fluid dynamics In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion ...

, 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 Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. Types of friction include dry, fluid, lubricated, skin, and internal -- an incomplete list. The study of t ...

. However, due to the mixing process, there is a net increase in the entropy of the system. Although there is an increase in

entropy Entropy is a scientific concept, most commonly associated with states of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the micros ...

, 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 The second law of thermodynamics is a physical law based on Universal (metaphysics), universal empirical observation concerning heat and Energy transformation, energy interconversions. A simple statement of the law is that heat always flows spont ...

Equations for a perfect gas

Stream

thrust Thrust is a reaction force described quantitatively by Newton's third law. When a system expels or accelerates mass in one direction, the accelerated mass will cause a force of equal magnitude but opposite direction to be applied to that ...

: :

F = \int \left(\rho \mathbf \cdot d \mathbf \right) \mathbf \cdot \mathbf +\int pd \mathbf \cdot \mathbf.

Mass flow: :

\dot m = \int \rho \mathbf \cdot d \mathbf.

Stagnation

enthalpy Enthalpy () is the sum of a thermodynamic system's internal energy and the product of its pressure and volume. It is a state function in thermodynamics used in many measurements in chemical, biological, and physical systems at a constant extern ...

: :

H =  \int \left( \right) \left( h+  \right),

\overline^2 \left(\right) -\overline +=0.

Solutions

Solving for

\overline

yields two solutions. They must both be analyzed to determine which is the physical solution. One will usually be a subsonic

root In vascular plants, the roots are the plant organ, organs of a plant that are modified to provide anchorage for the plant and take in water and nutrients into the plant body, which allows plants to grow taller and faster. They are most often bel ...

and the other a supersonic root. If it is not clear which value of

velocity Velocity is a measurement of speed in a certain direction of motion. It is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of physical objects. Velocity is a vector (geometry), vector Physical q ...

is correct, the

may be applied. :

\overline = ,

\overline =  -,

\overline = .

Second law of thermodynamics: :

\nabla s = C_p \ln() +R \ln().

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. :

\nabla s = C_p \ln(\overline) +R \ln(\overline).

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

* {{cite web , url=https://ntrs.nasa.gov/api/citations/19990062664/downloads/19990062664.pdf , title=Inlet Development for a Rocket Based Combined Cycle, Single Stage to Orbit Vehicle Using Computational Fluid Dynamics , first1=J.R. , last1=DeBonis , first2=C.J. , last2=Trefny , first3=C.J. , last3=Steffen, Jr. , publisher=NASA , year=1999 , work=NASA/TM—1999-209279 , accessdate=18 February 2013 Equations of fluid dynamics Fluid dynamics