Two-dimensional interaction between an incident shock and a turbulent boundary layer in the presence of an entropy layer

The results of an experimental and numerical investigation of flow and heat transfer in the region of the interaction between an incident oblique shock and turbulent boundary layers on sharp and blunt plates are presented for the Mach numbers M_∞ = 5 and 6 and the Reynolds numbers Re_∞L = 27×10⁶ and 14×10⁶. The plate bluntness and the incident shock position were varied. It is shown that the maximum Stanton number St _m in the shock incidence zone decreases with increase in the plate bluntness radius r to a certain value and then varies only slightly with further increase in r. In the case of a turbulent undisturbed boundary layer heat transfer is diminished with increase in r more slowly than in the case of a laminar undisturbed flow. In the presence of an incident shock the bluntness of the leading edge of the flat plate results in a greater decrease in the Stanton number than in the absence of the shock. With increase in the bluntness of the leading edge of the plate the separation zone first sharply lengthens and then decreases in size or remains constant.     

Interaction between an Inclined Shock and Boundary and High-Entropy Layers on a Flat Plate

The flow structure and heat exchange in the zone of interference between an inclined shock and the surface of a flat plate are investigated experimentally and theoretically as functions of many parameters, the interference being studied in both the presence and the absence of bluntness of the leading edge. The experiments were carried out at Mach numbers M = 6, 8, and 10 and the Reynolds numbers Re _L , calculated using the plate length L = 120 mm and the free-stream parameters, varied over the range from 0.24 ? 10⁶ to 1.31 ? 10⁶. The bluntness radius of the leading edge of the plate, the intensity of the impinging shock, and its location with respect to the leading edge were varied. The numerical simulation was carried out by solving the complete two-dimensional Navier-Stokes equations and averaged Reynolds equations using the q-ω turbulence model. The laminar boundary layer became turbulent inside the separation zone induced by the shock. It is shown that the plate bluntness significantly reduces the heat exchange intensity in the interference zone, this effect intensifying with increase in the Mach number.     

Leading edge bluntness effect on the flow in a model air-inlet

Flow in an idealized air-inlet with plane walls and a rectangular cross-section is experimentally investigated. The air-inlet is mounted on a plate, at a distance well removed from its leading edge. The experiments were conducted in a Ludwig tube at M_∞ = 5 and Re_∞L = 23×10⁶ and 13×10⁶. A panoramic (optical) technique of measuring the heat transfer coefficient is for the first time applied to study the internal flow in an air-inlet. The data on the effect of the bluntness of the leading edges of the plate and the air-inlet cowl on the heat transfer coefficient distribution and the flow structure within the air-inlet are obtained. It is shown that in an air-inlet with large channel constriction an even small bluntness of the plate or the cowl can lead to global changes in the flow structure.     

On the existence of a threshold value of the plate bluntness in the interference of an oblique shock with boundary and entropy layers

The heat transfer to sharp and slightly blunted flat plates in the zone of oblique shock incidence has been experimentally investigated. The experiments were performed at the Mach numbers M = 6, 8, and 10 and Reynolds numbers ranging from 0.2 × 10⁶ to 1.3 × 10⁶ corresponding to transitional (laminar-turbulent) flow in the shock-induced separation zone. Emphasis is placed on small values of the bluntness radius r. It is established that there exists a threshold value r _th of the radius that bounds the range of its influence on the heat transfer, namely, an increase in r to r _th leads to a sharp reduction in the maximum heat transfer coefficient in the interference zone, whereas a further increase (beyond r _th) has only a slight effect on the maximum heat transfer coefficient. The dependence of r _th on the main hypersonic flow parameters is analyzed. an explanation of the observable phenomena is given.     

Effect of Small Bluntness on Formation of Görtler Vortices in a Supersonic Compression Corner Flow

The influence of small cylindrical bluntness of the leading edge of a flat plate on formation of spatial structures in a nominally two-dimensional supersonic compression corner flow at the Mach number M∞ ≈ 8 and a laminar state of the undisturbed boundary layer is studied by the method of temperature-sensitive paints. Streamwise vortices are found in the region of reattachment of the separated flow in a wide range of Reynolds numbers (0.15 · 10⁶–2.55 · 10⁶) for various angles of flow deflection and plate lengths. It is demonstrated that the existence of these vortices induces spanwise oscillations of the heat transfer coefficient; the amplitude of these oscillations may reach 30%. The maximum deviations of the Stanton number reaching 80% are observed in the case with significant roughness of the leading edge of the flat plate. Both the maximum Stanton numbers in the reattachment region and the amplitude of spanwise oscillations of the Stanton number induced by streamwise vortices are found to decrease significantly in the case of small bluntness of the leading edge. Solutions of three-dimensional Navier–Stokes equations are obtained for some test conditions. The computed results are in good agreement with experimental data, which points to a significant stabilizing effect of small bluntness on the intensity of streamwise vortices.     

