Ben T. Zinn

Boundary integral solutions of three dimensional acoustic radiation problems

Abstract This paper is concerned with the development of a procedure for generating the sound fields radiated by arbitrarily shaped, three dimensional bodies from an integral representation of the solutions of the Helmholtz equation. The method of Burton and Miller is employed to eliminate the non-uniqueness in the external Helmholtz formulae which occurs at the internal eigenfrequencies of the geometry under consideration. Also, a representation of the most singular component in the Burton and Miller formulation is developed resulting in an integral equation which is amenable to numerical solutions. A simple numerical scheme is introduced which reduces the large amounts of computer storage and time normally required for the solution of similar problems. This numerical scheme is then used to obtain solutions for the radiated sound field generated by a vibrating piston set in a sphere. The numerical solutions for the surface and far field sound patterns are compared with exact analytical solutions and deviations of 10% at most are noted. Since the symmetry of the sphere was not taken advantage of in these computations, the numerical schemes employed are applicable to general three dimensional sound radiation problems.

The Role of Unmixedness and Chemical Kinetics in Driving Combustion Instabilities in Lean Premixed Combustors

Abstract This paper presents the results of a study of the potential causes of frequently observed combustion instabilities in low NOx gas turbines (LNGT) that burn gaseous fuels in a premixed mode. The study was motivated by indications that such systems are highly sensitive to equivalence ratio perturbations. An unsteady well-stirred reactor model was developed and used to determine the magnitude of the reaction rate and heat release oscillations produced by periodic flow rate, temperature or equivalence ratio perturbations in the combustors inlet flow at different mean equivalence ratios. This study shows that the magnitudes of the reaction rate and heat release oscillations produced by these perturbations remains practically unchanged, decreases, and significantly (i.e., by a factor of 5-100) increases, respectively, as the equivalence ratio decreases. These results strongly suggest that equivalence ratio perturbations, which are an indication of reactants unmixedness, playa key role in the driving o...

A theoretical study of non-linear damping by helmholtz resonators

A theoretical study of the interaction between finite-amplitude sound and a single Helmholtz resonator is hereby presented. The flows in the entrance region, orifice and cavity have been considered in detail with the aid of the appropriate conservation equations. To account for the non-linearities of the problem, the differential equations describing first-as well as second-order effects have been solved. The results of this study indicate that the experimentally observed losses can be attributed to the following two mechanisms: (i) viscous damping and (ii) energy loss which is associated with the dissipation of the kinetic energy of the jets which are periodically formed at both ends of the orifice; the latter is amplitude dependent. Plots of the theoretically predicted resistance (which includes both viscous and “jet” losses) as functions of velocity amplitude are in good agreement with available experimental data. Typical plots of resonator resistance and admittance are presented.

Nonlinear combustion instability in liquid- propellant rocket engines

The nonlinear stability characteristics of a liquid-propellant rocket motor with uniformly injected propellants, a distributed combustion process, and a multi-orifice nozle are investigated. It is shown that, for moderate amplitudes and low-Mach-number mean flow, the unsteady combustor flow can be described by a single nonlinear wave equation. This equation is solved with the aid of a modified version of the Galerkin method. Computed results predict the existence of both stable and unstable finite-amplitude limit cycles. It is shown that the amplitude of the pressure oscillation increases as one moves away from the linear stability limit. Decreasing the ratio ūe/ze and/or excitation of the radial modes improves the stability of the engine. Predicted nonlinear behavior as well as computed nonlinear waveforms are in agreement with experimental data as well as other theoretical predictions.

Pulse combustion: recent applications and research issues

The state of the art of pulse combustion and its applications are reviewed. Evidence showing that pulsations generally increase the rates of mass, momentum and heat transfer, and destabilize flows at certain unstable frequencies is presented. Next, the operational characteristics, advantages and disadvantages of pulse combustors are discussed. Advantages include simple design, compactness, self aspiration, and low emissions of CO and soot. Results showing that NOx emissions from pulse combustors can be significantly reduced using fuel staging, air staging and exhaust flow recirculation are presented. Noise remains a problem, but it can be damped to acceptable levels using acoustic decouplers and sound insulation. The paper closes with a discussion of a recently developed resonant driving method that utilizes a frequency tunable pulse combustor to excite large amplitude, resonant, pulsations in energy intensive and incineration processes. These pulsations increase the rates of mass, momentum and heat transfer within the process, which generally results in significant fuel savings and productivity increases. Evidence showing the benefits of resonant driving in water evaporation, limestone calcining and metal heating is presented. Finally, data obtained in recent tests in an EPA incinerator showing that resonant driving significantly, reduces soot emissions during the incineration of solid and hazardous wastes are presented.

