On the Optimal Choice of Type of Combustion Chamber for the

Initiation of Gas Detonation

D. V. VORONIN

Lavrentyev Institute of Hydrodynamics of SB RAS,

Lavrentyev str, 15, 630090 Novosibirsk,

RUSSIA

Abstract: - A numerical simulation of continuous gas detonation in the combustion chamber based on the

Navier-Stokes equations, taking into account turbulence and diffusion of substances, is carried out. A

comparative analysis of the efficiency of detonation combustion of fuel depending on the geometric parameters

of the chambers is performed. Three possible camera types are considered. Fuel and oxidizer were fed

separately into the chambers through nozzles at a certain angle to the chamber surface. The detonation process

was largely determined by the intensity of the turbulent mixing of reagents (hydrogen and oxygen).

Calculations show that the type of camera with a flat radial geometry is the most optimal to establish a stable

detonation regime.

Key-Words: - chamber geometry, modeling, turbulence, compressible flows, heat generation,

detonation, mixing.

Received: November 13, 2022. Revised: August 23, 2023. Accepted: October 2, 2023. Published: November 1, 2023.

1 Introduction

Recently, active research has been conducted on

the creation of an internal combustion engine based

on the detonation method of fuel combustion. In

this case, much more energy is released during the

detonation process with less fuel consumption than

during controlled combustion. The theoretical

possibility of using detonation in engines is shown

in, [1]. Since then, a number of research

laboratories have been working to create practical

installations and determine the optimal operating

modes of such cameras, [2]. In some cases,

significant progress has been made, [3]. Recent

experimental and theoretical studies, [4], have been

performed for various combustion mixtures and

installation parameters. The phenomenon of

detonation is a complex physicochemical process

that is realized at high speeds in the medium.

Therefore, the study of the phenomenon and its

possible technological applications requires the

involvement of detailed mathematical models

describing the process of fuel combustion in the

chamber. One of the most important aspects of the

problem is the geometric shape of the camera. It is

usually the volume between two metal cylinders.

But a simpler form is a flat, axisymmetric disk.

This work is devoted to a comparative

theoretical study of the initial stage of detonation

excitation for three different geometric types of

chambers. The first type is the volume formed by

two metal cylinders (Figure 1a). The second type is

an annular chamber inside the cylinder (Figure 1b).

The third simplest type is a plane axisymmetric

disk (Figure 1c).

2 Numerical Simulations

Consider a cylindrical vortex chamber of the first

type (Figure 1a). Here S1 is the inlet surface of the

chamber (the side surface of a circular cylinder

with a diameter of 204 mm and a height of 15 mm),

through which the reacting gas flows through the

nozzles from the collectors into the chamber, and

S2 is the surface of the gas outlet from the chamber

(a circle with a diameter of 40 mm). S3 is the side

surface of the central nozzle of the chamber (a

circular cylinder with a height of 42 mm along the

z-axis), which serves to release products into the

atmosphere. All external surfaces of the vortex

chamber except S1 and S2 are rigid, impermeable

walls. The z-axis is directed along the axis of

symmetry of the camera, and the r-axis is normal to

the z-axis.

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D. V. Voronin

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(a)

(b)

(c)

Fig. 1: Camera diagram.

The second type of chamber is an annular

cylinder with a diameter of 40 mm (Figure 1b). The

length of the camera (L) is a variable value. The Z

axis is the axis of symmetry of the cylinder. The

combustion of the mixture occurs in a narrow

annular channel at the outer surface of the chamber

with a diameter of 5 mm. Oxygen was supplied to

the chamber from the receiver through surface S11.

Fuel was supplied inside through nozzles on

surface S12. S2 is the surface of the gas detonation

product exiting the chamber. The incoming gas is

hydrogen with oxygen, and the fuel and oxidizer

enter the chamber separately and are already mixed

inside the chamber. All external surfaces of the

camera except S11, S12, and S3 are rigid,

impermeable walls. The z-axis is directed along the

axis of symmetry of the camera, and the r-axis is

normal to the z-axis.