Laminar-turbulent flow over wedges mounted on sharp and blunt plates

The flow pattern and the heat transfer on sharp and blunt flat plates near a wedge in a Mach 6 stream are experimentally investigated for two Reynolds numbers corresponding to the laminar and transitional states of the undisturbed boundary layer ahead of the wedge. It is shown that, as in a two-dimensional flow, plate bluntness leads to the attenuation of the heat transfer in the boundary layer/shock wave interference zone. However, when a certain threshold value of the bluntness is exceeded, a further increase in the bluntness has almost no effect on the heat transfer. For the first time, an experiment conducted in an intermittent (blow-down) wind tunnel has been based on the comprehensive use of panoramic (global) techniques for measuring the heat transfer and pressure coefficients and a method for visualizing the surface friction employing the luminescence effect after UV irradiation.     

Experimental study of the laminar-turbulent transition on a blunt cone

Results of an experimental study of the laminar-turbulent transition in a hypersonic flow around cones with different bluntness radii at a zero angle of attack, free-stream Mach number M _∞ = 6, and unit Reynolds number in the interval Re _∞,1 = 5.79 · 10⁶–5.66 · 10⁷ m^?1 are presented. Flow regimes in which a reverse of the laminar-turbulent transition (decrease in the length of the laminar segment with increasing bluntness radius) are studied. Heat flux distributions over the model surface are obtained with the use of temperature-sensitive paints. Lines of the beginning of the transition in the boundary layer are analyzed by using heat flux fields. The critical Reynolds number Re _∞,R ≈ 1.3 · 10⁵ beginning from which the laminar-turbulent transition substantially depends on uncontrolled disturbances, such as the model tip roughness, is found. In supercritical regimes, the line of the transition beginning is shifted in most cases toward the model tip (reverse of the transition). The results obtained are compared with available experimental data.     

Turbulent heat transfer in a flat plate boundary layer disturbed by a cylinder

Augmentation of heat transfer from a flat plate using a turbulence promoter has been studied. A circular cylinder 8 mm in diameter was placed in the turbulent boundary layer detached from the flat plate. It was located parallel to the plate and perpendicular to the flow direction. Clearance, c, between the cylinder and the flat plate was varied in nine steps: c=0, 1, 2, 3, 4, 6, 11, 20 and 29.5 mm. Measurements were made of the local heat transfer coefficients, mean velocity profiles, turbulence intensity profiles, static pressure and skin friction. Experimental results showed that the heat transfer deterioration which occurs just downstream of the cylinder at c=0 mm can be removed by displacing the cylinder a small distance from the wall. The improvement in heat transfer is mainly due to the unsteadiness of the recirculating flow on the plate and the effect of intense turbulence arriving at the near wall region from the lower shear layer of the cylinder wake. Heat transfer augmentation is most effective when c=4 mm and becomes less effective when c is increased more than 6 mm. The enhancement disappears far downstream from the cylinder.     

An experimental investigation of the combined effects of surface curvature and streamwise pressure gradients both in laminar and turbulent flows

Flow and heat transfer characteristics over flat, concave and convex surfaces have been investigated in a low speed wind tunnel in the presence of adverse and favourable pressure gradients (k), for a range of –3.6 × 10^–6 ≤ k ≤ +3.6 × 10^–6. The laminar near zero pressure gradient flow, with an initial momentum thickness Reynolds number of 200, showed that concave wall boundary layer was thinner and heat transfer coefficients were almost 2 fold of flat plate values. Whereas for the same flow condition, thicker boundary layer and 35% less heat transfer coefficients of the convex wall were recorded with an earlier transition. Accelerating laminar flows caused also thinner boundary layers and an augmentation in heat transfer values by 28%, 35% and 16% for the flat, concave and convex walls at k = 3.6 × 10^–6. On the other hand decelerating laminar flows increased the boundary layer thickness and reduced Stanton numbers by 31%, 26% and 22% on the flat surface, concave and convex walls respectively. Turbulent flow measurements at k = 0, with an initial momentum thickness Reynolds number of 1100, resulted in 30% higher and 25% lower Stanton numbers on concave and convex walls, comparing to flat plate values. Moreover the accelerating turbulent flow of k = 0.6 × 10^–6 brought about 29%, 30% and 24% higher Stanton numbers for the flat, concave and convex walls and the decelerating turbulent flow of k = –0.6 × 10^–6 caused St to decrease up to 27%, 25% and 29% for the same surfaces respectively comparing to zero pressure gradient values. An empirical equation was also developed and successfully applied, for the estimation of Stanton number under the influence of pressure gradients, with an accuracy of better than 4%.     

