Compressible Boundary Layer Research Articles

Local-Variable-Based Transition Model for Hypersonic Flows Considering Wall Mass Injection

Pyrolysis gas injection during the ablation process will affect the hypersonic boundary-layer transition. This paper proposes a three-equation γ-Reθ-fb transition model that considers wall mass injection. First, the boundary conditions of wall mass injection are established and verified. Second, based on analysis of the compressible boundary-layer solutions under wall mass injection, new transition correlations are developed. This allows an injection factor transport equation to be constructed using strictly local variables, and this equation is coupled with the γ-Reθ transition model. Additionally, to model the wall mass injection effects in the fully turbulent zone, the wall boundary conditions for the specific turbulence dissipation rate are amended. The results of numerical simulations show that the transition onset locations and the changes in the heat transfer rate are reasonably consistent with experimental data.

Effects of Mach number on space-time characteristics of wall pressure fluctuations beneath turbulent boundary layers

Wall pressure fluctuations beneath turbulent boundary layers are a fundamental source of aerodynamic noise by exciting the wall structure, with their space-time characteristics serving as the basic ingredient for predicting the wall structural response. To this end, direct numerical simulations of fully developed compressible turbulent boundary layers at Mach numbers of 0.5, 1.2, and 2.0 are conducted to investigate wall pressure fluctuations comprehensively. The effects of Mach number on the single-point statistics of wall pressure fluctuations, such as the root mean square, skewness and flatness factors, probability density function, and frequency spectrum, are assessed to be very weak. Regarding the space-time characteristics, the convection velocity Uc determined by the space-time correlation of wall pressure fluctuations increases slightly with the Mach number, which only reflects the convective behavior of turbulent vortices. On the wavenumber–frequency spectrum, characteristic peaks of both the acoustic wave and convective vortices are identified. At Mach 0.5, the peaks of the fast (Uc+c) and slow (Uc−c) acoustic waves are unattached to others with c denoting acoustic speed, while only the peak of the fast acoustic wave is distinguishable from the convective peak at Mach 1.2 and 2.0. Due to the aerodynamic heating at supersonic conditions, the thermal effect on acoustic speed should be taken into account in determining the acoustic wavenumber. By introducing a convective Prandtl–Glauert parameter, a refined relation is proposed to provide a more accurate depiction of the acoustic domain in the wavenumber–frequency spectrum.

The intrinsic scaling relation between pressure fluctuations and Mach number in compressible turbulent boundary layers

The intrinsic scaling relation between pressure fluctuations and Mach number in compressible turbulent boundary layers

Linear stability analysis of compressible boundary layer over an insulated wall using compound matrix method: Existence of multiple unstable modes for Mach number beyond 3

The linear spatial stability of a parallel two-dimensional (2D) compressible boundary layer on an adiabatic plate is investigated by considering both 2D and three-dimensional (3D) disturbances. The compound matrix method is employed here, for the first time, for compressible flows, which, unlike other conventional techniques, can efficiently eliminate the stiffness of the equations governing the spectral amplitudes. The method is first validated with published results in the literature corresponding to spatial and temporal instability of flows ranging from low subsonic to high supersonic Mach numbers (M), which shows a good match depending upon the proper choice of free-stream temperature and the wall dispersion relation. Subsequently, flow compressibility effects and the spanwise variation of disturbances are also investigated for M ranging from low subsonic to high supersonic cases (from M = 0.1 to 6). Mack (AGARD Report No. 709, 1984) reported the existence of two unstable modes for M > 3 from viscous calculations (the so-called “second mode”) that subsequently fuse to create only one unstable zone when M increases. Our calculations show a series of higher-order unstable modes for M > 3 in addition to the findings of Ma and Zhong [“Receptivity of a supersonic boundary layer over a flat plate. Part 1. Wave structures and interactions,” J. Fluid Mech. 488, 31–78 (2003)], where such higher-order modes for supersonic boundary layers are all noted to be spatially stable. The number and the frequency extent of the corresponding unstable zones increase with an increase in M beyond 3 while propagating downstream at a higher speed than those corresponding to incompressible, subsonic, and low supersonic (M < 2) cases.

