In this paper, some typical methods to promote mixing in supersonic combustion are reviewed, and the fluid-dynamic mechanism underpinning the development of the supersonic shear layer in the presence of a streamwise vortex is analyzed through computational fluid dynamics. It is proven that the streamwise vortex-couple method is an excellent approach to enhance mixing. A specific combustor design is proposed accordingly.

The scramjet differs from a typical ramjet in that it performs combustion in a supersonic flow rather than reducing the flow to subsonic levels. Although the concept of supersonic combustion has long been proposed, its engineering application has yet to be fully implemented. The difficulty results not only from the heat problem but also from the following two aspects: (1) the fuel mixing problem and (2) the combustion organization problem, including the Mach number, temperature, pressure, heating quantity, and pressure loss,

All numerical cases were simulated in a finite difference framework using an in-house code developed by the authors. The three-dimensional chemical non-equilibrium NS equations in Cartesian coordinates are as follows [

where:

In the above, _{i}_{2}_{2}_{2}O_{2}

The source term

The static enthalpy and the specific heat at constant pressure are considered with temperature and species-dependent thermodynamic properties as follows:

Thermal conductivity and molecular viscosity are calculated using the Sutherlands formula for each species. The Wilkes formula [

The total energy per unit mass of mixture

The high-order scheme has the advantage of less numerical dissipation in describing the flow field with high resolution and has less dependence on the grid for the same numerical accuracy. Meanwhile, both the accuracy and robustness of the scheme are required in engineering problems, making the third-order scheme a good compromise. Numerical verifications are conducted for a class of third-order schemes for engineering applications on different problem types [

The scheme is introduced in the form of one-dimensional hyperbolic equations as follows:

Consider the conservative difference scheme and write it in a semi-discrete form:

The positive flux portion with the third (or higher)-order scheme in the linear condition can be written as follows:

where:

where

To capture the discontinuous structure (such as the shock wave), however, the nonlinear mechanisms are needed to increase scheme dissipation in the weighted form:

A continuous variational rescale technology is proposed [

As shown in previous investigations, the turbulence model is crucial in predicting the flow-field variables and the interaction between turbulence and combustion for supersonic combustion simulations. Menter’s shear stress transport (SST) model [

The governing equations of the turbulence model are as follows:

Details of the equations can be found in reference [

The finite difference method is used in this study, and the compressible NS equations are discretized on a single structured grid. Based on its robustness and high resolution of stationary discontinuity, the nonoscillatory nonfree-parameters dissipative difference scheme (NND) [

Numerical simulations of the straight and expanded tubes are implemented in this study. From the straight tube problem, the distribution range of each species in the flow field and several vital parameters are analyzed, and the principle of using detonation waves to organize the combustion is illustrated. A more detailed study on the proposal of using a streamwise vortex couple to enhance supersonic combustion is achieved via the expanded tube problem. A third-order scheme is applied, and the turbulence model is considered. Some results which differ from previous studies are also obtained.

Lehr’s experiment [

4.513 | 250.0 | 42662.0 | 0.0283 | 0.2256 | 0.7452 |

First, the grid sensitivity analysis is studied to eliminate the influence of grid errors. Three grid spacing scales are then adopted to represent the grid’s independence: coarse, medium, and fine grids. The detailed grid information and the distribution of the medium grid are shown in

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

0.01 | 0.005 | 0.003 | |

Cell umber | 13725 | 20475 | 27225 |

Stagnation temperature (K) | 2788.8 | 2883.5 | 2895.2 |

The numerical method predicts an accurate ignition position as the temperature distribution is consistent with the experiment data. Thus, the numerical implementation can then be applied to supersonic combustion simulations.

The structure problem between fully mixed hydrogen and oxygen is discussed in the following part, and the combustion is proposed at _{H2} = 0.1, and _{O2} = 0.9, and the numerical results are shown in

Two important parameters related to the combustor temperature and pressure are given in [

where

It has been demonstrated that the streamwise vortex can enhance fuel mixing and improve the supersonic combustion efficiency from both flow mechanism and numerical simulations in [

A single-block body-fitted grid is used for the calculation, and compression is performed along the wall directions to meet the requirements of the viscous boundary layer for NS equations. The grid is taken as

Parallel computing using the aforementioned third-order scheme and the SST turbulence model is implemented with 30 CPUs under the following conditions (

Air | 3.0 | 68 | 1125 | 0.21 |

H2 | 1.0 | 150.9 | 242 | 0.15 |

First, the feasibility of the project for enhancing the supersonic combustion efficiency is quantitatively analyzed based on the five aspects of combustion organization mentioned in Section 1.1.

