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Rapid extensional flows of polymer-thickened motor oils through a small orifice
92
Journal
of Non-Newtonian
0 Elsevier
Scientific
Fluid
Publishing
Short Communication _~_______.._~_
Mechanics,
Company,
3 (1977/1978) 92-96 Amsterdam - Printed in The Netherlands
_ _~~~__ ~_~~~~.~
~~ ___.~~~_ ~.
RAPID EXTENSIONAL FLOWS OF POLYMER-THICKENED MOTOR OILS THROUGH A SMALL ORIFICE
D.R. OLIVER Department Birmingham
(Received
and R.C. ASHTON
of Chemical Engineering, (Gt. Britain)
February
University
of Birmingham,
1,1977)
Introduction
In previous work [ 11, polymer-thickened oils were subjected to rapid stretching flows by the use of contoured nozzles. The axial stress in the fluid was measured by comparing the jet thrust [2,3] of a polymer-thickened oil with that of the base oil at similar Reynolds numbers. Values of polymer-induced stress approaching lo5 dyn cmA2 were obtained at extensional strain rates of lo3 s-l and nozzle exit velocities of 800 cm s-l. It was suggested that the deformation was on an elastic nature, the stress being controlled by the strain rather than by the strain rate. Under these circumstances, nozzle shape becomes less important and the change of fluid velocity (contrclling principal extension) becomes the dominant influence. Thus, tests using a small orifice and velocities up to 4000 cm s- ’ have been performed on the oils in order to develop greater stresses and to further investigate the stress/strain relationship. Apparatus
The jet thrust apparatus has been described previously [ 11. A single new brass orifice has been made, of diameter 0.034 cm and length 0.029 cm. There is no surface shaping, and the orifice is merely a cylindrical hole through a flat plate. Liquids used
These were (225°C): (a) Iranian Light oil (0.5 poise, 0.8604 g/ml); (b) an Iranian Light oil/Shell oil 30 mixture (1.4 poise, 0.8890 g/ml);
93
(c) Iranian Light oil + 2% polymer (0.89 poise at lo* s-l, n = 0.95, 0.8647 g/ml); (d) Gas oil + 3.5% polymer (0.56 poise at lo4 s-l, n = 0.88, 0.8725 g/ml) The polymer is the same (styrene-butadiene copolymer) as used in earlier work [ 11. It was supplied by Shell’s Thornton Research Centre. Method
of calculation
of results
The extensional strain rate in the liquid approaching the hole is unknown because the flow pattern cannot be observed. The axial stress is related to the orifice exit velocity and to the Green measure of axial strain To, i.e. 3((ur2/uz2) - 1). The axial stress in the test liquid at the nozzle exit is taken as rll = (TIE T)/A, where T is the measured thrust, T,, is the thrust of a jet of inelastic liquid of similar density at the same Reynolds number and A is the crosssectional area of the orifice [ 11. Results Figure 1 shows the jet thrust results plotted non-dimensionally against the Reynolds number, using as a basis, TFT , the theoretical thrust of an inelastic liquid having a flat-topped velocity profile and the same density and velocity as the test liquid. Figure 2 shows values of the polymer-induced axial stress rii for the two doped oils as a function of orifice exit velocity, whilst Fig. 3 shows the same results plotted as a function of extensional strain To. As
I
I
IO
30
I 100 Re
Fig. 1. Normalised
jet thrust
as function
of Reynolds
number.
I 300
o 2x
I
POLYMER/IRANIAN
1.
LIGHT
o 3.S~PCWMEfQ’GASOk
8 /
4 /
x /
--
I
I /
3.5% P%LTMER/ iRANiAN ,@EF: 1 ,UNIAXIAC IO’
LIGHT N?ZZl 104
V, (CM. SEC-‘)
Fig, 2. Axial stress as a function, of orifice velocity.
