LDA measurements in low Reynolds number turbulent boundary layer

LDA measurements of the mean velocity in a low Reynolds number turbulent boundary layer allow a direct estimate of the friction velocity U from the value of /y at the wall. The trend of the Reynolds number dependence of / is similar to the direct numerical simulations of Spalart (1988).     

Zum Impuls-, Wärme- und Stoffaustausch in turbulenten Strömungen reagierender Binärgemische

Zusammenfassung Die in Teil I vorgestellten Reynolds 'schen Gleichungen und Transportgleichungen werden für Strömungen mit Grenzschichtcharakter angegeben. Weiter werden Integralbedingungen mitgeteilt. Nach einer Diskussion über die Schließung des Gleichungssystems werden Lösungsverfahren besprochen. Dabei wird speziell auf Integralverfahren eingegangen.

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About the transfer of momentum, heat and mass in turbulent flows of binary mixturesPart II: Thin shear flow layers

The Reynolds equations and transport equations given in part I are presented for thin shear flow layers. Integral relations are given. After a discussion of the closure problem methods of solution are described. Specially integral methods are discussed.

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Formelzeichen c Massenkonzentration der Komponente - c_t charakteristische Konzentrationsschwankung - c_o Bezugskonzentration - c spezifische Wärme bei konstantem Druck - c_f Reibungsbeiwert - c_D Dissipationsintegral - c_E Entrainment-Funktion - c Schubspannungsintegral - D binsrer Diffusionskoeffizient - H Formparameter - H₁₂ Formparameter - H₃₂ Formparameter - j Kassendiffusionsstrom - L Bezugslänge - p Druck - p_t charakteristische Druckschwankung - p_o Bezugsdruck - Pr Prandtl-Zahl - q Wärmestrom - q²/2 kinetische Energie der Schwankungsbewegung - Re_L mit L gebildete Reynolds-Zahl - Re mit gebildete Reynolds-Zahl - Re₂ mit ₂ gebildete Reynolds-Zahl - Sc Schmidt-Zahl - T absolute Temperatur - T_t charakteristische TemperaturSchwankung - T_o Bezugstemperatur - u,v,w Geschwindigkeitskomponenten - u_t charakteristische Geschwindigkeitsschwankung - u_o Bezugsgeschwindigkeit - U=/ü dimensionslose. x-Komponente der Geschwindigkeit - x,y,z Komponenten des Ortsvektors Griechische Symbole Grenzschichtdicke - ₁ Verdrängungsdicke - ₂ Impulsverlustdicke - ₃ Energieverlustdicke - _T Enthalpieverlustdicke - _c Konzentrationsverlustdicke - =d/dx Parameter für die Grenzschichtabsch:atzung - turbulente Impulsaustauschgröße - _D turbulente Stoffaustauschgröße - _q turbulente Energieaustauschgröße - Dissipationsfunktion - Wärmeleitfähigkeit - dynamische Viskosität - v=/ kinematische Viskosität - Dichte - Produktionsdichte - Schubspannung Indizes mol molekularer Anteil - tur turbulenter Anteil - res resultierender Anteil - Außenrand der Grenzschicht - w Wand     

Turbulent boundary layer over a smooth wall with widely separated transverse square cavities

Laser-Doppler velocimetry (LDV) measurements and flow visualizations are used to study a turbulent boundary layer over a smooth wall with transverse square cavities at two values of the momentum thickness Reynolds number (R =400 and 1300). The cavities are spaced 20 element widths apart in the streamwise direction. Flow visualizations reveal a significant communication between the cavities and the overlying shear layer, with frequent inflows and ejections of fluid to and from cavities. There is evidence to suggest that quasi-streamwise near-wall vortices are responsible for the ejections of fluid out of the cavities. The wall shear stress, which is measured accurately, increases sharply immediately downstream of the cavity. This increase is followed by a sudden decrease and a slower return to the smooth wall value. Integration of the wall shear stress in the streamwise direction indicates that there is an increase in drag of 3.4% at bothR .Nomenclature C _f skin friction coefficient - C _fsw friction coefficient for a continuous smooth wall - k height of the cavity - k ⁺ ku / - R Reynolds number based on momentum thickness (U ₁ /v) - Rx Reynolds number based on streamwise distance (U ₁ x/) - s streamwise distance between two cavities - t time - t ⁺ tu ₂ / - U ₁ freestream velocity - mean velocity inx direction - u,v,w rms turbulent intensities inx,y andz directions - u local friction velocity - u _sw friction velocity for a continuous smooth wall - w width of the cavity - x streamwise co-ordinate measured from the downstream edge of the cavity - y co-ordinate normal to the wall - z spanwise co-ordinate - y ⁺ yu / - boundary layer thickness - ₀ boundary layer thickness near the upstream edge of the cavity - _i thickness of internal layer - kinematic viscosity of water - ⁺ zu / - momentum thickness     

