Nonequilibrium Boundary Layer Research Articles

Cross-wavelet analysis of wall pressure fluctuations beneath incompressible turbulent boundary layers

Pressure fluctuations measured at the wall of a turbulent boundary layer are analysed using a bi-variate continuous wavelet transform. Cross-wavelet analyses of pressure signals obtained from microphone pairs are performed and a novel post-processing technique aimed at selecting events with strong local-in-time coherence is applied. Probability density functions and conditionally averaged equivalents of Fourier spectral quantities, usually introduced for modelling purposes, are computed. The analysis is conducted for signals obtained at low Mach numbers from two different non-equilibrium turbulent boundary layer experiments. It is found that that the selected events, though statistically independent, exhibit bi-modal statistics while the conditional coherence function coincides with its non-conditional Fourier equivalent. The physical nature of the selected events has been further explored by the computation of ensemble-averaged pressure time signatures and the results have been physically interpreted with the aid of numerical and experimental results from the literature. In both experiments, it has been found that the major physical mechanisms responsible for the observed conditional statistics are represented by sweep-type events which can be ascribed to the effect of streamwise vortices in the near-wall region. More precisely, the wavelet analysis highlights the convection of the selected structures in both cases. Conversely, compressibilty effects could be related to these events only in one case.

Spatio-temporal turbulent structures of thermal boundary layer subjected to non-equilibrium adverse pressure gradient

We have experimentally investigated a non-equilibrium turbulent boundary layer subjected to an adverse pressure gradient developing on a uniformly heated flat wall. The spatio-temporal structures educed from a multi-point simultaneous measurement are reasonably interpolated based on the “proper orthogonal decomposition (POD)”. In the near-wall region, elongated hot regions stay dull and less active, whereas, large-scale cold regions having strong energy frequently intrude into the near-wall region. The energy-containing events in the near-wall region are discussed based on the results of wavelet analysis.

A nonlinear critical layer in nonequilibrium gas

The method of matched asymptotic expansions is used to analyze the evolution of disturbances of a nonequilibrium compressible boundary layer on a flat plate in the region of nonlinear critical layer. A dispersion relation is obtained for low-amplitude subsonic disturbances. An equation is derived, which describes the evolution of disturbance in the nonlinear stage of its development. It is demonstrated that, similar to the case of equilibrium media, the increase in the disturbance amplitude in the given stage of development of turbulence exhibits an explosive pattern. The characteristic time of instability decreases with increasing degree of disequilibrium of the medium.

Improved turbulence generation techniques for hybrid RANS/LES calculations

Hybrid turbulence simulations that use a combination of Reynolds-averaged Navier–Stokes (RANS) equations and large-eddy simulation (LES) are becoming increasingly popular to increase predictive accuracy in complex flow situations without the cost of full large-eddy simulations. In a typical application, the RANS equations are solved in the equilibrium or near-equilibrium regions of the flow, while LES equations are used in regions where the flow is away from equilibrium. A difficulty in performing hybrid simulations stems from the mismatch between resolved turbulent scales between the RANS and LES regions: in the RANS region all turbulent scales are modeled, while in the LES region the energy containing scales are resolved. Interfacing these two regions requires the generation of turbulent eddies capable of supporting the Reynolds stresses in the LES field. Previous work by the authors proposed a combination of synthetic turbulence and a controlled forcing method that was capable of quickly generating these eddies. In this paper, we extend this earlier work by investigating the physical meaning of the model parameters to understand their effect on the flow development. We find that by matching the time-averaging window to the local integral time scale of the flow improved results can be obtained compared with previous work. We also determined the range of the controller parameters that give robust results. The method was applied to non-equilibrium boundary-layer flows far from the calibration case and was found to perform well. This technique gives best results if an outer-flow perturbation drives the flow; when the inner-layer dynamics are critical, less rapid establishment of the turbulence is achieved. Even in the worst result, however, the controller was able to establish a realistic flow within five boundary layer thicknesses of the end of the controlled region.