3
IO
IOJ
Fig. 3. Axiat stress as R Function of the Green measure of axial strain,
95
in earlier work [ 11, elastic deformation is presumed to become above a velocity uz of 118 cm s-i and this is used in obtaining Discussion
dominant
yo .
of results
The jet thrust data for undoped oils (Fig. 1) show a consistent trend up to a Reynolds number of 130, when the sudden formation of a vena contracta causes the jet thrust to rise rapidly. This tendency has been noticed in other measurements and the data so affected are not used for jet thrust comparisons. The fall in jet thrust which occurs at low Reynolds numbers may be caused by the extensional flow which must necessarily occur upstream of an orifice for Newtonian liquids. In the case of oil (b), the average semi-angles of convergence of the liquid necessary to give the observed thrust deductions vary from 6” to 24”) with an extensional viscosity of three times the shear viscosity. Although Newtonian fluids do not converge towards orifices at well-defined angles, reasonable values of the mean semi-angles lend support to the suggestion that axial stress is present in Newtonian liquids following the convergent flow into the orifice. The polymer-doped oils show non-dimensional jet thrust levels some lo20% below those of the straight oils and, at the upper jet, velocities become almost independent of Reynolds number. This implies that the axial stress in the fluid is rising approximately as ui2, since both T and TIE are functions of pur 2. Figure 2 illustrates this behaviour and compares the results with earlier data obtained in uniaxial, contoured nozzles for Iranian Light oil containing 3.5% polymer *. The agreement is fair, in view of the different nozzle geometries involved, the new data being of particular interest in showing that the relationship between rll and u1 extends to stress levels as high as 2 X 10” dyn/cm2. Polymer degradation, which may occur at these stress levels, was not investigated at this stage, the oils being passed only once through the orifice. The relationship between axial stress 7 i1 and the Green measure of strain To (Fig. 3) takes the form 7 11 = 7400y,“‘go
(I)
for the 3.5% doped oil. The data lie above the earlier data [l] for 3.5% polymer doped Iranian Light oil in uniaxial extensional flow, but slightly below comparable data for biaxial extensional flow. The use of the same value of uz as in earlier work is open to question, but has the advantage that all data are treated in a consistent manner. Figures 2 and 3 show that the stress in doped oils continues to rise in a predictable way with increase in
* This formulation could not be duplicated to the development of pressures in excess equipment.
exactly when using the small orifice, due of 300 p.s.i., which was a limit for the
96
velocity and extensional strain. The principal extension ratio (ul/uE) has a value of 35. These experiments are relevant to lubrication situations where stretching flows are important, e.g. in squeeze films, where work by Walters et al. 141 and by the authors [5] has shown that polymeric additives may improve the load bearing capacity. This improvement is greatly in excess of any change which can be explained on the basis of Newtonian fluid characteristics. Conclusions A small jet-thrust orifice operating at high fluid exit velocities has been used to demonstrate the existence of axial stresses in stretching polymerdoped oils an order of magnitude higher than values previously reported [ 11. The stress is a function of axial strain; it is suggested that this will have a bearing on the lubricating properties of the oils in flow situations where extensional deformation is present. Nomenclature Flow behaviour index of Power-Law fluid Cross-sectional area of the orifice T Measured thrust of jet T” Measured thrust of jet, corrected for surface tension effects Theoretical thrust of an inelastic liquid having a flat-topped velocity TFT profile and the same velocity and density as the liquid under test T IE Thrust of a jet of inelastic liquid of similar density, viscosity and velocity as the liquid under test Velocity of liquid in orifice Ul Velocity of liquid for which elastic component of stress first becomes UE significant Re Reynolds number for liquid in orifice, based on orifice diameter Green measure of axial strain, $ ~(u~‘/u~~) - 1) 7G Density of oil in use P Density of water Pw Axial stress, in 11 direction, in liquid at orifice exit 711 References D.R. Oliver and R.C. Ashton, The flow of polymer-thickened motor oils in convergent jet thrust nozzles, J. Non-Newtonian Fluid Mech., 2 (1977) 367. J.M. Davies, J.F. Hutton and K. Walters, Colloq. Int. C.N.R.S., No. 233, Polymires et Lubrification, Paris, 1975, p. 61. D.T.G. Morgan and K. Pannell, Rheol. Acta, 11 (X972) 185. G. Brindley, J.M. Davies and K. Walters, J. Non-Newtonian Fluid Mech., 1 (1976) 19. G. Wadelin and D.R. Oliver. Work as yet unpublished.
