In this study, the flow field structure inside a scramjet combustor is numerically simulated using the flamelet/progress variable model. Slope injection is considered, with fuel mixing enhanced by means of a streamwise vortex. The flow field structure and combustion characteristics are analyzed under different conditions. Attention is also paid to the identification of the mechanisms that keep combustion stable and support enhanced mixing. The overall performances of the combustion chamber are discussed.

Authors are encouraged to use the Microsoft Word template when preparing the final version of their manuscripts. In introduction, authors should provide a context or background for the study (that is, the nature of the problem and its significance). State the specific purpose or research objective of, or hypothesis tested by, the study or observation. Cite only directly pertinent references, and do not include data or conclusions from the work being reported. The theoretical performance of supersonic combustion for hypersonic vehicles has been discussed since the 1950s. However, because of the transitory residence time of inflow air in the combustor, many critical processes for supersonic combustion cannot be directly measured in experiments [

The traditional finite rate model treats turbulence and combustion as independent processes, ignoring the influence of turbulence fluctuations on the chemical reaction. However, the flamelet model assumes that the timescale of the chemical reaction is small enough that the thickness of the local instantaneous reaction layer is thinner than the Kolmogorov scale, and thus the chemical reaction in the reaction layer is unaffected by turbulence fluctuations. Previous studies [

However, the flamelet model was originally designed for low-Mach-number flows and could not be directly extended to supersonic flows. Given the application of the flamelet model in supersonic combustion, Oevermann [

In this paper, the application of the flamelet model in supersonic flow is studied, and a representative experimental example is selected. The experiment is extended by using numerical simulations, and the numerical results of various properties are discussed in detail.

All numerical cases were simulated in a finite volume framework using an in-house code developed by the authors. Reynolds-averaged Navier–Stokes (RANS) simulations were used to solve the compressible governing equations as follows.

Continuity equation:

Momentum equation:

Energy equation:

Species continuity equation:

The superscripts ‘−’ and ‘∼’ represent the Reynolds and Favre averages, respectively, and the specific variable symbols can be found in reference [

_{ij} is the Kronecker delta.

The state equation for the mixture gas is given as [_{u} is the universal gas constant and _{s} is the molecular weight of species s.

The flamelet model is used in this paper to evaluate the interactions between turbulence and combustion in supersonic flows because the mean chemical reaction rates

By numerically solving _{s} = _{s}(_{st}) and _{st}) can be obtained by solving the flamelet governing equation. In this work, Flamemaster V4.0 [

In general, the mixture fraction and scalar dissipation are physical quantities that vary with fluctuations of the flow field. Based on the instantaneous correlation of the mass fraction _{s}, temperature _{st}, the mean value of mass fraction and temperature can be obtained by integrating the joint probability density function (PDF) of the mixture fraction and scalar dissipation rate.

The joint PDF

In this work, the SST turbulence model [

The steady flamelet model (SF model) uses only the steady branch in the combustion solution of the flamelet equations, as shown in

Pierce [

The S-shaped curve of the maximum flame temperature

_{st} enhances the nonequilibrium effect, improves mixing and diffusion between substances, and increases the reactant concentration. The reaction intensity, product concentration, and maximum flame temperature all decrease. As _{st} continues to increase toward the tipping point, the flame temperature remains at a local critical minimum; the flame completely extinguishes when _{st} is slightly above the tipping point. However, there is an apparent transition state between the complete combustion and completely extinguished states known as the unsteady combustion branch. Along this branch, the dissipation rate decreases as the flame temperature decreases, and the mixing equilibrium state is maintained at a lower reaction rate. In the completely extinguished state, the effect of chemical kinetics is negligible, and the chemical state is independent of the dissipation rate.

