Flat Plate Boundary Layer Flow Research Articles

An Improved K-ω Model for High Speed Flows

An improved K-ω model, which allows for compressible corrections, is proposed in this paper. Numerical scheme was established utilizing the improved Total Variation Diminishing (TVD) scheme and applying implicit scheme to the negative source terms of the turbulence model. Hypersonic flat-plate boundary-layer flows and hypersonic compression ramp flows marked with separation, reattachment and shock/boundary layer interactions are then computed. Comparisons between the computational results, the experimental results and the semi-empirical formulations show that the compressible correction term of the K-ω turbulence model is a pressure-dilatation correlation. In addition, for flow with separation and without separation, calculation results of wall pressures, friction coefficients and wall heat transfer rate distributions using the improved model and established scheme agree better with the experimental results than that using the original K-ω model.

An Improved Shear Stress Transport(SST) Model for High Speed Flows

An improved Shear Stress Transport(SST) model, which allows for the compressible corrections, is proposed in this study. Numerical scheme was established by taking advantage of the improved Total Variation Diminishing (TVD) scheme and by applying implicit scheme to the negative source terms of the turbulence model. Hypersonic flat-plate boundary-layer flows and hypersonic compression ramp flows marked with separation, reattachment and shock/boundary-layer interactions are then computed. The comparisons between the computational results, the experimental results and the semi-empirical formulations show that the compressible correction term of the SST turbulence model is the scalar product of the weighted density average of the turbulent fluctuating velocity and the pressure gradients of the average flow field correlation quantities. In addition, for flow with separation and without separation, calculation results of wall pressures, friction coefficients and wall heat transfer rate distributions using the improved model and established scheme agree better with the experimental results than that using the original SST model.

Direct numerical simulations of roughness-induced transition in supersonic boundary layers

AbstractDirect numerical simulations are used to study the laminar to turbulent transition of a Mach 2.9 supersonic flat plate boundary layer flow due to distributed surface roughness. Roughness causes the near-wall fluid to slow down and generates a strong shear layer over the roughness elements. Examination of the mean wall pressure indicates that the roughness surface exerts an upward impulse on the fluid, generating counter-rotating pairs of streamwise vortices underneath the shear layer. These vortices transport near-wall low-momentum fluid away from the wall. Along the roughness region, the vortices grow stronger, longer and closer to each other, and result in periodic shedding. The vortices rise towards the shear layer as they advect downstream, and the resulting interaction causes the shear layer to break up, followed quickly by a transition to turbulence. The mean flow in the turbulent region shows a good agreement with available data for fully developed turbulent boundary layers. Simulations under varying conditions show that, where the shear is not as strong and the streamwise vortices are not as coherent, the flow remains laminar.

Numerical Simulation of Hydrogen–Air Boundary Layer Flows Augmented by Catalytic Surface Reactions

