Maximum Mach Number Research Articles

Thermodynamic modeling and analysis of ammonia injection pre-compressor cooling cycle: A novel scheme for high Mach number turbine engines

Mass injection pre-compressor cooling (MIPCC) is one of the significant technologies to extend the operating envelope of turbine engines. In this paper, a new high Mach number turbine scheme is proposed with liquid ammonia injection instead of water injection. The basic properties of ammonia, especially the boiling point, latent heat of vaporization and auto-ignition temperature, are introduced. To evaluate the engine performance, a thermodynamic model incorporating the ammonia mass injection pre-compressor cooling (Ammonia MIPCC) process is developed. The accuracy of the model is demonstrated by verifying the design point, operating line, and Ammonia MIPCC processes. Simulations show that the Ammonia MIPCC process is mainly suitable for extended operating Mach number envelopes. Ammonia injection should be avoided for normal operating conditions because it causes a decrease in specific impulse. Through liquid ammonia injection, the operating Mach number of the turbine engine is increased from 3.1 to about 3.5. Moreover, the maximum operating Mach number (MOM) limit of the Ammonia MIPCC engine is investigated. Pre-Compressor cooling requirements and combustor heat release limits jointly constrain the amount of ammonia injection, which prevents further expansion of the MOM. Furthermore, the Ammonia MIPCC engine has the advantage of greater specific thrust at the same Mach number compared to water injection, and with Mach numbers greater than 3.36, the Ammonia MIPCC engine has a specific impulse advantage. In general, the Ammonia MIPCC engine is an effective solution for a high Mach number turbine.

Carbon-dioxide-to-methanol intensification with supersonic separators: Extra-carbonated natural gas purification via carbon capture and utilization

A novel carbon-capture-and-utilization route from extra-carbonated natural gas using low-cost/low-carbon chloralkali hydrogen is disclosed. Methanol and methane-rich gas are produced without direct carbon emissions and also with low indirect emissions assuming the local electricity-matrix as 87% non-emitting. Carbon dioxide removed from raw natural gas via cryogenic extractive distillation with methanol entrainer, feeds a new Carbon-Dioxide-to-Methanol hydrogenation route intensified by supersonic separators with liquid water injection for greater methanol conversion per pass in the synthesis-loop and greater methanol recovery in the separation system. Intensified Carbon-Dioxide-to-Methanol is designed economically optimizing water/methanol injection-ratios and maximum Mach numbers of supersonic separators. Extra-carbonated natural gas processing coupled to intensified Carbon-Dioxide-to-Methanol is techno-economically assessed, demonstrating that supersonic intensification entails 2% greater methanol production, 11% less power consumption and 7.5% greater net value comparatively to non-intensified counterpart. The intensified process removes 99.2% of CO2 from extra-carbonated gas and was analyzed at two methanol scales [8021.5 t/d, 1692.3 t/d] giving, respectively, [9.5, 41.5] payback-years, and [2896.4MMUSD, 41.37MMUSD] net values (60years). A critical feasibility factor is low-cost/low-carbon by-product hydrogen from chloralkali industries, for which the break-even prices were respectively evaluated for the two scales as [685USD/tH2, 358USD/tH2]. A third, better and safer, option is to couple intensified Carbon-Dioxide-to-Methanol to large-scale Carbon-Dioxide-to-Enhanced-Oil-Recovery providing hedging against insufficient offer of low-cost/low-carbon hydrogen while practically keeping the project net value (60years) despite twofold investment.

Numerical investigations of the slot blowing technique on the hypersonic vehicle for drag reduction

In this paper, the slot blowing flow-control technique is numerically studied for the hypersonic vehicle, aiming for skin friction drag reduction. Firstly, the influence patterns of the slot blowing parameters on friction drag reduction are analyzed based on a flat-plate boundary layer flow. It is concluded that there is an optimal blowing Mach number to optimize the drag reduction effect with other parameters unchanged, while as the increase of blowing pressure ratio, the skin friction drag reduction effect first increases and then remains almost invariant. On this basis, a slot blowing methodology is designed for a typical lifting-body hypersonic vehicle with a 10 mm slot installed on the middle of the windward side. Under the typical freestream condition of Mach 15 and 60 km altitude, numerical results indicate that the slot blowing with the blowing maximum Mach number 2 and blowing pressure ratio 1 could achieve a remarkable control effect of increasing the lift-drag ratio by about 10.55%. After that, the parametric study of slot blowing for the lifting-body vehicle reveals that when the slot height is increased from 10 mm to 20 mm, the lift-to-drag ratio rises slightly after paying the price of doubling the blowing mass flow rate, which indicates that increasing the slot height does not obtain a more efficient result. As for the effect of the slot position along the streamwise, moving the slot position forward could receive a higher total drag reduction rate with less blowing mass flow rate while also leads to a slight decrease of lift. Thus, the practical application of the slot blowing technique needs to consider the variations of the drag and lift comprehensively.

