Multiple Unstable Modes in the Reacting Mixing Layer

Ignition in the planar, turbulent, reacting mixing layer was analyzed via several model approaches and comparisons were made. Both Favre and time-averaged forms of the equations were employed with various forms of the mixing length theory; k, e theory; and k, o> theory. A coordinate transform was employed to remove the singularity at the mixing layer edge where the turbulent diffusivity goes to zero. An iterative quasilinearized implicit finitedifference scheme was used to solve the governing set of parabolic partial differential equations. The nonreacting limit with temperature and density gradients was fully examined. Similarity solutions were obtained in the nonreacting limit. Comparisons were made among the computational results and with existing experimental data. The major differences between the models and types of averaging were in the predicted spreading parameter. The comparison between theory and data was better for velocity profiles than for density profiles. Additional nonreacting variable density data are needed, particularly for high Reynolds numbers. For reacting flows, two different approaches to the calculation of the ignition length were analyzed. Comparisons among the models indicated significant sensitivity to the form of averaging and the choice of kinetics with a lesser sensitivity to the choice of turbulence modeling.

A premixed propane/air flame was stabilized in a turbulent mixing layer formed at a rearward-facing step. The mean and rms averages of the turbulent velocity flowfield were determined by laser velocimetry for both reacting (phi = 0.57) and nonreacting flows (Re = 15,000-37,000 based on step height). The reacting-flow was visualized by high-speed schlieren photography. Large-scale structures dominate the reacting mixing layer. The growth of the large-scale structures was tied to the propagation of the flame. The linear growth rate of the reacting mixing layer defined by the mean velocity profiles was unchanged by combustion but the virtual origin moves downstream. The reacting mixing layer boundaries based on the mean velocity profiles were shifted toward the recirculation zone and reattachment lengths were shortened by 30 percent. The edge of the flame controlled by the large-scale structure development propagated faster into the incoming reactants than the boundary of the mixing layer given by the mean velocity flowfield. Thus, the region of high velocity gradient did not coincide with the region of high reaction and heat transfer.

Combustion instability due to thermo-acoustic interactions in high-speed propulsion devices such as gas turbines and rocket engines result from pressure waves with very large amplitudes propagating back and forth in the combustion chamber. Exposure to the pressure fluctuations over a long period of time can lead to a cataclysmic failure of engines. The underlying physics governing the generation of the thermo-acoustic instability is a complex interaction among heat release, turbulence, and acoustic waves. Currently, it is very difficult to accurately predict the expected level of oscillations in a combustor. Hence development of strategies and engineering solutions to mitigate thermo-acoustic instability is an active area of research in both academia and industry. In this work, we carry out numerical modeling of thermo-acoustic instability in a self-excited, laboratory scale, model rocket combustor developed at Purdue University. Two different turbulent combustion models to account for turbulence-chemistry interactions are considered in this study, the flamelet model and the transported probability density function (PDF) method. <br>In the flamelet modeling approach, detailed chemical kinetics can be easily incorporated at a relatively low cost in comparison to other turbulent combustion models and it also accounts for turbulence-chemistry interactions. The flamelet model study is divided into two parts. In first part, we examine the effect of different numerical approaches for implementing the flamelet model. In advanced modeling and simulations of turbulent combustion, the accuracy of model predictions is affected by physical model errors as well as errors that arise from the numerical implementation of models in simulation codes. Here we are mainly concerned with the effect of numerical implementation on model predictions of turbulent combustion. Particularly, we employ the flamelet/progress variable (FPV) model and examine the effect of various numerical approaches for the flamelet table integration, with presumed shapes of PDF, on the FPV modeling results. Three different presumed-PDF table integration approaches are examined in detail by employing different numerical integration strategies. The effect of the different presumed-PDF table integration approaches is examined on predictions of two real flames, a laboratory-scale turbulent free jet flame, Sandia Flame D and the self-excited resonance model rocket combustor. Significant difference is observed in the predictions both of the flames. The results in this study further support the claims made in previous studies that it is imperative to preserve the laminar flamelet structure during integration while using the flamelet model to achieve better predictions in simulations. In the second part of the flamelet modeling study, computational investigations of the coupling between the transient flame dynamics such as the ignition delay and local extinction and the thermo-acoustic instability developed in a self-excited resonance combustor to gain deep insights into the mechanisms of thermo-acoustic instability. A modeling framework that employs different flamelet models (the steady flamelet model and the flamelet/progress variable approach) is developed to enable the examination of the effect of the transient flame dynamics caused by the strong coupling of the turbulent mixing and finite-rate chemical kinetics on the occurrence of thermo-acoustic instability. The models are validated by using the available experimental data for the pressure signal. Parametric studies are performed to examine the effect of the occurrence of the transient flame dynamics, the effect of artificial amplification of the Damkohler number, and the effect of neglecting mixture fraction fluctuations on the predictions of the thermo-acoustic instability. The parametric studies reveal that the occurrence of transient flame dynamics has a strong influence on the onset of the thermo-acoustic instability. Further analysis is then conducted to localize the effect of a particular flame dynamic event, the ignition delay, on the thermo-acoustic instability. The reverse effect of the occurrence of the thermo-acoustic instability on the transient flame dynamics in the combustor is also investigated by examining the temporal evolution of the local flame events in conjunction with the pressure wave propagation. The above observed two-way coupling between the transient flame dynamics (the ignition delay) and the thermo-acoustic instability provides a plausible mechanism of the self-excited and sustained thermo-acoustic instability observed in the combustor.<br>The second turbulent combustion model considered in this study is the transported PDF method. The transported PDF method is one of the most attractive models because it treats the highly-nonlinear chemical reaction source term without a closure requirement and it is a generalized model for a wide range of turbulent combustion problems.Traditionally, the transported PDF method has been used to model low-Mach number, incompressible flows where the pressure is assumed to be thermodynamically constant. Since there is significant pressure fluctuations in the model rocket combustor, the flow is highly compressible and it is necessary to account for this compressibility in the transported PDF method. In the past there has been very little work to model compressible reactive flows using the transported PDF and no effort has been made to model thermo-acoustic instability using the transported PDF method. There is a pressing need to further examine and develop the transported PDF method for compressible reactive flows to broaden our understanding of physical phenomenon like thermo-acoustic instability, interaction between combustion and strong shock and expansion waves, coupling between acoustic and heat release which are observed in high-speed turbulent combustion problems. To address this, a modeling framework for compressible turbulent reactive flows by the using the transported PDF method is developed. This framework is validated in a series of test cases ranging from pure mixing to a supersonic turbulent jet flame. The framework is then used to study the thermo-acoustic interactions in the self-excited model rocket combustor.

