Heat transfer through a porous plate at cooling gas supply in an asymptotic suction regime

The analytical solution is carried out for the one- and two-dimensional problem of the thermal state of a porous plate surrounded by the flow of high-temperature and homogenous cooling gases in a permeable cooling system. Cooling gas flow in a laminar regime of asymptotic suction is considered, which provides effective heat shielding with minimum dependence on the parameters of the permeable wall. Heat exchange from the high-temperature gas is accepted for both laminar and turbulent boundary layers.     

Nonlinear instability of developing streamwise vortices with applications to boundary layer heat transfer intensification through an extended Reynolds analogy

The intent of the present contribution is to explain theoretically the experimentally measured surface heat transfer rates on a slightly concave surface with a thin boundary layer in an otherwise laminar flow. As the flow develops downstream, the measured heat transfer rate deviates from the local laminar value and eventually exceeds the local turbulent value in a non-trivial manner even in the absence of turbulence. While the theory for steady strong nonlinear development of streamwise vortices can bridge the heat transfer from laminar to the local turbulent value, further intensification is attributable to the transport effects of instability of the basic steady streamwise vortex system. The problem of heat transport by steady and fluctuating nonlinear secondary instability is formulated. An extended Reynolds analogy for Prandtl number unity, Pr=1, is developed, showing the similarity between streamwise velocity and the temperature. The role played by the fluctuation-induced heat flux is similar to momentum flux by the Reynolds shear stress. Inferences from the momentum problem indicate that the intensified heat flux developing well beyond the local turbulent value is attributed to the transport effects of the nonlinear secondary instability, which leads to the formation of 'coherent structures' of the flow. The basic underlying pinions of the non-linear hydrodynamic stability problem are the analyses of J. T. Stuart, which uncovered physical mechanisms of nonlinearities that are crucial to the present developing boundary layers supporting streamwise vortices and their efficient scalar transporting mechanisms.     

Modern Approaches for Calculating Flow Parameters during a Laminar–Turbulent Transition in a Boundary Layer

We analyze modern methods for calculating heat and hydrodynamic flow parameters in a boundary layer during the laminar–turbulent transition. The main approaches for describing the phenomenon of laminar–turbulent transition are examined. Each approach is analyzed. The manner in which different factors influence the laminar–turbulent transition is studied. An engineering model of the laminar–turbulent transition in a high-velocity flow is presented.     

Numerical study of light scattering by a boundary-layer flow

Temperature inhomogeneities in free, isotropic turbulence have the effect of scattering light in near-forward angles. We investigate numerically modifications of free turbulence by a rigid wall and its effect on the propagation of light through turbulence. The wall is a 5 cm optical window placed at the leading edge of an instrument towed with speeds of 0.1 and 1 m/s in free turbulence. The turbulent flow field presents inhomogeneities of an embedded passive scalar (Pr = 7, temperature in water), which are modified by the boundary layer developing on the window. We find that the developing laminar boundary layer has a negligible effect on light scattering for the investigated geometry when considered in terms of the volume-scattering function (differential cross section). This indicates that the boundary layer is not an obstacle for optical measurements of turbulence.     

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.     

Temperature stratification under suction of the boundary layer from a supersonic flow

A carried out numerical simulation showed that a considerable difference can be achieved between the temperatures of a gas in the boundary layer and a suctioned gas under the gas suction from a turbulent boundary layer in a supersonic flow on a permeable surface. The effect of the Prandtl and Mach numbers of the incident flux on the temperature stratification, which depends on the gas suction intensity, is studied. The stratification is the most pronounced for low-Prandtl-number gases. It was established that, due to laminarization of the boundary layer under an intense gas suction, in the region of the impermeable plate following the permeable wall, the wall temperature drops abruptly.     

The recovery factor in a supersonic flow of gas with a low Prandtl number

A three-parameter differential model of turbulence supplemented with a transport equation for turbulent heat flux is used to perform calculations of the boundary layer on a heat-insulated wall in a supersonic gas flow with a value of Prandtl number Pr ≤ 0.7. The dependences on the values of Prandtl, Reynolds, and Mach numbers and of intensity of injection are obtained for the recovery factor.     

