The project reviewed is Bettis 3 which is one of five projects in a programme referred to in the References as the Bettis Programme. The Bettis project measured loss coefficients for a 90 degree, short radius bend at high Reynolds numbers.

The Bettis 3 project illustrates the problem caused by not treating the literature review as part of a due diligence process. The project did not adequately research prior art and made the decision that the project would stand on its own. Trying to establish if the Bettis 3 project bend loss coefficients can be related to reference points in the literature illustrate important aspects of experimental studies. The review sets the scene for the checklist in Part 3.

One of the reasons for choosing the Bettis 3 project is the report is accessible through the commendable practice of the United States Government of making available on the web work sponsored by its agency's.

The Bettis projects use the term elbow whereas Internal Flow Systems uses the term bend. Both terms are used in this review.

The Bettis project dimensions are in inches and it is appropriate to use inches in this review.

2.2 The Bettis Project

To accurately define irrecoverable pressure loss coefficient for tight radius elbows to high Reynolds, and
To provide an accurate database for qualifying the irrecoverable pressure loss predictions for Computational Fluid Dynamic (CFD) computer code

To achieve high Reynolds numbers, testing was carried out using water at temperatures up to 290 degrees C. When water temperature rises viscosity drops more rapidly than density. This means that for a given water velocity, Reynolds numbers increase with water temperature. Projects to measure loss coefficients usually cover a Reynolds number range or 6 to 1 or so, whereas the Bettis 2 project achieved 74 to 1, from 0.5 x 10E6 to 37 x 10E6.

The project's tight radius 90 degree elbow is described as having a radius ratio of 1.2. No geometric measurements are provided for the bend. From plots of static pressure it would appear that the bend included short inlet and outlet sections of straight pipe.

Because the Bettis experiments involved both high temperatures and pressures the test facilities and measurements were more complex than for studies carried out at close to ambient temperatures and pressures. The problem of making measurements at high temperatures and pressures is not covered in the Bettis 3 report. I have no experience of measurements under the Bettis 3 conditions nor do I know of other published work under such conditions. However, the same geometric and system requirements as for ambient conditions apply. The pressure measurements are challenging because of temperature, and hence water density changes, between tapping points and the pressure scanning system.

2.3 Bettis 2 Literature Review

Considering the importance and cost of the project, the Bettis 3 literature review is brief. The review contains six references on bends: two research papers, one review paper and three design guides. Reference is made to the limited nature of the world’s database on piping bends. There is no indication that references in the design guides were followed up to access what is a substantial literature related to bends.

The first research paper is from the Bettis 1 project but loss coefficients from this paper are not used, even though they include measurements on a 90 degree, r/d = 1.2 bend.

The second research paper is by Ito. Ito's experimental studies on bends generated loss coefficients that meet class 1 criteria of Internal Flow Systems. The Ito paper included in the Bettis review was mainly concerned with correlating others results for high radius bends. Ito’s work was for Reynolds numbers below 0.5 x 10E6, whereas the Bettis 2 Reynolds were above 0.5 x 10E6.

A review and correlation paper by Piggot relates to experiments mainly made with commercial bends tested under ill-defined conditions. Piggot was aware that there were many deficiencies in the data he was using. Piggot commented that it would appear that if a real knowledge of bend losses is to be attained, we must consider a comprehensive research to get modern and more accurate data on a whole range of roughness and bend radius.

Crane bend data is over 60 years old and relates to commercial bends, tested under unknown conditions at low Reynolds numbers and not relevant to the Bettis 3 project.

In the review of design guides I express concern over the accuracy of data in Idelchik that was not generated in part by Idelchik himself. In the case of 90 degree bends, Idelchik’s predictions are based in part on his own data, so one can have confidence in Idelchik’s loss coefficients and reasonable confidence in his predicted Reynolds number trends.

Had the Bettis 3 project followed up the BHRA references they would have found that the BHRA work on bends was extensive and agreed with other high quality studies. Also the BHRA experimental facilities were used for studies on diffusers and combining and dividing T’s, and loss coefficients from these studies agreed with other high quality studies. The cross-referencing allowed me to rate the bend loss coefficients in Internal Flow Systems at a Reynolds number of 10E6 as Class 1.

Figure 1 from the Bettis 3 project shows the Bettis loss coefficient for a 90 degree r/d = 1.2 bend plotted against Reynolds numbers along with curves generated by the Bettis 3 project from its references.

The curves for Piggot and Crane on Figure 1 are unjustified extrapolations of low Reynolds number experiments on commercial fittings tested under unknown conditions and not relevant to the Bettis 3 project.

