Taylor-Culick Flow Research Articles

Application of immersed boundary method to the simulation of three-dimensional flow in solid rocket motors

The immersed boundary method (IBM) is currently utilized in the simulation of two-dimensional axisymmetric flow in solid rocket motors. In this paper, the IBM is applied to three-dimensional flow fields, keeping the grain surface fixed. Based on the Cartesian grid, a three-dimensional Euler flow solver is developed using the finite difference method. All boundaries of the flow field are processed using the IBM, including the slip walls, mass flow inlet, pressure outlet, and rotational periodic boundary. Specific implementation of these boundary conditions and the mesh generation process are described. Using the ray-casting approach and the alternating digital tree data structure, an efficient method is proposed to determine the intersection relationship between a rectangular volume grid cell and a triangular surface mesh element. The numerical results of Taylor–Culick flow verify that the developed solver has more than one-order accuracy in space. To conduct the validation of the established method, three typical grains are selected for flow simulations, namely, the perforated cylindrical grain with burning on both the ends and the inner surface, the end-slotted end-burning grain, and the finocyl grain, respectively. The simulated results are compared with those of the zero-dimensional interior ballistics, the two-dimensional axisymmetric IBM, and the body-fitted grid method, verifying the fidelity of the developed three-dimensional flow solver.

Application of immersed boundary method to the simulation of transient flow in solid rocket motors

To avoid the cumbersome re-meshing, an easy-to-implement immersed boundary method (IBM) is developed for simulating the coupling of gas flow and burning surface regression in solid rocket motors (SRM). The treatments of the slip wall boundary and the mass flow inlet boundary in the IBM are described. The Euler equations are discretized on a rectangular Cartesian grid based on the HLLC Riemann solver for inviscid fluxes. The interpolated primitive variables on cell boundaries are determined by using the third-order MUSCL method. The solution of the fluid flow is advanced in time by using the second-order TVD Runge–Kutta scheme. The proposed coupling method updates the burning surface and grid classification once when the movement distance is accumulated to half of the grid cell height. The numerical results of Taylor-Culick flow verify that the developed solver has second-order accuracy in space. To conduct the validation of our method, three typical grains are selected for coupling simulations, which are the perforated cylindrical grain with burning on both the ends and the inner surface, the end-slotted end-burning grain, and the perforated cylindrical grain with erosive burning on the inner surface, respectively. The calculation results show that the proposed IBM with the coupling method leads to low-frequency pressure fluctuations within 0.2% of the mean value during the burning surface regression. The accuracy of the calculation results is verified by the comparison with zero-dimensional interior ballistics, the body-fitted grid method, or experiments in literature.

A theoretical study of parietal vortex shedding in Taylor–Culick flow via linear stability analysis

In this theoretical study, we use linear stability analysis to investigate the cause of parietal vortex shedding in Taylor–Culick flow, which is representative of the flow in solid rocket motors. We focus on the effects of the lateral-injection Reynolds number and the length-to-radius ratio of the combustion chamber. Through a comparison with pipe flow, we find that flow turning is a major contributor to parietal vortex shedding. We explore the role of amphidromic points and find that they can divide the flow field into two distinct regions, an outer region with strong perturbations and an inner region with weak perturbations. In the outer region, we find that the velocity perturbations develop advection patterns with axial (streamwise) periodicity, while the pressure perturbations induce flow gradients that enhance shear stresses. Collectively, these effects are thought to combine to induce parietal vortex shedding in solid rocket motors.

On the grid dependence of hydrodynamic stability analysis in solid rocket motors

In this numerical study, we investigate the grid dependence of the Chebyshev collocation algorithm for flow stability analysis of solid rocket motors. Conventional analyses tend to focus on how the errors of the individual eigenvalues depend on the level of grid refinement. Here, we perform a structural error analysis to estimate the overall error of the computed spectrum. First, we validate the structural error analysis on a structural oscillation problem with analytical spectra, yielding a simple linear relation between the number of converged eigenvalues and the number of grid points. We then apply the analysis to Taylor–Culick flow, yielding a similar relation for the converged eigenvalue points. We find that the structural error analysis provides reliable criteria for the grid computation in flow stability analysis of a real solid rocket motor. In studies involving numerical spectra, the proposed structural error provides an alternative tool for error analysis of problems such as Taylor–Culick flow, where the computed individual eigenvalues do not necessarily converge to fixed values with increasing grid refinement.

Convergence of Two Internal Mean Flow Solutions for Spinning Rocket Motors

In this work, two mathematical procedures are used to derive the incompressible mean flow profile in a simulated solid rocket motor that is modeled as a spinning right-cylindrical porous tube. The first approach starts with the Navier–Stokes equations and leads to a large wall-injection Reynolds number approximation. The second begins with the inviscid Bragg–Hawthorne equation, where the variation of the stagnation head is taken to reproduce the classical Taylor–Culick flow approximation for nonspinning rockets. To permit swirl to develop, the injected fluid is introduced with a finite angular momentum that is prescribed by the spinning rate of the motor. The core singularity that naturally evolves in the inviscid formulation is overcome through the use of viscous matched-asymptotic expansions. The closed-form expressions emerging from both techniques are then compared and verified using finite volume simulations of the unabridged Navier–Stokes equations. Results from all three approaches are found to be in substantial agreement over a wide range of Reynolds numbers, thus helping to validate the asymptotic treatment of the core boundary-layer analysis pursued in this and similar studies. Additional flow features, such as the vorticity and pressure, are also described and compared to the nonspinning motor case.

