Turbulent Vortex Research Articles

Leakage Characteristics of a Novel Hole-Pattern Damping Seal With Dovetail-Like Diversion Grooves: Numerical Simulation and Experiment

Abstract Reasonable design of the cavity shape of the damping hole effectively reduces the leakage rate of the hole-pattern damping seal (HPDS). A novel HPDS with dovetail-like diversion grooves was proposed, and the geometry outline of the dovetail-like diversion groove was described by using the hyperelliptic curve. Computational fluid dynamics commercial software was used to simulate the three-dimensional flow field of the dovetail-like hole-pattern damping seal (D-HPDS). The leakage characteristics of the damping seals with a typical circular hole, leaf-like hole, and dovetail-like hole were compared numerically and experimentally. The three-velocity zone model of HPDS was proposed to reveal the mechanism of leakage reduction effect of the D-HPDS compared with typical circular hole-pattern damping seal (C-HPDS). The influence of operating parameters and key geometric parameters on leakage characteristics of the D-HPDS was studied. The results show that the leakage rate of the D-HPDS can be reduced significantly in a wide range of operating conditions and seal clearance compared with the typical C-HPDS, and the maximum reduction amplitude of leakage rate reaches up to 25% at a relatively small pressure ratio. The main reasons for the leakage reduction of the D-HPDS can be explained by the fact that the change of outflow direction from the cavity induced by the interaction effect of adjacent cavities, further resulting in the formation of turbulent vortex in the cavity and the low-speed flow zone in the sealing gap. For the design goal of low leakage rate, the inclined angle of the dovetail-like diversion groove is appropriate between 45 deg and 55 deg, the tip extension ratio is appropriate between 0.8 and 0.95.

Numerical investigation of cavitation-vortex structures around a sphere with boundary data immersion method

The boundary data immersion method (BDIM) coupled with the artificial compressibility method is applied to investigate the interaction of the cavitation-vortex dynamics around a sphere. The convolution of governing equation with a nascent delta kernel is employed to smooth the transition region between the solid and the fluid subdomain. Therefore, the BDIM addresses a key problem with smooth immersion boundary method in representing the discontinuity of the velocity gradient ∂u/∂y at the wall when considering flows with intermediate to high Reynolds numbers. In addition, a pseudo-time derivative of the pressure multiplied by an artificial-compressibility factor is added to the continuity equation. The developed coupling algorithm can accurately capture the unsteady cavitation characteristics, which is consistent with the previous experimental data. Subsequently, the typical vortex identification methods and the turbulent kinetic energy (TKE) transport equation are applied to analyze the interaction between the cavitation dynamics and turbulence vortices structures. A series of turbulent vortices are captured with the cloud cavity shedding. Moreover, it is found that the unsteady cavity topology will promote the generation of TKE.

A kinetic energy–and entropy-preserving scheme for compressible two-phase flows

Accurate numerical modeling of compressible flows, particularly in the turbulent regime, requires a method that is non-dissipative and stable at high Reynolds (Re) numbers. For a compressible flow, it is known that discrete conservation of kinetic energy is not a sufficient condition for numerical stability, unlike in incompressible flows.In this study, we adopt the recently developed conservative diffuse-interface method (Jain et al., 2020 [30]) for the simulation of compressible two-phase flows. This method discretely conserves the mass of each phase, momentum, and total energy of the system and consistently reduces to the single-phase Navier-Stokes system when the properties of the two phases are identical. We here propose discrete consistency conditions between the numerical fluxes, such that any set of numerical fluxes that satisfy these conditions would not spuriously contribute to the kinetic energy and entropy of the system. We also present a set of numerical fluxes—which satisfies these consistency conditions—that results in an exact conservation of kinetic energy and approximate conservation of entropy in the absence of pressure work, viscosity, thermal diffusion effects, and time-discretization errors. Since the model consistently reduces to the single-phase Navier-Stokes system when the properties of the two phases are identical, the proposed consistency conditions and numerical fluxes are also applicable for a broader class of single-phase flows.To this end, we present coarse-grid numerical simulations of compressible single-phase and two-phase turbulent flows at infinite Re, to illustrate the stability of the proposed method in canonical test cases, such as an isotropic turbulence and Taylor-Green vortex flows. A higher-resolution simulation of a droplet-laden compressible decaying isotropic turbulence is also presented, and the effect of the presence of droplets on the flow is analyzed.

