Hypersonic Turbulence Research Articles

Polarization and coherence properties of a partially coherent elegant Laguerre–Gaussian vortex beam in turbulent plasma

The analytical expressions for the cross-spectral density matrix elements of the partially coherent elegant Laguerre–Gaussian (eLG) vortex beam propagating through anisotropic turbulent plasma were derived based on the extended Huygens-Fresnel principle and used to study the changes in the polarization degree and the coherence degree of the partially coherent eLG vortex beam in the turbulent plasma. The numerical results show that the polarization degree of a partially coherent eLG vortex beam reaches a specific value (which is equal to the degree of polarization in the source plane) after a long propagation distance in the turbulent plasma. Moreover, this value is independent of the beam order, topological charge, correlation coefficient, wavelength of the source plane, anisotropy parameter, refractive index fluctuation variance, and outer and inner scales of the turbulent plasma. The results also show that with increasing distance, the coherence degree first decreases from unity and then oscillates around zero. However, this oscillation gradually disappears after traveling a long distance. Our results intuitively present the beam polarization and coherence properties through anisotropic hypersonic turbulence, which can be useful for optical communication in hypersonic turbulent environments.

Effect of bulk viscosity on the hypersonic compressible turbulent boundary layer

The impact of bulk viscosity is unclear with considering the increased dilatational dissipation and compressibility effects in hypersonic turbulence flows. In this study, we employ direct numerical simulations to conduct comprehensive analysis of the effect of bulk viscosity on hypersonic turbulent boundary layer flow over a flat plate. The results demonstrate that the scaling relations remain valid even when accounting for large bulk viscosity. However, the wall-normal velocity fluctuations $v_{rms}^{\prime \prime }$ decrease significantly in the viscous sublayer due to the enhanced bulk dilatational dissipation. The intensity of travelling-wave-like alternating positive and negative structures of instantaneous pressure fluctuations $p_{rms}^{\prime }$ in the near-wall region decreases distinctly after considering the bulk viscosity, which is attributed mainly to the reduction of compressible pressure fluctuations $p_{c,rms}^{+}$ . Furthermore, the velocity divergence $\partial u_{i} / \partial x_{i}$ undergoes a significant decrease by bulk viscosity. In short, our results indicate that bulk viscosity can weaken the compressibility of the hypersonic turbulent boundary layer and becomes more significant as the Mach number increases and the wall temperature decreases. Notably, when the bulk-to-shear viscosity ratio of the gas reaches a few hundred levels ( $\mu _b/\mu =O(10^2)$ ), and mechanical behaviour of the near-wall region ( $\kern 0.06em y^+\le 30$ ) is of greater interest, the impact of bulk viscosity on the hypersonic cold-wall turbulent boundary layer may not be negligible.

Turbulent heat flux and wall heat transfer in hypersonic turbulent boundary layers with wall disturbances

Hypersonic turbulence over disturbed walls can be encountered when the fuselage of the vehicles is ablated or installed with transpiration-cooling porous media, resulting in the variation of the wall heat transfer that complicates its accurate predictions. In this paper, we study the turbulent heat flux and wall heat transfer in hypersonic turbulent boundary layers at the free-stream Mach number of 6.0 subject to wall disturbances with different wall temperatures, with our focus on the compressibility effects. We found that the temperature fluctuation intensity and the turbulent heat flux are enhanced in the outer region, which is attributed to the higher mean temperature gradient induced by the wall disturbances. The solenoidal and dilatational components of the turbulent heat flux, obtained by the Helmholtz decomposition that splits the velocity fluctuations into the solenoidal and dilatational components, are of opposite signs, with the latter smaller in magnitude but showing the tendency of mitigating the former. The integration formula that decomposes the wall heat transfer into various physical processes reveals that the viscous dissipation generates the wall heat transfer, while the turbulent heat flux, work of pressure on dilatation and the mean flow convection transport it towards the free stream. The contribution of the dilatational motions to the viscous dissipation and turbulent heat flux is negligible compared with that of the solenoidal components.

