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Ejector is a component using high-pressure fluid to aspirate low-pressure fluid, whose potential in energy saving is increasingly emphasized. The upper limit of ejector performance is still an interesting and instructive issue. In this paper, an ideal ejector is constructed, in which the working process is thermodynamically optimized to achieve minimal entropy generation. While working with ideal gas, the optimal mixing pressure can be expressed analytically as a function of inlet fluid parameters if the inlet temperatures of primary and secondary fluids are different. Furthermore, the analytical solution for the maximum of outlet pressure or entrainment ratio is deduced. The model of ideal ejector is compared with existing ejector models to illustrate its reasonability as a thermodynamic benchmark for ejector performance. For ejector working with real gas, a semi-perfect gas approach is introduced to estimate the upper limit of ejector performance. The calculation results are compared with other theoretical ejector models as well as the experimental data at typical refrigeration conditions. The optimal mixing pressure and maximal entrainment ratio are also obtained for ejector having polytropic processes in nozzles and diffuser. The thermodynamic upper limits provided in this paper offer a more reasonable reference for evaluating ejector performance than those from previous models.

This manuscript is related to the construction of relativistic core-envelope model for spherically symmetric charged anisotropic compact objects. The polytropic equation of state is considered for core, while it is linear in the case of envelope. We present that core, envelope and the Reissner Nordstr$$\ddot{o}$$ o ¨ m exterior regions of stars match smoothly. It has been verified that all physical parameters are well behaved in the core and envelope region for the compact stars SAX J1808.4-3658 and 4U1608-52. Various physical parameters inside star are discussed herein, non-singularity and continuity at the junction has been catered as well. Impact of charged compact object together with core-envelope model on the mass, radius and compactification factor is described by graphical representation in both core and envelop regions. The stability of the model is worked out with the help of Tolman–Oppenheimer–Volkoff equations and radial sound speed.

The review analyzes the data concerning various manifestations of the exothermicity of catalytic reactions. The articles, related to various oxidation and hydrogenation reactions are considered. The diversity of experimental conditions in which exothermic heterogeneous catalysis reactions take place leads to a variety of observed phenomena. Depending on the features of the dynamics of the heat balance of the catalytic reaction, phenomena like the ignition and extinction action, activity oscillations, the appearance of hot zones in the reactor can be observed. In a state of high activity, the mass transfer limitation (MTL) regime is realized. In a flow-through reactor with a catalyst, the polytropic behavior of the reactor with a hot zone at the inlet can be observed. When temperature or reactant concentration is varied, a hysteresis of activity is possible. The influence of strong adsorption of the reagent, catalyst deactivation, and the simultaneous occurrence of an endothermic reaction is considered. The technique of measuring the surface temperature of the catalyst is important, which requires an analysis of the corresponding experimental procedure.

In this paper, we study the Polytropic Gas Dark Energy model and New Agegraphic Dark Energy model in the flat Friedmann Robertson Walker (FRW) Universe and establish a correspondence between them for the scalar fields. This correspondence allows reconstructing the potential of the Polytropic Gas scalar fields and dynamics of the scalar fields according to the evolutions of the New Agegraphic Dark Energy, which describes the accelerated expansion of the Universe.

In the presence of vacuum, the physical entropy for polytropic gases behaves singularly and it is thus a challenge to study its dynamics. It is shown in this paper that the boundedness of the entropy can be propagated up to any finite time provided that the initial vacuum presents only at far fields with sufficiently slow decay of the initial density. More precisely, for the Cauchy problem of the one dimensional heat conductive compressible Navier-Stokes equations, the global well-posedness of strong solutions and uniform boundedness of the corresponding entropy are established, as long as the initial density vanishes only at far fields with a rate no more than $O(\frac{1}{x^2})$. The main tools of proving the uniform boundedness of the entropy are some singularly weighted energy estimates carefully designed for the heat conductive compressible Navier-Stokes equations and an elaborate De Giorgi type iteration technique for some classes of degenerate parabolic equations. The De Giorgi type iterations are carried out to different equations in establishing the lower and upper bounds of the entropy.

