I would assume the mass of the combustion products, air and fuel, are present throughout the volume and the flame front propagates without mixing or changing the density of that mixture pre and post combustion. I would also assume the combustion rate is limited by the available surface area as the flame expands in a spherical shape. But those assumptions could be way off.Andrew1235 said:Homework Statement:: Problem description: https://i.stack.imgur.com/7T2OM.png
Relevant Equations:: Mass conservation for a spherical control volume
I am not sure what form of mass conservation to use to solve the above problem from An Introduction to Combustion by Stephen Turns. Can anyone explain what form of mass conservation applies to a sphere in this context?
Mass conservation in a sphere refers to the principle that the total mass of a closed system remains constant over time. This means that any changes in the distribution of matter within the system must be balanced by an equal and opposite change elsewhere in the system.
In the context of finding the radial velocity of a flame, mass conservation is important because it allows us to calculate the radial velocity of the flame based on the mass flow rate of the fuel and air entering the system. This is because the total mass entering the system must be equal to the total mass exiting the system, and this can be used to determine the velocity of the flame.
The radial velocity of a flame in a sphere is affected by several factors, including the mass flow rate of the fuel and air, the temperature and pressure of the system, and the geometry and size of the sphere. These factors can all impact the distribution of mass within the system and therefore affect the velocity of the flame.
The radial velocity of a flame in a sphere can be calculated using the equation v = m_dot / (ρ * A), where v is the velocity, m_dot is the mass flow rate, ρ is the density of the fluid, and A is the cross-sectional area of the sphere. This equation is based on the principle of mass conservation and can be used to determine the velocity of the flame at any point within the sphere.
Understanding mass conservation and radial velocity is important in studying flames because it allows us to accurately predict and control the behavior of flames in various systems. By understanding the principles of mass conservation, we can determine the velocity of a flame and how it will interact with its surroundings, which is crucial in applications such as combustion engines and industrial processes.