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Showing papers on "Axial compressor published in 2012"


Journal ArticleDOI
TL;DR: In this article, the authors used nonlinear numerical simulations in the slender body limit, based on an explicit description of the coupling between the fluid-solid and electric systems, to determine the harvesting efficiency of the system, namely the fraction of the flow kinetic energy flux effectively used to power the output circuit.
Abstract: Self-sustained oscillations resulting from fluid-solid instabilities, such as the flutter of a flexible flag in axial flow, can be used to harvest energy if one is able to convert the solid energy into electricity. Here, this is achieved using piezoelectric patches attached to the surface of the flag that convert the solid deformation into an electric current powering purely resistive output circuits. Nonlinear numerical simulations in the slender-body limit, based on an explicit description of the coupling between the fluid-solid and electric systems, are used to determine the harvesting efficiency of the system, namely the fraction of the flow kinetic energy flux effectively used to power the output circuit, and its evolution with the system's parameters. The role of the tuning between the characteristic frequencies of the fluid-solid and electric systems is emphasized, as well as the critical impact of the piezoelectric coupling intensity. High fluid loading, classically associated with destabilization by damping, leads to greater energy harvesting, but with a weaker robustness to flow velocity fluctuations due to the sensitivity of the flapping mode selection. This suggests that a control of this mode selection by a careful design of the output circuit could provide some opportunities of improvement for the efficiency and robustness of the energy harvesting process.

181 citations


Journal ArticleDOI
TL;DR: In this paper, the authors simulate three-dimensional, turbulent flow past an axial-flow marine hydrokinetic (MHK) turbine mounted on the bed of a rectangular open channel by adapting a computational framework developed for carrying out high-resolution large-eddy simulation (LES) in arbitrarily complex domains involving moving or stationary boundaries.

138 citations


Journal ArticleDOI
TL;DR: In this paper, an instantaneous casing pressure field measurement technique was developed, in which 30 pressure transducers were used to obtain the unsteady and transient pressure fields on the casing wall during the inception process of spike stall.
Abstract: The unsteady behavior and three-dimensional flow structure of spike-type stall inception in an axial compressor rotor were investigated by experimental and numerical analyses. Previous studies revealed that the test compressor falls into a mild stall after emergence of a spike, in which multiple stall cells, each consisting of a tornado-like vortex, are rotating. However, the flow mechanism from the spike onset to the mild stall remains unexplained. The purpose of this study is to describe the flow mechanism of a spike stall inception in a compressor. In order to capture the transient phenomena of spike-type stall inception experimentally, an instantaneous casing pressure field measurement technique was developed, in which 30 pressure transducers measure an instantaneous casing pressure distribution inside the passage for one blade pitch at a rate of 25 samplings per blade passing period. This technique was applied to obtain the unsteady and transient pressure fields on the casing wall during the inception process of the spike stall. In addition, the details of the three-dimensional flow structure at the spike stall inception were analyzed by a numerical approach using the detached-eddy simulation (DES). The instantaneous casing pressure field measurement results at the stall inception show that a low-pressure region starts traveling near the leading edge in the circumferential direction just after the spiky wave was detected in the casing wall pressure trace measured near the rotor leading edge. The DES results reveal the vortical flow structure behind the low-pressure region on the casing wall at the stall inception, showing that the low-pressure region is caused by a tornado-like separation vortex resulting from a leading-edge separation near the rotor tip. A leading-edge separation occurs near the tip at the onset of the spike stall and grows to form the tornado-like vortex connecting the blade suction surface and the casing wall. The casing-side leg of the tornado-like vortex generating the low-pressure region circumferentially moves around the leading-edge line. When the vortex grows large enough to interact with the leading edge of the next blade, the leading-edge separation begins to propagate, and then the compressor falls into a stall with decreasing performance.

