Dilatation Dissipation Research Articles

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.

Cyclic shear loading test for grout-sleeve joints in precast concrete shear wall structure

The reinforcement sleeve splicing technique has been utilized extensively in precast concrete shear wall structures, as it allows for achieving similar lateral capacity and deformation ability with cast-in-place (CIP) walls. However, investigation on shear behavior of the horizontal joint using this vertical connection is limited. In this study, six specimens of grout-sleeve (GS) joints designed for precast shear wall structures with single-row distributed reinforcements were subjected to cyclic loading tests under pure shear conditions, accompanied by three companion concrete-to-concrete (CC) joint specimens. The study investigated the influence of interfacial reinforcement ratio and surface roughness on the seismic performance of GS joints with different design details, aiming to understand their shear failure mechanism. The joint behavior under cyclic shear loading, including transverse dilation, strain development, and energy dissipation, was analyzed. Experimental results indicated that all specimens exhibited a significant pinching effect and strength degradation in hysteretic curves. Two types of shear failure, sliding failure along the grout-concrete interface with minimal wall cracking and diagonal compression failure with extensive concrete crushing above the grouted layer, are observed due to the roughness of the grout-concrete interface. This roughness also affects the curvature profile of interfacial reinforcement. A larger interfacial reinforcement ratio or a roughened interface can significantly increase the shear strength of the horizontal joints. However, although the GS joint and CC joint have similar failure modes, the variation in cracking patterns resulted in a reduction of up to 10.6 % in shear strength for the grout-sleeve joint. Nonetheless, it exhibited relatively ductile shear behavior compared to the concrete-to-concrete joint. A comparison of shear strength evaluation between five existing codes shows that Eurocode 2 gives the closest result to the test values.

Numerical Simulation of Supersonic Turbulent Separated Flows Based on k–ω Turbulence Models with Different Compressibility Corrections

The accurate prediction of supersonic turbulent separated flows involved in aerospace vehicles is a great challenge for current numerical simulations. Based on the k–ω equations, several different compressibility corrections are incorporated in turbulence models to improve their prediction capabilities. Two benchmark test cases, namely the ramped cavity and the compression corner, are adopted for the numerical validation. Detailed comparisons between simulations and experiments are conducted to evaluate the effect of compressibility corrections on turbulence models. The computed results indicate that compressibility corrections have a significant impact on turbulence model performance. The compressibility correction, considering the effects of both dilatation dissipation and pressure dilatation, is suitable for the prediction of compressible free shear layers, but it may have a negative impact on the prediction of low-speed flows in the near-wall region due to the severe underprediction of the wall skin friction coefficient. In comparison, the compressibility correction only considering the effects of dilatation dissipation is conservative, with decreased predictability of free shear layers in supersonic flows, although it improves the predictions of the original models without corrections.

Direct numerical simulations and spectral proper orthogonal decomposition analysis of shocklet-containing turbulent channel counter-flows

Counter-flow configurations in a confined channel flow provide an efficient framework to study high intensity turbulent mixing processes. In a previous study (Physical Review Fluids, 6(9), p.094603), a wall-bounded counter-flow turbulent channel configuration was presented as an effective framework for addressing certain challenges related to the study of compressibility effects on turbulence as an alternative to free shear layer and Poiseuille/Couette type flows. Here, the previous direct numerical simulations are extended to a higher Mach number (M=0.7) to quantify direct and indirect effects of compressibility. It is found that the configuration is able to produce large numbers of embedded shocklets, leading to significant asymmetry in probability density functions of dilatation. Reducing the Prandtl number from 0.7 to 0.2 increases the compressibility effect further by reducing the bulk heating in the channel. A peak turbulent Mach number close to unity is obtained, for which the contribution of the dilatational dissipation to the total dissipation is nevertheless found to be limited to ∼6%. Indirect effects of compressibility are much larger, with changes of up to 40% in Favre normal stresses, despite the mean flow and shear stress being almost unaffected by compressibility in this configuration. Given the inflectional nature of the turbulent mean flow it is also interesting to identify large structures. Spectral Proper Orthogonal Decomposition (SPOD) reveals a full spectrum with a slow decay of energy with mode number. Mode shapes are three-dimensional with the low frequencies displaying elongated streaks in the velocity field at the channel centre plane.