The third type is a flat axisymmetric disk

(Figure 1b) with an inner diameter of 100 mm (an

empty hole in the middle) and an outer diameter of

200 mm. The chemical reaction zone is a volume

between two flat rings (S3 surfaces), the distance

between them is 10 mm. The surface S1 is a wall on

which three round inlet openings are located. The

middle slot is the inlet nozzle for the oxidizer

(oxygen), and the other two slots are the inlet

nozzles for fuel (hydrogen). The surface S2 is the

output zone of the chamber (the output of

detonation products into the open space). S3

surfaces are the walls of the chamber. The Z axis is

the axis of symmetry of the body, and the R axis is

at right angles to the Z axis. The combustion of the

mixture takes place inside the chamber. Oxygen is

supplied to the channel from the receiver through a

gap in surface S1. The total area of the nozzle is 61

mm2. Fuel was supplied through the nozzle to the

same surface S1. The total area of the nozzle is 35

mm2. Fuel and oxidizer enter the chamber

separately and are mixed already inside the

chamber.

Fig. 2: Map of isotherms for the gas flow in the

chamber of the first type.

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For all chambers, initially, the internal volume

of the installation is filled with nitrogen at an initial

gas pressure of p0 = 1 atm and a temperature of T0

= 300 K. The initial velocity of the medium has

zero value. The gas in the receivers is at elevated

pressure values of 10–30 atm, temperature T0 = 300

K, and zero velocity. The jets of oxygen and

hydrogen are directed at an angle to each other for

better mixing of the components. At the initial time

t0 = 0, the valves are removed and the gas flows

from the receivers into the chamber. The detonation

was initiated by the concentrated release of energy

in the mixing zone. It is necessary to determine the

values of the gas parameters in the chamber after

ignition at t > 0.

The geometrical parameters of the installations

and the nature of the boundary conditions make it

possible to model the flow within the framework of

the axial symmetry approximation. The flow of a

viscous heat-conducting compressible medium

inside the chambers was described by non-

stationary two-dimensional Reynolds equations for

the laws of conservation of mass, momentum, and

energy, taking into account the effects of

turbulence. Changes in the mass concentration of

components of a chemically reacting gas mixture

were determined using Fick's second law for

diffusion in multicomponent mixtures. The model

of chemical reactions is based on a two-stage

model of chemical kinetics for the average

molecular weight of a gas, including ignition delay.

The problem posed above was solved numerically

using the large particle method. For verification of

the numerical algorithm and to check solution

stability, test simulations were made for various

sizes of numerical cells using the Fluent program.

The comparison of results shows the reliability of

our study. A detailed mathematical formulation of

the problem can be seen in, [5], [6].

The energy supply to the detonation initiation

chamber should be carried out when, as a result of

turbulent mixing, an area with the necessary

parameters of a combustible gas mixture arises, and

heat generation in the zone of chemical

transformations is mainly determined by the rate of

turbulent mixing of reacting gas components.

Figure 2 shows the cross-section of the

chamber of the first type at time t = 1.4∙10-3 s from

the beginning of the mixture supply to the chamber.

The flow moves from above here, and the output of

combustion products occurs to the right. Note that

at this point in time, there has not yet been a

concentrated supply of energy to initiate

detonation. Nevertheless, due to the complex

geometry of the rigid walls of the channel, "hot

spots" are formed in the boundary layers - local

areas where the gas temperature significantly

exceeds the ignition temperature Tig = 1200 K,

while the bulk of the gas in the chamber remains

quite cold. Such spontaneous ignition of the

mixture disrupts the optimal mode of operation of

the camera and creates technological problems.

Fig. 3: Map of the chemical reaction rate

(kgmoll/(m3 s)) at the instant t = 2.510-3 s.

Let the flow in the chamber of the first type

move in the opposite direction (Figure 3). S1 is the

surface of the exit of combustion products, and S2

is the entrance of reagents into the chamber. Here,

S21 is a slit through which a jet of oxygen enters,

and S22 is a jet of hydrogen. S4 is the axis of

symmetry of the chamber. It can be seen from the

figure that a stagnant zone is formed in the upper

left corner of the chamber, where the nitrogen

concentration decreases slowly. Heat generation in

this zone is low, the turbulent flame practically

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stops due to the low concentrations of reacting

components. This mode is also not an optimal

technological mode.

Consider the gas dynamic flow in an annular

chamber of the second type (Figure 4). Here, the

combustion of the mixture occurs in a narrow

annular channel at the outer wall of the chamber,

the channel width is 5 mm. Oxygen was supplied to

the channel from the receiver through surface S11.

