Flat Plate Boundary Layer Flow Research Articles

Validation case for supersonic boundary layer and turbulent aero-optical investigation in high-Reynolds-number freestream by WCNS-E-5

Turbulent flat-plate boundary layer flows have been widely employed for numerical validation in the aero-optical field. In present study, the laminar-to-turbulent evolution induced by wavy roughness in high-Reynolds-number supersonic freestream is investigated using a numerical technique based on the fifth-order weighted compact nonlinear scheme (WCNS-E-5). The computational procedure and post-processing method are described in detail, and the acquired instantaneous flow structure and statistical data are compared with other theoretical, experimental, and numerical results to demonstrate the feasibility of predicting turbulence using WCNS-E-5. Further, to reduce the computational resources required to simulate turbulent flow, a velocity correlation function is introduced to decrease the computational domain in the spanwise direction. Additionally, the effects of different grid sizes on the simulation results are examined by reducing the number of cells in the streamwise, wall-normal, and spanwise directions. Finally, the authors conduct a tentative investigation into the aero-optical effects of the laminar-to-turbulent flowfield using a ray-tracing method, considering both the feasibility of aero-optical detection and the effect of grid scale on the time-averaged imaging quality, as well as a deeper probe into the characteristic structures reflected by aero-optical frequency spectrum. The results elucidated that the wall-normal grid number has the strongest influence on the transitional location, and undoubtedly affects wavefront aberrations. However, different gird scales lead to similar aero-optical spectrum, and revealed the Kolmogorov-type turbulence at small-scale regime. As a prelude to further aero-optical simulations of wall-bounded flows, the current study provides some reference for the code validation process and aero-optical interrogation.

Wavelet-Based Adaptive Unsteady Reynolds-Averaged Navier–Stokes Simulations of Wall-Bounded Compressible Turbulent Flows

A wavelet-based adaptive approach, called wavelet-based adaptive unsteady Reynolds-averaged Navier–Stokes (WA-URANS), is proposed to solve the URANS equations for the computation of wall-bounded internal and external compressible turbulent flows. The new approach uses anisotropic wavelet-based mesh refinement, and its effectiveness is demonstrated for flow simulations with two different turbulence models, namely, the Spalart–Allmaras and models for a variety of two- and three-dimensional flow configurations with arbitrary geometries, different speed regimes, and various boundary conditions. Supersonic plane channel flow, a weakly compressible channel flow with periodic hill constrictions, a subsonic zero-pressure-gradient flat-plate boundary-layer flow, the separated flow over NASA wall-mounted hump, the Bachalo–Johnson flow (axisymmetric transonic bump flow), and a flow past a circular cylinder at a subcritical Reynolds number are tested as benchmark flows. The effectiveness and efficiency of the new wavelet-based approach are demonstrated by comparing the results of the WA-URANS simulations with literature data. This comprehensive validation of the WA-URANS approach encourages its application to practical problems of industrial interest, and demonstrates the feasibility of extending this approach to wavelet-based wall-modeled large-eddy simulation (LES) and hybrid URANS/LES. Finally, the current study serves as a baseline for the development of a unified hierarchical framework for eddy-resolving turbulence modeling, capable of performing computations of different fidelity, ranging from adaptive direct numerical simulations to adaptive URANS computations.

Criteria of computational grid generation for turbulence models taking into account laminar-turbulent transition

Criteria of structured and unstructured mesh generation for turbulence models taking into account laminar-turbulent transition were developed using flat plate boundary layer flow. It is shown the first near wall cell should be placed in the viscous sublayer in the transition region and stretching factor should not exceed 1.4. For the unstructured meshes all the boundary layer should be covered by prismatic layers. The results of the prediction of the flow around a NLF(1)-0414F airfoil show that the use of relatively coarse meshes provide acceptable accuracy of the solution.