A rotating hot-wire technique for spatial sampling of disturbed and manipulated duct flows

The documentation and control of flow disturbances downstream of various open inlet contractions was the primary focus with which to evaluate a spatial sampling technique. An X-wire probe was rotated about the center of a cylindrical test section at a radius equal to one-half that of the test section. This provided quasi-instantaneous multi-point measurements of the streamwise and azimuthal components of the velocity to investigate the temporal and spatial characteristics of the flowfield downstream of various contractions. The extent to which a particular contraction is effective in controlling ingested flow disturbances was investigated by artificially introducing disturbances upstream of the contractions. Spatial as well as temporal mappings of various quantities are presented for the streamwise and azimuthal components of the velocity. It was found that the control of upstream disturbances is highly dependent on the inlet contraction; for example, reduction of blade passing frequency noise in the ground testing of jet engines should be achieved with the proper choice of inlet configurations.List of symbols K _uv correlation coefficient= - P percentage of time that an azimuthal fluctuating velocity derivative dv/d is found - U streamwise velocity component U=U (, t) - V azimuthal or tangential velocity component due to flow and probe rotation V=V (, t) - mean value of streamwise velocity component - U _m resultant velocity from and - mean value of azimuthal velocity component induced by rotation - u fluctuating streamwise component of velocity u=u(, t) - v fluctuating azimuthal component of velocity v = v (, t) - u phase-averaged fluctuating streamwise component of velocity u=u(0) - v phase-averaged fluctuating azimuthal component of velocity v=v() - û average of phase-averaged fluctuating streamwise component of velocity (u()) over cases I-1, II-1 and III-1 û = û() - average of phase-averaged fluctuating azimuthal component of velocity (v()) over cases I-1, II-1 and III-1 - u fluctuating streamwise component of velocity corrected for non-uniformity of probe rotation and/or phase-related vibration u = u(0, t) - v fluctuating azimuthal component of velocity corrected for non-uniformity or probe rotation and/or phase-related vibration v=v (, t) - u ² rms value of corrected fluctuating streamwise component of velocity - rms value of corrected fluctuating azimuthal component of velocity - phase or azimuthal position of X-probe     

Instability of a plane axisymmetric flow with a shear discontinuity in the velocity profile

It is proposed to investigate the stability of a plane axisymmetric flow with an angular velocity profile (r) such that the angular velocity is constant when r < r_O – L and r > r_O + L but varies monotonically from ₁ to ₂ near the point r_O, the thickness of the transition zone being small L r_O, whereas the change in velocity is not small ¦₂ – ₁¦ ₂, ₁. Obviously, as L O short-wave disturbances with respect to the azimuthal coordinate (k=m/r_O 1/r_O) will be unstable with a growth rate-close to the Kelvin—Helmholtz growth rate. In the case L=O (i.e., for a profile with a shear-discontinuity) we find the instability growth rate _O and show that where the thickness of the discontinuity L is finite (but small) the growth rate does not differ from _O up to terms proportional to kL 1 and 1/m 1. Using this example it is possible to investigate the effect of rotation on the flow stability. It is important to note that stabilization (or destabilization) of the flow in question by rotation occurs only for three-dimensional or axisymmetric perturbations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 111–114, January–February, 1985.     