Three-dimensional hydrodynamics simulations of shell burning in Si/O-rich layer of pre-collapse massive stars

We perform three-dimensional (3D)hydrodynamics simulations of shell burning in the silicon-and oxygen-rich layers in pre-collapse massive stars.Weadoptanon-rotating27 M⊙ starhaving anextended O/Si/Ne layer and afast-rotating 38 M⊙ star having a Si/Olayer, that has experienced chemically homogeneousevolution. Both pre-collapse stars showlarge-scale turbulent motion with a maximum Mach number of ~0.1 in the convective layers activated byneonand oxygenshellburning.The radialproflieoftheangle-averaged mass fraction distributioninO/Si/Ne layer is more homogeneous in the 3D simulation compared to the 1D evolution for the 27 M⊙ star. The angle-averaged specific angular momentum in the Si/O layer of the fast-rotating 38 M⊙ star tends to become roughly constant in the convective layer of the 3D simulation, which is not considered in the 1D evolution.

Investigation of the Influence of Laval Nozzle Throat Width via Euler-based Flow Simulation

The nozzle is a kind of widely used fluid equipment. It is very important to study its internal flow for improving nozzle performance or improving nozzle design. In this paper, the numerical simulation method based on the Euler equation is used to solve the flow in the nozzle. Euler equations are solved by an explicit finite difference method, including discretization, pre-estimation and correction steps. Boundary treatment for the subsonic inlet and supersonic outlet are discussed. The flow characteristics inside a Laval nozzle are analysed based on the numerical results. The influence of Laval nozzle throat width on the nozzle flow is investigated by comparing three nozzles. It is observed that the dimensionless pressure, temperature, and density of the three nozzles have similar trends. While the maximum Mach number at the outlet decreases with the increase of the throat width. In short, the throat width should be decreased if a larger outlet speed of the flow is needed.

Nozzle Flow Simulation by Small Disturbance Approximation and Euler Method

The nozzle is a kind of equipment with a wide range of usage in the aerospace industry, of which its performance is vital for rocket engines by changing the geometry of the inner wall of the pipe section to accelerate the airflow. There are two types of nozzles commonly used: one is a tapered nozzle, and the other is a Laval nozzle. To analyze the flow phenomenon in nozzle is vital before transferring prototype design into industrial production, whether by laboratory experiment or computational simulation. In this paper, two different numerical methods are adopted to simulate gas behavior inside a simplified nozzle with upper and bottom symmetrical bumps. The first is to solve one dimensional Euler equations, and the other is to solve a scalar variable named velocity potential with small disturbance equations (SDE). The solutions under various inlet Mach numbers are compared by analysing the velocity fields and Mach number contours obtained by these two approaches. Similarities and differences between the Euler method and the potential SDE method for subsonic flow and supersonic flow are the key emphases in this work. For either subsonic or supersonic flow, the Mach number distribution along the nozzle’s center line shows a consistent trend for both methods. In contrast, the values of maximum or minimum Mach number have corresponding differences. Moreover, by using potential SDE simulation, several types of shock waves are successfully captured. All results show that the incoming airflow decelerates at the leading edge of the nozzle then accelerates when passing through the bumps, and finally decelerates back to the speed of inlet flow. The difference is that flows with varied Mach numbers has distinct velocity distributions in the nozzle.