Experimental investigation about the aerodynamic noise caused by hypersonic turbulence

In this study, experimental investigations pertaining to aerodynamic noise are conducted in a hypersonic quiet wind tunnel, which possesses the unique capability of operating in both quiet and conventional modes, achieved by controlling the bleed slot to regulate the boundary layer flow. The measurement of aerodynamic noise and analysis of coherent structures of hypersonic turbulence are accomplished employing pressure probes and the nano-tracer-based planar laser scattering technique. The characterization of aerodynamic noise within the freestream unveils that noise generated by turbulent structures on the nozzle wall is the primary factor affecting the turbulence intensity of the freestream flow. Regarding the acoustic radiation noise generated by the turbulence on the nozzle wall, a peak frequency ranging from 54 to 57 kHz is observed in its spectrum within a unit Reynolds number range of 0.3×107–1.1×107 m−1. Under different operation modes, the freestream pitot-pressure data feature the similar spectral slope of f−2.2 and f−12 before and after the aforementioned peak. Through wavelet analysis, scales of the coherent structure in the turbulent boundary layer are examined, revealing that the maximum energy streamwise scale of the coherent structure is approximately 2.47 mm under the unit Reynolds number of 0.7×107 m−1. The product of this scale with the characteristic frequency of 56 kHz obtained from fluctuating pressure measurements is close to the local sound speed of about 140 m/s.

Coherent structures and turbulent model refinement in oblique shock/hypersonic turbulent boundary layer interactions

In the present study, we investigate the evolution of turbulent statistics and coherent structures in hypersonic turbulent boundary layers at the Mach number of 5 impinged by oblique shock waves generated by the wedge with the angles of 14°, 10°, and 6°, inducing strong, mild, and incipient flow separation, by exploiting direct numerical simulation databases, for the purpose of revealing the underlying flow physics that are of significance to turbulent modeling. We found that the large-scale structures are amplified within the interaction zone, manifested in the form of large-scale low- and high-speed streaks with the spanwise length scale of boundary layer thickness, and gradually decay downstream, the process of which is extremely long. The abrupt variation in the characteristic length, time, and velocity scales as well as the incompatible viscous dissipation of the mean and turbulent kinetic energy results in the incorrect predictions by the Reynolds-Averaged Navier–Stokes (RANS) equation simulations, provided the models are established based on solving the transport equations of the turbulent kinetic equation and its viscous dissipation (k−ε or k−ω models, for instance). To amend this issue, we propose to refine the parameters in the model as the functions of wall pressure, the flow quantities related to multiple flow features. The RANS simulations with the k−ω SST model utilizing the proposed refinement improve greatly the accuracy of the skin friction, wall heat flux, and Reynolds shear stress downstream of the interaction zone, and the wall pressure distributions in hypersonic turbulence over compression ramp, suggesting its promising prospect in engineering applications.

An Aero-Optical Effect Analysis Method in Hypersonic Turbulence Based on Photon Monte Carlo Simulation

Aero-optical effects caused by hypersonic turbulence will affect the accuracy of optical sensors on aircraft. Traditional analysis methods, which do not consider absorption and scattering effects, cannot easily be used to completely describe the transmission process of light in hypersonic turbulence. In this paper, an aero-optical effect analysis method based on photon Monte Carlo simulation (MC-AOEA) was proposed to explain the distortion characteristics of aero-optical effects from the perspective of photon statistics. The energy distribution of photons in the transmission process was determined by taking a photon packet as a unit, and the microscopic statistics of the photon dissipation energy for all photon packets were calculated. The effectiveness of this method was verified by comparing the photon statistical parameters with the traditional optical distortion physical quantities. MC-AOEA was used to analyze the distortion of aero-optical effects at different altitudes and speeds. Additionally, the simulation results showed that, with the reduction in flight altitude and the enhancement of speed, the distortion of aero-optical effects was aggravated, and the energy loss was more serious, which provides a reference for the evaluation of aero-optical effect errors.

Calibrating hypersonic turbulence flow models with the HIFiRE-1 experiment using data-driven machine-learned models

In this paper we study the efficacy of combining machine-learning methods with projection-based model reduction techniques for creating data-driven surrogate models of computationally expensive, high-fidelity physics models. Such surrogate models are essential for many-query applications e.g., engineering design optimization and parameter estimation, where it is necessary to invoke the high-fidelity model sequentially, many times. Surrogate models are usually constructed for individual scalar quantities. However there are scenarios where a spatially varying field needs to be modeled as a function of the model’s input parameters. We develop a method to do so, using projections to represent spatial variability while a machine-learned model captures the dependence of the model’s response on the inputs. The method is demonstrated on modeling the heat flux and pressure on the surface of the HIFiRE-1 geometry in a Mach 7.16 turbulent flow. The surrogate model is then used to perform Bayesian estimation of freestream conditions and parameters of the SST (Shear Stress Transport) turbulence model embedded in the high-fidelity (Reynolds-Averaged Navier–Stokes) flow simulator, using shock-tunnel data. The paper provides the first-ever Bayesian calibration of a turbulence model for complex hypersonic turbulent flows. We find that the primary issues in estimating the SST model parameters are the limited information content of the heat flux and pressure measurements and the large model-form error encountered in a certain part of the flow.