Modified computation of the nozzle damping coefficient in solid rocket motors

In solid rocket motors, the bulk advection of acoustic energy out of the nozzle constitutes a significant source of damping and can thus influence the thermoacoustic stability of the system. In this paper, we propose and test a modified version of a historically accepted method of calculating the nozzle damping coefficient. Building on previous work, we separate the nozzle from the combustor, but compute the acoustic admittance at the nozzle entry using the linearized Euler equations (LEEs) rather than with short nozzle theory. We compute the combustor's acoustic modes also with the LEEs, taking the nozzle admittance as the boundary condition at the combustor exit while accounting for the mean flow field in the combustor using an analytical solution to Taylor–Culick flow. We then compute the nozzle damping coefficient via a balance of the unsteady energy flux through the nozzle. Compared with established methods, the proposed method offers competitive accuracy at reduced computational costs, helping to improve predictions of thermoacoustic instability in solid rocket motors.

Breakup structure of two-phase jets with various momentum flux from a porous injector

Spray structure and atomization characteristics were investigated through a comparison of a porous and a shear coaxial injector. The porous injector shows better atomization performance than the shear coaxial injector. To increase atomization performance and mixing efficiency of two-phase jets, a coaxial porous injector which can be applicable to liquid rocket combustors was designed and tested. The characteristics of atomization and spray from a porous and a shear coaxial injector were characterized by the momentum flux ratio. The breakup mechanism of the porous injector is governed by Taylor-Culick flow and axial shear forces. Momentum of injected gas flow through a porous material which is composed of sintered metal is radically transferred to the center of the liquid column, and then liquid column is effectively broken up. Although the shapes of spray from porous and shear coaxial jets were similar for various momentum ratio, spray structures such as spray angle and droplet sizes were different. As increasing the momentum flux ratio, SMD from the porous injector showed smaller value than the shear coaxial injector

Stability and sensitivity analysis in a simplified solid rocket motor flow

AbstractThe present article aims at enhancing the computation of the global stability modes of the internal flow of solid rocket motors (SRMs) approximated by the Taylor–Culick solution. This modal approach suffers from the consequences of the non-normality of the global linearized incompressible Navier–Stokes operator, namely the lack of robustness of the eigenvalues that can lead to the computation of pseudo-modes rather than actual eigenmodes. In this respect, the effects of non-normality associated with strongly amplified eigenfunctions are highlighted on a simplified convective–diffusive stability problem with uniformly accelerated base state, the latter property being a typical characteristic of the Taylor–Culick flow. Non-convergence zones for the eigenvalues are exhibited for large Reynolds numbers and are related to the critical sensitivity to disturbances applied to one of the boundary conditions. For this reason, and according to experimental and numerical data related to the stability of simplified SRMs, a global stability analysis is performed assuming that the hydrodynamic fluctuations emerge from a geometrical defect applied at the sidewall. This comes to fix the upstream boundary condition at the abscissa of the sidewall disturbance. The resulting eigenmodes are shown to be discrete, numerically converged, well identified by a finite number of points of undefined phase of the velocity fluctuations. They marginally depend on Reynolds number variations, but are modified by changes on the boundaries location. As in the simplified problem, the inflow boundary condition is the most critical in terms of sensitivity to numerical errors, although not dramatic. Finally, the sensitivity analysis to infinitesimal base flow changes indicates that the variations applied close to the inflow boundary condition induce the largest move of the eigenvalues. In spite of the large non-normal effects induced by the large polynomial growth of the eigenfunctions, this paper shows that discrete instabilities may emerge from a wall defect, in contrast to configurations without such a geometrical perturbation whose dynamics may be rather driven by pseudo-modes.

다공성재를 이용한 동축형 분사기의 미립화특성

To improve the mixing and atomizing performance at the center region of the conventional coaxial shear injector spray, the concept of a coaxial porous injector was invented. This novel injection concept for liquid rocket engines utilizes the Taylor-Culick flow in the cylindrical porous tube. The 2-dimensional injector, which can be converted in three injection configurations, was fabricated, and several cold flow tests using water-air simulant propellant was performed. The hydraulic characteristics and the effects of a gas flow condition on the spray pattern and the Sauter mean diameter (SMD) was analyzed for each configuration. The atomizing mechanism of coaxial porous injector was different with the coaxial shear injector, and it was explained by the momentum of the gas jet, which is injected normally against the center liquid column, and by the secondary disintegration at the wavy interface of liquid jet, which was generated at the recessed region. The SMD of 2D coaxial porous injector, which has higher gas momentum, was measured and it shows better atomizing performance at the center and outer side of spray than the 2D coaxial shear injector.

Investigation of the Taylor-Culick Flow Through Particle Image Velocimetry and Numerical Simulation

DOI: 10.2514/1.44616 The Taylor–Culick flow corresponds to the flow injection through the lateral wall of a semi-infinite channel. This flow is intrinsically unstable downstream of a critical axial position. The flow disturbances develop in vortices that could couple with the acoustics of the channel, generating pressure oscillations. This is what occurs in large solid rocket motors in which the Taylor flow is induced by the propellant combustion. Depending mainly on the Reynolds number, three different flow regimes can be observed: laminar, transitional, or turbulent. The current paper presents an experimental and numerical investigation of that flow instability. The setup consists of a rectangular shape channel in which air is introduced through the bottom wall due to a porous plate. Quantitative measurements are performed with particle image velocimetry while unsteady numerical simulations are carried out using large eddy simulation. A special injection system for the seeding particles and a special arrangement for the laser sheet provide good quality particle image velocimetry data. The numerical simulations are validated against the particle image velocimetry results. They complete the particle image velocimetry investigation by following chronologically theinstantaneousphenomenon.Theexperimentsandthenumericalsimulationsareperformedatdifferentinjection velocities and channel heights.