72 citations


Journal ArticleDOI
TL;DR: In this paper, the authors present new experimental measurements of spike-type stall inception in a single-stage Deverson compressor at the Whittle Laboratory and characterize the flow field in the tip clearance gap during stall inception using instrumentation to give high spatial and temporal resolution.
Abstract: This paper presents new experimental measurements of spike-type stall inception. The measurements were carried out in the single stage Deverson compressor at the Whittle Laboratory. The primary objective was to characterize the flow field in the tip clearance gap during stall inception using sufficient instrumentation to give high spatial and temporal resolution. Measurements were recorded using arrays of unsteady pressure transducers over the rotor tips and hot-wires in the tip gap. Pre-stall ensemble averaged velocity and pressure maps were obtained as well as pressure contours of the stall event. In order to study the transient inception process in greater detail, vector maps were built up from hundreds of stalling events using a triggering system based on the stalling event itself. The results show an embryonic disturbance starting within the blade passage and leading to the formation of a clear spike. The origins of the spike and its relation to the tip leakage vortex are discussed. It has also been shown that before stall the flow in the blade passage which is most likely to stall is generally more unsteady, from revolution to revolution, than the other passages in the annulus. Copyright © 2012 by ASME.

65 citations


Proceedings ArticleDOI
11 Jun 2012
TL;DR: In this paper, the results from detailed and validated CFD calculations are used to study the origins of the secondary loss in axial turbines and to highlight the sources of entropy generation in the cascade.
Abstract: Endwall loss, often termed “secondary loss”, in axial turbines has been intensively studied for many years, despite this the physical origin of much of the loss is not really understood. This lack of understanding is a serious impediment to our ability to predict the loss and to the development of methods for reducing it. This paper aims to study the origins of the loss by interrogating the results from detailed and validated CFD calculations. The calculation method is first validated by comparing its predictions to detailed measurements in a turbine cascade. Very good agreement between the calculations and the measurements is obtained. The solution is then examined in detail to highlight the sources of entropy generation in the cascade, several different sources of loss are found to be significant.The same blade row is then used to study the effects of the of the inlet boundary layer thickness on the loss. It is found that only the inlet boundary layer loss and the mixing loss vary greatly with inlet boundary layer thickness. Finally a complete 50% reaction stage, with identical stator and rotor blade profiles, is examined using both steady calculations, with a mixing plane model, and the time average of unsteady calculations. It is found that the endwall flow in the rotor is completely different from that in the stator. Because of this it is considered that results from endwall flow and loss measurements in cascades are of limited relevance to the endwall flow in a real turbine. The results are also used to discuss the validity of the mixing plane model.Copyright © 2012 by ASME

57 citations


Journal ArticleDOI
TL;DR: In this article, the rotor tip gap with respect to a large industrial gas turbine was evaluated using numerical simulations on an embedded stage representative of that of a large gas turbine with Reynolds number ∼ 2 to 7×106.
Abstract: Compressor efficiency variation with rotor tip gap is assessed using numerical simulations on an embedded stage representative of that in a large industrial gas turbine with Reynolds number ∼ 2 to 7×106. The results reveal three distinct behaviors of efficiency variation with tip gap. For relatively small tip gap (less than 0.8% span), the change in efficiency with tip gap is non-monotonic with an optimum tip gap for maximum efficiency. The optimum tip gap is set by two competing flow processes: decreasing tip leakage mixing loss and increasing viscous shear loss at the casing with decreasing tip gap. An optimum tip gap scaling is established and shown to satisfactorily quantify the optimal gap value. For medium tip gap (0.8%–3.4% span), the efficiency decreases approximately on a linear basis with increasing tip clearance. However, for tip gap beyond a threshold value (3.4% span for this rotor), the efficiency becomes less sensitive to tip gap as the blade tip becomes more aft-loaded thus reducing tip flow mixing loss in the rotor passage. The threshold value is set by the competing effects between increasing tip leakage flow and decreasing tip flow induced mixing loss with increasing tip gap. Thus, to desensitize compressor performance variation with blade gap, rotor should be tip aft-loaded and hub fore-loaded while stator should be tip fore-loaded and hub aft-loaded as much as feasible. This reduces the opportunity for clearance flow mixing loss and maximizes the benefits of reversible work from unsteady effects in attenuating the clearance flow through the downstream blade-row. The net effect can be an overall compressor performance enhancement in terms of efficiency, pressure rise capability, robustness to end gap variation and potentially useful operable range broadening.© 2012 ASME

57 citations


Patent
02 Aug 2012
TL;DR: An aircraft pressurization system includes an auxiliary compressor (42) for further compressing compressed air received from a low pressure compressor section (22) of a gas turbine engine (10) while the compressed air is below a predetermined pressure level.
Abstract: An aircraft pressurization system, includes an auxiliary compressor (42) for further compressing compressed air received from a low pressure compressor section (22) of a gas turbine engine (10) while the compressed air is below a predetermined pressure level; a bleed passage (40) for fluidically connecting the auxiliary compressor (42) to the low pressure compressor section (22); and an environmental control system (38) coupled to an output of the auxiliary compressor (42) for conditioning the compressed air to a predetermined level.

