Effect of longitudinal riblets on the aerodynamic characteristics of a straight wing

The results of balance aerodynamic tests on model straight wings with smooth and ribbed surfaces at an angle of attack =–4°–12°, Mach number M=0.15–0.63, and Reynolds number Re=2.4·10⁶–3.5·10⁶ are discussed. The nondimensional riblet spacings ⁺, which determines the effect of the riblets on the turbulent friction drag, and the effect of riblets on the upper and/or lower surface of a straight wing on its drag, lift, and moment characteristics are estimated.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 33–38, March–April, 1995.     

Optimum lifting wings with specified longitudinal trim characteristics

The case of an infinitely slender wing that slightly disturbs a supersonic ideal gas flow is considered. The plan form and the free-stream Mach number M are given. The optimum surface of the wing y=g(x, z) is determined as a result of finding a bounded function of the local angles of attack _M=g(x, z)/x that minimizes the drag coefficient c_x for given values of the lift coefficient c_y and the pitching moment coefficient m_z. The problem is solved in the class of piecewise-constant functions for wings of complex geometry [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 185–189, July–August, 1987.     

Unsteady supersonic flow around blunt bodies with detached shock wave

The numerical method of calculating the supersonic three-dimensional flow about blunt bodies with detached shock wave presented in [1–3] is applied to the case of unsteady flow. The formulation of the unsteady problem is analogous to that of [4], which assumes smallness of the unsteady disturbances.The paper presents some results of a study of the unsteady flow about blunt bodies over a wide range of variation of the Mach number M=1.50– and dimensionless oscillation frequency l/V=0–1.0. A comparison is made with the results obtained from the Newton theory.     

Approximate relationships for the determination of the pressure on the surface of a sphere or cylinder with an arbitrary mach number in the free stream

Numerical calculations have been made [1–4] of the pressure distribution over the surface of a sphere or cylinder during transverse flow in the range 0 /2, where is the angle reckoned from the stagnation point along the meridional plane, and on the basis of these results simple analytical equations have been proposed in order to determine the pressure for arbitrary Mach numbers M in the free stream. The gas is assumed to be ideal and perfect.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 185–188, March–April, 1985.     

Heat transfer in supersonic flow over a single spherical cavity

The flow and heat transfer on a plate with a single spherical cavity has been experimentally investigated for M=4 and Re_,L=3.1 · 10⁶. The flow pattern over the cavity has been obtained. Zones of enhanced heat transfer have been detected, and the heat transfer coefficients in and near the cavity have been determined. It has been established that a single spherical cavity has almost no effect on the integral heat flux.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 48–52, September–October, 1991.The authors are grateful to V. N. Brazhko for assistance in carrying out the experiments and to T. A. Ershova for assistance in analyzing the results.     

Some supersonic flow regimes on the windward side of V-shaped wings

The conditions of realization of regimes, detected in ideal gas theory [1, 2], with a floating Ferri point on the windward side of a wing with supersonic leading edges and breakdown of the conical flow in the presence of turbulent boundary layer separation are studied using experimental data on the flow over conical V-shaped wings. The experiments were carried out on three models of V-shaped wings with sharp leading edges having a convergence angle=40°, apex angles=30, 45, and 90° and lengths along the central chordL=100, 100, and 70 mm, respectively. The free-stream Mach numberM =3, and the unit Reynolds number Re=1.6 ·10⁸ m^–1. Boundary layer transition took place 10 mm from the leading edges of the models at a local Reynolds number Re=(1.5–2)·10⁶. Thus, on most of the wing surface the inner shock waves interacted with a turbulent boundary layer. In the experiments we employed; optical methods, which made it possible to observe shadow flow patterns in a plane normal to the rib of the V-shaped wing [3], as well as in the wake behind the wing and its leading edges (Töpler schlieren method); the oil-film visualization method for obtaining data on the position and dimensions of the separation zones and limiting streamline patterns on the surface of the model. The pressure distribution over the wing span was recorded by means of an automated data collection and processing system based on IKD6TD transducers. The errors of the pressure measurements did not exceed 1 %.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 137–150, March–April, 1992.     