The ESCIMO theory of turbulent combustion is applied to turbulent plane reacting mixing layers. A set of transport equations describing population distributions of folds in such layers is solved, taking into account the property variation in the cross-stream direction.

The effect of Mach number on the evolution of instabilities in the compressible mixing layer is investigated. The full time-dependent compressible Navier–Stokes equations are solved numerically for a temporally evolving mixing layer using a mixed spectral and high-order finite difference method. The convective Mach number Mc (the ratio of the velocity difference to the sum of the free-stream sound speeds) is used as the compressibility parameter. Simulations with random initial conditions confirm the prediction of linear stability theory that at high Mach numbers (Mc &gt; 0.6) oblique waves grow more rapidly than two-dimensional waves. Simulations are then presented of the nonlinear temporal evolution of the most rapidly amplified linear instability waves. A change in the developed large-scale structure is observed as the Mach number is increased, with vortical regions oriented in a more oblique manner at the higher Mach numbers. At convective Mach numbers above unity the two-dimensional instability is found to have little effect on the flow development, which is dominated by the oblique instability waves. The nonlinear structure which develops from a pair of equal and opposite oblique instability waves is found to resemble a pair of inclined A-vortices which are staggered in the streamwise direction. A fully nonlinear computation with a random initial condition shows the development of large-scale structure similar to the simulations with forcing. It is concluded that there are strong compressibility effects on the structure of the mixing layer and that highly three-dimensional structures develop from the primary inflexional instability of the flow at high Mach numbers.

By direct numerical simulations, the non-isothermal effects on turbulent structures and asymmetric properties are investigated in the spatially developing supersonic mixing layers with high convective Mach numbers (Mc &amp;gt; 0.6). Hot air is blown in the high-speed stream, and cold air is added on the low-speed side. Two non-isothermal simulations with different temperature gradients are conducted and compared with the isothermal mixing layer. The self-similar model of the spatially developing supersonic turbulent mixing layer is analyzed to reveal the physical mechanisms for the asymmetry of non-isothermal mixing layers. The supersonic mixing layer is characterized by diverse vortices and unsteady shocklets, which increase in the initial shear layer and then decrease in the self-similar turbulent region. Also, the mixing layer is asymmetric between the high- and low-speed streams, and the shear layer center skews toward the low-speed side with more vortices and less shocklets, which is attributed to the streamwise momentum gradient. The effects of temperature gradients enhance the flow instability and accelerate the growth of vortices and shocklets in the initial mixing layer. Nevertheless, the turbulent structures are attenuated in the fully developed region, as the viscous dissipation is augmented and turbulence decays more strongly. In addition, the streamwise momentum gradient is reduced in the non-isothermal mixing layers. The vortical structures suffer from stronger attenuation on the cold side, while the shocklets are more significantly reduced on the hot side. Thus, the skewness of the shear layer center toward the low-speed side is reduced, and the mixing layer asymmetry is attenuated.