Analysis of Gaussian beam broadening and scintillation index in anisotropic plasma turbulence

In this paper, new expressions for the long-term beam spreading and scintillation index of Gaussian beams in anisotropic plasma turbulent media are derived on the basis of the anisotropic hypersonic plasma turbulent refractive index undulation power spectrum combined with the Rytov approximation theory. Considering the asymmetry of turbulent eddies in the orthogonal xy-plane throughout the path, two anisotropy factors are introduced to parameterize the anisotropy properties of turbulent cells in the horizontal and vertical directions. The spreading and scintillation index of Gaussian beams in plasma turbulence are calculated, and the propagation characteristics of Gaussian beams in anisotropic plasma turbulence are analyzed. Results show that enhancing the anisotropic properties of hypersonic plasma turbulence can significantly improve the propagation performance of Gaussian beams in hypersonic plasma turbulence. The effect of hypersonic plasma turbulence on Gaussian beam increases with the increase of the refractive index undulation variance and the decrease of the turbulent outer scale and anisotropy parameters. The results provide a theoretical basis for the further study of the propagation properties of electromagnetic waves in hypersonic plasma turbulence.

Transitional flow structures in heated hypersonic boundary layers

Transition in a Mach 6 flared cone boundary layer over a heated wall has been investigated in the Mach 6 wind tunnel at Peking University using visualization, focused laser differential interferometry, infrared imaging, particle image velocimetry (PIV), and direct numerical simulation (DNS). The model's wall-temperature ratio η=Tw/T0 (where Tw and T0 are, respectively, the wall temperature and oncoming stream stagnation temperature) can be controlled to vary from 0.66 to 1.77. An ultrafast illumination image system has been used for Rayleigh-scattering visualization and PIV to experimentally capture the dynamics of the transition. Lagrangian flow structures are revealed by both the DNS results and the time-resolved PIV data. The effect of wall temperature on the transition is investigated, and it is found that increasing η initially delays but then promotes the transition to turbulence, with the reversal point being near η≈1. The turbulence onset mechanism over the heated wall for η=1.50, where first-mode-induced oblique breakdown dominates, is then investigated, and it is shown that lifting-up three-dimensional (3D) waves appear around the critical layer owing to the nonlinear development of the oblique first mode. Consequently, a downward sweep motion occurs to compensate for the lifting low-speed fluid, with the formation of a warped wave front. High-shear layers are created around the 3D Lagrangian waves and strengthened to cause the formation of a Λ-vortex. In general, this lifting-up 3D wavepacket has been confirmed to play a determining role in hypersonic turbulence production over a heated wall, which is similar to the findings in incompressible boundary layers.

Effect of an adverse pressure gradient on hypersonic wall pressure fluctuations

Measurements based on a plate-perpendicular fin model were conducted to investigate the effect of an adverse pressure gradient on hypersonic wall pressure fluctuations. The leading edge diameter of the perpendicular fin is designed to be 25 mm with a height of 200 mm. A linear sensor-array was used to measure the wall pressure fluctuation, and a numerical computation was carried out to validate the measurement. Wall pressure fluctuations were discussed in terms of two aspects: the time–frequency domain and spatial correlation. The flow types on the plate could be estimated by the sound pressure level distribution, and the dominant flow type that substantially contributes to the wall pressure fluctuations could be determined. The spatial correlation of wall pressure fluctuations was analyzed using the phase array technique, and two disturbance modes could be identified from the wavenumber map obtained using the beamforming algorithm. The investigation results revealed that the change in the unit Reynolds number caused by the variation in the inflow dynamic pressure leads to the change in the flow type and the distribution of wall pressure fluctuations. The small-scale vortices within the hypersonic laminar flow lead to the difference in the signs of the convective mode wavenumber and that generated by hypersonic turbulence.

