Static Pressure Ratio Research Articles

Comprehensive Experimental Assessment Of Unsteady Pressure And Heat Flux In A Small-Core Turbine Over-Tip Shroud

Abstract For novel high-speed small core turbines, with tip clearance below 0.5mm, even small blade-to-blade tip clearance variation is significant. The assessment of these complex flows is pertinent to the design of the next generation of small-core turbines. This manuscript provides a thorough experimental analysis of the shroud?s unsteady heat flux and static pressure in a small-core squealer-tip blade turbine. Atomic Layer Thermopile sensors and fast response pressure transducers were used to perform high-frequency acquisition at 2MHz around the 51% axial blade chord on the shroud. Measurements were taken at engine-representative conditions at several operational conditions and tip clearances. The signals were phase-locked averaged over the revolution period and synchronized to identify individual blade and row signatures. The linear relationship between the rotational tip Reynolds and the static pressure ratio across the blade tip reveals the transition point to reverse over-tip flows. Total heat flux is decomposed into different steady and unsteady heat flux contributions. It is demonstrated that the adiabatic wall temperature governs the unsteady heat flux and contributes to one third of the total surface heat flux. A linear trend was observed between the unsteady heat flux and the tip clearance measured at the pressure and suction side rims. Similar trends were observed between the local heat flux and the pressure ratio across the tip. A comparison with CFD predictions highlights some limitations on resolving the detached and secondary flows, evidencing the necessity of complementary experimental data.

An experimental investigation of supersonic conical cooling films with angles of attack

While the flow mechanisms of two-dimensional supersonic cooling films have been studied in-depth, this paper used the nanoparticle planar laser scattering and particle image velocimetry techniques to investigate the flow of supersonic conical cooling films at different angles of attack (AOAs). The mainstream Mach number was Ma∞=3.8, and the supersonic conical cooling film was tangentially injected via a precisely calibrated Maj=2.8 annular nozzle. Initially, the streamwise boundary layer transition process without cooling film injection was analyzed. The boundary layer transition on the leeward side occurred prematurely, whereas on the windward side, the transition process was notably delayed. Subsequently, the supersonic conical cooling film flow was qualitatively and quantitatively evaluated from the perspectives of turbulent structures, and the time-averaged and statistical characteristics of the velocity field. On the windward side, as the ratio of static pressure decreased, the effective cooling length also decreased with an increase in AOA. On the leeward side, at a small positive AOA, the supersonic conical cooling film mixed with the low-energy fluid within the thickened inner layer of the mainstream boundary layer, which mitigated the growth rate of the mixing layer and ultimately enhanced the effective cooling length. With a further increase in AOA, the supersonic conical cooling film experienced the three-dimensional detrimental effects of crossflow-separation vortices and downwash mainstream on the leeward surface, resulting in a decrease in the effective cooling length.

Experimental and simulation study of energy loss mechanism of low pressure ratio radial turbine

Low-pressure ratio conditions are commonly encountered in radial turbines. When operating at low pressure ratio condition, a significant portion of the turbine energy loss occurs as residual velocity loss in the form of swirling flow at the outlet pipe. Typically, this energy can be recovered by the next stage turbine or reduced by the diffuser. However, there is a lack of experimental and simulation studies on the swirling flow at the outlet of turbines. The mechanism governing the changing pattern of swirling flow remains unclear, limiting the effective utilization and reduction of residual velocity loss. This study conducts theoretical and experimental research on turbine outlet swirling flow. Firstly, this paper introduces a novel two-dimensional hot-wire anemometry stepping mechanism for measuring swirling flow at a turbine outlet cross-section. Experimental results demonstrate that the proposed measurement method effectively captures the morphological changes of turbine outlet swirling flow. The results indicate a strong coupling relationship between axial and circumferential velocity. Subsequently, to elucidate the reasons for the coupling of velocity in two directions and the development of swirling flow in the outlet pipeline, simulations of turbine performance under different velocity ratio conditions were conducted. Results show that under a wide range of velocity ratios, not only does the direction of the turbine outlet swirling flow change, but it also leads to the swirl number exceeding the critical swirl ratio under high velocity ratio conditions, resulting in the formation of a central recirculation zone (CRZ) at the pipe outlet. The main cause of the strong coupling effect between velocities in two directions is attributed to the increased swirl intensity leading to enhanced adverse pressure gradients at the core of the vortex. Lastly, a model describing the variation of VGT turbine outlet swirling flow is established, indicating a linear relationship between the swirl number and the velocity ratio, with a steeper change as the pressure ratio decreases.

