Tangential gas blowing and boundary layer stability of a compressible gas

The effect of distributed blowing of a gas mass through a porous surface on the stability characteristics of a supersonic boundary layer is studied at a moderate supersonicMach numberM= 2. Tangential blowing when only the U-component of the mean velocity is not equal to zero on the wall is considered. The effect of the porous surface parameters on vortex perturbations is investigated and a comparison with the variant of the so-called “cutoff” regime is carried out. Different-density gas blowing is simulated by means of variation of the temperature factor (wall heating or cooling), namely, blowing of a heavy gas is simulated via blowing of a cold gas and vice versa.     

Numerical simulation of the interaction of a transverse jet with a supersonic flow using different turbulence models

This paper presents a numerical simulation of the flow resulting from transverse jet injection into a supersonic flow through a slot nozzle at different pressures in the injected jet and the crossflow. Calculations on grids with different resolutions use the Spalart–Allmaras turbulence model, the k–ε model, the k–ω model, and the SST model. Based on a comparison of the calculated and experimental data on the wall pressure distribution, the length of the recirculation area, and the depth of jet penetration into the supersonic flow, conclusions are made on the accuracy of the calculation results for the different turbulence models and the applicability of these models to similar problems.     

Direct Numerical Simulation and Theory of a Wall-Bounded Flow with Zero Skin Friction

We study turbulent plane Couette-Poiseuille (CP) flows in which the conditions (relative wall velocity ΔU _w ≡ 2U _w , pressure gradient dP/dx and viscosity ν) are adjusted to produce zero mean skin friction on one of the walls, denoted by APG for adverse pressure gradient. The other wall, FPG for favorable pressure gradient, provides the friction velocity u _τ , and h is the half-height of the channel. This leads to a one-parameter family of one-dimensional flows of varying Reynolds number Re ≡ U _w h/ν. We apply three codes, and cover three Reynolds numbers stepping by a factor of two each time. The agreement between codes is very good, and the Reynolds-number range is sizable. The theoretical questions revolve around Reynolds-number independence in both the core region (free of local viscous effects) and the two wall regions. The core region follows Townsend’s hypothesis of universal behavior for the velocity and shear stress, when they are normalized with u _τ and h; on the other hand universality is not observed for all the Reynolds stresses, any more than it is in Poiseuille flow or boundary layers. The FPG wall region obeys the classical law of the wall, again for velocity and shear stress. For the APG wall region, Stratford conjectured universal behavior when normalized with the pressure gradient, leading to a square-root law for the velocity. The literature, also covering other flows with zero skin friction, is ambiguous. Our results are very consistent with both of Stratford’s conjectures, suggesting that at least in this idealized flow turbulence theory is successful like it was for the classical logarithmic law of the wall. We appear to know the constants of the law within a 10% bracket. On the other hand, that again does not extend to Reynolds stresses other than the shear stress, but these stresses are passive in the momentum equation.     

Turbulent flows in channels with injection. results of large eddy simulation and the two-equation turbulence model

Turbulent flows in channels with intense distributed injection are modeled using the large eddy method and the two-equation k-? turbulence model. The calculations are carried out for different velocities of injection from the channel walls. For a channel with one-sided injection the results of large eddy simulation are in good agreement with the measured data, whereas the calculations in accordance with the k-? model give a less convex cross-sectional velocity profile and an appreciable error in determining the surface friction coefficient on the impermeable wall and also have certain other shortcomings. In the case of two-sided injection, the results of the calculations by the large eddy method and the k-? model are in good agreement with one another and the data of physical experiments.     