Experimental investigation of the distribution of the pressure on a triangular airfoil with blunt edges at small angles of attack

The article gives the results of an experimental investigation of the pressure on a triangular airfoil with blunt edges with a half aperture angle =45° under angles of attack =0,5,10°, with M=11.6 and Re1.5×10⁶. It has been observed that in a region adjacent to the axis of symmetry, at a certain distance from the apex, there is observed a considerable lowering of the pressure.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 166–169, March–April, 1972.     

Hypersonic tail-fin heat transfer

The flow and heat transfer on the windward surface of tail fins has been experimentally investigated for Mach numbersM =5 and 8 and Re_L=(0.6–1.1)·10⁶ (L is the length of the central chord of the wing on which the fins are mounted). Two lines of flow divergence and, consequently, two zones of enhanced heat transfer on the surface of the fin have been detected. The angle of inclination of the fin to the wing surface, the angle of attack of the wing and the radius of the wing-fin junction were varied.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 18–25, March–April, 1993.The authors wish to thank S. D. Fonov and T. A. Ershova for the digital analysis of the photographs obtained by the thermal indicator coating and laser knife-edge methods.     

Flow around stepped bodies with strong compression in a shock layer

This article discusses plane and axisymmetric flows of a nonviscous ideal gas around bodies of stepped form, forming with a Mach number M= and an adiabatic indexN1. The greatest amount of attention is paid to the case where there is no Newtonian free layer, but the shock layer is detached at great distances from the nose of the body.Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 4, pp. 104–112, July–August, 1973.     

Study of heat transfer in the separation zones formed in front of supersonic jets in a subsonic carrier flow

The heat transfer taking place between the gas and the surface of the plate in the zone of three-dimensional separation of the turbulent boundary layer in front of a set of supersonic jets injected perpendicularly to a subsonic carrier flow is considered. The aim of this investigation is to establish the main physical characteristics of heat transfer in the separation zones in front of jet obstacles and to obtain the distributions of the local heat-transfer coefficients and the temperature of the thermally insulating wall as functions of the parameters of the carrier flow and the injected jets. Analysis of the experimental results yields certain approximating relationships for the distribution of the local heat-transfer coefficients as functions of the Mach number of the carrier flow M, the Mach number of the jet M_j, the relative boundary-layer displacement thickness _s= _s ^* /d, and the degree of jet superheating T_ojT_o relative to the separation zones in front of supersonic jet obstacles.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 68–72, July–August, 1975.     

Theoretical investigation of the effect of an internal heat source on turbulent liquid metal heat transfer in a channel with uniform heat flux