Adjoint-based optimisation of time- and span-periodic flow fields with Space–Time Spectral Method: Application to non-linear instabilities in compressible boundary layer flows

We aim at computing time- and span-periodic flow fields in span-invariant configurations. The streamwise and cross-stream derivatives are discretised with finite volumes while time and the span-direction are handled with pseudo-spectral Fourier-collocation methods. Doing so, we extend the classical Time Spectral Method (TSM) to a Space–Time Spectral Method (S-TSM), by considering non-linear interactions of a finite number of time and span harmonics. For optimisation, we introduce an adjoint-based framework that allows efficient computation of the gradient of any cost functional with respect to a large-dimensional control parameter. Both theoretical and numerical aspects of the methodology are described: evaluation of matrix–vector products with S-TSM Jacobian (or its transpose) by algorithmic differentiation, solution of fixed-points with quasi-Newton method and de-aliasing in time and space, solution of direct and adjoint linear systems by iterative algorithms with a block-circulant preconditioner, performance assessment in CPU time and memory. We illustrate the methodology on the case of 3D instabilities (first Mack mode) triggered within a developing adiabatic boundary layer at M = 4.5. A gradient-ascent method allows to identify a finite-amplitude 3D forcing that triggers a non-linear response exhibiting the strongest time- and span-averaged drag on the flat-plate. In view of flow control, a gradient-descent method finally determines a finite amplitude 2D wall-heat flux that minimises the averaged drag of the plate in presence of the previously determined non-linear optimal forcing.

Estimating Velocity Correlations Using Single Pixel PIV

In this work, we analyze the possibility of determining correlations of turbulent velocity fluctuations from PIV data with improved spatial resolution. The analysis is based on the method presented by Oldenziel et al. (2023), where a joint probability density function of the velocity at two locations is calculated from the single-pixel ensemble correlation for these locations. Synthetic PIV images are used to discuss the occurrence of random and systematic errors and to derive the number of image pairs required for a determination of the correlation coefficient with desired uncertainty, depending on the particle image density. Compared to classical window correlation, the presented method can improve the spatial resolution by about one order of magnitude if a very large number of PIV image pairs are available and/or many statistically independent points with identical flow properties can be used. As an example of application, we show the spatial distribution of a two-point correlation in a compressible turbulent boundary layer flow for a reference point near the wall.

Similar Solutions for Changing Characteristics of Natural Convection Laminar Flow around a Vertical Rectangular Inclined Plane Surface

The study investigates laminar natural convection flow around a vertical rectangular inclined plane surface, specifically focusing on the effects of viscous and pressure stress work. Previous research primarily addressed these effects in two-dimensional natural convection flow scenarios, while this study extends the analysis to encompass three exterior situations, accounting for variations in fluid properties outside compressible boundary layers. Employing numerical methods, the study aims to predict essential flow parameters including Prandtl’s number (Pr), controlling parameter (C), and additional parameters (A, B, D, E, ∅). The investigation yields velocity profiles (F'(0), S'(0)), temperature profiles , skin frictions (F''(0), S''(0)), and heat transfer coefficients θ'(0). Numerical results are presented to illustrate the impact of different parameters on these flow characteristics. Additionally, tabulated data in Tables-2 and Tables-3 offer further insights into the predicted flow parameters and their variations under varying conditions.

Eddy-viscosity-improved resolvent analysis of compressible turbulent boundary layers

An improved resolvent analysis is proposed in the regime of compressible turbulent boundary layers. To better model nonlinear processes in the input, the resolvent framework is augmented by adding eddy viscosity. To this end, we propose two eddy-viscosity models: a modified Cess eddy-viscosity model coupling the compressibility transformation and outer-layer correction, and a new eddy-viscosity model based on an empirical relationship and mixing-length theory. Both are incorporated into the resolvent operator to examine the performance of the eddy-viscosity-improved resolvent-based reduced-order modelling. Results of the augmented resolvent analysis are compared qualitatively and quantitatively with the first leading mode of spectral proper orthogonal decomposition, by checking the profiles and cross-spectral densities of velocities, density and temperature in two hypersonic turbulent boundary layers under different wall conditions. Higher accuracy of the turbulence prediction is achieved by adding the proposed eddy-viscosity models, particularly for the energetic cycle in the outer-layer region where strong nonlinear energy transfer exists.

