Large Eddy Simulation of Hypersonic Turbulent Boundary Layers

The recent revival of interest in developing new hypersonic vehicles brings attention to the need for accurate prediction of hypersonic flows by computational methods. One of the challenges is prediction of aerothermodynamic loading over the surface of the vehicles. Reynolds Average Navier-Stokes (RANS) methods have not shown consistent accuracy in prediction of such flows. Therefore, new methods including Large Eddy Simulations (LES) should be investigated. In this paper, the LES method is used for prediction of the boundary layer over a flat plate. A new recycling-rescaling method is tested. The method uses total enthalpy and static pressure along with the velocity components to produce the best results for the Law of the Wall, turbulent statistics and turbulent Prandtl number.

Pressure fields in the airflow over wind-generated surface waves

The quantification of pressure fields in the airflow over water waves is fundamental for understanding the coupling of the atmosphere and the ocean. The relationship between the pressure field, and the water surface slope and velocity, are crucial in setting the fluxes of momentum and energy. However, quantifying these fluxes is hampered by difficulties in measuring pressure fields at the wavy air-water interface. Here we utilise results from laboratory experiments of wind-driven surface waves. The data consist of particle image velocimetry of the airflow combined with laser-induced fluorescence of the water surface. These data were then used to develop a pressure field reconstruction technique based on solving a pressure Poisson equation in the airflow above water waves. The results allow for independent quantification of both the viscous stress and pressure-induced form drag components of the momentum flux. Comparison of these with an independent bulk estimate of the total momentum flux (based on law-of-the-wall theory) shows that the momentum budget is closed to within approximately 5%. In the partitioning of the momentum flux between viscous and pressure drag components, we find a greater influence of form drag at high wind speeds and wave slopes. An analysis of the various approximations and assumptions made in the pressure reconstruction, along with the corresponding sources of error, is also presented.

Development of an Analytical Wall Function for Bypass Transition

The objective of the present work is to propose an extended analytical wall function that is capable of predicting the bypass transition from laminar to turbulent flow. The algebraic γ transition model, the k−ω turbulence model and the analytical wall function are integrated together in this work to detect the transition onset and start the transition process. The present analytical wall function is validated with the experimental data, the Blasius solution and the law of the wall. With this analytical wall function, the transition onset in the skin friction coefficient is detected and the growth rate of transition is properly generated. The predicted mean velocity profiles are found to be in good agreement with the Blasius solution in the laminar flow, the experimental data in the transition zone and the law of the wall in the fully turbulent flow.

Velocity transformation for compressible wall-bounded turbulent flows with and without heat transfer

In this work, a transformation, which maps the mean velocity profiles of compressible wall-bounded turbulent flows to the incompressible law of the wall, is proposed. Unlike existing approaches, the proposed transformation successfully collapses, without specific tuning, numerical simulation data from fully developed channel and pipe flows, and boundary layers with or without heat transfer. In all these cases, the transformation is successful across the entire inner layer of the boundary layer (including the viscous sublayer, buffer layer, and logarithmic layer), recovers the asymptotically exact near-wall behavior in the viscous sublayer, and is consistent with the near balance of turbulence production and dissipation in the logarithmic region of the boundary layer. The performance of the transformation is verified for compressible wall-bounded flows with edge Mach numbers ranging from 0 to 15 and friction Reynolds numbers ranging from 200 to 2,000. Based on physical arguments, we show that such a general transformation exists for compressible wall-bounded turbulence regardless of the wall thermal condition.

Adjoint Complement to the Universal Momentum Law of the Wall

The paper is devoted to an adjoint complement to the universal Law of the Wall (LoW) for fluid dynamic momentum boundary layers. The latter typically follows from a strongly simplified, unidirectional shear flow under a constant stress assumption. We first derive the adjoint companion of the simplified momentum equation, while distinguishing between two strategies. Using mixing-length arguments, we demonstrate that the frozen turbulence strategy and a LoW-consistent (differentiated) approach provide virtually the same adjoint momentum equations, that differ only in a single scalar coefficient controlling the inclination in the logarithmic region. Moreover, it is seen that an adjoint LoW can be derived which resembles its primal counterpart in many aspects. The strategy is also compatible with wall-function assumptions for prominent RANS-type two-equation turbulence models, which ground on the mixing-length hypothesis. As a direct consequence of the frequently employed assumption that all primal flow properties algebraically scale with the friction velocity, it is demonstrated that a simple algebraic expression provides a consistent closure of the adjoint momentum equation in the logarithmic layer. This algebraic adjoint closure might also serve as an approximation for more general adjoint flow optimization studies using standard one- or two-equation Boussinesq-viscosity models for the primal flow. Results obtained from the suggested algebraic closure are verified against the primal/adjoint LoW formulations for both, low- and high-Re settings. Applications included in this paper refer to two- and three-dimensional shape optimizations of internal and external engineering flows. Related results indicate that the proposed adjoint algebraic turbulence closure accelerates the optimization process and provides improved optima at no computational surplus in comparison to the frozen turbulence approach.

