Guoping Xia

Computational Investigation of Acoustics and Instabilities in a Longitudinal-Mode Rocket Combustor

A computational fluid dynamics analysis of acoustic modes and instabilities in an experimental longitudinal test chamber is presented. The experimental configuration is a uni-element recessed injector post combined with a variable-length combustion chamber. The computations employ the nonlinear Euler equations with mass and heat addition in the injector and combustion chamber and response functions to represent combustion dynamics. Analytical solutions and experimental comparisons are used to verify and validate the computational model. The results demonstrate the importance of including the full Euler equations for predicting the frequencies and mode shapes in the injector-combustor configuration as well as for representing nonlinear phenomena such as wave steepening and the excitation of higher harmonics. The present approach therefore promises to be a useful platform for testing and calibrating combustion response functions for combustion instability models.

Solution-limited time stepping to enhance reliability in CFD applications

A method for enhancing the reliability of implicit computational algorithms and decreasing their sensitivity to initial conditions without adversely impacting their efficiency is investigated. Efficient convergence is maintained by specifying a large global Courant (CFL) number while reliability is improved by limiting the local CFL number such that the solution change in any cell is less than a specified tolerance. The method requires control over two key issues: obtaining a reliable estimate of the magnitude of the solution change and defining a realistic limit for its allowable variation. The magnitude of the solution change is estimated from the calculated residual in a manner that requires negligible computational time. An upper limit on the local solution change is attained by a proper non-dimensionalization of variables in different flow regimes within a single problem or across different problems. The method precludes unphysical excursions in Newton-like iterations in highly non-linear regions where Jacobians are changing rapidly as well as non-physical results such as negative densities, temperatures or species mass fractions during the computation. The method is tested against a series of problems all starting from quiescent initial conditions to identify its characteristics and to verify the approach. The results reveal a substantial improvement in convergence reliability of implicit CFD applications that enables computations starting from simple initial conditions without user intervention.

Modeling of Turbulent Mixing Layer Dynamics in Ultra-High Pressure Flows

*† ‡ § The dynamics of air/nitrogen mixing layers under high pressure are studied using a computational approach, which embodies real gas equations of state, an advanced flux formulation for accurate unsteady solutions and detached eddy simulations (DES) of the turbulent dynamics. Real-fluid properties are obtained through efficient interpolation of adaptive property tables. Advanced preconditioned flux formulations are employed to reduce the inherent artificial dissipation in second-order finite-volume schemes. The DES method is employed within a ω − k turbulence model. The effectiveness of our computational approach is demonstrated using an exact solution for Taylor vortices and by computing decay of isotropic turbulence in a box. The paper focuses on the dynamics of air-nitrogen mixing layers for various Reynolds numbers and momentum thicknesses under high pressures. Both 2D and 3D DES simulations are obtained and the results are compared with 2D unsteady-RANS simulations to highlight the differences.

