A review of frictional pressure losses for flow of Newtonian and non-Newtonian slurries through valves V G Pienaar, P T Slatter, Cape Technikon, RSA N J Alderman & N I Heywood, Aspen Technology, UK

Objectives To identify, collate, review, categorise information published on frictional pressure losses arising from flow of Newtonian and non-Newtonian fluids through various types of valves. To list both laminar and turbulent flow for non-Newtonian fluids modelled using several alternative rheological models. To compare experimental results with empirical predictive equations. To provide additional loss coefficient data for three different sizes of globe valves and a rubber-lined diaphragm valve.

Types of valves Isolation (on-off) (knife gate, parallel gate, diaphragm, pinch, plug, ball, butterfly, rotating disc) Regulating (throttling) (globe, diaphragm, pinch segmented ball)

Issues to address Work with non-settling, non-Newtonian slurries restricted to gate and globe valves Uncertainties exist regarding results obtained Especially true for laminar-turbulent transition Edwards et al. (1985) quoted a critical Re MR of 12 for globe valves and 900 for an elbow, demonstrating effect of valve geometry on loss coefficient. Critical Reynolds number not well understood and needs to be validated

Definition of Loss Coefficient

Experimental Procedure Preferred experimental procedure is to –measure overall friction loss in a system made up of two pieces of straight pipe connected in series by valve, and –subtract losses in straight pipes from measured total loss to obtain loss due to valve. This method is preferred over that of measuring loss just across valve because difficulties of distinguishing between developed and incompletely developed flow as fluid enters and exits valve. Total length of straight pipe can either include or exclude physical length of valve resulting in (k v ) gross if only straight pipe losses are subtracted and (k v ) net if length of the valve is included Non-Newtonian fluids modelled using power law, Bingham plastic or viscoplastic models.

Laminar Flow Loss coefficient, k is inversely proportional to Reynolds number raised to some power Most workers found x = 1 Turbulent Flow Loss coefficient k is independent of Reynolds number

Definition of Laminar/Turbulent Transition

Values of Re crit

Discussion of Laminar/Turbulent Transition Discrepancies in Re crit values not clearly understood. Kittredge & Rowley (1957) and Banerjee et al. (1994) obtained similar Re crit values for 12.7 mm globe valves. Re crit values obtained by Edwards et al. (1985) for 25.4 and 50.8 mm globe valves and Pal & Hwang (1999) for 27.2 mm globe valve were 30 times lower than those obtained by Kittredge & Rowley (1957). These observations suggest Re crit is a function of the valve size – it appears that test work carried out at Re 10. Kimura et al (1995) supported this observation and referred to 1 < Re < 10 region where loss coefficient is inversely proportional to Reynolds number as region of Stokes flow. Another factor affecting value of Re crit could be in the author definition of Re crit. – intersection between laminar and turbulent flow lines gives higher values for Re crit – than those defined at point where deviation from laminar flow line starts

Discussion of Laminar/Turbulent Transition A further problem is that some researchers did not investigate at Re < 100. –There is experimental evidence that the transition takes place at Re < 100 –Ma (1987) and Banerjee et al (1994). in their test work started testing at Re = 100. –In order to ensure that best value of Re crit is obtained, their work should have gone down to at least two orders of magnitude of Re below their minimum values. Critical Reynolds number for laminar-turbulent transition is strongly influenced by valve design and needs to be addressed. Differences in Re crit stem from –differences in type and size of valve –range of Reynolds numbers tested –different bases for defining Re crit

Prediction of loss coefficients and comparison with experimental results for globe valves

Prediction of loss coefficients and comparison with experimental results for gate valves

Observations Comparisons of these correlations with experimental data obtained by various workers for globe valves and gate valves seem to suggest –predictions for Newtonian fluids using loss coefficient data given by Hooper (1981) similar to those for some non-Newtonian fluids. –results for gate valves more consistent than those for globe valves. Correlations of Banerjee et al (1994) yielded lower values for loss coefficient compared to values using correlations of Edwards et al (1985). and Hooper (1981). –Correlations derived assuming flow was laminar for 0 < Re MR < 1700 –Only three points were in laminar regime, suggesting a transition to turbulent flow at Re MR = 400. –Plot of their data in this form in good agreement with that given in Perry(1997). Individual workers carried tests over a limited range of Reynolds numbers making it difficult to compare results.

Loss coefficient data obtained at Cape Technikon Test work conducted at Cape Technikon Flow Process Research Centre – to resolve some of the issues surrounding globe valves – to provide some information on diaphragm valves. 12.5, 25 and 40 mm globe valves tested 40 mm diaphragm valve tested Eight Newtonian and non-Newtonian fluids Rheological properties measured using Paar-Physica MC1 rheometer fitted with cup-and-bob geometry Reynolds numbers ranged from 0.01 to 10 6

Loss coefficients for globe valve

Discussion of Results Edwards et al. (1985) suggested Re crit = 10, i.e. the point where data start to deviate from laminar flow predictions. There is good agreement for the various sizes of valves – showing that dynamic similarity has been established – by using appropriate Reynolds number to account for rheological behaviour of the fluids tested. – Both geometric and kinematic similarity have been obtained. Results are encouraging as two different rigs with different principles of operations were used. Another rig presently being constructed where valves up to 100 mm in size can be tested.

Loss coefficients for diaphragm valve

Conclusions Literature on loss coefficient data for Newtonian and non-Newtonian fluids flowing through various types of valves was reviewed. Experimentally-determined loss coefficients have been summarised and compared with predictive equations Better agreement obtained for gate valves than for globe valves. Dynamic similarity obtained for gate valves in existing literature, but not for globe valves. Work at Cape Technikon provided experimental data for loss coefficient over eight orders of magnitude of Reynolds numbers for three differently-sized (12.5 mm, 25 mm and 40 mm) geometrically similar globe valves. This work carried out using eight Newtonian and non-Newtonian fluids on two different test rigs, demonstrating that dynamic similarity can be achieved for globe valves. More experimental work is, however, needed to determine loss coefficient data for other types of globe valves. No experimental data found for non-Newtonian fluids flowing through diaphragm valves. Preliminary experimental results produced in good agreement with those given in literature for Newtonian fluids.