Mach number: The Mach number is taken as 3.0 for the combustor inlet and 1.0 for the injection hole.

The problem of _{2} = 3 and

The pressure distribution of a spanwise section through one of the injection holes is shown in

The Mach number of the outlet is

The problem of

satisfying the aforementioned requirement:

Other results related to organizational problems are given in

The discontinuity in the flow field is caused by weak detonation waves and the supersonic combustion, of which occurs all over the field. From the aforementioned analysis, the design parameters of the project satisfy the requirements of the five aspects of supersonic combustion organization, and supersonic combustion can be theoretically achieved.

The phenomenon of streamwise vortex couple acting on the flow field to enhance mixing and improve combustion efficiency is further analyzed. According to the theory of streamwise vortex couple enhancing mixing [

The combustion efficiency curve shows that the combustion efficiency increases with an increase in x, but does not reach a relatively constant value, implying that the reaction is unsaturated. More research is needed on how to continuously increase the mixture to improve combustion efficiency within a limited range of combustor length.

Numerical results on fuel mixing are given in

By introducing a streamwise vortex couple, the vortex circumrotates from inside to outside under a pressure gradient, forming the mass transport. Thus, the incoming air and jet hydrogen are fully mixed and burned. Oxygen is almost entirely burned out in most of the middle area at the exit of the combustor. Concurrently, the hydrogen is exhausted, implying that the streamwise vortex couple significantly enhances supersonic combustion.

Under the condition in which the grid is compressed near the wall, and considering the influence of the boundary layer, the combustion mostly occurs in the combustor’s internal region, which is different from the results in previous calculations. The air vortex occurs near the bottom area, and a ribbon shape is formed by exhausting the oxygen with water generation, indicating that combustion occurs in the boundary layer. Concurrently, there are obvious differences between the results of laminar and turbulent flows. Under turbulent conditions, the combustion is more efficient considering the effect of turbulence in the boundary layer. For simplicity, only the turbulent numerical results are presented in this study.

The Mach number contours and streamlines at different locations are given in

The distributions of species and streamlines in different sections of the flow field correspond to each other. Taking the H_{2}O distribution as an example, the distribution of H_{2}O is obviously in the shape of a vortex at different sections. Vortexes coalesce near the injection holes in the front half of the combustor. The transport phenomenon is formed by rolling up the substance to the vortex center in the vortex movement. Two small vortical regions with low content, corresponding to H_{2}O distribution, exist inside a sizable vortical region with high content, implying that the hydrogen and oxygen are constantly rolled up into the vortex center with combustion. The vortex in the combustor’s rear half is not as strong as that in the front half. Because the reactions have been sufficiently conducted, the vortex in the H_{2}O contours has become slightly more prominent, whereas small vortical regions with low water content gradually disappear along the flow direction, indicating that combustion is complete and hydrogen and oxygen are exhausted. In conclusion, the distribution of species contours and flow structures are related. The vortex enhances combustion by mass transport and changes the content of each species, whereas the temperature and density of flow vary because of the reactions. Thus, component distribution and flow structure are related and influence each other.

It gives the speed of sound distribution at the center cross-section in

A numerical simulation of the process of supersonic combustion is performed with a fine grid using a third-order scheme and an SST turbulence model. The numerical results illustrate the following points:

First, the discontinuity in the flow field is a weak detonation wave in terms of combustion organization, which is consistent with the original purpose of organizing combustion using the detonation wave principle. In terms of fuel mixing, the introduction of a streamwise vortex couple enhances the mixing of hydrogen and oxygen and improves combustion efficiency.

Second, because of the numerical scheme, grid, and turbulence model, the flow field details are partly different from the prevenient laminar numerical results based on a second-order scheme. The numerical results show that supersonic combustion occurs almost all over the combustor. Concurrently, the subsonic region is mainly concentrated in the boundary layer region near the wall, which theoretically supports the proposal’s design.

Third, based on the aforementioned two points, the numerical simulation results show that achieving supersonic combustion in a hypersonic ramjet is theoretically feasible.

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