The effect of turbulence on steady and unsteady spontaneous condensation of steam in transonic nozzles

A transonic turbulent flow of spontaneously condensing steam in Laval nozzles is treated. Analysis is made of the effect of flow turbulence at the nozzle inlet on steady and unsteady spontaneous condensation.     

Transonic flow past thin wings

This paper is devoted to a discussion of steady inviscid transonic flow past thin wings, with subsonic free-stream Mach number M_∞ < 1, by the integral equation method. The integral equation formulation is developed for a thin unsymmetric wing at small incidence. A simple approximate analytical solution is presented for shock-free supercritical flow past a thin symmetric wing at zero incidence. The direct iteration scheme of Niyogi and Chakraborty is then extended to the three-dimensional zero incidence case, which may be used to obtain more accurate solutions for shockfree flows as well as for flows with shocks. The question of the existence and the uniqueness of a solution has been studied by means of the Banach contraction mapping principle in the spaceL ₂ (E₃), which establishes the condition of convergence of the direct iteration scheme. Simultaneously it provides us with an error estimate for the solution.     

Bifurcation of a transonic ideal-gas flow around a symmetric airfoil with a concavity

A transonic flow around a symmetric airfoil with a concavity in its central part has been numerically investigated. The dependences of the lift coefficient on the Mach number of the incident flow M_∞ and on the angle of attack α were determined. It is shown that, depending on M_∞, in the flow past the upper part of the indicated airfoil there can arise one or two supersonic-flow regions. It has been established that, at fairly large angles of attack, the coalescence and separation of supersonic-flow regions are realized in a discrete way. For these angles of attack, singular Mach numbers M_s, in the neighborhood of which the structure of the flow is transformed, were determined and the physical processes occurring in this case were analyzed. It was found that the flow being considered is characterized by a large hysteresis in M_∞. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 4, pp. 63–68, July–August, 2007.     

The Initial Equations and the Equations for Measuring the Mass and Volume Flow Rates of a Gas

A mathematical model of the flow of a gas in Laval nozzles is analyzed. The model is used to obtain equations for measuring the mass and volume flow rates of a gas.__________Translated from Izmeritel’naya Tekhnika, No. 4, pp. 44–48, April, 2005.     

Development of a flow field structure in the vicinity of a circular cylinder in the presence of a laminar-turbulent transition

The Reynolds equations and the two-parameter differentialq-Ω model of turbulence are used to investigate a flow past a circular cylinder with an isothermal surface (temperature factorT _w0 = 0.5) at the Mach numberM _∞ = 5 in the range of Reynolds numbers Re = 10⁴-10⁸. It is demonstrated that the turbulization of flow leads to a shift of the separation point downstream, a reduction and stabilization of the separation zone length, a decrease in the maximum velocity in the separation zone, and an increase in the heat flux at the rear stagnation point compared with its value at the forward stagnation point.     

音速喷嘴一元流动模型详解及其激波计算

针对文丘里音速喷嘴,阐述了如临界背压比等概念,指出了ISO 9300中背压比定义存在容易造成歧义的缺陷。然后基于一元等熵流动理论,从数学上证明了：当文丘里喷嘴喉部压力与上游滞止压力之比达到临界压比时,喉部产生音速,通过喷嘴的质量流量达到最大值;推导了实际条件下喷嘴的流量公式,导出的流量公式相较于ISO 9300给出的相应公式,增加了喉部状态参数下的压缩性系数修正项■。最后从气体动力学基本方程出发,讨论了在较大背压比范围内,喷嘴扩散段中产生激波的机理,给出了激波产生的位置、激波前、后的压力和马赫数的一元流动计算模型,并运用数值模拟方法对计算结果进行了验证,同时还与Craig A的实验数据作了对比。对最小出口压比对比的结果显示,一元流动模型与实验数据的最大误差≤17%。     

An efficient numerical method for highly loaded transonic cascade flow

In this paper, an efficient numerical method for transonic viscous flow in a highly loaded turbine vane cascade, where the interaction of a shock wave and boundary layer often leads to very complicated flow phenomena, is developed. The numerical code, a modified implicit flux-vector-splitting solver of the Navier–Stokes equations (MIFVS), is extended to simulate such transonic cascade flow. A compressible low-Reynolds-number k–ɛ model, together with a transition-modified damping function, has been implemented into the MIFVS code. With this extended MIFVS solver, the main feature of transonic flow and shock and boundary-layer interactions in the highly loaded transonic turbine vane are efficiently predicted with satisfactory accuracy. The convergence rate is found to be three times faster than that of flux-vector-splitting (FVS) methods.     