Journal
of Non-Newtonian
0 Elsevier
Scientific
Fluid
Publishing
Short Communication _~_______.._~_
Mechanics,
Company,
3 (1977/1978) 92-96 Amsterdam - Printed in The Netherlands
_ _~~~__ ~_~~~~.~
~~ ___.~~~_ ~.
RAPID EXTENSIONAL FLOWS OF POLYMER-THICKENED MOTOR OILS THROUGH A SMALL ORIFICE
D.R. OLIVER Department Birmingham
(Received
and R.C. ASHTON
of Chemical Engineering, (Gt. Britain)
February
University
of Birmingham,
1,1977)
Introduction
In previous work [ 11, polymer-thickened oils were subjected to rapid stretching flows by the use of contoured nozzles. The axial stress in the fluid was measured by comparing the jet thrust [2,3] of a polymer-thickened oil with that of the base oil at similar Reynolds numbers. Values of polymer-induced stress approaching lo5 dyn cmA2 were obtained at extensional strain rates of lo3 s-l and nozzle exit velocities of 800 cm s-l. It was suggested that the deformation was on an elastic nature, the stress being controlled by the strain rather than by the strain rate. Under these circumstances, nozzle shape becomes less important and the change of fluid velocity (contrclling principal extension) becomes the dominant influence. Thus, tests using a small orifice and velocities up to 4000 cm s- ’ have been performed on the oils in order to develop greater stresses and to further investigate the stress/strain relationship. Apparatus
The jet thrust apparatus has been described previously [ 11. A single new brass orifice has been made, of diameter 0.034 cm and length 0.029 cm. There is no surface shaping, and the orifice is merely a cylindrical hole through a flat plate. Liquids used
These were (225°C): (a) Iranian Light oil (0.5 poise, 0.8604 g/ml); (b) an Iranian Light oil/Shell oil 30 mixture (1.4 poise, 0.8890 g/ml);
93
(c) Iranian Light oil + 2% polymer (0.89 poise at lo* s-l, n = 0.95, 0.8647 g/ml); (d) Gas oil + 3.5% polymer (0.56 poise at lo4 s-l, n = 0.88, 0.8725 g/ml) The polymer is the same (styrene-butadiene copolymer) as used in earlier work [ 11. It was supplied by Shell’s Thornton Research Centre. Method
of calculation
of results
The extensional strain rate in the liquid approaching the hole is unknown because the flow pattern cannot be observed. The axial stress is related to the orifice exit velocity and to the Green measure of axial strain To, i.e. 3((ur2/uz2) - 1). The axial stress in the test liquid at the nozzle exit is taken as rll = (TIE T)/A, where T is the measured thrust, T,, is the thrust of a jet of inelastic liquid of similar density at the same Reynolds number and A is the crosssectional area of the orifice [ 11. Results Figure 1 shows the jet thrust results plotted non-dimensionally against the Reynolds number, using as a basis, TFT , the theoretical thrust of an inelastic liquid having a flat-topped velocity profile and the same density and velocity as the test liquid. Figure 2 shows values of the polymer-induced axial stress rii for the two doped oils as a function of orifice exit velocity, whilst Fig. 3 shows the same results plotted as a function of extensional strain To. As
I
I
IO
30
I 100 Re
Fig. 1. Normalised
jet thrust
as function
of Reynolds
number.
I 300
o 2x
I
POLYMER/IRANIAN
1.
LIGHT
o 3.S~PCWMEfQ’GASOk
8 /
4 /
x /
--
I
I /
3.5% P%LTMER/ iRANiAN ,@EF: 1 ,UNIAXIAC IO’
LIGHT N?ZZl 104
V, (CM. SEC-‘)
Fig, 2. Axial stress as a function, of orifice velocity.