46 citations


Journal ArticleDOI
TL;DR: In this article, a three-dimensional unsteady RANS simulation of a high-pressure compressor is performed to better understand rotor-stator interactions and tip leakage flow effects on overall performance and aerodynamic stability.
Abstract: This paper describes the investigations performed to better understand unsteady flows that develop in a three-stage high-pressure compressor. More specifically, this study focuses on rotor-stator interactions and tip leakage flow effects on overall performance and aerodynamic stability. The investigation method is based on three-dimensional unsteady RANS simulations, considering the natural spatial periodicity of the compressor. Indeed, all information related to rotor-stator interactions can be computed. A comparison is first done with experimental measurements to outline the capacity of the numerical method to predict overall performance and unsteady flows. The results show that the simulation correctly estimates most flow features in the multistage compressor. Then numerical data obtained for three configurations of the same compressor are analyzed and compared. Configurations 1 and 2 consider two sets of tip clearance dimensions and a casing treatment based on a honeycomb design is applied for configuration 3. Detailed investigations of the flow at the same operating line show that the tip leakage flow is responsible for the loss of stability in the last stage. An increase by 30% of the tip clearance dimension dramatically reduces the stable operating range (by 40% with respect to the standard configuration). A modal analysis shows that the stall process in this case involves the perturbation of the flow in the last rotor by upstream stator wakes, leading to the development of a rotating instability. The control device designed and investigated in this study allows for reducing the sensitivity of the compressor to tip leakage flow by recovering the initial stable operating range.

45 citations


Journal ArticleDOI
TL;DR: In this article, a flexible cantilevered cylinder in confined axial flow is investigated theoretically and experimentally, in the case where the flow is directed from the free end towards the clamped one.

44 citations


Proceedings ArticleDOI
11 Jun 2012
TL;DR: In this paper, a fully coupled fluid/strcuture interaction (FSI) was used to simulate non-synchronous vibration (NSV) of a GE axial compressor, where the predicted dominant frequencies using the blade tip response signals are not harmonic to the engine order, which is the NSV.
Abstract: In this paper non-synchronous vibration (NSV) of a GE axial compressor is simulated using a fully coupled fluid/strcuture interaction (FSI). Time accurate NavierStokes equations are solved with a system of 5 decoupled structure modal equations in a fully coupled manner. A 3rd order WENO scheme for the inviscid flux and a 2nd order central differencing for the viscous terms are used to resolve nonlinear interaction between vibrating blades and fluid flow. 1=7th annulus is used with a time shifted phaselag (TSPL) boundary condition to reduce computational efforts. A fully conservative rotor/stator sliding boundary condition is employedto accuratelycaptureunsteady wakepropagation between the rotor and stator blades. The predicted dominant frequencies using the blade tip response signals are not harmonic to the engine order, which is the NSV. The blade vibration is torsionally coupled with highly oscillating blade pressure and is not damped out during the NSV. No resonance to the blade natural frequencies is found. The instability of tornado vortices in the vicinity of the rotor tip due to the strong interaction of incoming flow, tip vortex and tip leakage flow is the main cause of the NSV observed in this study.