The Area of Application of Laval Nozzles in Flow-Rate Measurement Technique

Using examples of their use in standard and working instruments for measuring mass flow rate and a variety of gas volume flow rates, it is shown that critical nozzles and, particularly the Laval nozzle, can occupy an important place in the system of metrological facilities for this form of measurement.__________Translated from Izmeritel’naya Tekhnika, No. 4, pp. 48–52, April, 2005.     

Design of multimode axisymmetric hypersonic nozzles with the use of optimization methods

On the basis of the solution of direct problems with the use of various medium models and numerical methods of integration of gas flow equations, methods for designing super- and hypersonic nozzles have been developed. Multimode nozzles in the ranges of Mach numbers 8–14 and 14–20 satisfying given conditions have been designed.     

Circular cylinder in a transonic flow at high Reynolds numbers: Thermal problem

The results of numerical simulation of transonic cross flow of a perfect gas around a circular cylinder at high Reynolds numbers are used to solve the thermal problem. The temperature distributions along the central line and the influence of Reynolds and Mach numbers on them are presented. The temperature fields and the transition of the near-wake solution to the far-wake solution are studied.     

基于质量守恒原理的临界流喷嘴动态检定方法研究

针对低雷诺数临界流喷嘴喉径小,几何测量困难,常用的负压式PVTt装置难以对喷嘴进行最大背压比试验等问题,设计了一种以步进电机为动力的主动活塞式气体流量校准器。依据流体力学质量守恒原理,提出按PcTt参数动态检定临界流喷嘴流出系数的方法,建立了数学模型。经比对验证,动态检定方法准确、可行,流出系数Cd的重复性达到(0.02~0.05)%。     

音速喷嘴喉径对边界层过渡影响研究

滞止压力0.1 ～2.5 MPa下,喉径1.921 ～12.444 mm范围内,21支音速喷嘴的518组流出系数测量结果表明:滞止压力对同一块音速喷嘴流出系数的影响可超过2.3％;2.721 mm音速喷嘴边界层的过渡出现在雷诺数0.48×106;喉径12.444 mm音速喷嘴的边界层过渡出现在雷诺数0.94 ×106,音速喷嘴边界层过渡雷诺数与喉径直接相关.基于测试结果,提出了流出系数与雷诺数之间的经验公式,该公式对流出系数预测偏差小于0.3％.此外,得到边界层过渡雷诺数与音速喷嘴喉径之间的经验公式,该公式外延到日本NMIJ-2013实验工况,预测结果与实验结果具有很好的一致性.     

Finite element computation of unsteady viscous transonic flows past stationary airfoils

Results are presented for computations of unsteady viscous transonic flows past a stationary NACA0012 airfoil at various angles of attack. The Reynolds number, based on the chord-length of the airfoil, is 10,000 and the Mach number is 0.85. Stabilized finite-element formulations are employed to solve the compressible Navier-Stokes equations. The equation systems, resulting from the discretization, are solved iteratively by using the preconditioned GMRES technique. Time integration of the governing equations is carried out for large values of the non-dimensional time to understand the unsteady dynamics and long-term behavior of the flows. The results show interesting flow patterns and a complex interaction between the boundary/shear layers, shock/expansion waves and the lateral boundaries of the computational domain. For transonic flow past an airfoil at various angles of attack in a narrow channel/wind-tunnel one can observe solutions that are qualitatively different from each other. At low angles of attack an unsteady wake is observed. At moderate angles of attack the interaction between the shock system and the lateral walls becomes significant and the temporal activity in the wake decreases and eventually disappears. At high angles of attack a reflection shock is formed. Hysteresis is observed at an angle of attack 8^∘. For the flow in a domain with the lateral boundaries located far away, the unsteadiness in the flow increases with an increase in the angle of attack. Computations for a Mach 2, Re 106 flow past an airfoil at 10^∘ angle of attack compare well with numerical and experimental results from other researchers     

Effects of an airfoil and shock waves on vortex shedding process behind a square cylinder