Control of Scramjet Inlet Recirculations Using Fuel Injection

A novel approach using ramp fuel injectors is here proposed to reduce or eliminate shock-induced recirculation regions in scramjet inlets. The study is performed using UArizona’s CFDWARP code solving the Favre-averaged Navier–Stokes equations closed by the revised Wilcox model with dilatational dissipation and rapid compression corrections. The results obtained are representative of hydrogen fuel injected after the second shock of a three-shock scramjet inlet at a flight Mach number of 7.5 and an altitude of 34 km. Injecting fuel in the inlet leads to particularly high values of the cross-stream velocities that reduce the size of the recirculation bubbles. This is attributed to be due to i) large cross-stream shearing created by the bow shock above the ramp injectors, to ii) the large density difference between the fuel and the air leading to baroclinicity, and to iii) the greater acceleration of the light fuel by the pressure gradients. As opposed to previous methods that achieved partial reduction of the separation region, fuel injection can lead to a complete elimination of the recirculation bubbles in scramjet inlets. To eliminate recirculations, only half of the fuel needs to be injected in the inlet with the rest injected in the combustor as usual.

Compressible correction for separated and shear flow based on structural compressibility

In this paper, different compressible correction strategies for k-ω turbulence model are proposed. The dilatation dissipation term, which is significant in compressible flow, is taken into account and modeled in the Favre-averaged k-equation and ω-equation. We propose correction model for the dilation dissipation term based on the gradient Mach number in this paper, the coefficients of which are calibrated from experimental data on compressible turbulent mixed layers, and compare it to the Wilcox, Sarkar, and Heinz correction models. In slope-cavity flow and oblique shock wave/boundary layer interactions, the performance of these corrections is evaluated and compared to experimental data. The new correction has a similar or even better effect in separation prediction, heat flux prediction, and other aspects, and the uncertainty of model form and coefficients can be investigated further.

Double shear layer evolution on the non-uniform computational mesh

This paper considers the problem of a thin shear layer evolution at Reynolds number rmRe = 400000 using the novel Compact Accurately Boundary Adjusting high-Resolution Technique (CABARET). The study is focused on the effect of the specific mesh refinement in the high shear rate areas on the flow properties under the influence of the developing instability. The original sequence of computational meshes (2562, 5122, 10242, 20482 cells) is modified using an iterative refinement algorithm based on the hyperbolic tangent. The properties of the solutions obtained are discussed in terms of the initial momentum thickness and the initial vorticity thickness, viscous and dilatational dissipation rates and also integral enstrophy. The growth rate for the most unstable mode depending on the mesh resolution is considered. In conclusion the accuracy of calculated mesh functions is estimated via L 1, L 2, L ∞ norms.

Assessment of turbulence models using DNS data of compressible plane free shear layer flow

The present paper uses the detailed flow data produced by direct numerical simulation (DNS) of a three-dimensional, spatially developing plane free shear layer to assess several commonly used turbulence models in compressible flows. The free shear layer is generated by two parallel streams separated by a splitter plate, with a naturally developing inflow condition. The DNS is conducted using a high-order discontinuous spectral element method (DSEM) for various convective Mach numbers. The DNS results are employed to provide insights into turbulence modelling. The analyses show that with the knowledge of the Reynolds velocity fluctuations and averages, the considered strong Reynolds analogy models can accurately predict temperature fluctuations and Favre velocity averages, while the extended strong Reynolds analogy models can correctly estimate the Favre velocity fluctuations and the Favre shear stress. The pressure–dilatation correlation and dilatational dissipation models overestimate the corresponding DNS results, especially with high compressibility. The pressure–strain correlation models perform excellently for most pressure–strain correlation components, while the compressibility modification model gives poor predictions. The results of an a priori test for subgrid-scale (SGS) models are also reported. The scale similarity and gradient models, which are non-eddy viscosity models, can accurately reproduce SGS stresses in terms of structure and magnitude. The dynamic Smagorinsky model, an eddy viscosity model but based on the scale similarity concept, shows acceptable correlation coefficients between the DNS and modelled SGS stresses. Finally, the Smagorinsky model, a purely dissipative model, yields low correlation coefficients and unacceptable accumulated errors.

