Growth Of Turbulent Kinetic Energy Research Articles

Interactions Between Flame Topology and Turbulent Transport in High-Pressure Premixed Combustion

Direct numerical simulations of a turbulent premixed stoichiometric methane-oxygen flame were conducted. The chosen combustion pressure was 20 bar, to resemble conditions encountered in modern rocket combustors. The chemical reactions followed finite rate detailed mechanism integrated into the EBI-DNS solver within the OpenFOAM framework. Flame geometry was thoroughly investigated to assess its interaction with the transport of turbulent properties. The resulting flame front was remarkably thin, with high density gradients and moderate Karlovitz and Damköhler numbers. At mid-flame positions, the variable-density transport mechanisms dominated, leading to the generation of both vorticity and turbulence. A reversion of this trend towards the products was observed. For intermediate combustion progress, vorticity transport is essentially a competition between the baroclinic torque and vortex dilatation. The growth of turbulent kinetic energy is strongly correlated to this process. A geometrical analysis reveals that the generation of enstrophy and turbulence is restricted to specific topologies. Convergent and divergent flame propagation promote turbulence creation due to pressure fluctuation gradients through different physical processes. The possibility of modeling turbulence transport based on curvature is discussed along with the inherent challenges.

Assessment and improvement of k-ω-γ model for separation-induced transition prediction

The purpose of this work is to improve the k-ω-γ transition model for separation-induced transition prediction. The fundamental cause of the excessively small separation bubble predicted by k-ω-γ model is scrutinized from the perspective of model construction. On the basis, three rectifications are conducted to improve the k-ω-γ model for separation-induced transition. Firstly, a damping function is established via comparing the molecular diffusion timescale with the rapid pressure-strain timescale. The damping function is applied to prevent the effective length scale from incorrect distribution near the leading edge of the separation bubble. Secondly, the pressure gradient parameter λζ, is proposed as an indicator for local susceptibility to the separation instability. Additionally, λζ,-based separation intermittency γsep is constructed to accelerate the substantial growth of turbulent kinetic energy after flow separation. The improved model appropriate for both low- and high-speed flow has been calibrated against a variety of diverse and challenging experiments, including the subsonic T3L plate, Aerospatial A airfoil, transonic NLR-7301 airfoil and deformed hypersonic inflatable aerodynamic decelerator aeroshell. The improved model is strictly based on local variables and Galilean invariance. Besides, the proposed improvement for k-ω-γ model can be fairly convenient to incorporate into other existing intermittency-based transition models.

Nonlinear spectral model for rotating sheared turbulence

We propose a statistical model for homogeneous turbulence undergoing distortions, which improves and extends the MCS model by Mons, Cambon & Sagaut (J. Fluid Mech., vol. 788, 2016, 147–182). The spectral tensor of two-point second-order velocity correlations is predicted in the presence of arbitrary mean-velocity gradients and in a rotating frame. For this, we numerically solve coupled equations for the angle-dependent energy spectrum${\mathcal{E}}(\boldsymbol{k},t)$that includes directional anisotropy, and for the deviatoric pseudo-scalar $Z(\boldsymbol{k},t)$, that underlies polarization anisotropy ($\boldsymbol{k}$ is the wavevector,$t$the time). These equations include two parts: (i) exact linear terms representing the viscous spectral linear theory (SLT) when considered alone; (ii) generalized transfer terms mediated by two-point third-order correlations. In contrast with MCS, our model retains the complete angular dependence of the linear terms, whereas the nonlinear transfer terms are closed by a reduced anisotropic eddy damped quasi-normal Markovian (EDQNM) technique similar to MCS, based on truncated angular harmonics expansions. And in contrast with most spectral approaches based on characteristic methods to represent mean-velocity gradient terms, we use high-order finite-difference schemes (FDSs). The resulting model is applied to homogeneous rotating turbulent shear flow with several Coriolis parameters and constant mean shear rate. First, we assess the validity of the model in the linear limit. We observe satisfactory agreement with existing numerical SLT results and with theoretical results for flows without rotation. Second, fully nonlinear results are obtained, which compare well to existing direct numerical simulation (DNS) results. In both regimes, the new model improves significantly the MCS model predictions. However, in the non-rotating shear case, the expected exponential growth of turbulent kinetic energy is found only with a hybrid model for nonlinear terms combining the anisotropic EDQNM closure and Weinstock’s return-to-isotropy model.

Turbulent Kinetic Energy Production in the Vane of a Low-Pressure Linear Turbine Cascade with Incoming Wakes

Incompressible large eddy simulation and direct numerical simulation of a low-pressure turbine atRe=5.18×104and1.48×105with discrete incoming wakes are analyzed to identify the turbulent kinetic energy generation mechanism outside of the blade boundary layer. The results highlight the growth of turbulent kinetic energy at the bow apex of the wake and correlate it to the stress-strain tensors relative orientation. The production rate is analytically split according to the principal axes, and then terms are computed by using the simulation results. The analysis of the turbulent kinetic energy is followed both along the discrete incoming wakes and in the stationary frame of reference. Both direct numerical and large eddy simulation concur in identifying the same production mechanism that is driven by both a growth of strain rate in the wake, first, followed by the growth of turbulent shear stress after. The peak of turbulent kinetic energy diffuses and can eventually reach the suction side boundary layer for the largest Reynolds number investigated here with higher incidence angle. As a consequence, the local turbulence intensity outside the boundary layer can grow significantly above the free-stream level with a potential impact on the suction side boundary layer transition mechanism.