In this paper, the compressible Navier–Stokes equations are discretized using the finite volume method based on a multiblock structured grid framework. A second-order MUSCL scheme with a minmod limiter is used to calculate the inviscid flux vector, and a second-order central difference scheme is used to calculate the viscous flux vector. The LDFSS flux splitting scheme [

The German Aerospace Center (DLR) provided experimental schlieren diagrams of a supersonic combustor, flow field pressure distributions, and experimental velocity and temperature measurement results [

Schematic diagrams of the experimental device and the central strut are given in

_{∞} |
_{∞}( |
_{∞}( |
|||||
---|---|---|---|---|---|---|---|

2.0 | 340.0 | 100000.0 | 0.0 | 0.032 | 0.232 | 0.736 | |

_{2} |
1.0 | 250.0 | 100000.0 | 1.0 | 0.0 | 0.0 | 0.0 |

Previous studies have shown that the grid spacing in the normal direction of the wall is critical for obtaining reliable numerical simulation results. Based on previous numerical experience, the grid Reynolds number [_{∞}, _{∞}, _{∞} are the freestream density, velocity and viscosity, respectively, and Δ is the first grid scale in the wall-normal direction.

To ensure the reliability of the following calculation, the convergence of the grid spacing needs to be verified first. Based on the empirical grid setting strategy [

Coarse grid | Medium grid | Fine grid | |
---|---|---|---|

Δ( |
0.01 | 0.005 | 0.003 |

200 | 100 | 60 | |

Cell umber | 1320000 | 2110000 | 2540000 |

Two typical locations (X = 78 mm and X = 207 mm) were selected to investigate the distribution of the flow field variables calculated by the three types of grids.

A comparison between the experimental schlieren image and the density gradient distribution of the calculated results is shown in

Three specific positions along the flow direction are selected for comparisons between the numerical results and the experimental data.

In this paper, the numerical simulation of a slope injection with fuel-enhanced mixing by the streamwise vortex is studied. When supersonic air flows through the edge of the slope, it follows the incoming flow downstream and gradually develops into a pair of streamwise vortexes. A recirculation zone can be formed at the bottom of the slope, where the high enthalpy inlet flow slows down and increases the temperature, creating an ideal combustion environment. After injection, the fuel is rolled into the main flow area by the streamwise vortex and thoroughly mixed with oxygen for intense combustion. After the reflection of the upper wall, the oblique shock wave generated by the slope collides with the vortex structure in the main flow area of the combustion chamber, potentially causing the vortex to break up. At the same time, the reflected shock wave collides with the turbulent boundary layer of the lower wall, resulting in separation and the formation of new streamwise vortices.

The numerical simulation is based on a supersonic combustion flow experiment with increased slope and cavity mixing conducted by Arail [

_{∞} |
_{∞}( |
_{∞}( |
_{∞}( |
|||||
---|---|---|---|---|---|---|---|---|

2.4 | 0.0 | 1150.0 | 100000.0 | 0.0 | 0.21 | 0.0 | 0.79 | |

_{2} |
1.0 | 0.0 | 250.0 | 100000.0 | 1.0 | 0.0 | 0.0 | 0.0 |

After hydrogen fuel is injected into the combustion chamber along the flow direction from the bottom of the step, it is thoroughly mixed with the incoming air via the entrapment action of the streamwise vortex to form a stable turbulent combustion flow. In this section, the mixing and combustion characteristics of the ramp injection fuel scheme and the influence of the upper wall cavity on the flow are studied.

The temperature distributions and superposition of sound velocity lines at the spanning center cross-section and various flow direction cross-sections are shown in

The density gradient distribution in _{2}O and OH, respectively, in the central section with or without a square cavity. The distributions of intermediate OH and water in the two configurations is nearly identical. This shows that the square cavity has no effect on the intermediate or final stages of combustion.

In the current study, the influence of the flamelet/progress variable model on the flow field prediction of a scramjet is numerically analyzed. The standard SST turbulence model is used for turbulent transport, and the flamelet model is used for chemical reactions. The main conclusions are summarized as follows. A pair of streamwise vortices form in opposite directions after the airflow bypasses the slope and the step. The shock waves generated by the front edge of the step are reflected by the upper wall and collide with the vortex region, accelerating the vortex rupture and amplifying the mixing effect. Unfortunately, the steady-state method used in this paper does not capture the oscillating flow at the inlet of the square cavity. However, when the influence of the wave structure in the flow field is considered, the influence of the square cavity on flow and turbulent combustion is minimal.

The first author, Yongkang Zheng acknowledges the National Laboratory for Computational Fluid Dynamics for the computational resources and technical support.