Solenoidal linear forcing for compressible, statistically steady, homogeneous isotropic turbulence with reduced turbulent Mach number oscillation

This study investigates a solenoidal linear forcing scheme with reduced oscillation of a turbulent Mach number MT for direct numerical simulations (DNS) of statistically steady, homogeneous isotropic turbulence. A conventional linear forcing scheme results in a large temporal oscillation of MT, where the maximum MT reaches about 1.1 times the time-averaged MT. Therefore, strong shocklets are generated when MT becomes large although such strong shocklets hardly appear when MT is close to the time-averaged value. DNS with the proposed forcing scheme confirms that the temporal oscillation of MT is effectively reduced by adjusting a forcing coefficient with a ratio between velocity variance and its steady state value prescribed as a parameter. The time-dependent forcing coefficient results in the variation of the power input to kinetic energy. Therefore, the temporal oscillation of the Reynolds number for this forcing scheme is as large as that for the conventional linear forcing. The ratio between the solenoidal and dilatational kinetic energy dissipation rates increases with MT, and the MT dependence is consistent between the present solenoidal linear forcing and the low-wavenumber solenoidal forcing in wavenumber space. The skewness and flatness of the velocity derivative become large compared with incompressible turbulence when MT exceeds 0.6. Both average and root-mean-squared fluctuation of the shock Mach number of shocklets increase with MT. The most typical thickness of shocklets decreases with MT and asymptotically approaches about 1.5 times the Kolmogorov scale. The shocklet thickness normalized by the Kolmogorov scale hardly depends on the Reynolds number.

Dissipation and dilatation rates in premixed turbulent flames

Velocity dilatation and total, solenoidal, and dilatational dissipation rates of the total flow kinetic energy are extracted from three different direct numerical simulation databases obtained by three independent research groups using different numerical codes and methods (e.g., single-step chemistry and complex chemistry flames) from six different premixed turbulent flames associated with flamelet, thin reaction zone, and broken reaction zone regimes of turbulent burning. The results show that dilatational dissipation can be larger than solenoidal dissipation in the flamelet regime and is substantial in the thin reaction zone regime. Accordingly, the influence of combustion-induced thermal expansion on the dissipation rate is not reduced to an increase in the mixture viscosity by the temperature. A simple criterion for identifying conditions associated with significant dilatational dissipation is discussed, and dilatational dissipation due to the influence of turbulence on mixing in preheat zones is argued to play a role even at high Karlovitz numbers Ka. In particular, the magnitude of dilatation fluctuations and probability of finding negative local dilatation are increased by Ka, thus implying that the impact of molecular transport of species and heat on the dilatation increases with increasing Karlovitz number.

Assessment of Low-Dissipative Shock-Capturing Schemes for the Compressible Taylor–Green Vortex

Interactions between shock waves and turbulence are ubiquitous in high-speed flows of practical aeronautical interest. Recent advances in computational power have made implicit large-eddy simulation and direct numerical simulation feasible tools for investigating the underlying physical mechanisms involved. However, numerical methods for shock capturing introduce high levels of numerical dissipation to the whole flowfield, making them a poor choice for resolving the small scales of turbulence. In this work, the efficacy of a selection of low-dissipative and hybrid weighted and targeted essentially nonoscillatory (WENO/TENO) shock-capturing methods is assessed. An extension of the classic subsonic Taylor–Green vortex problem is presented up to Mach 1.25, where compressibility and dilatational dissipation become important. The presence of strong shock waves is demonstrated, and the shock waves merge and interact with one another to form complex shock systems. A supersonic test case is then specified, using a Reynolds number of 1600 to ensure a wide range of scales is present to test the numerical schemes. Low-dissipative TENO schemes are found to offer substantial improvements in resolution over established WENO methods for a comparable computational cost.