3
IO
IOJ
Fig. 3. Axiat stress as R Function of the Green measure of axial strain,
95
in earlier work [ 11, elastic deformation is presumed to become above a velocity uz of 118 cm s-i and this is used in obtaining Discussion
dominant
yo .
of results
The jet thrust data for undoped oils (Fig. 1) show a consistent trend up to a Reynolds number of 130, when the sudden formation of a vena contracta causes the jet thrust to rise rapidly. This tendency has been noticed in other measurements and the data so affected are not used for jet thrust comparisons. The fall in jet thrust which occurs at low Reynolds numbers may be caused by the extensional flow which must necessarily occur upstream of an orifice for Newtonian liquids. In the case of oil (b), the average semi-angles of convergence of the liquid necessary to give the observed thrust deductions vary from 6” to 24”) with an extensional viscosity of three times the shear viscosity. Although Newtonian fluids do not converge towards orifices at well-defined angles, reasonable values of the mean semi-angles lend support to the suggestion that axial stress is present in Newtonian liquids following the convergent flow into the orifice. The polymer-doped oils show non-dimensional jet thrust levels some lo20% below those of the straight oils and, at the upper jet, velocities become almost independent of Reynolds number. This implies that the axial stress in the fluid is rising approximately as ui2, since both T and TIE are functions of pur 2. Figure 2 illustrates this behaviour and compares the results with earlier data obtained in uniaxial, contoured nozzles for Iranian Light oil containing 3.5% polymer *. The agreement is fair, in view of the different nozzle geometries involved, the new data being of particular interest in showing that the relationship between rll and u1 extends to stress levels as high as 2 X 10” dyn/cm2. Polymer degradation, which may occur at these stress levels, was not investigated at this stage, the oils being passed only once through the orifice. The relationship between axial stress 7 i1 and the Green measure of strain To (Fig. 3) takes the form 7 11 = 7400y,“‘go
(I)
for the 3.5% doped oil. The data lie above the earlier data [l] for 3.5% polymer doped Iranian Light oil in uniaxial extensional flow, but slightly below comparable data for biaxial extensional flow. The use of the same value of uz as in earlier work is open to question, but has the advantage that all data are treated in a consistent manner. Figures 2 and 3 show that the stress in doped oils continues to rise in a predictable way with increase in
* This formulation could not be duplicated to the development of pressures in excess equipment.
exactly when using the small orifice, due of 300 p.s.i., which was a limit for the
96
velocity and extensional strain. The principal extension ratio (ul/uE) has a value of 35. These experiments are relevant to lubrication situations where stretching flows are important, e.g. in squeeze films, where work by Walters et al. 141 and by the authors [5] has shown that polymeric additives may improve the load bearing capacity. This improvement is greatly in excess of any change which can be explained on the basis of Newtonian fluid characteristics. Conclusions A small jet-thrust orifice operating at high fluid exit velocities has been used to demonstrate the existence of axial stresses in stretching polymerdoped oils an order of magnitude higher than values previously reported [ 11. The stress is a function of axial strain; it is suggested that this will have a bearing on the lubricating properties of the oils in flow situations where extensional deformation is present. Nomenclature Flow behaviour index of Power-Law fluid Cross-sectional area of the orifice T Measured thrust of jet T” Measured thrust of jet, corrected for surface tension effects Theoretical thrust of an inelastic liquid having a flat-topped velocity TFT profile and the same velocity and density as the liquid under test T IE Thrust of a jet of inelastic liquid of similar density, viscosity and velocity as the liquid under test Velocity of liquid in orifice Ul Velocity of liquid for which elastic component of stress first becomes UE significant Re Reynolds number for liquid in orifice, based on orifice diameter Green measure of axial strain, $ ~(u~‘/u~~) - 1) 7G Density of oil in use P Density of water Pw Axial stress, in 11 direction, in liquid at orifice exit 711 References D.R. Oliver and R.C. Ashton, The flow of polymer-thickened motor oils in convergent jet thrust nozzles, J. Non-Newtonian Fluid Mech., 2 (1977) 367. J.M. Davies, J.F. Hutton and K. Walters, Colloq. Int. C.N.R.S., No. 233, Polymires et Lubrification, Paris, 1975, p. 61. D.T.G. Morgan and K. Pannell, Rheol. Acta, 11 (X972) 185. G. Brindley, J.M. Davies and K. Walters, J. Non-Newtonian Fluid Mech., 1 (1976) 19. G. Wadelin and D.R. Oliver. Work as yet unpublished.