One Dimensional Flow with Heat Addition

1 / 34

One Dimensional Flow with Heat Addition - PowerPoint PPT Presentation

One Dimensional Flow with Heat Addition. P M V Subbarao Professor Mechanical Engineering Department I I T Delhi. A Gas Dynamic Model for Combustors…. Conservation Laws for a Real Fluid. One Dimensional Stead Flow. A+dA, V+dV r+ d r. A, V r. dl.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

One Dimensional Flow with Heat Addition

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

One Dimensional Flow with Heat Addition

P M V Subbarao

Professor

Mechanical Engineering Department

I I T Delhi

A Gas Dynamic Model for Combustors…..

A+dA,

V+dV r+dr

A,

V

r

dl

Conservation of Momentum For A Real Fluid Flow

No body forces

A+dA,

V+dV r+dr

A,

V

r

dl

Conservation of Energy Applied to 1 D Steady Flow

Steady flow with negligible Body Forces

For a real fluid the rate of work transfer is due to viscous stress and pressure.

The effect of viscous dissipation can be modified as flow with some extra heat addition.

Using continuity and gas equations:

We get

Momentum equation gives

Substitute gas equation in momentum equation to get:

Mach number equation:

This shows that dV has same sign as dM.

is positive

Subsonic Flows

At low velocities, adding heat increases the velocity.

Removing heat decreases the velocity.

is negative

Supersonic Flows

At high velocities, adding heat decreases the velocity.

Removing heat increases the velocity.

Change over A Finite Length

2

1

Momentum equation gives

Integrating from point 1 to point 2:

At low velocities, adding heat increases the velocity.

At low velocities, removal of heat dereases the velocity.

Removal of heat leads to leads the flow to move away from M=1.

Therefore T0 will be maximum when M=1.

Variation of Stagnation Temperature with Mach Number

Heat Removal

Heat Removal

T0