Liquefaction resistance of fibre-reinforced silty sands under cyclic loading

Whether the so-called double porosity in soils with a loose and natural packing state is a concept with real-world implications is a fundamental yet controversial question in the study of cyclic undrained shear behaviour of fibre-reinforced silty sands. An attempt is made here to clarify the question by means of particle-level modelling combined with 41 undrained cyclic triaxial shear tests. The study shows that the initial Random Loose Packing changes to Random Close Packing and then Close Packing with silt content increments. The transition from random to close packing occurs at a threshold silt content which is relatively lower in coarser sands. For sands with <40% silt content, the rate of pore pressure growth with loading-unloading cycles increase with silt content increment. Reverse trend applies to silty sands with >40% silt content. Irrespective of fine content, fibres tend to sit deep into the silt pellets and encrust the macro-pore spaces. Generally, increasing fibre content leads to an increase in the average number of contacts per particle, dilation and easier dissipation of excess pore water pressure, a decrease in contact forces and improved liquefaction resistance. For sands with >40% silt content, effectiveness of fibre reinforcement diminishes with increasing sand median size.

Analysis of Compressibility Corrections for Turbulence Models in Hypersonic Boundary-Layer Applications

To accurately predict the hypersonic turbulent boundary layer, the compressibility corrections for a two-equation turbulence model are investigated substantially. The two-equation shear-stress-transport model based on the assumption of an eddy-viscous coefficient is adopted. The closure approximations for pressure work, pressure dilatation, and dilatation dissipation are examined by a priori and a posteriori analyses. The direct numerical simulation (DNS) of a hypersonic boundary layer shows that the pressure work term has little influence on the turbulent energy transport, whereas the effect of pressure expansion and pressure diffusion terms can be counteracted. The individual closure assumptions are evaluated by using the DNS data. Furthermore, Reynolds-averaged Navier–Stokes simulations with compressibility corrections are conducted for the hypersonic boundary layers of a flat plate and a cone. Comparisons with the experimental data and engineering correlations show that the original turbulence model overestimates the heat flux, and the pressure dilation and dilation dissipation corrections lead to a decrease in heating transfer rates. The combination of a priori and a posteriori analyses comes to the conclusion that the Zeman correction of the dilation dissipation term is applicable in hypersonic boundary layers.

Newly identified principle for aerodynamic heating in hypersonic flows

Instability evolution in a transitional hypersonic boundary layer and its effects on aerodynamic heating are investigated over a 260 mm long flared cone. Experiments are conducted in a Mach 6 wind tunnel using Rayleigh-scattering flow visualization, fast-response pressure sensors, fluorescent temperature-sensitive paint (TSP) and particle image velocimetry (PIV). Calculations are also performed based on both the parabolized stability equations (PSE) and direct numerical simulations (DNS). Four unit Reynolds numbers are studied, 5.4, 7.6, 9.7 and$11.7\times 10^{6}~\text{m}^{-1}$. It is found that there exist two peaks of surface-temperature rise along the streamwise direction of the model. The first one (denoted as HS) is at the region where the second-mode instability reaches its maximum value. The second one (denoted as HT) is at the region where the transition is completed. Increasing the unit Reynolds number promotes the second-mode dissipation but increases the strength of local aerodynamic heating at HS. Furthermore, the heat generation rates induced by the dilatation and shear processes (respectively denoted as$w_{\unicode[STIX]{x1D703}}$and$w_{\unicode[STIX]{x1D714}}$) were investigated. The former item includes both the pressure work$w_{\unicode[STIX]{x1D703}1}$and dilatational viscous dissipation$w_{\unicode[STIX]{x1D703}2}$. The aerodynamic heating in HS mainly arose from the high-frequency compression and expansion of fluid accompanying the second mode. The dilatation heating, especially$w_{\unicode[STIX]{x1D703}1}$, was more than five times its shear counterpart. In a limited region, the underestimated$w_{\unicode[STIX]{x1D703}2}$was also larger than$w_{\unicode[STIX]{x1D714}}$. As the second-mode waves decay downstream, the low-frequency waves continue to grow, with the consequent shear-induced heating increasing. The latter brings about a second, weaker growth of surface-temperature HT. A theoretical analysis is provided to interpret the temperature distribution resulting from the aerodynamic heating.

