fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) an ...

, 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. There are several types of friction: *Dry friction is a force that opposes the relative lateral motion 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, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...

, 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 experience concerning heat and Energy transformation, energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects ( ...

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 syst ...

: :

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

Mass flow Mass flow, also known as mass transfer and bulk flow, is the movement of fluids down a pressure or temperature gradient,Moyes & Schulte (2008). Principles of Animal Physiology. Pearson Benjamin Cummings. San Francisco, California particularly in ...

: :

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

Stagnation

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

: :

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 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 below the sur ...

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

velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...

is correct, the

second law of thermodynamics The second law of thermodynamics is a physical law based on universal experience concerning heat and Energy transformation, energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects ( ...

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