimental results. The stability map and limit cycle characteristics of thermoacoustic oscillation can be accurately estimated. It indicates that this experimental method and theoretical model can be used to capture the limit cycle behavior, and provide a new scheme for predictions of thermoacoustic oscillation in solid rocket motors.

Introducing compressibility with SIMPLE algorithm

A comparative assessment between SIMPLE and its variant SIMPLE-C is conducted based on two-dimensional (2-D) incompressible flows, using a cell-centered finite-volume Δ-formulation on a collocated grid. The SIMPLE-C (SIMPLE Compressibility) scheme additionally combines the concept of artificial compressibility (AC) with the pressure Poisson equation, provoking the diagonal dominance of influence coefficients. An improved nonlinear momentum interpolation scheme is employed at the cell face in discretizing the continuity equation to suppress pressure oscillations. The pseudo-time step Δti remains the same in both schemes to conserve an analogous scaling with momentum and scalar nodal influence coefficients. Numerical experiments in reference to buoyancy-driven cavity flow dictate that both contrivances execute a residual smoothing enhancement, facilitating an avoidance of the velocity/pressure under-relaxation (UR). However, compared with the SIMPLE approach, included benefits of the SIMPLE-C method are the use of larger Courant numbers, enhanced robustness and convergence. Excellent consistency is obtained between results available in the literature and numerical solutions obtained by both SIMPLE and SIMPLE-C solvers. The segregated SIMPLE algorithm is finally reformulated in conjunction with a new slope/flux limiter function to predict fluid flow at all speeds. Numerical results show that the compressible variant of SIMPLE replicates correct shock speed, well-resolved shock front, contact discontinuity and rarefaction waves when compared with analytical solutions. Compressible laminar flows are computed to further support the accuracy and robustness of proposed algorithm.

Numerical evaluation of acoustic characteristics of a thrust chamber with quarter-wave resonators

Acoustic characteristics of a thrust chamber with quarter-wave resonators are numerically studied based on the unsteady Reynolds-averaged Navier-Stokes (URANS) method. Organized pressure disturbance model and constant-volume bomb model are applied as artificial disturbances to excite pressure oscillations in the chamber. Eigenfrequencies and amplitudes of acoustic modes of the chamber are obtained by fast fourier transform (FFT) analysis, while damping characteristics are evaluated by the half-power bandwidth method. Predicted damping capacities of the chamber with and without quarter-wave resonators agree well with experimental results. Pressure oscillations can be controlled by a quarter-wave resonator mainly through reducing the amplitude of target acoustic mode, rather than increasing damping capacity of the chamber. Major damping mechanism of the resonator is cutting down pressure peak of target acoustic mode and raising up its pressure trough (CPRT); therefore the amplitude of target acoustic mode is reduced significantly. Moreover, acoustic energy can be dissipated by vortex at the orifice and by viscosity on the surface of a resonator, which increase damping capacity of the chamber slightly. Under the condition with multi-modes pressure oscillations, a resonator can still suppress pressure oscillations of target acoustic mode through CPRT. However, it may enhance pressure oscillations of other modes due to redistribution of oscillation energy among all acoustic modes.

Control of Pressure Oscillations Induced by Supersonic Cavity Flow

A control method is developed to suppress pressure oscillations induced by supersonic cavity flow using high-speed upstream injection. The injection is generated with a large blowing coefficient through a channel, which guides the airflow blowing off in the leading edge of the cavity. Wind tunnel experiments are performed to validate the method with Mach 1.8 and 2.0 flows over a length-to-depth 6 cavity. Six dynamic pressure transducers are used to characterize the cavity oscillation. A remarkable suppression of pressure fluctuation is realized in the controlled cavity flow. The overall sound pressure level can be reduced by larger than 10 dB in both configurations. The most remarkable reduction in pressure fluctuation occurs near the cavity trailing edge, wherein flow-induced oscillation is strongest. Almost no cavity tones are observed near the cavity trailing edge under control. Further, the control method is proven effective and stable over time. The feedback loop is interrupted in the controlled cavity flow with a weak impact of shear vortices on the cavity aft wall. The control method may be a practical and potential candidate for use in engineering applications because it does not need additional gas supply in the control system.

