Reply to the Comment by Tan Mingxuan et al.(2017), on “A new Discovery of the Early Cretaceous Supercritical Hyperpycnal Flow Deposits on the Lingshan Island, East China”

We thank Tan Mingxuan et al. （2017） for their comments stimulated by our short paper in the recent Acta Geologica Sinica （English edition）. We are grateful for the opportunity to expand on the model of the supercritical hyperpycnal flow deposits in the Beilaishi section on the Lingshan Island, and to explain why the model proposed by Tan Mingxuan et al. （2017） cannot explain the bulk of the deposits in the Beilaishi section. We do not dispute that the recognition of supercritical flow deposits remains ambiguous （Ono and Plink-Bjorklund, 2017）. To some extent, the morphology of deep-water supercritical flow deposits is similar to hummocky and swaley cross- stratification （Ono and Plink-Bjorklund, 2017）. Besides, distinguishing the deposits laid down by gravity flows in deep-water systems from those produced by storm-related combined flows in continental shelf systems is not an easy task （Ono and Plink-Bjorklund, 2017）. However, a correct interpretation is crucial for understanding the paleogeographic and depositional model.

Numerical models and theoretical analysis of supercritical bend flow

The flow pattern of supercritical flow in bend channels is complicated due to the shock wave phenomenon, which creates difficulties with regard to research and design of bend channels. Using the spillway of an actual project as an example, a three-dimensional numerical investigation was conducted to simulate the flow in a steep-slope bend based on the renormalization group(RNG) k-ε turbulence flow model and the volume of fluid(VOF) method. The validity of the numerical simulation was demonstrated by comparison between the results of numerical simulation and physical model tests. An optimal scheme of setting vertical vanes in the bend channel is presented. The results of numerical simulation and physical model tests are in agreement, which demonstrates the effectiveness of optimization of vertical vanes and the validity of the three-dimensional numerical simulation. Water depths along both bend walls were analyzed numerically and theoretically. The formula for calculating supercritical water depth along either bend wall was derived, and the critical condition of flow separation from the inner wall was determined.

Characteristics of compressible flow of supercritical kerosene

In this paper, compressible flow of aviation kerosene at supercritical conditions has been studied both numerically and experimentally. The thermophysical properties of supercritical kerosene are calculated using a 10- species surrogate based on the principle of extended corresponding states （ECS）. Isentropic acceleration of supercritical kerosene to subsonic and supersonic speeds has been analyzed numerically. It has been found that the isentropic relationships of supercritical kerosene are significantly dif- ferent from those of ideal gases, A two-stage fuel heating and delivery system is used to heat the kerosene up to a tem- perature of 820 K and pressure of 5.5 MPa with a maximum mass flow rate of 100 g/s. The characteristics of supercritical kerosene flows in a converging-diverging nozzle （Laval nozzle） have been studied experimentally. The results show that stable supersonic flows of kerosene could be established in the temperature range of 730 K-820 K and the measurements in the wall pressure agree with the numerical calculation.

A new discovery of The Early Cretaceous Supercritical Hyperpycnal Flow Deposits on Lingshan Island,East China

Objective Understanding the dynamics of sediment gravity flows is of great importance to correctly interpret their related deposits. The discovery of supercritical sediment gravity flows provides some new viewpoints for the explanation of controversial sediment gravity flow deposits. However, the dynamics, formation, evolution processes of supercritical sediment gravity flows and their recognition criteria from their associated deposits are still worldwide controversial. The supercritical hyperpycnal flow deposits recognized in the upper part of Early Cretaceous Lingshandao Formation provide a rare opporttmity to understand their sedimentary characteristics. This work is aimed at documenting the typical sedimentary structures associated with the supercritical hyperpycnal flow, and discussing the vertical stacking and its relationship with flow evolution.

3D anatomy and flow dynamics of net-depositional cyclic steps on the world’s largest submarine fan:a joint 3D seismic and numerical approach

Supercritical flows are ubiquitous in natural environments;however,there is rare 3D anatomy of their deposits.This study uses high-quality 3D seismic datasets from the world’s largest submarine fan,Bengal Fan,to interpret 3D architectures and flow processes of Pliocene undulating bedforms that were related to supercritical flows.Bengal undulating bedforms as documented in this study were developed in unconfined settings,and are seismically imaged as strike-elongated,crescentic bedforms in plan view and as rhythmically undulating,upstream migrating,erosive,discontinuous reflections in section view.Their lee sides are overall 3 to 4 times steeper(0.280 to 1.19°in slope)and 3 to 4 times shorter(117 to 419 m in length)than their stoss flanks and were ascribed to faster(high flow velocities of 2.70 to 3.98 m/s)supercritical flows(Froude numbers of 1.53 to 2.27).Their stoss sides,in contrast,are overall 3 to 4 times gentler(0.120 to 0.270 in slope)and 3 to 4 times longer(410 to 1139 m in length)than their lee flanks and were related to slower(low velocities of 2.35 to 3.05 m/s)subcritical flows(Froude numbers of 0.58 to 0.97).Bengal wave-like features were,thus,created by supercriticalto-subcritical flow transformations through internal hydraulic jumps(i.e.,cyclic steps).They have crests that are positive relative to the surrounding region of the seafloor,suggesting the predominant deposition of draping sediments associated with net-depositional cyclic steps.Turbidity currents forming Bengal wave-like features were,thus,dominated by deposition,resulting in net-depositional cyclic steps.Sandy deposits associated with Bengal net-depositional cyclic steps are imaged themselves as closely spaced,strike-elongated high RMS-attribute patches,thereby showing closely spaced,long and linear,strike-elongated distribution patterns.