Analysis of slip and temperature jump coefficients in a binary gas mixture

The possibility of simplifying the formulas obtained by the Maxwell-Loyalka method for the velocity _u, temperature _T and diffusion _d slip coefficients and the temperature jump coefficient in a binary gas mixture with frozen internal degrees of freedom of the molecules is considered. Special attention is paid to gases not having sharply different physicochemical properties. The formulas are written in a form convenient for use without linearization in the thermal diffusion coefficient. They are systematically analyzed for mixtures of inert gases, N₂, O₂, CO₂, and H₂ at temperatures extending from room temperature to 2500°K. It is shown that for the molecular weight ratios m^* = m₂/m₁ considered the expressions for _u and can be radically simplified. With an error acceptable for practical purposes (up to 10%) it is possible to employ expressions of the same structural form as for a single-component gas: for _u if 1 m^* 6, and for if 1 m^* 3. When 1 m^* 2 the expression for _T can be simplified with a maximum error of 5%. Within the limits of accuracy of the method the expression for _t can be linearized in the thermal diffusion coefficient. An approximate expression convenient for practical calculations is proposed for _d Finally, the , _u, and _T for a single-component polyatomic gas with easy excitation of the internal degrees of freedom of the molecules are similarly analyzed; it is shown that these expressions can be considerably simplified.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 152–159, November–December, 1990.     

Transient laminar free convection in horizontal cylinders

A numerical study of laminar natural convection inside uniformly heated, partially or fully filled horizontal cylinders is made. A coordinate transformation which simplifies the discretization of the equations of motion and energy is utilized. The resulting system of partial differential equations with their boundary conditions is solved using central differences for various Prandtl and Grashof numbers for two different grid sizes. The flow in completely filled cylinders for which experimental data are available is predicted. Close agreement between steady-state predictions and experiments is obtained for temperature and velocity profiles as well as for the streamline contours and isotherms. The technique is further demonstrated by solving the transient natural convection flow inside a partially filled horizontal cylinder with an adiabatic free surface and subjected to uniform wall heating.

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Laminare freie Konvektion in horizontalen Zylindern

Zusammenfassung Es wurde eine numerische Berechnung der laminaren, freien Konvektion in gleichmäßig beheizten, teilweise oder ganz gefüllten, horizontalen Zylindern durchgeführt. Dabei wird eine Koordinatentransformation benützt, welche die Diskretisierung der Bewegungs- und der Energiegleichung vereinfacht. Das so resultierende System von partiellen Differentialgleichungen wird, zusammen mit seinen Randbedingungen, unter Verwendung einer Differenzenmethode für verschiedene Prandtl und Grashof-Zahlen sowie für zwei verschiedene Gittergrößen gelöst. Für den vollständig gefüllten Zylinder, für den experimentelle Daten verfügbar sind, wird die Strömung vorhergesagt. Dabei wird für stationäre Zustände gute Übereinstimmung zwischen Rechnung und Experiment erzielt. Dies gilt sowohl für den Verlauf der Stromlinien als auch für den der Isothermen. Das Verfahren wird weiterhin am Beispiel der Berechnung instationärer, freier Konvektion in einem partiell gefüllten, horizontalen Zylinder demonstriert, wobei eine adiabate, freie Oberfläche und gleichmäßige Beheizung der Wand angenommen sind.

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Nomenclature g acceleration due to gravity, m/s² - Gr _R ^* modified Grashof number =gqR⁴/kv² - Gr _R Grashof number =gTR³/v² - H heat function vector, dimensionless - k thermal conductivity, W/mK - L(Y) cord length associated with coordinateY, dimensionless - Pr Prandtl number=v/ - q wall heat flux, W/m² - R radius, m - r(X, Y,Z) distance of a boundary point from the reference axis, dimensionless - S vector derived from the flow field solution, dimensionless - T temperature, K - T _w wall temperature, K - T reference temperature, K - t time, s - u, v velocity components inx, y directions, m/s - U, V dimensionless velocity components inX- and Y-direction normalized withU - U reference velocity=gqR²/k or gTR, m/s - V velocity vector, dimensionless - W vorticity vector, dimensionless - W vorticity, dimensionless - x, y, z cartesian coordinates, m - X, Y, Z cartesian coordinates normalized with a reference length, dimensionless Greek letters thermal diffusivity, m²/s - coefficient of thermal expansion, K^–1 - ,,, non-dimensional coordinates in the transformed domain - non-dimensional temperature =(T–T)_k/q^R or T–T/T_w–T - v kinematic viscosity, m²/s - non-dimensional time=v/R² Gr_Rt or v/R² G _R ^* t - angle measured from the bottom of the cylinder, rads - ^* angle measured from the axis on (– ) plane, rads - heat potential, dimensionless - angle of incidence of the heat flux vector, rads - non-dimensional stream function - vector potential, dimensionless - grid size, dimensionless - ² Laplacian operator - gradient vector     