42 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigated the pre-stall behavior of axial flow compressor rotor, which was experimentally observed with spike-type stall inception, systematic experimental and whole-passage simulations were laid out to analyze the internal flow fields in the test rotor.
Abstract: To investigate the pre-stall behavior of an axial flow compressor rotor, which was experimentally observed with spike-type stall inception, systematic experimental and whole-passage simulations were laid out to analyze the internal flow fields in the test rotor. In this part, emphases were put on the analyses of experimental results and the predicted results from steady simulations and unsteady simulations, which converged to equilibrium solutions with nearly periodic fluctuations of efficiency. The objective was to uncover the unsteady behavior of tip clearance flow and its associated flow mechanism at near-stall conditions. To validate the steady simulation results, the predicted total characteristics and spanwise distributions of aerodynamic parameters were first compared with the measured steady data, and a good agreement was achieved. Then, the numerically obtained unsteady flow fields during one period of efficiency fluctuations were analyzed in detail. The instantaneous flow structure near casing showed that tip secondary vortex (TSV), which appeared in the previous unsteady single-passage simulations, did exist in tip flow fields of whole-passage simulations. The cyclical motion of this vortex was the main source of the nearly periodic variation of efficiency. The simulated active period of TSV increased when the mass flow rate decreased. The simulated frequency of TSV at flow condition very close to the measured stall point equaled the frequency of the characteristic hump identified from the instantaneous casing pressure measurements. This coincidence implied that the occurrence of this hump was most probably a result of the movement of TSV. Further flow field analyses indicated that the interaction of the low-energy leakage fluid from adjacent passages with the broken-down tip leakage vortex (TLV) was the flow mechanism for the formation of TSV. Once TSV appeared in tip flow fields, its rearward movement would lead to a periodic variation in near-tip blade loading, which in turn altered the strength of TLV and TSV, accordingly, the low-energy regions associated with the breakdown of TLV and the motion of TSV, thus establishing a self-sustained unsteady flow oscillation in tip flow fields.

Journal ArticleDOI
TL;DR: In this article, a series of simulations performed on compressor geometries, ranging from a Controlled Diffusion Cascade stator blade to the periodic sector of a stage in a 3.5 stage axial compressor, were presented.

Journal ArticleDOI
TL;DR: In this paper, the fluid-structure interaction for an elastic cylinder in an axial fluid flow is numerically studied based on the ALE Navier-Stokes equations and Euler-Bernoulli beam dynamic equation.

Journal ArticleDOI
01 Sep 2012-Energy
TL;DR: In this paper, a two-step method for the optimization of two-dimensional blade sections of an axial-flow impulse air turbine for OWC wave energy converters is described, where an inverse design method imposes an almost constant pressure load along the axial chord by changing the camber line slope.

Journal ArticleDOI
TL;DR: In this article, an experimental study on the design of counter-rotating axial-flowfans was carried out, where the axial spacing between fans can vary from 17% to 310%.
Abstract: An experimental study on the design of counter-rotating axial-flowfans was carried out. The fans were designed using an inversemethod. In particular, the system is designed to have a pure axialdischarge flow. The counter-rotating fans operate in a ducted-flowconfiguration and the overall performances are measured in a nor-malized test bench. The rotation rate of each fan is independentlycontrolled. The relative axial spacing between fans can vary from17% to 310%. The results show that the efficiency is stronglyincreased compared to a conventional rotor or to a rotor-statorstage. The effects of varying the rotation rates ratio on the overallperformances are studied and show that the system has a very flexi-ble use, with a large patch of high efficient operating points in theparameter space. The increase of axial spacing causes only a smalldecrease of the efficiency. [DOI: 10.1115/1.4007591]

Journal ArticleDOI
TL;DR: In this paper, a two-stage turbulence model based on the RNG κ-e model combined with the Reynolds stress model is developed to analyze the gas flow in an axial flow cyclone separator.

Journal ArticleDOI
TL;DR: In this article, the meridional profiles of the impeller impact the overall compressor efficiency and pressure ratio at the same rotational speed, and the authors presented some recent studies of meridial impacts of the compressor.
Abstract: Centrifugal compressor developments are interested in using optimization procedures that enable compressor high efficiency and wide operating ranges. Recently, high pressure ratio and efficiency of the centrifugal compressors require impeller design to pay attention to both the blade angle distribution and the meridional profile. The geometry of the blades and the meridional profile are very important contributions of compressor performance and structure reliability. This paper presents some recent studies of meridional impacts of the compressor. Studies indicated that the meridional profiles of the impeller impact the overall compressor efficiency and pressure ratio at the same rotational speed. Proper meridional profiles can improve the compressor efficiency and increase the overall pressure ratio at the same blade back curvature.