Ab initio chemical kinetics and shock-tube experimental study on nitrocyclohexane pyrolysis and combustion

Nitrocyclohexane (NCH) is a model nitroalkane compound with naphthenic structural groups for studying the combustion properties of nitro-based energetic fuels, and also demonstrates significant potential applications for advanced engines. However, accurate description of the detailed kinetic mechanisms for pyrolysis and combustion of NCH receives little attentions. Herein, the detailed pyrolysis and oxidation mechanism of NCH is studied by using quantum chemistry calculations and chemical kinetic theory. The potential energy surfaces of the CN bond dissociation reaction, HONO elimination reaction, abstraction reactions of NCH as well as the subsequent β-scission reactions are calculated using G4//M06–2X/6–311++G(d, p) method, which are subsequently employed for reaction rate constant computations via transition state theory (TST) and RRKM/master-equation (RRKM/ME) method. The ab initio chemical kinetic study results are used to develop a detailed kinetic mechanism to predict the pyrolysis experimental results of NCH, which are performed using a single-pulse shock tube (SPST). The SPST experiment is performed at pressure of 10 bar, temperature ranging from 1070 to 1560 K, reaction time of around 1.77 microsecond with fuel concentrations of 0.5 % diluted by Argon gas. The developed detailed kinetic mechanism exhibits reasonable prediction results of the pyrolysis product distributions together with literature ignition delay times across a wide range of temperature, pressure, and equivalence ratio conditions. Rate-of-production analysis is conducted to gain insight into the pyrolysis chemical kinetics of NCH. The present work should be valuable for the study of the combustion chemistry of nitro-alkane energetic fuels.

New insights into coarse particle lifting performance of a hydraulic ejector with an ultra-large area ratio

Hydraulic ejectors with ultra-large area ratios (HE-ULAR) have potential applications as particle lifting equipment in fluidized coal mining. This study analyzed the effects of area and pressure ratios on the coarse particle lifting performance of HE-ULAR. The cavitation, valid, and failure zones for coarse particle lifting were mapped out. The results show that the pressure gradient force acting on each particle is approximately 2.02–3.70 times greater than the drag force, indicating that the pressure gradient force is the more significant interaction force for particle migration under the influence of HE-ULAR compared to the drag force. Additionally, insufficient energy transfer between the energetic fluid and particles in the valid zone of HE-ULAR reduces the fluid energy density and particle lifting concentration at low pressure ratio conditions. The HE-ULAR exhibits optimal particle performance at the operating conditions with an area ratio of 12.51 and a pressure ratio of 0.0735. Finally, a series of prediction formulas for fluidized coal mining parameters were established based on the optimal operating condition of the HE-ULAR. These results will guide the application of the HE-ULAR in a fluidized mining system.

Influence of Herringbone Grooves Inspired by Bird Feathers on Aerodynamics of Compressor Cascade under Different Reynolds Number Conditions

Nowadays, high aerodynamic load has made blade separation an issue for compact axial compressors under high-altitude low-Reynolds-number conditions. In this study, herringbone grooves inspired by bird feathers were applied to suppress the suction side separation and reduce loss. To study the effect of bio-inspired herringbone grooves on the aerodynamic performance of compressor cascades, a high subsonic compressor cascade was taken as the research object. Under the conditions of different Reynolds numbers, the effects of herringbone grooves of different depths on the flow separation were numerically studied. The research results show that at a high-Reynolds-number condition (Re = 5.6 × 105), the sawtooth-shaped wake induced by herringbone grooves increases the turbulent mixing loss near the suction surface, and the blade performance deteriorates. At a low-Reynolds-number condition (Re = 1.3 × 105), the span-wise secondary flow and micro-vortex structure induced by the herringbone grooves effectively suppress the laminar separation on the suction surface of the blade, and there is an optimal depth for the herringbone grooves that reduces the profile loss by 8.33% and increases the static pressure ratio by 0.55%. The selection principle of the optimal groove depth with the Re is discussed based on the research results under six low-Reynolds-number conditions.

