Supersonic flow past a slender cone with asymmetric nosetip

Supersonic flow of an inviscid gas that does not conduct heat past a slender cone with asymmetric nosetip has been investigated at zero and nonzero angle of attack. The flow is calculated by the Babenko-Voskresenskii numerical method. It is shown that the asymmetry of the nosetip has a strong influence on the distribution of the parameters of the gas over the surface of the slender cone even at a large distance from the nosetip. The results of the calculations are compared with experimental data.     

Drag of a slender cone in a supersonic rarefied gas flow

On the basis of an analysis of experimental data, obtained by the authors or taken from the literature, on the drag of a slender cone with half-angle =2.5–20° an average correlation curve is proposed for the range of flow regimes extending from continuum to free molecular flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 187–189, January–February, 1987.     

A sharp slender cone in an incompressible flow

The range of applicability of the asymptotic solution of the problem of incompressible flow past a slender cone is studied. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 197–200, July–August, 1998.     

Supersonic viscous perfect-gas flow past a slender sharp elliptic cone

The supersonic M_∞ = 5 flow past slender elliptic cones with the semi-vertex angle in the plane of the major semi-axis ? _c = 4° and an isothermal surface is investigated under the assumption of the flow symmetry. Calculations on the basis of the time-dependent three-dimensional Navier-Stokes and Reynolds equations are carried out on the Reynolds number and angle of attack ranges 10⁴ ≤ Re ≤ 108 and 0 ≤ α ≤ 15° for cones with ellipticity coefficients 1/32 ≤ δ= b/a ≤ 1. The effect of the relevant parameters of the problem on the flowfield structure and the aerodynamic characteristics of the cones is demonstrated.     

水下亚声速细长锥型射弹超空泡流的数值计算方法

采用理想可压缩流体无旋定常流动及超空泡尾部Riabushinsky闭合方式假定,基于水动力学势流理论及细长体理论,建立了描述水下亚声速条件下细长锥型射弹超空泡流动的积分微分方程。发展了求解该方程的数值离散方法,提出多种超空泡外形初始解,分析了它们对超空泡形态计算结果的影响,优化了计算过程,简化了初始迭代条件。分析了流体压缩性对超空泡流动参数的影响,当马赫数大于0.3时,超空泡外形、射弹表面压力系数及射弹运动压差阻力系数均明显增大。计算得到的超空泡流动参数与相关文献的理论和实验结果吻合良好。     

Laminar natural convection over a slender vertical frustum of a cone

The problem of laminar, natural convection flow over a slender frustum of a cone is treated in this paper. The governing differential equations are solved by a combination of quasi-linearization and finite-difference methods. Numerical solutions are obtained for Pr=0.7 and for a range of values of the transverse curvature parameter. It is shown that the effect of transverse curvature is of great significance in such flows.

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Laminare natürliche Konvektion an einem dünnen, senkrechten Kegelstumpf

Zusammenfassung In diesem Bericht ist das Problem der laminaren natürlichen Konvektionsströmung an einem dünnen Kegelstumpf behandelt. Die maßgebliche Differentialgleichung ist durch eine Verbindung von Quasilinearisation und Differenzenverfahren gelöst. Eine numerische Lösung für Pr=0.7 wird für verschiedene Werte eines Krümmungsparameters angegeben. Es ist gezeigt, daß in solchen Strömungen dieser Krümmungsparameter eine große Bedeutung besitzt.

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Nomenclature f dependent variable, defined in Eq. (7) - g dependent variable, defined in Eq. (7) - g_e gravitational acceleration - h heat transfer coefficient, or -grid - k heat conductivity, or -grid - L characteristic length - Nu Nusselt number - Pr Prandtl number - r radial distance from the axis of the cone - R transverse curvature effect ratio, defined in Eq. (23) - Re Reynold number - T temperature - u, v velocity components in the x- and y-directions, respectively - x, y rectangular coordinates Greek letters dimensionless temperature, definedinEq. (4) - bulk modulus - cone angle - dynamic viscosity - stream function - , independent variable, defined in (7) - transverse curvature parameter     

An experimental investigation of hypervelocity flow in a conical nozzle

The flow in a conical nozzle is examined experimentally for a range of hypervelocity conditions in a free-piston shock tunnel. The pitot pressure levels compare reasonably well with an inviscid numerical prediction which includes a correction for the growth of the nozzle wall boundary layer. The size of the nozzle wall boundary layer seems to be well predicted by semi-empirical expressions developed for perfect gas flows, as do data from other free-piston shock tunnels.     

Spatial direct numerical simulation of high-speed boundary-layer flows Part II: Transition on a cone in Mach 8 flow

The laminar breakdown of the boundary-layer flow of an axisymmetric sharp cone in a Mach 8 flow is simulated by a synergistic approach that combines the parabolized stability equation (PSE) method and spatial direct numerical simulation (DNS). The transitional state is triggered by a symmetric pair of oblique second-mode disturbances whose nonlinear interactions generate strong streamwise vorticity, which leads in turn to severe spanwise variations in the flow and eventual laminar breakdown. The PSE method is used to compute the weakly and moderately nonlinear initial stages of the transition process and, thereby, to derive a harmonically rich inflow condition for the DNS. The strongly nonlinear and laminar-breakdown stages of transition are then computed by well-resolved DNS, with a highly accurate algorithm that exploits spectral collocation and high-order compact-difference methods. Evolution of the flow is presented in terms of modal energies, mean quantities (e.g., skin friction), Reynolds stresses, turbulent kinetic energy, and flow visualization. The numerical test case is an approximate computational analog of one of the few stability experiments performed for hypersonic boundary-layer flows. Comparisons and contrasts are drawn between the experimental and the computational results. Rope-like waves similar to those observed in schlieren images of high-speed transitional flows are also observed in the numerical experiment and are shown to be visual manifestations of second-mode instability waves.This research was supported under NASA Contracts NAS1-19831 and NAS1-20059 for the first and second authors, respectively.     