A Study on Swirling Jets Flow Controlled by Two Tandem Bodies

This study presents the effects of using two centerbodies arranged in tandem on the flow and velocity properties of swirling jets. The centerbodies are installed concentrically downstream of the jets to modify the wake. Smoke flow visualization was employed to illustrate the flow behaviors, while the particle image velocimetry technique was utilized to investigate the velocity fields, turbulent properties, vorticities, and Lagrangian time and length scales. The toroidal recirculation and vortex shedding are found near the field using one centerbody. The recirculation zone is evolved from the edge of the centerbody, while the vortex shedding is formed by the interaction between the central and the annular jets. Since two centerbodies are installed, two four-way saddles are located near the rim of the upstream centerbody to associate two pairs of vortices. A large momentum of the annular jet dominates the flow field; therefore, the central jet forms dual-rotating vortices at downstream centerbody. The turbulent intensity and vorticity along the central axis in the case of two centerbodies are extremely lower than those in the case of one centerbody. Large turbulent intensity and vorticity are located around the shear layers of jets. This promotes a better mixing efficiency of the swirling jets.

Self-similar hierarchy of coherent tubular vortices in turbulence.

Energy transfers from larger to smaller scales in turbulence. This energy cascade is a process of the creation of smaller-scale coherent vortices by larger ones. In our recent study (Yoneda, Goto and Tsuruhashi 2022 Nonlinearity 35, 1380-1401), we reformulated the energy cascade in terms of this stretching process and derived the law of the energy spectrum under physically reasonable assumptions. In the present study, we provide a quantitative verification of these assumptions by using direct numerical simulations. We decompose developed turbulence in a periodic cube into scales by using the band-pass filter and identify the axes of coherent tubular vortices by the low-pressure method. Even when the turbulent kinetic energy and its dissipation rate temporally fluctuate about their temporal means, the total length of the vortices at each scale varies little with time. This result is consistent with our assumption of the temporal stationarity on the vorticity decomposition. The present numerical analysis also shows that the hierarchy of vortex axes is self-similar in a wide range of scales, i.e. in the inertial range and a lower part of the dissipation range and that the volume fraction occupied by the tubular vortices at each scale is independent of the scale.This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 2)’.

Shock wave formation from head-on collision of two subsonic vortex rings.

Vortex ring collisions have attracted intense interest in both water and air studies (Baird in Proc R Soc Lond Ser Math Phys Sci 409:59–65, 1987, Poudel et al. in Phys Fluids 33:096105, 2021, Lim and Nickels in Nature 357:225, 1992, New et al. in Exp Fluids 57:109, 2016, Suzuki et al. in Geophys Res Lett 34, 2007, Yan et al. in J Fluids Eng 140:054502, 2018, New et al. in J Fluid Mech 899, 2020, Cheng et al. in Phys Fluids 31:067107, 2019, Hernández and Reyes in 29:103604, 2017, Mishra et al. in Phys Rev Fluids, 2021, Zednikova et al. in Chem Eng Technol 42:843–850, 2019, Kwon et al. in Nature 600:64–69, 2021). These toroidal structures spin around a central axis and travel in the original direction of impulse while spinning around the core until inertial forces become predominant causing the vortex flow to spontaneously decay to turbulence (Vortex Rings, https://projects.iq.harvard.edu/smrlab/vortex-rings). Previous studies have shown the collision of subsonic vortex rings resulting in reconnected vortex rings, but the production of a shock wave from the collision has not been demonstrated visibly (Lim and Nickels in Nature 357:225, 1992, Cheng et al. in Phys Fluids 31:067107, 2019). Here we present the formation of a shock wave due to the collision of explosively formed subsonic vortex rings. As the vortex rings travel at Mach 0.66 toward the collision point, they begin to trap high pressure air between them. Upon collision, high pressure air was imploded and released radially away from the axis of the collision, generating a visible shock wave traveling through and away from the colliding vortices at Mach 1.22. Our results demonstrate a pressure gradient with high pressure release creating a shock wave. We anticipate our study to be a starting point for more explosively formed vortex collisions. For example, explosives with different velocities of detonation could be tested to produce vortex rings of varying velocities.