Fuel was supplied inside through nozzles on

surface S12. S2 is the surface of the gas detonation

product exiting the chamber. One of the features of

the flow in this chamber is the formation of an area

of increased pressure near the surfaces S11 and S12

when oxygen and hydrogen jets collide. Moreover,

the gas pressure in the area may exceed the

pressure in the receivers, leading to a temporary

blocking of the flow and the cessation of the flow

of reagents into the chamber. As a result, the

detonation is disrupted, and, consequently, the

output is suboptimal. In addition, the zone of

chemical transformations with heat release is

located in the center of the channel. Therefore, the

jets of unreacted oxygen and hydrogen are pressed

against the walls of the channel and move in the

direction of surface S2. At the same time, a

significant part of the unreacted mixture (up to

30%) leaves the chamber through the S2 surface.

This reduces the efficiency of fuel combustion in

such a chamber.

Now let's look at the picture of chemical

transformations in the chamber of the third type

(Figure 5). Reagents are supplied to the chamber

through annular slots on surface S1. Through the

middle slit, a jet of oxygen enters at right angles to

the surface, through the other two slits, there are

hydrogen jets at an angle of 450 to the surface. This

position of the jets allows for a more intensive

mixing process and the formation of a combustible

mixture. It is shown that the zone of chemical

transformations occupies a more significant part of

the camera than the second type of camera.

Moreover, a secondary flame front is located at the

exit surface S2, which ensures that the mixture

burns out inside the chamber. This mode seems to

be the most optimal compared to the previous ones.

Fig. 4: Pressure field (left, there) and water vapor

concentration distribution (right) in the second type

chamber at t = 3.0∙10-3s.

3 Conclusions

In combustion engines, the process of fuel burning

at constant pressure is usually used. An important

technological task is the use of a detonation method

of fuel combustion with the formation of shock

waves, which leads to an increase in the efficiency

of the engine. One of the goals of this paper is to

determine the effective and optimal types of

combustion chambers to develop detonation

processes.

A comparative analysis of geometrically

different types of combustion chambers is carried

out based on the initial stage of the formation of the

detonation process in a gaseous hydrogen-oxygen

mixture. It is shown that the most optimal

detonation combustion mode occurs for the

geometrically simplest type of chamber – a plane

radial disk.

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Present investigations concern the triggering of

detonation processes in combustion cameras. The

next stage of our study will be simulations of stable

self-supported spin detonation in camera for

various types of combustion mixtures (not only the

hydrogen-oxygen case).

Fig. 5: Distribution of water vapor concentration

(left) and chemical reaction rate (kgmoll/(m3 s)) at

the instant t = 2.510-3 s for the third type chamber.

Acknowledgements:

This work was carried out within the framework

and with the financial support of the project

2.3.1.2.4. "Non-classical combustion and

detonation processes as the basis of new

fundamental knowledge and technologies". The

author thanks the organizers and managers of the

project for their support.

References:

[1] Vojciechowski B. W. Stationary detonation,

Dokl. USSR Academy of Sciences. 1959. Vol.

129, No. 6. pp.1254-1256.

[2] Bykovskii F. A., Zhdan S. A. Continuous spin

detonation. Novosibirsk. Publishing house of

SB RAS. 2013.

[3] Frolov, S. M., Dubrovskii A.V., Ivanov V. S.

Three-dimensional numerical simulation of

working process in the chamber with a

continuous detonation // Chemical physics.

2012. Vol. 31, № 3. P. 32 - 45.

[4] Bykovskii F. A., Zhdan S. A., Vedernikov E. F.

Continuous spin detonation of a kerosene-air

mixture in a flowing vortex radial chamber

with a diameter of 500 mm // Combustion,

explosion and shock waves. 2022. Vol. 58, No

1. P. 40-52.

[5] Voronin D. V. On the self-ignition of gas in the

flat vortex camera // Physics of combustion and

explosion. 2017. Vol. 53, No. 5. P. 24-30.

[6] Voronin D. V. On the initiation of detonation in

a ring propulsion chamber // Physics of

combustion and explosion. 2018. Vol. 54, No.

Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

The author contributed in the present research, at

all stages from the formulation of the problem to

the final findings and solution.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

No funding was received for conducting this study.

Conflict of Interest

The author has no conflicts of interest to declare.

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