Wall Bounded Flows and a General Proof of the Validity of the Universal Logarithmic Law of the Wall

The logarithmic law of the wall is usually derived for the flat plate assuming stationary, two-dimensional fully developed flow with no external pressure gradient. The Prandtl mixing length model for the turbulence is applied, which assumes homogeneous turbulence and two empirical constants, and the logarithmic wall law is derived. It is than stated in the textbooks that it is universally valid without a proof. As a justification experimental evidence is shown. First this proof will be shown in detail. Than a more general approach based on similarity considerations is made to show the universal validity of the logarithmic law of the wall. Starting from the Navier-Stokes equation a general non dimensional form of this equation is derived showing its dependency from four non-dimensional numbers, the Strouhal, Euler, Reynolds and the Froude number. Then wall bounded laminar flows are analyzed by dimensional analysis. The laminar boundary length and time scales are derived and used to non-dimensionalize the Navier-Stokes equation. With this specific non-dimensionalization for the laminar boundary layer a more specific non dimensional Navier-Stokes equation is derived. Then the high Reynolds limit is taken with considerations of orders of magnitude and the boundary layer equations are derived. Finally, for turbulent near wall flows a dimensional analysis is made and the corresponding near wall non-dimensional velocities and coordinates y+ and u+ are derived from the Buckingham-Π theorem. Using these variables to non-dimensionalize the Navier-Stokes equations in the near wall turbulent region the third author Malcherek showed that the so derived non-dimensional Navier-Stokes equations do not depend on any non-dimensional number and has a unique solution. Hence, the logarithmic law of the wall must be universally valid, without any simplification, any turbulence model, empirical constant or further assumptions. In such a way the students do not have to believe anymore in the universality of the logarithmic law of the wall based on empirical evidence only, now this fact has been proven by the third author Malcherek and the larger context has been elaborated by all authors for an advanced teaching of wall bounded flows.

A Rapid Viscous-Inviscid Interaction Method for the Preliminary Design of S-Shaped Transition Ducts

For preliminary design of compressor transition ducts, knowledge-based tools for the rapid assessment of aerodynamic performance of S-shaped ducts are not currently available in the open literature. This is due to the highly complex flow developing under the combined influence of pressure gradients and streamline curvature. This paper presents a new approach enabling an agile design process avoiding premature use of time-consuming high-fidelity CFD calculations. The features of a 2D axisymmetric incompressible steady flow field are captured with a semi-analytical viscous inviscid interaction method. A potential core, based on streamline curvature and implicit velocity profile by parametric spline reconstruction, is coupled to an integral method predicting the turbulent boundary layer growth up to separation. The shear stress distribution is generated by a modified mixing length model for strongly curved flows and wall shear stress closure is performed by inverse calculation of a composite law-of-the-wall. When compared to CFD, the aerodynamic loading is generally predicted to within ±3% but convergence is achieved 20 times faster.

An Enhanced Treatment of Boundary Conditions for 2D RANS Streamwise Velocity Models in Open Channel Flow

A 2D streamwise velocity model based on the Reynolds Averaged Navier–Stokes (RANS) is a useful approach to predict the boundary shear stress and the streamwise velocity in a free surface stream where secondary flows are not relevant. Boundary conditions treatment is a key aspect implementing these models. A low computational cost and fully predictive numerical model with a novel treatment of boundary conditions is presented. The main features of the modified model are the employment of a modified law of the wall valid for any roughness condition, the estimation of the boundary shear stress is done only focusing on the near-contour region, the use of a full-predictive physical based model for the eddy viscosity distribution and the incorporation of the free surface shear stress due to water–air interface. The validation of the proposed changes was performed with a substantial number of experimental cases available in the literature using different cross-section shapes (circular, rectangular, trapezoidal and compound section) and roughness condition with quite good agreement. Preliminary results suggest that the influence of the free surface boundary layer has a significant impact on the results for both the streamwise velocity and boundary shear stress in windy conditions. The proposed approach allows its considerations in practical applications.