Swirling turbulent flow through a curved pipe

An experimental study of swirling turbulent flow through a curved bend and its downstream tangent has been carried out. This study reports on the recovery from swirl and bend curvature and relies on measurements obtained in the downstream tangent and data reported in Part 1 to assess the recovery. Unlike the nonswirling flow case, the present measurements show that the cross-stream secondary flow is dominated by the decay of the solid-body rotation and the total wall shear stress measured at the inner and outer bend (furthest away from the bend center of curvature) is approximately equal. The shear distribution is fairly uniform, even at 1 D downstream of the bend exit. At 49D downstream of the bend exit, the mean axial velocity has recovered to its measured profile at 18D upstream of the bend entrance. Furthermore, the mean tangential velocity is close to zero everywhere and the turbulent shear and normal stresses take another 15D to approximately approach their stationary straight pipe values. Therefore, complete flow recovery from swirl and bend curvature takes a total length of about 85D from the bend entrance. This compares with a recovery length of about 78D for bend curvature alone. The recovery length is substantially shorter than that measured previously in swirling flow through straight pipes and is a consequence of the angular momentum decreasing by approximately 74% across the curved bend. Consequently, the effect of bend curvature is to accelerate swirl decay in a pipe flow.List of symbols C _f total skin friction coefficient, = 2 _w / w ₀ ² - D pipe diameter, = 7.62 cm - De Dean number, = ^1/2 Re = 13,874 - M angular momentum - N _s swirl number, = D/2 W ₀ = 1 - r radial coordinate - R mean bend radius of curvature, = 49.5 cm - Re pipe Reynolds number, = DW ₀ /v= 50,000 - S axial coordinate along the upstream (measured negative) and downstream (measured positive) tangent - U, V, W mean velocities along the radial, tangential and axial directions, respectively - u, v, w mean fluctuating velocities along the radial, tangential and axial directions, respectively - u, v, w root mean square normal stress along the radial, tangential and axial directions, respectively - W ₀ mean bulk velocity, 10 m/s - w total wall friction velocity, = _w / - (w ) _s total wall friction velocity measured as S/D = -18 - turbulent shear stresses - pipe-to-bend radius ratio, = D/2R = 0.077 - axial coordinate measured from bend entrance - fluid kinetic viscosity - fluid density - _w total wall shear stress - azimuthal coordinate measured zero from pipe horizontal diameter near outer bend - angular speed of the rotating section     

The dynamics of solid-solid phase transitions 2. Incoherent interfaces

Incoherent phase transitions are more difficult to treat than their coherent counterparts. The interface, which appears as a single surface in the deformed configuration, is represented in its undeformed state by a separate surface in each phase. This leads to a rich but detailed kinematics, one in which defects such as vacancies and dislocations are generated by the moving interface. In this paper we develop a complete theory of incoherent phase transitions in the presence of deformation and mass transport, with phase interface structured by energy and stress. The final results are a complete set of interface conditions for an evolving incoherent interface.Frequently used symbols A_i,C_i generic subsurface of S_t - B_i undeformed phase-i region - C configurational bulk stress, Eshelby tensor - F deformation gradient - G inverse deformation gradient - H relative deformation gradient - J bulk Jacobian of the deformation - ¯K, K_i total (twice the mean) curvature of and S_i - Lin (U, V) linear transformations from U into V - Lin⁺ linear transformations of ³ with positive determinant - Orth⁺ rotations of ³ - Q^a external bulk mass supply of species a - ¯S bulk Cauchy stress tensor - S bulk Piola-Kirchhoff stress tensor - S_i undeformed phase i interface - U_i relative velocity of S_i - Unim⁺ linear transformations of ³ with unit determinant - ¯V, V_i normal velocity of and S_i - intrinsic edge velocity of S and A _i S - W_i volume flow across the phase-i interface - X material point - b external body force - e internal bulk configurational force - f_i external interfacial force (configurational) - ¯g external interfacial force (deformational) - grad, div spatial gradient and divergence - gradient and divergence on - h relative deformation - h^a, diffusive mass flux of species a and list of mass fluxes - ¯m outward unit normal to a spatial control volume - ¯n, n_i unit normal to and S_i - n subspace of ³ orthogonal to n - ¯q^a external interfacial mass supply of species a - s ......... - ¯v, v_i compatible velocity fields of and S_i - ¯w, w_i compatible edge velocity fields for and A_i - x spatial point - y_i deformation or motion of phase i - y^. material velocity - generic subsurfaces of - , _i deformed body and deformed phase-i region - () energy supplied to by mass transport - symmetry group of the lattice - _i, surface jacobians - lattice - () power expended on - spatial control volume - S deformed phase interface - lattice point density - interfacial power density - , A total surface stress - C configurational surface stress for phase 1 (material) - ¯C_i configurational surface stress (spatial) - F_i tangential deformation gradient - G_i inverse tangential deformation gradient - H incoherency tensor - ¯1(x), 1_i(X) inclusions of ¯n(x) and n _i (X) into ³ - K configurational surface stress for phase 2 (material) - ¯L, l_i curvature tensor of and S_i - ¯P(x), P_i(X) projections of ³ onto ¯n(x) and n_i (X) - ¯S, S deformational surface stress (spatial and material) - ¯a, a normal part of total surface stress - c normal part of configurational surface stress for phase 1 (material) - e_i internal interfacial configurational force - ¯v, v_i unit normal to and A _i - (x),_i(X) projections of ³ onto ¯n(x) and n _i (X) - _i normal internal force (material) - bulk free energy - slip velocity - _i=(–1)ⁱ _i ......... - ^a, chemical potential of species a and list of potentials - ^a, bulk molar density of species a and list of molar densities - _i normal internal force (spatial) - surface tension - , _i effective shear - referential-to-spatial transform of field - interfacial energy - grand canonical potential - l unit tensor in ³ - x, vector and tensor product in ³ - (...)^., _t(...) material and spatial time derivative - , Div material gradient and divergence - gradient and divergence on S_i - (...), (...) normal time derivative following and S_i - (...) limit of a bulk field asx ,x_i - [...],...> jump and average of a bulk field across the interface - (...)_ext extension of a surface tensor to ³ - tangential part of a vector (tensor) on and S_i     