We present resolved thermodynamic profiles out to 500 kpc, about $r_{500}$, of the $z=1.75$ galaxy cluster IDCS J1426.5+3508 with 40 kpc resolution. Thanks to the combination of Sunyaev-Zel'dovich and X-ray datasets, IDCS J1426.5+3508 becomes the most distant cluster with resolved thermodynamic profiles. These are derived assuming a non-parametric pressure profile and a very flexible model for the electron density profile. The shape of the pressure profile is flatter than the universal pressure profile. The IDCS J1426.5+3508 temperature profile is increasing radially out to 500 kpc. To identify the possible future evolution of IDCS J1426.5+3508 , we compared it with its local descendants that numerical simulations show to be $0.65\pm0.12$ dex more massive. We found no evolution at 30 kpc, indicating a fine tuning between cooling and heating at small radii. At $30, Comment: MNRAS, in press. In v2 we only corrected author affiliations and spelling

This paper is concerned with an initial and boundary value problem of the compressible Navier-Stokes equations for one-dimensional viscous and heat-conducting ideal polytropic fluids with temperature-dependent transport coefficients. In the case when the viscosity μ ( θ ) = θ α and the heat-conductivity κ ( θ ) = θ β with α , β ∈ [ 0 , ∞ ) , we prove the global-in-time existence of strong solutions under some assumptions on the growth exponent α and the initial data. As a byproduct, the nonlinearly exponential stability of the solution is obtained. It is worth pointing out that the initial data could be large if α ≥ 0 is small, and the growth exponent β ≥ 0 can be arbitrarily large.

We are concerned with the shock diffraction configuration for isothermal gas modeled by the conservation laws of nonlinear wave system. We reformulate the shock diffraction problem into a linear degenerate elliptic equation in a fixed bounded domain. The degeneracy is of Keldysh type—the derivative of a solution blows up at the boundary. We establish the global existence of solutions and prove the $${C^{0,{1 \over 2}}}$$ -regularity of solutions near the degenerate boundary. We also compare the difference of solutions between the isothermal gas and the polytropic gas.

In this paper, we have checked the stability of some anisotropic charged generalized polytropic models by using the concept of cracking, founded by Nasim and Azam (Astrophys. Space Sci. 363, 132 (2018). doi: 10.1007/s10509-018-3356-4 ). The process of cracking is intuitive and shows the points where the dissipation of radial forces appear in the system on account of perturbation and carries the system out of its equilibrium state. We have employed the local density perturbation technique to the hydrostatic equilibrium equation and on all the physical parameters engaged in the models. We concluded that under the local density perturbation scheme all the generalized polytropic models are potentially stable.

The question of the application of Poisson’s law PVγ = сonst in the analysis of spatiotemporal variations in the parameters of the neutral atmosphere in this region is considered in relation to the existence of heat fluxes in the mesosphere-lower thermosphere (MLT). Poisson’s law is valid for adiabatic processes, i.e., in the absence of heat transfer (ΔQ = 0). When internal gravitational waves propagate in this region, which, when dissipated, transfer energy and angular momentum to the medium and can enhance turbulent motions, as well as during the development of the frequently observed dynamic and convective instabilities, the processes in MLT can also be nonadiabatic. In this study, we obtained the values ​​of the n index in the lower thermosphere for polytropic processes PVn = const, when only the heat capacity is constant. To estimate the n index, we use measurements of the temperature and density of the neutral atmosphere by the method of resonant scattering on artificial periodic irregularities of the ionospheric plasma. It is shown that above the turbopause, the polytropic index n lies in the range of 1.8 to 2. The fact that n > γ indicates the importance of taking the heat transfer in the lower thermosphere into account.

The internal temperature of a gas bubble caused by a fault arc is a key basic parameter for investigating the bubble behavior and the pressure rise inside oil-filled power equipment. Due to the constraints imposed by the measurement methods and experimental conditions, this temperature has always been estimated as a constant value of 2000 K in past decades. In this letter, we present direct experimental evidence of the gas bubble temperature around an arc. A large oil-filled transformer was reformed and used to conduct arcing fault tests. A sapphire fiber optic infrared thermometer was established and used to detect the internal gas bubble temperature. The experimental results confirm that this internal temperature is not constant but rather varies over a wide range from 2100 K to 1500 K, plummeting with rapid bubble growth and then exhibiting small variations until arc extinction. Furthermore, the bubble growth process throughout the arc duration can be approximately regarded as first polytropic and then isothermal.