A Preconditioner-Based Data-Driven Polynomial Expansion Method: Application to Compressor Blade With Leading Edge Uncertainty

Abstract In engineering practice, the amount of measured data is often scarce and limited, posing a challenge in uncertainty quantification (UQ) and propagation. Data-driven polynomial chaos (DDPC) is an effective way to tackle this challenge. However, the DDPC method faces problems from the lack of robustness and convergence difficulty. In this paper, a preconditioner-based data-driven polynomial chaos (PDDPC) method is developed to deal with UQ problems with scarce measured data. Two numerical experiments are used to validate the computational robustness, convergence property, and application potential in case of scarce data. Then, the PDDPC is first applied to evaluate the uncertain impacts of real leading edge (LE) errors on the aerodynamic performance of a two-dimensional compressor blade. Results show that the overall performance of compressor blade is degraded and there is a large performance dispersion at off-design incidence conditions. The actual blade performance has a high probability of deviating from the nominal performance. Under the influence of uncertain LE geometry, the probability distributions of the total pressure loss coefficient and static pressure ratio have obvious skewness characteristics. Compared with the PDDPC method, the UQ results obtained by the fitted Gaussian and Beta probability distributions seriously underestimate the performance dispersion of compressor blade. The mechanism analysis illustrates that the large flow variation around the leading edge is the main reason for the overall performance degradation and the fluctuations of the entire flow field.

Aerodynamic design of supersonic compressor cascade and vorticity dynamic diagnosis of flow field structure

High-load counter-rotating compressor plays a crucial role in reducing the axial length and weight of the compressor and increasing the thrust-to-weight ratio of the aero-engine. However, the boundary layer flow separation induced by shock waves in the channel of high adverse pressure gradient also brings more aerodynamic losses. This paper proposed a supersonic compressor cascade modeling method based on the unique inlet angle theory and the superimposing thickness on the suction surface method. It carried out aerodynamic optimization design of cascade with inlet Mach number of 1.85 combined with numerical optimization technology, vorticity dynamics diagnosis, and planar cascade experiment. The results show that multiple shock wave combination pressurization can be realized in the supersonic cascade channel. At the design point, the static pressure ratio is 3.285, and the total pressure recovery coefficient reaches 86.82%, and the experimental results of planar cascade also verify the correctness of the simulation method. In addition, the correlation laws between the distribution of the vorticity dynamic parameter, shock wave structure, and aerodynamic performance of cascade were analyzed by the vorticity dynamic flow field diagnosis method, which provides a beneficial reference for the subsequent compressor design.

Optimization of Thrust of a Generic X-51 Hypersonic Vehicle

A prune-and-search optimization algorithm was combined with a reduced-order model of the scramjet engine within a generic X-51 vehicle. The goal was to maximize the thrust in order to achieve thrust-to-drag ratios that equal or exceed 1, even for the difficult cases of flight at high altitudes and high Mach numbers up to 10. For the inlet to the engine, the lengths and inclination angles of three wall panels were varied. For the combustor, three parameters were varied: the diameter and number of fuel injector ports and the wall divergence angle. These variables affect both the combustion efficiency and the finite-rate chemistry of the surrogate JP-7 fuel. The optimization algorithm showed that at higher flight Mach numbers an inlet that maximizes static pressure ratio is preferred over one that maximizes the stagnation pressure ratio, because good combustion efficiency requires a sufficient static pressure in the combustor. As the flight Mach number is increased, thrust decreases while the drag increases. Thus, it becomes difficult to achieve thrust that exceeds drag. A solution is shown to be increasing the engine inlet area above a critical value that was computed. Advantages of a reduced-order model over a high-fidelity CFD approach are discussed when thousands of computations of all components within an entire engine are required for optimization.

