Isentropic Changes Research Articles

Preliminary evaluation of interferometry measurements of the flow field in the vicinity of a self-excited single profile

This paper deals with the interferometry measurement of the flow field in the vicinity of the surface of the self-excited single profile NACA 0015 in subsonic air flow. The pressure and velocity on the profile surface, the total forces and total moments acting on the profile are evaluated in the range of the Mach number Ma = 0.18-0.45 and the Reynolds number Re = (3-6)·105 . Since the interferogram processing was conducted with simplified assumptions of the isentropic changes of the flow field, the results have a limited accuracy especially in the case with flow separation. Results were not compared with the direct pressure measurement on the profile surface. The optical measurement method enabled the forces and moments to be evaluated separately for the suction and pressure surface of the airfoil.

Reversible adiabatic and isentropic changes in quantum systems

In traditional thermodynamics it is assumed that isentropic, reversible, adiabatic processes can be summoned up on demand and straightforwardly accomplished. By contrast, taking entropy as the maximised uncertainty of a final equilibrium state of a quantised system, it is not obvious that an associated process can always be found that is both rigorously isentropic and reversibly adiabatic. In fact, we find that linear relations between generalized forces Xj (such as pressures Pj) and energies Ej are necessary and sufficient conditions for a reversible quasi-static and adiabatic change to be truly isentropic. However, such relationships only hold for a few especially simple systems, such as the perfect gas and the idealised paramagnet. They do not generally hold to all orders for more complicated systems. By considering the associated entropy increases up to second order in small changes of the conjugate displacements (such as the volume Vj) we argue that the consequences are nevertheless in practice negligible.

海底パイプラインを模擬した水中ラプチャーディスク試験及びガス減圧の数値モデル開発

In this research, atmospheric and underwater small-scale pipe rupture disk tests were conducted. Tested pipes with rupture disk were pressurized by pure nitrogen, in which internal pressure changes and external pressure changes were measured by pressure transducers. By comparing results of the underwater tests with results of the atmospheric tests, water effects were clarified: (1) gas decompression in the underwater tests delays due to constrained gas leak by bubble generation and growth as compared to gas decompression in the atmospheric tests, and (2) larger external pressure changes were measured in the underwater tests. In addition, 1D finite-difference based coupled model for gas decompression, in which gas flow inside a pipe and bubble growth are considered, was developed. In the model, governing equations for gas flow inside a pipe and a bubble are derived from mass conservation law and momentum conservation law assuming isentropic changes of gas. Bubble growth is formulated based on Rayleigh-Plesset equation. The calculated results for the rupture disk tests using the model showed good agreements with the experimental results, which analytically clarified the above stated water effects. This research reveals an importance of considering the water effects in evaluating fractures in offshore pipelines. In the future, it is expected that the model is extended to incorporate crack propagation and pipe deformation together with gas decompression and bubble growth.

Analytical calculation and evolutionary regression method for isentropic exponent of hydrogen gas at the throat of critical nozzle

As one of the most promising renewable energy resources, the hydrogen has been used in the fields such as aerospace, industry, and fuel cells. Critical nozzles are widely used for mass flow-rate measurement of high hydrogen gas, since the flow measurement process is not affected by its downstream flow disturbance. The flow rule of real hydrogen gas through a critical nozzle is complicated and the thermophysical property of hydrogen at the nozzle throat is vital to the accurate measurement of hydrogen flow. In this paper, based on explicit Helmholtz energy and entropy-enthalpy equations, the basic flow parameter and isentropic volume change exponent are analytically calculated. In addition, an accurate explicit equation is determined by the nonlinear regression analysis where the ways of selection, exchange and mutation derived from evolutionary algorithm are introduced to search for optimal population individual. The regression standard deviation is 0.0089%, mean residual deviation is 0.0285%, and maximum residual deviation is 0.1781%. The result shows that it not only can rapidly find the optimal solution which has the lowest number of equation items and the great overfitting suppression capability, but also has a high computation accuracy. This algorithm can also be applied to modeling flow characteristic parameters for every other flow device.

