Open Journal of Fluid Dynamics
Vol.04 No.05(2014), Article ID:52856,6 pages

Improvement of a Propulsion Equipment with a Supersonic Nozzle for Single Pulse Detonation

Kazuhiko Toshimitsu1, Shuuto Mikajiri2, Ryo Takahashi3

1Department of Mechanical Engineering, Oita National College of Technology, Oita, Japan

2Mechanical-Environmental System Engineering Major, Oita National College of Technology, Oita, Japan

3Department of Computer Science and System Engineering, Kyushu Institute of Technology, Kitakyushu, Japan


Copyright © 2014 by authors and Scientific Research Publishing Inc.

This work is licensed under the Creative Commons Attribution International License (CC BY).

Received 27 October 2014; revised 20 November 2014; accepted 18 December 2014


A pulse detonation engine (PDE) is one of candidates of aerospace engines for supersonic cruse. In the paper, a supersonic nozzle ejector is designed to increase thrust of single pulse detonation for methane-oxygen and hydrogen-oxygen mixtures. The design method is based on the conventional characteristic method and inlet condition is averaged value of detonations of methane-oxygen and hydrogen-oxygen mixtures. Comparison of thrusts with a design nozzle and no nozzle (straight- type) is conducted to ensure the designed nozzle performance. Furthermore, the flow velocity, temperature and velocity of the designed nozzle are calculated to ensure its appropriateness with the commercial software ANSYS CFX. Consequently, we succeed in increasing the thrusts of the single pulse detonation with the nozzle, which are 1.4 and 2.0 times as large as ones of straight- type for methane-oxygen and hydrogen-oxygen mixtures respectively.


Thruster, Detonation, Impulse, Supersonic Flow, Method of Characteristics, CFD, Nozzle

1. Introduction

The increase thrust performance for a space-plane and a rocket is important. In particular, the development of high-efficiency propulsion is required in supersonic cruising. According to the background, a pulse detonation engine (PDE) was proposed on 1990s, and PDE has been studied in many institutions [1] [2] .

Our final goal is to design, manufacture and operate PDE for the space and air-breathing propulsion devices at laboratory level.

In order to increase the thrust of PDE, we will conduct to design and manufacture an optimum supersonic nozzle, which is based on the characteristics method of the supersonic nozzle for single pulse detonation in the paper. Furthermore, performance of the nozzle ejector is investigated by experiment and CFD analysis to validate appropriateness of the design.

2. Experimental Procedure

2.1. Experimental Apparatus

Figure 1 shows a schematic diagram of the entire experimental apparatus. The total length, inner diameter and tube thickness of the detonation tube (DT tube) are 1000 mm, 30 mm and 10 mm, respectively. DT tube is suspended by the two stainless wires of diameter 1 mm, and oscillates freely by single impulsive detonation.

Its impulse can be calculated from Equation (1) of the ballistic pendulum method proposed by Yatsufusa et al. [3] .


Here, , , and denote the suspended weight [kg], the maximum displacement from the neutral position [m], the damping coefficient and the oscillation period [s], respectively.

2.2. Design of the Axisymmetric Supersonic Nozzle

An axisymmetric supersonic nozzle is designed through the characteristic method based in Foelsch [4] . Figure 2 schematically illustrates the characteristics method for the nozzle. It is assumed that flow is steady and isentropic without boundary layer. The thrust is increased by attaching the nozzle at the outlet of DT tube.

Figure 1. Experimental apparatus to measure thrust on the basis of ballistic pendulum method.

Figure 2. Method of characteristic of axisymmetric supersonic nozzle flow.

2.3. Design Conditions of Nozzle

Table 1 shows the design conditions. Nozzle inlet conditions are the average values of the detonation combustion states of both gas mixtures of H2-O2 and CH4-O2 for equivalence ratio is one. The specific heat ratio of the combustion mixture is assumed as 1.31. Mach number, static pressure and static temperature at the nozzle inlet are 1.7 (700 m/s), 354.6 kPa and 1530 K, respectively. The inlet diameter of the nozzle is 30 mm as same as the inner diameter of the detonation tube. Furthermore, outlet pressure is set as atmospheric pressure. Other outlet values are automatically determined. Here, the nozzle profile is shown in Figure 3.

2.4. CFD Analysis

In order to validate the previous design, CFD analysis of the nozzle internal flow is conducted using commercial software ANSYS CFX Ver.14.

Table 1 shows the calculation conditions. Turbulent model of the calculation is eddy-viscosity model that includes vortex scale and turbulent intensity are 2.0 mm and 5% respectively.

Figure 4 shows computational domain which is consisted of non-structured mesh with 2,701,865 tetrahedron elements and 472,930 nodes.

The calculated pressure, temperature, velocity distribution are illustrated in Figure 5. It is ensured that the exit velocity and pressure are substantially uniform on the nozzle exit surface. In addition, the boundary layer is not so thick. As the results, we can consider that the nozzle design is appropriate.