In-Cylinder Cold-Flow Analysis - ‘A Comparison of Crank-Slider Engine and Crank-Rocker Engine’

Researchers and engineers are continuously working to improve the overall efficiency of internal combustion engines by modifying the engine designs and configurations. As new engine designs are introduced, the in-cylinder flow behaviour becomes more and more complex. The maximum output and efficiency that can be achieved from a single cylinder engine depends upon the amount of air entrapped in the combustion chamber during intake stroke. A novel crank-rocker (C-R) engine was designed and fabricated in Universiti Teknologi PETRONAS (UTP), Malaysia and is currently under optimization phase. This paper narrates the in-cylinder cold-flow analysis of the C-R engine considering widely used industrial automotive software, Converge CFD. The turbulent behaviour of the C-R engine was compared with that of the conventional crank-slider engine. The initial and boundary conditions for the C-R engine simulations were set according to the benchmarked crank-slider engine. RNG k-ε turbulence model was used to generate the data plots for tumble & swirl ratios, cylinder pressure, TKE, turbulent dynamic viscosity and vorticity at cold-flow conditions. It was observed that the C-R engine has better air scavenging properties and can achieve better air-fuel mixing that can lead to emission-free combustion. This study will help in understanding the turbulent airflow behaviour within the curved cylinder under the influence of rocking piston motion, and its advantageous flow properties compared to those in crank-slider engines.

Effects of cloud size and built-in obstacles on hydrogen cloud explosion using large eddy simulation

The purpose of this work is to evaluate hydrogen cloud explosion using large eddy simulation. The LES model combined with acoustical theory is firstly established and validated. Then the effects of cloud scale on flame dynamics and explosion pressure are explored. Finally, the effects of obstacle-induced turbulence on hydrogen cloud explosion are analyzed. The research works indicated that the LES model combined with acoustical theory could be able to reproduce flame acceleration and explosion pressure evolution. Maximum explosion pressure and maximum flame front velocity continue to increase with increasing cloud scale. The deviation values of flame radius of four cloud scales are 0.25 m, 0.5 m and 0.75 m, once beyond the critical value, the flame front velocity of larger cloud scale is lower than that of smaller cloud scale. The increase rate of flame front velocity and explosion pressure, not their peak value, will be certainly increased by built-in obstacles, which could be attributed to the couplings of turbulent vortex and moving flame.

Improving internal fluid stability of pump turbine in load rejection process by co-adjusting inlet valve and guide vane

Pumped storage plant(PSP) is a high efficient emission-free technology to balance the unstable electricity generation from renewable energy. In order to meet the variable requirements from power grid, the pumped storage units need to change working conditions frequently and quickly. Pump turbines have to run in transient processes, which stability affects safe operation of PSP directly. The load rejection of pump turbine is studied in this work, wherein the coordinated regulation of valve and guide vane is applied in this transition. This work aims at increasing the internal fluid stability of pump turbine, by reducing the change rate of pressure and improving flow regime. The combination of theoretical analysis and numerical simulation is the main research method, wherein wall sliding mesh technique is used to achieve continuous movements of valve core and guide vanes. Detached eddy simulation is adopted to solve the transient flow field, the fluid is characterized by a series of parameters like turbulent kinetic energy, pressure fluctuation and vortex evolution, etc. The results prove that a great contribution made by this co-adjusting method, it is beneficial to operation stability of system, especially for the final phase of load rejection.

Simultaneous measurement of the structures of the velocity and thermal boundary layers in the rod bundle channel

The complex geometry of the rod bundle fuel assemblies makes the measurement of velocity and temperature difficult, which hinders the design and optimization of the thermohydraulic performance of the advanced fuel assemblies. In the present study, Particle Image Velocimetry (PIV) and Laser-Induced Fluorescence (LIF) techniques are used to simultaneously measure and reconstruct the structures of the velocity and thermal boundary layers. The velocity and temperature distributions near the rod surface under different flow and heat transfer conditions are quantitatively analyzed and compared. The experimental results indicate that increasing the heat flux would increase the near-wall velocity gradient and decrease the temperature gradient. The buoyancy increases with the increase of the heat flux, reducing the turbulent fluctuation in the channel, thereby weakening the generation and diffusion of the turbulent vortex. The dimensionless velocity distribution is obtained by fitting the experimental data to the Spalding formula. Based on the structure of the boundary layer, the increase of buoyancy significantly reduces the proportion of the logarithmic law layer in comparison to the inner layer of the boundary layer. This weakens the convective heat transfer in the channel. The increase of the Reynolds number increases the turbulent fluctuation in the channel and weakens the influence of the buoyancy. Thus, under constant heat flux, the increase of the Reynolds number increases the proportion of the logarithmic law layer in comparison to the inner layer, which enhances the convective heat transfer in the channel.

