Double-cone Flow Research Articles

High-fidelity state-to-state modeling of hypersonic flow over a double cone

The state-of-the-art high-fidelity state-to-state (StS) model is performed to investigate the hypersonic shock wave/laminar boundary layer interaction over a 25°–55° double cone. This work aims to clarify whether the shortcomings of thermochemical models are the underlying source for the discrepancies between the simulations and experiments. A high-enthalpy nitrogen flow with a Mach number of 11.54 and a unit Reynolds number of 4.394×105/m is considered. We first find that the StS and widely used two-temperature models yield two different shock reflection patterns (i.e., the regular reflection and Mach reflection, respectively). However, the surface pressure and heat flux distributions predicted by the two models are generally consistent, which are not influenced by the differences in the shock patterns, dissociation rates, and non-Boltzmann vibrational distributions in the flowfields. Moreover, the StS model fails to match the experiments in spite of fairly limited improvement. Our findings indicate that the shortcomings of thermochemical models are not the main reason for the discrepancies in the simulations and experiments for the high-enthalpy nitrogen double-cone flow.

Three-dimensionality of hypersonic laminar flow over a double cone

Hypersonic laminar flow over a canonical 25°–55° double cone is studied using computational fluid dynamics and global stability analysis (GSA) with a free-stream Mach number of 11.5 and various unit Reynolds numbers. Axisymmetric simulations reveal that secondary separation occurs beneath the primary separation bubble beyond a critical Reynolds number. The numerical results agree well with existing experiments and the triple-deck theory with the axisymmetric effect on the incoming boundary layer treated by the Mangler transformation. The GSA identifies a three-dimensional global instability that is azimuthally periodic immediately prior to the emergence of secondary separation. The criterion of the onset of global instability in terms of a scaled deflection angle established for supersonic compression corner flows (Hao et al., J. Fluid Mech., vol. 919, 2021, A4) can be directly applied to double-cone flows. As the Reynolds number is further increased, the flow is strongly destabilized with the coexistence of multiple stationary and low-frequency oscillating unstable modes. Direct numerical simulations confirm that the supercritical double-cone flow is intrinsically three-dimensional, unsteady and exhibits strong azimuthal variations in the peak heating.

An implicit kinetic inviscid flux for predicting continuum flows in all speed regimes

In this study, the kinetic inviscid flux (KIF) is improved and coupled with an implicit strategy. The KIF is a recently proposed numerical method, which is a dynamic combination of the kinetic flux vector splitting (KFVS) method and the totally thermalized transport (TTT) method. The inherent microscopic mechanism of the KFVS makes the KIF good at solving shock waves and avoiding the numerical shock instability phenomenon. When developing the implicit KIF, it is noticed that, in boundary layers, the KFVS part of the KIF not only reduces the accuracy but also seriously reduces the Courant–Friedrichs–Lewy (CFL) number. As a result, a new weight is proposed in this paper to combine the KFVS method with the TTT method properly. Besides admitting the use of larger CFL numbers, this new weight also contributes to more accurate numerical results like pressure, friction coefficient, and heat flux when solving shock waves, boundary layers, and complex supersonic/hypersonic flows. To examine the validity, accuracy, and efficiency of the proposed method, six numerical test cases covering the whole speed regime are conducted, including the hypersonic viscous flow past a cylinder, the hypersonic double-cone flow, the hypersonic double-ellipsoid flow, the laminar shock-boundary layer interaction, the supersonic flow around a ramp segment and the subsonic lid-driven cavity flow.

Hypersonic flow over spherically blunted double cones

A hypersonic shock wave/laminar boundary-layer interaction over a canonical double-cone configuration is numerically investigated. A moderate-enthalpy flow of with a Mach number of 9.87 and a unit Reynolds number of is considered. Special emphasis is given to the influence of leading-edge bluntness. The results indicate that the double-cone flow is insensitive to small bluntness in terms of shock structures, separation region sizes and surface pressure and heat flux distributions. A critical nose radius is observed, beyond which the separation bubble grows dramatically. The numerical data are analysed and interpreted based on a triple-deck formulation. It is shown that the sudden change in flow features is mainly caused by pressure overexpansion on the first cone due to leading-edge bluntness, such that the skin friction upstream of the separation is significantly reduced and the upstream pressure can no longer resist the large adverse pressure gradient induced by shock impingement. An estimation of the critical radius is established based on the pressure correlations of Blick & Francis (AIAA J., vol. 4 (3), 1966, pp. 547–549) for spherically blunted cones. Simulations at a higher enthalpy with the presence of both vibrational relaxation and air chemistry show a similar trend with increasing nose radius. The proposed criterion agrees well with the experimental observations.