Summary The effect of an internal heat source on the heat transfer characteristics for turbulent liquid metal flow between parallel plates is studied analytically. The analysis is carried out for the conditions of uniform internal heat generation, uniform wall heat flux, and fully established temperature and velocity profiles. Consideration is given both to the uniform or slug flow approximation and the power law approximation for the turbulent velocity profile. Allowance is made for turbulent eddying within the liquid metal through the use of an idealized eddy diffusivity function. It is found that the Nusselt number is unaffected by the heat source strength when the velocity profile is assumed to be uniform over the channel cross section. In the case of a 1/7-power velocity expression, the Nusselt numbers are lower than those in the absence of internal heat generation, and decrease with diminishing eddy conduction. Nusselt numbers, in the absence of an internal heat source, are compared with existing calculations, and indications are that the present results are adequate for preliminary design purposes.Nomenclature A hydrodynamic parameter - a half height of channel - a ₁ a constant, 1+0.01 Pr Re ^0.9 - a ₂ a constant, 0.01 Pr Re ^0.9 - C _p specific heat at constant pressure - D _h hydraulic diameter of channel, 4a - h heat transfer coefficient, q _w/(t _w–t _b) - I ₁ integral defined by (17) - I ₂ integral defined by (18) - k diffusivity parameter, (1+0.01 Pr Re ^0.9)^1/2 - m exponent in power velocity expression - Nu Nusselt number, hD _h/ - Nu ₀ Nusselt number in absence of internal heat generation - Pr Prandtl number, / - Q heat generation rate per volume - q _w wall heat flux - Re Reynolds number for channel, 2/ - s ratio of heat generation rate to wall heat flux, Qa/q _w - T dimensionless temperature, (t _w–t)/(t _w–t _b) - t fluid temperature, t _w wall temperature, t _b fluid bulk temperature - u fluid velocity in x direction, , fluid mean velocity - x longitudinal coordinate measured from channel entrance - x ⁺ dimensionless longitudinal coordinate, 2(x/a)/Pr Re - y transverse coordinate measured from channel centerline - z transverse coordinate measured from channel wall, a–y - molecular diffusivity of heat, /C _p - dummy variable of integration - dummy variable of integration - _H eddy diffusivity of heat - _M eddy diffusivity of momentum - dummy variable of integration - fluid thermal conductivity - _T dimensionless diffusivity, Pr ( _H/) - fluid kinematic viscosity - dummy variable of integration - fluid density - dummy variable of integration - ratio of eddy diffusivity for heat transfer to that for momentum transfer, _H/ _M - average value of - dimensionless velocity distribution, u/     

Investigation of supersonic viscous flow past a sphere in the presence of subsonic and sonic injection

Supersonic flow past a sphere with a given rate of gas injection along the generator is investigated numerically on the range Re=10²–10⁴. Calculations have been made on the interval 0 90°, where is the angle between the axis of symmetry and the normal to the surface. It is shown that for high subsonic and sonic injection rates it is possible to observe qualitatively new features in the flow structure and in the distribution of the local supersonic flow characteristics around the perimeter of the sphere not previously noted in [9]. In the case of sonic injection the changes in flow structure occur only in the supersonic zone. In the neighborhood of the transition from a subsonic to sonic injection velocity the heat flux has a local maximum, which in absolute value does not exceed the heat flux in the absence of injection. It is shown that there may be qualitative differences in the pressure distribution over the surface of the body with increase in the injection parameter depending on the distribution and value of the injected gas flow rate and, moreover, the number Re.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 83–89, January–February, 1988.     

Die scheinbare Wärmedurchgangszahl von Plattenwärmeaustauschern

Zusammenfassung Um bei Platten-Wärmeaustauschern die übertragene Wärme richtig zu erhalten, muß das Produkt aus der Wärmedurchgangszahl k=1/(1/a ₁ + / + 1/a ₂), der gesamten Heizfläche A und der mittleren logarithmischen Temperatur differenz _m im allgemeinen noch mit einem Korrekturfaktor Z multipliziert werden, der von der Fließweganzahl n und der dimensionslosen Größe =(k A₀)/(M c) abhängt: Q=Z (kA_m) =k_sA_m (k_s=scheinbare Wärmedurchgangszahl). Unter der Voraussetzung, daß Gegenstrom herrscht und das Umwälzverhältnis U=M₁c₁/M₂c₂=1 ist, konnte diese Funktion Z=Z (n, )=k_s/k jetzt im Anschluß an eine frühere Rechnung für die reine Hintereinanderschaltung beliebig vieler Fließwege bestimmt werden. Die gefundenen Formeln weisen für gerade und ungerade Fließweganzahlen kleine Unterschiede auf. Doch verlaufen beide Kurvenscharen so gleichartig, daß sie sich gegenseitig ergänzend sehr gut ineinander fügen. — Eine wichtige Folgerung aus den Rechnungsergebnissen ist, daß die scheinbare Wärmedurchgangszahl k_s bei einem gegebenem Austauscher für jeden Massenstrom einen absoluten Höchstwert hat.