Ozone friendly binary blends R 32/R 134a and the ternary R 407b

The objective of this paper is to present thermodynamic properties and characteristics of the binary refrigerant mixtures R 32/R 134a in compositions 20/80%, 30/70%, 40/60% by mass and of the ternary mixture R 407b: 10 wt% R 32+70 wt% R 125+20 wt% R 134a. A computer code has been developed and by use of a Peng–Robinson type equation of state, PVT data for all working fluids are determined. Based on the thermodynamics theory, analytical relationships for the enthalpy, entropy, constant pressure and constant volume specific heats as well as for k-type isentropic change exponents are given. Furthermore, comparisons are provided by means of diagrams illustrating the influence of state conditions on the k-type exponents k p , V , k T , V , k p , T , and classical k ( k= c P/ c V). A systematic study has also been carried out and the data obtained are plotted for a better physical feeling related to the sound velocity of real gas for the R 32/R 134a blend in composition 20/80%. The results are compared with corresponding ones of the ternary R 407b.

Thermodynamic Correlations, k – Exponents, Speed of Sound, and COP Data for Binary Refrigerant Mixtures

Our study covers thermodynamic performance quantities for binary refrigerant mixtures of R-32/R-134a with compositions of 20/80%, 30/70%, 40/60% by mass for a wide range of thermodynamic conditions (pressure: 0.2 - 3.0 MPa, temperature: 240 - 480 oK and saturated conditions). The primary thrust of the study is the calculation of coefficient of performance (COP) values for refrigeration systems. Additional attention is also given to speed of sound data and to isentropic process changes. The relevant COPs are derived based on a simplified reference refrigeration cycle with one stage compression and throttling, saturated vapor and no liquid sub-cooling prior to the throttling valve. The COP values are given for various condensing and evaporating temperatures. For all calculations, a Peng – Robinson type equation of state is used to determine the necessary fluid properties. The enthalpy, entropy, and constant-pressure and constant-volume specific heats as well as the k-type isentropic change exponents are presented for all mixtures for the range of thermodynamics conditions listed above. Comparisons are made illustrating the influence of pressure and temperature on the k-type exponents kp,v, kT,v, and kp,T, and on the ratio of specific heats k (k = cp/cv). Furthermore, graphs with speed of sound data for this extended range of conditions are also given.

Binary and ternary blends of R-134a as alternative refrigerants to R-22

Refrigerant mixtures may be used to solve the ozone layer depletion problem as they offer the optimum combination of favorable technical performance with environmentally acceptable behavior. This work reports the thermodynamic properties and characteristics of the binary mixtures R-32/R-134a in compositions 20–80%, 30–70%, 40–60% by mass and of the ternary mixture R-407c: 23 wt% R-32 + 25 wt% R-125 + 52 wt% R-134a. A computer code has been developed for the phase equilibrium relationship of the binary mixtures using related activity and fugacity coefficients. Our results are in good agreement with existing experimental data. For the ternary blend, we present enthalpy and entropy correlations, diagrams illustrating the real gas behavior by means of k-type isentropic change exponents ( k= c p / c V , k p, V , k T, V , k p, T ) and figures for the refrigerating systems efficiency expressed by coefficient of performance values.

Thermodynamic property formulations and heat transfer aspects for replacement refrigerants: R-123 and R-134a

This paper reports analytical relations for the thermodynamic properties enthalpy, entropy, heat capacities at constant pressure and temperature of the replacement refrigerants R-123 and R-134a. These refrigerants are considered promising as substitutes for the fluids R-11 and R-12, respectively, which are two of the most widely used CFC refrigerants. In addition to the properties, the three real gas isentropic exponents kp,v,kv,T, kp,T are calculated, which may be used instead of the classical exponent k=cp/cv in the ideal gas isentropic change equations to describe with good accuracy the real gas behaviour. A systematic study to research the influence of various parameters on heat transfer during condensation of R-123 and R-134a on horizontal integral-fin tubes is also carried out. The results are useful in refrigeration applications to improve the basic design, as a significant concern about new refrigerants to replace the CFCs has increased very rapidly due to the destruction of stratospheric ozone and global warming. © 1997 John Wiley & Sons, Ltd.

Isentropic Efficiency and Entropy Change in a Rankine Cycle

Isentropic Efficiency and Entropy Change in a Rankine Cycle

Blowdown of carbon dioxide from initially supercritical conditions

The paper presents experimental investigations of the thermohydraulic phenomena of top vented blowdown processes of initially supercritical carbon dioxide. The initial fluid conditions were chosen such that flashing occurred after saturation conditions were reached. The investigations were focused on pressure and temperature transients. It was observed that the pressure at which flashing occurred first depends mainly on the initial fluid conditions due to the almost isentropic change of state during the supercritical/subcooled blowdown. Furthermore, void fraction profiles along the axis of the vessel were measured by means of a gamma densitometer. The void fraction profile is influenced strongly by phase separation effects. Various stages of characteristic void profile were observed.