A noninvasive method for the measurement of flow-induced surface displacement of a compliant surface

A noninvasive optical method is described which allows the measurement of the vertical component of the instantaneous displacement of a surface at one or more points. The method has been used to study the motion of a passive compliant layer responding to the random forcing of a fully developed turbulent boundary layer. However, in principle, the measurement technique described here can be used equally well with any surface capable of scattering light and to which optical access can be gained. The technique relies on the use of electro-optic position-sensitive detectors; this type of transducer produces changes in current which are linearly proportional to the displacement of a spot of light imaged onto the active area of the detector. The system can resolve displacements as small as 2 m for a point 1.8 mm in diameter; the final output signal of the system is found to be linear for displacements up to 200 m, and the overall frequency response is from DC to greater than 1 kHz. As an example of the use of the system, results detailing measurements obtained at both one and two points simultaneously are presented.List of symbols C _t elastic transverse wave speed = (G/)^1/2 - d ⁺ spot diameter normalized by viscous length scale - G frequency average of G() - G() shear storage modulus - G() shear loss modulus - l. viscous length scale = v/u _* - N total number of sampled data values - r separation vector for 2-point measurements = (, ) - rms root-mean-square value - R momentum thickness Reynolds number = U _t8/v - t time - u (y) mean streamwise component of velocity in boundary layer - u _* friction velocity = (t _w/)^1/2 - U free-stream velocity - x, y, z longitudinal, normal and spanwise directions - y _o undisturbed surface position - vertical component of compliant surface displacement - ₉₉ boundary layer thickness for which u(y) = 0.99 U _t8 - _l viscous sublayer thickness 5 l _* - frequency average of G()/ - boundary layer momentum thicknes = - fluid dynamic viscosity - v fluid kinematic viscosity = / - , longitudinal, spanwise components of separation vector r - fluid density - time delay - _w wall shear stress     