Impact of Sensor Placement on Mode Observability and LQG Control of a Thermoacoustic System

This paper investigates the effect of sensor placement on the observability and LQG control of a thermoacoustic model. This model describes combustion instability in a one-dimensional combustor, called a Rijke tube. The transfer function describing this model is transcendental because of the time delay terms in the heat release dynamics. We apply Padé approximation to achieve a finite-dimensional transfer function and truncate the system by neglecting states with low Hankel singular values. We then analyze the impact of the placement and number of sensors on the observability of each mode of the resulting reduced-order model. Next, we design an LQG controller for suppressing pressure oscillations in the simplified thermoacoustic system. We find that placing sensors near the model’s pressure nodes slows down the rate at which LQG control attenuates pressure oscillations, increases the control effort required for this attenuation, and worsens the controller’s robustness.

Nonlinear controller design and testing for chatter suppression in an electric-pneumatic braking system with parametric variation

Abstract Accurate pressure control is essential for an electric-pneumatic braking system (EPBS). However, component wear and prolonged service can cause EPBS parameters to drift, which results in system chatter with high frequency. Such is a state of nonlinearity and instability that leads to the gradual deterioration of pressure control. Designing a viable controller for the system is challenging as it requires that system nonlinearity, sensor configuration, and computing capacity be considered. This article addresses the issue and presents a 2-step nonlinear control strategy. An LMS-based adaptive feedforward amplitude-phase regulator is first employed to reduce the frequency of the high frequency pressure oscillation to low frequency’s, followed by applying an output feedback controller based on high gain observer to mitigate the low frequency oscillations to realize steady state. A logic rule is designed to ensure that the two controllers work to suppress pressure oscillations of high and low frequencies in coordination. A comprehensive system model is derived to help characterize system nonlinearities and for designing the high gain observer. Numerical and physical validation are executed to demonstrate the feasibility of the strategy and for the performance of the controller design. Experiments results shows that the nonlinear controller can supress the chatter within 0.1 s either in step response or sinusoid tracking when system parameters vary.

A radial basis function based ghost cell method with improved mass conservation for complex moving boundary flows

A sharp interface immersed boundary method is presented for simulating flows around moving boundaries with arbitrary complex geometries. A time semi-implicit finite difference method is used to solve the incompressible Navier–Stokes equations on a fixed, staggered Cartesian grid. The boundary conditions at the immersed interface are enforced by a ghost cell method. Tracking complex moving boundaries and suppressing pressure oscillations are two major challenges in the sharp interface method. In this work, a polynomial radial basis function (PRBF) is introduced to the ghost cell method to implicitly represent and reconstruct the arbitrary immersed boundaries. In addition, a simple and robust signed identification strategy is used to determine the phase state of the grid cells. To suppress violent pressure oscillations on the moving boundaries, a fractional area representation (FAR) method, together with a mass force term, is introduced to the pressure Poisson equation. This FAR method not only retains the desirable property of consistent discretization in the ghost cell method but also takes advantage of the mass conservation property of the cut cell method. The proposed method is validated using five test cases, including the flow around a hydrofoil, in-line oscillation of a cylinder in a static fluid, uniform flows around a transversely oscillating cylinder, twin oscillating cylinders, and a pitching hydrofoil. The present results are in good agreement with the reference results, which validates the accuracy and capability of the proposed method.

Development of the generalized MacCormack scheme and its extension to low Mach number flows

SummaryThe low Mach number performance of the MacCormack scheme is examined. The inherent dissipation in the scheme is found to suffer from the degradation in accuracy observed with traditional, density‐based methods for compressible flows. Two specific modifications are proposed, leading to the formation of the generalized MacCormack scheme within a dual‐time framework (called GMC‐PC). The first modification involves reformulating the flux by splitting it into particle convection and acoustic parts, with the former terms treated using the traditional MacCormack discretization and the latter terms augmented by the addition of a pressure‐based artificial dissipation. The second modification involves a reformulation of the traditional nonlinear fix introduced by MacCormack in 1971, which is found to be necessary to suppress pressure oscillations at low Mach numbers. The new scheme is demonstrated to have superior performance, independent of Mach number, compared with standard MacCormack implementations using several canonical test problems. Copyright © 2017 John Wiley & Sons, Ltd.