The effect of artificial bulk viscosity in simulations of forced compressible turbulence

The use of an artificial bulk viscosity for shock stabilization is a common approach employed in turbulence simulations with high-order numerics. The effect of the artificial bulk viscosity is analyzed in the context of large eddy simulations by using as a test case simulations of linearly-forced compressible homogeneous turbulence (Petersen and Livescu, 2010 [12]). This case is unique in that it allows for the specification of a priori target values for total dissipation and ratio of solenoidal to dilatational dissipation. A comparison between these target values and the true predicted levels of dissipation is thus used to investigate the performance of the artificial bulk viscosity. Results show that the artificial bulk viscosity is effective at achieving stable solutions, but also leads to large values of artificial dissipation that outweigh the physical dissipation caused by fluid viscosity. An alternate approach, which employs the artificial thermal conductivity only, shows that the dissipation of dilatational modes is entirely due to the fluid viscosity. However, this method leads to unwanted Gibbs oscillations around the shocklets. The use of shock sensors that further localize the artificial bulk viscosity did not reduce the amount of artificial dissipation introduced by the artificial bulk viscosity. Finally, an improved forcing function that explicitly accounts for the role of the artificial bulk viscosity in the budget of turbulent kinetic energy was explored.

Effects of the Mach number on the evolution of vortex-surface fields in compressible Taylor-Green flows

We investigate the evolution of vortex-surface fields (VSFs) in compressible Taylor--Green flows at Mach numbers ($Ma$) ranging from 0.5 to 2.0 using direct numerical simulation. The formulation of VSFs in incompressible flows is extended to compressible flows, and a mass-based renormalization of VSFs is used to facilitate characterizing the evolution of a particular vortex surface. The effects of the Mach number on the VSF evolution are different in three stages. In the early stage, the jumps of the compressive velocity component near shocklets generate sinks to contract surrounding vortex surfaces, which shrink vortex volume and distort vortex surfaces. The subsequent reconnection of vortex surfaces, quantified by the minimal distance between approaching vortex surfaces and the exchange of vorticity fluxes, occurs earlier and has a higher reconnection degree for larger $Ma$ owing to the dilatational dissipation and shocklet-induced reconnection of vortex lines. In the late stage, the positive dissipation rate and negative pressure work accelerate the loss of kinetic energy and suppress vortex twisting with increasing $Ma$.

Small-scale dynamics of dense gas compressible homogeneous isotropic turbulence

The present paper investigates the influence of dense gases governed by complex equations of state on the dynamics of homogeneous isotropic turbulence. In particular, we investigate how differences due to the complex thermodynamic behaviour and transport properties affect the small-scale structures, viscous dissipation and enstrophy generation. To this end, we carry out direct numerical simulations of the compressible Navier–Stokes equations supplemented by advanced dense gas constitutive models. The dense gas considered in the study is a heavy fluorocarbon (PP11) that is shown to exhibit an inversion zone (i.e. a region where the fundamental derivative of gas dynamics $\unicode[STIX]{x1D6E4}$ is negative) in its vapour phase, for pressures and temperatures of the order of magnitude of the critical ones. Simulations are carried out at various initial turbulent Mach numbers and for two different initial thermodynamic states, one immediately outside and the other inside the inversion zone. After investigating the influence of dense gas effects on the time evolution of mean turbulence properties, we focus on the statistical properties of turbulent structures. For that purpose we carry out an analysis in the plane of the second and third invariant of the deviatoric strain-rate tensor. The analysis shows a weakening of compressive structures and an enhancement of expanding ones. Strong expansion regions are found to be mostly populated by non-focal convergence structures typical of strong compression regions, in contrast with the perfect gas that is dominated by eddy-like structures. Additionally, the contribution of non-focal expanding structures to the dilatational dissipation is comparable to that of compressed structures. This is due to the occurrence of steep expansion fronts and possibly of expansion shocklets which contribute to enstrophy generation in strong expansion regions and that counterbalance enstrophy destruction by means of the eddy-like structures.

