Control of low-speed turbulent separated flow using jet vortex generators

A parametric study has been performed with jet vortex generators to determine their effectiveness in controlling flow separation associated with low-speed turbulent flow over a two-dimensional rearward-facing ramp. Results indicate that flow-separation control can be accomplished, with the level of control achieved being a function of jet speed, jet orientation (with respect to the free-stream direction), and jet location (distance from the separation region in the free-stream direction). Compared to slot blowing, jet vortex generators can provide an equivalent level of flow control over a larger spanwise region (for constant jet flow area and speed).Nomenclature C _p pressure coefficient, 2(P-P_)/V ² - C _Q total flow coefficient, Q/ v - D ₀ jet orifice diameter - Q total volumetric flow rate - R Reynolds number based on momentum thickness - u fluctuating velocity component in the free-stream (x) direction - V free-stream flow speed - VR ratio of jet speed to free-stream flow speed - x coordinate along the wall in the free-stream direction - jet inclination angle (angle between the jet axis and the wall) - jet azimuthal angle (angle between the jet axis and the free-stream direction in a horizontal plane) - boundary-layer thickness - momentum thickness - lateral distance between jet orifices A version of this paper was presented at the 12th Symposium on Turbulence, University of Missouri-Rolla, 24–26 Sept. 1990     

Supersonic nonequilibrium flow past segmental bodies of a mixture simulating the atmosphere of venus

Calculations of the flow of the mixture 0.94 CO₂+0.05 N₂+0.01 Ar past the forward portion of segmentai bodies are presented. The temperature, pressure, and concentration distributions are given as a function of the pressure ahead of the shock wave and the body velocity. Analysis of the concentration distribution makes it possible to formulate a simplified model for the chemical reaction kinetics in the shock layer that reflects the primary flow characteristics. The density distributions are used to verify the validity of the binary similarity law throughout the shock layer region calculated.The flow of a CO₂+N₂+Ar gas mixture of varying composition past a spherical nose was examined in [1]. The basic flow properties in the shock layer were studied, particularly flow dependence on the free-stream CO₂ and N₂ concentration.New revised data on the properties of the Venusian atmosphere have appeared in the literature [2, 3] One is the dominant CO₂ concentration. This finding permits more rigorous formulation of the problem of blunt body motion in the Venus atmosphere, and attention can be concentrated on revising the CO₂ thermodynamic and kinetic properties that must be used in the calculation.The problem of supersonic nonequilibrium flow past a blunt body is solved within the framework of the problem formulation of [4].Notation V body velocity - shock wave standoff - universal gas constant - ratio of frozen specific heats - hRt/m enthalpy per unit mass undisturbed stream P pressure - density - T temperature - m molecular weight - c_p specific heat at constant pressure - (X) concentration of component X (number of particles in unit mass) - R body radius of curvature at the stagnation point - _j rate of j-th chemical reaction shock layer P V ² pressure - density - TT temperature - mm molecular weight Translated from Izv. AN SSSR. Mekhanika Zhidkosti i Gaza, Vol. 5, No. 2, pp. 67–72, March–April, 1970.The author thanks V. P. Stulov for guidance in this study.     

Asymptotic analysis of equilibrium states for rotating turbulent flows

The equilibrium states of homogeneous turbulence simultaneously subjected to a mean velocity gradient and a rotation are examined by using asymptotic analysis. The present work is concerned with the asymptotic behavior of quantities such as the turbulent kinetic energy and its dissipation rate associated with the fixed point (/kS)=0, whereS is the shear rate. The classical form of the model transport equation for (Hanjalic and Launder, 1972) is used. The present analysis shows that, asymptotically, the turbulent kinetic energy (a) undergoes a power-law decay with time for (P/)<1, (b) is independent of time for (P/)=1, (c) undergoes a power-law growth with time for 1<(P/)<(C ₂–1), and (d) is represented by an exponential law versus time for (P/)=(C ₂–1)/(C ₁–1) and (/kS)>0 whereP is the production rate. For the commonly used second-order models the equilibrium solutions forP/,II, andIII (whereII andIII are respectively the second and third invariants of the anisotropy tensor) depend on the rotation number when (P/kS)=(/kS)=0. The variation of (P/kS) andII versusR given by the second-order model of Yakhot and Orzag are compared with results of Rapid Distortion Theory corrected for decay (Townsend, 1970).     

