Mathematical modeling of turbulent combustion of hydrogen in a boundary layer

Turbulent flow in a boundary layer with injection of hydrogen through a permeable plate into an external air flow is modeled. To calculate turbulence characteristics the Lam-Bremhorst modification of the k-ε model is employed. Calculations are made both with and without account for the non-unity of the Lewis number. In determining the concentrations of the intermediate and end combustion products and the temperature the assumption of chemical equilibrium is made. The obtained distribution of turbulent pulsations allows the conclusion of flow laminarization under combustion conditions to be made. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 71, No. 1, pp. 86–91, January–February, 1998.     

Algebraic model of turbulent boundary layer on a convex curvilinear surface

A simple algebraic model of turbulent boundary layer on convex curvilinear surfaces is suggested that is based on the generalization of the two-layer one-parameter algebraic model for a flat plate [ 1 ]. The model is tested in a wide range of variation of the curvature parameter (0.01 ≤ δ₀/R _w ≤ 0.09, where δ₀ is the thickness of the boundary layer at the initial cross section of the curvilinear region andR _w is the curvature radius of the surface), the results of which are indicative of a good agreement between the experimental and calculated data on the integral characteristics of the boundary layer, namely, the friction coefficientC _f , the displacement thickness δ^* and momentum thickness δ^**, and the form parameterH = δ^*/δ^**. Based on the comparison between the calculated and experimental data on the distribution of tangential turbulent stresses, a conclusion is made that the model predicts a much lower effect of the curvature on the suppression of turbulence in the outer region of boundary layers at a mild curvature of the surface (δ ₀ /R _w = 0.01) than in experiments. However, this difference has a tendency to decrease as the surface curvature increases. An analysis of the calculated and experimental velocity profiles plotted in the variables of the wall law leads to a conclusion that the generalized Townsend wall law is partially realized on a curvilinear surface.     

The temperature of an adiabatic surface at a turbulent boundary layer

A calculation of the temperature decrease of an adiabatic surface at a supersonic turbulent boundary layer is conducted. It is shown that the temperature decrease is a consequence of the appearance of a vortex chain in the flow near the walls. Comparison of calculated data with experimental gives qualitative agreement.Notation V incident flow velocity - V_v vortex velocity - v local velocity - u induced velocity - T thermodynamic temperature - T_w, T recovery temperature and undisturbed flow temperature - L length of depression - h₀ depth of depression - h distance from vortex center to wall - b relative vortex velocity - l _v vortex spacing - r recovery coefficient - R₀ recovery coefficient on smooth surface - c_p gas heat capacity at constant pressure - n vortex passage frequency - Re Reynolds number - M Mach number - velocity potential - time - vortex intensity Translated from Ihzhenerno-Fizicheskii Zhurnal, Vol. 20, No. 5, pp. 903–908, May, 1971.     

Allowance for ionization in the analysis of a multicomponent turbulent boundary layer

Diffusion in a multicomponent turbulent boundary layer is investigated with allowance for ionization.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 20, No. 1, pp. 161–165, January, 1971.     

Parameters of a turbulent boundary layer at a permeable surface with pronounced roughness

On the basis of an empirical law of the drag at a rough porous plate, the Kutateladze-Leont'ev method of calculating the turbulent dynamic boundary layer at a smooth surface is extended to the case of flow around a surface in conditions of pronounced roughness.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 3, pp. 412–418, September, 1979.     

The structure of a turbulent boundary layer

According to the wave mechanism of turbulence, pulsation in the hydrodynamic parameters results from a superposition of perturbations arising at the wall and then spreading in the flow in the form of spherical wave packets. At the flow boundary, where the fluid velocity is characterized by a large gradient, the acoustic rays of these waves exhibit bending and reversal toward the wall, whereby the trajectories with various initial orientations are interweave and the wave packets are broken. The pulsation of parameters in the region of wave packet breakage results in the formation of a turbulent boundary layer. Upon the reflection of waves, the flow velocity oscillations immediately at the wall cease that corresponds to a laminar sublayer of the turbulent boundary layer.     

Interaction of a shock wave with a turbulent boundary layer on a heated surface

The interaction of a shock wave with a turbulent boundary layer has been studied. A stream has been diagnosed using non-invasive visualization (schlieren method). During the investigation the effect of surface heating on the length of boundary layer separation has been studied. It has been discovered that during surface heating the dependence of the length of separation on the temperature ratio is approximated using a linear law.     

Laminar superlayer in a turbulent boundary layer

We confirm the existence of a sharp boundary between the turbulent and non-turbulent fluid at the outer region of a zero-pressure-gradient turbulent boundary layer at a low Reynolds number. For the first time, using the Tomographic Particle Image Velocimetry technique, we determine mean statistical parameters of the boundary: its thickness and relative velocity jump.     