Kerosene/GOx dynamic combustion characteristics in a mixing layer under supercritical conditions using the LES-FPV approach

A large eddy simulation (LES) for kerosene/GOx combustion in a mixing layer under supercritical conditions is conducted using the flamelet progress variable (FPV) method. To apply real gas effects, several real gas equations of states (EOSes) are validated with extended corresponding states (ECSes) by comparing thermodynamic properties. The Redlich-Kwong Peng-Robinson (RK-PR) EOS is applied in this study to achieve greater accuracy. The flamelet solution indicates that the flame structure is not affected by varying the oxidizer inlet temperature, but the flame surface location is influenced. A non-reacting calculation shows a finger-like structure rotating in counterclockwise with a certain periodic interval. For the reacting case, totally different flow characteristics are observed because of the dilatation and flame dissipation rate locally various. The shear layer in the reacting case has a wider angle in the downward direction than the shear layer in the non-reacting case. Because the FPV method treats all possible flame states, the dynamic flame structures are observed – detached, folded, quenched, stretched and reignited. In particular, the isolated flame is discussed in detail, and its creation process is introduced. After its creation, the isolated flame is divided into two areas – extinction and re-ignition. The premixed flame regime initiates the re-ignition process. The flame anchoring process behind a splitter tip is also investigated. Scattering species profiles in mixture fraction space are evaluated in this simulation. The averaged flame temperature is much lower (except near the splitter tip) than the instantaneous flame temperature due to the constant flame shedding downstream.

Turbulent kinetic energy transport in head-on quenching of turbulent premixed flames in the context of Reynolds Averaged Navier Stokes simulations

This paper investigates the statistical behaviour of the turbulent kinetic energy transport for moderate values of turbulent Renolds number Ret in turbulent premixed flames by using Direct Numerical Simulation (DNS) data in the case of head-on quenching by an isothermal inert wall for different Lewis numbers (i.e. Le=0.8–1.2). The magnitudes of turbulent kinetic energy and the terms of its transport equation have been found to increase with a reduction in global Lewis number. The magnitudes of all the terms except the viscous dissipation rate drops sharply near the wall whereas the magnitude of viscous dissipation rate exhibits a sharp increase in the near-wall region. The statistical behaviours of the terms arising from turbulent transport, pressure fluctuation transport, mean pressure gradient, pressure dilatation and viscous dissipation have been analysed by explicit Reynolds averaging of DNS data. It has been found that the viscous dissipation term acts as a major sink for all cases and all locations. The mean pressure gradient acts as the leading order source for all cases. However, the magnitudes of the mean pressure gradient, pressure dilatation and transport terms diminish with increasing Lewis number. Moreover, turbulent flux of kinetic energy has been found to exhibit counter-gradient transport and its extent diminishes with increasing Lewis number as a result of the weakening of flame normal acceleration. Detailed physical explanations have been provided for the observed behaviour of the turbulent kinetic energy transport. Existing models for the unclosed terms have been modified for accurate prediction of the corresponding terms extracted from DNS data especially in the near-wall region.

Dilation and breakage dissipation of granular soils subjected to monotonic loading

Dilation and breakage energy dissipation of four different granular soils are investigated by using an energy balance equation. Due to particle breakage, the dilation curve does not necessarily pass through the origin of coordinates. Breakage energy dissipation is found to increase significantly at the initial loading stage and then gradually become stabilised. The incremental dissipation ratio between breakage energy and plastic work exhibits almost independence of the confining pressure. Accordingly, a plastic flow rule considering the effect of particle breakage is suggested. The critical state friction angle is found to be a combination of the basic friction between particles and the friction contributed by particle breakage.