In today’s world where fuel prices have increased drastically and there are great concerns about environmental issues, there is the need to properly match centrifugal compressors to their Gas Turbine (GT) drivers, so as to achieve an efficient overall package, lower turbine fuel consumption, longer time between overhauls, and most importantly, package operational flexibility in meeting alternate process conditions. This study highlights the influence of operating and environmental conditions on the overall performance of the gas turbine compressor set. GasTurb and CMap simulation softwares were employed to model and simulate the performances of the GT and centrifugal compressors respectively. The outcome of the performance plots show that at a design inlet flow volume of 15928 cubic meters per hour, the compressor required power from the gas turbine drive to transport RaNatGas is approximately 7450kW as against 7065kW and 6500kW for MaNatGas and LaNatGas mixtures respectively. Techno-economic analysis of the gas turbine compressor set shows that the fuel cost of transporting a given volume flow of RaNatGas to a specific location for a year gives about$13.5million when compared with MaNatGas and LaNatGas mixtures which cost about $13.02million and 12.3million respectively. Keywords: Natural Gas, Performance Simulations, Polytropic Efficiency, Polytropic Head, Gas Compositions

Generally, the differential equations of integer order do not properly model various phenomena in different areas of science and engineering as compared to differential equations of fractional order. The fractional-order differential equations provide the useful dynamics of the physical system and thus provide the innovative and effective information about the given physical system. Keeping in view the above properties of fractional calculus, the present article is related to the analytical solution of the time-fractional system of equations which describe the unsteady flow of polytropic gas dynamics. The present method provides the series form solution with easily computable components and a higher rate of convergence towards the targeted problem’s exact solution. The present techniques are straightforward and effective for dealing with the solutions of fractional-order problems. The fractional derivatives are expressed in terms of the Caputo operator. The targeted problems’ solutions are calculated using the Adomian decomposition method and variational iteration methods along with Shehu transformation. In the current procedures, we first applied the Shehu transform to reduce the problems into a more straightforward form and then implemented the decomposition and variational iteration methods to achieve the problems’ comprehensive results. The solution of the nonlinear equations of unsteady flow of a polytropic gas at various fractional orders of the derivative is the core point of the present study. The solution of the proposed fractional model is plotted via two- and three-dimensional graphs. It is investigated that each problem’s solution-graphs are best fitted with each other and with the exact solution. The convergence of fractional-order problems can be observed towards the solution of integer-order problems. Less computational time is the major attraction of the suggested methods. The present work will be considered a useful tool to handle the solution of fractional partial differential equations.

Recently, simultaneous measurements of the masses and the radii of neutron stars from X-ray observations by the Neutron Star Interior Composition Explorer (NICER) have been reported. In addition, gravitational wave detections from the mergers of neutron star binaries allowed us to estimate the tidal deformability of neutron stars. Based on these recent observations and our works, we review their implications for the masses, radii and tidal deformabilities of neutron stars. We also discuss the basic principles of the polytropic equations of state, including sound velocities, and the implications of those equations to the properties of neutron stars.

Many massive stars appear to undergo enhanced mass loss during late stages of their evolution. In some cases, the ejected mass likely originates from non-terminal explosive outbursts, rather than continuous winds. Here we study the dependence of the ejecta mass, $m_{\rm ej}$, on the energy budget $E$ of an explosion deep within the star, using both analytical arguments and numerical hydrodynamics simulations. Focusing on polytropic stellar models, we find that for explosion energies smaller than the stellar binding energy, the ejected mass scales as $m_{\rm ej} \propto E^{\varepsilon_{m}}$, where $\varepsilon_m = 2.4-3.0$ depending on the polytropic index. The loss of energy due to shock breakout emission near the stellar edge leads to the existence of a minimal mass-shedding explosion energy, corresponding to a minimal ejecta mass. For a wide range of progenitors, from Wolf-Rayet stars to red supergiants, we find a similar limiting energy of $E_{\rm min} \approx 10^{46}-10^{47} \rm \, erg$, almost independent of the stellar radius. The corresponding minimal ejecta mass varies considerably across different progenitors, ranging from $\sim \! 10^{-8} \, \rm M_\odot$ in compact stars, up to $\sim \! 10^{-2} \, \rm M_\odot$ in red supergiants. We discuss implications of our results for pre-supernova outbursts driven by wave heating, and complications caused by the non-constant opacity and adiabatic index of realistic stars., 9 pages, 5 figures. Submitted to MNRAS

In this research, we study the polytropic gas cosmology in a 5-dimensional form of the flat Friedmann–Robertson–Walker framework. In this context, we focus on the evolution of corresponding energy density and use the most recent data from the Type Ia Supernova, observational data of the cosmic Hubble parameter and the updated Planck-results to place constraints on the free parameters defined in the model. Making use of the calculations, we investigate also some physical features of the model in order to obtain some constraints on the auxiliary parameters given in the proposal.