Experimental study on flow excursion instability of supercritical hydrocarbon fuel in scramjet regenerative cooling parallel channels

Flow instability of supercritical hydrocarbon fuel is a crucial issue in scramjet regenerative cooling structure. In this study, flow excursion instability and flow distribution in parallel tubes were experimentally studied for supercritical fluids. Two types of flow excursion occur in a single tube. Type Ⅰ and Type Ⅱ excursions, and they are corresponding to decreasing and increasing flow rate respectively. They can trigger flow maldistribution between parallel tubes and the hysteresis phenomenon of flow distribution. The effects of system parameters, including inlet temperature,system pressure, and heat flux, on flow distribution were analyzed. In addition, the relationship between flow excursion and the pseudo-critical interval proposed in the literature was established according to the heated tube outlet temperature at the onset of flow instability. Finally, the flow excursion instability boundary was obtained using two dimensionless parameters. These experimental results can provide helpful insight on the mechanism of Scramjet regenerative cooling.

LARGE EDDY SIMULATION OF OPEN CHANNEL FLOWS WITH NONSUBMERGED VEGETATION

Results of several Large Eddy Simulations （LES） this article. It is shown that the vegetation can make the flow of open channel flows with non-submerged vegetation are presented in structure in the mainstream direction uniform for both supercritical and subcritical flows. For subcritical flows, the LES results of the ensemble-average of time-averaged velocity distributions at four vertical sections around a single plant are in good agreement with measurements. The velocity sees double peaks at the upper and lower positions of flows. For supercritical flows, the ensemble-average velocities see some discrepancy between LES and measurement results. Some secondary flow eddies appear near the single plant, and they just locate in the positions of the double peaks in stream-wise velocity profiles. It is also found that the vegetation drag coefficient deceases as the Froude number increases.

ABRUPT DEFLECTED SUPERCRITICAL WATER FLOW-REVISED THEORY OF SHOCK WAVE

The shock wave angle and depth ratio of the abrupt deflected supercritical water flow due to deflector was investigated experimentally and theoretically. A correction coefficient of the hydro-dynamic pressure ξ was introduced to generalize the momentum equation in the perpendicular direction to the shock front. An extensive series of tests were conducted in a 1 m wide flume with the Froude number ranging from 1.70 to 8.37, the deflection angle ranging from 5° to 40° and the length of deflector ranging from 0.28 m to 1 m. A dimensionless parameter K was defined to depict the ratio of the flow height to flow thickness. Test results show that the val ue of ~, the correction coefficient of the non-hydrostatic pres- sure distribution, decreases with the increase of the value of K An empirical relationship between the value of ξ and the val ue of K was proposed. It is indicated that the relative errors of the results calculated by the revised theory is much smaller than that obtained from the Ippen theory. Finally, a simple explicit expression was suggested to calculate the shock wave height ratio in consideration of the effect of the non-hydrostatic pressure distribution.

ABRUPT DEFLECTED SUPERCRITICAL WATER FLOW IN SLOPED CHANNELS

The effect of the bottom slope on abrupt deflected supercritical water flow was experimentally and theoretically studied. Model tests were conducted in a flume of 1.2 m wide and 2.6 m long with sloped bottom at an angle 35.54°, its length of deflector was 0.2 m and the deflection angles were 15° and 30°. An approximate method for calculating the shock wave angle and depth ratio of the abrupt deflected supercritical water flow was suggested, and a correction coefficient for the hydrodynamic pressure was introduced to generalize the momentum equation in the direction perpendicular to the shock front. It must be noticed that in the sloped channel the shock wave angle and the depth ratio are no longer constant as those in the horizontal channels, but slowly change along the shock front. The calculated results are in good agreement with measured data.