Journal ArticleDOI
TL;DR: In this article, an overview is given on the research maintained by the author about design aspects of three-dimensional blade passage flow in low-speed axial flow industrial fan rotors, affected by spanwise changing design blade circulation due to controlled vortex design (CVD), blade forward sweep (FSW), and their combination.
Abstract: An overview is given on the research maintained by the author about design aspects of three-dimensional blade passage flow in low-speed axial flow industrial fan rotors, affected by spanwise changing design blade circulation due to controlled vortex design (CVD), blade forward sweep (FSW), and their combination.It was pointed out that, comparing the CVD method to free vortex design, the fluid in the blade suction side boundary layer has increased inclination to migrate radially outward, increasing near-tip blockage and loss. It was concluded that the benefit of FSW, in terms of moderating loss near the tip, can be better utilized for rotors of CVD, in comparison to free vortex design.Compared to free vortex design, FSW applied to blades of CVD was found especially beneficial in loss reduction also away from the endwalls, via shortening the flow paths on the suction side — being anyway elongated by the radially outward flow due to CVD —, and thus, reducing the effect of wall skin friction. The necessity of correcting the swept blades was pointed out for matching with the prescribed CVD circulation distribution.Copyright © 2012 by ASME

Journal ArticleDOI
TL;DR: In this paper, an analytical solution of the equation of motion for the axial flow of an incompressible viscoplastic fluid (represented by the Hershel-Bulkley equation) in a long concentric annulus under isothermal, fully developed, and creeping conditions and subject to true or apparent wall slip is provided.
Abstract: The flow of non-Newtonian fluids in annular geometries is an important problem, especially for the extrusion of polymeric melts and suspensions and for oil and gas exploration. Here, an analytical solution of the equation of motion for the axial flow of an incompressible viscoplastic fluid (represented by the Hershel–Bulkley equation) in a long concentric annulus under isothermal, fully developed, and creeping conditions and subject to true or apparent wall slip is provided. The simplifications of the analytical model for Hershel–Bulkley fluid subject to wall slip also provide the analytical solutions for the axial annular flows of Bingham plastic, power-law, and Newtonian fluids with and without wall slip at one or both surfaces of the annulus.

Journal ArticleDOI
TL;DR: In this paper, the flow in a centrifugal compressor was computed using large eddy simulation (LES) and the investigated geometry is that of a ported shroud compressor with a 10 blade impeller with an exducer.
Abstract: The flow in a centrifugal compressor has been computed using large eddy simulation (LES). The investigated geometry is that of a ported shroud compressor with a 10 blade impeller with an exducer di ...

Journal ArticleDOI
TL;DR: It was found that the experimental results were close to those obtained by CFD and had thus validated the CFD model, which could complement the limitation of the measurement in assessing the more detailed flow fields of the axial flow pump.
Abstract: A magnetically suspended axial flow blood pump is studied experimentally in this article. The pump casing enclosed a three-blade straightener, a two-blade impeller shrouded by a permanent magnet-embedded cylinder, and a three-blade diffuser. The internal flow fields were simulated earlier using computational fluid dynamics (CFD), and the pump characteristic curves were determined. The simulation results showed that the internal flow field was basically streamlined, except the diffuser region. Particle image velocimetry (PIV) measurement of the 1:1 pump model was conducted to validate the CFD result. In order to ensure the optical access, an acrylic prototype was fabricated with the impeller driven by a servomotor instead, as the magnet is opaque. In addition to the transparent model, the blood analog fluid with the refractive index close to that of acrylic was used to avoid refraction. According to the CFD results, the axial flow blood pump could generate adequate pressure head at the rotating speed of 9500rpm and flow rate of 5L/min, and the same flow condition was applied during the PIV measurement. Through the comparisons, it was found that the experimental results were close to those obtained by CFD and had thus validated the CFD model, which could complement the limitation of the measurement in assessing the more detailed flow fields of the axial flow pump.

Patent
01 Sep 2012
TL;DR: In this article, a prechamber spark plug may have an aspect ratio and hole pattern to induce a rotational flow of fuel-air in-filling streams inside the pre-chamber volume.
Abstract: A prechamber spark plug may have a prechamber having a pre-determined aspect ratio and hole pattern to achieve particular combustion performance characteristics. The aspect ratio and hole pattern may induce a rotational flow of fuel-air in-filling streams inside the prechamber volume. The rotational flow of the fuel-air mixture may include both radial flow and axial flow characteristics based on the aspect ratio and hole pattern. Axial flow characteristics can include a first axial direction proximate the periphery of the rotational flow and a counter second axial direction approaching the center of the rotational flow. The radial and axial flow characteristics may further include radial air-fuel ratio stratification and/or axial air-fuel ratio stratification. The rotational flow, the radial flow and the axial flow may be adjusted by alteration of the aspect ratio and hole pattern to achieve particular combustion performance characteristics in relation to a wide variety of spark gap geometries.

