The Response of Normal Shocks in Diffusers

The frequency response of a normal shock in a diverging channel is calculated for application to problems of pressure oscillations in ramjet engines. Two limits of a linearized analysis arc discussed: one represents isentropic flow on both sides of a shock wave; the other may be a crude appr'l'I;imation to the influence of flow separation induced hy the wave. Numerical results arc given, and the influences of the shock wave on oscillations in the engine are discus,ed

Local stability analysis for a planar shock wave

A procedure to study the local stability of planar shock waves is presented. The procedure is applied to a Rankine-Hugoniot shock in a divergent/convergent nozzle, to an isentropic shock in a divergent/convergent nozzle, and to Rankine-Hugoniot shocks attached to wedges and cones. It is shown that for each case, the equation governing the shock motion is equivalent to the damped harmonic oscillator equation

Nonlinear Aspects of Combustion Instability in Liquid Propellant Rocket Motors. Second Yearly Progress Report for the Period 1 June 1961 to 31 May 1962

Combustion instability in liquid-propellant rocket engine

Linear Theory of Pressure Oscillations in liquid-Fueled Ramjet Engines

Pressure oscillations in ramjet engines are studied. within quasi one-dimensional linear acoustics. The flow field in the dump combustor is approximated by division into three parts: a flow of reactants, a region containing combustion products, and a recirculation zone, separated by a flame sheet and a dividing streamline. The three zones are matched by considering kinematic and conservation relations. Acoustic fields in the inlet section and in the combustion chamber are coupled to provide an analytical equation for the complex wave number characterizing the linear stability. The calculated results are compared with the experimental data reported by the Naval Weapons Center. Reasonable agreements are obtained

Response of a nozzle to an entropy disturbance example of thermodynamically unsteady aerodynamics

The larger number of problems that qualify as unsteady aerodynamics relate to non-uniform motion of surfaces -- such as pitching of airfoils -- or the correspondingly non-uniform motion of a fluid about a surface -- such as a gust passing over an airfoil. Experiment and analysis concerning these problems aims to determine the non-steady forces or surface stresses on the object. These may be thought of as "kinematically" non-steady problems. Another class of problems presents itself when the undisturbed gas stream temperature (or density) is non-steady although the velocity and pressure are steady; such non-uniformities are associated with entropy variations from point to point of the stream. In a locally adiabatic flow these entropy variations are transported with the stream, and when a fixed boundary -- such as an airfoil -- is encountered, the flow field undergoes a non-steady change because the density variations alter the pressure field -- or the stresses at the boundaries. This happens in spite of the fact that the undisturbed free -stream velocity field and the surface boundaries of the flow are independent of time. A gas turbine blade, for example, will experience a time-dependent load simply because of temperature fluctuations in the combustion products flowing over it, although the angle of attack is independent of time. We shall call these "thermodynamically" unsteady flows in contrast with the more familiar kinematically unsteady flows

Nonlinear behavior of acoustic waves in combustion chambers—II

The approximate analysis developed in Part I of Ihis work is apllied to severa1 specific problems. One purpose is to illustrate the use of the formalism, and second is to demostrate the validity of the method by comparing results with numerical solutions, obtained elsewhere, for the "exact" equations. A simple problem is treated first, the decay of a standing wave in a box containing a mixture of gas and suspended particles; one example of the steepening of an initially sinusoidal wave in pure gas is included. Viscous losses on an inert surface are treated essentially according to classical linear theory; recent experimental results are used as the basis for incorporating approximately the influence of nonlinear heat transfer in unsteady flow. All of the preceding results are combined in calculations of two examples of unstable motions in a solid propellant rocket motor and in a T-burner

Compositional and entropy indirect noise generated in subsonic non-isentropic nozzles

Abstract Gonville and Caius College; EPSRC/DTA studentship (University of Cambridge); Qualcomm/DTA Studentship; Royal Academy of Engineering Research Fellowships Scheme; EPSRC grant EP/K02924X/