Perspectives on the Phenomenology and Modeling of Boundary Layer Transition

The characteristics of the coherent structures in a strongly decelerated large-velocity-defect boundary layer are analysed by direct numerical simulation. The simulated boundary layer starts as a zero-pressure-gradient boundary layer, decelerates under a strong adverse pressure gradient, and separates near the end of the domain, in the form of a very thin separation bubble. The Reynolds number at separation is R e _?? =3912 and the shape factor H=3.43. The three-dimensional spatial correlations of (u, u) and (u, v) are investigated and compared to those of a zero-pressure-gradient boundary layer and another strongly decelerated boundary layer. These velocity pairs lose coherence in the streamwise and spanwise directions as the velocity defect increases. In the outer region, the shape of the correlations suggest that large-scale u structures are less streamwise elongated and more inclined with respect to the wall in large-defect boundary layers. The three-dimensional properties of sweeps and ejections are characterized for the first time in both the zero-pressure-gradient and adverse-pressure-gradient boundary layers, following the method of Lozano-Durán et al. (J. Fluid Mech. 694, 100–130, [2012]). Although longer sweeps and ejections are found in the zero-pressure-gradient boundary layer, with ejections reaching streamwise lengths of 5 boundary layer thicknesses, the sweeps and ejections tend to be bigger in the adverse-pressure-gradient boundary layer. Moreover, small near-wall sweeps and ejections are much less numerous in the large-defect boundary layer. Large sweeps and ejections that reach the wall region (wall-attached) are also less numerous, less streamwise elongated and they occupy less space than in the zero-pressure-gradient boundary layer.     

Experimental Control of Turbulent Boundary Layers with In-plane Travelling Waves

The experimental control of turbulent boundary layers using streamwise travelling waves of spanwise wall velocity, produced using a novel active surface, is outlined in this paper. The innovative surface comprises a pneumatically actuated compliant structure based on the kagome lattice geometry, supporting a pre-tensioned membrane skin. Careful design of the structure enables waves of variable length and speed to be produced in the flat surface in a robust and repeatable way, at frequencies and amplitudes known to have a favourable influence on the boundary layer. Two surfaces were developed, a preliminary module extending 152 mm in the streamwise direction, and a longer one with a fetch of 2.9 m so that the boundary layer can adjust to the new surface condition imposed by the forcing. With a shorter, 1.5 m portion of the surface actuated, generating an upstream-travelling wave, a drag reduction of 21.5% was recorded in the boundary layer with Re _τ =?1125. At the same flow conditions, a downstream-travelling produced a much smaller drag reduction of 2.6%, agreeing with the observed trends in current simulations. The drag reduction was determined with constant temperature hot-wire measurements of the mean velocity gradient in the viscous sublayer, while simultaneous laser Doppler vibrometer measurements of the surface recorded the wall motion. Despite the mechanics of the dynamic surface resulting in some out-of-plane motion (which is small in comparison to the in-plane streamwise movement), the positive drag reduction results are encouraging for future investigations at higher Reynolds numbers.     

Inviscid vortex structures in the shock layers of conical flows around V wings

The applicability of the criteria of existence of inviscid vortex structures (vortex Ferri singularities) is studied in the case in which a contact discontinuity of the corresponding intensity proceeds from the branching point of the λ shock wave configuration accompanying turbulent boundary layer separation under the action of an inner shock incident on the leeward wing panel. The calculated and experimental data are analyzed, in particular, those obtained using the special shadow technique developed for visualizing supersonic conical streams in nonsymmetric, Mach number 3 flow around a wing with zero sweep of the leading edges and the vee angle of 2π /3. The applicability of the criteria of existence of inviscid vortex structures is established for contact discontinuities generated by the λ shock wave configuration accompanying turbulent boundary layer separation realized under the action of a shock wave incident on the leeward wing panel. Thus, it is established that the formation of the vortex Ferri singularities in a shock layer is independent of the reason for the existence of the contact discontinuity and depends only on its intensity.     

Effect of surface permeability on the structure of a separated turbulent flow and heat transfer behind a backward-facing step

The structure and heat transfer in a turbulent separated flow in a suddenly expanding channel with injection (suction) through a porous wall are numerically simulated with the use of two-dimensional averaged Navier–Stokes equations, energy equations, and v ²–f turbulence model. It is shown that enhancement of the intensity of the transverse mass flux on the wall reduces the separation region length in the case of suction and increases the separation region length in the case of injection up to complete boundary layer displacement. The maximum heat transfer coefficient as a function of permeability is accurately described by the asymptotic theory of a turbulent boundary layer.     