Supersonic flow over a slender wing with subsonic edges

The method of integral equations is generalized to calculate steady flow past wings with an arbitrary shape in plan with subsonic leading and trailing edges. The determination of the velocity potential in the leading part of the wing, where there is no influence of the vortex sheet, is reduced to the solution of a two-dimensional integral equation of the second kind. The trailing part, which is subject to the influence of the vortex sheet, is divided into a number of subregions, in which the calculation of the acceleration potential reduces to the solution of one-dimensional equations of the type of Fredholm equations of the second kind and to quadrature. The unique solvability of the obtained integral equations is investigated; it is shown that they can be solved by successive approximation. As an example, the solution to the problem of flow past a flat delta-shaped wing is found and compared with the exact solution to the problem found by the method of conic flows [4, 6].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 119–127, September–October, 1981.I thank G. Yu. Stepanov for discussing the paper.     

Laminar natural convection over a slender vertical frustrum of a cone with constant wall heat flux

The problem of laminar natural convection flow over a slender frustrum of a cone with constant wall heat flux is treated in this paper. The governing differential equations are solved by a combination of quasilinearization and finite-difference methods. Numerical solutions are obtained for Prandtl numbers from 0.1 to 100 for a range of values of transverse curvature parameter. It is found that the effect of transverse curvature is of great significance in such flows.

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Laminare natürliche Konvektion über einem dünnen, senkrechten Kegelstumpf mit konstantem Wand wär mestrom

Zusammenfassung In dieser Arbeit wird das Problem der laminaren, natürlichen Konvektionsströmung öber einem dünnen Kegelstumpf mit konstantem Wandwärmestrom behandelt. Die maßgeblichen Differentialgleichungen werden mit Hilfe einer Kombination von Quasilinearisierung und Differenzenverfahren gelöst. Numerische Lösungen werden für die Prandtl ' sehen Zahlen zwischen 0. l und 100 innerhalb eines Bereiches von Querkrüm mungswerten erhalten. Es wird gezeigt, daß der Einfluß der Querkrümmung in solchen Strömungen von großer Bedeutung ist.

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Nomenclature A,B,C constants in the transformation, defined in Eq.(14) - f dependent variable, defined in Eq. (7) - g dependent variable, defined in Eq. (7) - g_e gravitational acceleration - k heat conductivity - k_n -grid - L characteristic length - Nu Nusselt number - Pr Prandtl number - q_w wall heat flux - r radial distance from the axis of the cone - R_TVC transverse curvature ratio, defined in Eq.(28) - Re Reynolds number - T temperature - u,v velocity components in the x- and y-directions, respectively - x,y rectangular coordinates Greek Letters dimensionless temperature, defined in Eq.(4) - bulk modulus - cone angle - dynamic viscosity - stream function - , transformed independent variables, defined in Eq. (7) - transverse curvature parameter     

Pressure-sensitive paint on a truncated cone in hypersonic flow at incidences

The flow over a truncated cone is a classical and fundamental problem for aerodynamic research due to its three-dimensional and complicated characteristics. The flow is made more complex when examining high angles of incidence. Recently these types of flows have drawn more attention for the purposes of drag reduction in supersonic/hypersonic flows. In the present study the flow over a truncated cone at various incidences was experimentally investigated in a Mach 5 flow with a unit Reynolds number of 13.5 × 10⁶ m⁻¹. The cone semi-apex angle is 15° and the truncation ratio (truncated length/cone length) is 0.5. The incidence of the model varied from −12° to 12° with 3° intervals relative to the freestream direction. The external flow around the truncated cone was visualised by colour Schlieren photography, while the surface flow pattern was revealed using the oil flow method. The surface pressure distribution was measured using the anodized aluminium pressure-sensitive paint (AA-PSP) technique. Both top and sideviews of the pressure distribution on the model surface were acquired at various incidences. AA-PSP showed high pressure sensitivity and captured the complicated flow structures which correlated well with the colour Schlieren and oil flow visualisation results.     

Spectral measurements of hypervelocity flow in an expansion tunnel

Atmospheric reentry vehicles and planetary probes fly through the atmosphere at hypervelocity speed. At such speed, there is a significant proportion of heat load to the vehicle surface due to radiative heating. Accurate prediction needs a good knowledge of the radiation spectrum properties. In this paper, a high-speed camera and spectrograph coupled to an intensified charge-coupled device have bee n impleme nted to inv estigate the rad i at io n flow over a semi-cylinder model. The experiments were carried out in the JF16 expansi on timnel with secondary shock velocity of 7.9 km·s^-1. Results show that the emissio n spectrum comprises several atomic lines and molecular band systems. We give detailed data of the radiation spectrum, shock shape, shock detached distance and radiation intensity varying with space and wavelength. This valuable experimental dataset will be helpful to validate computational fluid dynamics codes and radiation models, which equates to increased prediction accuracy of radiation heating. Also, some suggestions for spectral measurement in hypervelocity flow field were list in the end.