Flow behavior and thermal separation mechanism on vortex tube

Flow behaviour and thermal separation mechanism on vortex tubes have been studied numer-ically. Rapid expansion indicated by high-pressure gradient near the inlet and the exit ports contributes to energy separation on the parallel and the counter flow vortex tubes. It creates a cooling process at the core region and drives an internal and rotational energy transfer to the peripheral region, then increases the gas temperature at the periphery along with friction due to the presence of the confined wall. Static temperature is related to static pressure in such a way that low pressure leads to the low static temperature at the same region inside the vortex tube. On the other hand, the high total temperature is found in the region with the low dynamic velocity. For both vortex tubes, the flow fields are mainly governed by the tangential velocity at the periphery and by the axial velocity at the core region. The maximum Mach number values based on the maximum tangential velocities in the inlet area for the counter and the parallel flow vortex tubes are 0.689 and 0.726, respectively, so both are compressible and subsonic flows. For the same size of geometry and boundary conditions, the parallel flow vortex tube has higher COP than the counter flow vortex tube i.e. 0.26 and 0.25, respectively.

The general applicability of self-similar solutions for thermal disc winds

ABSTRACT Thermal disc winds occur in many contexts and may be particularly important to the secular evolution and dispersal of protoplanetary discs heated by high energy radiation from their central star. In this paper, we generalize previous models of self-similar thermal winds – which have self-consistent morphology and variation of flow variables – to the case of launch from an elevated base and to non-isothermal conditions. These solutions are well-reproduced by hydrodynamic simulations, in which, as in the case of isothermal winds launched from the midplane, we find winds launch at the maximum Mach number for which the streamline solutions extend to infinity without encountering a singularity. We explain this behaviour based on the fact that lower Mach number solutions do not fill the spatial domain. We also show that hydrodynamic simulations reflect the corresponding self-similar models across a range of conditions appropriate to photoevaporating protoplanetary discs, even when gravity, centrifugal forces, or changes in the density gradient mean the problem is not inherently scale free. Of all the parameters varied, the elevation of the wind base affected the launch velocity and flow morphology most strongly, with temperature gradients causing only minor differences. We explore how launching from an elevated base affects Ne ii line profiles from winds, finding it increases (reduces) the full width at half maximum (FWHM) of the line at low (high) inclination to the line of sight compared with models launched from the disc midplane and thus weakens the dependence of the FWHM on inclination.

Effect of orifice spacing on twin circular parallel compressible jets

Abstract The interaction of Mach 0.5, 0.8, and 1.0, parallel, twin circular jets issuing from orifices with center-to-center spacing S/D, where S is the center-to-center distance and D is orifice diameter, 2, 4 and 6 has been investigated experimentally. The characteristics of twinjets are analyzed based on the centerline Mach number decay, exit Mach number and ratio of orifice spacing. As the spacing between the orifice increases, the maximum Mach number point of the combined jet moves downstream. For the Mach numbers studied it is found that as the S/D increases the effect of the counter-rotating vortices on jet mixing decreases. The rate of the twinjet interaction also decreases with S/D increase. As the jets propagate downstream their center-to-center distance decreases continuously and the jets merge to become single jet, for all S/D studied.

Dynamics of Shock Waves Interacting With Laminar Separated Transonic Turbine Flow Investigated by High-Speed Schlieren and Surface Hot-Film Sensors

Abstract The results presented in this paper are based on experimental investigations on a generic transonic low pressure turbine profile at high subsonic exit Mach numbers. Here, the flow on the suction side reaches a maximum isentropic Mach number of approximately 1.2 and features a large separation bubble in a transonic flow regime characterized by surface hot-film measurements. The measurements are supplemented by Schlieren images recorded with a high-speed camera at 19.2 kHz. A highly unsteady normal shock wave on the suction side is observable upstream of the trailing edge. It is interacting with laminar separated flow which is rarely documented in literature. The interaction of the normal shock with the boundary layer flow seems to amplifies the ongoing transition process over the separation bubble and the flow reattaches shortly downstream. A statistical analysis of the Schlieren images reveals characteristic low frequencies of the shock wave motions and a pulsation of the separation bubble. Additionally, the statistical information of the time-dependent signal from the surface hot-film sensors demonstrate the instabilities influencing the boundary layer linked to the unsteadiness in the main flow.