Improved pressure calculation for the moving particle semi-implicit method

We developed a practical technique for calculating pressures and pressure gradients for the moving particle semi-implicit (MPS) method. Specifically, a new free-surface boundary condition for the pressure Poisson equation was developed by assuming that there are virtual particles over the surface. We treat the pressure of the virtual particles as a known value. A single liquid-phase flow is simulated taking into account the pressure of these virtual particles. A technique for detecting surface particles also was developed and used for accurately imposing the free-surface boundary condition. The pressure gradient model was modified to mitigate particle clustering and a single-layer wall model was developed to reduce the number of wall particles. We applied our technique to several problems, verifying that virtual surface particles suppress pressure oscillations and particle clusterings. The technique enables reliable differences in free-surface pressures to be taken and simulates instances of lower fluid pressure than that of a free surface.

Suppressing Pressure Oscillations in Offshore Drilling: Control Design and Experimental Results

As oil exploration and development costs rise, the oil industry increases its efforts to improve oil recovery (IOR) from existing fields. IOR is achieved mainly by drilling more wells, but drilling in partially depleted reservoirs is challenging due to narrow pressure margins. Offshore drilling in harsh environments, such as the North Sea, presents additional challenges, since the heaving motion from a floating rig induces large surge and swab pressures in the well. This brief suggests a remedy for this problem using automatic control of well pressure. Taking advantage of an experimental lab facility recently completed at NTNU, a model of the drilling system is developed using subspace identification methods. The model serves as a basis for state estimation and controller design using model predictive control. Applying the controller to the lab facility, pressure oscillations are suppressed by 70%-90% compared with the open-loop case, depending on the period of the heave motion.

Acoustic damping enhanced by gaps in baffled injectors in an acoustic chamber

Acoustic damping enhanced by gap width in baffled injectors is investigated numerically, which are installed to suppress pressure oscillations in a model acoustic chamber. The previous experimental works reported that baffled injectors show larger acoustic damping with gaps between adjoining injectors than baffled injectors without the gap or conventional baffles. Acoustic-damping behaviors of baffled injectors are simulated numerically and the damping mechanism is examined. Damping factors are calculated as a function of baffle gap and it is found that the maximum acoustic damping is observed at a gap of 0.1–0.2 mm. The enhanced damping by gaps is attributed to viscous dissipation on the surfaces of the injectors or baffle blades. The optimum gap for maximum damping depends on the viscosity of the medium in the chamber and it increases with the viscosity. As a quantitative parameter of viscous dissipation, the dissipation rate of kinetic energy is calculated as a function of baffle gap. The parameter shows its maximum value at a specific gap and especially, the viscous dissipation rate has the same profile as that of damping factor. It verifies that the enhanced damping by gaps is attributed to the viscous dissipation of acoustic energy increased by gaps in baffled injectors.

AN IMPROVED SIMPLE METHOD ON A COLLOCATED GRID

A pressure-based method characterized by the SIMPLE algorithm is developed on a nonorthogonal collocated grid for solving two-dimensional incompressible fluid flow problems, using a cell-centered finite-volume approximation. The concept of artificial density is combined with the pressure Poisson equation that provokes density perturbations, assisting the transformation between primitive and conservative variables. A nonlinear explicit flux correction is utilized at the cell face in discretizing the continuity equation, which functions effectively in suppressing pressure oscillations. The pressure-correction equation principally consolidates a triplicate-time approach when the Courant number CFL > 1. A rotational matrix, accounting for the flow directionality in the upwinding, is introduced to evaluate the convective flux. The numerical experiments in reference to a few familiar laminar flows demonstrate that the entire contrivance executes a residual smoothing enhancement, facilitating an avoidance of the pressure underrelaxation. Consequently, included benefits are the use of larger Courant numbers, enhanced robustness, and improved overall damping properties of the unfactored pseudo-time integration procedure.