We establish the future non-linear stability of Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) solutions to the Einstein-Euler equations of the universe filled with a large class of perfect fluids (the equations of state are allowed to be certain nonlinear or linear types both). Several previous results as specific examples can be covered in the results of this article. We emphasize that the future stability of FLRW metric for polytropic fluids with positive cosmological constant has been a difficult problem and can not be directly generalized from the previous known results. Our result in this article has not only covered this difficult case for the polytropic fluids, but also unified more types of fluids in a same scheme of proofs., Comment: 47 pages. Agrees with published version

We investigate a hyperbolic system of one-dimensional isothermal fluid with liquid-vapor phase transition. The refraction-reflection phenomena are intensively analyzed when elementary waves travel across the two-phase interface. We apply the characteristic method and hodograph transform of Riemann to reduce the nonlinear PDEs to a concise form. Specially for the case of incident rarefaction wave, reduced linear equations are convenient to solve by Laplace transform. Then an integral formula in wave interaction region is derived in this paper, instead of the hypergeometric functions solutions for non-isothermal polytropic gases. It is also observed that when incident waves travel from the vapor phase to the liquid phase, the refracted waves must be accelerated and move forward.

Near-wall transient heat transfer and flame-wall interaction (FWI) are topics of great importance in the development of downsized internal combustion (IC) engines and gas turbine technology. In this work we perform measurements using 1D hybrid fs/ps rotational CARS (HRCARS), thermographic phosphors (TGP) and CH* imaging in an optically-accessible chamber designed to study transient near-wall heat transfer processes relevant to IC engine operation. HRCARS provides single-shot gas-phase temperatures (40μm spatial resolution and up to 3mm wall-normal distances), while thermographic phosphors measures wall temperature and CH* measures the flame front position. These simultaneous measurements are used to resolve thermal boundary layer (TBL) development and associated gaseous heat loss for three important processes of gas/wall interactions: (1) an unburned-gas polytropic compression process, (2) FWI, and (3) post-flame and gas expansion processes. During a mild polytropic compression process, measurements emphasize that even a relatively small wall heat flux (≤ 5kW/m^2) yields an appreciable temperature stratification through a developing TBL. During FWI, thermal gradients induced by the flame are resolved within the TBL. Gases closest to the wall (y

In this study, a hybrid steady-state compressor model is proposed that can be used in the real-time performance monitoring, control and optimization of the vapor compression cycle. In the proposed model, first, a detailed analysis of the mass flow rate is presented, which is based on the volumetric efficiency concept and the assumption of a polytropic compression process. Then, discharge temperature of the refrigerant and power consumption of the compressor are also investigated. Three semiempirical models are constructed respectively. Further, to tune the unknown empirical parameters of the models, a social learning particle swarm optimization (SLPSO) algorithm is developed by using the real-time experimental data. An experimental apparatus of a refrigerant system is tested to validate the proposed models. The experimental results demonstrate that the proposed models accurately predict the performance of real-time operating compressors. Meanwhile, the models identified by the SLPSO algorithm are more accurate than those identified by the traditional least-squares method.

This paper is concerned with the large-time behavior of solutions to the outflow problem of full compressible Navier-Stokes equations in the half line. This is one of the series of papers by the authors on the stability of nonlinear waves to the outflow problem. We show the time asymptotic stability of degenerate (transonic) stationary solution for the general gas including ideal polytropic gas. The key point of the proof is based the new property of the degenerate stationary solution and the delicate energy estimates.

In engineering practice, mechanical equipment is usually in polytropic working conditions, where the data distribution of training set and test set is inconsistent, resulting in insufficient generalization ability of the intelligent diagnosis model. Simultaneously, different tasks often need to be modeled separately. Domain adaptation, as one of the research contents of transfer learning, has certain advantages in solving the problem of inconsistent feature distribution. This article designs and establishes a domain adaptation framework based on multiscale mixed domain feature (DA-MMDF) for cross-domain intelligent fault diagnosis of rolling bearings under polytropic working conditions. The proposed method first uses the MMDF extractor to obtain features from the collected data, which constructs a complete feature space through variational mode decomposition (VMD) and mixed domain feature extraction to fully mine the state information and intrinsic attributes of the vibration signal. Second, the dimensionality reduction and optimization of features are achieved through extreme gradient promotion, and meaningful and sensitive features are selected according to the importance of features to eliminate redundant information. The optimized important features are combined with the manifold embedded distribution alignment method to realize the distribution alignment of data in different fields and cross-domain diagnosis. In order to verify the effectiveness of the proposed approach, the rolling bearing data sets gathered from the laboratories are employed and analyzed. The analysis result confirms that DA-MMDF is able to achieve effective transfer diagnosis between polytropic working conditions. Compared with traditional intelligent fault diagnosis methods and DA methods, the method proposed in this article achieved the state-of-the-art performances.