The stability of low-amplitude three-dimensional disturbances in a nonequilibrium compressible boundary layer

The stability of Tollmien-Schlichting waves propagating at an angle to the main flow in a nonequilibrium compressible supersonic boundary layer is investigated within the linear theory of hydrodynamic stability. The dependences of the critical Reynolds number on the degree of disequilibrium and on the Mach number of undisturbed flow are found at different angles of wave propagation. It is demonstrated that the critical Reynolds number in a nonequilibrium medium may decrease appreciably with increasing degree of disequilibrium, which results in the reduction of the characteristic length of the linear region of transition to turbulence.

Nonequilibrium thermal boundary layer in a capillary discharge with an ablative wall

A thermal nonequilibrium region near wall in a capillary discharge is considered. The proposed model suggests that nonequilibrium thermal boundary layer thickness strongly depends on the capillary wall ablation rate. It is shown that the applicability of the thermal equilibrium condition, widely employed in capillary models, is limited to a case with a large ablation rate.

Chemical Nonequilibrium Boundary Layer

The nonequilibrium boundary layer is considered as a binary mixture of atoms and molecules with finite dates of dissociation and recombination. To obtain accurate solutions to the partial differential equations for this type of flow without any necessary simplifying assumptions, an implicit finite-difference scheme is developed for solving these equations with a digital computer. Accurate solutions to the nonequilibrium boundary-layer equations have been obtained in a reasonable amount of computer time and are presented for a flat plate, cone, and hemisphere cylinder. The results show that the nonequilibrium boundary-layer temperature and composition can be considerably different from local equilibrium and frozen results. For a cone at 21,000 fps and 100,000 ft alt, the computations show that, at 60 ft from the tip, the flow has not reached equilibrium.

Effect of Surface Roughness on Unseparated Shock-Wave/Turbulent Boundary-Layer Interactions

The effect of surface roughness and step changes of surface roughness on an unseparated incipient shockwave/turbulent boundary-layer interaction has been studied using complementary experimental and theoretical investigations. Step changes in surface roughness lead to nonequilibrium boundary layers displaying different characteristics in the near-wall and far-wall regions. Both theory and experiment confirmed that the dominant effect of roughness, even in configurations featuring step changes of surface properties, is a change of boundary-layer displacement thickness and that the upstream influence of the interaction scales very well with the roughness modified incoming displacement thickness in all cases. The theory also identified small additional roughness effects, particularly for configurations featuring a smooth/rough wall transition ahead of the interaction

Consistent analysis of the boundary layer of a Saha plasma

The non-equilibrium boundary layer of a Saha plasma contactingmaterial walls or electrodes is analysed in the parameter regimeλD<<λCX<<λi, whereλD is the Debye length, λCX is the mean freepath for charge exchange collisions and λi is the ionizationlength. According to this scaling, the boundary layer is split up into theseparate model zones of: (i) a space-charge zone (scale λD); (ii) a Knudsen layer (scale λCX); (iii) a transitionlayer (scale λi). The collision dominated transition layer isanalysed in the mobility-diffusion approximation. The Knudsen layer,which is characterized by strong inhomogeneities and by strong deviationsfrom an equilibrium distribution, is treated kinetically. The model zonesare related to each other by a consistent matching procedure. Handyformulae for overall quantities are supplied for convenient applications.

Investigation of distribution of lithium atoms in the boundary layer of the flow of combustion products

The results are given of measurements of the profiles of temperature and concentration of lithium in the cross section of the boundary layer formed under conditions of flow of combustion products of propaneair flame past the surface of a flat metal plate. A model of chemically nonequilibrium laminar boundary layer is used to perform numerical simulation of various components of the combustion products. A comparison of the measured profiles of lithium concentration and profiles of hydrogen atoms obtained from the experimental data with the predicted results on a cooled and uncooled plate demonstrates that the suggested model of chemical kinetics describes the measurement results with good accuracy.