Roughness effects on compressible turbulent boundary layers under different Mach numbers and wall temperature conditions

Compressible turbulent boundary layers over a zero-pressure gradient flat plate with three-dimensional sinusoidal roughness are simulated by direct numerical simulation. The roughness effects on surface drag, velocity transformation, and turbulence fluctuation characteristics are analyzed in a wide range of Mach numbers (Ma∞ = 2.25–7.25) and different ratios of wall-to-recovery temperature (Tw/Taw = 0.43 and 0.84) conditions. It is found that the roughness significantly amplifies the surface drag coefficient due to the extra pressure drag induced by roughness, and the relative increase in surface drag induced by the roughness rises by 31.1% when Ma∞ changes from 2.25 to 7.25. Current compressible velocity transformations cannot make the logarithmic region of velocity profiles independent of Tw/Taw conditions for rough cases due to the strong wall heat transfer effect below roughness peak. Therefore, a new velocity transformation (Uρt+) is proposed to make the logarithmic region of Uρt+ profiles and roughness induced a downward shift of Uρt+ profiles (ΔUρt+) in a logarithmic region independent of Ma∞ and Tw/Taw conditions. Further numerical experiments validate that, in hypersonic boundary layers, the relation between ΔUρt+ and equivalent sand-grain roughness height Reynolds number still satisfies the roughness function proposed earlier for incompressible flows. Moreover, roughness significantly changes the distribution of mean turbulent kinetic energy (TKE) in compressible turbulent boundary layers: TKE is suppressed at the bottom of roughness, while reaching its maximum at the roughness peak, which is 50%–60% larger than that in smooth case. Finally, the expansion/compression wave patterns induced by roughness alter the turbulence fluctuations in outer layer.

Inflow turbulence generation for compressible turbulent boundary layers

It is still challenging to generate high-quality inflow turbulence for the direct numerical and large-eddy simulations of compressible turbulent boundary layers (CTBL). Recently, Wang et al. [“Inflow turbulence generation using an equivalent boundary layer model,” Phys. Fluids 35, 075110 (2023)] proposed a new inflow turbulence generation method based on an equivalent boundary layer model for incompressible turbulent boundary layers. In the present study, the compressible equivalent boundary layer (CEBL) model is proposed and applied to the direct numerical simulation of supersonic turbulent boundary layers. The streamwise equilibrious CEBL approximates the streamwise developing CTBL by adding source terms to the governing equations to recover the mean mass, momentum, and energy balances at a given Reynolds number. Direct numerical simulation is performed to CEBL at free-stream Mach number 5.86 and friction Reynolds number 380. Comparison with the CTBL statistics at the same parameters validates the fidelity and reliability of the CEBL model. Turbulence generated by CEBL as well as the digital filtering and recycling-rescaling methods is used, respectively, to construct the inflow conditions for the direct numerical simulation of supersonic turbulent boundary layers. Results show that the CEBL method has great superiority in reducing the adjustment length compared with the other two methods. In addition, a correction method designed for the high inflow Reynolds number is also introduced.

Attenuation of the acoustic noise radiated by a compressible boundary layer through injection of a vibrationally active gas

Attenuation of the acoustic noise radiated by a compressible boundary layer through injection of a vibrationally active gas

Asymptotic boundary condition for numerical modeling of wave packets in a supersonic boundary layer

Within the framework of linear stability theory, a simple non-stationary boundary condition is developed to simulate the far-field asymptotic behavior of linear wave packets propagating in a compressible boundary layer. This condition allows us to skip the linear stage of instability evolution in direct numerical simulations (DNS) of laminar-turbulent transition. It is also suggested to perform numerical simulations of the linear stage without recalculating the Jacobi matrix in the Newton iteration procedure. Robustness and efficiency of the both approaches are evaluated by computations of the first-mode wave packet propagating in the boundary layer on a flat plate at freestream Mach number 2. DNS of the nonlinear stage show that the wave packet quickly breaks down into a turbulent spot, if its hump amplitude is umax′≥0.1U∞. This confirms an amplitude nature of the transition onset criterion. The spectral analysis indicates that the breakdown mechanism differs from the oblique, fundamental or subharmonic resonance and requires additional studies.