Modification to Improved Delayed Detached-Eddy Simulation Regarding the Log-Layer Mismatch

The wall-modeled large-eddy simulation branch of the widely used improved delayed detached-eddy simulation (IDDES) method is supposed to resolve the problems of log-layer mismatch and underprediction of skin friction, as claimed by the authors of the IDDES (Shur, M. L., Spalart, P. R., Strelets, M. K., and Travin, A. K., "A Hybrid RANS-LES Model with Delayed DES and Wall-Modeled LES Capabilities," International Journal of Heat and Fluid Flow, Vol. 29, 2008, pp. 1638–1649). But, some researchers did meet these problems when using the IDDES. Aiming at finding out the reason and seeking a remedy, an analysis of the IDDES is carried out that focuses on the relation between the wall-parallel grid size and the length scale of the energetic turbulent structures at the Reynolds-averaged Navier–Stokes (RANS)/large-eddy simulation (LES) interface, and it reveals that the flaw of the IDDES arises from the fact that, in the IDDES approach, the energetic, large-scale, and stress-carrying turbulent structures in the vicinity of the RANS/LES interface are essentially impossible to well resolve by the LES mode. On the basis of the analysis, a modification to the IDDES is proposed by moving the RANS/LES interface further away from the wall so that, at the RANS/LES interface, the wall-parallel grid size is sufficient to resolve the turbulent structures. The modification is simple in form but has clear physical meaning. Through a series of sensitivity tests, it can be concluded that the modified IDDES does resolve the problems of log-layer mismatch and underprediction of skin friction, and it is applicable to low-, moderate-, and high-Reynolds-number flat plate boundary-layer flows without exception.

Stability Analysis on Nonequilibrium Supersonic Boundary Layer Flow with Velocity-Slip Boundary Conditions

This paper presents our recent work on investigating velocity slip boundary conditions’ effects on supersonic flat plate boundary layer flow stability. The velocity-slip boundary conditions are adopted and the flow properties are obtained by solving boundary layer equations. Stability analysis of two such boundary layer flows is performed by using the Linear stability theory. A global method is first utilized to obtain approximate discrete mode values. A local method is then utilized to refine these mode values. All the modes in these two scenarios have been tracked upstream-wisely towards the leading edge and also downstream-wisely. The mode values for the no-slip flows agree well with the corresponding past results in the literature. For flows with slip boundary conditions, a stable and an unstable modes are detected. Mode tracking work is performed and the results illustrate that the resonance phenomenon between the stable and unstable modes is delayed with slip boundary conditions. The enforcement of the slip boundary conditions also shortens the unstable mode region. As to the conventional second mode, flows with slip boundary conditions can be more stable streamwisely when compared with the results for corresponding nonslip flows.

Mean flow compressibility effects in transonic turbulence modeling

The mean flow compressibility effects greatly influence the behavior of turbulent flows, as long as the flow is compressible. The fact is even though Favre average has taken into account the variation of the density, less accurate CFD results are always obtained when the flow is compressible. Thus, many compressibility corrections are made for high Mach number flows. As for the transonic turbulence flow, the mean flow compressibility effects are not mentioned. In this paper, it is demonstrated that the mean flow compressibility effects are not ignorable in transonic flows on some flow features. The mean flow compressibility effects are taken into account by introducing a characteristic turbulence length scale. The key is a new definition of vorticity by the curl of momentum. A compressible von Kármán length scale is introduced to obtain a new turbulence model CKDO (Compressible Kinetic Dependent Only) for complex compressible flows on the basis of the KDO. The only two empirical coefficients in the KDO model are not changed, which were calibrated by a slice of the incompressible flat plate boundary layer flow. Numerical simulations of transonic flows around RAE2822 airfoil, axisymmetric bump pipe and ONERA-M6 wing show that compressibility is non-negligible, and the new length scale definition can improve the prediction accuracies of aerodynamic features, such as the onset locations of shock waves, skin friction and pressure coefficients.

Experimental Investigation of Boundary Layer Relaminarization in Accelerated Flow

Flow in turbomachines is generally highly turbulent. Nonetheless, boundary layers may exhibit laminar-to-turbulent transition, and relaminarization of the turbulent flow may also occur. The state of flow of the boundary layer is important since it influences transport phenomena like skin friction and heat transfer. In this paper, relaminarization in accelerated flat-plate boundary-layer flows is experimentally investigated, measuring flow velocities with laser Doppler anemometry (LDA). Besides the mean values, statistical properties of the velocity fluctuations are discussed in order to understand the processes in relaminarization. It is shown that strong acceleration leads to a suppression of turbulence production. The velocity fluctuations in the accelerated boundary layer flow “freeze,” while the mean velocity increases, thus reducing the turbulence intensity. This leads to a laminar-like velocity profile close to the wall, resulting in a decrease of the local skin friction coefficient. Downstream from the section with enforced relaminarization, a rapid retransition to turbulent flow is observed. The findings of this work also describe the mechanism of retransition.