Catalytic combustion of hydrogen–air boundary layers involves the adsorption of hydrogen and oxygen into a platinum coated surface, chemical reactions of the adsorbed species, and the desorption of the resulting products. Re-adsorption of some produced gases is also possible. The catalytic reactions can be beneficial in porous burners and catalytic reactors that use low equivalence ratios. In this case, the porous burner flame can be stabilized at low temperatures to prevent any substantial gas emissions, such as nitrogen oxides. The present paper is concerned with the numerical computation of heat transfer and chemical reactions in hydrogen–air mixture boundary layers that flow over platinum coated hot plates and inside rectangular channels. Chemical reactions are included in the gas-phase as well as on the solid platinum surface. In the gas-phase, eight species are involved in 26 elementary reactions. On the platinum hot surface, additional surface species are included that are involved in 16 additional surface chemical reactions. The platinum surface temperature distribution is prespecified, while the properties of the reacting flow are computed. The flow configurations investigated in the present paper are those of a flat plate boundary layer and a rectangular channel reacting flow. Finite-volume equations are obtained by formal integration over control volumes surrounding each grid node. Hybrid differencing is used to ensure that the finite-difference coefficients are always positive or equal to zero to reflect the real effect of neighboring nodes on a typical central node. The finite-volume equations are solved iteratively for the reacting gas flow properties. On the platinum surface, surface species balance equations, under steady-state conditions, are solved numerically. A nonuniform computational grid is used, concentrating most of the nodes in the boundary sub-layer adjoining the catalytic surface. For the flat plate boundary layer flow, the computed OH concentration is compared with experimental and numerical data of similar geometry. The obtained agreement is fairly good, with differences observed for the location of the peak value of OH. Surface temperature of 1170 K caused fast reactions on the catalytic surface in a very small part at the leading edge of the catalytic flat plate. The flat plate computational results for heat and mass transfer and chemical surface reactions at the gas-surface interface are correlated by nondimensional relations. The channel flow computational results are also compared with recent detailed experimental data for similar geometry. In this case, the catalytic surface temperature profile along the x-axis was measured accurately and is used in the present work as the boundary condition for the gas-phase energy equation. The present numerical results for the gas temperature, water vapor mole fraction, and hydrogen mole fraction are compared with the corresponding experimental data. In general, the agreement is very good especially in the first 105 mm. However, some differences are observed in the vicinity of the exit section of the rectangular channel.

A hybrid time-stepping method of local preconditioning on high aspect ratio grids

Time-derivative preconditioning methods have provided robust convergences and accurate solutions for low-speed inviscid flows by using local flow properties as the reference scaling parameter in the preconditioning matrix. During viscous or turbulent flow calculations, the use of high aspect ratio grids to obtain accurate solutions near the wall often results in stiff convergence and nonphysical solutions in the singular regions. In this paper, a switching method is proposed as a remedy to that problem by combining the advantages of the typical local time-stepping and min-CFL/max-VNN methods. The proposed method is based on results of our study of the inviscid bump flow and flat plate boundary layer flows and also proved to be effective to a turbulent flow simulation around the NACA 4412 airfoil.

Implicit large eddy simulation of a supersonic flat-plate boundary layer flow by weighted compact nonlinear scheme

The performance of implicit large eddy simulation (ILES) of a supersonic flat-plate turbulent boundary layer flow by weighted compact nonlinear scheme (WCNS) has been investigated. In view of features of WCNS and ILES, it was expected that ILES by WCNS could be an efficient approach to perform LES of supersonic turbulent flows. The flowfield calculated by WCNS was of lower turbulent intensity compared with an explicit LES data obtained by a numerical scheme of the same order of accuracy on a computational grid of similar resolution. It was concluded that the numerical dissipation inherent in WCNS is so large that applying WCNS to ILES of this flowfield is inefficient compared with explicit LES.

Numerical study of the stabilisation of boundary-layer disturbances by finite amplitude streaks

Well-resolved large-eddy simulations of passive control of the laminar-turbulent transition process in flat-plate boundary-layer flows are presented. A specific passive control mechanism is studied, namely the modulation of the laminar boundary-layer profile by a periodic array of steady boundary-layer streaks. This has been shown experimentally to stabilise the exponential growth of Tollmien-Schlichting (TS) waves and delay transition to turbulence. Here we examine the effect of the steady modulations on the amplification of different types of disturbances such as TS-waves, stochastic noise and free-stream turbulence. In our numerical simulations, the streaks are forced at the inflow as optimal solutions to the linear parabolic stability equations (PSE), whereas the additional disturbances are excited via volume forcing active within the computational domain. The simulation results show, in agreement with experimental and theoretical studies, significant damping of unstable two-dimensional TS-waves of va...

Control of Tollmien–Schlichting instabilities by finite distributed wall actuation

Tollmien–Schlichting waves are one of the key mechanisms triggering the laminar-turbulent transition in a flat-plate boundary-layer flow. By damping these waves and thus delaying transition, skin friction drag can be significantly decreased. In this simulation study, a wall segment is actuated according to a control scheme based on a POD-Galerkin model driven extended Kalman filter for state estimation and a model predictive controller to dampen TS waves by negative superposition based on this information. The setup of the simulation is chosen to resemble actuation with a driven compliant wall, such as a membrane actuator. Most importantly, a method is proposed to integrate such a localized wall actuation into a Galerkin model.