Improvement of a Turbulence Model for Conjugate Heat Transfer Simulation

For the conjugate heat transfer simulation, two-equation turbulence models will predict an anomalously large growth of turbulent kinetic energy in high strain rate flows, and then the flow and heat transfer will be unreasonable. The current study improved the low Reynolds number Chien k-ϵ two-equation model using the “realizability” based C μ limiter and the production term P k limiter. This study was conducted based on a developed preconditioned density-based conjugate heat transfer algorithm. Calculations are presented for the flat plate turbulence flow and the conjugate heat transfer of the MarkII cooling turbine blade using the improved model. The results were analyzed and compared with semi-empirical formula and experimental data. Significant improvement in the turbulent kinetic energy anomaly was obtained using both limiters. The prediction accuracy of the Chien k-ϵ model for the flow and heat transfer in the conjugate heat transfer simulation was significantly enhanced. The changes in the model are guaranteed to not have unfavorable influence on the simulation of low strain rate flows.

A new compressibility modification k-ε turbulence model with shock unsteadiness effect

A new compressibility modification k-ε model, including shock unsteadiness effect and the previous compressibility modification of pressure dilatation and dilatational dissipation rate, was developed with a simple formulation for numerical simulation in supersonic complex turbulent flows. The shock unsteadiness effect was modeled by inhibiting turbulent kinetic energy production in the governing equations of turbulent kinetic energy and the turbulent kinetic energy dissipation rate. Sarkar’s correction models were employed accounting for the dilatational compressibility effects in the new model. Two types of flows, the free supersonic mixing layers and complex supersonic flow with transverse injection were simulated with different flow conditions. Comparisons with experimental data of the free supersonic mixing layers showed that the new compressibility modification k-ε model significantly inhibited the excessive growth of turbulent kinetic energy and improved predictions. On the supersonic mixing layer flows, prediction results with the new model were in close agreement with experimental data, accurately predicting the decreasing trend of the mixing layer spreading rate with the increase of the convective Mach number. Due to the complicated flow field with flow separation, shock unsteadiness modification inhibited excessive growth of the turbulent kinetic energy in shock regions and wider shock regions are predicted, thereby significantly improving results of the flow with a strong separation forecast. The flow separation was stronger, which was the primary modification effect of the new model. Predictions accord with experimental results even in strong separation flows.

One- and two-equation turbulence models for the prediction of complex cascade flows using unstructured grids

One- and two-equation, low-Reynolds eddy-viscosity turbulence models are employed in the context of a primitive variable, finite volume, Navier–Stokes solver for unstructured grids. Through the study of the complex flow in a controlled-diffusion compressor cascade at off-design conditions, the ability of the models under consideration to predict the laminar separation bubble close to the leading edge and the boundary layer development is investigated. In order to control the unphysical growth of turbulent kinetic energy near the leading edge stagnation point, appropriate modifications to the conventional models are employed and tested. All of them improve the leading edge flow patterns and significantly affect the size of the predicted laminar separation bubble. The use of an adequately refined mesh around the airfoil, that is formed by triangles placed in a quasi-structured way, allows for the generation of grid elements of moderate aspect ratios. This helps to readily overcome any relevant problems of accuracy; a second-order upwind scheme without flux limiters or least squares approximations is successfully employed for the gradients. The test case includes quasi-3D effects by considering the streamtube thickness variation in the governing equations.

Compressibility Effects on Turbulence Growth in High-Speed Shear Flows

Compressibility effects on the evolution of turbulence are obtained from direct numerical simulation of homogeneous shear flow. It is found that when the gradient Mach number - a parameter based on the mean shear rate, integral length scale and speed of sound - increases, the growth of turbulent kinetic energy is inhibited. The reduced ‘efficiency’ of production is shown to lead to the inhibited growth of turbulent kinetic energy. Implications for inhomogeneous shear flows are discussed.

Direct simulation of compressible turbulence in a shear flow

The purpose of this study is to investigate compressibility effects on the turbulence in homogeneous shear flow. Physical experiments have not been and perhaps cannot be performed for homogeneous shear flows at flow speeds which are sufficiently high to introduce compressible effects on the turbulence. However, direct numerical simulation (DNS) of this problem could provide meaningful data, especially since DNS for the incompressible problem ([1], [2]) has been successful in giving realistic flow fields akin to those obtained in physical experiments. The present simulations of the homogeneous shear problem augment and extend our previous results ([3], [4]) for compressible isotropic turbulence. The compressible Navier-Stokes equations are written in a frame of reference moving with the mean flow u. We use a Fourier collocation method for the spatial discretization of the governing equations. A third order, low storage Runge-Kutta scheme is used for advancing the solution in time. Up to 1283 points are used for the simulations. The simulated turbulent fields have Taylor microscale Reynolds numbers Re? up to 35 and turbulent Mach numbers Mt up to 0.6. The results are summarized below. We find that an increase in initial compressibility level, either due to increased turbulent Mach number or increased dilatational fraction of the velocity field decreases the growth of turbulent kinetic energy (and all its components) in the case of homogeneous shear flow. This is reminiscent of the reduction in turbulent velocity intensities observed in experiments on supersonic free shear

Turbulence Measurements and Secondary Flows in a Turbine Rotor Cascade

This paper presents results for turbulence measurements that have been made using hot-wire anemometry in the endwall region of a high turning rotor blade cascade. It is shown that the levels of turbulence are very high in the regions of the flowfield containing the passage vortex and its associated loss core. A comparison with the total pressure loss measurements illustrates the mechanisms of loss generation within the cascade. The growth of turbulent kinetic energy was much less than the growth of loss indicating significant viscous dissipation.