Effects of Strong Irregular Roughness on the Turbulent Boundary Layer

Some recent studies with irregular roughness suggest that the Nikuradse [Nikuradse, J., NACA TM 1292, National Advisory Committee on Aeronautics (1933)] equivalent sand-grain roughness measure gives inconsistent results of the flow characteristics. In situations where the roughness is very strong to stifle or diminish the viscous effects the viscous scaling laws alone will not be very meaningful. The present study aims to find an alternative scaling parameter for such cases. Here, the measured mean and turbulent velocity profiles on a nonuniform roughness surface, simulating a gas turbine blade roughness, are presented. A nonzero wall normal pressure gradient is caused which is believed to contribute to the velocity deficit in the near-wall rough boundary layer velocity profile. The surface pressure variation is also directly influenced by the local roughness. The normal turbulent stresses are increased on the rough surface, the vertical component more than the longitudinal component. A pressure gradient velocity scale (similar to that proposed for adverse pressure gradient boundary layer modeling by Durbin and Belcher [Durbin, P.A. and Belcher, S.E., J. Fluid Mech. 238 (1992), 699-722] is defined to capture the pressure effects induced by such roughness on the inner layer properties.     

Vortical structures behind a transverse jet in a supersonic flow at high jet to crossflow pressure ratios

A three-dimensional supersonic turbulent flow with symmetric normal injection of circular jets from the channel walls is numerically simulated. The initial Favre-averaged Navier–Stokes equations closed by the k–ω turbulence model are solved by an algorithm based on an ENO scheme. The mechanism of the formation of vortical structures due to the interaction of the jet with the free stream is studied for jet to crossflow total pressure ratios ranging from 3 to 50. It is known from experiments reported in the literature that, for n ? 10, mixing of the jet with the high-velocity flow leads to the formation of a pair of vortices and of an additional separation zone near the wall behind the jet. It is demonstrated that the present numerical results are consistent with such findings and that the pressure distribution on the wall ahead of the jet in the plane of symmetry is also in reasonable agreement with available experimental data.     

Experimental study on flow control of the turbulent boundary layer with micro-bubbles

The effect of micro-bubbles on the turbulent boundary layer in the channel flow with Reynolds numbers (Re) ranging from \(0.87\times 10 ^{5}\) to \(1.23\times 10^{5}\) is experimentally studied by using particle image velocimetry (PIV) measurements. The micro-bubbles are produced by water electrolysis. The velocity profiles, Reynolds stress and instantaneous structures of the boundary layer, with and without micro-bubbles, are measured and analyzed. The presence of micro-bubbles changes the streamwise mean velocity of the fluid and increases the wall shear stress. The results show that micro-bubbles have two effects, buoyancy and extrusion, which dominate the flow behavior of the mixed fluid in the turbulent boundary layer. The buoyancy effect leads to upward motion that drives the fluid motion in the same direction and, therefore, enhances the turbulence intense of the boundary layer. While for the extrusion effect, the presence of accumulated micro-bubbles pushes the flow structures in the turbulent boundary layer away from the near-wall region. The interaction between these two effects causes the vorticity structures and turbulence activity to be in the region far away from the wall. The buoyancy effect is dominant when the Re is relatively small, while the extrusion effect plays a more important role when Re rises.     

A Simple Approach for Specifying Velocity Inflow Boundary Conditions in Simulations of Turbulent Opposed-Jet Flows