Flow in vicinity of blunt body stagnation point in diverging hypersonic stream

In the hypersonic thin shock layer approximation for a small ratio k of the densities before and after the normal shock wave the solution of [1] for the vicinity of the stagnation point of a smooth blunt body is extended to the case of nonuniform outer flow. It is shown that the effect of this nonuniformity can be taken into account with the aid of the effective shock wave radius of curvature R_*, whose introduction makes it possible to reduce to universal relations the data for different nonuniform outer flows with practically the same similarity criterion k. The results of the study are compared with numerical calculations of highly underexpanded jet flow past a sphere.Notations x, y a curvilinear coordinate system with axes directed respectively along and normal to the body surface with origin at the forward stagnation point - R radius of curvature of the meridional plane of the body surface - uV, vV., , p V ² respectively the velocity projections on the x, y axes, density, and pressure - and V freestream density and velocity The indices =0 and=1 apply to plane and axisymmetric flows Izv. AN SSSR, Mekhanika Zhidkosti i Gaza, Vol. 5, No. 3, pp. 102–105, 1970.     

Calculation of the pressure on the side surface of bodies consisting of a spherical segment joined to an inverted cone in a supersonic stream

The results of investigations of inviscid flow over inverted cones with nose consisting of a spherical segment were published for the first time in Soviet literature in [1–4]. In the present paper, a numerical solution to this problem is obtained using the improved algorithms of [5, 6], which have proved themselves well in problems of exterior flow over surfaces with positive angles of inclination to the oncoming flow. It is shown that the Mach number 2 M , equilibrium and nonequilibrium physicochemical transformations in air (H = 60 km, V = 7.4 km/sec, R₀ = 1 m), and the angle of attack 0 40° influence the investigated pressure distributions. A comparison of the results of the calculations with drainage experiments for M = 6, = 0-25° confirms the extended region of applicability of the developed numerical methods. Also proposed is a simple correlation of the dependence on the Mach number in the range 1.5 M of the shape of the shock wave near a sphere in a stream of ideal gas with adiabatic exponent = 1.4.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 178–183, January–February, 1981.     

On nonlinear problems of mixed type: A qualitative theory using infinite-dimensional center manifolds

We consider the equation a(y)u_xx+div_y(b(y)_yu)+c(y)u=g(y, u) in the cylinder (–l,l)×, being elliptic where b(y)>0 and hyperbolic where b(y)<0. We construct self-adjoint realizations in L₂() of the operatorAu= (1/a) div_y(b_yu)+(c/a) in the case ofb changing sign. This leads to the abstract problem u_xx+Au=g(u), whereA has a spectrum extending to + as well as to –. For l= it is shown that all sufficiently small solutions lie on an infinite-dimensional center manifold and behave like those of a hyperbolic problem. Anx-independent cross-sectional integral E=E(u, u_x) is derived showing that all solutions on the center manifold remain bounded forx ±. For finitel, all small solutionsu are close to a solution on the center manifold such that u(x)-(x) Ce ^-(1-|x|) for allx, whereC and are independent ofu. Hence, the solutions are dominated by hyperbolic properties, except close to the terminal ends {±1}×, where boundary layers of elliptic type appear.     

Penetration depth of a jet injected into an oncoming supersonic flow

The geometrical characteristics of jets injected through an opening in a flat plate into an oncoming supersonic flow have been studied on a number of occasions [1, 3]. However, the results were analyzed under different suppositions about the important dimensionless parameters. In [1], the degree of underexpansion of the jet, characterized by n = p _a /p, was regarded as decisive; in [3], the experimental points were plotted against the relative dynamic head _a u² _a /(u² ) of the jet. In the present paper, dimensional considerations are used to determine the dimensionless parameters which influence the flow field when an injected jet interacts with an oncoming supersonic gas flow. The influence of these determining dimensionless parameters on the depth of penetration of injected jets into a flow was investigated experimentally. It is shown that the relative depth of penetration is determined basically by the relative specific impulse of the jet, the injection angle, and the shape of the blowing nozzle section.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 151–154, July–August, 1980.     