Investigation of non-ideal effects in compressible boundary layers of dense vapors through direct numerical simulations

In this work, we present an investigation about the sources of dissipation in adiabatic boundary layers of non-ideal compressible fluid flows. Direct numerical simulations (DNS) of transitional, zero-pressure gradient boundary layer flows are performed for two fluids characterized by different complexity of the fluid molecules, namely, “air” and siloxane MM. Different sets of thermodynamic free-stream boundary conditions are selected to evaluate the influence of the fluid state on both the frictional loss and the dissipation mechanisms. The thermophysical properties of siloxane MM are calculated with a state-of-the-art equation of state. Results show that the dissipation due to both time-mean strain field, irreversible heat transfer, and turbulent dissipation differs significantly depending on both the molecular complexity of the fluid and its thermodynamic state. The dissipation coefficient calculated from the DNS results is then compared against the one obtained using a reduced-order model (ROM), which solves the two-dimensional boundary layer flow equations for an arbitrary fluid [M. Pini and C. De Servi, “Entropy generation in laminar boundary layers of non-ideal fluid flows,” in 2nd International Seminar on Non-Ideal Compressible Fluid Dynamics for Propulsion and Power (Springer, 2020), pp. 104–117]. Results from both the DNS and the ROM show that low values of the overall dissipation are observed in the case of fluids made of simple molecules, e.g., air, and if the fluid is at a thermodynamic state in the proximity of that of the vapor–liquid critical point.

Linear stability of a compressible flow in a channel

Summary Modal instabilities in a compressible flow through a channel at high Reynolds numbers are studied for three-dimensional (3D) perturbations. In addition to the Tollmien–Schlichting (TS) mode, there exist compressible modes in a channel flow that do not have a counterpart in the incompressible limit. The stability characteristics of these compressible modes, obtained through numerical calculations, are compared with boundary layer and Couette flows that have been previously studied. The dominant compressible instabilities in a channel flow are shown to be viscous in nature, in contrast to compressible boundary layer modes. For general compressible bounded-domain flows, a necessary condition for the existence of neutral modes in the inviscid limit is obtained, and this criterion is used to determine critical Mach numbers below which the compressible modes remain stable. This criterion also delineates a range of wave-angles which could go unstable at a specified Mach number. Asymptotic analysis is carried out for the lower and upper branches of the stability curve in the limit of high Reynolds number for both the T-S and the compressible modes. A common set of relations are identified for the scaling exponents, and the leading order eigenvalues for the unstable modes are obtained through an adjoint-based procedure. The asymptotic analysis shows that the stability boundaries for 3D perturbations at high Reynolds numbers can be calculated from the strain rate and the temperature of the base flow at the wall.

Analysis of improved digital filter inflow generation methods for compressible turbulent boundary layers

We propose several enhancements to improve the accuracy and performance of the digital filter turbulent inflow generation technique and assess their efficacy in the context of wall-resolved large-eddy simulations of a compressible turbulent boundary layer. Improvements of accuracy include a more realistic correlation function for the transversal directions, target length scales that vary with wall-distance, and a counter-intuitive approach that involves the suppression of streamwise velocity fluctuations at the inflow. For improving the computational performance, we propose to generate the inflow data in parallel in single precision and at a prescribed time interval based on the turbulence time scale, and not at every time-step of the simulation. Based on the results of 7 wall-resolved large-eddy simulations, we find that the new correlation functions and the considered performance improvements are beneficial and therefore desired. Suppressing streamwise velocity fluctuations at the inflow leads to the fastest relaxation of the pressure fluctuations; however, this approach increases the adaptation length defined in terms of compliance with the von Kármán integral equation. The adaptation length can be shortened by artificially increasing the wall-normal Reynolds stresses, thereby preserving the desired turbulence kinetic energy level. A detailed inspection of the Reynolds stress transport budgets reveals that the observed spurious spatial transients are largely driven by pressure-related terms. For instance, increased values of u′p′¯ are found throughout the computational domain when a physical Reynolds stress distribution is prescribed at the inflow. Therefore, efforts to enhance digital filter techniques should aim at modeling pressure fluctuations as well as their correlation with the velocity components.

