With reference particularly to the work of Peter Bradshaw and his associates, some remarks are made about the recovery of previously distorted shear flows. It is emphasized that such recovery is usually extremely slow, and this is further illustrated by new measurements of the velocity field and turbulence structure in the relaxing flow downstream of a separated region. Data have been obtained for downstream distances (x) up to about 20 times the length of the separated region (xr), or about 75 times the flow thickness at reattachment. This is a significantly more extensive region than has been previously studied, and the data are more comprehensive than any previously available.
It is shown that the recovery is even slower than previously surmized. Furthermore, the measurements demonstrate that the turbulence stresses eventually fall below standard boundary-layer values (at the same Reynolds number), although around reattachment they are very much higher, having values more akin to those in plane mixing layers. This undershoot is apparently a new finding and is argued to be a result of the influence of the outer part of the flow on the growing inner region. The usual log-law only begins to appear beyond x/xr = 2.5. It effectively “sees” a turbulent outer region that recovers even more slowly than itself, and the response of the inner region therefore has similarities to the response of an ordinary boundary layer to free-stream turbulence.
It is concluded that even current second-order (i.e., Reynolds stress) models may not capture the exquisitely slow decay of the strong, large eddy motions in the outer part of the flow and the subtleties of their influence on the inner region. 相似文献
The rheology of tetrafluoroethylene/hexafluoropropylene (TFE/HFP) copolymers, also known as Teflon FEP polymers, having different
molecular weight and composition (HFP content) was studied by means of a parallel-plate rheometer. Two groups of polymers
having different molecular weights with nearly constant polydispersity (around 2.5) were considered; namely, one group having
a relatively low melting temperature (amorphous with a high content of HFP) and a second group having a higher melting point
(semi-crystalline with a lower content of HFP). The relaxation time spectrum, H(λ), calculated by use of the BSW model (developed for monodisperse linear polymers) followed a scaling relationship in the
terminal zone with scaling exponent of 0.13. However, at higher frequencies the model fails to predict adequately the experimental
data. The longest relaxation time calculated from both the BSW model and discrete relaxation spectra (λi,gi), which was determined by use of a parsimonious fitting software, depends on the molecular weight in a similar way as the
zero-shear viscosity does with the well-established scaling factor of 3.4. The critical molecular weight for the onset of
entanglements, Mc, was found to be about 100000, a value much higher than those previously reported in literature for other polymers. The rheology
of resins in the second group (higher melting point) was found to exhibit a strong dependence on thermal history during oscillatory-shear
measurements. The data obtained in experiments at different temperatures without a preheating to a certain value (330°C) exhibited
a violation of the time-temperature superposition principle and no well-defined values of the zero-shear viscosity. This is
attributed to residual crystallinity even at temperatures well above their melting point (260°C). However, the same experiments
with preheating and subsequent cooling to desired temperature resulted into a very good time-temperature scaling.
Received: 13 January 1998 Accepted: 6 April 1998 相似文献
Based on the complex viscosity model various steady-state and transient material functions have been completed. The model is investigated in terms of a corotational frame reference. Also, BKZ-type integral constitutive equations have been studied. Some relations between material functions have been derived.
C–1
Finger tensor
-
F[], (F–1[])
Fourier (inverse) transform
-
rate of deformation tensor in corotating frame
-
h(I, II)
Wagner's damping function
-
J(x)
Bessel function
-
m
parameter inh (I, II)
-
m(s)
memory function
-
mk, nk
integers (powers in complex viscosity model)
-
P
principal value of the integral
-
parameter in the complex viscosity model
-
rate of deformation tensor
-
shear rates
-
[], []
incomplete gamma function
-
(a)
gamma function
-
steady-shear viscosity
-
*
complex viscosity
-
,
real and imaginary parts of
*
-
0
zero shear viscosity
-
+,
1+
stress growth functions
-
–,
1-
stress relaxation functions
-
(s)
relaxation modulus
-
1(s)
primary normal-stress coefficient
-
ø(a, b; z)
degenerate hypergeometric function
-
1, 2
time constants (parameters of
*)
-
frequency
-
extra stress tensor 相似文献
In the first part of this contribution, the Lie-symmetries of the principle of least action associated to the constitutive equations of the DNLR formalism of relaxation have been presented. We examine in this second part the continuous symmetries corresponding to the simple case of stress relaxation under isothermal conditions. The well-known principle of time/temperature equivalence is discussed in terms of variational symmetry for the Jacobi’s action functional, and connected to the Onsager’s relation near the thermodynamic equilibrium. 相似文献
Embedded vertical cracks are very often encountered in structural components necessitating reliable procedure for determining their size. Specialized ultrasonic techniques are required for estimation of through thickness height of these cracks [Mater. Eval. (1970) 28; J. NDI 26 (1977) 320; NND (1975) 146]. The conventional pulse-echo technique has serious limitations for quantitative estimation of vertical cracks because it is subject to variations due to reflectivity, coupling factors etc. The present study aims to improve the accuracy of embedded crack height measurement based on transit time rather than the reflected amplitude [NDT Int. (1982) 315; J. JSNDT 27 (1978) 118]. A unique method has been developed for generating known sizes of fatigue cracks ranging from 2.5 to 18 mm in height and 15 mm in length. These cracks were generated in rectangular steel specimens and subsequently embedded at predetermined locations using welding. These welded specimens containing the embedded vertical cracks were examined using ultrasonic techniques based on transit time like (a) flaw tip echo method and (b) mode conversion method. Using both the techniques excellent agreement was obtained between the estimated crack height and actual crack height with an accuracy of ±1 mm. 相似文献