Instability wave-streak interactions in a supersonic boundary layer.

Optimal initial conditions for transient growth in a two-dimensional boundary layer flow correspond to stationary, counter-rotating vortices that subsequently develop into streamwise elongated streaks, which are characterized by an alternating pattern of low and high streamwise velocity. For incompressible flows, previous studies have shown that boundary layer modulation due to streaks below a threshold amplitude level can stabilize the Tollmien-Schlichting instability waves, resulting in a delay in the onset of laminar-turbulent transition. In the supersonic regime, the linearly, most-amplified waves become three-dimensional, corresponding to oblique, first-mode waves. This change in the character of dominant instabilities leads to an important change in the transition process, which is now dominated by oblique breakdown via nonlinear interactions between pairs of first-mode waves that propagate at equal but opposite angles with respect to the free stream. Because the oblique breakdown process is characterized by a rapid amplification of stationary streamwise streaks, artificial excitation of such streaks may be expected to promote transition in a supersonic boundary layer. Indeed, suppression of those streaks has been shown to delay the onset of transition in prior literature. Consistent with those findings, the present study shows that optimally growing stationary streaks indeed destabilize the first-mode waves, but only when the spanwise wavelength of the instability waves is equal to or smaller than twice the streak spacing. Transition in a benign disturbance environment typically involves first-mode waves with significantly longer spanwise wavelengths, and hence, these waves are stabilized by the optimal growth streaks. Thus, as long as the amplification factors for the destabilized, short wavelength instability waves remain below the threshold level for transition, a significant net stabilization is achieved, yielding a transition delay that is comparable to the length of the laminar region in the uncontrolled case.

Active and Natural Suction at Forward-Facing Steps for Delaying Laminar–Turbulent Transition

Two-dimensional, direct numerical simulations are used to study the impact of active and natural (passive) suction at forward-facing steps on laminar–turbulent transition. Suction is applied through a gap in front of a step that is located in a flat-plate boundary-layer flow without streamwise pressure gradient. A steady base flow is used with a Mach number of 0.6. Subsequently, Tollmien–Schlichting waves are introduced by suction and blowing at the wall, and their growth over the surface imperfection is evaluated by factors. The investigated step heights are in the range of one to two times the local displacement thickness of the smooth flat plate. Both sharp and rounded step corners are investigated. Cases with and without suction are compared with the smooth flat plate without suction based on factors according to the method. Thus, it is shown that suction is capable to compensate or even overcompensate the negative impact of different steps on laminar–turbulent transition. The work concludes with a configuration that allows natural (passive) suction in front of a forward-facing step. Here, a significant reduction of the factor compared to the smooth flat plate without suction is possible. Further estimations indicate that a net drag reduction may be possible as well.

Energy efficiency and performance limitations of linear adaptive control for transition delay

A reactive control technique with localised actuators and sensors is used to delay the transition to turbulence in a flat-plate boundary-layer flow. Through extensive direct numerical simulations, it is shown that an adaptive technique, which computes the control law on-line, is able to significantly reduce skin-friction drag in the presence of random three-dimensional perturbation fields with linear and weakly nonlinear behaviour. An energy budget analysis is performed in order to assess the net energy saving capabilities of the linear control approach. When considering a model of the dielectric-barrier-discharge (DBD) plasma actuator, the energy spent to create appropriate actuation force inside the boundary layer is of the same order as the energy gained from reducing skin-friction drag. With a model of an ideal actuator a net energy gain of three orders of magnitude can be achieved by efficiently damping small-amplitude disturbances upstream. The energy analysis in this study thus provides an upper limit for what we can expect in terms of drag-reduction efficiency for linear control of transition as a means for drag reduction.

Drag reduction via wall‐normal oscillations in turbulent flat plate boundary layer flow at very high Reynolds number

AbstractThe effects of wall‐normal single point oscillations in turbulent boundary layers at very high Reynolds number are investigated by numerical simulation. The impact on the friction drag and on the turbulent structures is analyzed. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Instability and transition mechanisms induced by skewed roughness elements in a high-speed laminar boundary layer

