# Comparison of Dual-Combustion Ramjet and Scramjet Performances Considering Combustion Efficiency
## 1 Introduction  
Choosing a suitable propulsion system for a hypersonic vehicle is an important issue for engine designers. Four types of propulsion system [1; 2] have been proposed, namely ramjet, scramjet, dual-mode ramjet (DMR), and dual-combustion ramjet (DCR). Previous studies [3; 4; 5; 6] have shown that the ramjet is suitable for low Mach-number flight, the scramjet is suitable for high Mach-number flight, and DMR and DCR are suitable for medium-Mach number flight because they combine the characteristics of ramjet and scramjet, as shown in Figure 1. Since the scramjet/ramjet mode of DMR can be considered as a scramjet/ramjet, it is not discussed in this paper. The flight Mach numbers of the DCR and scramjet overlap, and the performance of the two cannot be accurately determined in this region. In fact, it is of great significance to determine which type of engine performance is dominant for engine selection under predetermined operating conditions. Engine performance is mainly related to combustion efficiency and total pressure loss, which is generally measured by specific impulse or specific thrust. The higher the combustion efficiency and the lower the total pressure loss, the better the engine performance, and  
Figure 1: Operating Mach number range for different types of engines. vice versa. To avoid excessive total pressure loss [7], the air flow in the scramjet combustor maintains a supersonic state, which is bound to cause low static temperature and ignition difficulty. For this reason, scholars [8; 9; 10] mainly rely on passive mixing technologies (direct injection, cavity, strut, etc.) to achieve stable and reliable flame combustion, which have obtained certain results. On the other hand, in order to solve the problem of difficult ignition of traditional hydrocarbon fuel in a scramjet engine, the concept of DCR was proposed by Hopkins University [4] in 1979. It is mainly used in the field of naval air defense and for anti-missile purposes. The fuel is injected into the subsonic combustor, and through mixing-ignition-combustion, high-temperature and high-pressure oil-rich gas is formed, which enters the supersonic combustor and is further burned with the secondary air flow. In the supersonic combustor, the high temperature gas and secondary air are further mixed and combusted, and finally discharged from the tail nozzle to generate thrust. Combined the advantages of both ramjet and scramjet [4], the DCR is considered not only to have a wide flight Mach number [6; 11; 12], but also to achieve a zero-speed start through combined rocket assistance [13], which is likely to become one of the first practical hypersonic weapons [14]. Up to now, most studies on DCR have focused on parts of the performance, such as improving combustion efficiency by improving mixing [15], predicting the shock train length by studying the coupling effect of combustor back pressure and shock waves [16; 17; 18], verifying DCR combustion efficiency via a ground direct test bench [19], etc. Most of the above studies either studied scramjet or DCR separately, without comparing the engine performance of the two under the same operating condition, so it is impossible to determine which type of engine is better. The one-dimensional mathematical model was used in most studies on the overall performance of DCR. [PERSON] et al. [4] and [PERSON] [5] compared the performance of three types of ramjets: ramjet, scramjet, and DCR. The results showed that when the Mach number was less than 5-6, the ramjet was dominant; when the Mach number was greater than 6-7, the scramjet was dominant; and the DCR was between the two. [PERSON] et al. [20] studied DCR with three intake air ratios and found that the DCR with an intake air ratio of 1:4 afforded the best performance. [PERSON] [11] modeled every component of the DCR using empirical data and an analytical relation based on a quasi-one-dimensional mathematical model, obtaining a mathematical model of DCR. [PERSON] et al.