A generative adversarial network for enhancing over-expansion flow field perception of nozzles with large expansion ratio

Over-expansion flow and separation phenomena exist inside the nozzle during the startup and shutdown of the rocket engine, and the transition between the separation modes is prone to cause significant side loads and jeopardize the safety of the engine. Accurate, comprehensive and prompt nozzle flow field state perception is of great significance to the stable operation of the engine. Here, a generative adversarial network is proposed to reconstruct the internal Mach number and temperature fields for different nozzle pressure ratios and flow separation modes based on the discrete pressure at the nozzle wall. The proposed generative adversarial network employs Wasserstein distance and gradient penalty to improve the problems of gradient vanishing and pattern collapse during discriminator network training. The large expansion ratio nozzle selected was the VOLVO S1 nozzle and numerical simulations were carried out under different nozzle pressure ratio conditions to obtain data for the training of data-driven model. The results indicate that generative adversarial networks can accurately reconstruct restricted shock separation and free shock separation modes under different nozzle pressure ratios based on discrete pressure and temperature measurement points on the nozzle wall, with a relative error of less than 1.2%, and accurately identify important flow field characteristics such as Mach disk, supersonic jet flow, and multiple recirculation regions. The advantages of the generative model in recognizing the strong normal shock Mach disk are compared with those of the supervised learning model. This study lays the foundation for the subsequent study of nozzle side load and structural fatigue life based on three-dimensional flow field.

Variations of the shock and secondary flow structure in a transonic compressor cascade with outlet back pressure

The effects of back pressure on the transonic cascade operating state are crucial and can determine the structure of internal shock waves and secondary flows. In this paper, numerical methods validated by experiments were employed to investigate the evolution mechanisms of the inlet flow field, shock structure, secondary flow structure, and cascade performance under different back pressures. Analysis revealed that transonic cascade exhibited unique incidence characteristics in the inlet flow field under both subsonic and supersonic regimes, although these two regimes involved different physical mechanisms. The results revealed that the operating state of the transonic compressor cascade under the unique incidence condition was influenced by the outlet back pressure, and there existed a critical static pressure ratio. The critical static pressure ratio shifted from 1.61 for two-dimensional flow to 1.37 for three-dimensional (3D) flow at M1 = 1.1, due to the corner separation and the characteristics of 3D shocks. The 3D shock structure exhibited a non-uniform distribution along the spanwise direction due to the influence of back pressure and the separated boundary layer. The vortex structures analysis revealed that the secondary flow structure on the sidewalls of the transonic compressor cascade was primarily dominated by corner vortices, whose formation mechanism was related to the interaction between the shock wave and the sidewall boundary layer. Additionally, this interaction also led to the formation of detached shock and lip shock vortex structures. Finally, loss analysis indicated that the wake region of the transonic cascade primarily includes six types of loss, and the total loss of the cascade decreased with the rise in back pressure.

Experimental investigation of storm sewer geyser using a large-scale setup

The storm sewer geyser is a process where an air–water mixture violently erupts from a manhole. Despite the low hydrostatic pressure, violent eruptions can achieve a height of tens of meters above the ground. This current study experimentally investigates large-scale violent geysers using a large air pocket inserted from a pressurized air tank. The total length of the pipe system is approximately 88 m with a 0.1572 m diameter pipe. This large-scale experiment facilitates the investigation of spontaneous geyser eruptions. This study identifies the role of air–water volume ratio and coefficient of pressure (ratio of absolute initial static pressure to initial dynamic pressure) on the geyser intensity using eruption images and pressure plots. A total of 116 cases are tested, in which the volume ratio is parametrically increased from 0 to 1.1 under various operating conditions. A geyser score is defined to quantify the geyser eruption nature based on visual observations. The key findings are as follows: first, a sharp transition in geyser intensity is observed at the critical volume ratio of 0.5, and pre-transition and post-transition intensity exhibit a linear relationship with the volume ratio; and second, the critical volume ratio linearly varies with the coefficient of pressure.