Global three-dimensional optimal disturbances in the Blasius boundary-layer flow using time-steppers

The global linear stability of the flat-plate boundary-layer flow to three-dimensional disturbances is studied by means of an optimization technique. We consider both the optimal initial condition leading to the largest growth at finite times and the optimal time-periodic forcing leading to the largest asymptotic response. Both optimization problems are solved using a Lagrange multiplier technique, where the objective function is the kinetic energy of the flow perturbations and the constraints involve the linearized Navier–Stokes equations. The approach proposed here is particularly suited to examine convectively unstable flows, where single global eigenmodes of the system do not capture the downstream growth of the disturbances. In addition, the use of matrix-free methods enables us to extend the present framework to any geometrical configuration. The optimal initial condition for spanwise wavelengths of the order of the boundary-layer thickness are finite-length streamwise vortices exploiting the lift-up mechanism to create streaks. For long spanwise wavelengths, it is the Orr mechanism combined with the amplification of oblique wave packets that is responsible for the disturbance growth. This mechanism is dominant for the long computational domain and thus for the relatively high Reynolds number considered here. Three-dimensional localized optimal initial conditions are also computed and the corresponding wave packets examined. For short optimization times, the optimal disturbances consist of streaky structures propagating and elongating in the downstream direction without significant spreading in the lateral direction. For long optimization times, we find the optimal disturbances with the largest energy amplification. These are wave packets of Tollmien–Schlichting waves with low streamwise propagation speed and faster spreading in the spanwise direction. The pseudo-spectrum of the system for real frequencies is also computed with matrix-free methods. The spatial structure of the optimal forcing is similar to that of the optimal initial condition, and the largest response to forcing is also associated with the Orr/oblique wave mechanism, however less so than in the case of the optimal initial condition. The lift-up mechanism is most efficient at zero frequency and degrades slowly for increasing frequencies. The response to localized upstream forcing is also discussed.

Intermediate Reynolds number flat plate boundary layer flows over catalytic surfaces for “micro”-combustion applications

The reactive, flat plate, boundary layer flow of close-to-stoichiometric, combusting methane–air mixtures over small size Pt plates was studied experimentally for the range of intermediate Reynolds numbers that pertain to micro-combustion applications. The emphasis was on detecting combustion features that differentiate this flow from similar flows that have been studied extensively of leaner mixtures at higher Reynolds numbers. Surface temperature was measured with infrared thermography and was correlated to reactant concentration profiles that were acquired with gas chromatography/mass spectroscopy. Additionally, particle image velocimetry was used in order to investigate the streamwise and transverse velocity profiles along the reacting plate. It was established that combustion took place in three subsequent phases: in the immediate vicinity of the leading edge of the flat plates, a first phase of combustion was established with high surface temperature (>1200 °C), intense fuel depletion and product formation, and maximum streamwise and transverse velocities. This was followed by a second, relatively long phase, where temperature leveled out to an intermediate value, product formation and reactant depletion slowed, and velocities were further reduced. In a third phase, combustion was completed and the surface temperature was reduced to the temperature of the free–stream mixture. The flow field differs significantly from the classical flat plate boundary layer with strong transverse velocities due primarily to chemistry. It is suggested that phase I combustion can be used for burner miniaturization through boundary layer interruption.