Numerical investigation on startup characteristics of high temperature heat pipe for nuclear reactor

Heat pipe cooled reactor (HPR) has a good adaptability to portable power system, which is popular in recent years. Due to the particularity of alkali-metal working fluid, the deep understanding of startup characteristics of high temperature heat pipe from frozen state is essential for the development of HPRs. In this paper, a three-stage frozen startup model is developed to describe the thermal behavior of heat pipe during the startup process, and the continuum flow in the vapor space is modeled as a one-dimensional compressible flow. A numerical code is carried out, in which the governing equations are discretized by Finite Element Method (FEM), and then the code is used to simulate the startup performance of a NaK heat pipe in HPRs. Numerical results indicate that the heat pipe startup behavior can be well described by the three-stage model. The NaK heat pipe is successfully started with a final consistency temperature of 834 K, although the entire second stage is restricted by the sonic limitation. The startup lasts 1550 s in total, and enters the second and third stage at 230 s and 650 s, respectively. After 1500 s, the maximum Mach number of vapor flow is lower than 0.1, which verifies the rationality of the one-dimensional compressible flow model of vapor. This work could provide a reference for the design and application of HPRs.

Relationship between solar energetic particle intensities and coronal mass ejection kinematics using STEREO/SECCHI field of view

Solar energetic particles (SEPs) accelerated from shocks driven by coronal mass ejections (CMEs) are one of the major causes of geomagnetic storms on Earth. Therefore, it is necessary to predict the occurrence and intensity of such disturbances. For this purpose we analyzed in detail 38 non-interacting halo and partial halo CMEs, as seen by the Solar and Heliospheric Observatory/Large Angle and Spectrometric Coronagraph, generating SEPs (in > 10 MeV, > 50 MeV, and > 100 MeV energy channels) during the quadrature configuration of the Solar TErrestrial RElations Observatory (STEREO) twin spacecrafts with respect to the Earth, which marks the ascending phase of solar cycle 24 (i.e., 2009–2013). The main criteria for this selection period is to obtain height–time measurements of the CMEs without significant projection effects and in a very large field of view. Using the data from STEREO/Sun Earth Connection Coronal and Heliospheric Investigation (STEREO/SECCHI) images we determined several kinematic parameters and instantaneous speeds of the CMEs. First, we compare instantaneous CME speed and Mach number versus SEP fluxes for events originating at the western and eastern limb; we observe high correlation for the western events and anticorrelation for the eastern events. Of the two parameters, the Mach number offers higher correlation. Next we investigated instantaneous CME kinematic parameters such as maximum speed, maximum Mach number, and the CME speed and Mach number at SEP peak flux versus SEP peak fluxes. Highly positive correlation is observed for Mach number at SEP peak flux for all events. The obtained instantaneous Mach number parameters from the emperical models was verified with the start and end time of type II radio bursts, which are signatures of CME-driven shock in the interplanetary medium. Furthermore, we conducted estimates of delay in time and distance between CME, SEP, and shock parameters. We observe an increase in the delay in time and distance when SEPs reach peak flux with respect to CME onset as we move from the western to the eastern limb. Western limb events (longitude 60°) have the best connectivity and this decreases as we move towards the eastern limb. This variation is due to the magnetic connectivity from the Sun to the Earth, called the Parker spiral interplanetary magnetic field. Comparative studies of the considered energy channels of the SEPs also throw light on the reacceleration of suprathermal seed ions by CME-driven shocks that are pre-accelerated in the magnetic reconnection.

Simulation of propagation and diffraction of a shock wave in a planar curvilinear channel

Subject of Research. Numerical simulation of a shock wave propagation in a plane curved channel is considered on the basis of numerical simulation data. Method. Calculations of an inviscid compressible gas were carried out on the basis of unsteady two-dimensional Euler equations. Discretization of the basic equations was carried out using the finite volume method. Calculations were carried out for different channels with different radius of curvature and Mach numbers of the initial wave. To find the angular position of the front at the current time, the absolute value of the derivative of the density with respect to the angular coordinate was used. The calculation results were compared with the data of a physical experiment. Main Results. The features of the emerging shock-wave flow pattern and its development in time are discussed. The shock-wave configuration observed in channels with different radii of curvature is compared. Some differences in the curvature change of the front of shock waves formed in channels with different radius of curvature are shown. The size of the Mach leg and its change with time depending on the intensity of the initial wave and the size of the annular gap is the angular coordinate function corresponding to the position of the shock wave at the current time. While the maximum Mach number on the outer wall is relatively weakly dependent on the initial wave velocity, the Mach number on the bottom wall decreases with increasing Mach number at the channel entrance. The performed numerical studies show that in all variants there are no non-physical oscillations of the solution. Practical Relevance. The study of shock-wave and detonation processes is of interest for using their potential in pulsed installations and power systems for aircraft and rockets. The calculation results are important for the search of the new flow patterns that guarantee the formation of self-sustained detonation combustion in the combustion chambers of promising propulsion systems. Adjusting the size of the annular gap gives the possibility to select a geometric configuration that will provide the formation of an optimal triple shock wave structure, as well as the required intensity and size of the Mach wave.