Numerical investigation of dynamic characteristics of dual throat nozzle and bypass dual throat nozzle in thrust vectoring starting process

The Bypass Dual Throat Nozzle (BDTN) is a novel fluidic Thrust Vectoring (TV) nozzle, it switches to TV state by opening the valve in the bypass. To greatly manipulate the BDTN, the dynamic characteristics in the TV starting process should be analyzed. This paper conducts numerical simulations to grasp the variation processes of performances and the flow field evolution of BDTN and Dual Throat Nozzle (DTN). The dynamic responses of TV starting in typical DTN models are investigated at first. Then, the TV starting processes of BDTN in different Nozzle Pressure Ratio (NPR) conditions are simulated, and the valve opening durations (T) are also considered. Before the expected TV direction is achieved in the DTN, the jet is deflected to the opposite direction at the beginning of the dynamic process, which is called the reverse TV phenomenon. However, this phenomenon disappears in the BDTN. The larger injection width of DTN intensifies unsteady oscillations, and the reverse TV phenomenon is strengthened. In the BDTN, T determines the delay degree of performance variations compared to the static results, which is called hysteresis effect. At NPR = 10, the hysteresis affects the final stable performance of BDTN. This study analyses the dynamic characteristics in DTN and BDTN, laying a foundation for further design of nozzles and control strategies.

Study on the characteristics of a novel wrap-around cooled diaphragm compressor for hydrogen refueling station

This study introduces a novel wrap-around cooled diaphragm compressor, designed for employment in hydrogen refilling station. The performance of this innovative compressor is evaluated using a specially developed experimental platform. The analysis focused on the impact of pressure ratio and suction gas temperature on the compressor's performance, and the cooling effect is assessed under varying temperatures of the cooling medium. The findings indicate that both the isentropic and volumetric efficiencies of the diaphragm compressor decrease with an increase in pressure ratio, with maximum values reaching 70% and 65% respectively. Under constant pressure ratio conditions, the exhaust temperature is found to increase with the rise in suction temperature. For a given suction temperature, a higher-pressure ratio resulted in a higher exhaust temperature. Furthermore, the cooling effect of the wrap-around cooling pipeline is found to be more pronounced under high pressure ratio conditions, with a maximum temperature reduction of 189.5 °C.

Supersonic cooling film flow evolution on a curved wall under hypersonic flow

Curvature plays a crucial role in evolving supersonic cooling film flow-field structures. Flow-field structural images were captured using nanotracer-based planar laser scattering,, and wall pressure values were obtained using experimentally validated numerical simulations. A supersonic cooling film is tangentially injected at the Mach number of Maj = 2.3 into a laminar boundary layer at a mainstream of Ma = 6. The supersonic cooling film inhibits mixing-layer instability on the convex curved wall (CV) and promotes it on the concave curved wall (CC). After increasing the total incoming pressure, the reduction ratio of static pressure (RSP) between the supersonic cooling film and the mainstream flow causes a delay in the position of the mixing-layer instability, smaller-scale vortex structures, and decreased flow velocity of the typical vortex structures on the CC and CV. The wall pressure increases for the CV and decreases for the CC, indicating that the supersonic cooling film suppresses the changes in wall pressure due to curvature. The supersonic cooling film suppresses the decrease in the impulses for bulk dilatation (Ip) due to convex curvature and the increase in Ip due to concave curvature. The growth rate of Ip on the CC increases from −15% to −8% and decreases on the CV from 31% to 12% in the bending impulse (IΦ) range of |IΦ| = 1.337–3.624 for a total inlet pressure of 0.5 MPa. Increasing the RSP could control the Ip values on curved surfaces more effectively. The results of this study can be applied to cooling the infrared optics window on hypersonic vehicles.