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The apparent overall heat transfer coefficient of plate heat exchangers

In order to get the correct value of the transfered heat Q of plate heat exchangers one must multiply the product of the overall heat transfer coefficient k=(1/a ₁ + / + 1/a ₂), the total heating area A and the logarithmic mean temperature difference _m with a correction factor Z: Q=Z · k · A · _m =k_s · A_m, where k_s means the so called apparent overall heat transfer coefficient. Z is, as was shown in a previous paper, a function of the numbers of flow channels and the dimensionless quantity =(k · A₀)/M · c. In this paper, assuming counter flow and the validity of the relation U=M₁c₁/M₂c₂=1, the correction factor Z is determined for the pure series con nexion of any desired number of flow channels. — An important conclusion drawn from our results is, that for a given heat exanger, k_s has an absolute maximum value for every mass flow rate.

     

A new interpretation of viscosity and yield stress in dense slurries: Coal and other irregular particles

Illinois coal was ground and wet-sieved to prepare three powder stocks whose particle-size distributions were characterized. Three suspending fluids were used (glycerin, bromonaphthalene, Aroclor), with viscosities _s that differed by a factor of 100 and with very different chemistries, but whose densities matched that of the coal. Suspensions were prepared under vacuum, with coal volume fractions that ranged up to 0.46. Viscosities were measured in a cone-and-plate over a shear rate range 10^–3–10² s^–1. Reduced viscosity _r = /_s is correlated in the high-shear limit ( ) with/ _M, where _M is the maximum packing fraction for the high-shear microstructure, to reveal the roles of size distribution and suspending fluid character. A new model that invokes the stress-dependence of _M is found to correlate _r well under non-Newtonian conditions with simultaneous prediction of yield stress at sufficiently high; a critical result is that stress and not governs the microstructure and rheology. Numerous experimental anomalies provide insight into suspension behavior.     

Asymptotic solution to the problem of hypersonic flow over bodies in the neighborhood of the separation point of a thin shock layer

A study is made of the problem of hypersonic flow of an inviscid perfect gas over a convex body with continuously varying curvature. The solution is sought in the framework of the asymptotic theory of a strongly compressed gas [1–4] in the limit M when the specific heat ratio tends to 1. Under these assumptions, the disturbed flow is situated in a thin shock layer between the body and the shock wave. At the point where the pressure found by the Newton-Buseman formula vanishes there is separation of the flow and formation of a free layer next to the shock wave [1–4]. The singularity of the asymptotic expansions with respect to the parameter ₁ = ( –1)/( + 1) associated with separation of the strongly compressed layer has been investigated previously by various methods [3–9]. Local solutions to the problem valid in the neighborhood of the singularity have been obtained for some simple bodies [3–7]. Other solutions [7, 9] eliminate the singularity but do not give the transition solution entirely. In the present paper, an asymptotic solution describing the transition from the attached to the free layer is constructed for a fairly large class of flows.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 99–105, January–February, 1982.     

Entropy effects in hypersonic flow over blunt delta wings

The problem of hypersonic flow over blunt delta wings is considered. It is shown that in the case of large wing lengths x -100, where x is the longitudinal coordinate measured in blunt nose radii, extremal flow regimes characterized by an essentially nonuniform distribution of the gas dynamic parameters (density, entropy, Mach number) may be realized in the shock layer near the windward surface of the wing. The location of the zones of flow convergence or divergence on the surface of a delta wing with sweep angle x=75° is established. For the same wing the ranges of Mach numbers M and angles of attack leading to extremal flow regimes are indicated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, 178–181, March–April, 1991.     

