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Governing Equations

Posted by admin in Theoretical and Applied Aerodynamics on February 5, 2016

Assuming 2-D, steady, inviscid and irrotational compressible flow with uniform con­ditions at infinity, the governing equations of conservation of mass, the irrotationality condition and energy equation (generalized Bernoulli) read in terms of the perturba­tion velocity components (u, w) © Springer Science+Business Media Dordrecht 2015

J. J. Chattot and M. M. Hafez, Theoretical and Applied Aerodynamics,

DOI 10.1007/978-94-017-9825-9_4

Fig. 4.1 Holographic interferometry of transonic flow fields, (from history. nasa. gov)

 

dp(U + u) | dpw 0 dx + dz

(4.1)

dw du dx dz ^

(4.2)

Y p V 2

+ = H0 = const. (Y – 1)P 2 0

(4.3)

where y = cr is the ratio of specific heats, ~V = (U + u, w) the total velocity and

cv

Ho is the uniform stagnation enthalpy for isoenergetic flow. The entropy for such flows is uniform and can be written

p p o

= Y = const.

p1 pY

(4.4)

For air, the gas index is y = 1.4. The subscript “0”

stands for undisturbed,

incoming flow quantities.

Elimination of pressure between the energy equation and the entropy condition yields a density-velocity relation

 

P_

P0

 

(4.5)

 

where the incoming Mach number and speed of sound are M0 respectively.

 

a0and a0

 

Governing EquationsGoverning EquationsGoverning Equations



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