Stagnation and Sonic Properties

Stagnation and Sonic Properties

The stagnation properties at a point are defined as those which are to be obtained if the local flow were imagined to cease to zero velocity isentropically. As we will see in the later part of the text, stagnation values are useful reference conditions in a compressible flow.

Let us denote stagnation properties by subscript zero. Suppose the properties of a flow (such as T, p , ρ etc.) are known at a point, the stangation enthalpy is, thus, defined as

where h is flow enthalpy and V is flow velocity.

For a perfect gas , this yields,

(40.1)

which defines the Stagnation Temperatur

Now, can be expressed as

Since,

(40.2)

If we know the local temperature (T) and Mach number (Ma) , we can find out the stagnation temperature T₀ .

Consequently, isentropic(adiabatic) relations can be used to obtain stagnation pressure and stagnation density as

	(40.3)
	(40.4)

Values of and as a function of Mach number can be generated using the above relationships and the tabulated results are known as Isentropic Table . Interested readers are suggested to refer the following books

1. J.Spruk, Fluid Mechanics, Springer, Heidelberg , NewYork, 1997
2. K.Muradidhar and G.Biswas, Advanced Engineering Fluid Mechanics, Second Edition, Narosa, 2005

Note that in general the stagnation properties can vary throughout the flow field.

Let us consider some special cases :-

Case 1: Adiabatic Flow:

(from eqn 39.10) is constant throughout the flow. It follows that the are constant throughout an adiabatic flow, even in the presence of friction.

Hence, all stagnation properties are constant along an isentropic flow. If such a flow starts from a large reservoir where the fluid is practically at rest, then the properties in the reservoir are equal to the stagnation properties everywhere in the flow Fig (40.1)

Fig 40.1: An isentropic process starting from a reservoir

Case 2: Sonic Flow (Ma=1)

The sonic or critical properties are denoted by asterisks: p*, ρ*, a*, and T* . These properties are attained if the local fluid is imagined to expand or compress isentropically until it reaches Ma = 1.

Important-

The total enthalpy, hence T₀ , is conserved as long as the process is adiabatic, irrespective of frictional effects.

From Eq. (40.1), we note that

(40.5a)

This gives the relationship between the fluid velocity V, and local temperature (T), in an adiabatic flow.

Putting T=0 we obtain maximum attainable velocity as,