Stream thrust averaging - Alchetron, the free social encyclopedia

In fluid dynamics, stream thrust averaging is a process used to convert three-dimensional flow through a duct into one-dimensional uniform flow. It makes the assumptions that the flow is mixed adiabatically and without friction. However, due to the mixing process, there is a net increase in the entropy of the system. Although there is an increase in entropy, the stream thrust averaged values are more representative of the flow than a simple average as a simple average would violate the second Law of Thermodynamics.

Equations for a perfect gas

Stream thrust:

F = ∫ ( ρ V ⋅ d A ) V ⋅ f + ∫ p d A ⋅ f .

Mass flow:

m ˙ = ∫ ρ V ⋅ d A .

Stagnation enthalpy:

H = 1 m ˙ ∫ ( ρ V ⋅ d A ) ( h + | V | 2 2 ) , U ¯ 2 ( 1 − R 2 C p ) − U ¯ F m ˙ + H R C p = 0.

Solutions

Solving for U ¯ yields two solutions. They must both be analyzed to determine which is the physical solution. One will usually be a subsonic root and the other a supersonic root. If it is not clear which value of velocity is correct, the second law of thermodynamics may be applied.

ρ ¯ = m ˙ U ¯ A , p ¯ = F A − ρ ¯ U ¯ 2 , h ¯ = p ¯ C p ρ ¯ R .

Second law of thermodynamics:

∇ s = C p ln ⁡ ( T ¯ T 1 ) + R ln ⁡ ( p ¯ p 1 ) .

The values T 1 and p 1 are unknown and may be dropped from the formulation. The value of entropy is not necessary, only that the value is positive.

∇ s = C p ln ⁡ ( T ¯ ) + R ln ⁡ ( p ¯ ) .

One possible unreal solution for the stream thrust averaged velocity yields a negative entropy. Another method of determining the proper solution is to take a simple average of the velocity and determining which value is closer to the stream thrust averaged velocity.

References

Stream thrust averaging Wikipedia

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Contents

Equations for a perfect gas

Solutions

References