Effects of vibrational nonequilibrium on hypersonic shock-wave/laminar boundary-layer interactions

Recent numerical simulations of hypersonic double-cone and hollow-cylinder flare experiments have incorrectly predicted the sizes of separation regions, even at total enthalpies as low as 5.44 and 5.07 MJ/kg. This study investigates the effects of vibrational nonequilibrium to explain these discrepancies. According to an assessment of various flow models under post-shock conditions in comparison with state-specific simulations, the predictions obtained by treating the vibrational modes of molecular nitrogen and oxygen as a single mode, a strategy adopted routinely by the aerospace computational fluid dynamics community, are in close agreement with the state-specific results in terms of post-shock temperature and density profiles, whereas separation of the vibrational modes and assumption of calorically perfect gases would lead to evident errors. The double-cone flow is found to be sensitive to different flow models. In contrast, their effects on hollow-cylinder flare flow are insignificant. Given that the most representative flow model still underestimates the sizes of the separation regions for double cone flow and overestimates those for hollow-cylinder flare flow, it is concluded that inaccurate modeling of vibrational nonequilibrium may not be responsible for the discrepancies observed at the lowest total enthalpies. Suggestions for further study are also presented.

Numerical investigation of oxygen thermochemical nonequilibrium on high-enthalpy double-cone flows

Hypersonic thermochemical nonequilibrium flows over a double-cone configuration are numerically investigated. Simulations with oxygen as the test gas are performed using different coupling models of vibrational excitation and dissociation, including a conventional two-temperature model as the baseline and an improved model established on elementary kinetics and validated against existing shock tube experimental data. For the condition with the highest total enthalpy, the improved model predicts a larger separation region and greater peak heat flux with relative differences of 20.3% and 29.2%, respectively, compared with the baseline two-temperature model. The differences are attributed to inaccurate modeling of the vibration–dissociation coupling effects by the conventional two-temperature model, which overestimates the post-shock degree of dissociation and underestimates the post-shock temperature. The size of the separation bubble is therefore altered due to the change in its density. These findings may help to explain the large discrepancies found between numerical results and experimental data for high-enthalpy double-cone flows in hypersonic studies.

Global Sensitivity Analysis and Uncertainty Quantification for a Hypersonic Shock Interaction Flow

Hypersonic gas flows over concentric double-cone configurations are commonly used to investigate shock–shock and shock wave/boundary-layer interaction phenomena, and are characterized by the formation of interacting flow structures that are highly sensitive to models used in flow simulation. The work presented here is intended to clarify the influence of several modeling parameters and approximations on simulation output quantities through a more general and systematic approach than has previously been employed for this type of flow, with the ultimate goal of improved model validation for simulation of hypersonic shock interactions. Global sensitivity analysis and uncertainty quantification techniques are integrated with a direct simulation Monte Carlo gas flow simulation code, and a large number of these Monte Carlo simulations are performed for a representative hypersonic double-cone flow. Aleatory and epistemic uncertainties are considered in sensitivity analysis/uncertainty quantification calculations, both independently and in combination, through a variety of probabilistic sampling procedures. These procedures include a novel uncertainty quantification technique that combines elements of importance sampling sensitivity analysis with Latin hypercube sampling, as an efficient surrogate-free means of simultaneously considering mixed uncertainty types. Following a strong engineering interest in surface heating augmentation due to hypersonic shock wave/boundary-layer interaction, this paper focuses on surface heat flux at a shock impingement point as an output quantity in sensitivity analysis/uncertainty quantification calculations; other output quantities of interest include impingement point pressure and the integrated force and heat transfer rate over the model surface.

Simulation and Experimental Validation of Hypersonic Shock Wave Interaction

The present paper examines the relevance of grid and simulation accuracy of hypersonic CFD in terms of hypersonic sharp double-cone flow. The flow grid and normal grid each adopted 250×100, 500×100, 1000×100, 500×200, 1000×200, 1000×400 and so on grids. When the normal grid was 100, the wall pressure and heat flux distribution obtained from flow grid 500 and 1000 were consistent, indicating that the solution of flow grid convergence was obtained. However, some difference was observed when the separation zone was compared with the experimental data. In increasing the normal grid number and adopting grid 500×200, the position of the separation point, wall pressure and heat flux peak was shown to be consistent with the experiment. When the grid was further encrypted, the calculation using grid 1000×200 and 1000×400 was equal to that using grid 500×200. The simulation of hypersonic sharp double-cone flow also showed that when the separation zone of the simulation was less than the experimental measurement, the wall pressure and heat flux peak moved forward. This is because the backwardness of the intersection of the separation shock and the first shock resulted in the forwardness of the intersection of the first shock and the second shock after interference, making the work region of the induction shock and boundary layer move forward. The key challenge in achieving the correct simulation of the hypersonic sharp double-cone flow is explained as follows: the algorithm can not only capture shock wave strength correctly and give the adverse pressure gradient formed by the interfering shock wave near the wall accurately. It can also prevent the numerical dissipation of the algorithm from affecting the simulation accuracy of the viscous boundary layer to ensure the correct prediction of the size of the separation zone.