Thermoacoustic instability: model-based optimal control designs and experimental validation

Active control of thermoacoustic instability has been increasingly sought after in the past two decades to suppress pressure oscillations while maintaining other performance objectives such as low NO/sub x/ emission, high efficiency, and power density. We have developed a feedback model of a premixed laminar combustor which captures several dominant features in the combustion process such as heat release dynamics, multiple acoustic modes, and actuator effects. In this paper, we study the performance of optimal control designs including LQG-LTR and H/sub /spl infin// methods using the model with additional effects of mean heat and mean flow actuator dynamics, and input saturation. We also verify these designs experimentally using a 1 kW bench-top combustor rig and a 0.2-W loudspeaker over a range of flow rates and equivalence ratios. Our results show that the proposed controllers, which are designed using a two-mode finite dimensional model, suppress the thermoacoustic instability significantly faster than those obtained using empirical approaches in similar experimental setups without creating secondary resonances, and guarantee stability robustness.

A Model-based Self-tuning Controller forThermoacoustic Instability

Active Control of thermoacoustic instabilities in continuous premixed combustion processes is being increasingly investigated for operating at lean low NOx conditions. Recently, we have developed a model-based approach for active control design which accounts for the underlying acoustics, heat release dynamics, and sensor and actuator dynamics. While this model captures a number of the dominant dynamic features of a premixed laminar combustor, there are a number of uncertainties associated with it as well. In this paper, we study the sensitivity of this model with respect to parametric uncertainties, and the efficacy of a fixed control design for suppressing pressure oscillations. We show that under certain conditions, the fixed controller is inadequate and present a self-tuning controller which is capable of delivering the desired performance in the presence of these uncertainties. The controller proposed is based on a rigorous analytical foundation, and is shown through simulation results to lead to better performance than corresponding fixed controllers. Adaptive algorithms based on the LMS-filter are shown to result in numerical instabilities.

A simplified marker and cell method for unsteady flows on non‐staggered grids

AbstractThe SMAC (simplified marker and cell) time‐advancing method for solving the unsteady incompressible Navier‐Stokes equations on non‐staggered grids is developed in generalized co‐ordinate systems. The primitive variable formulation uses Cartesian velocities and pressure, all defined at the centre of the control volume, as the dependent variables. A special elliptic flux correction at the faces of the finite volume is utilized in discretizing the continuity equation to suppress pressure oscillations. The test flows considered are a polar cavity flow starting from rest and the flow around a circular cylinder. The numerical results are compared with experimental results and results obtained by the well‐known SIMPLEC and PISO methods. The comparisons show that the elliptic flux correction technique works well in suppressing pressure oscillations and that the SMAC method is more efficient than the SIMPLEC and PISO methods for both steady and unsteady flows.

PREDICTION OF FAST TRANSIENT SPRAY-COMBUSTING FLOWS

Abstract A numerical model has been developed to predict the fast transient spray-combusting flows. This method is pressure based, noniterative, and applicable to flows at all speeds. Special emphasis is given to the overall behavior of nonlinear combustion instabilities in the liquid-fueled rocket engines. Computations were carried out for various combustion parameters such as initial spray conditions and baffle lengths. The present numerical model successfully predicts high-frequency combustion instability as well as fast transient flow. The baffle length as well as variations in droplet size have significant effects on engine stability. The numerical results indicate that the baffle can effectively suppress pressure oscillations.

Multistep dump combustor design to reduce combustion instabilities

Based on the understanding of the critical role of large-scale structures as drivers of pressure oscillations, a multistep dump was sucessfully tested to suppress pressure oscillations in a coaxial dump combustor. The multistep concept, which prevents development of large-scale structures, was studied in nonreacting air and water flows and in an annular diffusion flame before it was applied to the dump combustor burning gaseous fuel. The nonreacting tests in water and air showed that there is an optimal geometric configuration of the multisteps to achieve the highest level of turbulence. At this geometry the shear layer that is separated from the upstream step impinges on the next downstream step edge. When this geometry was tested in a dump combustor, the fuel injection pattern was found to be critical to obtain suppression of instabilities . With fuel injection distributed into the small-scale turbulence downstream of each step and not interfering with the flow impingement, the pressure oscillation in the dump combustor was suppressed.