Modulation of wall turbulence by propagating flame of premixed hydrogen–air combustion

The mechanism of modulation of turbulent structures in the vicinity of a combustion engine wall is not yet clarified. Thus, we conducted direct numerical simulations of wall turbulence based on premixed hydrogen–air combustion using a detailed chemical reaction mechanism to clarify the mechanism of modulation of turbulence structures such as quasi-streamwise vortices by a flame propagating toward a wall. In particular, the turbulence modulation can alter the momentum and heat fluxes through the wall surface. In the simulations, we solved the fundamental equations for the compressible flow of multiple chemical species under combustion. The flame propagation speed was affected by the turbulence and was 2.04 times larger than that of the laminar flame. Moreover, upon examining the variation in the flow field, we determined that the turbulence kinetic energy in the flow field increased temporarily owing to the newly produced vortices along the flame surface including the existing turbulence vortices. In contrast, the turbulence vortices along the wall were suppressed as the flame approached the wall, and the turbulent flow tended to become laminar. In terms of vorticity transport equation, the suppression of the turbulence vortices was caused by the thermal expansion of the combustion rather than the increased viscosity. Furthermore, we determined that the vortex structure slightly influenced the chemical reaction process, but it strongly influenced the heat release rate distribution and concentration distribution of the chemical species. The current findings on the stated mechanism will aid in improving the accuracy of practical prediction and control methods for wall turbulence with combustion.

Numerical analysis of interaction between turbulent structures and transient sheet/cloud cavitation

This paper through the in-house code numerically examines the cavitation–vortex–turbulence interaction mechanism. The high grid resolution can obtain a more detailed flow field structure, which is helpful to reveal the relationship between cavitation occurrence and development and local turbulent flow field. Results are presented for a three-dimensional NACA66 hydrofoil fixed at an 8° angle of attack under a moderate Reynolds number of 1 × 106 and sheet/cloud cavitating conditions. Numerical simulations are performed via the boundary data immersion method coupled with the artificial compressibility method through a Fortran-based code. The results show that the numerical predictions are capable of capturing the unsteady cavitation characteristics, in accordance with the quantitative features observed in high-speed cavitation tunnel experiments. The evolution of the transient cavitating flow can be divided into three stages: growth of the attached sheet cavity, development of a re-entrant jet, and cloud shedding downstream. The Liutex method is applied to capture the vortex structure. Further analysis of the process of enstrophy transport reveals that cavitation promotes vortex production and increases the enstrophy as the cavity becomes more unstable. Moreover, the structure of the vortex gradually evolves from a vortex tube to a U-type vortex, Ω-type vortex, and streamwise vortex. Finally, the interaction between cavitation and turbulence is expounded using the turbulent energy transport equation, which demonstrates that cavitation promotes the production, diffusion, and dissipation of turbulent kinetic energy, while the viscous transport term only acts during the process of cloud cavity shedding.

Quantum Turbulence and Planckian Dissipation

The notion of the Planckian dissipation is extended to the system of the Caroli–de Gennes–Matricon discrete energy levels in the vortex core of superconductors and fermionic superfluids. In this extension, the Planck dissipation takes place when the relaxation time τ is comparable with the quantum Heisenberg time {{t}_{H}} = hbar {text{/}}Delta E, where Delta E is the interlevel distance in the vortex core (the minigap). This type of Planck dissipation has two important physical consequences. First, it determines the regime, when the effect of the axial anomaly becomes important. The anomalous spectral flow of the energy levels along the chiral branch of the Caroli–de Gennes–Matricon states becomes important in the super-Planckian region, i.e., when tau < hbar {text{/}}Delta E. Second, the Planck dissipation separates the laminar flow of the superfluid liquid at tau < hbar {text{/}}Delta E and the vortex turbulence regime at tau > hbar {text{/}}Delta E.