Compressibility effects on hypersonic turbulent channel flow with cold walls

Compressibility effects on velocity and temperature fluctuations in hypersonic turbulence over cold walls are investigated by exploiting a direct numerical simulation database. We found that the compressibility effects are enhanced by the decrease in wall temperature, which is directly reflected by the rapid increase in velocity divergence and turbulent Mach number. Helmholtz decomposition is adopted to evaluate the genuine compressibility effects by splitting the velocity fluctuation into a solenoidal component and a dilatational component. As the wall temperature decreases, the vertical motion is gradually dominated by the dilatational component, while the wall-parallel motions still by the solenoidal component. The dilatational components tend to decrease the skin friction by around 4%–6%. The instantaneous and conditionally averaged field around strong compressive motions further suggests that the dilatational structures behave as traveling-wave packets surrounded by vortex clusters. To improve the strong analogy between temperature and velocity fluctuations, their correlation in spectral space is studied. The results show that they are strongly correlated at the scales of energy-containing motions, but they are mutually independent at small scales.

Dust Growth by Accretion of Molecules in Supersonic Interstellar Turbulence

Abstract We show that the growth rate of dust grains in cold molecular clouds is enhanced by the high degree of compressibility of a turbulent, dilute gas. By means of high-resolution (10243) numerical simulations, we confirm the theory that the spatial mean growth rate is proportional to the gas-density variance. This also results in broadening of the grain-size distribution (GSD) due to turbulence-induced variation of the grain-growth rate. We show, for the first time in a detailed numerical simulation of hydrodynamic turbulence, that the GSD evolves toward a shape that is a reflection of the gas-density distribution, regardless of the initial distribution. That is, in case of isothermal, rotationally forced turbulence, the GSD tends to be a lognormal distribution. We also show that in hypersonic turbulence, decoupling of gas and dust becomes important and that this leads to an even further accelerated grain growth.

Acoustic-wave-induced cooling in onset of hypersonic turbulence

We report a newly identified aerodynamic cooling mechanism in the onset of hypersonic wall-bounded turbulence. We first experimentally investigated a flared cone with a smooth surface in a Ma 6 wind tunnel using fast-response pressure sensors, Rayleigh scattering flow visualization, and infrared thermography, which confirmed a cooled region (denoted as CS) downstream of a highly heated region (denoted as HS) on the model, as shown by Franko and Lele [J. Fluid Mech. 730, 491–532 (2013)] and Sivasubramanian and Fasel [J. Fluid Mech. 768, 175–218 (2015)]. We then performed calculations based on both linear stability theory and direct numerical simulations to understand this mechanism. We found that the phase difference ϕpθ between the periodic pressure and dilatation waves plays an important role in the interchange between thermal and mechanical energy in a hypersonic wall-bounded flow. Using porous steel to modify the model surface’s sound admittance, we experimentally show that it is possible to modify the cosine value of ϕpθ to be negative near the wall and thus reduce the temperature growth. These results can provide insight into the thermal protection design of future hypersonic vehicles.

Statistical properties of Gaussian Schell-model beams propagating through anisotropic hypersonic turbulence

Hypersonic turbulence, causing the environment disturbance, is an important factor influencing optical propagation and optical communication. Based on the extended Huygens-Fresnel principle and second-order moments of the Wigner distribution function, we have derived the analytical expressions of the average intensity, the normalized propagation factor, and the normalized mean-squared beam width of Gaussian Schell-model beams in anisotropic hypersonic turbulence. The evolution properties demonstrate the severe beam expansion and beam quality degradation, and the influences of the source and turbulent parameters are discussed in detail. The comparison between anisotropic hypersonic turbulence and atmosphere turbulence is given, and it is proved that the influence of anisotropic hypersonic turbulence is much stronger. Our results play a guiding role in optical signal transmission in the turbulent environment induced by hypersonic aircraft.

Statistical properties of Gaussian Schell-model beams propagating through anisotropic hypersonic turbulence

Statistical properties of Gaussian Schell-model beams propagating through anisotropic hypersonic turbulence

Galactic dust evolution with rapid dust formation in the interstellar medium due to hypersonic turbulence

ABSTRACT Turbulence can significantly accelerate the growth of dust grains by accretion of molecules. For dust dynamically coupled to the gas, the growth rate scales with the square of the Mach number, which means that the growth time-scale can easily be reduced by more than an order of magnitude. The limiting time-scale is therefore rather the rate of molecular cloud formation, which means that dust production in the interstellar medium can rapidly reach the levels needed to explain the dust masses observed at high redshifts. Thus, turbulence may be the solution to the replenishment problem in models of dust evolution in high-redshift galaxies and explain the dust masses seen at $z$ = 7–8. A simple analytic galactic dust-evolution model is presented, where grain growth nicely compensates for the expected higher rate of dust destruction by supernova shocks. This model is simpler, relies on fewer assumptions and seems to yields a better fit to data derived from observations, compared to previous models of the same type.

