The stability of oblique detonation waves (ODWs) is a fundamental problem, and resistance of ODWs against disturbances is crucial for oblique detonation engines in high-speed propulsion. In this work, numerical studies on ODW stability in disturbed flows are conducted using the two-dimensional reactive Euler equations with a two-step induction-reaction kinetic model. Two kinds of flow disturbances are, respectively, introduced into the steady flow field to assess ODW stability, including upstream transient high-pressure disturbance (UTHD) and downstream jet flow disturbance (DJFD) with different durations. Generally, an ODW is susceptible to disturbances at larger wedge angles and stable at smaller wedge angles. In the unstable wedge angle range, different ODW structures and transition patterns are obtained after disturbances, including different locations of the primary triple points, different numbers of the steady triple points on the wave surface, and different transition patterns from the leading oblique shock wave to the ODW. It is found that the primary triple point tends to move upstream for the disturbances that can form a local strong detached bow shock wave near the wedge tip. In contrast, the wave surface and the transition pattern are susceptible to all of the disturbances introduced in this study. Despite the unstable responses of the ODWs to the disturbances, the ODWs can keep standing stability after disturbances, which is beneficial to the propulsion application of ODWs.

Standing stability of ODWs is important for oblique detonation engines because it involves the realization of its advantages in hypersonic propulsion, including fast heat release and high thermodynamic cycle efficiency. A standing ODW should first satisfy the requirement of the wedge angle according to Pratt et al. [

The aforementioned studies are based on two-dimensional flow fields. If a conical shock wave is considered, the flow field will differ from the wedge flow to some extent due to the curvature effect and the presence of the Taylor-Maccoll flow [

One feature of a stabilized ODW is its stability or resistance to disturbances. If an ODW cannot maintain standing stabilization when experiencing additional disturbances, propulsion using ODW will be meaningless because, during a flight process, changes in the inflow conditions and flow disturbances are usually inevitable. The previous studies on the ODW disturbance resistance examined responses of ODWs to transient disturbances inside the flow field (see Li et al. [

The governing equations to be numerically solved are the two-dimensional unsteady reactive Euler equations given as follows.

The continuity equation is

The conservation equation of

The conservation equation of

The conservation equation of energy is

The equation of state for perfect gas is

A two-step induction-reaction kinetic model proposed by Ng et al. [

Clearly, at any instant, the local heat release

The governing equations above are numerically solved using an open-source adaptive mesh refinement computational fluid dynamic program called AMROC [

Numerical parameter setup.

Inflow Mach number, | Inflow static temperature, | Inflow static pressure, | Specific heat ratio, | Dimensionless heat release, |
---|---|---|---|---|

4.0 | 650 | 20000 | 1.2 | 8 |

Dimensionless activation energy of the induction step, | Dimensionless activation energy of the heat release step, | Induction length corresponding to a CJ detonation, | Thermal pulse width corresponding to a CJ detonation, | Gas constant, |

4.8 | 1.0 | 2.12 | 0.95 | 377.9 |

The computational domain.

In this study, all the original steady flow fields are obtained through the following method: an inert shock wave is obtained by turning off the chemical reactions, and then an ODW is obtained by turning on the reactions in the cold flow. As introduced in Section ^{-7} seconds. All of the results in this study are presented in the form of numerical schlieren,

Three different wedge angles including

Evolution of the flow field after UTHD at

To assess whether the aforementioned results are grid-independent, Figure

Grid convergence test at

Considering that the primary triple point being stable to UTHD may be due to insufficient disturbance time, a longer-term DJFD disturbance is introduced into the original steady flow field at

Evolution of the flow field after DJFD of

Figure

Evolution of the flow field after DJFD of

Pressure distributions on the bottom boundary of the steady flow fields after the DJFD of

Now, we start to consider the case of

Steady flow fields before and after UTHD at

Pressure distributions on the bottom boundary of the steady flow fields before and after UTHD at

Figure

Evolution of the flow field after DJFD of

Finally, the case of

Evolution of the flow field after DJFD of

The stability of the steady ODW flow field after the disturbance is also worth discussing. At

Although the ODW is unstable to flow disturbances in a certain wedge angle range, it can maintain standing stabilization on the wedge, which is beneficial to propulsive ODW applications.

The disturbance resistance of ODWs was numerically studied in this work using the two-dimensional reactive Euler equations with a two-step induction-reaction kinetic model. In contrast to previous studies by other researchers [

The (numerical schlieren) and (pressure distribution) data used to support the findings of this study are included within the article.

The authors declare that there is no conflict of interest regarding the publication of this paper.

This work was supported by the National Natural Science Foundation of China (NSFC) (nos. 11702316 and 91641126).