The effect of Reynolds number on boundary layer turbulence

Abstract A new facility for studying high Reynolds number incompressible turbulent boundary layer flows has been constructed. It consists of a moderately sized wind tunnel, completely enclosed by a pressure vessel, which can raise the ambient air pressure in and around the wind tunnel to 8 atmospheres. This results in a Reynolds number range of about 20:1, while maintaining incompressible flow. Results are presented for the zero pressure gradient flat plate boundary layer over a momentum thickness Reynolds number range 1500–15 000. Scaling issues for high Reynolds number non-equilibrium boundary layers are discussed, with data comparing the three-dimensional turbulent boundary layer flow over a swept bump at Reynolds numbers of 3800 and 8600. It is found that successful prediction of these types of flows must include length scales which do not scale on Reynolds number, but are inherent to the geometry of the flow.

Determination of the catalytic activity of materials by solving the equations of a nonequilibrium multicomponent boundary layer on a flat plate

A method is presented for determining the dependence of the probability of heterogeneous recombination γw from results of measurements of the heat flux Qw to the surface of a catalytic sensor exposed to a pulsed supersonic flow of gas dissociated by an incident shock wave propagating in a shock tube. It is shown that the accuracy of the determination of γw depends not only on the accuracy of the measurements in the experiment, but also on the results of mathematical modeling of the flow of the dissociated gas over the surface of the body. Results from an analysis of an experiment are presented.

The effect of an applied magnetic field on non-equilibrium plasma flow along a biased flat plate

An experimental study was conducted to clarify the control characteristics of a non-equilibrium plasma boundary layer flow over a biased and water-cooled flat plate in the tube induced by applying a magnetic field. Argon gas was partially ionized by a DC arc discharge at low pressure. The flat plate was set along the direction of flow in the tube, to which the positive and negative voltage could be alternatively biased. A mirror-type magnetic field was applied to the plasma boundary layer flow over the flat plate by two solenoids. The electron temperature was increased by applying the magnetic field, but the electron number density increased for the negative bias and decreased for the positive bias. Under these conditions, enhancement of the transport properties of electrons occurred. The heavy-particle temperature was increased and the thermal boundary layer thickness over the flat plate was decreased by applying the magnetic field, which resulted in an increase in the heat flux into the plate. The visualization study showed that the relative variation of the radiative temperature nearly corresponded to the electron temperature field in the applied magnetic field. This implies that the application of a combined electromagnetic field is an effective method by which to control the flow of a non-equilibrium plasma boundary layer over a flat plate.

Evaluation of the rate constants of dissociative and ternary recombination reactions of argon ions on the basis of the results of ballistic experiments

AbstractExperimental data on the change in the electron density in the wake of a ballistic object traveling at velocities V ∞=3.4–4.9 km/s in argon at pressures p ∞=30–100 Torr are processed and analyzed. A reaction scheme is proposed which takes into account the recombination of charged particles, processes of ionic conversion, and the excited states of the atom. The solution of the equations of a nonequilibrium boundary layer for flow in the wake is used to formulate the inverse problem of determining the rate constants for dissociative recombination Ar 2 + +e→Ar+Ar and ternary recombination Ar++e+Ar→Ar+Ar. The “nearest-neighbor” approximation is used to obtain theoretically an expression for the ternary recombination coefficient as a function of temperature and pressure. Numerous solutions of inverse problems and a comparison with experiments demonstrates the validity of the expression obtained for the ternary recombination coefficient. It is shown that this expression is valid for moderate pressures and complements the Pitaevskii result for low pressures and the Langevin result for high pressures.