LDV measurements of a turbulent air-solid two-phase flow in a 90° bend

Simultaneous measurements of the mean streamwise and radial velocities and the associated Reynolds stresses were made in an air-solid two-phase flow in a square sectioned (10×10 cm) 90° vertical to horizontal bend using laser Doppler velocimetry. The gas phase measurements were performed in the absence of solid particles. The radius ratio of the bend was 1.76. The results are presented for two different Reynolds numbers, 2.2×10⁵ and 3.47×10⁵, corresponding to mass ratios of 1.5×10^–4 and 9.5×10^–5, respectively. Glass spheres 50 and 100 m in diameter were employed to represent the solid phase. The measurements of the gas and solid phase were performed separately. The streamwise velocity profiles for the gas and the solids crossed over near the outer wall with the solids having the higher speed near the wall. The solid velocity profiles were quite flat. Higher negative slip velocities are observed for the 100 m particles than those for the 50 gm particles. At angular displacement =0°, the radial velocity is directed towards the inner wall for both the 50 and 100 m particles. At =30° and 45°, particle wall collisions cause a clear change in the radial velocity of the solids in the region close to the outer wall. The 100 m particle trajectories are very close to being straight lines. Most of the particle wall collisions occur between the =30° and 60° stations. The level of turbulence of the solids was higher than that of the air.List of symbols D hydraulic diameter (100 mm) - De Dean number,De = - mass flow rate - number of particles per second (detected by the probe volume) - r radial coordinate direction - r _i radius of curvature of the inner wall - r ₀ radius of curvature of the outer wall - r ^* normalized radial coordinate, - R mean radius of curvature - Re Reynolds number, - R _r radius ratio, - U ,U _z mean streamwise velocity - U _r ,U _y mean radial velocity - U _b bulk velocity - , _z rms fluctuating streamwise velocity - _r , _y rms fluctuating radial velocity - -r shear stress component - z-y shear stress component - x spanwise coordinate direction - x ^* normalized spanwise coordinate, - y radial coordinate direction in straight ducts - y ^* normalized radial coordinate in straight ducts, - z streamwise coordinate direction in straight ducts - z ^* normalized streamwise coordinate in straight ducts, Greek symbols streamwise coordinate direction - kinematic viscosity of air     

Uniformly convergent difference method for the convection-diffusion singular perturbation problem in a curved boundary region

In this paper we construct a difference scheme for the convection-diffusion singular perturbation problem in a convex curved boundary region, and discuss the uniform convergence of its solution. We have proved that the order of uniform convergence of its solution isO (h +^/2) (0<<1/2), where h, are the mesh steps in the space and time directions respectively.     

Nonlinear rheological behavior of a concentrated spherical silica suspension

Linear and nonlinear viscoelastic properties were examined for a 50 wt% suspension of spherical silica particles (with radius of 40 nm) in a viscous medium, 2.27/1 (wt/wt) ethylene glycol/glycerol mixture. The effective volume fraction of the particles evaluated from zero-shear viscosities of the suspension and medium was 0.53. At a quiescent state the particles had a liquid-like, isotropic spatial distribution in the medium. Dynamic moduli G^* obtained for small oscillatory strain (in the linear viscoelastic regime) exhibited a relaxation process that reflected the equilibrium Brownian motion of those particles. In the stress relaxation experiments, the linear relaxation modulus G(t) was obtained for small step strain (0.2) while the nonlinear relaxation modulus G(t, ) characterizing strong stress damping behavior was obtained for large (>0.2). G(t, ) obeyed the time-strain separability at long time scales, and the damping function h() (–G(t, )/G(t)) was determined. Steady flow measurements revealed shear-thinning of the steady state viscosity () for small shear rates (< ^–1; = linear viscoelastic relaxation time) and shear-thickening for larger (>^–1). Corresponding changes were observed also for the viscosity growth and decay functions on start up and cessation of flow, + (t, ) and _– (t, ). In the shear-thinning regime, the and dependence of ₊(t,) and _–(t,) as well as the dependence of () were well described by a BKZ-type constitutive equation using the G(t) and h() data. On the other hand, this equation completely failed in describing the behavior in the shear-thickening regime. These applicabilities of the BKZ equation were utilized to discuss the shearthinning and shear-thickening mechanisms in relation to shear effects on the structure (spatial distribution) and motion of the suspended particles.Dedicated to the memory of Prof. Dale S. Parson     

Analysis of melt spinning transients in Lagrangian coordinates

Transients in melt spinning of isothermal power law and Newtonian fluids were found to be governed by an extremely simple partial differential equation ² ( ^1/n )/() = 0 in Lagrangian coordinates where is the cross-sectional area,n the power law exponent, the time and the the time at which a fluid molecule constituting the spinline left the spinneret. The general integral ^1/n =f() +g () of the above governing equation containing two arbitrary functions represents physically attainable spinline transients. Hitherto unknown analytical transient solutions of the above governing equation were obtained for the response of isothermal constant tension spinlines to a stepwise change in tension, spinneret hole area, extrusion speed or extrusion viscosity and for the starting transient in gravitational spinning. Linearized perturbation solutions and the stability limit of the spinline derived from the above new found nonlinear solutions were in agreement with previous findings and the above nonlinear response of the spinline to a step increase in the spinneret hole area was found to be equivalent to Orowan's tandem cylinder model of dent growth in filament stretching.     