Analysis of Real Fluid Flows in Converging Diverging Nozzles

A computational method for the simulation of general fluids with arbitrary equation of state and multiple component and multiple phases is outlined along with corresponding boundary condition methods. The capabilities of the approach are demonstrated by nozzle flow calculations for four fluids with very different properties: air at normal pressures and temperatures where perfect gas assumptions apply, air at ultra-high pressures where real-gas effects dominate the solutions, argon expanded to low pressures where condensation and two-phase flow take place, and a purely incompressible fluid to demonstrate the method in this ‘singular’ limit. The results show a variety of interesting physical phenomena that are introduced by the unique fluid physics. INTRODUCTION In the present paper we use computational methods to compare the flowfield characteristics of four fluids whose physical properties are very different. Our goals are twofold. First, we wish to highlight the interesting effects that fluid properties can have on the ensuing flowfields, and second, we wish to demonstrate that computational algorithms can be unified such that they remain accurate and efficient for essentially all classes of fluids over wide ranges of flow conditions. As specific examples of this capability, we present results of calculations for three compressible fluids with distinct equations of state as well as for an incompressible fluid. Research Associate Professor; Department of Mechanical Engineering, Computational Fluids Dynamics Research roup; Member AIAA. G PhD Student; Department of Mechanical Engineering, tudent Member AIAA. S Professor, Department of Mechanical Engineering; H. H. Arnold Chair of Excellence in Computational Mechanics; Senior Member AIAA. As a representative geometry, we consider the internal flow through converging-diverging nozzles. This geometry allows us to investigate flow conditions from subsonic through hypersonic speeds in a single example for the compressible fluids while also providing an effective geometry for which the characteristics of incompressible fluids can be contrasted. Because of the very different properties of the chosen fluids, as well as particular applications of interest to us, we use different nozzle shapes for each fluid to ensure that the flow conditions remain interesting. For the compressible fluids, we have selected nozzle shapes that are characterized by strong convergence in the subsonic portion leading to very low inlet speeds followed by expansion sufficient to produce hypersonic speeds in the divergent section. Typical Mach number ranges go from M = 0.01 to 8. The incompressible calculations are based on the nozzle shape from one of the compressible flow cases and serve to demonstrate the computation of incompressible flow as the limit of a compressible flow system. The geometric scales and thermodynamic conditions are chosen to give Reynolds numbers ranging from less than 1000 to greater than ten million based on diameter. This combination of factors (Mach number range, Reynolds number range, diverse equation of state) provides a severe test of any CFD algorithm. The equations of state for the three compressible fluids are chosen as follows. As a first case, we consider the familiar perfect gas relations and express the equation of state in algebraic fashion. In this simplest example, we introduce isolated streams of air and carbon dioxide into the upstream end of the flowfield and observe the effect of two distinct ratios of specific heats on the downstream flow. For the second case, we choose the ultra-high pressure limit of recent equation of state information for air [5] where the density of air exceeds that of water and realgas effects dominate. Here we use a table look-up procedure for the equation of state and choose a 1 American Institute of Aeronautics and Astronautics 33rd AIAA Fluid Dynamics Conference and Exhibit 23-26 June 2003, Orlando, Florida AIAA 2003-4132 Copyright

Computational Simulations of the Effect of Backstep Height on Nonpremixed Combustion Instability

Detailed computational simulations are used to compare the effect of backstep height on the stability characteristics of an axisymmetric dump combustor fed by separate fuel and oxidizer streams. Companion experiments demonstrate a dramatic increase in the amplitude of pressure oscillations for the smaller backstep due to combustion instability. The goal of the present simulations is to ascertain whether computations can predict combustion instability for this configuration and the degree to which they can replicate this experimental trend. Two different oxidizer-inlet boundary conditions were used: a subsonic inlet and a choked inlet. Both predicted stronger oscillations for the smaller backstep, although the disturbances in the uniform inlet case decayed to relatively low levels. The oscillations in the choked-inlet case were sustained but were still somewhat smaller than in the experiment. The simulations suggest the effect of backstep height arises because of stronger wall/vortex impingement in the smaller-step-height combustor. The instantaneous pressure and heat release are more strongly in phase for the smaller-step-height simulations, resulting in larger Rayleigh indices. Power spectral density results likewise show larger peaks for the smaller step. The sensitivity to upstream conditions suggests that care should be taken in designing both simulations and experiments.

Consistent properties reconstruction on adaptive Cartesian meshes for complex fluids computations