Mars2020 Entry Shock Layer Thermochemical Kinetics Examined by Megahertz-Rate Laser Absorption Spectroscopy

A mid-infrared laser absorption diagnostic was deployed to examine the evolution of thermophysical properties across a simulated Mars2020 shock layer in the Electric Arc Shock Tube (EAST) facility at NASA Ames. Rapid laser tuning techniques using bias-tee circuitry enabled quantitative temperature and number density measurements of CO2 and CO with microsecond resolution over a shock velocity range of 1.30–3.75 km/s. Two interband cascade lasers were utilized at 4.17 and 4.19 μm to resolve rovibrational CO2 lines spanning across J′′=58 to J′′=140 in the asymmetric stretch fundamental bands. In test cases with enough energy to dissociate CO2, a quantum cascade laser scanned multiple transitions of the CO fundamental bands near 4.98 μm. The results are compared to the Data Parallel Line Relaxation (DPLR) code and Lagrange shock tube analysis (LASTA) simulations of the shock layer. A numerical simulation of the compressible boundary layer is used to account for measurement sensitivities to this flow feature in the EAST facility. Temperature and species transients are compared to multiple chemical kinetic models. The laser absorption data presented in this work can be used to refine the models used to simulate the aerothermal environment encountered during Mars entry.

Conditional analysis on extreme wall shear stress and heat flux events in compressible turbulent boundary layers

This study presents a comprehensive analysis on the extreme positive and negative events of wall shear stress and heat flux fluctuations in compressible turbulent boundary layers (TBLs) solved by direct numerical simulations. To examine the compressibility effects, we focus on the extreme events in two representative cases, i.e. a supersonic TBL of Mach number $M=2$ and a hypersonic TBL of $M=8$ , by scrutinizing the coherent structures and their correlated dynamics based on conditional analysis. As characterized by the spatial distribution of wall shear stress and heat flux, the extreme events are indicated to be closely related to the structural organization of wall streaks, in addition to the occurrence of the alternating positive and negative structures (APNSs) in the hypersonic TBL. These two types of coherent structures are strikingly different, namely the nature of wall streaks and APNSs are shown to be related to the solenoidal and dilatational fluid motions, respectively. Quantitative analysis using a volumetric conditional average is performed to identify and extract the coherent structures that directly account for the extreme events. It is found that in the supersonic TBL, the essential ingredients of the conditional field are hairpin-like vortices, whose combinations can induce wall streaks, whereas in the hypersonic TBL, the essential ingredients become hairpin-like vortices as well as near-wall APNSs. To quantify the momentum and energy transport mechanisms underlying the extreme events, we proposed a novel decomposition method for extreme skin friction and heat flux, based on the integral identities of conditionally averaged governing equations. Taking advantage of this decomposition method, the dominant transport mechanisms of the hairpin-like vortices and APNSs are revealed. Specifically, the momentum and energy transports undertaken by the hairpin-like vortices are attributed to multiple comparable mechanisms, whereas those by the APNSs are convection dominated. In that, the dominant transport mechanisms in extreme events between the supersonic and hypersonic TBLs are indicated to be totally different.

Near-wall model for compressible turbulent boundary layers based on an inverse velocity transformation

In this work, a near-wall model, which couples the inverse of a recently developed compressible velocity transformation (Griffin et al., Proc. Natl Acad. Sci., vol. 118, 2021, p. 34) and an algebraic temperature–velocity relation, is developed for high-speed turbulent boundary layers. As input, the model requires the mean flow state at one wall-normal height in the inner layer of the boundary layer and at the boundary-layer edge. As output, the model can predict mean temperature and velocity profiles across the entire inner layer, as well as the wall shear stress and heat flux. The model is tested in an a priori sense using a wide database of direct numerical simulation high-Mach-number turbulent channel flows, pipe flows and boundary layers (48 cases, with edge Mach numbers in the range 0.77–11, and semi-local friction Reynolds numbers in the range 170–5700). The present model is significantly more accurate than the classical ordinary differential equation (ODE) model for all cases tested. The model is deployed as a wall model for large-eddy simulations in channel flows with bulk Mach numbers in the range 0.7–4 and friction Reynolds numbers in the range 320–1800. When compared to the classical framework, in the a posteriori sense, the present method greatly improves the predicted heat flux, wall stress, and temperature and velocity profiles, especially in cases with strong heat transfer. In addition, the present model solves one ODE instead of two, and has a computational cost and implementation complexity similar to that of the commonly used ODE model.

Numerical study of the influence of local foreign-gas injection on the linear stability of compressible boundary layer

Numerical study of the influence of local foreign-gas injection on the linear stability of compressible boundary layer

Compressible boundary layer velocity transformation based on a generalized form of the total stress

Compressible boundary layer velocity transformation based on a generalized form of the total stress