A methodology for simulation of molecular mixing, and the resulting velocity and temperature fields has been developed. The ideas are applied to the flow conditions present in the NASA Lewis Research Center Planar Reacting Shear Layer (PRSL) facility, and results compared to experimental data. A gaussian transverse turbulent velocity distribution is used in conjunction with a linearly increasing time scale to describe the mixing of different regions of the flow. Equilibrium reaction calculations are then performed on the mix to arrive at a new species composition and temperature. Velocities are determined through summation of momentum contributions. The analysis indicates a combustion efficiency of the order of 80 percent for the reacting mixing layer, and a turbulent Schmidt number of 2/3. The success of the model is attributed to the simulation of large-scale transport of fluid. The favorable comparison shows that a relatively quick and simple PC calculation is capable of simulating the basic flow structure in the reacting and nonreacting shear layer present in the facility given basic assumptions about turbulence properties.

An efficient time accurate algorithm is presented for numerical simulations of low-Mach number variable density flows in the context of non-premixed flames. The algorithm is based on a segregated solution formalism in the class of pressure-correction methods. It shows good conservation properties and returns stable results, regardless of the difference in density between neighboring cells. In the illustrative example, a flamesheet model is used to describe the combustion of fuel and oxidizer. The stability of the method is discussed for a 1D channel flow, containing both fuel and oxidizer. Results for a 2D testcase of a reacting mixing layer are also shown.

The study focuses on enhancing the accuracy of numerical solutions for Euler’s equations, essential for aerospace, engineering, and scientific simulations. To improve the numerical solution accuracy and efficiency of nonlinear problems, this study proposes a high-precision and high stability scheme for the Euler equation system, combining the fifth-order explicit weighted compact nonlinear scheme with the third-order semi-implicit implicit-explicit Runge-Kutta method. The results show that the scheme maintains design order accuracy in both high and low Mach number flows, with a spatial discretization error of 4.95 orders and a time discretization error convergence order of 5.86 orders. The width of the shock transition zone is reduced by 40% compared to traditional weighted compact nonlinear scheme. This demonstrates the accuracy advantage of this format. And this format remains stable even when Courant-Friedrichs-Lewy&gt;1, making it suitable for large-scale industrial simulation, which is beneficial for improving efficiency. In one-dimensional shock tubes, bimodal acoustic pulse collisions, and Lax/Sod problems, the density, velocity, and pressure results of this format are consistent with the reference solution, with no oscillation phenomenon. The rigid processing error of the pressure term is less than 1.134 × 10 −8 . It has good stability, which provides a new approach for numerical research to further understand complex flow phenomena.

Long-range rotating wrap-around-fin rockets may exhibit non-convergent conical motion at high Mach numbers, causing increased drag, reduced range, and potential flight instability. This study employs the implicit dual time-stepping method to solve the unsteady Reynolds-averaged Navier–Stokes (URANS) equations for simulating the flow field around a high aspect ratio wrap-around-fin rotating rocket at supersonic speeds. Validation of the numerical method in predicting aerodynamic characteristics at small angles of attack is achieved by comparing numerically obtained side force and yawing moment coefficients with experimental data. Analyzing the rocket’s angular motion process, along with angular motion equations, reveals the necessary conditions for the yawing moment to ensure stability during angular motion. Shape optimization is performed based on aerodynamic coefficient features and flow field structures at various angles of attack and Mach numbers, using the yawing moment stability condition as a guideline. Adjustments to parameters such as tail fin curvature radius, tail fin aspect ratio, and body aspect ratio diminish the impact of asymmetric flow induced by the wrap-around fin on the lateral moment, effectively resolving issues associated with near misses and off-target impacts resulting from dynamic instability at high Mach numbers.

A supersonic, two-dimensional, turbulent free mixing layer was experimentally investigated in the GALCIT Supersonic wind tunnel to clarify the Mach number dependence of this flow field. The tests were conducted with a nominal Mach number of 2.47 with an ambient stagnation condition. Self similarities of the mean and turbulent flow fields were established. The mean and fluctuating flow measurements were made. In addition, the actual entrainment rate of the turbulent free mixing layer through the low speed interface was also measured and it was verified that this quantity equals the growth rate of momentum thickness. The spreading rate, the entrainment rate and the maximum shear stress were appreciably smaller than the respective incompressible values. Velocity profile scaled to an incompressible form. by a linear transformation of the lateral coordinate. The maximum streamwise velocity fluctuation was approximately 1/3 of the incompressible value. The flow field of turbulent free mixing layer was found to be highly dependent upon the supersonic compressibility effect.