The disturbance evolution in a Mach-4.8 zero-pressure-gradient flat-plate boundary-layer flow altered by discrete three-dimensional roughness elements is investigated including a laminar breakdown scenario. Direct numerical simulation (DNS), as well as the biglobal linear stability theory based on two-dimensional eigenfunctions in flow cross-sections, are applied. Roughness elements with high ratios of spanwise width to streamwise length are compared at varying height and skewing angles with respect to the oncoming flow. For an oblique roughness, the element’s height is varied between 27 % and 68 % of the undisturbed boundary-layer thickness. Compared to a symmetric roughness element an obliquely placed element generates a more pronounced low-speed streak in the roughness wake. The linear stability analysis reveals the occurrence of eigenmodes that can be associated with the first and second modes in the flat-plate flow. At identical roughness height, larger amplification is found for the eigenmodes of the oblique set-up. The results are confirmed by unsteady DNS showing very good agreement with stability theory; transient-growth behaviour in the near wake of the roughness is of minor importance. The comparison of the results gained for adiabatic wind-tunnel flow conditions with those for atmospheric-flight conditions with wall cooling reveals significant differences in the wake vortex system with subsequent impact on the stability properties of the flow. The hot-flow cases are less unstable at identical roughness Reynolds numbers. A variation of the wall cooling shows that the roughness-wake first- and second-mode behaviour is similar to that of the flat-plate flow: wall cooling stabilizes the first-mode and destabilizes the second-mode instabilities of the roughness wake.

A high-performance finite-volume algorithm for solving partial differential equations governing compressible viscous flows on structured grids

This work focuses on the development of a high-performance fourth-order finite-volume method to solve the nonlinear partial differential equations governing the compressible Navier–Stokes equations on a Cartesian grid with adaptive mesh refinement. The novelty of the present study is to introduce the loop chaining concept to this complex fourth-order fluid dynamics algorithm for significant improvement in code performance on parallel machines. Specific operations involved in the algorithm include the finite-volume formulation of fourth-order spatial discretization stencils and optimal inter-loop parallelization strategies. Numerical fluxes of the Navier–Stokes equations comprise the hyperbolic (inviscid) and elliptic (viscous) ​components. The hyperbolic flux is evaluated using high-resolution Godunov’s method and the elliptic flux is based on fourth-order centered-difference methods everywhere in the computational domain. The use of centered-difference methods everywhere supports the idea of fusing modular codes to achieve high efficiency on modern computers. Temporal discretization is performed using the standard fourth-order ​Runge–Kutta method. The fourth-order accuracy of solution in space and time is verified with a transient Couette flow problem. The algorithm is applied to solve the Sod’s shock tube and the transient flat-plate boundary layer flow. The numerical predictions are validated by comparing to the analytical solutions. The performance of the baseline code is compared to that of the fused scheme which fuses modular codes via loop chaining concept and a significant improvement in execution time is observed.

Surface capillary currents: Rediscovery of fluid-structure interaction by forced evolving boundary theory

Any boundary surface evolving in viscous fluid is driven with surface capillary currents. By step function defined for the fluid-structure interface, surface currents are found near a flat wall in a logarithmic form. The general flat-plate boundary layer is demonstrated through the interface kinematics. The dynamics analysis elucidates the relationship of the surface currents with the adhering region as well as the no-slip boundary condition. The wall skin friction coefficient, displacement thickness, and the logarithmic velocity-defect law of the smooth flat-plate boundary-layer flow are derived with the advent of the forced evolving boundary method. This fundamental theory has wide applications in applied science and engineering.

Investigation of turbulence models with compressibility corrections for hypersonic boundary flows

The applications of pressure work, pressure-dilatation, and dilatation-dissipation (Sarkar, Zeman, and Wilcox) models to hypersonic boundary flows are investigated. The flat plate boundary layer flows of Mach number 5–11 and shock wave/boundary layer interactions of compression corners are simulated numerically. For the flat plate boundary layer flows, original turbulence models overestimate the heat flux with Mach number high up to 10, and compressibility corrections applied to turbulence models lead to a decrease in friction coefficients and heating rates. The pressure work and pressure-dilatation models yield the better results. Among the three dilatation-dissipation models, Sarkar and Wilcox corrections present larger deviations from the experiment measurement, while Zeman correction can achieve acceptable results. For hypersonic compression corner flows, due to the evident increase of turbulence Mach number in separation zone, compressibility corrections make the separation areas larger, thus cannot improve the accuracy of calculated results. It is unreasonable that compressibility corrections take effect in separation zone. Density-corrected model by Catris and Aupoix is suitable for shock wave/boundary layer interaction flows which can improve the simulation accuracy of the peak heating and have a little influence on separation zone.