Arbitrary amplitude ion acoustic double layer in plasma with k-distributed electrons and negative ions

In this paper we have discussed the consequence of superthermal electrons and negative ion concentration on the arbitrary amplitude ion-acoustic double layers (IA-DLs) for plasma comprising the hot negative and positive ions with kappa distribution electrons. The energy equation is deduced for ion acoustic waves using Pseudo potential technique. We have investigated different parametric regimes for the existence of rarefactive and compressive ion acoustic DLs. The existence of double layers in term of minimum and maximum Mach number has calculated numerically. The effect of spectral index k on the amplitude of DLs and depth of Sagdeev potential has been discussed in detail. From numerical analysis, it is found that the compressive DLs exist at low values of α and rarefactive double layer exist at higher values of α. On the other hand, the effect of ionic temperature ratio (σ 1 and σ 2) plays significant role for the formation of double layer. Our analytical work also shows that the system supports coexistence of compressive and rarefactive DLs. It is also observed that the mass ratio affect the basic properties of DLs. We expect that the present results may be used to explain the ion-acoustic double layer in space plasma, where two ionic species and superthermal electrons are observed NO52.35g.

Preliminary study on heat flux measurement data of TT-0 flight test

With the explosive development of aerospace science, the design of the new generation airliner at higher speeds is attracting more attentions. To achieve this goal, it is necessary to achieve accurate prediction of the aerodynamic heating / force loads and successful reduction of drag and heat flux. As a remedy for the existing studies which are based upon the CFD and wind tunnel tests, this study presents a flight test for the drag and heat reduction spike technology. The principal goals of this flight test were to provide reference for verifying the accuracy of the prediction technology on ground and promote the development of the drag and heat reduction technology. By adopting the OS-X rocket, the TT-0 test vehicle designed by Shenyang Aircraft Design & Research Institute reached a maximum Mach number of 5.8 and a maximum altitude of 38 km. Hypersonic and supersonic pressure data by pressure scanning valves and heat fluxes by gauges at different locations were obtained successfully. Also, heat fluxes obtained by in-house CFD code are illustrated in comparison with the flight data. The results indicate that the numerical errors are large in most cases. More technologies, such as more CFD codes and more numerical procedures, should be adopted to conduct studies on this issue in the future.

Flight Tests of Passive Flow Control for Suppression of Cavity Aeroacoustics

This research focused on furthering the current understanding of the flowfield inside a cavity under typical flight conditions. The flight envelope included altitudes of up to 40,000 ft and maximum Mach number of 1.28 and included several test points between Mach 0.9 and 1.1, which are challenging to isolate in wind tunnel testing due to tunnel wall interference. The pod was instrumented to collect aeroacoustic pressures and qualitative flowfield imaging for a cavity with a length-to-depth ratio of four. Test missions were flown with several different passive flow control configurations, and their respective effect on acoustic properties and flow patterns were collected. Flow control comprising a rod-in-a-crossflow or a traditional sawtooth spoiler was generally found to reduce sound pressure level, though the extent of effectiveness varied with flight condition. The flow control devices installed at or below the cavity exit plane were found to have little influence. Tuft-based flow visualization complemented the effort, for one example, by demonstrating the outward flow near the cavity lip for the sawtooth spoiler.

Energy and configuration management strategy for battery/fuel cell/jet engine hybrid propulsion and power systems on aircraft

Hybridization of power sources by combining their performance advantages and balancing disadvantages is becoming a feasible solution during the process of designing electricity propulsion systems on aircraft. Novel hybrid propulsion and power (HPP) systems combining batteries, fuel cells, jet engines are proposed in this paper, which can respectively provide high thrust and low thrust specific fuel consumption in the take-off and cruise segment. The mathematical models are built and the main parts are validated to determine the performance and size parameters of these components. The main conclusions are as follows: (1) Under the cruise segment, the reduction rate of fuel cell weight slows with decreasing fuel utilization. Meanwhile, the thrust and thrust specific fuel consumption are both increased. These values of 4 kN and 15.32 g/s/kN are reached to achieve the endurance of 19.6 hours. (2) The speed characteristic of the HPP system is complicated, but the thrust of the system is almost only affected by air mass flow with varying altitudes. It can vary from 100% to about 50% by adjusting the fuel flow rate in the afterburner. (3) The flight envelop of the aircraft are limited by the thrust/drag balance and fuel cell operating temperature. The highest operating altitude is about 27.5 km, with a maximum working Mach number of 1.8. (4) The weight ratios of the fuel cell, motor, battery, and fuel loaded are 15%, 12%, 8%, and 56%. Most of the fuel (89%) is consumed in the cruise segment.

