The adiabatic transformation The adiabatic expansion of the vapor in the Mollier density of air tab

The adiabatic transformation The adiabatic expansion of the vapor in the Mollier density of air table diagram The isobaric transformation The vapor pressure of water The isothermal transformation The transformation isochoric The density of water The engine Manson free piston double-acting engine Manson free piston - Episode 07 Density of water vapor side considerations
The first post dedicated to the world of the motors to the liquid-vapor phase transition was that relating to the vapor pressure of water. The graph shown PT at this juncture can be used to determine if the water vapor is in its saturated state: the steam is saturated when its temperature and its pressure are those of a point on the curve of the vapor pressure as a function temperature. For convenience, below is the graph mentioned.
As already seen, the adiabatic expansion of an ideal gas causes a lowering of its pressure and its temperature. The saturated steam has a similar behavior as pressure and temperature decrease in the expansion adiabatic, but presents a fundamental difference: the process of adiabatic expansion of the saturated steam is accompanied by a partial condensation of the vapor. This phenomenon gives off heat and makes sure that the pressure and the temperature decrease less rapidly than a similar expansion of a gas. In this post is presented a numerical approach / experimental which allows to determine the trend of the pressure and of the condensed density of air table fraction as a function of the degree density of air table of expansion of the steam. INITIAL STATE The state of departure from which begins the expansion is known and is constituted by a certain amount of saturated steam at a defined pressure and temperature (P T initial and initial). The following equations are valid for the more general case in which there are both phases (liquid and vapor) and are then reported to the specific case in which the condensed fraction is absent in the initial state. m = m + m initial liquid saturated vapor saturated vapor initial initial m = (1 - Fraction condensed initial) * m = (1 - FC) * mm = initial liquid fraction condensed initial * m * m H = FC saturated steam @ initial P (T initial) = H vap sat in PRINTOUT = ρ saturated steamP initial (initial T) = ρ vap sat in PRINTOUT = HP initial liquid (initial T) = H liq in PRINTOUT = ρ fluidP Home (initial T) = ρ liq = PRINTOUT density of air table then in the enthalpy density of air table and internal energy of the initial state appear to be H = H * m vap sat in saturated steam at initial liq + H * m initial liquid = = H vap sat in * m * (1 - FC) + H in liq * m * FC U = H + P * V = = H + P * (m saturated vapor Home / ρ + m vap sat in liquid initial / ρ liq in) = = H + P * [(1 - FC) * m / ρ sat in vap + FC * m / ρ liq in] In the case where the initial state is constituted only by steam the condensed density of air table fraction density of air table is zero and the general equations given just met are simplified in H = H vap sat in * m U = H + P * V = H + P * m / ρ vap sat in STATE FINAL To effect the process of adiabatic expansion a part of the steam condenses. The liquid form is in addition to the possible condensed fraction already present in the initial state. The final state can then be represented as follows. m = m + m initial liquid saturated vapor saturated vapor final final m = (1 - Fraction condensed final) * m = (1 - FC fin) * mm = final liquid fraction condensed final * m * m H = FC since saturated steam @ P end (T end) = H vap sat right PRINTOUT = ρ saturated steamP final (final T) = ρ vap sat right PRINTOUT = HP liquid end (T end) = H liq since PRINTOUT = ρ fluidP final (final T) = ρ liq = PRINTOUT since then the enthalpy and internal energy of the final state since become H = H vap sat right * m * (1 - FC fin) + H * m * FC liquidation density of air table since since since U = H + P from the right fin = V * = H + P from the right * (m vap sat right / ρ vap sat far from the liq + m / ρ liq fin) = = H + P from the right * [(1 - FC final ) * m / ρ vap sat far from the FC + * m / ρ liq fin] Since in an adiabatic expansion, the relation L = -ΔU = - (since U - U) = U - U since knowing the value of work becomes possible to determine the amount of the condensed density of air table fraction. From the mathematical point of view it is convenient to adopt the linear approximation density of air table consists density of air table of assuming that the transformation curve on the plane PV equal to a line segment joining the initial state to the final one. In this case, the work volume is the area of a right-angled trapezium in which the height is given by the volume change, the larger base from the initial pressure and the minor base of the final pressure L = (P + P fin) * (since V - V) / 2 = = (P + P fin) * [(m vap sat right / ρ vap sat far from the liq + m / ρ liq fin) - (m vap sat in / ρ vap sat in + m liq