Interference between a blunt edge shock layer and an impinging inclined shock at low Reynolds numbers

The interference between the shock layer on a cylinder modeling the leading edge of an air intake and an impinging plane inclined shock is investigated experimentally and numerically for a Reynolds number Re₀=32. The low-pressure wind tunnel experiments made it possible to visualize the flow and determine the local heat transfer in the presence of interference. The corresponding flow regimes were calculated numerically within the framework of the system of Navier-Stokes equations by the through-calculation method. The principal properties of the distribution of the flow characteristics for a low value of the Reynolds number were obtained for various types of interference and the differences with respect to the previously investigated interference regimes for high Reynolds numbers were examined.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 166–171, January–February, 1993.     

Hypersonic interference heating in the vicinity of surface protuberances

The understanding of the behaviour of the flow around surface protuberances in hypersonic vehicles is developed and an engineering approach to predict the location and magnitude of the highest heat transfer rates in their vicinity is presented. To this end, an experimental investigation was performed in a hypersonic facility at freestream Mach numbers of 8.2 and 12.3 and Reynolds numbers ranging from Re _∞/m = 3.35 × 10⁶ to Re _∞/m = 9.35 × 10⁶. The effects of protuberance geometry, boundary layer state, freestream Reynolds number and freestream Mach numbers were assessed based on thin-film heat transfer measurements. Further understanding of the flowfield was obtained through oil-dot visualizations and high-speed schlieren videos. The local interference interaction was shown to be strongly 3-D and to be dominated by the incipient separation angle induced by the protuberance. In interactions in which the incoming boundary layer remains unseparated upstream of the protuberance, the highest heating occurs adjacent to the device. In interactions in which the incoming boundary layer is fully separated ahead of the protuberance, the highest heating generally occurs on the surface just upstream of it except for low-deflection protuberances under low Reynolds freestream flow conditions in which case the heat flux to the side is greater.     

Prediction of hypersonic boundary layer transition on sharp wedge flow considering variable specific heat

When the air temperature reaches 600 K or higher, vibration is excited. The specific heat is not a constant but a function of temperature. Under this condition, the transition position of hypersonic sharp wedge boundary layer is predicted by using the improved eN method considering variable specific heat. The transition positions with different Mach numbers of oncoming flow, half wedge angles, and wall conditions are computed condition, the nearer to the Mach number The results show that for the same oncoming flow condition and wall transition positions of hypersonic sharp wedge boundary layer move much leading edge than those of the flat plate. The greater the oncoming flow the closer the transition position to the leading edge.     

Heating characteristics of blunt swept fin-induced shock wave turbulent boundary layer interaction

An experimental study was conducted on shock wave turbulent boundary layer interactions caused by a blunt swept fin-plate configuration at Mach numbers of 5.0, 7.8, 9.9 for a Reynolds number range of (1.0∼4.7)×10⁷/m. Detailed heat transfer and pressure distributions were measured at fin deflection angles of up to 30° for a sweepback angle of 67.6°. Surface oil flow patterns and liquid crystal thermograms as well as schlieren pictures of fin shock shape were taken. The study shows that the flow was separated at deflection of 10° and secondary separation were detected at deflection of ϑ≥20°. The heat transfer and pressure distributions on flat plate showed an extensive plateau region followed by a distinct dip and local peak close to the fin foot. Measurements of the plateau pressure and heat transfer were in good agreement with existing prediction methods, but pressure and heating peak measurements atM≥6 were significantly lower than predicted by the simple prediction techniques at lower Mach numbers. The project supported by China Academy of Launch Vehicle Technology     

The effect of suction or injection on the boundary layer flows induced by continuous surfaces stretched with prescribed skin friction

The boundary layer flow and heat transfer on a stretched surface moving with prescribed skin friction is studied for permeable surface. Three major cases are studied for isothermal surface (n=0) stretched corresponding to different dimensional skin friction boundary conditions namely; skin friction at the surface scales as (x ^?1/2) at m=0, constant skin friction at m=1/3 and skin friction scales as (x) at m=1. The constants m and n are the indices of the power law velocity and temperature exponent respectively. Similarity solutions are obtained for the boundary layer equations subject to power law temperature and velocity variation. The effect of various governing parameters, such as Prandtl number Pr, suction/injection parameter f _w , m and n are studied. The results show that for isothermal surface increasing m enhances the dimensionless heat transfer coefficient for fixed f _w at the suction case and the reverse is true at the injection case. Furthermore, for fixed m, as f _w increases the dimensionless heat transfer coefficient increases. Large enhancements are observed in the heat transfer coefficient as the temperature boundary condition along the surface changes from uniform to linear where the dimensional skin friction is of order (x) at m=1. This enhancement decreases as the suction increases.     