3. Experimental Results

We will make sure the designed nozzle performance though comparisons of impulse and specific impulse with the nozzle and no nozzle (i.e. exhaust straightly).

3.1. Impulse

Figure 6 shows impulses with nozzle and no nozzle, which are varying the equivalence ratio of CH4-O2 and H2-O2 gas mixture. Since all impulse is constant with varying φ from 0.8 to 1.8. Thus it does not depend on equivalence ratio. The impulses with CH4-O2 and H2-O2 mixtures with nozzle are about as 1.4 and 2 times as the no nozzle case respectively.

Table 1. Conditions for characteristic method.

Figure 3. Designed supersonic nozzle profile.

Figure 4. Computational mesh on center plane.

Figure 5. CFD analysis results of the supersonic nozzle with pressure, temperature, velocity and velocity on nozzle exit surface.

3.2. Specific Impulse

The specific impulse is defined by Equation (2). It represents continuous time which thrust can be maintained as 1 N with propellant mass 1 kg.


Here, , and mean thrust, impulse and combustible propellant mass, respectively. We should mention that is defined as fuel only for air-breathing engine or fuel plus oxidizer for rocket engine. The former and latter are called as “fuel-base” and “mixture-base” specific impulses.

The experimental specific impulse with varying equivalence ratio of CH4-O2 and H2-O2 gas mixtures are shown in Figure 7 to Figure 10. The fuel-base decreases with increasing of both mixtures of CH4-O2 and H2-O2. In particular, specific impulse is large at lean fuel combustion with the nozzle. Namely, the maximum specific impulses of CH4-O2 and H2-O2 are 1463 s at φ = 0.6 and 3096 s at φ = 0.39 respectively. This means that of CH4-O2 and H2-O2 correspond to a ramjet engine (500 - 1500 s) and a turbo-jet engine (2300 s - 2900 s), respectively.

We will discuss about the mixture-base for rocket engine as follows. The mixture-base of CH4-O2 show almost constant value for the equivalence ratio (except φ = 0.6 and 2.2), and with nozzle is about as 1.4 times as one with no nozzle. In particular, of no nozzle slightly decreases at φ = 2.2, while with the nozzle does not decrease. This is concerned about combustion state. Here, we should consider that the range of detonation combustion is and one of non-detonation combustion is φ = 2.2 with CH4-O2, so that the nozzle can operate as an effective thrust generator for both combustion states.

The specific impulse of H2-O2 is increased in proportion to equivalent ratio.

Figure 6. Effects of the nozzle, mixture gases and equivalence ratio on impulse.

Figure 7. Effects of the nozzle and equivalence ratio on fuel-base specific impulse with CH4-O2 mixture.

Figure 8. Effects of the nozzle and equivalence ratio on fuel-base specific impulse with H2-O2 mixture.

Figure 9. Effects of the nozzle and equivalence ratio on mixture-base specific impulse with CH4-O2 mixture.

Figure 10. Effects of the nozzle and equivalence ratio on mixture-base specific impulse with H2-O2 mixture.

4. Conclusions

In the study, we design and manufacture a supersonic nozzle through method of characteristics to increase thrust of single pulse detonation. In order to confirm the effectiveness of the nozzle, we compare the impulse and specific impulse with nozzle and no nozzle (straight exhaust) for methane-oxygen and hydrogen-oxygen gas mixtures through the ballistic pendulum method. The results obtained are as follows.

• The impulses of CH4-O2 and H2-O2 gas mixtures with the nozzle are about as 1.4 and 2 times as the straight exhaust respectively. Thus, the present design is useful to increase thrust by the detonation.

• The fuel-base specific impulses of CH4-O2 and H2-O2 gas mixtures decrease with increasing equivalence ratio. As the result, lean combustion is suitable for large fuel-base specific impulse.

• The designed nozzle can keep a constant value of the impulse and mixture-base specific impulse in CH4-O2 for detonation and non-detonation combustions. Hence, it is an effective thrust generator for the combustion states.


  1. Eidelman, S., Grossmann, W. and Lottati, I. (1991) Review of Propulsion Applications and Numerical Simulations of the Pulsed Detonation Engine Concept. Journal of Propulsion, 7, 857-865.
  2. Kailasanath, K. (2001) A Review of PDE Research-Performance Estimates. The 39th Aerospace Sciences Meeting & Exhibit, AIAA Paper-2001-0474.
  3. Yatsufusa, T., Endo, T. and Taki, S. (2008) Effect of Initiator Conditions on Detonation Initiation and Impulse in Pulse-Detonation Engines. Transactions of Mechanical Engineer, 74, 2055-2062. (In Japanese)
  4. Crown, B.J.C. (1948) Supersonic Nozzle Design. NACT Technical Note, No. 1651.