Conditional analysis in a turbulent boundary layer with strong density differences

Summary A study of the fine structure of wall turbulence in the presence of strong density variations through a conditional analysis of experimental data obtained in a wind tunnel is presented in this paper. Density variations within the boundary layer are produced by injection of air or helium into a mixture of these two components. The conditional analysis carried out in this study shows that the injection of helium into the boundary layer generates more violent ejections than in the case of an injection of air. This result is confirmed by the significant contribution of the ejections to the turbulent mass flux. The results obtained show that in the fully turbulent zone the ejections are associated with strong velocity fluctuations for the two injected gases. This is even more so for the fluctuations of density when an injection of helium is considered. At two locations of the flow (x/e = 8.3 and x/e = 33.3, where e = 3 mm is the slot width) we show that the contributions of a large excursion in the two quadrants of the u' – ρ' plane, corresponding to the two events of the fluid movement, the ejection and sweeping, are very intermittent owing to the fact that they are associated only to a very low number of measurement points. The ejections at y⁺ > 50 are more significant and much more energetic in the case of helium.     

Direct spatial resonance in the laminar boundary layer due to a rotating-disk

Numerical treatment of the linear stability equations is undertaken to investigate the occurrence of direct spatial resonance events in the boundary layer flow due to a rotating-disk. A spectral solution of the eigenvalue problem indicates that algebraic growth of the perturbations shows up, prior to the amplification of exponentially growing instability waves. This phenomenon takes place while the flow is still in the laminar state and it also tends to persist further even if the non-parallelism is taken into account. As a result, there exists the high possibility of this instability mechanism giving rise to nonlinearity and transition, long before the unboundedly growing time-amplified waves.     

Local and integral turbulent boundary layer characteristics on a convex surface in diffusor flow

A semiempirical method is proposed for computing the local and integral characteristics of the turbulent boundary layer on a convex surface under conditions of a positive longitudinal pressure gradient. By using the method proposed, graphical dependences are obtained that characterize the influence of curvature on the form-parameter, the thickness of the momentum loss, the thickness of the viscous sublayer, and the relative flow coefficient.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 58, No. 6, pp. 916–920, June, 1990.     

One approach to calculating a turbulent boundary layer on a surface with a compliant coating

A method is proposed for calculating a turbulent boundary layer on a surface with a viscoelastic coating. The method is based on the introduction of the van Driest damping function to account for the effect of the coating on the boundary layer.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 4, pp. 657–663, April, 1981.     

Critical displacement parameters of a turbulent boundary layer

The interferometer method was used for determining the critical displacement parameters of a turbulent diffusion boundary layer at a porous plate with injection of helium, nitrogen, carbon dioxide, krypton, xenon, and Freon-12. Velocity and concentration profiles were obtained for the critical flow modes.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 23, No. 1, pp. 94–103, July, 1972.     

Approximate solution of the internal problem for a turbulent boundary layer

The development of a turbulent boundary layer in an axisymmetric channel is analyzed with an an account of the mutual effects of the boundary layer and the core of the flow. The coordinates of the separation point, the coordinates of the junction, and other characteristics are found as functions of the Reynolds number and the channel geometry. A simple approximate method is proposed for calculating the boundary layer in a channel with an arbitrary curvilinear generatrix.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 18, No. 2, pp. 224–232, February, 1970.     

Heat transfer and friction in the turbulent boundary layer of a compressible gas at a permeable surface

Test data on heat transfer and friction are generalized for a wide range of the injection factor with the Mach number equal to 0.3, 2.05, 3.05, and 4. The test results agree with the theoretical analysis also given here.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 23, No. 5, pp. 785–791, November, 1972.     

Effect of boundary conditions on the heat transfer law for a turbulent boundary layer

The heat transfer at an impermeable plate has been experimentally investigated under various boundary conditions. The conservativeness of the heat transfer law St₀=f(Re _T ^** ) is demonstrated for a monotonic increase of temperature and heat flux along the surface.     

Wave properties and shear stress of a turbulent boundary layer

The wave theory of turbulence [1–3] is applied to the problem of a turbulent boundary layer near a planar wall. Preliminary results earlier published have been refined.     

Heat and mass transfer in a binary turbulent boundary layer with natural convection at vertical surface

An approximate solution is given for binary turbulent natural convection, with allowance for diffusive heat conduction. Analytic expressions are obtained for the boundary-layer outlet characteristics (coefficients of heat exchange and mass transfer). The solution is compared with experiments on heat and mass transfer during condensation of vapors from mixtures with various gases.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol.17, No. 2, pp. 226–232, August, 1969.     

Surface-friction coefficient in turbulent flow at a boundary layer

Using Thompson two-parameter velocity profiles equations defining the dependence of the surface-friction coefficient on the integral characteristics of the boundary layer are obtained.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol.46, No. 1, pp. 51–56, January, 1984.