Effect of the flow regime in an underexpanded jet issuing into a subsonic counterstream on the pressure distribution on a body

The pressure distribution on a cone with a half-angle =75°, from which a single central underexpanded jet issues into a subsonic counterstream, has been experimentally investigated. The effect of the flow regime in the jet on the pressure distribution is demonstrated. Generalized relations for the pressure on the body are obtained for various jet-flow momentum ratios J and flow Mach numbers M = 0.35–0.9; the Mach number M_a at the exit of the conical nozzle with half-angle _a=10° was equal to 2.9. The working medium of the jet and the flow was air with stagnation temperatures T_0a = T₀ 260–265°K. The ratio of the nozzle outlet radius to the radius of the maximum cross section of the cone _a/R_M=0.1.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 182–185, January-February, 1988.     

Calculation of a wall-stabilized argon arc with account for radiative energy transfer

It was shown experimentally in [1, 2] and in a study by E. I. Asinovskii and A. V. Kirillin reported at the Scientific Technical Conference of the High-Temperature Scientific Research Institute held in 1964 that the heat transfer mechanism in a wall-stabilized argon arc was not purely purely conductive at gas temperatures greater than 11 000° K. Asinovskii and Kirillin also showed that radiative energy transfer is the reason why similarity is lost when the current-voltage characteristics are constructed in dimensionless form. The radiation of an argon arc has been studied experimentally by a number of authors [3–5], Dautov [6] calculated an argon arc without allowing for radiation.In this article an argon arc stabilized by the cooled duct walls is calculated with account for radiation using theoretically computed relationships describing the transport properties of argon plasma. A large portion of the radiated energy pertains to spectral lines whose role has been studied by L. M. Biberman. The authors have used I. T. Yakubov's data on argon radiation published in the journal Optics and Spectroscopy. A method of calculation and data on argon plasma radiation are also given in [7].Reference [8] deals with the problem of the role of radiation in an arc burning in nitrogen. In particular, the above-mentioned loss of similarity follows from the results of this work. However, the relationships used in this article to describe the transport properties of nitrogen plasma were obtained experimentally in [9].Notation r₀ arc radius (cm) - r variablesradius (cm) - T temperature (°K) - heat transfer coefficient (ergcm^–1sec^–1deg^–1) - E electric field intensity (g^1/2cm^–1/2sec^–1) - electrical conductivity (sec^–1) - q₁ heat flux density due to conduction - q₂ heat flux density due to radiation - u divergence of radiative energy flux density in the transparent part of the spectrum (ergcm^–3sec^–1) - u₂ same for part of the spectrum where reabsorption is taken taken into account - m₀ atomic mass - m_e electronic mass - Stefan-Boltzmann constant - h Planck constant - k Boltzmann constant - e electronic charge - p pressure - degree of ionization - N_e electron concentration (cm^–3) - n₀ neutral atom concentration - Q_0e electron-neutral collision cross section - Q_ie electron-ion collision cross section (cm²) - ₀ line center frequency (sec^–1) - ₊ line halfwidth (distance from line center to contour for ) due to effects giving dispersion contour - k _v absorption coefficient (cm^–1) - energy radiated by a hemispherical volume - emissivity of hemispherical volume - radius of hemispherical volume - S line intensity The authorS thank I. T. Yakubov for allowing them to use his data on arc plasma radiation.     

Relaminarization of a turbulent boundary layer with a mach number M∞=4

Results of experimental studies are presented on relaminarization of a supersonic turbulent boundary layer behind an expansion fan for a freestream Mach number M=4 within a range of Reynolds numbers Re₁=8·10⁶ – 26·10⁶ m^–1. Experimental data on distributions of the mean velocity and massflow fluctuations and the skin friction force are obtained. Partial relaminarization of the boundary layer is reached in the experiments. The calculations of relaminarization criteria show that they can be used to predict the onset of the relaminarization process at high supersonic flow velocities.     

Aspects of a method of investigating the distributed load on oscillating wings

The paper discusses the method and technique of an experiment and also some results of the investigation of the unsteady pressure on the surface of a rectangular wing executing oscillations with angular amplitude * = 3° at Strouhal numbers p* = 0.113 (p* = /v, where * is the angular frequency, b is the chord of the wing, and v is the velocity of the oncoming flow).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 178–181, September–October, 1981.