Electromagnetic scattering characteristics of foil in hypersonic plasma turbulence

To investigate the electromagnetic scattering problem related to a foil in a turbulent hypersonic plasma environment, the scattering field formulas for hypersonic plasma turbulence were improved by applying the anisotropic power spectrum. Using the theory of electromagnetic scattering of a conducting object, the second moment of a conducting object's scattering field is obtained in the hypersonic plasma turbulence. Finally, the backscattering cross-section of the foil surrounded by the hypersonic plasma turbulence was calculated. The results showed that the fractal dimension led to an increase in the complexity of the hypersonic turbulent structure, and thus had a greater influence on the electromagnetic wave scattering. The scattering cross-section of the foil in the hypersonic turbulence decreases rapidly. Meanwhile, the anisotropic parameters in the model represent scale-dependent stretching of the turbulent eddy. As the anisotropic parameters of the turbulence increase, there will be less scattering of the hypersonic turbulence. At this point, the total scattering cross-section of the foil in hypersonic plasma turbulence increases gradually. By improving the aerodynamic shape of the aircraft, it can produce a large number of anisotropic turbulent eddies which can effectively improve the passive jamming capability when the foil is cast.

Influence of hypersonic turbulence in plasma sheath on synthetic aperture radar imaging

On the basis of the fractal theory and measurements of hypersonic turbulence, the spectral index, and two-dimensional (2D) power spectrum of the refractive index fluctuation are derived, and the 2D band-limited Weierstrass fractal function is applied to simulate the refractive index fluctuation in hypersonic turbulence. Thus, the impact of hypersonic turbulence on synthetic aperture radar (SAR) imaging system is simulated using the fractal phase screen method. Results show that the resolution of SAR imaging is severely deteriorated under the influence of hypersonic turbulence. The phase error caused by the turbulence microstructures in the plasma sheath becomes more apparent with the increase in the fractal dimension of the hypersonic turbulence. The larger Reynolds number associated with the hypersonic turbulence results in a more evident microstructure fluctuation and inferior imaging quality. Furthermore, when an aircraft flies at high speed, the azimuth focus is considerably sensitive to the turbulence microstructure along the direction of flow field. Consequently, hypersonic turbulence in the plasma sheath has a significantly larger effect on the azimuth than on the range in point-target imaging.

Power Spectrum of Refractive-Index Fluctuation in Hypersonic Plasma Turbulence

Anisotropic spatial distribution data of refractive-index fluctuation in hypersonic turbulence are obtained based on the experimental images of hypersonic turbulence. Furthermore, taking re-entry turbulent plasma fluctuation into consideration, the variance of the refractive-index fluctuation in hypersonic plasma is calculated based on the Saha equation and the expression of refractive index in hypersonic plasma. On this basic, the anisotropic power-spectral model of hypersonic plasma turbulence is established by introducing the orientation factor to the modified von Karman spectrum. Finally, the mutual coherence function (MCF) and the angle-of-arrival fluctuations of electromagnetic (EM) waves propagation in hypersonic plasma turbulence are calculated. Results show that the angle-of-arrival fluctuations have obvious differences between the directions of vertical to turbulent plasma flow field and parallel to it. The various gradients of the electron density along the direction of vertical to turbulent plasma flow field are far greater than the parallel to it, which causes the horizontal scale is larger than perpendicular scale of plasma eddies. Therefore, when EM waves propagating through plasma turbulence, the refractive effect of plasma eddies show obvious anisotropy. The results of this paper can be used to analyze the EM waves propagation characteristics in hypersonic plasma turbulence.

Electromagnetic waves propagation in hypersonic turbulence using fractal phase screen method

The experimental fractal measurements of hypersonic turbulence are used to calculate the scaling exponent, spectral index, and power spectrum of hypersonic turbulence. The characteristics of electromagnetic wave propagation through hypersonic turbulence are studied using the fractal phase screen method based on the Weierstrass fractal function. The effects of the fractal dimension, inner scale, outer scale, variance of the refractive index fluctuation, and the wavelength of incident electromagnetic wave on the diffracted average-intensity distribution by a fractal phase screen are analyzed. Results show that the variance of the refractive index fluctuation determines the ratio of coherent to incoherent intensity. The fractal dimension, Reynolds number, and outer scale of hype- rsonic turbulence determine the incoherent field distribution. As the variance of the refractive index decreases, the coherent portion of the diffracted average intensity becomes clearer. With the increasing fractal dimension, the maximum diffracted average intensity decreases and the incoherent intensity becomes more evident.