Elucidation of the singularity of fluid equations and the statistical properties of turbulence by vortex motion

Large-scale flows and small-scale turbulent motions are closely linked and understanding their dynamics can help to better predict and hope to mitigate climate events. This involves the detailed analysis of the Navier-Stokes equations combined with hard numerical calculations. Professor Yoshifumi Kimura, Graduate School of Mathematics, Nagoya University, Japan, wants to understand the intrinsic mechanisms of large-scale flows in the atmosphere and ocean that are known as Global-Scale Flows (GSFs). To do this he is developing methodologies for extraction and reduction of dynamical information in GSFs and taking into consideration the contrasting sides of GSFs; they appear chaotic but follow deterministic equations. In his work, Kimura is using mathematical, computational and data-scientific approaches, nonlinear singularity/vortex analysis, statistical theory/modelling of turbulence and wavelet analysis combined with high-quality observation and simulation data. It is important for Kimura to understand flow phenomena from the geometrical viewpoint, which has enabled him to unearth hidden relationships. He also relies on the use of supercomputers to perform simulations that allow him to understand and verify theories. A central idea for Kimura's studies is vortex motion, which is a key fundamental process in turbulence. He is therefore exploring the unique properties of vortex motions and their relationship to flows. Kimura has already been able to unearth new concepts and relations in vortex motion and turbulence and will continue in particular to explore vortex reconnections in greater detail.

A dynamic particle scale-driven interphase force model for water-sand two-phase flow in hydraulic machinery and systems

The water–sand two-phase flow in hydraulic machinery and systems has a strong inter-phase interaction due to the effect of rotating turbulence, but many engineering computations do not consider turbulent effects into the interphase force, affecting the prediction accuracy of inner flow characteristics. The objective of this paper is to provide a new dynamic particle scale-driven interphase force model, and its notable features are shown as follows. In the Euler-Euler framework, the time-scale-driven hybrid URANS/LES model is introduced to extend the resolution scale of rotating turbulence. On this basis, (1) the turbulent factor and the wall factor based on a dynamic particle scale are determined to reflect the effects of turbulent fluctuation and wall surface on the drag force; (2) a new turbulent dispersion force model based on a dynamic particle scale is proposed to characterize the following behavior of heavy particles and their interaction with energetic eddies. Four typical flow cases of sediment-laden flows are tested. It is found that the eddy viscosity of water turbulence is effectively adjusted, thereby allowing more turbulent vortices to be resolved on the same URANS grids. The settling motion and inertial motion of sand are reasonably controlled by the improved interphase force model, thereby giving the prediction results of two-phase flow fields with higher accuracy. The new model improves the simulation accuracy of water–sand two-phase flow with rotation and curvature while does not significantly increase the computational cost, which enables efficient engineering computations of water–sand two-phase flow in hydraulic machinery and systems.

Research on natural gas leakage and diffusion characteristics in enclosed building layout

There are many people in urban construction areas, and natural gas leakage can potentially cause serious accident consequences. Predicting the consequences of gas dispersion is important to react rapidly and adequately in the event of an incident. Currently, computational fluid dynamics (CFD) models are an important tool to predict gas dispersion. However, in most cases, considering computational cost, the building layouts is ignored, so the flow field influence near the building area cannot be considered. In this research process, a realizable k-ε turbulence model is used to simulate the natural gas leakage process in a typical building layout (enclosed building layout), while focusing on wind speed and the leakage position. The validity of realizable k-ε turbulence model is verified by experimental data. The results show that under conditions of high wind speed (wind speed≥ 6 m/s), the reverse vortex formed by the shear flow of wind can cause the natural gas cloud to sink. When the leak hole is located in the influence area of the turbulent vortex, it easily induces R-H instability. When combined with the stronger K-H instability at high wind speeds, natural gas clouds may accumulate. This then leads to serious leakage accidents, knowledge of which may be the key component of emergency management during an accidental natural gas leakage. The research results can guide the building layout plan and gas pipeline construction to prevent accidents.