The present study aims to clarify the effect of the polytropic index (i.e., the ratio of specific heats in the context of a perfect gas) on the detonation structure. This is addressed by two-dimensional numerical simulations. To ease the clarification of the role of gasdynamics, a simple Arrhenius kinetic law is used for the chemical model. The activation energy, normalized by the shock temperature, is kept constant to obtain the same reaction rate sensitivity to temperature in all considered mixtures. This procedure dissociates the gasdynamic effects from the chemistry effects. The numerical results reveal that in mixtures with low polytropic indicies, the convective mixing is enhanced compared to mixtures with higher polytropic indicies. The mixing is evaluated using Lagrangian tracers. Moreover, mixtures with low polytropic indicies are found to have a shorter reaction length than mixtures with high polytropic indicies. Also, for the range of parameters considered in this study the results indicate that Mach stem bifurcation in detonations due to jetting is primarily a gasdynamic driven mechanism.

Jupiter’s magnetic field is thought to be generated in its deep metallic hydrogen region through dynamo action, yet the detailed dynamic process remains poorly understood. Numerical simulations have produced Jupiter-like magnetic fields, albeit using different control parameters and reference state models. In this study, we investigate the influence of different reference state models, based on ab initio calculations and based on the polytropic equation of state. In doing so, we perform five anelastic convection dynamo simulations that can be divided into two groups. In each group, different reference states are used while other control parameters and conditions are set to be identical. We find the reference state model can be very influential for the simulations in which buoyancy force is dominant over the Lorentz force. In this regime, different dynamical outcomes can be attributed to the effective buoyancy force resulting from different reference states. For simulations in which the Lorentz force is dominant over the buoyancy force, however, dynamo actions tend to be insensitive to different reference state models. If Jupiter’s dynamo is in a strong field regime, i.e., the Lorentz force plays a dominant role, our numerical results suggest that Jupiter’s internal reference state, which remains poorly constrained, may play a minor role in the dynamo process of the planet.

A special subclass of solutions of the three-dimensional system of ideal polytropic gas equations corresponding to an atmospheric model is considered. The properties of these solutions are completely characterized by a high-order nonlinear system of ordinary differential equations. Unlike the corresponding two-dimensional model, all singular points of this system have been found to be unstable. Some first integrals of this system have been found. In the case of axial symmetry, the system can be reduced to a single equation. If the adiabatic exponent is equal to 2, the system is integrable.

Two-dimensional polytropic gas flows representable as endless series are constructed as solutions of the corresponding standard characteristic Cauchy problems in the space of self-similar variables. The convergence of the series is proved, and a procedure for constructing the coefficients of the series is described. It is found that in one particular case, the series terminates and coincides with the well-known analytical solution that was used by V. A. Suchkov to describe gas flow along an oblique wall into vacuum and by A. F. Sidorov to describe infinite compression of prismatic gas volumes. It is shown that in the case of compressive flow of the gas, its infinite compression by impermeable pistons moving according to different laws is possible, and the gas-dynamic parameters of the flow are studied. Highly nonuniform pressure distribution during compression of prismatic targets is obtained.

Calculations of characteristics of stars with axial rotation in the frame of polytropic model are based on the solution of mechanical equilibrium equation – differential equation of second order in partial derivatives. Different variants of approximate determinations of integration constants are based on traditional in the theory of stellar surface approximation, namely continuity of gravitational potential in the surface vicinity. We proposed a new approach, in which we used simultaneously differential and integral forms of equilibrium equations. This is a closed system and allows us to define in self-consistent way integration constants, the polytrope surface shape and distribution of matter over volume of a star. With the examples of polytropes n=0 and n=1, we established the existence of two rotation modes (with small and large eccentricities). It is proved that the polytrope surface is the surface of homogeneous rotational ellipsoid for the case n=0. The polytrope characteristics with n=1 in different approximations were calculated as the functions of angular velocity. For the first time it has been calculated the deviation of polytrope surface at fixed value of angular velocity from the surface of associated rotational ellipsoid.