A Numerical Investigation of Unsteady Bubbly Cavitating Nozzle Flows

The effects of unsteady bubbly dynamics on cavitating flow through a converging-diverging nozzle are investigated numerically. A continuum model that couples the Rayleigh-Plesset equation with the continuity and momentum equations is used to formulate unsteady, quasi-one-dimensional partial differential equations. Flow regimes studied include those where steady-state solutions exist, and those where steady-state solutions diverge at the so-called flashing instability. these latter flows consist of unsteady bubbly shock waves traveling downstream in the diverging section of the nozzle. An approximate analytical expression is developed to predict the critical backpressure for choked flow. The results agree with previous barotropic models for those flows where bubbly dynamics are not important, but show that in many instances the neglect of bubbly dynamics cannot be justified. Finally the computations show reasonable agreement with an experiment that measures the spatial variation of pressure, velocity and void fraction for steady shockfree flows, and good agreement with an experiment that measures the throat pressure and shock position for flows with bubbly shocks. In the model, damping of the bubbly raidal motion is restricted to a simple "effective" viscosity, but many features of the flow are shown to be independent of the specific damping mechanism

An Experimental and Computational Study of Pulsating Flow within a Double Entry Turbine with Different Nozzle Settings

This thesis presents a detailed study of the performance of a nozzled, double entry turbine. This configuration is primarily found in the turbocharger application and encompasses two different entries, each feeding 180° of a single turbine wheel. The primary motives for this research are to enhance the knowledge and understanding of the behaviour of such a device under steady and pulsating flows including the effect of three different nozzle vane geometries. The work incorporates both experimental and computational analyses. Experimental results show that with unequal admission between the two volute entries the performance of the turbine is greatly affected compared to when both entries are flowing equally. A methodology was developed which successfully linked the unequal admission performance of the turbine to the full admission maps which are more readily available. Pulsating flow was found to affect the average performance of the turbine compared to the steady state characteristics. Examination of the instantaneous mass flow showed a large degree of mass storage in the turbine domain for all conditions of pulsating flow. A new parameter was developed based upon the conservation of mass in order to quantify unsteadiness taking into account both pulse amplitude and frequency. Steady and unsteady computational simulations were undertaken for one of the different nozzle configurations. Entropy generation rate was used to establish the distribution of loss within the turbine. In partial admission the loss distribution within the rotor wheel was found to be different to any case during full admission operation. Under pulsed flow conditions the computational analysis showed that the loss distribution changes throughout a pulse cycle showing that the flow regime will also undergo a large change. The loss distribution within the rotor wheel at one point within the pulse cycle was found to be very similar the equivalent steady state condition.Open Acces

Finite element investigation of steady and unsteady quasi one-dimensional gas dynamic flows with wall friction and heat transfer

This study developed and validated a finite element procedure to investigate both steady and unsteady gas dynamic flows. Variable cross-sectional area, wall friction, and heat transfer within the duct affect compressible flows. Closed form solutions exist for steady flows determined by only one of these effects at a time. A quasi one dimensional algorithm was refined to combine all of these effects into multiple simulations. Moreover, the effects of an unsteady back pressure were also investigated and compared to the steady results. The back pressure was varied sinusoidally. The convergent divergent nozzle used had an outlet to throat ratio of 1.5 and a friction coefficient f = 0.005 (or f = 0.02) depending on how the coefficient is defined. The steady results indicated that for this type of nozzle, friction effects could be neglected while the effects of heat transfer significantly affected the flow. For specific magnitudes of heating, the normal shock found in the diverging nozzle disappeared and the flow became subsonic throughout the nozzle. An important question was how the flow reacts to a periodic unsteady back pressure. The exit speed, density, and temperature had the same fundamental frequency than the pressure although the unsteady flow was positioned behind the steady due to inertia