コルモゴロフ複雑度による乱流のランダムさ表現（周期的吹き出しによる円管助走部境界層の乱流遷移の場合）

The complexity or randomness of the laminar-turbulent transition process of an inlet boundary layer in a circular pipe was analyzed by use of Kolmogorov complexity which is a very important measure of the randomness of various events. In the inlet region of the circular pipe, a jet that triggered a turbulent patch in the flow was periodically injected radially, and then propagated downstream periodically. Periodic velocity data which satisfies the phase constancy obtained from a hot-wire anemometer were compressed using a compression program running on a Windows PC. From the compressed data, the approximated Kolmogorov complexity, named AK, and normalized compression distance NCD were obtained. Although the distribution of AK of irregularly fluctuating velocity in the flow showed a slight discrepancy from the profile of fluctuating velocity intensity and intermittency factor, they exhibited qualitative consistency. Therefore, the objective judgment of the laminar-turbulent transition process based on the approximated Kolmogorov complexity mostly supports the conventional judgment. In conclusion, our study established the validity and usefulness of Kolmogorov complexity or algorithmic complexity to describe objectively the laminar-turbulent transition process in the mixing layer, flat plate boundary layer and pipe flow. With the aid of the AK we can distinguish the complexity within the turbulent region; on the other hand, the intermittency factor cannot.

Effusion Cooling and Flow Tripping in Laminar Supersonic Boundary-Layer Flow

Effusion cooling of a laminar flat-plate boundary-layer flow at Mach 2.7 is investigated using direct numerical simulations. Air is employed as hot and cooling gas and is blown in the wall-normal direction through discrete orifices into the boundary layer to generate a cooling film. In the present investigations, the inclusion of the flow in the blowing pipes enables a comparison with modeled blowing where the coolant mass flux and temperature are prescribed in the respective areas at the wall. Attention is turned to 1) the blowing through multiple rows of holes, under the assumption of a fixed plenum pressure for all pipes; 2) the temperature modeling, which plays an important role when the cooling gas and wall temperature differ; and 3) the flow tripping to turbulence by the blowing. It is demonstrated that simple modeling fails for narrow hole spacing, which lowers (together with the pipe/main-flow interaction) the critical blowing ratio for flow tripping.

Numerical study of a dynamic resonant wall shear stress sensor with spectral element method

A numerical study with spectral element method for a dynamic resonant shear stress sensor concept is presented in this paper, in which the numerical model of the sensor consisted of an unsteady three-dimensional boundary layer model for the flow and a simple mechanical model for the sensor itself. Spectral element method was used to explore fluid flow properties around the sensor in the three-dimensional boundary layer model. The three-dimensional unsteady spectral element method code was first verified with Blasius solutions in a flat plate boundary layer flow. The sensor's sensitivity to wall shear stress was then numerically determined in a laminar boundary layer. Finally, the physical mechanism of the dynamic resonant shear stress sensor was analyzed by using the verified model. The results showed that the sensitivity of the dynamic resonant shear stress sensor was due to the energy lost produced by the oscillating interaction between the sensor and fluid flow.

Comparison of several models of the laminar/turbulent transition

The contribution deals with modelling of the laminar/turbulent transition using several transition models. Transition models of various types were tested: a) the model with the algebraic equation for the intermittency coefficient according to Straka and Pøíhoda; b) the three-equation transition model with the transport equation for the energy of non-turbulent fluctuations proposed by Walters and Cokljat; c) the γ-Reθ model with the transport equation forthe intermittency coefficient of Langtry and Menter. The transition models were compared by means of test cases covering both flat-plate boundary-layer flows with various free stream turbulence and the flow over an airfoil including the effect of foregoing wake on the transition. The agreement of numerical results with experimental data is in all cases quite satisfactory.

Variation of friction drag via spanwise transversal surface waves

AbstractIntroducing spanwise velocity components into the near‐wall flow field of a turbulent boundary layer has shown to be an effective mean of influencing the wall shear stress. The underlying physical mechanisms leading to the drag reduction have however not been fully understood. The presented investigation uses sinusoidal transversal travelling surface waves to influence the near‐wall turbulence to achieve drag reduction. Two distinct wave configurations are analysed in detail and compared to an unactuated turbulent flat plate boundary layer flow to gain inside into the drag reducing mechanisms. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)