A new methodology is developed to specify inflow boundary conditions for the velocity field at the nozzle exit planes in turbulent counterflow simulations. The turbulent counterflow configuration consists of two coaxial opposed nozzles which emit highly-turbulent streams of varying species compositions depending on the mode considered. The specification of velocity inflow boundary conditions at the nozzle exits in the counterflow configuration is non-trivial because of the unique turbulence field generated by the turbulence generating plates (TGPs) upstream of the nozzle exits. In the method presented here, a single large-eddy simulation (LES) is performed in a large domain that spans the region between the TGPs of the nozzles, and the time series of the velocity fields at the nozzle exit planes are recorded. To provide inflow boundary conditions at the nozzle exit planes for simulations under other conditions (e.g., different stream compositions, bulk velocity, TGP location), transformations are performed on the recorded time series: the mean and r.m.s. (root-mean-square) quantities of velocity, as well as the longitudinal integral length scale on the centerline, at the nozzle exits in simulations are matched to those observed in experiments, thereby matching the turbulent Reynolds number R e _t . The method is assessed by implementing it in coupled large-eddy simulation/probability density function (LES/PDF) simulations on a small cylindrical domain between the nozzle exit planes for three different modes of the counterflow configuration: N ₂ vs. N ₂; N ₂ vs. hot combustion products; and C H ₄/N ₂ vs. O ₂. The inflow method is found to be successful as the first and second moments of velocity from the LES/PDF simulations agree well with the experimental data on the centerline for all three modes. This simple yet effective inflow strategy can be applied to eliminate the computational cost required to simulate the flow field upstream of the nozzle exits. It is also emphasized that, in addition to the predicted time series data, the availability of experimental data close to the nozzle exit planes plays a key role in the success of this method.     

Experimental and Numerical Simulations of Spray Impingement and Combustion Characteristics in Gasoline Direct Injection Engines under Variable Driving Conditions

Gasoline direct injection (GDI) increases engine power output and reduces emissions. In GDI engines, increasing injection pressure improves atomization, which increases thermal efficiency at the cost of wall wetting. When wall wetting occurs, both soot emissions and fuel consumption increase. Wall wetting in GDI engines under cold driving conditions has rarely been considered. In this study, experimental data characterizing droplet splashing/spreading phenomena were collected to inform numerical simulations of combustion characteristics and wall wetting subject to variable driving conditions and excess air ratio, λ. Fully 3D and unsteady numerical simulations were carried out to predict flow-field, combustion, and spray-impingement characteristics. To simulate a GDI engine, a spray-impingement model was developed using both experimental data and previous modeling efforts. The excess air ratio and driving-condition temperature were the variable parameters considered in this study. When decreasing λ from 1.0 to 0.7 by increasing the fuel-injection rate (fuel rich), the cylinder pressure increases to 61 % of the pressure when λ=1.0. Because of increasing the fuel-injection rate, the increased momentum in the fuel spray increases both wall wetting and soot generation. At low driving-condition temperatures, the cylinder pressure was up to 63 % less than that under warm conditions, but with increased soot generation. Simulations revealed a correlation between wall wetting and the soot emissions. Soot generation was most sensitive to changes in wall wetting.     

Simulation of a Large-Eddy-Break-up Device (LEBU) in a Moderate Reynolds Number Turbulent Boundary Layer

A well-resolved large eddy simulation (LES) of a large-eddy break-up (LEBU) device in a spatially evolving turbulent boundary layer is performed with, Reynolds number, based on free-stream velocity and momentum-loss thickness, of R e _θ ≈ 4300. The implementation of the LEBU is via an immersed boundary method. The LEBU is positioned at a wall-normal distance of 0.8 δ (δ denoting the local boundary layer thickness at the location of the LEBU) from the wall. The LEBU acts to delay the growth of the turbulent boundary layer and produces global skin friction reduction beyond 180δ downstream of the LEBU, with a peak local skin friction reduction of approximately 12 %. However, no net drag reduction is found when accounting for the device drag of the LEBU in accordance with the towing tank experiments by Sahlin et al. (Phys. Fluids 31, 2814, 1988). Further investigation is performed on the interactions of high and low momentum bulges with the LEBU and the corresponding output is analysed, showing a ‘break-up’ of these large momentum bulges downstream of the LEBU. In addition, results from the spanwise energy spectra show consistent reduction in energy at spanwise length scales for \(\lambda _{z}^{+} > 1000\) independent of streamwise and wall-normal location when compared to the corresponding turbulent boundary layer without LEBU.     

Kinetic Fokker-Planck equation for free-molecular,thermally nonequilibrium Brownian particles in an inhomogeneous gas

A kinetic equation for the translational and angular velocity distribution function of spherical rigid Brownian particles in an inhomogeneous monatomic gas is derived. The particle diameters are much smaller than the average free path of the gas molecules and the interaction between the particles and their effect on the carrier (gas) phase are neglected. The particle temperatures T _p are the same and differ from the local gas temperature T. The molecular velocity distribution function is specified by the first approximation of the Chapman-Enskog method. The difference between the characteristic phase velocities is small as compared with the mean thermal molecular velocity. The dependences of the diffusion coefficients in velocity space on the ratio T _p/T, which characterize the effect of thermal nonequilibrium, i.e., violation of the thermodynamic equilibrium between the phases of the disperse system, are found using a specular-diffuse law of reflection of the molecules from the particle surface.     