Supersonic air flow past a sphere with account for vibrational relaxation

A numerical solution is obtained for the problem of air flow past a sphere under conditions when nonequilibrium excitation of the vibrational degrees of freedom of the molecular components takes place in the shock layer. The problem is solved using the method of [1]. In calculating the relaxation rates account was taken of two processes: 1) transition of the molecular translational energy into vibrational energy during collision; 2) exchange of vibrational energy between the air components. Expressions for the relaxation rates were computed in [2]. The solution indicates that in the state far from equilibrium a relaxation layer is formed near the sphere surface. A comparison is made of the calculated values of the shock standoff with the experimental data of [3].Notation uV_max, vV_max velocity components normal and tangential to the sphere surface - V_max maximal velocity - P V _max ² pressure - density - TT temperature - e_viRT vibrational energy of the i-th component per mole (i=–O₂, N₂) - =rb–1 shock wave shape - a _f the frozen speed of sound - HRT/m gas total enthalpy     

Classification of linear viscoelastic solids based on a failure criterion

An isotropic, incompressible linear viscoelastic solid subjected to a step shear displacement fails if the relaxation function G(s) is such that 0<G(0)< and –<G(0)0. In this case, the discontinuity in displacement propagates into the interior of the body. The discontinuity will not propagate however if G(0)= or G(0)=–. In the former case there is a diffusion-like smoothening of discontinuous data characteristic of parabolic equations. The case G(0)= may be achieved by composing the kernel as a sum of a smooth kernel and a delta function at the origin times a viscosity coefficient. If the viscosity is small, the smoothing will take place in a propagating layer which scales with the small viscosity. The case of G(0)=– is interesting in the sense that the solution is C smooth but the boundary of the support of the solution propagates at a constant wave spped. If 0<G(0)< and –<G(0)<0, then the material accomodates stress waves under step traction leading to an elastic steady state.     

Stability of the T ∞FT < T ∞α relation between Vogel temperatures of flow and glass transition against determination variants

Dynamic shear measurements in the frequency range from 10^–4 to 500 rad/s at the flow and main transition of a polydisperse poly(vinyl acetate) and a monodisperse polystyrene sample are presented. For both samples the Vogel temperature of the flow transition T _FT is smaller than the Vogel temperature of the main transition T , independent of the criteria used for data evaluation. The difference between the two Vogel temperatures corresponds to results for samples with other molecular weight and polydispersity from the literature. The T _FT <T relation is discussed in terms of short () and long (FT) dynamic glass transitions in entangled polymers. The relation is explained by preaveraging of the energy landscape for the long flow transition by the short glass transition.     

Jet methods of gas injection into fluid boundary layer for drag reduction

Two jet methods for saturating the fluid boundary layer with microbubbles for drag reduction in contrust with gas injection through porous materials are considered. The first method is the gas injection through the slot under a special fluid wall jet. The second method is the saturation of boundary layer by microbubbles via the gas-water mixture injection through the slot. Experimental data, reflecting the skin friction drag reduction on the flat plate and total drag reduction of axisymmetric bodies, are presented. The comparison between a jet methods of gas injection and gas injection through porous materials is made.Nomenclature v free-stream velocity - v _j mean velocity of a water through slot - v _g mean velocity of a gas through slot - h width of slot for realizing water jet - h ₁ width of slot for gas injection - incidence angle - Q volume airflow rate - C _Q airflow rate coefficient (v _g/v ) - C _f skin friction coefficient - v _j/v - C _f0 C _f ifQ=0 andv _j=0 - _f C _f/C _{f 0} - d diameter of an axisymmetric body - L length of body - C _Q 4 · ·Q/d ² v - C _D 4 ·D/1/2v ² ·d ² - C _Q 4 ·Q/d ² v - Q _j volume flow rate of water jet - C 8 ·Q _jv_j/d ² v ² - 1 fluid density of main flow - 2 fluid density of wall jet - B ₁ main stream total pressure - B ₂ wall jet total pressure - v ₁ main stream velocity - Be (B ₂ –B ₁)/1/2₁ v ₁ ² = Bernoulli number - ₂ v ₂/₁ v ₁ - p _st static pressure - p _at atmospheric pressure - p _st/p _at - D hydrodynamic drag of body     