Feasibility assessment of transition metal carbides applied to chemical looping reforming – A proof-of-concept for tungsten carbide

This paper is the first study to present an innovative technology for hydrogen and syngas production named Carbide Chemical Looping Reforming (CCLR). Nine different Transition Metal Carbides (TMC) were assessed in a thermodynamic study to evaluate potential materials to be applied in the system that could possibly form hydrogen and carbide when in the presence of methane. Out of all the materials, tungsten proved to be the best suitable due to its known high resistance to carbon deposits [1], low-temperature range to form carbides (at least 750 °C), no formation of undesired compounds, and considerably high hydrogen quality in syngas range. A sensitivity analysis is performed in order to assess the better conditions of temperature, pressure and methane ratio for the process to maximize the formation of hydrogen. A study of the heat balance between the air reactor and fuel reactor is shown to prove the system can work as an autothermal process and exclude external heat sources as well as an analysis of the carbon emission potential to prove the technology accounts for lower emission when compared to current technologies, such as Steam Methane Reforming and Steam Methane Reforming with Carbon Capture and Storage. Experimental thermogravimetric analysis showed a high formation of hydrogen and carbide in the system with high selectivity towards hydrogen/syngas reactions, proving the formation of carbides in a process and replicability of the system. Lastly, an economic assessment is performed with tungsten carbide to show that the application of tungsten in CCLR could achieve a competitive level to current technologies with a hydrogen cost price of USD 3.23, with the potential to be reduced even more depending on the process configuration.

Experimental and modeling study on ignition kinetics of ethyl methyl carbonate

Ethyl methyl carbonate (EMC) is an essential electrolyte of lithium-ion batteries (LIBs), and the spontaneous ignition of electrolyte is considered to be an important inducement for the thermal runaway (TR) combustion of LIBs. To better understand its ignition chemistry and combustion kinetics, the ignition delay times (IDTs) of ethyl methyl carbonate were measured by using a Rapid Compression Machine (RCM) over a wide range of temperatures (810–980 K), pressures (20 and 40 bar), equivalence ratios (φ = 0.5, 1.0, and 2.0), and a fuel concentration of 2 %, yielding results that are in substantial variance with those calculated with detailed kinetics in the literature over the entire range of conditions investigated. An improved chemical kinetic model was developed to simulate the ignition and combustion characteristics of EMC under intermediate-temperature region by employing the updated kinetic parameters. Results show that the overall performance of the present kinetics model is substantially improved with respected to the prediction of ignition delay times, intermediate species profiles, as well as laminar flame speeds across different temperature, pressure, and equivalence ratio conditions. Furthermore, sensitivity and pathway analyses show that the ignition chemistry of EMC is mainly controlled by retro-ene reaction and H abstraction reactions.

Combustion performance and flame front morphology of producer gas from a biomass gasification-based cookstove

The present work investigates the last phase of the biomass gasification-based cookstove, which is the combustion process of biomass producer gas (BGP). A constant volume combustion bomb and kinetic simulation are used to characterize the behavior of the biomass producer gas and its pollutant emissions under a conventional premixed combustion process. The BGP combustion processes of two types of biomasses available in Colombia (Pinus Patula and Cordia Alliodora) are studied under certain conditions of pressure, temperature, and equivalence ratio. To characterize the combustible mixture of gases obtained after biomass gasification, a combustion chamber with cylindrical geometry equipped with a Schlieren optical diagnostic system to visualize the combustion process, and a piezoelectric pressure transducer to register the instantaneous pressure are used. By visualizing the flame front, the flame propagation speed at which the flame propagates through the combustion chamber and the morphology of the flame are studied. Instantaneous pressure is the input of a two-zone diagnostic model through which variables, such as burning velocity, temperature, mass burned fraction, etc., are obtained to characterize the combustion process of the mentioned gasification gases. Experimental results are compared and complemented with kinetic modeling results obtained with the Cantera package using the Gri-Mech 3.0 and Aramko 1.3 kinetic mechanisms, in terms of laminar burning velocity and NO, NO2, CO, and CO2 exhaust emissions. Results show that Cordia Alliodora presents higher burning velocities than Pinus Patula BP. However, lower CO2 emissions are obtained during the Cordia Alliodora combustion, and NOx emissions are not influenced by the type of biomass considered.

