Numerical analysis of simulation accuracy for hypersonic heat transfer in subsonic jets of dissociated nitrogen

One-dimensional problems of the flow in a boundary layer of finite thickness on the end face of a model and in a thin viscous shock layer on a sphere are solved numerically for three regimes of subsonic flow past a model with a flat blunt face exposed to subsonic jets of pure dissociated nitrogen in an induction plasmatron [1] (for stagnation pressures of (10⁴–3·10⁴) N/m² and an enthalpy of 2.1·10⁷ m²/sec²) and three regimes of hypersonic flow past spheres with parameters related by the local heat transfer simulation conditions [2, 3]. It is established that given equality of the stagnation pressures, enthalpies and velocity gradients on the outer edges of the boundary layers at the stagnation points on the sphere and the model, for a model of radius R_m=1.5·10^–2 m in a subsonic jet the accuracy of reproduction of the heat transfer to the highly catalytic surface of a sphere in a uniform hypersonic flow is about 3%. For surfaces with a low level of catalytic activity the accuracy of simulation of the nonequilibrium heat transfer is determined by the deviations of the temperatures at the outer edges of the boundary layers on the body and the model. For this case the simulation conditions have the form: dU_e/dx=idem, p₀=idem, T_e=idem. At stagnation pressuresP ₀2·10⁴ N/m² irrespective of the catalycity of the surface the heat flux at the stagnation point and the structure of the boundary layer near the axis of symmetry of models with a flat blunt face of radius R_m1.5·10^–2 m exposed to subsonic nitrogen jets in a plasmatron with a discharge channel radius R_c=3·10^–2 m correspond closely to the case of spheres in hypersonic flows with parameters determined by the simulation conditions [2, 3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 135–143, March–April, 1990.     

Transverse subsonic flow past a cylinder

At around the critical Reynolds number Re = (1.5–4.0)·10⁵ there is an abrupt change in the pattern of transverse subsonic flow past a circular cylinder, and the drag coefficient C_x decreases sharply [1]. A large body of both experimental and computational investigations has now been made into subsonic flow past a cylinder [1–4]. A significant contribution to a deeper understanding of the phenomenon was made by [4], which gives a physical interpretation of a number of theoretical and experimental results obtained in a wide range of Re. Nevertheless, the complicated nonstationary nature of flow past a cylinder with separation and the occurrence of three-dimensional flows when two-dimensional flow is simulated in wind tunnels do not permit one to regard the problem as fully studied. The aim of the present work was to make additional experimental investigations into transverse subsonic flow past a cylinder and, in particular, to study the possible asymmetric stable flow regimes near the critical Reynolds number.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 154–157, March–April, 1980.     

Interferometric study of natural convection in rectangular air cavities of various orientations

The results of an experimental investigation into the temperature profiles and heat transfer associated with natural convection in rectangular air cavities are presented, the angle of inclination varying from 0 (heating at the bottom) to 180° (heating at the top). The range of Rayleigh numbers was R=2.68·10³–2.57·10⁵, and n=H/d=5.06–18.3. The investigation was carried out by an optical method, using an IZK-454 interferometer. For a horizontal orientation of the cavity the heat-transfer data satisfy the relation N=0.216 R^0.25, for a vertical orientation N=0.144 R^0.3h^–0.129, where N is the Nusselt number. In the region of an inclination of 30° the heat transfer passes through a maximum under all conditions studied.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 89–93, July–August, 1972.     

Fluctuations of the flow parameters of an incompressible viscous fluid in a collar-type flow throttling device

The flow in channels of the labyrinth seal type with one or two throttling stages is calculated on the interval of Reynolds numbers Re from 1.9·10⁴ to 4.5·10⁵. The nonsteady flow structure and the distribution and fluctuations of the pressure on the body of the labyrinth are investigated. The results are compared with the data of a physical experiment.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 3–8, January–February, 1990.     