Dynamic inflow model for a floating horizontal axis wind turbine in surge motion

Abstract. Floating offshore wind turbines may experience large surge motions, which can cause blade–vortex interaction if they are similar to or faster than the local wind speed. Previous research hypothesized that this blade–vortex interaction phenomenon represented a turbulent wake state or even a vortex ring state, rendering the actuator disc momentum theory and the blade element momentum theory invalid. This hypothesis is challenged, and we show that the actuator disc momentum theory is valid and accurate in predicting the induction at the actuator in surge, even for large and fast motions. To accomplish this, we develop a dynamic inflow model that simulates the vorticity–velocity system and the effect of motion. The model's predictions are compared to other authors' results, a semi-free-wake vortex ring model, other dynamic inflow models, and CFD simulations of an actuator disc in surge. The results show that surge motion and rotor–wake interaction do not result in a turbulent wake or vortex ring state and that the application of actuator disc momentum theory and blade element momentum theory is valid and accurate when applied correctly in an inertial reference frame. In all cases, the results show excellent agreement with the higher-fidelity simulations. The proposed dynamic inflow model includes a modified Glauert correction for highly loaded streamtubes and is accurate and simple enough to be easily implemented in most blade element momentum models.

Numerical Study of Porous Treatments on Controlling Flow around a Circular Cylinder

Porous materials fixed on and downstream the cylinder can reach a much better effect in suppressing wall pressure fluctuations. In the present paper, numerical comparative studies have been conducted to investigate passive control of flow past a cylinder surface, in which three schemes with different porous treatments are applied to compare their pros and cons. The results show all of the three schemes of porous materials increase the time-averaged flow drag and reduce fluctuations of lift and drag forces. It can be concluded the velocity gradient reduction inside the boundary layer and the vortex shedding delay through porous coating, as well as reverse transition from turbulent vortex shedding into laminar through porous treatment downstream the cylinder, are main flow control mechanisms of porous materials. These mechanisms all reduce fluctuations of lift and drag fluctuations, but have a distinct effect on the features of wake evolution, such as the wake width and length as well as the fluctuating components of the flow velocity. In addition, the wake evolution is highly affected by the location of porous materials.

Modulation of turbulent Couette flow with vortex cavitation in a minimal flow unit

Modulation of turbulent flow by cavitation in fluid machinery can cause vibrations, noise, and erosion. In this study, we confirm the cavitation phenomenon and observe its characteristics to predict the flow and control it accordingly. We perform a direct numerical simulation of the turbulent Couette flow of water with vortex cavitation using a cavitation model to predict phase change based on pressure distribution. In this simulation, we investigate the characteristics of the local interaction between turbulence vortices and cavitation and the global modulation of the turbulent flow, i.e. mean velocity and wall friction coefficient. We observe that a cavity is generated where a low-pressure region is created in the centre of the turbulence vortex; the growth of the cavity weakens the vortex and reduces the intensity of the turbulence. Further, the vortex becomes stronger as the cavity contracts; this phenomenon occurs repeatedly in a turbulent flow field with vortex cavitation. In a turbulent flow field with vortex cavitation, mechanical oscillations can occur spontaneously. In addition, we found that the turbulence vortex weakened by cavitation regenerates around the cavity. The unsteady phenomenon of the turbulence vortex cavitation repeatedly grows and decays monotonically; however, it does not necessarily repeat these spatially in the same manner. The spatial characteristics of the turbulence structure are different from those observed in single-phase turbulent flow.

Large eddy simulation of aerosol particle dispersion mechanism in aircraft exhaust plume

Aerosol Infrared Stealth Technology is a novel method to suppress the infrared by releasing aerosol particles around the hot exhaust plume. However, the Infrared Radiation (IR) suppression rate is much lower in flight tests, which is caused by the unclear particle dispersion mechanism in high-speed non-isothermal shear flow. Hence, the large eddy simulation (LES) and particle discrete phase model (DPM) are coupled to solve the turbulent shear flow and the aerosol particle motion. The effects of aircraft flight speed on the turbulent flow characteristics and particle motion behaviors are systematically studied. It is found that the Mach rings appear in flight conditions, and they are getting blurry when increasing the flight speed. Both γ-like vortex and horseshoe-like vortex are observed when Ma < 1, and the horse-like could disappear when Ma > 1. The aerosol particle distribution is closely related to the turbulent gas vortices. The particle lateral dispersion is obviously restricted with the rising flight speed. Besides, the drag force plays a dominant role, the Saffman force and the thermophoretic force are of the same order of magnitude, all of these three forces are much greater than the gravity.