A criterion of similarity and transition to turbulence for electric arc flows

A method is suggested for determining the similarity criterion and the criterion of transition of an electric arc flow in a plasmatron channel from a laminar regime to a turbulent one (equivalent Reynolds number) that does not require using any reference temperature. Application of this method to the available experimental data on the transition to turbulence demonstrates its correctness and efficiency. The critical value of the proposed similarity criterion corresponding to the boundary of the transition from a laminar regime to a turbulent one has been revealed. A marginal curve separating the regions of the laminar and turbulent regimes of the plasma flow has been plotted in the space of the operating plasmatron parameters. A phenomenon of a double change of the electric arc flow regime with electric current rise upon constant plasma-forming gas flow rate has been discovered.     

The temperature recovery factor in a boundary layer on a permeable plate

A numerical investigation of the boundary layer on a permeable wall in a supersonic gas flow is performed using a differential turbulence model. Temperature recovery factors are obtained for a series of Prandtl numbers and gas suction or injection in a wide range of the permeability factor from critical injection to asymptotic suction. With the example of air injection into a supersonic air flow, two methods for determining the temperature of a heat-insulated permeable wall are considered. The first is to solve the problem with a boundary condition of zero heat flux to the wall. The second is similar to an experimental method when the temperature of the gas injected at a section along the plate length becomes equal to the wall temperature. The heat-insulated wall temperatures and temperature recovery factors obtained by these two methods for injection below the critical one are close to each other. In case of critical injection, these two methods yield different results.     

Transport processes in a reacting boundary layer

An approximate calculation has been made for the boundary layer of a compressible gas in a laminar flow over a semi-infinite porous plate reacting with an injected substance in a homogeneous reaction at an infinite rate. The possibility of applying the solutions obtained to a turbulent boundary layer is also examined.     

Compressible magnetohydrodynamic boundary layer swirling nozzle and diffuser flows with a magnetic field

The flow, heat and mass transfer problem for boundary layer swirling flow of a laminar steady compressible electrically conducting gas with variable properties through a conical nozzle and a diffuser with an applied magnetic field has been studied. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme after they have been transformed into dimensionless form using the modified Lees transformation. The results indicate that the skin friction and heat transfer strongly depend on the magnetic field, mass transfer and variation of the density-viscosity product across the boundary layer. However, the effect of the variation of the density-viscosity product is more pronounced in the case of a nozzle than in the case of a diffuser. It has been found that large swirl is required to produce strong effect on the skin friction and heat transfer. Separationless flow along the entire length of the diffuser can be obtained by applying appropriate amount of suction. The results are found to be in good agreement with those of the local nonsimilarity method, but they differ quite significantly from those of the local similarity method.     

Direct resonance analysis and modeling for a turbulent boundary layer over a corrugated surface

Summary Effects of surface corrugation on turbulent flow in a boundary layer are studied using a model based on the direct resonance theory. The induced mean flow due to weakly nonlinear waves, superimposed on the mean and fluctuating components of turbulence, is determined. The mean turbulent flow is affected by the surface corrugation throughout the boundary layer. The corrugated surface generates higher harmonics and affects the streamwise vortices generated by the waves superimposed on turbulence whose mean flow includes secondary induced mean flow components due to the corrugation.     

A multidomain boundary element method for two equation turbulence models

The paper deals with the multidomain Boundary Element Method (BEM) for modelling 2D complex turbulent flow using low Reynolds two equation turbulence models. While the BEM is widely accepted for laminar flow this is the first case, where this method is applied for a complex flow problems using k–ε turbulence model. The integral boundary domain equations are discretised using mixed boundary elements and a multidomain method also known as subdomain technique. The resulting system matrix is overdetermined, sparse, block banded and solved using fast iterative linear least squares solver. The simulation of turbulent flow over a backward step is in excellent agreement with the finite volume method using the same turbulent model.     

Theory and experiment in the problem of the interaction of high-velocity gas flows with materials

An analysis is made of the intensive thermal action of a gas flow on a body in the flow. An examination is made of features of failure of such bodies and the difference between the melting and vaporization points of glass-plastics in a turbulent boundary layer compared to a laminar boundary layer.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 53, No. 5, pp. 765–774, November, 1987.     