Optimum Design of a Screw-In Venturi Flow Sensor

To study discharge coefficient linearity of screw-in venturi flow sensor, the effect of the screw-in blade attached to the sensor on discharge coefficient was analyzed, the structure of the screw-in blade was optimized by CFD software. Through the observation of velocity field, it was found that discharge coefficient will basically remain unchanged at low Reynolds number, while it declines greatly at high Reynolds number because of the guidance of the screw-in blade, as a result discharge coefficient linearity becomes better at the same measurement range. Orthogonal array of DN100 was designed for 10:1 measurement range to explore effect of geometric parameters of the screw-in blade on discharge coefficient linearity. Optimum structure for the screw-in blade is determined as follows: number of blade is 4, back slip angle of blade is 50°, front slip angle of blade is 5° and height of blade is 10.5mm. The numerical simulation indicates discharge coefficient linearity of the optimal screw-in venturi flow sensor is 0.601%,which is better than that of double-cone venturi flow sensor.

Hypersonic Double-Cone Flow with Applied Magnetic Field

The electrodynamic effect on the partially ionized flow around magnetized bodies was numerically investigated. In particular, the double-cone model was considered because, unlike a simple blunt-nosed model, it generates a complex flow including shock-shock and shock-boundary-layer interactions. Such flows are significantly affected by an applied magnetic field. The modification of the flowfield due to the applied magnetic field causes drag force enhancement and/or the mitigation of the aerodynamic heating. This is enhanced with increasing magnetic field intensity. Furthermore, local flow features such as the separation bubble and the local peak heating that appears near the kink point of the double-cone model are significantly affected. The size of the separation bubble increases with increasing magnetic field intensity and is clearly influenced by the configuration of the magnetic field. The local peak heating is reduced with increasing magnetic field intensity, but the effect of the magnetic field configuration is weak.

Numerical Simulation and Optimum Design of a Double-Cone Flow Sensor

This research based on a new type of Double-cone flow sensor, using computational fluid dynamics (CFD) method and orthogonal experiment to investigate the influence of key geometric factors, such as fore-and-aft cone angle, equivalent diameter ratio and channel flow length, on discharge coefficient, discharge coefficient linearity and relative pressure loss of double-cone flow sensor, and finally predict the best optimal match of these geometric factors. The turbulence model is RNG and the medium for simulation is water. After the simulation, a special device for calibration was set up to verify the computational conclusion. The results show that the biggest deviation of simulation on discharge coefficient linearity and relative pressure loss are less than 0.4% and 1.2%, the results simulated by CFD are in good agreement with that by experiment.

Numerical Investigation of Hypersonic Double-Cone Flow

Hypersonic flow of Mach number 8 past a 25°-50° double cone geometry is numerically simulated at ReD=4.8E5. Complicated flow structures, including Type V shock-shock interaction, shock-boundary layer interaction, separation and reattachment at the corner are presented and discussed. The surface pressure and heat transfer rate distributions are also calculated and compared with the experimental data. Results show that both the 2nd order MUSCL and 5th order WENO could accurately reproduce the shock structures, while the higher order scheme could predict a more accurate size of separation zone. Generally, the size of the separation zone is underestimated with an overvalued pressure distribution after reattachment employing the full turbulent models. On the other hand, transition induced by the reattachment shock has been calculated using transition model and the results of pressure peak and the size of separation zone show good agreement with the experimental measurements.

Effects of Numerics on Navier-Stokes Computations of Hypersonic Double-Cone Flows

A systematic study of the effects of the numerics on the simulation of a steady hypersonic flow past a sharp double cone is presented. Previous studies have shown that the double-cone flow is challenging to compute, making it useful for testing both numerical schemes and physical models. We focus on the numerical aspects only and show that the results are very sensitive to the numerical flux evaluation method and slope limiter used

Gas diffusion in polymer solutions: A double‐cone flow technique

AbstractA new double‐cone flow technique for an experimental investigation of gas diffusion in polymer solutions is described. A theoretical development of the pertinent convective diffusion problem for the flow of a non‐Newtonian fluid over the double cone is presented. Experimental investigation of diffusion of carbon dioxide in aqueous solutions of certain polymers was carried out. The diffusion coefficient deduced from this work shows a marginal enhancement over its value in pure solvent. Possible mechanistic explanations for this phenomenon are explored.