On the part played by the local pressure gradient in forming the flow in a corner

Special experiments were made in the subsonic low-turbulence wind tunnel T-324 of the Institute of Theoretical and Applied Mechanics of the Siberian Branch, USSR Academy of Sciences with the aim of making a more detailed study of the conditions of occurrence of transverse flows in the case of laminar flow along a corner. The velocity U of the undisturbed flow was varied from 2.3 to 5.5 m/sec [Re₁ = (1.5–3.5) · 10⁵ m^–1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 95–100, March–April, 1982.     

Experimental investigation of the heat exchange in separation zones ahead of cylindrical obstacles

Results of an experimental investigation of the heat exchange in turbulent boundary layer separation zones ahead of cylindrical obstacles at a subsonic air stream velocity are elucidated. The investigation was conducted for changes in the ratio between the obstacle diameter and altitude between 0.25 and 4, between the boundary layer thickness at the separation point and the obstacle altitude between 0.09 and 0.7, between the Reynolds number computed by means of the free stream parameters and the obstacle height between 10⁴ and 4·10⁵. The Mach number reached 0.85. The temperature factor was 0.7. It is shown that the distribution of the heat transfer coefficients in the separation zone depends on the Reynolds and Euler numbers, the ratio between the boundary layer displacement thickness and the diameter (or altitude) of the obstacle, and the ratio between the diameter and the altitude. Criterial dependences are obtained which extend the heat-exchange results at characteristic points of the separation zones, as are also dimensionless distributions of the heat transfer coefficients to determine the heat fluxes on a plate in the plane of symmetry of the separation zone ahead of obstacles.Translated from Zhurnal Prikladnoi Mekhanikii Tekhnicheskoi Fiziki, No. 6, pp. 83–89, November–December, 1972.The authors are grateful to V. S. Avduevskii for discussing the research results.     

Experimental investigation of the separation of flow around a sphere

The results of an experimental investigation of the flow around a sphere over a broad range of Mach numbers M=0.3–3 and Reynolds numbers Re=3·10⁴–3·10⁷ are presented. The experiments were carried out on a ballistic test stand and in a wind tunnel. Flow patterns and pressure distributions were obtained. In particular, the effect of the Mach and Reynolds numbers on the position of the separation point and the edge shock was studied; the pressure distribution on the sphere was measured; and a nonmonotonic displacement of the flow separation point upon passage through the speed of sound was established.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 152–156, January–February, 1991.     

Influence of Mach and Reynolds numbers on heat transfer to the leeward surface of a half-cone at hypersonic speed

Results are given of an investigation of heat transfer on the flat surface of a blunted half-cone, washed at zero angle of attack by a helium flow at high Mach number (up to 23.5). A correlation is given for the experimental data obtained over a wide range of Mach numbers (M = 3–23.5) and Reynolds numbers (Re_a = 10⁴–3.5·⁵, wherea is the nose radius).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 105–109, September–October, 1976.     

Thermal effect of a freely expanding gas jet on a flat plate

An experimental investigation was made into the thermal effect of a single gas jet on a plate at Mach numbers of the nozzles in the range 2–6.1, specific heat ratio = 1.4, total pressure difference up to 6·10⁷, gas temperature 450–520 °K in the forechamber, and pressure in the forechamber (10–20)· 10⁵ Pa. The proposed dimensionless numbers made it possible to obtain generalized dependences of the distribution of the heat flux to the plate on the conditions of the problem. A method of approximate calculation of the heat fluxes is proposed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 119–126, July–August, 1981.     

Thermoconcentration convection under uniform lateral heating

The fine structure of thermoconvective flow near an inclined- plane heat source within a fluid with a stable density stratification due to salinity gradient is investigated using optical and probe techniques. The time dependence of the parameters of optical refraction coefficient gradient, specific electric conductivity, velocity and temperature fields is determined for different values of the heat source inclination angle. The difference in the spatial scales of variation of the different variables is demonstrated. The Nusselt numbers range from 1.8 to 5.4 for the structures under the plate and from 1.8 to 10.6 for the structures above the plate for Rayleigh numbers on the range from 2·10⁵ to 2·10⁶.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 112–124, September–October, 1995.     

