Energy Equation for Compressible Viscous Flows

There are six types of energy important in our analysis (we exclude, chemical, elec­tromagnetic and nuclear energies):

Mechanical energy

Thermodynamic energy

Kinetic energy

Internal energy

Potential energy

Heat

—- Work done by pressure ^

—- Work done by friction ^

For inviscid flow, the Euler equations have the following energy balance:

Подпись:dpuH dpv H

dx + dy

where H = h + 2 (u2 + v2) + potential energy, and h = e + p. Here we have ignored heat and viscous dissipation.

Подпись: dpuH dpv H dx + dy Energy Equation for Compressible Viscous Flows Подпись: (8.55)

For the Navier-Stokes equations, the energy equation is

Подпись: (V .V.T ) Energy Equation for Compressible Viscous Flows Подпись: (8.56)

where k is the heat conductivity coefficient, and the viscous dissipation term is given by:

corresponding to the rate of work done by viscous forces.

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