Existence theorem for a minimum problem with free discontinuity set

We study the variational problem Where is an open set in ⁿ ,n2gL ^q () L (), 1q<+, O<, <+ andH _n–1 is the (n–1)-dimensional Hausdorff Measure.     

Oscillatory free convection heat transfer along a semi-infinite vertical plate

Summary The fluctuating free convection flow along a semi-infinite vertical plate is considered when the plate temperature is of the form T _p –T =(T ₀ –T ) where 0 < 1, denotes the frequency of oscillation and the mean temperature T ₀–T is proportional to ⁿ (0 n < 1). Flow and temperature fields have been obtained by means of two asymptotic expansions. For small values of the frequency parameter , a regular expansion is obtained while for large the method of matched asymptotic expansion is used. It is found that the skin friction and the rate of heat transfer obtained from two expansions overlap satisfactorily for a certain value of . For n=1 the flow governing equations to a semisimilar form, and have been solved by finite difference method. The results obtained from the series and the finite difference methods are in good agreement.

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Oszillierender Wärmeübergang an einer halbunendlichen senkrechten Platte bei freier Konvektion

Übersicht Betrachtet wird die fluktuierende freie Konvektionsströmung längs einer halbunendlichen senkrechten Platte, deren Temperatur dem Gesetz T _p –T =(T ₀–T ) [1+ sin {ie1-03}] folgt, wobei 0 < 1 gelte, {ie1-04} die Frequenz ist und der Temperatur-Mittelwert T ₀–T proportional zu ⁿ (0 n < 1) ist. Mit Hilfe zweier asymptotischer Entwicklungen werden die Strömungs- und Temperaturfelder gewonnen. Für kleine Werte des Frequenzparameters wird eine gewöhnliche Entwicklung benutzt, für große die Methode angepaßter asymptotischer Entwicklungen. Es stellt sich heraus, daß die Oberflächenreibung und die Wärmeübergangsrate aus zwei Entwicklungen für ein bestimmtes zufriedenstellend aufeinander fallen. Für n=1 werden die Grundgleichungen zueinander ähnlich und werden nach der Finite-Differenzen-Methode gelöst. Die Ergebnisse nach den Reihenentwicklungen und der Finite-Differenzen-Methode stimmen gut überein.

     

Rheology of molten polymers

Summary TheCross equation describes the flow of pseudoplastic liquids in terms of an upper and a lower Newtonian viscosity corresponding to infinite and zero shear, and ₀, and of a third material constant related to the mechanism of rupture of linkages between particles in the intermediate, non-Newtonian flow regime, Calculation of of bulk polymers is important, since it cannot be determined experimentally. The equation was applied to the melt flow data of two low density polyethylenes at three temperatures.Using data in the non-Newtonian region covering 3 decades of shear rate to extrapolate to the zero-shear viscosity resulted in errors amounting to about onethird of the measured ₀ values. The extrapolated upper Newtonian viscosity was found to be independent of temperature within the precision of the data, indicating that it has a small activation energy.The ₀ values were from 100 to 1,400 times larger than the values at the corresponding temperatures.The values of were large compared to the values found for colloidal dispersions and polymer solutions, but decreased with increasing temperature. This shows that shear is the main factor in reducing chain entanglements, but that the contribution of Brownian motion becomes greater at higher temperatures.