Quantitative Analysis of Axisymmetric Nozzle Flow Field with Shock Wave by Image Processing of Mach-Zehnder Interferogram.

This paper describes a method by which axisymmetric nozzle flow can be analyzed quantitatively from Mach-Zehnder interferograms. The method applies image processing to obtain fringe shifts from the interferograms rapidly. Using a Laplace transform, the density distributions are calculated from the fringe shifts. In order to calculate the density in the shock wave region, a step function is used to describe the fringe shifts. Pressure can be calculated from the density assuming an isentropic change. The results are compared with those from measurement and numerical simulations, and good agreement is found.

A correlation of the isentropic exponents of real gases

In previous publications, three isentropic exponents, k pv , k Tv , k pT , have been introduced, which when used in place of the classical isentropic exponent k = c p c v in the ideal gas isentropic change equations, the latter can describe very accurately the isentropic change of real gases. The present work provides a general method for determining the values of k pv , k Tv , k pT within the ranges of reduced pressure p r = 0 to 10 and of reduced temperature T r = 1 to 3.5, thus allowing the calculation of the isentropic flow of those real gases for which no detailed thermodynamic data are available. The accuracy obtained is limited only by the accuracy of the generalized Lee-Kesler equation of state, which is employed in the method developed.

An Exact Solution of the Riemann Problem for Solids with the Grüneisen Equation of State

An exact and analytical solution of the Riemann problem for solids has been obtained. It is assumed that the square of the acoustic impedance along an isentropic change of state can be expressed as the quadratic function of pressure. A Gruneisen-type equation of state calculated from this assumption has been used and the solution of the Riemann problem obtained after a rather simple calculation. The solution can also be extended to the case of powders, and a numerical example is presented for solid and porous aluminum.

カプセル走行特性に関する種々の計算法と解析結果との関係

Theoretical analyses on the capsule running were carried out by the method of characteristics under the three different conditions; polytropic, irreversible adiabatic (based on the energy equation) and isentropic changes. The results of comparing the characteristics obtained by each method are summarized as follows;(1) Analytical results based on the polytropic change (n=1.01, 1.20) and irreversible adiabatic change agree well with each other. Therefore, the former analysis is more useful because of the more simplicity.(2) The results obtained under the polytropic change with n=1.40 have a little difference from the others for the pressure change in the pipe.(3) For the same convergence condition, the iterative calculation is necessary for the analysis based on the irreversible adiabatic change, but not necessary in other analyses.(4) Calculated results based on the isentropic change don't agree with the results obtained by the other methods or experimental results.

The three isentropic exponents of wet steam

Real gas isentropic changes may be described using the three well known ideal gas relations,pv k =const, p(1−k)Tk=const andTv k-1=const, where exponent k has for each equation a different value kp, ν, kp, T and kT, ν respectively. In this paper the three isentropic exponents theory for real gases is extended to the two phase region. As an application the numerical values of the three exponents are calculated for wet steam.

Sound velocity and isentropic exponents for gases with different acentric factors by using the Redlich-Kwong-Soave equation of state

In previous publications, three real gas isentropic exponentsk pv ,k Tv ,k pT have been introduced, which when used instead of the classical isentropic exponentk=c p /c v in the ideal gas isentropic change equations, the latter may be applied with great accuracy to real gases. The first of the exponents may also be employed for calculating the real gas sound velocity as α=(k pv pv)1/2. The exact values of the sound velocity α and of the three isentropic exponentsk pv ,k Tv ,k pT of a real gas may be calculated only if the exact thermal and caloric equations of state of this real gas are available. For most real gases, however, such equations are not available. In the present work, correlations are presented for calculating quantities α,k pv ,k Tv ,k pT for all real gases, in terms of the acentric factor which characterises their deviation from the ideal gas. The correlations, which are based on the Redlich-Kwong-Soave generalized equation of state, provide the above quantities in a generalized reduced form in terms of the reduced temperature, of the reduced volume and of the compressibility factor, i.e. independently of any gas properties except for the acentric factor. Therefore, it becomes possible to plot the generalized sound velocity and isentropic exponents on the generalized compressibility chart (Nelson-Obert diagram) for various values of the acentric factor. Comparisons with exact values in the case of real air, calculated by use of exact thermal and caloric equations, show that the accuracy of the correlations developed is satisfactory.