THE MACCORMACK SCHEME AND THE BOUNDARY-FITTED COORDINATE SYSTEM FOR NUMERICAL SIMULATION OF SUPER CRITICAL FREE SURFACE FLOWS

This paper is concerned with the mathematical model for the numerical simulation of supercritical surface flows. A boundary-fitted coordinate system was used to overcome the difficulties and inaccuracy associated with the determination of flow characteristics near the fl ow boundaries. The MacCormack scheme was applied for the solution of the transfo rmed system of equations. Comparisions between computed results and experimental data show a satisfactory agreement.

Numerical simulations of morphological changes in barrier islands induced by storm surges and waves using a supercritical flow model

In this paper, an advanced explicit finite volume flow model in two-dimensions is presented for simulating supercritical coastal flows and morphological changes in a tidal/coastal inlet and barrier islands due to storm surges and waves. This flow mode/ is coupled with existing wave-action mode/and sediment transport mode/. The resulting integrated coastal process model is capable of simulating flows induced by extreme conditions such as waves, surge tides, river flood flows, etc., and morphological changes induced by rapid coastal currents and waves. This developed supercritical ftow model is based on the solution of the conservative form of the nonlinear shallow water equations with the effects of the Coriolis force, uneven bathymetry, wind stress, and wave radiation stresses. The forward Euler scheme is used for the unsteady term; and the convective term is discretized using the Godunov-type shock- capturing scheme along with the HLL Riemann solver on non-uniform rectilinear grids. The accuracy of the developed model is investigated by solving an experimental dam-break test case. Barrier island breaching, overflow and overwash due to severe storm attack are simulated and the predicted morphological changes associated to the events are analyzed to investigate the applicability of the model in a coast where all the physical forces are present.

Cyclone separation in a supercritical water circulating fluidized bed reactor for coallbiomass gasification： Structural design and numerical analysis

A new concept of a supercritical water （SCW） circulating fiuidized bed reactor is proposed to produce hydrogen from coal/biomass gasification. The cyclone is a key component of the reactor system, in this paper, cyclones with a single circular inlet （SCI） or a double circular inlet （DCI） were designed to adapt to the supercritical conditions. We evaluated the separation performance of the two cyclones using numerical simulations. A three-dimensional Reynolds stress model was used to simulate the turbulent flow of the fluid, and a stochastic Lagrangian model was used to simulate the particle motion. The flow fields of both cyclones were three-dimensionally unsteady and similar to those of traditional gas-solid cyclones. Secondary circulation phenomena were discovered and their influence on particle separation was estimated. Analyzing the distribution of the turbulence kinetic energy revealed that the most intensive turbulence existed in the zone near the vortex finder while the flow in the central part was relatively stable. The particle concentration distribution was non-uniform because of centrifugal forces. The distribution area can be divided into three parts according to the motion of the particles. In addition, the separation efficiency of both cyclones increased with the inlet SCaN velocity. Because of its perturbance flow, the DCI separator had higher separation efficiency than the SCI separator under comparable simulations. However, this was at the expense of a higher pressure drop across the cyclone.

Numerical investigation of separation efficiency of the cyclone with supercritical fluid-solid flow

The utilization of hydrogen is gaining increasing attention due to its high heating value and environmentally friendly combustion product.The supercritical water circulating fluidized bed reactor is a promising and potentially clean technology that can generate hydrogen from coal gasification.Cyclone is a vital part of the reactor which can separate incomplete decomposition of pulverized coal particles from mixed working fluid.This paper aims to gain in-depth understanding of the cyclone separation mechanisms under supercritical fluid by computational fluid dynamics(CFD).Although the amount of supercritical carbon dioxide in mixed working fluid is minor,it obviously influences the flow fields and separation efficiency of a cyclone.The simulation results suggest that both the decreasing content of supercritical carbon dioxide and adding the extra dipleg cause the promoting performance of cyclones.Research findings could refine the design of supercritical fluid-solid cyclones.

Numerical Analysis of Flow Instability in the Water Wall of a Supercritical CFB Boiler with Annular Furnace

In order to expand the study on flow instability of supercritical circulating fluidized bed(CFB) boiler,a new numerical computational model considering the heat storage of the tube wall metal was presented in this paper.The lumped parameter method was proposed for wall temperature calculation and the single channel model was adopted for the analysis of flow instability.Based on the time-domain method,a new numerical computational program suitable for the analysis of flow instability in the water wall of supercritical CFB boiler with annular furnace was established.To verify the code,calculation results were respectively compared with data of commercial software.According to the comparisons,the new code was proved to be reasonable and accurate for practical engineering application in analysis of flow instability.Based on the new program,the flow instability of supercritical CFB boiler with annular furnace was simulated by time-domain method.When 1.2 times heat load disturbance was applied on the loop,results showed that the inlet flow rate,outlet flow rate and wall temperature fluctuated with time eventually remained at constant values,suggesting that the hydrodynamic flow was stable.The results also showed that in the case of considering the heat storage,the flow in the water wall is easier to return to stable state than without considering heat storage.