Flow field characterization of a rotating cylinder

Direct numerical simulation is used to study the flow field around an infinitely long circular cylinder rotating in fluid with no outer boundary. Wall shear stresses and normal pressure fluctuations are considered with reference to flat, non-rotating geometries to help identify any flow field differences introduced by Coriolis forces. In the present case, Coriolis forces are experienced only by the turbulence field. The dominant effect is to decrease the streamwise turbulent velocity level relative to the other two components. A consequential effect is that the two components of wall shear stress fluctuations become almost equal and spectra for streamwise and spanwise wall shear stress fluctuations become almost identical. This is a distinctly different behaviour from that of non-rotating flat plate and straight pipe flows. Instantaneous wall shear stress fluctuations indicate a near wall flow structure similar to that of other boundary layers with sweeps and ejections. No flow reversals of wall shear stress are indicated. A good correlation of the wall shear stresses and the turbulent kinetic energy exists for y + < 10. Budgets of Reynolds normal stress components illustrate the role played by Coriolis forces in the production and redistribution of turbulence energies. Wall pressure fluctuations are found to be of much larger spatial extent than velocity fluctuation scales while the probability density distribution of pressure fluctuations is almost Gaussian but does display a Reynolds number effect for skewness and Kurtosis. The ratio of rms pressure fluctuations to mean streamwise wall shear stress follows closely that for flat plate boundary layer and channel flows.

DNS of compressible turbulent boundary layer around a sharp cone

Direct numerical simulation of the turbulent boundary layer over a sharp cone with 20° cone angle (or 10° half-cone angle) is performed by using the mixed seventh-order up-wind biased finite difference scheme and sixth-order central difference scheme. The free stream Mach number is 0.7 and free stream unit Reynolds number is 250000/inch. The characteristics of transition and turbulence of the sharp cone boundary layer are compared with those of the flat plate boundary layer. Statistics of fully developed turbulent flow agree well with the experimental and theoretical data for the turbulent flat-plate boundary layer flow. The near wall streak-like structure is shown and the average space between streaks (normalized by the local wall unit) keeps approximately invariable at different streamwise locations. The turbulent energy equation in the cylindrical coordinate is given and turbulent energy budget is studied. The computed results show that the effect of circumferential curvature on turbulence characteristics is not obvious.

Implicit LES applied to zero-pressure-gradient and adverse-pressure-gradient boundary-layer turbulence

Further development of large-eddy simulation (LES) faces as major obstacles the strong coupling between subgrid-scale (SGS) modeling and the truncation error of the numerical discretization. One can exploit this link by developing discretization methods where the truncation error itself functions as an implicit SGS model. The adaptive local deconvolution method (ALDM) is an approach to LES of turbulent flows that represents a full coupling of SGS model and discretization scheme. To provide evidence for the validity of this new SGS model, well resolved large-eddy simulations of a fully turbulent flat-plate boundary-layer flow subjected to a constant adverse pressure gradient are conducted. Flow parameters are adapted to an available experiment. The Reynolds number based on the local free-stream velocity and momentum thickness is 670 at the inflow and 5100 at the separation point. Clauser’s pressure-gradient parameter increases monotonically from 0 up to approximately 100 since a constant pressure gradient is prescribed. The adverse pressure gradient leads to a highly unsteady and massive separation of the boundary layer. The numerical predictions agree well with theory and experimental data.

DNS and LES of estimation and control of transition in boundary layers subject to free-stream turbulence

Transition to turbulence occurring in a flat-plate boundary-layer flow subjected to high levels of free-stream turbulence is considered. This scenario, denoted bypass transition, is characterised by the non-modal growth of streamwise elongated disturbances. These so-called streaks are regions of positive and negative streamwise velocity alternating in the spanwise direction inside the boundary layer. When they reach large enough amplitudes, breakdown into turbulent spots occurs via their secondary instability. In this work, the bypass-transition process is simulated using direct numerical simulations (DNS) and large-eddy simulations (LES). The ADM-RT subgrid-scale model turned out to be particularly suited for transitional flows after a thorough validation. Linear feedback control is applied in order to reduce the perturbation energy and consequently delay transition. This case represents therefore an extension of the linear approach (Chevalier, M., Hoepffner, J., Åkervik, E., Henningson, D.S., 2007a. Linear feedback control and estimation applied to instabilities in spatially developing boundary layers. J. Fluid Mech. 588, 163–187, 167–187.) to flows characterised by strong nonlinearities. Control is applied by blowing and suction at the wall and it is both based on the full knowledge of the instantaneous velocity field (i.e. full information control) and on the velocity field estimated from wall measurements. The results show that the control is able to delay the growth of the streaks in the region where it is active, which implies a delay of the whole transition process. The flow field can be estimated from wall measurements alone: The structures occurring in the “real” flow are reproduced correctly in the region where the measurements are taken. Downstream of this region the estimated field gradually diverges from the “real” flow, revealing the importance of the continuous excitation of the boundary layer by the external free-stream turbulence. Control based on estimation, termed compensator, is therefore less effective than full information control.