An efficient reconstruction procedure for evaluating the constitutive properties of a complex fluid from general or specialized thermodynamic databases is presented. Properties and their pertinent derivatives are evaluated by means of an adaptive Cartesian mesh in the thermodynamic plane that provides user-specified accuracy over any selected domain. The Cartesian grid produces a binary tree data structure whose search efficiency is competitive with that for an equally spaced table or with simple equations of state such as a perfect gas. Reconstruction is accomplished on a triangular subdivision of the 2D Cartesian mesh that ensures function continuity across cell boundaries in equally and unequally spaced portions of the table to C^0, C^1 or C^2 levels. The C^0 and C^1 reconstructions fit the equation of state and enthalpy relations separately, while the C^2 reconstruction fits the Helmholtz or Gibbs function enabling EOS/enthalpy consistency also. All three reconstruction levels appear effective for CFD solutions obtained to date. The efficiency of the method is demonstrated through storage and data retrieval examples for air, water and carbon dioxide. The time required for property evaluations is approximately two orders of magnitude faster with the reconstruction procedure than with the complete thermodynamic equations resulting in estimated 3D CFD savings of from 30 to 60. Storage requirements are modest for todays computers, with the C^1 method requiring slightly less storage than those for the C^0 and C^2 reconstructions when the same accuracy is specified. Sample fluid dynamic calculations based upon the procedure show that the C^1 and C^2 methods are approximately a factor of two slower than the C^0 method but that the reconstruction procedure enables arbitrary fluid CFD calculations that are as efficient as those for a perfect gas or an incompressible fluid for all three accuracy levels.

Computational Studies of the Effects of Oxidizer In jector Length on Combustion Instability

Computational analyses of the effects of oxidiser injector length on combustion instability in a choked high pressure combustor are described. The configuration is based on companion experiments using gaseous methane and decomposed hydrogen peroxide as reactants. The generic behaviour of one injector length is first investigated in detail to investigate the general character of the flow-fields. Comparisons between computation and experiment are then given for five lengths. The predictions for the intermediate lengths are in good agreement with the experiments in terms of most unstable frequency, its amplitude and the rate of decay of higher harmonics. The computations for the shortest injector predict the second mode is most unstable whereas the experiment indicates the fundamental was more unstable. At the longest length the computations show a character similar to the other lengths, while the experiments indicate the instability jumps to much higher frequencies that did not appear in the computations. A series of post-processing diagnostics is used to assess the mechanisms causing instability and to give possible explanations for the experimental behaviour.

Experimental and Computational Investiagtion of Combustor Acoustics and Instabilities, Part II: Transverse Modes

A combined experimental-computational study of transverse acoustic modes and combustion instabilities in a rectangular liquid rocket chamber is presented. Experimental results show that transverse modes can be spontaneously excited in the rectangular chamber. The amplitudes of the acoustic response are governed by the number and location of the injector elements. In general, stronger response of the 1W mode is observed when the injector element is positioned near a pressure anti-nodal location. Companion CFD solutions of the Euler and Navier-Stokes solutions are also performed and compared with the experimental measurements. Good qualitative agreement of the acoustic chamber response is obtained. Further, the computational studies are utilized to perform parametric studies of the eects of non-linear forcing and viscous eects due to the presence of side-wall boundary layers.

Experimental and Computational Investigation of Combustor Acoustics and Instabilities, Part I: Longitudinal Modes

Combined experimental and computational studies of acoustic modes and combustion instabilities in a longitudinal chamber configuration are presented. The experiments utilize a recessed swirl-coaxial pressure-sensitive injector element and a variable length combustion chamber. Tests for different chamber lengths indicate that high-amplitude pressure oscillations are spontaneously generated, with the unstable frequencies typically being in the 1200-1700 Hz range. The computational simulations indicate that the acoustic mode frequencies and mode shapes are very well predicted by the model. In addition, non-linear forcing studies indicate that higher harmonics are excited, which is also in good agreement with the experimental data.

Numerical Modeling of Injection of Shear-Thinning Gel Propellants Through Plain-Orifice Atomizer

A series of axisymmetric Navier–Stokes simulations were performed to study the mean and unsteady characteristics of gel propellant orifice flows at conditions representative of rocket injectors. The rheology of the gel was simulated assuming a shear-thinning fluid behaving in accordance with the Carreau–Yasuda model. The effects of Reynolds number (flow velocity), orifice L=D, fluid rheology, and orifice inlet chamfering were studied in a series of 200 independent simulations. Unsteady conditions were observed in most cases, due to the high injection velocities typical of rocket injection conditions. The magnitude and frequency of pulsations were characterized in these cases. In general, steady flows were obtained for lower Reynolds numbers and smoother inlet (i.e., greater chamfering) conditions. Mean discharge coefficients were computed for all cases to support design studies and engineering analyses.