Ito carried out tests at Reynolds numbers below 0.5x10E6 and his data should not have been extrapolated to high Reynolds numbers.

Figure 2 shows Figure 1 with Piggot and Crane curves removed and Ito's results plotted for his experimental range. Also plotted on Figure 2 is the loss coefficient curve for a 90 degree, r/d = 1.2 bend taken from the Bettis 1 project report. No reason is given for not including the Bettis 1 project results on Figure 1. The Bettis 1 project tested an accurately made 90 degree bend of r/d = 1.2 and, although there were problems with the pressure tapings, there is no obvious reason for not acknowledging the Bettis 1 measurements.

Loss coefficient predictions by Idelchik and my work at BHRA show good agreement. Above Reynolds numbers of 0.5x10E6 we both observed r/d = 1 bend loss coefficients had become independent of Reynolds numbers. It would be expected that the loss coefficient for a 90 degree, r/d = 1.2 bend would become independent of Reynolds number below 10E6.

The Bettis project wrongly assumed that the Idelchik and BHRA data was gathered at low Reynolds numbers, whereas the Reynolds numbers overlapped substantially with those of the Bettis 3 project.

The Bettis project concluded “all existing correlation’s had been based on extrapolations of measurements which were several orders of magnitude lower in Reynolds numbers”. Presumably having made this incorrect assumption they felt justified in ignoring all prior experimental work and as a result the Bettis project had no reference points.

The following Sections look at the Bettis 3 project report to see if it is possible to reconcile the bend loss coefficients measured with hydraulically smooth pipes with the loss coefficient predictions from Idelchik and Internal Flow Systems.

2.4 Experimental Facility

Two sets of inlet and outlet pipes were used. One set was mechanically polished to produce a smooth surface and one set finished by abrasive particle blasting. Pipes where made of carbon steel and passivated to maintain surface finish. Pressure tapings were drilled and finished using an appropriate level of care and pipe to bend joints made without steps. These mechanical aspects of the project were to an exemplary standard.

Pressure measurements were made using a scanning system connected to appropriate differential pressure transducers.

2.5 Fluid Dynamic Aspects

No details are given of the pipework upstream of the flow straightener but it is likely to have caused swirl into the test configuration. At moderate Reynolds numbers swirl can affect flow meters located over 100 pipe diameters downstream of a pump or bend combinations. As Reynolds numbers increase damping of swirl decreases, so disturbances can be detected even further downstream.

The Bettis 3 project had concerns over inlet conditions to the venturi meter and installed a multi hole straightener with 1.2inch diameter holes and an area ratio of about 2. Just downstream of this type of flow straightener the velocity profile would be reasonably flat with a high level of small-scale turbulence. The turbulence structure and flow profile would have changed before reaching the venturi meter.

Flow straighteners of the type used by the Bettis 3 project are not effective in removing swirl. Tube bundle type flow straighteners or straightners with experimentally determined pattern of holes of different sizes are commonly used when the pipework configurations upstream of a flow meter gives rise to swirl.

In the Bettis 4 project the venturi meter was sent to a calibration facility and found to be satisfactory. A calibration of a flow meter is effectively a check on a meter's geometric parameters and not on its performance when installed in a particular pipe layout. It is necessary to include sufficient of the pipework upstream of a flow meter, that influences a flow meter’s performance, for a meaningful calibration.

Although no geometric details of the venturi meter are provided, it is likely that flow measurement errors were substantially greater than reported, with the flow rate over estimated if swirl was present, and the error increasing with Reynolds number.

Velocity traverses were made in the inlet pipe to the test bend. A 5 hole probe was located 15 diameters or so after the contraction from the flow metering pipe. No details of the probe are provided. Measurements commenced 1 inch from the wall which meant they covered less than 40% of the flow area, and this area was remote from the near wall high energy dissipation region. A 10% tangential velocity component was recorded which was attributed to the probe blockage. From the measurements a number of conclusions were drawn including:

Fluid dynamically, there is no justification for these statements. The velocity measurements were too far downstream of the straightener to draw any conclusions on the performance of a flow straighter upstream of a venturi meter. With regards to the flow profile entering the test bend some 20-pipe diameters downstream of the contraction, the profile should have been described as a developing profile:

The inlet pipe was about 20 pipe diameters long. Friction gradients were established by static pressure measurements over part of this pipe.

In the BHRA tests that generated much of the data in Internal Flow Systems it was found that, at a Reynolds number of 10E6, near steady state pressure gradients were established after 15 to 45 pipe diameters, depending on the level of flow disturbance at entry to a pipe.