Large-Eddy Simulation for the Roughness Sublayers over Real Urban Surfaces

<p><strong>ABSTRACT: </strong></p><p>    With the continuous spreading of global pandemic, environmental issues have aroused worldwide unprecedented attention. Airflow plays a crucial role in aerosol motions and pollutants removal in dense cities. Large-eddy simulation (LES) is conducted for a typical metropolitan, Hong Kong, to investigate the dynamics in the atmospheric boundary layer (ABL) over real urban surfaces. Full-scale building models (average building height h<sub>m</sub> = 36 m) from Tsim Sha Tsui to Sham Shui Po, Kowloon Peninsula, are digitalized. Southerly wind with speed U<sub>∞</sub> (= 10 m sec<sup>-1</sup>) in neutral stratification is prescribed at the domain inlet. The turbulence statistics extracted from three subdomains in Mong Kok neighborhood, each with size 800 m (streamwise) × 100 m (spanwise) × 500 m (vertical), are analyzed. Linear regression of the wind profile with the logarithmic law of the wall (log-law) show that the interface between inertial sublayer (ISL) and roughness sublayer (RSL) is in the range of 2.5h<sub>m</sub> to 4.5h<sub>m</sub>. In the RSL, the streamwise and vertical velocities are positively (S<sub>u</sub> > 0) and negatively (S<sub>w</sub> < 0) skewed, respectively. Their kurtosis K<sub>u</sub> and K<sub>w</sub> is less than 3. Conditional sampling of vertical momentum, flux u’’w’’ showed that ejection Q2 occurs more frequently than does sweep Q4. On the contrary, the contribution of Q4 exceeds that of Q2. These characteristics switch to the other way round in the ISL. Furthermore, the difference between Q4 and Q2, either in terms of occurrence or contribution, shows a local maximum around 50% of the total momentum flux, suggesting the major energy-carrying scales. Coherent structures depict elongated, (massive,) accelerating (decelerating) and descending (ascending) RSL (ISL) flows. Hence, the fresh (aged) air entrainment (detrainment) are signified by fast and extreme (slow and frequent) flows. These distinct features of RSL flows over real urban morphology provide an inspiration to improve the ground-level air quality by proper urban planning.</p><p><strong>KEYWORDS:</strong> Large-eddy simulation (LES), real urban morphology, turbulent boundary layer (TBL), conditional sampling, hole filtering</p><p> </p><p> </p>

Wind Speed Parameterization and Turbulence Intermittency in the Roughness Sublayers over Urban Areas: a Wind Tunnel Study

<p>The flow in inertial sublayer (ISL) is horizontally homogeneous where the Monin–Obukhov similarity theory (MOST) well describes the flux-gradient relationship.  In contrast, roughness sublayer (RSL) flow is highly inhomogeneous. Its dynamics is influenced by the length scale of individual roughness elements. This study presents an analytical solution to the mean wind profile for both ISL and RSL by adding a new function in the flux-gradient relationship to handle the RSL dynamics. The mean wind speeds measured in the wind tunnel experiments over a range of idealized and real urban geometries are well predicted by the new analytical solution. The root-mean-square errors (RMSE) are reduced over an order of magnitude compared with the conventional logarithmic law of the wall (log-law). Its key parameter, the RSL constant converges asymptotically to μ = 1.7 for urban setting which is different from that (μ = 2.6) for vegetation canopy. The RSL turbulence intermittency is revealed by higher-order moments of velocities, probability density function (PDF), quadrant analysis, and conditional sampling. Ejection Q2 (-u’’, +w”) and sweep Q4 (+u’’, -w”) dominate in both RSL and ISL but with different share. Unlike the ISL, Q2 occurs more frequently (but contributes less to momentum flux) than Q4 in the RSL. It is thus suggested that RSL turbulent transport is driven by occasional, fast motions of accelerating downward flow (Q4) and bulk, slow decelerating upward flow (Q2).</p>