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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.

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One Dimensional Flow with Heat Addition


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one dimensional flow with heat addition

One Dimensional Flow with Heat Addition

P M V Subbarao

Professor

Mechanical Engineering Department

I I T Delhi

A Gas Dynamic Model for Combustors…..

one dimensional stead flow
One Dimensional Stead Flow

A+dA,

V+dV r+dr

A,

V

r

dl

conservation of momentum for a real fluid flow
Conservation of Momentum For A Real Fluid Flow

No body forces

One Dimensional Steady flow

A+dA,

V+dV r+dr

A,

V

r

dl

conservation of energy applied to 1 d steady flow
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.

slide11

Using continuity and gas equations:

We get

Momentum equation gives

Substitute gas equation in momentum equation to get:

slide14

Mach number equation:

This shows that dV has same sign as dM.

subsonic flows

is positive

Subsonic Flows

At low velocities, adding heat increases the velocity.

Removing heat decreases the velocity.

supersonic flows

is negative

Supersonic Flows

At high velocities, adding heat decreases the velocity.

Removing heat increases the velocity.

change over a finite length
Change over A Finite Length

2

1

Momentum equation gives

slide27

Integrating from point 1 to point 2:

At low velocities, adding heat increases the velocity.

At low velocities, removal of heat dereases the velocity.

Addition of heat leads to leads the flow to move towards M=1.

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
Variation of Stagnation Temperature with Mach Number

Heat Removal

Heat Removal

T0

Heat Addition

Heat Addition

M