Experimental investigation of laminar flow of a liquid with a free surface in triangular-shaped channels

Results are given of an experimental study of laminar flow of a liquid in triangular-shaped open channels with tangential frictional stress at the free surface. Experiments were carried out when the liquid flow in inclined triangular-shaped channels had Reynolds numbers R < 10 and the working range of Reynolds numbers of the approach air stream was R = (1.6–3.6)·10⁴. The data are presented in relative coordinates as a dependence of the hydraulic resistance coefficient of the liquid on the tangential frictional stress at the free surface. It is shown that with an increase of the tangential frictional stress the hydraulic resistance coefficient considerably increases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 168–170, January–February, 1977.     

A comprehensive experimental study of the rheological behaviour of HDPE.

Extensional properties of four high density polyethylenes with different molecular weights and molecular weight distributions are presented. The samples have already been well characterized in shear and non-isothermal extensional flow. The data were collected at 180 °C for elongational rates between 3 · 10^–1 and 10^–4s^–1. Some qualitative and quantitative generalizations of the results are given.     

Generation and direct viscous dissipation of turbulent energy

Existing information about the generation and viscous dissipation of turbulent energy is based, as a rule, on the Laufer test data obtained for fluid flow in circular tubes at two Reynolds numbers (5 · 10⁵ and 5 · 10⁴). Computational dependences are presented herein for the generation and viscous dissipation of turbulent energy, common over the whole stream section and for the whole range of variation of the Reynolds number. The equation of the average energy balance during fluid flow in a circular tube and a flat channel is solved taking account of the equation of motion and the turbulent friction profile obtained by the author [1]. The computational dependences satisfy all the evident boundary conditions, agree with the Laufer test results [2] and yield a well-founded passage to the limit modes of average turbulent motion.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 30–36, November–December, 1973.     

Heat transfer to an isothermal flat plate in turbulent flow of a liquid over a wide range of prandtl and reynolds numbers

The study of heat transfer in turbulent flow over a flat plate is very important, not only because this situation frequently arises in practice, but also in that data for an isothermal flat plate are used to calculate heat transfer in more complex cases. In particular, such data are necessary when one uses the limiting relative laws which allow calculation of the effect of compressibility, pressure gradient, blowing, and other perturbing factors [1]. Most papers dealing with heat transfer for an isothermal flat plate refer to comparatively low Re values, when the velocity distribution in the boundary layer over almost its entire thickness can be described by the universal law of the wall. However, as Re increases there is an increasing layer adjacent to the outer boundary in which the velocity distribution cannot be described by the law of the wall, and therefore the results obtained for low Re are inapplicable. In the present paper coefficients of heat transfer from a turbulent flow to an isothermal flat plate have been obtained by numerical integration of the thermal boundary-layer equations over a wide range of the parameters 3 · 10⁵ Re 2.5·10¹², 10² Pr 10³.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 94–100, July–August, 1976.     

Turbulent boundary layer at the initial portion of a pipe with rough walls

The development of a turbulent boundary layer at the initial portion of a pipe with rough walls is considered in the framework of the boundary-layer theory. It is shown that the consideration of roughness can be carried out by introducing into the standard law of friction a function which takes into account this factor. An experimental investigation is carried out on a test portion of a pipe with natural roughness whose relative value equals 10^–3. The range of Reynolds numbers is 5.1 · 10⁴-3.4 · 10⁵. The method of calculation proposed here leads to results which satisfactorily agree with the data of the experimental investigation.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 109–116, September–October, 1971.     

Electrical breakdown in air in a transverse magnetic field

The electrical breakdown of gases in a transverse magnetic field is discussed in references [1–16]. Attention has mainly been concentrated on the case of coaxial electrode geometry [1–10]. The existing experimental data on breakdown between plane-parallel electrodes [11–14] relate to a narrow range of variation of the parameters characterizing breakdown (P, d, H, U). The author has made an experimental study of the process of electrical breakdown in air in a transverse magnetic field between plane-parallel electrodes of finite size in the pressure interval from 650 to 5·10^–3 mm Hg at gap lengths of from 1 to 140 mm and magnetic inductions from 0 to 10 600 G.     

