Download document 39183

Isentropic flow Wikepedia In thermodynamics, an isentropic process or isoentropic process (ισον = "equal" (Greek); εντροπία entropy = "disorder"(Greek)) is one in which for purposes of engineering analysis and calculation, one may assume that the process takes place from initiation to completion without an increase or decrease in the entropy of the system, i.e., the entropy of the system remains constant.[1][2] It can be proven that any reversible adiabatic process is an isentropic process. A simple more common definition of isentropic would be " No change in entropy". An isentropic flow is a flow that is both adiabatic and reversible. That is, no heat is
added to the flow, and no energy transformations occur due to friction or dissipative
effects. For an isentropic flow of a perfect gas, several relations can be derived to define
the pressure, density and temperature along a streamline.
Note that energy can be exchanged with the flow in an isentropic transformation, as long
as it doesn't happen as heat exchange. An example of such an exchange would be an
isentropic expansion or compression that entails work done on or by the flow.
The Free Dictionary by Farlex (encyclopedia2.thefreedictionary.com) Compressible flow in which entropy remains constant throughout the flowfield. A slight distinction is sometimes made, especially in Europe, as follows. If the entropy of a fluid element moving along a streamline in a flow remains constant, the flow is isentropic along a streamline. However, the value of the entropy may be different along different streamlines, thus allowing entropy changes normal to the streamlines. An example is the flowfield behind a curved shock wave; here, streamlines that pass through different locations along the curved shock wave experience different increases in entropy. Hence, downstream from this shock, the entropy can be constant along a given streamline but differs from one streamline to another. This type of flow, with entropy constant along streamlines, is sometimes defined as isentropic. Flow with entropy constant everywhere is then called homentropic. See Compressible flow, Entropy, Isentropic process Because of the second law of thermodynamics, an isentropic flow does not strictly exist. From the definition of entropy, an isentropic flow is both adiabatic and reversible. However, all real flows experience to some extent the irreversible phenomena of friction, thermal conduction, and diffusion. Any nonequilibrium, chemically reacting flow is also irreversible. However, there are a large number of gas dynamic problems with entropy increase negligibly slight, which for the purpose of analysis are assumed to be isentropic. Examples are flow through subsonic and supersonic nozzles, as in wind tunnels and rocket engines; and shock-­‐free flow over a wing, fuselage, or other aerodynamic shape. For these flows, except for the thin boundary-­‐layer region adjacent to the surface where friction and thermal conduction effects can be strong, the outer inviscid flow can be considered isentropic. If shock waves exist in the flow, the entropy increase across these shocks destroys the assumption of isentropic flow, although the flow along streamlines between shocks may be isentropic. See Adiabatic process, Boundary-­‐layer flow, Shock wave, Thermodynamic principles, Thermodynamic processes 1st law of thermodynamics (Wikepedia) The first law of thermodynamics is a version of the law of conservation of energy,
specialized for thermodynamical systems. It is usually formulated by stating that the
change in the internal energy of a closed system is equal to the amount of heat supplied to
the system, minus the amount of work done by the system on its surroundings. The law of
conservation of energy can be stated: The energy of an isolated system is constant.
The first explicit statement of the first law of thermodynamics, by Rudolf Clausius in
1850, referred to cyclic thermodynamic processes.
"In all cases in which work is produced by the agency of heat, a quantity of heat is consumed which is proportional to the work done; and conversely, by the expenditure of an equal quantity of work an equal quantity of heat is produced."[1] Clausius stated the law also in another form, this time referring to the existence of a
function of state of the system called the internal energy, and expressing himself in terms
of a differential equation for the increments of a thermodynamic process. This equation
may be translated into words as follows:
In a thermodynamic process of a closed system, the increment in the internal energy is equal to the difference between the increment of heat accumulated by the system and the increment of work done by it.[2] 2nd law of thermodynamics (Wikepedia) The second law of thermodynamics states that the entropy of an isolated system never
decreases, because isolated systems spontaneously evolve towards thermodynamic
equilibrium—the state of maximum entropy. Equivalently, perpetual motion machines of
the second kind are impossible.
The second law is a postulate of thermodynamics, but it can be understood and proven
using the underlying quantum statistical mechanics. It is an expression of the fact that
over time, differences in temperature, pressure, and chemical potential decrease in an
isolated physical system, leading eventually to a state of thermodynamic equilibrium. In
the language of statistical mechanics, entropy is a measure of the number of microscopic
configurations corresponding to a macroscopic state. Because equilibrium corresponds to
a vastly greater number of microscopic configurations than any non-equilibrium state, it
has the maximum entropy, and the second law follows because random chance alone
almost guarantees that the system will evolve towards equilibrium.