Eine Methode zur Bestimmung des Transportkoeffizienten bei nichtlinearen Transportvorgängen

Zusammenfassung Es wird gezeigt, daß man nichtlineare Transportkoeffizienten aus Potentialprofilmessungen auch ohne die Lösung der nichtlinearen Transportgleichung bestimmen kann. Die Methode wird auf zwei Ziegeltone angewendet, deren Feuchtigkeitsdiffusionskoeffizienten recht komplizierte Funktionen des Feuchtegehaltes sind. Die Ergebnisse werden mit den Ergebnissen aus einer numerischen Lösung für einen empirischen Ansatz nach Fujita verglichen.

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A method for evaluation of conductive properties in nonlinear transport phenomena

A prediction procedure for the conductive properties based upon the measured data on potential field has been developed. The method is particularly related to the nonlinear phenomena when the analytical solution is not available. The approach proposed is applied to the determination of the moisture diffusivity for two kinds of brick clay that posses a pronounced dependance of properties on moisture content. The results are used for Fujita's numerical solution which is compared with measured moisture field. The comparison has been performed and an agreement was found.

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Bezeichnungen u [kg_w/kg_s] Feuchtigkeit bezogen auf trockene Substanz - w [kg_w/kg_s] nach Gl. (10) - V allgemeines Potential - _s, _so [kg_s/m³] Dichte des trockenen Skeletts - D, D₀ [m²/s] isotherme Feuchteleitkoeffizient; Diffusionskoeffizient - x [m] Koordinate längs Zylinder - , ₀ [s] Zeit - J_w [kg_w /m²s] Feuchtestrom - , Koeffizienten der allgemeinen Leitungsgleichung (4) - A, B, Konstanten der Gl. (6) - , Konstanten der Gl. (7) auch der Gl. (12) - d [m] Zylinderdurchmesser - PE Petrovaradin - SK Sremski Karlovci     

Rheologie pathologischer Gelenkflüssigkeiten

Zusammenfassung Die eingehende Analyse des viskoelastischen Verhaltens von 193 Kniegelenkspunktaten verschiedenster entzündlicher und nichtentzündlicher Gelenkerkrankungen ließ keine wesentlichen diagnostischen Hilfen für klinische Problemfälle erkennen. Untersucht wurden im einzelnen Fließkurven einschließlich der Anfangsviskosität ₀ und durch eine Normierungsmethode ermittelte master-curves, sowie Normalspannungen und in 3 Fällen gleichzeitig auch der SpeichermodulG und der VerlustmodulG mit Hilfe von dynamischen Messungen.Durch Vergleich der pathologischen Gelenkpunktate mit normaler, post mortal gewonnener gepoolter Synovia ließ sich ein Eindruck vom Grad der gestörten Viskoelastizität gewinnen. Dabei lassen die erniedrigten Hyaluronsäure-Konzentrationen, die Veränderungen der konzentrationsunabhängigen Knickzeitt _k> und die master-curve erkennen, daß hierfür sowohl eine verringerte Konzentration als auch ein geringeres Molekulargewicht der Hyaluronsäure verantwortlich ist. Konzentrierungsversuche pathologischer Synovia ergaben den Hinweis auf die Entstehung von Mikrogelen und ließen in Fällen zuvor fehlender Normalspannungen auch nach der Eindickung keine Normalspannungen erkennen. Es wird deshalb auch die Möglichkeit gestörter intermolekularer Interaktionen in der pathologischen Synovia diskutiert.

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Summary A thorough analysis of the viscoelastic behaviour of 193 synovial fluid samples of knee joints concerning different joint diseases (inflammatory and non-inflammatory) gives no essential diagnostic help in case of clinical problems.Investigations were done particularly on flow curves including the Newtonian viscosity ₀ and normal forces, and with the help of a standardization-method we got master curves. In three cases we also got dynamic properties i.e. the elastic modulusG and the loss modulusG. By comparison of the pathological synovial fluid samples with normal, post-mortem pooled synovial fluid one gets an idea of the degree of disturbance on viscoelasticity. It was found that the reduced concentration and the lower molecular weight of the hyaluronic acid are responsible for the pathological variation of the concentration independent bending timet _k as well as the shape of the master curves.Tests on concentrated pathological synovial fluids indicate the beginning formation of micro-gels. In cases of absence of normal forces even after concentration no normal forces could be detected. Therefore the possibility of disturbed intermolecular interactions in pathological synovial fluids will be discussed, too.