Streak interactions and breakdown in boundary layer flows

The objective of this paper is to show that the interaction of streamwise velocity streaks of finite length can lead to turbulent breakdown in the flat-plate boundary layer flow. The work is motivated by previous numerical and experimental studies of transitional flows where the high-frequency oscillations leading to turbulence are seen to form in the region of strongest shear induced by streaks in relative motion. Therefore, a model for the interaction of steady and unsteady (i.e., slowly moving in the spanwise direction) spanwise periodic streaks is proposed. The interaction of two subsequent streaks is investigated for varying collision parameters. In particular, the relative spanwise position and angle are considered. The results show that the interaction is able to produce both a symmetric and asymmetric breakdown without the need for additional random noise from the main stream. Velocity structures characteristic of both scenarios are analyzed. Hairpin and Λ vortices are found in the case of symmetric collision between a low-speed region and an incoming high-speed streak, when a region of strong wall-normal shear is induced. Alternatively, when the incoming high-momentum fluid is misaligned with the low-speed streak in front, single quasi-streamwise vortices are identified. Despite the different symmetry at the breakdown, the detrimental interaction involves for both cases the tail of a low-speed region and the head of a high-speed streak. Further, the breakdown appears in both scenarios as an instability of three-dimensional shear layers formed between the two streaks. The streak interaction scenario is suggested to be of relevance for turbulence production in wall-bounded flows.

Investigation of a turbulent spot and a tripped turbulent boundary layer flow using time-resolved tomographic PIV

In this feasibility study the tomographic PIV technique has been applied to time resolved PIV recordings for the study of the growth of a turbulent spot in a laminar flat plate boundary layer and to visualize the topology of coherent flow structures within a tripped turbulent flat plate boundary layer flow. The experiments are performed around (Re x )1/2 ≈ 450 in a low speed wind-tunnel using four high speed CMOS cameras operating up to 5 kHz. The volume illumination required a multiple-reflection system able to intensify light intensity within the measurement volume. This aspect is deemed essential when a high-speed tomographic PIV system is applied in air flows. The particle image recordings are used for a three dimensional tomographic reconstruction of the light intensity distribution within the illuminated volume. Each pair of reconstructed three-dimensional light distributions is analyzed by 3D spatial cross-correlation using iterative multi-grid schemes with volume-deformation, yielding a correlated time sequence of three-dimensional instantaneous velocity vector volumes. The coherent structures organization is analyzed by 3D-vorticity and -swirling-strength iso-surfaces visualization. In both flow types streaks and hairpin-like or arch vortical structures are most prominent. The data gives insight into the role of these structures for the spatio-temporal arrangement of the wall normal flow exchange mechanisms, especially of the instantaneous Reynolds stress events Q2 and Q4. A description of different self-sustainable flow organizations based on modifications of the hairpin-vortex- and streak-models is given. Two preliminary results are essential: Self-sustainability of a coherent vortical structure depends on the ability to entrain high momentum fluid, initially Q4. And, stream-wise swirl at the near-wall region of arch or hairpin-like vortices has been observed to be rare.