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Zusammenfassung Die Gleichung vonCross beschreibt das Fließverhalten von pseudoplastischen Flüssigkeiten durch drei Konstante: Die obereNewtonsche Viskosität (bei sehr hohen Schergeschwindigkeiten), die untereNewtonsche Viskosität ₀ (bei Scherspannung Null), und eine Materialkonstante, die vom Brechen der Bindungen zwischen Partikeln im nicht-Newtonschen Fließbereich abhängt. Die Berechnung von ist wichtig für unverdünnte Polymere, wo man sie nicht messen kann.Die Gleichung wurde auf das Fließverhalten der Schmelzen von zwei handelsüblichen Hochdruckpolyäthylenen bei drei Temperaturen angewandt. Die Werte von ₀, durch Extrapolation von gemessenen scheinbaren Viskositäten im Schergeschwindigkeitsbereich von 10 bis 4000 sec^–1 errechnet, wichen bis 30% von den gemessenen ₀-Werten ab. Die Aktivierungsenergie der war so klein, daß die-Werte bei den drei Temperaturen innerhalb der Genauigkeit der Extrapolation anscheinend gleich waren. Die ₀-Werte waren 100 bis 1400 mal größer als die-Werte.Im Verhältnis zu kolloidalen Dispersionen und verdünnten Polymerlösungen war das der Schmelzen groß, nahm aber mit steigender Temperatur ab. Deshalb wird die Verhakung der Molekülketten hauptsächlich durch Scherbeanspruchung vermindert, aber der Beitrag derBrownschen Bewegung nimmt mit steigender Temperatur zu.

     

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.     

Hyperbolic phenomena in a strongly degenerate parabolic equation

We consider the equation u _t =((u) (u _x )) _x , where >0 and where is a strictly increasing function with lim _s = <. We solve the associated Cauchy problem for an increasing initial function, and discuss to what extent the solution behaves qualitatively like solutions of the first-order conservation law u _t = ((u)) _x . Equations of this type arise, for example, in the theory of phase transitions where the corresponding free-energy functional has a linear growth rate with respect to the gradient.     

Linearized dynamics for step jumps of velocity and displacement of shearing flows of a simple fluid

We consider linearized dynamics associated with step jumps in the velocity or displacement of the boundary of a fluid in a shearing motion. The discontinuity will propagate into the interior with a speed ( is the density) if the initial valuesG(0) andG(0) of the fading memory kernels are bounded, 0 <G(0) < , – <G (0) < 0. IfG(0) butG(0) = – , then the boundary of the support of the solution still propagates with the speedC. However, the solutions on both sides of the boundary match together in aC -fashion. IfG(0) butG(0) = 0, the amplitude of the discontinuity will not damp as in a purely elastic fluid. IfG(0) = , the step change is felt immediately throughout the fluid, without shocks, as in Navier-Stokes fluids. This same type of parabolic behavior can be achieved by a small Newtonian contribution added to the integral form of the stress but if this contribution is small, a smooth transition layer around the shock will propagate with the speedC. In the case of step displacement, from rest to rest, singular surfaces of infinite velocity can propagate into the interior with speed of propagationC. The singular surfaces undergo multiple reflections off bounding walls, but the final steady state reached asymptotically is in universal form independent of material.     

Aerodynamic force measurements over missile configurations in IISc shock tunnel at M∞ =3.85 and 9.15

Conclusions Three most commonly used missile configurations are tested in a shock tunnel, and a new set of aerodynamic data is obtained at M = 3.85 and 9.15 by using an accelerometer balance system. The agreement between theory and experiment is generally good for all the cases. Noticeable decreases in measured C _Land C _mvalues are obtained at M =9.15, compared to those at M = 3.85. The dependence of C _Don M seems to be insignificant.     