Flame Driving of Longitudinal Instabilities in Dump Type Ramjet Combustors

Abstract Coaxial, dump type ramjet combustors are often prone to combustion instability problems that can seriously affect their performance. This study is concerned with the highly detrimental low frequency instabilities which often occur in such engines and investigates the coupling between wedge shaped flames and longitudinal acoustic fields in an experimental apparatus specifically developed for this purpose. The presence of burning vortical structures is observed in the flame region. These structures appear at frequencies close to the first natural acoustic frequency of the apparatus and are believed to be connected with a shear layer type of instability of the flame. Experiments conducted show that the unsteady combustion in these structures is capable of driving the acoustics at the fundamental mode frequency. with increase in fuel-air ratio, a spontaneous instability involving the fundamental mode is observed and explained in terms of increased driv ing associated with the higher, unsteady heat re...

Application of the Galerkin Method in the Solution of Non-linear Axial Combustion Instability Problems in Liquid Rockets

Abstract A nonlinear analysis of the stability of longitudinal combustion-driven oscillations in liquid propellant rocket motors is presented. A modified version of the Galerkin method is used to obtain solutions valid for moderate amplitude instabilities in rocket combustors having a low Mach number mean flow. Linear stability of a variety of liquid-rocket motors is investigated. Computed nonlinear results show that the resultant instability will exhibit a shock-type behavior with the number of shocks present in the system determined by the characteristics of the unsteady combustion process. These predictions are in qualitative agreement with available experimental data. Contrary to other solution techniques, the approach presented in this paper can predict both the transient and final periodic behavior of the instability. The final limit cycles are independent of the nature of the initial conditions. The relationship between the final limit cycles and the characteristics of the unsteady combustion proce...

Sound generation by ducted flames

The sound field established by a v-shaped flame confined in a rectangular duct is investigated both theoretically and experimentally. A theoretical model is developed to predict pressure spectra caused by the unsteady heat release from the flame. Comparisons between the theoretical and experimentally measured spectra confirm the validity of the model and are also reported. It is also found that changes in the flowfield in the flame zone can significantly modify combustion rates. These modifications, in turn, affect the generated sound field and are important in determining the pressure levels in the duct. The results of this investigation are applicable to combustion noise and instability studies in a variety of burner and propulsion system configurations. 15 references.

Prediction of the sound field radiated from axisymmetric surfaces

A general analytical method for determining the radiated sound fields from axisymmetric surfaces of arbitrary cross section with general boundary conditions is developed. The method is based on an integral representation for the external solutions of the Helmholtz equation. An integral equation is developed governing the surface potential distribution which gives unique solutions at all wavenumbers. The axisymmetric formulation of the problem reduces its solution to the numerical evaluation of line integrals by Gaussian quadrature. The applicability of the solution approach for both a sphere and finite cylinder is demontrated by comparing the numerical results with exact analytical solutions for both discontinuous and continuous boundary conditions. The method is then applied to a jet‐engine‐inlet configuration and the computed results are in good agreement with exact values.

Experimental determination of three dimensional liquid rocket nozzle admittances.

The three-dimensional nozzle admittance, an important parameter in combustion instability studies, was experimentally measured for several nozzle configurations. The admittance values were obtained using a modification of the classical impedance tube technique. The modified impedance tube method measures the admittance of a duct termination in the presence of one-dimensional mean flow and three-dimensional oscillations. Values of the nozzle admittance were obtained from pressure amplitude measurements taken at discrete points along the length of the tube. To determine the effects of nozzle geometry, nozzles were tested with half-angles of 15°, 30°, and 45° and entrance Mach numbers of 0.08, 0.16, and 0.20. The admittance results are presented as functions of nondimensional frequency for mixed first tangential-longitudinal modes. These results are compared with available theoretical predictions, and good agreement between theory and experiment is shown. Nomenclature a = kM/(i — M2), rad/ft A = a constant proportional to the amplitude of the pressure oscillation, psi Amn = AJm(Smn], psi A + = complex amplitude of the incident pressure wave, psi A- = complex amplitude of the reflected pressure wave, psi c = steady-state speed of sound, fps Et = pressure amplitude measured at a distance zt from the nozzle entrance, psi F = quantity defined in Eq. (7), psi Jm = Bessel function of the first kind of order m k — wave number, a)/c, rad/ft L — length of the impedance tube, ft M = mean flow Mach number, dimensionless p = pressure perturbation, psi q = nondimensional mean flow velocity Qmn = real part of the energy released by the unsteady combustion process, dimensionless r = radial coordinate, ft S = nondimensional frequency, wrjc Smn = nth root of the equation dJm(x}/dx = 0 t = time, sec Tt = theoretically predicted pressure amplitude at a distance zt from nozzle entrance, psi u = axial component of the velocity perturbation, fps y = specific admittance, dimensionless z = axial coordinate, ft a = parameter defined by the relation