Entropy (Wikepedia)
Entropy was originally defined by Rudolf Clausius in 1865 as an extensive thermodynamic function of state that is the measure of a system’s thermal energy per unit temperature that is unavailable for doing mechanical work. Unlike most other functions of state, entropy cannot be directly measured but must be calculated. The need for an entropy function emerges from the fundamental thermodynamic relation. Entropy has the dimension of energy divided by temperature, which has a unit of joules per kelvin (J/K) in the International System of Units. The term entropy was Clausius based on the Greek εντροπία [entropía], a turning toward, from εν-­‐ [en-­‐] (in) and τροπή [tropē] (turn, conversion).[2][note 2] The infinitesimal change in the entropy (dS) of a system is the infinitesimal transfer of heat energy (δQ) to a closed system driving a reversible process, divided by the equilibrium temperature (T) of the system. Enthalpy (Wikepedia) Enthalpy is a measure of the total energy of a thermodynamic system. It includes the
internal energy, which is the energy required to create a system, and the amount of
energy required to make room for it by displacing its environment and establishing its
volume and pressure.
Enthalpy is a thermodynamic potential. It is a state function and an extensive quantity.
The unit of measurement for enthalpy in the International System of Units (SI) is the
joule, but other historical, conventional units are still in use, such as the British thermal
unit and the calorie.
The enthalpy is the preferred expression of system energy changes in many chemical,
biological, and physical measurements, because it simplifies certain descriptions of
energy transfer. This is because a change in enthalpy takes account of energy transferred
to the environment through the expansion of the system under study.
The total enthalpy, H, of a system cannot be measured directly. Thus, change in enthalpy,
ΔH, is a more useful quantity than its absolute value. The change ΔH is positive in
endothermic reactions, and negative in heat-releasing exothermic processes. ΔH of a
system is equal to the sum of non-mechanical work done on it and the heat supplied to it.
For processes under constant pressure, ΔH is equal to the change in the internal energy of
the system, plus the work that the system has done on its surroundings.[1] This means that
the change in enthalpy under such conditions is the heat absorbed (or released) by a
chemical reaction. Enthalpies for chemical substances at constant pressure assume
standard state: most commonly 1 bar pressure. Standard state does not, strictly speaking,
specify a temperature (see standard state), but expressions for enthalpy generally
reference the standard heat of formation at 25 °C.
The word enthalpy is based on the Greek word enthalpos (ἔνθαλπος), which means to put
heat into. It comes from the Classical Greek prefix ἐν-, en-, meaning to put into, and the
verb θάλπειν, thalpein, meaning "to heat". The word enthalpy is often incorrectly
attributed[citation needed] to Benoit Paul Émile Clapeyron and Rudolf Clausius through the
1850 publication of their Clausius-Clapeyron relation. This misconception was
popularized by the 1927 publication of The Mollier Steam Tables and Diagrams.
However, neither the concept, the word, nor the symbol for enthalpy existed until well
after Clapeyron's death.
The earliest writings to contain the concept of enthalpy did not appear until 1875,[2] when
Josiah Willard Gibbs introduced "a heat function for constant pressure". However, Gibbs
did not use the word "enthalpy" in his writings.[note 1] Instead, the word "enthalpy" first
appears in the scientific literature in a 1909 publication by J. P. Dalton. According to that
publication, Heike Kamerlingh Onnes (1853-1926) actually coined the word.[3]
Over the years, many different symbols were used to denote enthalpy. It was not until
1922 that Alfred W. Porter proposed the symbol "H" as the accepted standard,[4] thus
finalizing the terminology still in use today.
Streamline
Fluid flow is characterized by a velocity vector field in three-dimensional space, within
the framework of continuum mechanics. Streamlines, streaklines and pathlines are
field lines resulting from this vector field description of the flow. They differ only when
the flow changes with time: that is, when the flow is not steady.[1] [2]
•
Streamlines are a family of curves that are instantaneously tangent to the velocity vector of the flow. These show the direction a fluid element will travel in at any point in time. By definition, different streamlines at the same instant in a flow do not intersect, because
a fluid particle cannot have two different velocities at the same point. Similarly,
streaklines cannot intersect themselves or other streaklines, because two particles cannot
be present at the same location at the same instant of time; unless the origin point of one
of the streaklines also belongs to the streakline of the other origin point. However,
pathlines are allowed to intersect themselves or other pathlines (except the starting and
end points of the different pathlines, which need to be distinct).
Streamlines and timelines provide a snapshot of some flowfield characteristics, whereas
streaklines and pathlines depend on the full time-history of the flow. However, often
sequences of timelines (and streaklines) at different instants—being presented either in a
single image or with a video stream—may be used to provide insight in the flow and its
history.
If a line, curve or closed curve is used as start point for a continuous set of streamlines,
the result is a stream surface. In the case of a closed curve in a steady flow, fluid that is
inside a stream surface must remain forever within that same stream surface, because the
streamlines are tangent to the flow velocity. A scalar function whose contour lines define
the streamlines is known as the stream function.