Global two-dimensional stability measures of the flat plate boundary-layer flow

The stability of the two-dimensional flat plate boundary-layer is studied by means of global eigenmodes. These eigenmodes depend both on the streamwise and wall-normal coordinate, hence there are no assumptions on the streamwise length scales of the disturbances. Expanding the perturbation velocity field in the basis of eigenmodes yields a reduced order model from which the stability characteristics of the flow, i.e. the initial condition and forcing function leading to the largest energy growth, are extracted by means of non-modal analysis. In this paper we show that, even when performing stability analysis using global eigenmodes, it is not sufficient to consider only a few of the least damped seemingly relevant eigenmodes. Instead it is the task of the optimization procedure, inherent in the non-modal analysis, to decide which eigenmodes are relevant. We show that both the optimal initial condition and the optimal forcing structure have the form of upstream tilted structures. Time integration reveals that these structures gain energy through the so called Orr mechanism, where the instabilities extract energy from the mean shear. This provides the optimal way of initiating Tollmien–Schlichting waves in the boundary layer. The optimal initial condition results in a localized Tollmien–Schlichting wavepacket that propagates downstream, whereas the optimal forcing results in a persistent Tollmien–Schlichting wave train.

Flow control with plasma synthetic jet actuators

This paper presents an experimental investigation of the characteristics of a plasma actuator design for flow control consisting of an annular electrode in quiescent and flat plate boundary layer flows. In quiescent flow, the circular plasma region produced on actuation was observed to generate a vertical zero-net mass flux (or synthetic) jet, hence the name plasma synthetic jet actuator, the characteristics of which were found to be affected by the actuator operation mode (steady or unsteady). Pulsed operation of the actuator results in the formation of a starting vortex ring that advects ahead of the jet and secondary vortex rings near the actuator surface due to the additional plasma-induced fluid entrainment in the boundary layer. By varying the actuator pulsing frequency, multiple vortex rings were created in the flowfield and the resulting vortex ring interactions were found to increase both the peak velocity and streamwise extent of the jet. The interaction of the actuator with a crossflow was observed to be similar to that seen in conventional or non zero-net mass flux jets with the plasma synthetic jet penetrating into the mean flow. As expected, the influence of the jet on the freestream was found to decrease with increasing mean velocity and the impact on displacement and momentum thickness values diminishes as well.

Intermediate Reynolds/Peclet number, flat plate boundary layer flows over catalytic surfaces for micro-combustion applications

The reactive, flat plate boundary layer flow of close-tostoichiometric, methaneair mixtures over small size Pt plates is studied experimentally for intermediate Reynolds and Peclet numbers which pertain to micro-combustion applications. The surface temperature was measured with infrared thermography and correlated to reactant concentration profiles acquired with line-Raman imaging. Three phases of combustion were observed. Immediately after the leading edge, a first phase was established with a high surface temperature (>1200C) and intense fuel depletion. The Reynolds number and equivalence ratio strongly influenced this first phase. It was followed by a second, longer phase, where temperature reached an intermediate value near 1000C that exhibited little sensitivity to Reynolds number and equivalence ratio. In a third phase, combustion was completed and the surface temperature was reduced to the free-stream mixture temperature. It is suggested that this 'Phase I' combustion can be used for burner miniaturisation through boundary layer interruption.

Nonlinear global instability in buoyancy-driven boundary-layer flows

Direct numerical simulation (DNS) and a linear analysis of the global instability of a buoyancy layer have been performed. The spatially developing basic flow under consideration is induced by a vertical heated flat plate immersed in a thermally stratified medium. It is revealed numerically that, depending on the modified Grashof number, the disturbed flat-plate boundary-layer flows may not relax to the basic state but instead oscillate with an intrinsic frequency. The front of globally unstable waves in numerical simulations agrees very well with the position of marginal absolute instability, and the dominant frequencies in the oscillating region are identical and tuned to the marginal absolute frequency derived from the local linear dispersion relation based on the unperturbed basic state. The front of the nonlinear global modes is thus of a pulled type in this buoyancy-driven flow system.