Multiple scale modeling of turbulent nonequilibrium boundary layer flows

Multiple scale models are investigated in order to improve modeling of turbulent nonequilibrium boundary layers. The model is first calibrated on the standard equilibrium boundary layer and then applied to several nonequilibrium flows. Applications include the flow around an airfoil, the shock–boundary layer interaction, the transonic bump flow, and a three-dimensional bump. The multiple scale model predictions are compared with experimental results and with standard one-scale models. Several improvements are obtained that make the multiple scale model an interesting tool for tackling the prediction of nonequilibrium turbulent flows.

Formulas for the heat and diffusion fluxes to a catalytic surface in a chemically nonequilibrium multicomponent boundary layer

On the basis of an asymptotic expansion of the solution of the equations of a multicomponent chemically nonequilibrium boundary layer for large Schmidt numbers, formulas are obtained for the heat flux and the diffusion fluxes of the reaction products and chemical elements on a surface with arbitrary catalytic activity. The results are compared with well-known analytic and numerical solutions. The comparison reveals the high accuracy of the formulas proposed. The results of calculating the diffusional separation of the mixture due to the selectivity of the catalytic properties of the surface with respect to recombination of oxygen and nitrogen atoms are presented. Values of the reduction of the convective heat fluxes due to the catalytic properties of the surface are obtained over a wide range of conditions in the free stream.

Non-equilibrium boundary layer effects on the aerodynamic heating of hypersonic vehicles

The aerodynamic heating of a generic lifting hypersonic vehicle configuration is examined in that high altitude hypersonic flight regime where non-equilibrium dissociation/recombination in the boundary layer and finite surface catalysis effects are both important. Analytical treatment of these effects is given for highly-cooled surfaces in three important heating regions: the nose, the swept wing leading edge attachment line and the windward body centerline. Relationships for the relative non-equilibrium effects are developed for each region that enable both computer code-prediction validation and cost-effective parametric engineering studies.

Nonequilibrium boundary layer of potassium-seeded combustion products

Results are reported from numerical modeling and experimental study of a chemically reacting boundary layer, formed on a body inserted into a stream of potassium-seeded combustion products of gaseous hydrocarbon fuels. The numerical model developed in previous work is modified to incorporate current data on patassium chemical kinetics. The temperature and potassium atom number density profiles are measured across the boundary layer formed on a cylindrical specimen of Al 2O 3 dense ceramics by flow of combustion products of a propane-air mixture. The numerical results are compared with present experimental data as well as those available from the literature. The comparison is carried out for a broad range of experimental conditions including the postflame burned-gas region, and the boundary layers on a cylinder and on a flat plate. It provides verification of the proposed model, revision of the rate constants of some reactions of potassium-containing species, and supports the value of potassium superoxide dissociation energy of 247 kJ/mol.

Effects of nonequilibrium chemistry on the reference temperature method and Reynolds analogy

The effect of nonequilibrium air chemistry on skin friction and Stanton number and the applicability of the reference temperature method and Reynold's analogy for such conditions was investigated. The nonequilibrium laminar boundary layer equations were solved on a flat plate geometry for different Mach numbers, altitudes and wall to edge temperature ratios. A correlation of a modification to the reference temperature method is made for application in the presence of nonequilibrium dissociated air at hypersonic speeds. 17 refs.

Fluid boundary layer effects in atmospheric-pressure plasma diamond film deposition

Diamond films were deposited in an atmospheric-pressure radio frequency plasma reactor. Hydrogen and methane were injected coaxially into the plasma as a high-velocity jet which impinged on the molybdenum substrate. In some cases argon was added to the reactant jet to increase its momentum, thereby reducing the boundary layer thickness. In most cases argon addition substantially, improved diamond growth. A numerical model was developed, which calculated two-dimensional reactor temperature and velocity, distributions, and the chemical kinetics in the boundary layer. The calculations indicate that under the experimental conditions argon addition reduced the thickness of the hydrogen nonequilibrium boundary layer from 3.5 to 1.0 mm. In addition, the calculations suggest that monatomic carbon may be a key diamond growth species under thermal plasma conditions.