Mixed convection in the presence of horizontal impermeable surfaces in saturated porous media with variable permeability

Boundary layer approximation is applied for mixed convection about a horizontal flat plate in a saturated porous medium with aiding external flows. Similarity solutions are obtained, incorporating the variation of permeabilty, for 1) horizontal flat plate at zero angle of attack with constant heat flux; 2) stagnation point flows about horizontal flat plates with wall temperature varying asT _w ∝x ². The temperature and velocity profiles for different values of Ra/(RePr)^3/2 and the parameters governing the flow are obtained. The heat transfer rate is calculated and its implications in a geothermal application is discussed. Further, the criteria for pure mixed convection about horizontal flat plates in a porous media are established.     

Thermal protection characteristics of a vertical rectangular cell filled with PCM/air layer

The present paper presents a numerical analysis concerning thermal protection characteristics of a vertical rectangular composite cell filled with a solid-liquid phase change material (PCM) and air layer. Inside the composite cell the PCM layer is separated from air layer by a solid partition of negligible thickness. The buoyancy-induced flows developed in both the air-filled layer and the molten PCM zone inside the PCM layer were modeled as two-dimensional laminar Newtonian fluid flow adhering to the Boussinesq approximation. Meanwhile, two-dimensional conduction heat transfer was accounted for the unmelted solid PCM region. Delineation is made via a parametric simulation of the effects of the pertinent parameters:Ste (Stefan number),Sc (subcooling factor),Ra (Rayleigh number), aspect ratio of composite cell,A, and relative thickness ratioA _p /A _a , on the transient thermal protection performance of the composite cell. Results demonstrate that by means of the latent-heat absorption inside the PCM layer, heat penetration across the composite cell can be greatly retarded over an effective duration until a critical instant until the melting front of PCM reaches the partition wall. Such an effective thermal protection duration is found to be a strong function ofRa, Ste, A _p /A _a , andA. In addition, the results of the transient heat transfer rate penetrating through the composite cell are examined as a function of the pertinent parameters of the problem.     

Experimental study of the effect of a passive porous coating on disturbances in a hypersonic boundary layer 2. Effect of the porous coating location

The effect of the location of a passive porous coating on natural disturbances in a hypersonic boundary layer is studied experimentally. The experiments are performed in the flow around a sharp cone aligned at a zero angle of attack with the free-stream Mach number M_∞ = 5.8, stagnation temperature T ₀ = 370 ± 5 K, and unit Reynolds numbers Re_1∞ = 2.6 · 10⁶, 4.6 · 10⁶, 6.6 · 10⁶, and 10⁷ m^?1. The wave characteristics of the boundary layer are calculated with the use of the linear stability theory for flow parameters corresponding to experimental values. A comparison of experimental and predicted results shows that the presence of a porous coating in the region where the second mode is unstable leads to reduction of its amplitude at the measurement point, whereas the presence of a porous coating in the region of second mode stability leads to enhancement of the amplitude.     

The effect of variable properties on laminar boundary layer flow

The influence of temperature dependent fluid properties on laminar boundary layer flows is examined for wedge flows (Falkner-Skan). An asymptotic expansion for small heat transfer rates is applied under the boundary conditionsT _w= const andq _w=const. Linear deviations from the zero order solution (constant properties) can be given in a form known as the property ratio method. As a consequence this method is no longer an empirical one.     

Mixed convection boundary layer flow over a horizontal circular cylinder with Newtonian heating

The steady mixed convection boundary layer flow over a horizontal circular cylinder, generated by Newtonian heating in which the heat transfer from the surface is proportional to the local surface temperature, is considered in this study. The governing boundary layer equations are first transformed into a system of non-dimensional equations via the non-dimensional variables, and then into non-similar equations before they are solved numerically using a numerical scheme known as the Keller-box method. Numerical solutions are obtained for the skin friction coefficient Re ^1/2 C _f and the local wall temperature θ _w (x) as well as the velocity and temperature profiles with two parameters, namely the mixed convection parameter λ and the Prandtl number Pr.     

Effect of flow diverters on free convection heat transfer from a pair of vertical arrays of isothermal cylinders

Laminar free convection heat transfer from two vertical arrays of five isothermal cylinders separated by flow diverters is studied experimentally using a Mach-Zehnder interferometer. The width of flow diverters is kept constant to two-cylinder diameters and the cylinders vertical center-to-center spacing is equal to three-cylinder diameter. Effect of the ratio of the horizontal spacing between two cylinder arrays to their diameter (S_h/D) on heat transfer from the cylinders is investigated for various Rayleigh numbers. The experiments are performed for S_h/D = 2-4, and the Rayleigh number based on the cylinder diameter ranging from 10³ to 3 × 10³. It is observed that for small S_h/D ratios, the flow diverters have a negative effect on the total rate of heat transfer from the arrays; while by increasing the horizontal center to center spacing, they tend to enhance the overall cooling rate of the array. Moreover, increasing Ra and S_h/D generally results in a higher average Nusselt number for each cylinder in the array.