Theoretische Untersuchung der laminaren Zweistoff-grenzschichtströmung längs eines verdunstenden Flüssigkeitsfilms bei nichtadiabater Verdunstung

Zusammenfassung Zur Klärung der physikalischen Vorgänge im Verdampferteil einer Filmverdampfungsbrennkammer wird in Erweiterung der adiabaten Verdunstung der Fall der einseitig benetzten ebenen Platte behandelt, die sowohl im Gleichals auch im Gegenstrom von der heißen Außenluft umströmt wird. Die für beide Strömungsfälle maßgebenden Grenzschichtgleichungen werden simultan unter Berücksichtigung temperatur- und konzentrationsabhängiger Stoffwerte mit einem impliziten Differenzenverfahren gelöst. Dabei ergeben sich für den Gleichstrom ähnliche Lösungen des gekoppelten Gleichungssystems, die mit den ähnlichen, für die adiabate Verdunstung geltenden Lösungen verglichen werden. Die Berechnung der durch den Stoffübergang beeinflußten Grenzschicht parameter zeigt, daß das Modell der Gegenstromanordnung, bei der sich nichtähnliche Profile entlang der Filmoberfl äche einstellen, für einen möglichen Einsatz in einer Filmverdampfungsbrennkammer am besten geeignet ist.

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Theoretical investigation on the binary laminar boundary-layer flow along a vaporizing liquid layer at non-adiabatic evaporation

For clarification the physical process in the evaporating part of a film-evaporation combustion-chamber in addition to the adiabatic evaporation the case of a one-sided wet plate in co- and counter-current hot air flow is presented. The boundary-layer equations for both streams are solved simultaneously with an implicit finite-difference method taking into account variable fluid properties. Thereby the similar solutions obtained for the co-current flow are compared with the corresponding similar solutions for the case of the adiabatic evaporation. Contrary to the co-current flow the counter-current flow yields non-similar solutions and the computation of the boundary-layer parameters influenced by the evaporation mass-flow shows, that the model of counter-current flow is best suitable for application in a film-evaporation combustion-chamber.

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Bezeichnungen A_j, B_j Abkürzungen in der allg. Differenzen - C_j gleichung (36) - c Massenkonzentration, bezogen auf Gemischmasse - c_f Dimensionsloser örtlicher Reibungsbeiwert - c_p Spezifische Wärmekapazität - D₁₂ Diffusionskoeffizient - h Enthalpie des Gasgemisches - K₁, K₂ Abkürzungen in der Gl. (5) - K₅, K₆ Abkürzungen in der Gl.(22) - L Plattenlänge - M Molmasse - m₁ Massenstromdichte, verdunstende Masse je Flächen- und Zeiteinheit - m^* Dimensionslose Massenstromdichte, Verdunstungsparameter nach Gl.(32) - m^** Örtliche dimensionslose Massenstromdichte nach Gl. (33) - P_Gr Stellvertretende Größe für die Grenzschicht parameter c_f, St_T und St_m nach Gl. (34) - p Statischer Druck (=Summe der Partialdrücke) - p_1w Sättigungsdruck an der Filmoberfläche - q Wärmestromdichte - r Verdampfungsenthalpie - r _1w ^* Dimensionslose Verdampfungsenthalpie nachGl.(25) - u Geschwindigkeit in x-Richtung - v Geschwindigkeit in y-Richtung - x Längskoordinate - ¯x Längskoordinate für den Gegenstrom s. Bild 14 - x_A Wärmeisolierte Anlaufstrecke s. Bild 14 - x^* Dimensionslose Längskoordinate für das Dreipunkt-Differenzenverfahren x^*=x/_s - y Querkoordinate - y^* Normierte Querkoordinate für das Drei punkt-Differenzenverfahren y^*=y/_s - ₁ Dimensionslose Verdrängungsdicke nach Gl.(27) - ₂ Dimensionslose Impulsverlustdicke nach Gl.(28) - _c Konzentrationsgrenzschichtdicke (y-Wert für =0.99) - _s Strömungsgrenzschichtdicke (y-Wert für u/u=0.99) - _T Temperaturgrenzschichtdicke (y-Wert für = 0.99) - _T Dimensionsloser Wandabstand nach Gl.(37) - Normierte absolute Temperatur (= (T – T_w)/(T _{– T w}) - Wärmeleitfähigkeit - Dynamische Zähigkeit - Kinematische Zähigkeit - Dichte - Schubspannung - Allgemeine abhängige Variable (s. Tabelle 1) Normierte Massenkonzentration (=(c₁–c_1w/(c₁–c_1w)) - Nu Nußelt-Zahl (= L(T/yT/y)_w/(T–T_w)) - Pr Prandtl-Zahl (=c_p/) - Re_x Reynolds-Zahl (=ux/) - Re_L Reynolds-Zahl (=uL/) - Re_s Reynolds-Zahl (= u_s/) - Sc Schmidt-Zahl (=/D₁₂) - St_m Stanton-Zahl des Stoffübergangs nach Gl.(31) - St_T Stanton-Zahl des Wärmeübergangs nach Gl.(30) Indizes 0 Bezogen auf Strömung ohne Stoffübergang - 1 Gas 1 (Benzoldampf) - 2 Gas 2 (Luft) - Ungestörter Anströmzustand der Luft - ad Charakteristische Werte des adiabaten Strömungsfalles - Geg Charakteristische Werte des Gegenstroms - Gl Charakteristische Werte des Gleichstroms - j Diskreter Punkt in y-Richtung - k Diskreter Punkt in x-Richtung - w Werte an der Plattenoberfläche - + Werte an der benetzten Plattenoberseite - – Werte an der trockenen Plattenunterseite Auszug aus der von der Fakultät für Maschinenbau und Elektrotechnik der Technischen Universität Braunschweig zur Erlangung des akademischen Grades eines Doktor-Ingenieurs genehmigten Dissertation über Theoretische Untersuchung der laminaren Zweistoffgrenzschichtströmung längs einer benetzten, ebenen Platte bei nichtadiabater Verdunstung des Diplom-Ingenieurs Klaus Pientka. Berichterstatter: Prof. Dr. phil. Dr.-Ing. E.h. H. Schlichting und Prof. Dr.-Ing. D. Hummel. - Die Dissertation wurde am 14 Juni 1976 bei der Technischen Universität eingereicht. Die mündliche Prüfung fand am 23. November 1976 statt.     