Formulas for drive power of centrifugal supercharger of natural gas are obtained, where efficiency factor (EF) of centrifugal supercharger is equal to product of three EF of centrifugal supercharger: mechanical, polytropic, gas-dynamic. The gas dynamic EF of the centrifugal supercharger is usually not taken into account and is taken equal to one. Gas dynamic EF takes into account the pressure loss of the centrifugal supercharger pumped in the stages and the energy loss due to friction of the centrifugal supercharger impellers in the gas medium. Also in the formula of calculation of drive power of the operated centrifugal supercharger the presence of condensate and water vapors in the natural gas is taken into account, which affects the accuracy of measuring the flow rate of pumped gas in the diaphragm flowmeter. Pumping of pure natural gas is impossible in reality and there are always impurities in natural gas, which must be taken into account to estimate the mass flow rate of gas. For formulas of practical (operated) and theoretical calculations of the drive power of the centrifugal natural gas blower received constant (equal to 0.004) for daily standard gas flow, which simplifies the calculation. The paper presents both precise and simplified formulas for the drive power of a centrifugal natural gas blower.

In this paper, we consider an inflow problem for the non-isentropic Navier-Stokes-Poisson system in a half line (0, ∞). For the general gas including ideal polytropic gas, we first give some results for the existence of the stationary solution with the aid of center manifold theory on a 4 × 4 system of autonomous ordinary differential equations. We also show the time asymptotic stability of the stationary solutions with small strength under smallness assumptions on the initial perturbations by using an elementary energy method.

The accretion of test fluids flowing onto a black hole is investigated. Particularly, by adopting a dynamical Hamiltonian approach, we are capable to find the critical points for various cases of black hole in conformal gravity. In these cases, we have analyzed the general solutions of accretion employing the isothermal equations of state. The steady state and spherically symmetric accretion of different test fluids onto the conformal gravity black hole has been considered. Further, we have classified these flows in the context of equations of state and the cases of conformal gravity black hole. The new behavior of polytropic fluid accretion is also discussed in all three cases of black hole. Black hole mass accretion rate is the most important part of this research in which we have investigated that the Schwarzschild black hole produce a typical signature than the conformal gravity black hole and Schwarzschild de-Sitter black hole. The critical fluid flow and the mass accretion rate have been presented graphically by the impact parameters $\beta$, $\gamma$, $k$ and these parameters have great significance. Additionally, the maximum mass rate of accretion fall near the universal and Killing horizons and minimum rate of accretion occurs in between these regions. Finally, the results are compared with the different cases of black hole available in the literature., Comment: 36 pages, 33 figures, accepted for publications in EPJC

The present work is devoted to investigate compressor performance (positive displacement or dynamic compressor) from two different points of view that are; energy and exergy. The studied compressor parameters are; compressor polytropic efficiency, compressor pressure ratio, inlet temperature, and inlet humidity. The effect of these parameters on compressor specific work consumption, compressor operating range, energy destruction, energy destruction ratio, and the first and second law efficiencies are demonstrated. The results show how the compressor behaves under different conditions. Also, the results illustrate that first and second law efficiencies provide quantitative and qualitative compressor performance assessments. The result charts help in selecting different types of compressors that having higher second law efficiency or having less exergy destruction ratio. The present paper may give an insight to understand deeply compressor performance and how to evaluate or choose the compressor with less exergy losses ratio.

Storm geysers have received significant attention lately due to its more frequent occurrences and the induced severe local flooding and infrastructure damages. Previous studies suggested that the air pocket pressure oscillated during geyser events especially in rapid filling process, but only the peak values were studied and the oscillation period was not discussed in detail. In this paper, a theoretical model was developed focusing on the period of the pressure oscillation induced by the expansion/compression of the air pocket below a water column in a vertical riser with film flow. It was found that the oscillation period was a function of the initial air pocket volume, initial air pocket pressure head, the riser diameter, and the initial water column length. The oscillation period increased with the air pocket pressure head and the air pocket volume, but decreased with the riser diameter and the polytropic coefficient. The oscillation period increased then decreased with an increasing water column length. Further, when considering the film flow along the riser, the oscillation period decreased slightly from the analytical solution. It was also found that the inflow rate change did not significantly influence the oscillation period.