Current research paper deals with the numerical analysis of an idealized fighter jet wing in a multi-module aero-thermal-structural environment during supersonic flights. At high Mach number, heat is generated due to the friction between the body and the fluid flow, which must be considered for structural analyses. Six different Mach numbers ranging from 1.25 to 2.5 are chosen to understand the effect of viscous heating on the wing model. Ansys CFD is coupled with thermal/structural module to calculate the numerical results. It is observed that for Mach number 1.75 and beyond, equivalent Von-mises stress due to pressure load is almost identical. However, with viscous heating consideration, equivalent stress values are increased with higher Mach number which magnifies the significance of thermal loading on the structure

The mixing properties of a two-dimensional reacting shear layer have been studied numerically. Effects of heat release by combustion on the mixing properties have been discussed based on the viewpoint of the transport of vorticity. The numerical simulation is concerned with an unstable, two-dimensional, two-stream, spatially developing, confined reacting shear layer. The numerical method is based on the modified HSMAC method which can handle the change in temperature. The chemical model is a one-step irreversible methane-oxygen reaction with a finite reaction rate defined by the Arrhenius law. The numerical results have revealed that in the reacting mixing layer the vorticity thickness and the carbon element mixing layer thickness defined by the difference in the carbon element mixture fraction of 99% between the fuel and the oxidizer flows, increase in comparison to the cold mixing layer. The baroclinic torque suppresses the vorticity and the viscous term to increase the vorticity thickness.

The increasing demand for the wide-range aircraft technique requires the ground test facilities with continuous variation of the Mach number. Owing to the rigorous aerodynamic foundation and simple operation, the single-jack flexible nozzle is widely used. However, there are still some problems in the original single-jack flexible nozzle, such as low Mach number and insufficient flow uniformity. This paper presents a novel design of the single-jack flexible nozzle with high flow uniformity and continuous variable Mach number, adopting flow field inverse design and elasticity inverse design. The new nozzle adopts a three-order transonic asymptotic solution and a B-spline axial velocity distribution, designed by the method of characteristics. By comparing with the original nozzle, the new nozzle no longer requires the conical flow assumption, and the flow fields are more uniform. Another improvement is the continuous contour curvature to ensure the coincidence of the aerodynamic profile and the elastic profile, avoiding the negative Mach waves generated by the curvature discontinuity. In addition, the new nozzle has the advantage of two Mach number design points. Similar to the squeeze theorem, the flow fields are uniform at the non-design points between two design points. The numerical results show that the new nozzle eliminates the Mach waves at different Mach number cases. Within the design range of Mach 2.0–4.0, the flow angle's maximum deviations do not exceed 0.2°, and the average deviations do not exceed 0.1°, meeting the national standard of 0.3°. The Mach number's maximum deviations are around 0.5% of Ma¯, the average deviations are less than 0.2% of Ma¯, and the standard deviations meet the national advanced standard. Even at Mach 1.5 and Mach 4.5 outside the design range, the new nozzle still performs well. The evaluation results validate the feasibility of the novel design, supporting the future construction of the variable Mach number facility.

Observations made in the Scotia Sea during the May 2015 Surface Mixed Layer Evolution at Submesoscales (SMILES) research cruise captured submesoscale, O(1–10) km, variability along the periphery of a mesoscale O(10–100) km meander precisely as it separated from the Antarctic Circumpolar Current (ACC) and formed a cyclonic eddy ~120 km in diameter. The meander developed in the Scotia Sea, an eddy-rich region east of the Drake Passage where the Subantarctic and Polar Fronts converge and modifications of Subantarctic Mode Water (SAMW) occur. In situ measurements reveal a rich submesoscale structure of temperature and salinity and a loss of frontal integrity along the newly formed southern sector of the eddy. A mathematical framework is developed to estimate vertical velocity from collocated drifter and horizontal water velocity time series, under certain simplifying assumptions appropriate for the current dataset. Upwelling (downwelling) rates of O(100) m day−1 are found in the northern (southern) eddy sector. Favorable conditions for submesoscale instabilities are found in the mixed layer, particularly at the beginning of the survey in the vicinity of density fronts. Shallower mixed layer depths and increased stratification are observed later in the survey on the inner edge of the front. Evolution in temperature–salinity (T–S) space indicates modification of water mass properties in the upper 200 m over 2 days. Modifications along σθ = 27–27.2 kg m−3 have climate-related implications for mode and intermediate water transformation in the Scotia Sea on finer spatiotemporal scales than observed previously.