Constituency measurements in the mixing region of a cross flow jet using a laser velocimeter

The velocities in the mixing region of a cross flow jet injected into a freestream were studied in detail with a laser velocimeter. Three jet to freestream momentum ratios were used (3.1, 8.1, 16.2). By purposely seeding the jet and freestream separately (as well as both simultaneously), marking the fluid was feasible. Thus, determining the velocities that emanated from the different streams was possible. By methodically analyzing the three sets of dependent data, the size and location of the mixing region was determined. The mixing regions for the three momentum ratios were found to be of different sizes and at different locations. By proper scaling, however, the regions for the three momentum ratios were found to collapse to one scaled region. Because of the intermittent behavior of the mixing, conventional turbulence models for such mixing may not be applicable; however, detailed velocities and turbulence quantities are included for benchmarking predictions.List of symbols B slot width - H channel height - MR momentum ratio, jet to free stream = _j V _j ²/ U ² - Re _H Reynolds number, U H/v - U free stream velocity - u axial velocity - u rms of axial velocity fluctuation - v transverse velocity - v rms of transverse velocity fluctuation - V _j slot exit transverse velocity - x axial direction (Fig. 3) - x _c x-center of mixing region - scaled value of x, = x/B - y transverse direction (Fig. 3) - y _c y-center of mixing region - scaled value of y, = y/ MRB - _x mixing region width in x-direction - _y mixing region width in y-direction - scaled mixing region width in x-direction, = _x /B - scaled mixing region width in y-direction, = _y / MRB - free stream density - _j slot exit density - v kinematic viscosity of freestream This research was sponsored in part by the Fulbright Commission (Bonn, Germany), the Institut für Thermische Strömungsmaschinen, Universität Karlsruhe (Karlsruhe, Germany), and the Rotating Machinery and Controls Industrial Research Program, University of Virginia (Charlottesville, VA, USA)