Flow evolution of mixed layer on convex curvature wall under hypersonic conditions

With the continuous upgrading of hypersonic vehicles, a new requirement for designing imaging window i.e. conformal window for improving aerodynamic characteristics, is put forward, in which the supersonic cooling film and optical window are required to maintain the same curvature shape as the aircraft body. In this work, the mixed-layer flow evolution on a convex wall (CV) is investigated. A nanoparticle-based planar laser scattering technique is used to design the flow field structure of the mixed layer in <i>Ma</i> = 6 hypersonic static wind tunnel, and the location of the mixed-layer instability is studied by combing fractal dimension. The results of pressure, and impulse of compression (<i>I</i><sub>p</sub>) evolution along the flow direction are obtained by numerical simulation, showing that the total incoming pressure (<i>P</i><sub>0</sub>) has a significant effect on the flow evolution of the mixed layer: as <i>P</i><sub>0</sub> increases, the ratio of static pressure (RSP) decreases, that the position of the mixed-layer instability is delayed, and that the flow velocity of the typical vortex structure increases. The favorable gradient existing at the CV wallleads the pressure to drop along the flow direction, and the pressure is enhanced when the supersonic air film along the tangential direction of the wall is under the operating condition. However, as <i>P</i><sub>0</sub> increases, the RSP decreases, and the lifting effect of the pressure on the CV decreases. The flow field is affected by the expansion effect of the CV, and <i>I</i><sub>p</sub> decreases along the flow direction. The supersonic air film can weaken the expansion effect on the CV and thus suppressing the decrease of <i>I</i><sub>p</sub>. The change rate of <i>I</i><sub>p</sub> (Δ<i>I</i><sub>p</sub>) is significantly affected by <i>P</i><sub>0</sub>, in a range of bending impulse |<i>I</i><sub><i>Φ</i></sub>| = 0.191–3.62, Δ<i>I</i><sub>p</sub> decreases from 178.67% to 12.02% when <i>P</i><sub>0</sub> = 0.5 MPa, and Δ<i>I</i><sub>p</sub> decreases from 40.38% to 5.64% when <i>P</i><sub>0</sub> = 1.0 MPa. Δ<i>I</i><sub>p</sub> decreases as |<i>I</i><sub><i>Φ</i></sub>| increases, but the decrease becomes less as <i>P</i><sub>0</sub> increases. The results reveal the flow evolution law of hypersonic mixed layer under the influence of convex curvature, and provide a certain reference for designing the shape of hypersonic vehicle to achieve aerodynamic drag reduction and thermal protection characteristics.

Creep characteristics and damage model of coal–rock combinations with different height ratios

Numerous coal pillars are left after the coal mining process. The composite structure comprising a roof and coal pillar has prominent creep characteristics, which threaten safe underground mining. Therefore, the creep characteristics of coal-rock combinations should be studied to ensure the safety of quarry and surface. Uniaxial creep tests under static load axial pressure and different height ratios were performed using a self-designed rock creep disturbance test device to determine the effect of height ratio and axial pressure on the creep characteristics of coal–rock combinations. From the test results, a creep damage model for coal–rock combinations was established by combining the elastomer, fractional Kelvin body, plastic body, Abel dashpot, and modified nonlinear viscoplastic body; introducing damage variables D related to stress, height ratio, and time; and deriving a one-dimensional creep equation. An improved nonlinear least squares method based on pattern search was utilized to invert the creep parameters. The results of the creep equation calculation were fitted with the experimental results with good results. The creep curve with a height ratio of 2:1 was predicted with good results. The research results provide theoretical references for long-term stability analysis of rock engineering.