Experimental investigation of diaphragm material combinations in a small-scale shock tube

PurposeThe purpose of this study is to experimentally investigate the trends in shock wave Mach number that were observed when different diaphragm material combinations were used in the small-scale shock tube.Design/methodology/approachA small-scale shock tube was designed and fabricated having a maximum Mach number production capacity to be 1.5 (theoretically). Two microphones attached in the driven section were used to calculate the shock wave Mach number. Preliminary tests were conducted on several materials to obtain the respective bursting pressures to decide the final set of materials along with the layered combinations.FindingsAccording to the results obtained, 95 GSM tracing paper was seen to be the strongest reinforcing material, followed by 75 GSM royal executive bond paper and regular 70 GSM paper for aluminium foil diaphragms. The quadrupled layered diaphragms revealed a variation in shock Mach number based on the position of the reinforcing material. In quintuple layered combinations, the accuracy of obtaining a specific Mach number was seen to be increasing. Optimization of the combinations based on the production of the shock wave Mach number was carried out.Research limitations/implicationsThe shock tube was designed taking maximum incident shock Mach number as 1.5, the experiments conducted were found to achieve a maximum Mach number of 1.437. Thus, an extension to further experiments was avoided considering the factor of safety.Originality/valueThe paper presents a detailed study on the effect of change in the material and its position in the layered diaphragm combinations, which could lead to variation in Mach numbers that are produced. This could be used to obtain a specific Mach number for a required study accurately, with a low-cost setup.

Steam ejector performance considering phase transition for multi-effect distillation with thermal vapour compression (MED-TVC) desalination system

The multi-effect distillation with thermal vapour compression (MED-TVC) desalination system is efficient to produce freshwater. The steam ejector performance is not fully understood as the phase transition has been ignored in many studies. The present work develops a two-phase condensing flow model to assess the steam ejector performance considering nonequilibrium condensation phenomena. The transition of the flow structure from an under-expanded flow to an over-expanded flow in the steam ejector is investigated in detail. We present that the maximum Mach number can reach 4.02 in the under-expanded flow, which is weakened to 2.88 in the over-expanded flow. The steam undergoes several expansion-compression processes in the steam ejector in the under-expanded flow, which induces the formation and evaporation of massive droplets. In the over-expanded flow, the steam is compressed and then expanded after leaving the primary nozzle and the condensation process is not observed in mixing and constant sections. The increasing suction chamber pressure significantly improves the entrainment ratio while leading to an increasing entropy loss coefficient. The entrainment ratio is improved from 0.25 for the under-expanded flow to 1.69 for the over-expanded flow, while the entropy loss increases from 0.081 for the under-expanded flow to 0.29 for the over-expanded flow. This indicates that the transition of the flow structure from an under-expanded flow to an over-expanded flow can entrain more steam from the last effect while causes more entropy losses in a steam ejector for the MED-TVC desalination system.

Comparison of Swing and Tilting Check Valves Flowing Compressible Fluids.

Although check valves have attracted a lot of attention, work has rarely been completed done when there is a compressible working fluid. In this paper, the swing check valve and the tilting check valve flowing high-temperature compressible water vapor are compared. The maximum Mach number under small valve openings, the dynamic opening time, and the hydrodynamic moment acting on the valve disc are chosen to evaluate the difference between the two types of check valves. Results show that the maximum Mach number increases with the decrease in the valve opening and the increase in the mass flow rate, and the Mach number and the pressure difference in the tilting check valve are higher. In the swing check valve, the hydrodynamic moment is higher and the valve opening time is shorter. Furthermore, the valve disc is more stable for the swing check valve, and there is a periodical oscillation of the valve disc in the tilting check valve under a small mass flow rate.