Journal ArticleDOI
TL;DR: In this paper, the performance of a closed cycle gas turbine with supercritical carbon dioxide as a working fluid was evaluated using a reduced scale turbomachine and the aerodynamic characteristics of a compressor were examined.

Journal ArticleDOI
TL;DR: In this paper, a viscous 3D turbulent simulation has been carried out in an experimentally tested model of axial flow hydraulic turbine at different operating regimes and global and local parameters have been computed.

Journal ArticleDOI
TL;DR: In this paper, the laminar swirl flow in a straight pipe is revisited and solved analytically by using prescribed axial flow velocity profiles based on two axial velocity profiles, namely a slug flow and a developed parabolic velocity profiles.

Journal ArticleDOI
TL;DR: In this article, a numerical simulation of 3D flow field is performed in a 1.5-stage axial compressor with airfoil-probes installed at the stator leading-edge (LE).

Journal ArticleDOI
TL;DR: In this paper, the authors used CFD coupled with semi-empirical aeroacoustic models to predict the wall pressure fluctuations in axial flow fans, using Reynolds Averaged Navier-Stokes (RANS) equations.

Journal ArticleDOI
TL;DR: In this article, the authors propose an optimization strategy for the preliminary stage of turbomachinery design, based on the application of a throughflow code in the context of a fully automated optimization strategy.
Abstract: This work proposes an optimization strategy for the preliminary stage of turbomachinery design, based on the application of a throughflow code in the context of a fully automated optimization strategy. The code solves for the circumferentially-averaged flow equations, including the effects of aerodynamic and friction forces and of blade thickness; the outcome of the code is the flow distribution on the meridional surface. In this research the definition of an ‘optimal’ mean flow surface is the final aim of a multi-objective optimization procedure, in which non-concurrent goals are simultaneously considered. Evolutionary algorithms are used in the global optimization process, based on the coupling of a Genetic Algorithm with a metamodel.The optimization method is applied to a low speed axial compressor, for which the optimization goals are the minimization of aerodynamic loss and discharge kinetic energy at the exit of the stage, as well as the uniformity of work exchange along the blade span. The method proves to match all the objectives, providing a clear improvement with respect to classical and well-established design methods.Copyright © 2012 by ASME

Journal ArticleDOI
TL;DR: In this paper, an axial cyclone-based inline oil/water separator is studied numerically and experimentally, showing an annular region with reversed axial flow and declining rotation due to friction at the wall, giving a qualitative agreement between numerical and experimental data.
Abstract: An inline oil/water separator based on an axial cyclone is studied numerically and experimentally. Single phase measurements were done with LDA and compared with numerical data, obtained with Reynolds avaraged Navier-Stokes equations with the Reynolds-stress model SSG. Results show an annular region with reversed axial flow and declining rotation due to friction at the wall, giving a qualitative agreement between numerical and experimental data. A method is introduced to determine the phase distribution inside a liquid-liquid axial cyclone, based on electric conductivity. Preliminary results indicate a time-dependent oil-rich kernel. Presented results for the separation efficiency of the tested axial cyclone indicate the need for better understanding of swirling flow.

Journal ArticleDOI
TL;DR: In this paper, a two-stage compression system consisting of two compressors with the low-pressure end as inverter twin rolling piston and the high pressure end as non-inverter isolated rolling piston, based on the geometric model of compressor, and by application of the theories such as mass or energy conservation equations, mass leakage loss model, heat transfer, etc.
Abstract: Aimed at a two-stage compression system consisting of two compressors with the low-pressure end as inverter twin rolling piston and the high-pressure end as non-inverter isolated rolling piston, based on the geometric model of compressor, and by application of the theories such as mass or energy conservation equations, mass leakage loss model, heat transfer, etc, this paper established a dynamic compressor coupling model in a two-stage compression system with variable capacity, which was experimentally verified. It was revealed that the two-stage compression was not a continuous compression process. The intermediate pressure has the fluctuation characteristics. Among all factors related to the intermediate pressure, the effect of the ratio of the theoretical displacement of the low-stage compressor to that of the high-stage compressor on the intermediate pressure was the most vital determinant. The intermediate pressure was sensitive to the variation of heating capacity, but it was passivated to the heating COP.