Effect of the mode of flow in the initial boundary layer on the turbulence attenuation effect in a jet exposed to acoustic irradiation

Based on an analysis of experimental data on high-frequency acoustic excitation of turbulent jets, we investigate the effect of the mode of flow in the boundary layer of the outlet section of the nozzle on realization of the turbulence attenuation effect. It is claimed that high-frequency acoustic excitation of jets leads to a decrease in turbulent fluctuations on the axis of the initial stretch of the jet and to reduction of noise in both initially laminar and initially turbulent boundary layers at the nozzle outlet. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 71, No. 1, pp. 81–85, January–February, 1998.     

Thermal boundary layers over a wedge with uniform suction or injection in forced flow

Summary The behavior of incompressible laminar boundary layers in forced flow over a wedge with uniform suction or injection was theoretically investigated. The boundary layer equations along a wedge are transformed into non-similar partial differential ones, and the ordinary differential equations were obtained by means of the difference-differential method. The solutions of the resulting equations are expressed in a form of integral equations which are in turn solved by iterative numerical quadratures. The numerical results are given for the velocity distribution, temperature distribution and the coefficient of skin friction and heat transfer for various values of suction/injection parameter.     

The thermal state of a porous wall under conditions of transpiration cooling

Results of numerical experiment are used for analysis of fields of temperature in a laminar boundary layer, in a porous wall, and in a cooling gas delivery chamber, as well as for analysis of heat transfer and of distribution of the temperature difference between the cooling gas and the porous wall frame and cooling efficiency. It is demonstrated that heat transfer between a porous wall of finite thickness and a high-temperature gas flow differs significantly from heat transfer with preassignment of the same intensity of injection and of the homogeneous thermal boundary condition directly on the surface subjected to flow. One of the reasons for this is the formation of wall temperature variable along the boundary layer.     

An Algebraic Model of Turbulence for Flows with a Maximum of Tangential Stress Inside the Boundary Layer

The two-layer Klauser scheme of turbulent boundary layer is used to construct a new algebraic model of turbulence for a fairly wide class of flows characterized by the presence of a maximum of tangential stress inside the layer. A distinguishing feature of the model is the method of determination of the velocity scale of turbulence in the outer region of the boundary layer, based on the use of the Bradshow–Ferriss–Atwell (BFA) equation for turbulent stresses. This provides the possibility of taking into account the effect on the scale of both the external factors (longitudinal pressure gradient, injection, suction, transverse curvature of the surface) and the basic mechanisms of transport of turbulent tangential stresses (convection, diffusion, generation, and dissipation). In the final analysis, this defines the rather wide capabilities of the model confirmed by the results of its testing on the basis of experimental data for boundary layers with a positive differential pressure, injection, and transverse curvature of the surface.     

Turbulent biomagnetic fluid flow in a rectangular channel under the action of a localized magnetic field

The fundamental problem of the turbulent flow of a biomagnetic fluid (blood) between two parallel plates under the action of a localized magnetic field is studied. The blood is considered to be an electrically conducting, incompressible and Newtonian fluid and its flow is steady, two-dimensional and turbulent. The turbulent flow is described by the Reynolds averaged Navier–Stokes (RANS) equations. For the numerical solution of the problem under consideration, which is described by a coupled and non-linear system of PDEs, with appropriate boundary conditions, the stream function–vorticity formulation is used. For the eddy-kinematic viscosity, the low Reynolds number k–ε turbulence model is adopted. The solution of the problem, for different values of the dimensionless parameter entering into it, is obtained by developing and applying an efficient numerical technique based on finite differences scheme. Results concerning the velocity and temperature field, skin friction and rate of heat transfer, indicate that the presence of the localized magnetic field, appreciable influences the turbulent flow field. A comparison is also made with the corresponding laminar flow, indicating that the influence of the magnetic field decreases in the presence of turbulence.     

Free convection in the laminar boundary layer flow of a thermomicropolar fluid past a vertical flat plate with suction/injection

Summary The effect of suction/injection in the laminar free convection flow of a thermomicropolar fluid past a nonuniformly heated vertical flat plate has been considered. The conditions under which similarity exists have been examined. The resulting system of non-linear ordinary differential equations has been solved numerically after transforming the infinite domain of boundary layer coordinate into a finite domain. The effects of variation of the boundary condition parameter and suction/injection parameter on the velocity, microrotation and temperature fields and the heat transfer coefficient have been studied graphically. The skin-friction parameter and the gradient of microrotation on the wall have been tabulated. It is found that there is significant increase in velocity, skin-friction and the heat transfer coefficient with the decreasing concentration of microelements.With 4 Figures