Because of the short length on the inlet pipe, the Bettis 3 project measured inlet pipe friction gradients could have been expected to be above developed flow gradients. Compared to smooth pipe friction factors (5) at high Reynolds number, measured friction factors were 6% high at a Reynolds number of 10E6 and 11% at 10E7. Even higher values would not have seemed unreasonable given the short length of the inlet pipe.

Bend loss coefficients where based on the pressure difference between a tapping upstream of the bend and a pressure tapping downstream of the bend, minus the friction loss in the straight pipe between the tappings. Derived bend pressure loss depended on the difference between two pressures, one measured and one calculated using the inlet pipe friction factors. The calculated friction loss would have been 5 or so times the bend loss. Under these circumstances, considerable uncertainty would exist as to bend loss coefficient values because the friction factors were for developing flow in a short inlet pipe.

Flow separation occurs on the inside of the outlet of a 90 degree, r/d = 1.2 bend. The extent of the flow separation depends on flow conditions into a bend.

At the high Reynolds numbers of the Bettis 2 project boundary layers would be classes as thin and decrease with increasing Reynolds numbers. Losses due to separation could be expected to increase with Reynolds number, whilst losses due to secondary flows decrease. The best estimate is these effects would cancel out, resulting in other researchers observations that loss coefficients for bends with r/d < 1.5 become independent of Reynolds numbers below 10E6.

There is good reason to look at the project in detail because it calls into question the validity the work of other researchers and in particular the validity of the Class 1 bend data in Internal Flow Systems
It provides sufficient information to be able to comment sensibly on the project
The measurements made did not record flow conditions within the experimental facility and this presents challenges in reasoning what flow conditions may have been present and whether or not the loss coefficient data is valid

Since the Bettis 3 project was carried out experimental measurements for water flows through 12, 16, 20 and 24 inch diameter bends of 90 degree and r/d = 1.5 have been published (2.3). It was observed that the bend loss coefficients become independent of Reynolds numbers below 10E6. These observations, combined with the observations and predictions in Idelchik and in Internal Flow Systems indicate that the Bettis 3 project bend loss coefficients included substantial Reynolds number effects that were related to the test facility and not to the bend.

Measuring bend loss coefficients may seem a simple task, in reality it is a very challenging task if the aim is to produce definitive data. The Bettis 3 Project test facilities had physical constraints that prevented defined conditions for the measurement of:

Water flows within the Bettis test facilities involved a series of complex flow events, with events upstream affecting events downstream. Within our current understanding of fluid flow behaviour, particularly at high Reynolds numbers, it is not possible to correct the Bettis 3 loss coefficients to be compatible with the loss coefficients in Internal Flow Systems.

Actions taken on mechanical aspects of the project, such as the polishing of the pipe internal surface, passivation of the pipe surface, extreme care in making pressure tappings, showed that the project aimed to produce definitive data. Events went astray in the understanding the fluid dynamics involved and particularly in the need to generate defined flow conditions.

Engineering fluid dynamics is an experimental subject that requires many years of hands on experience combined with an investigative approach and a wide knowledge of the literature. Very few engineers have such a background, and industry in general does not understand that fluid dynamic projects need such backgrounds, or at least a code of practice that embodies such experience.

Virtually the only fluid dynamic measurements the Bettis project team made were static pressures. These tell very little about flow behaviour, so the project team were fluid dynamically blind. Although the Bettis programme involved experiments over a number of years, with three experimental facilities, there was no evidence of a developing understanding of flow behaviour within these facilities.

The Bettis projects highlight the need to treat a literature review as part of a project’s due diligence process. An experimental project should face the same rigorous procedures as any well thought through and managed engineering project. The due diligence process should identify and justify accessing the fluid dynamic expertise needed for a successful project.

One should always ask the question are my measured loss coefficients realistic? At a Reynolds number of 10E7 the Bettis 3 loss coefficient for the 90 degree, r/d = 1.2 bend was 0.075. This is an unreasonably small value as it is considerably below the minimum predicted value of 0.10 for the lowest loss 90 degree bend at a Reynolds number of 10E7. The lowest loss bend r/d would be between 2 and 3 compared to 1.2 of the Bettis bend.

Internal Flow Systems

Experimental Measurement of Loss Coefficients

Part 2 - A Project Review (Carrying out Due Diligence)

2.1 Introduction

2.2 The Bettis Project

2.3 Bettis 2 Literature Review

2.4 Experimental Facility

2.5 Fluid Dynamic Aspects