Flow visualization of supersonic laminar flow over a backward-facing step via NPLS

An experimental study on a supersonic laminar flow over a backward-facing step of 5 mm height was undertaken in a low-noise indraft wind tunnel. To investigate the fine structures of Ma = 3.0 and 3.8 laminar flow over a backward-facing step, nanotracer planar laser scattering was adopted for flow visualization. Flow structures, including supersonic laminar boundary layer, separation, reattachment, redeveloping turbulent boundary layer, expansion wave fan and reattachment shock, were revealed in the transient flow fields. In the Ma = 3.0 BFS (backward-facing step) flow, by measuring four typical regions, it could be found that the emergence of weak shock waves was related to the K–H (Kelvin–Helmholtz) vortex which appeared in the free shear layer and that the convergence of these waves into a reattachment shock was distinct. Based on large numbers of measurements, the structure of time-averaging flow field could be gained. Reattachment occurred at the location downstream from the step, about 7–7.5 h distance. After reattachment, the recovery boundary layer developed into turbulence quickly and its thickness increased at an angle of 4.6°. At the location of X = 14h, the redeveloping boundary layer was about ten times thicker than its original thickness, but it still had not changed into fully developed turbulence. However, in the Ma = 3.8 flow, the emergence of weak shock waves could be seen seldom, due to the decrease of expansion. The reattachment point was thought to be near X = 15h according to the averaging result. The reattachment shock was not legible, which meant the expansion and compression effects were not intensive.     

Large-Scale Streamwise Vortices in Turbulent Channel Flow Induced by Active Wall Actuations

Direct numerical simulations of turbulent flow in a plane channel using spanwise alternatively distributed strips (SADS) are performed to investigate the characteristics of large-scale streamwise vortices (LSSVs) induced by small-scale active wall actuations, and their role in suppressing flow separation. SADS control is obtained by alternatively applying out-of-phase control (OPC) and in-phase control (IPC) to the wall-normal velocity component of the lower channel wall, in the spanwise direction. Besides the non-controlled channel flow simulated as a reference, four controlled cases with 1, 2, 3 and 4 pairs of OPC/IPC strips are studied at M =?0.2 and R e =?6,000, based on the bulk velocity and the channel half height. The case with 2 pairs of strips, whose width is Δz ⁺ =?264 based on the friction velocity of the non-controlled case, is the most effective in terms of generating large-scale motions. It is also found that the OPC (resp. IPC) strips suppress (resp. enhance) the coherent structures and that leads to the creation of a vertical shear layer, which is responsible for the LSSVs presence. They are in a statistically steady state and their cores are located between two neighbouring OPC and IPC strips. These motions contribute significantly to the momentum transport in the wall-normal and spanwise directions showing potential for flow separation suppression.     

Consequences of the Translation Invariance on the Darcy Free Convection Flow Past a Vertical Surface

It is shown that the governing equation for the stream function of the Darcy free convection boundary layer flows past a vertical surface is invariant under arbitrary translations of the transverse coordinate y. The consequences of this basic symmetry property on the solutions corresponding to a prescribed surface temperature distribution T _w (x) are investigated. It is found that starting with a “primary solution” which describes the temperature boundary layer on an impermeable surface, infinitely many “translated solutions” can be generated which form a continuous group, the “translation group” of the given primary solution. The elements of this group describe free convection boundary layer flows from permeable counterparts of the original surface with a transformed temperature distribution \({\tilde {T}_w \left( x \right)}\), when simultaneously a suitable lateral suction/injection of the fluid is applied. It turns out in this way that several exact solutions discovered during the latter few decades are in fact not basically new solutions, but translated counterparts of some formerly reported primary solutions. A few specific examples are discussed in detail.