High Frequency Injection Coupled Combustion Instabilities - Study of Combustion Chamber/Feed System Coupling

A computational analysis of transverse acoustic instability is presented for an experimental combustion chamber with rectangular cross section. The analysis is shown to be efficient and accurate. The governing equations are solved on multiple, coupled grids, which are two-dimensional in the combustion chamber and nozzle and one-dimensional in the injector port. Thus, they allow for a fast simulation, even in a serial run. Because of the lengthscale difference, the jet flame behavior at the injectors (including effects of turbulence) can be decoupled from the acoustic effects and solved on a local grid for each jet flame emerging from an injector. Wave propagation through the injector feed ports is evaluated on additional, one-dimensional grids for each injector port. The overall algorithm is used to simulate the Purdue seven-injector rocket engine; good quantitative agreement between simulations and experiment is achieved. All simulations that are predicted to be unconditionally unstable are confirmed by the Purdue experiment. Small perturbations grow to a limit cycle for which the shape is a first transverse acoustic mode of the chamber. Only one result differs from experiment, albeit very slightly. Nomenclature a = speed of sound, m∕s C x , C η = rapid-distortion strain of velocity field c p = specific heat at constant pressure, J∕°K · kg D = mass diffusivity, m 2 ∕s E = energy release rate, J∕kg · s L = chamber thickness, m l m = mixing length p = pressure, N∕m 2 R c = chamber wall radius of curvature, m r = radial position, m S ij = velocity field strain tensor T = temperature, K t = time, s Y F = fuel mass fraction Y O = oxidizer mass fraction α, β = Schwab-Zel'dovich variables γ = Ratio of specific heats η = local radial coordinate for the injector grids ν T = turbulent kinematic viscosity, m 2 ∕s ρ = density, kg∕m 3 ω i = reaction rate of species i, s −1 Subscripts F = fuel i, j = index for Cartesian coordinates O = oxidizer 0 = undisturbed state

mentioning

confidence: 98%

Transverse Combustion Instability in a Rectangular Rocket Motor

Popov

Sirignano

2016

“…For a homogenous, quiescent medium, the expressions for E and I result in the well-known formulas from classical acoustics given in Eqs. (6) and (7):…”

Section: Acoustic Energy Conservation Principlesmentioning

confidence: 99%

“…In the case of rocket stability problems, they are used to model the acoustic behavior of the feed system [4,5]. They supply the boundary condition for the feed system, which is then used in the stability analysis of the whole thrust system [6]. The stability analysis itself is then performed with a different method.…”

mentioning

confidence: 99%

Simulation of Combustion Instabilities in Liquid Rocket Engines with Acoustic Perturbation Equations

Pieringer

Sattelmayer

Fassl³

2009

The authors present a new method for predicting combustion instabilities in liquid rocket engines. This method is based on the solution of the linearized governing equations for a three-dimensional combustor geometry in the time domain. The aim of this paper is to show the general feasibility of the approach and to explain the general behavior of the model. The computational domain comprises the combustion chamber itself and the convergent part of the nozzle. The heat release is included via a source term in the linearized energy equation. In the example of the European Aestus engine, it is shown that the model is able to predict the different oscillation modes without any preliminary assumptions about them. An analysis of the influence of the nozzle illustrates that its behavior is automatically included in the approach by design. In comparison to the solution of the full Navier-Stokes equations, the method has the advantage of a much lower numerical cost. Nomenclature a = velocity of sound b = half-value radius of Gaussian pulse D = diameter E = acoustic energy density f = frequency I = acoustic flux i = imaginary unit k = wave number L = length M = Mach number n = interaction index n = normal vector p = pressure _ q = heat release rate R CH = radius of the combustion chamber r = radius (polar coordinates) T S = oscillation period t = time u = velocity component in direction of the symmetry axis V = volume x = coordinate Y = admittance Z = impedance = decay/growth coefficient = angle (polar coordinates) = ratio of specific heats = density = delay time ' = phase angle ! = angular frequency Subscripts CH = combustion chamber c = center char = characteristic Im = imaginary part N = nozzle num = numerical max = maximum Re = real part sim = simulation theo = theoretical V = volumetric Superscripts 0 = fluctuating quantity = mean quantity = complex conjugate = nondimensional quantity

“…Interesting discussions of coupled injector-system acoustics by Nestlerode, Fenwick, and Sack and by Harrje and Reardon can be found in pages 106-126 of the well-known NASA SP-194 [1]. More recent overviews and analyses are provided by Hutt and Rocker [8] and DeBenedictus and Ordonneau [9]. Yang et al [10] provided several interesting papers on the design and modeling of rocket injector systems.…”

Section: Nomenclaturementioning

confidence: 99%

Propellant Injector Influence on Liquid-Propellant Rocket Engine Instability

Popov

Sirignano

Sideris

2015

The avoidance of acoustic instabilities, which may cause catastrophic failure, is demanded for liquid-propellant rocket engines. This occurs when the energy released by combustion amplifies acoustic disturbances; it is therefore essential to avoid such positive feedback. Although the energy addition mechanism operates in the combustion chamber, the propellant injector system may also have considerable influence on the stability characteristics of the overall system, with pressure disturbances in the combustion chamber propagating back and forth in the propellant injector channels. The introduced time delay may affect stability, depending on the ratio of the wave propagation time through the injector to the period of the combustion chambers acoustic modes. This study focuses on transverse-wave liquid-propellant rocket engine instabilities using a two-dimensional polar coordinate solver (with averaging in the axial direction) coupled to one-dimensional solutions in each of the coaxial oxygen-methane injectors. A blockage in one (or more) of the injectors is analyzed as a stochastic event that may cause an instability. A properly designed temporary blockage of one or more injectors can also be used for control of an oscillation introduced by any physical event. The stochastic and design variables parameter space is explored with the polynomial chaos expansion method.