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D Schergeschwindigkeit - D _K D-Koordinate des Tangentenschnittpunktes - t _k Knickzeit - s Steigung des geradlinigen Anteils der Fließkurve - scheinbare Viskosität - _m mittlere Viskosität beiD = 10² s^–1 - ₀ Anfangsviskosität, Nullviskosität - Endviskosität - _{N 11} – ₂₂ 1. Normalspannungsdifferenz - G ₀ Ruheschermodul - G ^* komplexer (dynamischer) Schermodul - G Speichermodul - G Verlustmodul - Winkelgeschwindigkeit - Winkel der Phasendifferenz - Kegelwinkel - d Durchmesser von Kegel und Platte des Meßsystems - f Frequenz der vorgegebenen Oszillation - f _n Eigenfrequenz des Torsionskopfes - _IA Amplitude der Eingangsschwingung - _TA Amplitude der Ausgangsschwingung - _I axiale Bewegung der Schneckenwelle - _T Bewegung des Torsionskopfverminderers - [] Grenzviskositätszahl (Staudinger-Index) - v Verhängungszahl - r Korrelationskoeffizient - m Mittelwert - s Standardabweichung - p Signifikanzniveau - n.s. nicht signifikant p > 0,05 Auszugsweise vorgetragen auf der Jahrestagung der Deutschen Rheologischen Gesellschaft in Berlin vom 8.–10. Mai 1978.Mit 9 Abbildungen und 8 Tabellen     

A note on three-dimensional boundary layer growth

Summary This note is an extension of the work of Görtler²) on two-dimensional boundary layer growth to the three-dimensional case. The solutions of three-dimensional boundary layer equations are obtained by considering the potential flow of the body to be governed by the functions At U ₀(, ) and At U ₀(, ) where is any positive number.     

Momentum balance in highly distorted turbulent pipe flows

An in depth study into the development and decay of distorted turbulent pipe flows in incompressible flow has yielded a vast quantity of experimental data covering a wide range of initial conditions. Sufficient detail on the development of both mean flow and turbulence structure in these flows has been obtained to allow an implied radial static pressure distribution to be calculated. The static pressure distributions determined compare well both qualitatively and quantitatively with earlier experimental work. A strong correlation between static pressure coefficient Cp and axial turbulence intensity is demonstrated.List of symbols C _p static pressure coefficient = (pw-p)/1/2 - D pipe diameter - K turbulent kinetic energy - (r, , z) cylindrical polar co-ordinates. / 0 - R, y pipe radius, distance measured from the pipe wall - U, V axial and radial time mean velocity components - mean value of u - u, u/ , / - u, , w fluctuating velocity components - axial, radial turbulence intensity - turbulent shear stress - u friction velocity, (u ² = ₀/p) - ₀ wall shear stress - ^* boundary layer thickness A version of this paper was presented at the Ninth Symposium on Turbulence, University of Missouri-Rolla, October 1–3, 1984     

Analysis of suddenly started laminar flow in the entrance region of a circular tube

Suddenly started laminar flow in the entrance region of a circular tube, with constant inlet velocity, is investigated analytically by using integral momentum approach. A closed form solution to the integral momentum equation is obtained by the method of characteristics to determine boundary layer thickness, entrance length, velocity profile, and pressure gradient.Nomenclature M(, , ) a function - N(, , ) a function - p pressure - p* p/1/2U ², dimensionless pressure - Q(, , ) a function - R radius of the tube - r radial distance - Re 2RU/, Reynolds number - t time - U inlet velocity, constant for all time, uniform over the cross section - u velocity in the boundary layer - u* u/U, dimensionless velocity - u ₁ velocity in the inviscid core - x axial distance - y distance perpendicular to the axis of the tube - y* y/R, dimensionless distance perpendicular to the axis - boundary layer thickness - * displacement thickness - /R, dimensionless boundary layer thickness - momentum thickness - absolute viscosity of the fluid - /, kinematic viscosity of the fluid - x/(R Re), dimensionless axial distance - density of the fluid - tU/(R Re), dimensionless time - _w wall shear stress