Summary Effects of an airfoil and shock waves on vortex shedding process behind a square cylinder have been examined experimentally at a Mach number of about 0.91 and at a Reynolds number (based on the side lengthD of the square cylinder) of about 4.2×10⁵. The main experimental parameter is the spacing ratioL/D, and is varied from 1.125 to 5.5, whereL is the spacing between the square cylinder and the airfoil.It is found that similarly to the case at subcritical Mach numbers at the supercritical Mach number there exist three patterns of the flow around the square cylinder and airfoil arranged in tandem depending upon the spacing ratioL/D: In the first flow pattern with small spacing ratio, the downstream airfoil is enclosed completely in the vortex formation region of the square cylinder. In the second flow pattern, the shear layers separating from the square cylinder reattach to the airfoil. In the third flow pattern with large spacing the shear layers roll up upstream of the airfoil. The Strouhal number at the supercritical Mach number is higher than that at the subcritical Mach numbers. Shock waves hasten the vortex shedding behind the square cylinder by decreasing the area of asymmetrical part of the vortex formation region with respect to the wake axis, and let the streamwise length of the separating shear layers longer than otherwise.With 8 Figures     

Mixed convection flow near an axisymmetric stagnation point on a vertical cylinder

The mixed convection flow near an axisymmetric stagnation point on a vertical cylinder is considered. The equations for the fluid flow and temperature fields reduce to similarity form that involves a Reynolds number R and a mixed convection parameter λ, as well as the Prandtl number σ. Numerical solutions are obtained for representative values of these parameters, which show the existence of a critical value λ _c  = λ _c (R, σ) for the existence of solutions in the opposing (λ < 0) case. The variation of λ _c with R is considered. In the aiding (λ > 0) case solutions are possible for all λ and the asymptotic limit λ → ∞ is obtained. The limits of large and small R are also treated and the nature of the solution in the asymptotic limit of large Prandtl number is briefly discussed.     

Aeroacoustic tonal noise prediction of open cavity flows involving feedback

 A new hydrodynamic/acoustic splitting method isemployed to predict aeroacoustic tonal noise of self-sustained oscillatory flows over the open cavity at low Mach numbers. Acoustic field is computed using a sixth-order compact scheme and a fourth-order Runge–Kutta method, with acoustic sources obtained from the unsteady incompressible Navier–Stokes calculation. First, numerical accuracy of the present splitting method is assessed for the aeolian tone generated by Karman vortex shedding from a circular cylinder at Re _D = 200 and M _∞ = 0.3. A direct comparison was made with solutions of direct acoustic numerical simulation (DaNS) and Curle's acoustic analogy. The fundamental mode characteristics of the cavity flows at (i) Re_δ* = 850 and M _∞ = 0.077 and (ii) Re_δ* = 1620 and M _∞ = 0.147 are examined by the present method, verifying the solution with the experimentally measured sound pressure level (SPL) spectra. A dual tone characteristic observed in experiment (Henderson 2000) for case (i) is also confirmed computationally by the present method. Received: 15 April 2002 / Accepted: 5 March 2003 The authors wish to express gratitude to Prof. Henderson at the Kettering University for kindly providing the experimental data. This work was partially supported by the Korea Science and Engineering Foundation (1999-1-305-001-5).     

Transonic similarity solution for aligned field MHD nozzle flow

Summary The transonic flow near the throat of a converging-diverging nozzle of a gas with infinite electrical conductivity is considered. The magnetic fieldB is everywhere aligned with the velocityq so that the equations describing the flow are reducible to those of ordinary gasdynamics. Thus, it is possible to utilize the transonic similarity solution of Tomotika and Tamada [3] to study aligned field magnetohydrodynamic flow near a nozzle throat. Only transonic flows are considered, and the structures of sub- and supersonic flows with speeds greater and less than the Alfvén speed are investigated.     

The freezing property (stabilization law) of transonic flows

Summary It is well known that for transonic profile flow the local values of the fluid field freeze ifM 1. This is true in many cases even in second order. We give a simple heuristic proof for this behaviour. A control by the Prandtl-Meyer-expansion shows the limits of this property.Dedicated to Prof. Dr. Ing. U. Müller on the occasion of his 60th birthday.     

Interaction of a combination of bodies in supersonic flow. Interference and diffraction of shock waves in flow over two bodies of revolution

Results are presented of numerical investigations of three-dimensional supersonic flows in a disturbed region of jointly streamlined two identical bodies arranged in parallel which represent combinations of a cone with a semivertex angle of 20° and a cylinder with a fineness ratio of 5. Longitudinal flow over bodies has been studied numerically based on the Euler equation at a Mach number of incident flow equal to 4.03 and a zero angle of attack. The effect has been shown of the distance between the axes of models on the flow structure and disturbed and total aerodynamic characteristics of bodies. Calculated results have been compared with data of the physical experiment. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 79, No. 4, pp. 81–90, July–August, 2006.