Low-density jets beyond a sonic nozzle at large pressure drops

The gas-dynamical structure of jets of a low-density diatomic gas beyond a sonic nozzle at large pressure drops under conditions of a transition from continuous medium processes to rarefied gas processes is examined on the basis of experimental data obtained in low-density gas-dynamical tubes using electron-beam diagnostics and the Pitot tube method. Isomorphism is shown in the density distribution and total pressure in all cross sections of the jet with respect to pressures at a constant value of the complex R_L=R_*/N^1/2(R_* is the Reynolds number in the critical cross section of the nozzle, and N is the ratio of the Pitot pressure and the pressure in the discharge chamber). It is shown on the basis of a comparison of local Reynolds numbers for all zones of the jet that this is an analog complex. The experimental data on the variation in the jet structure are presented as a function of the number R_L in the range of 5–600. For R_L> 100 the flow in the jet can be considered as continuous; for R_L< 5–10 the flow corresponds to a scattering process; the range of 5–10< R_L< 100 corresponds to a transitional state. Ranges of isomorphism of the jet with respect to R_* and N are indicated. Based on the results of the measurements, it is shown that the flow behind a Mach disk for R_L> 200 remains subsonic on the axis to a distance of several lengths of the primary cycle. A transition to supersonic velocity on the jet axis can occur with a decrease in the numbers R_L owing to ejection acceleration by the supersonic ring-shaped compressed layer.This word is apparently interchangeable with self-similarity-Translator.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 64–73, March–April, 1973.     

Experimental study of heat and mass transfer from a horizontal cylinder in downward air-water mist flow with blockage effect

An experimental study was made on convective heat and mass transfer from a horizontal heated cylinder in a downward flow of air-water mist at a blockage ratio of 0.4. The measured local heat transfer coefficients agree fairly well with the authors' numerical solutions obtained previously for the front surface of a cylinder over the ranges mass flow ratio 0–4.5×10⁻², a temperature difference between the cylinder and air 10–43 K, gas Reynolds number (7.9–23)×10³, Rosin-Rammler size parameter 105–168 μm, and dispersion parameter 3.4–3.7. Heat transfer augmentation, two-pahse to single-phase of greater than 19 was attained at the forward stagnation point. For heat transfer in the rear part of the cylinder, an empirical formula is derived by taking into account the dimensionless governing variables, that is, coolant-feed and evaporation parameters.     

Behaviors of flow mechanisms and heat transfer of non-Newtonian fluids through a spinneret

This investigation examines non-Newtonian flow mechanisms and heat transfer characteristics for a micro spinneret. The working fluid, Polyethylene terephthalate (PET), is the raw material of micro fiber, and a large-scale experimental test model was designed to visualize the complex viscous flow system in the micro spinneret. To visualize the complex convective flow system, an experimental test model was constructed, using glycerin instead of PET. The related parameters of PET were compared with those of glycerin. The power law correlates the shear strain with PET viscosity at various temperatures. The pressure distribution along the flow direction was measured and the flow pattern was visualized using polyethylene (PE) powder of 20–40 m. Similar configurations were calculated for micro spinneret physical parameters to determine the thermal flow characteristics. The Reynolds number in the test model is not less than 10^–2. In the non-Newtonian PET working fluid of practical micro spinneret, flows with Re = 10⁴ to 10^–2 are in the same low Reynolds number flow regime. Therefore, the working fluid is expected to have the same flow characteristic. A numerical solution covering the range of approximately Re = 10^–4 at PET confirms that the flow characteristics of glycerin are constant for Re = 1.228 × 10^–2. The Peclet number in the test model can be adjusted to a value similar to that in the micro spinneret. The flow visualization was compared with that of the numerical solution, and the friction factor and Nusselt number in the micro spinneret were analyzed. Finally, numerical results and friction factor with various exit angles of micro spinneret in a triangular zone flow system were also summarized.     

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.