Isentropic exponents of real gases and application for the air at temperatures from 150 K to 450 K

Three real gas isentropic exponentskTv,krv,kpT are introduced, which when used in place of the classical isentropic exponentk=cp/c in the ideal gas isentropic change equations, the latter may describe very accurately the isentropic change of real gases. The usual practice of employing exponentk may lead to considerably incorrect results even when the value ofk corresponds to the correct local value ofcp/cv of the real gas under examination. The numerical values of the new exponents are calculated in the case of real air for temperatures from 150 K to 450 K and pressures from 1 bar to 1000 bar. It is seen that at low temperatures and high pressures the values of the new exponents differ considerably from the values of the classical exponentk. Therefore, the error resulting by approximating, as is usually the case, the behaviour of real gases by the ideal gas isentropic change equations in a stepwise fashion with exponentk instead of the new exponents, is considerable. It follows that exponentk, which appears in various relations in thermodynamics, fluid mechanics, gasdynamics, heat transfer etc., should be suitably replaced by combinations of the three exponents. Related numerical examples, made in the case of real air, showed that the use ofk leads (in the temperature and pressure ranges examined) to a 5% error in the calculation of blowby rate in internal combustion enginers, high pressure compressors or steam turbines and to a 50% error in the calculation of the isentropic expansion or compression.

On the three exponents of the isentropic change of the refrigerant R22

The differential isentropic change of real gases is usually calculated by using the corresponding equation of ideal gases, with the isentropic exponent taken as the ratio of the specific heats at constant pressure and constant volume. A closer examination shows that there exist three isentropic exponents, having different values, corresponding to the three possible pairs of variables selected among temperature, pressure and volume. The numerical values of these exponents were calculated for the refrigerant R22. It was found that calculations performed with the conventional isentropic exponent can show significant deviations from the real values.

Ideal gas relations for the description of the real gas isentropic changes

Using the best available relations describing the thermal and caloric behaviour of the media H2O, air, NH3 and of the refrigerants R12 and R22, numerous isentropic expansions starting at different initial points, have been computed. The results obtained were approximated by explicit relations having mathematical forms similar to those of the ideal gas but with different constants and exponents. The obtained accuracy is remarkable, being for the most cases better than 0.5% and in any case better than 3%. In this way the isentropic change, of the above mentioned media, can be computed by simple explicit relations having as independent variable the Mach number. Considering all the above media, the following general rules can be traced. The specific volume, reduced by the corresponding value of the stagnation point, up to a Mach number of less than 0.7, follows a parabolic law common to all gases considered. The reduced pressure, in the transonic region 0.7≦M≦1.3, has a nearly linear decrease, having a slope, common to all media, and equal to about −0.605. The reduced nozzle cross-sectional area, for M≦1,2 has a common form given by the relation F*/F=−0.034+M(2.04−M). The values of the constants and exponents used in the relations cannot be derived from the k id =Cp/Cv values since they are all the three different isentropic exponents kp,v, kT,v and kp,T involved and further since the true sound velocity α is given by the relation α=(zkp,v RT)1/2 and is not approximated by the ideal gas sound velocityα id=(k id RT)1/2.

The three isentropic exponents of dry steam

The isentropic change of an ideal gas is described by the well known relations pvk=const, Tv(k−1) =const and p(1−k)Tk=const, where the exponent k is defined as the ratio of the constant pressure to the constant volume specific heat, k=cp/cv. The same relations are also used for real gases if small or differential isentropic changes are considered. A better examination of the differential isentropic change shows that for p, v, T systems, there are three different isentropic exponents corresponding to each pair formed out of the variables p, v, T. These three exponents noted kT,p, kT,v, kp,v after the corresponding pair of variables used, are interconnected by one relation, and accordingly only two out of the three are independent. The analysis of the present paper leads to the conclusion that calculations encountered in real gas isentropic change, with the exponent k taken as the ratio of the local specific heat values may lead to incorrect results. The numerical values of these exponents for steam, have been calculated and are presented. It can be seen that the deviations obtained, in comparison to the use of conventional k=cp/cv values are considerable.