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Optimising shaft pressure losses through computational fluid dynamic modelling
Applied Thermal Engineering xxx (2015) 1e11
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Research Paper
Optimising shaft pressure losses through computational fluid dynamic modelling W.J. Kempson a, b, c, *, R.C.W. Webber-Youngman b, J.P. Meyer c a
Hatch, 40 Elm Street, Unit ND 255, Sudbury, Ontario P3C 1S8, Canada University of Pretoria, Department of Mining Engineering, Private Bag X20 Hatfield, Pretoria 0028, South Africa c University of Pretoria, Department of Mechanical and Aeronautical Engineering, Private Bag X20 Hatfield, Pretoria 0028, South Africa b
h i g h l i g h t s We measure the pressure losses on five shaft systems. We calculate the pressure losses for the above shafts using current theory. All of the shafts which were measured are evaluated using CFD analysis. The results of the measured shaft, the theoretical evaluation and the CFD analysis are compared. An economic evaluation of the different shaft layouts is completed.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 May 2014 Received in revised form 11 April 2015 Accepted 24 April 2015 Available online xxx
In recent years, substantial progress has been made with respect to the definition and control of the primary energy requirements in underground mines. Little has, however been done to develop a more detailed understanding of how to limit the various pressure losses which are intrinsic to shaft systems. This is in spite of the fact that more than half of the pressures generated by the ventilation fans in deep level mines are dissipated as pressure losses within the shaft system. This paper presents research which has been completed to optimize the pressure losses which occur in shaft systems as a result of the ventilation air flowing through them. In this regard, the response of various shafts to the ventilation air flowing through them was measured. These results were evaluated against the current theory for the calculation of shaft pressure losses. Finally the results of the measurements and calculations were used to calibrate a Computational Fluid Dynamics model of the shaft systems. This model was then iterated to allow meaningful conclusions as to the specific make up of the shaft equipment which contributes the most to pressure losses in shaft. The results of the above analysis demonstrated that the current theory used for the evaluation of these pressure losses is deficient. The paper discusses these conclusions and the specific ramifications of the analysis. Finally, the understandings gained with regards to the above research are applied to the design and layout of equipment in mine shafts. In this regard, the shape and orientation of the shaft steelwork is evaluated and its specific interaction with the piping and fitting is evaluated. Coming out of this evaluation are specific recommendations for the design of future shaft systems. These recommendations are based on the above models and offer specific savings on the lifetime operating costs of shaft systems. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Mine shaft Deep level mines Pressure losses Shaft ventilation Shaft CFD evaluation Shaft design recommendation Bunton design
1. Introduction
* Corresponding author. 40 Elm Street, Unit ND 255, Sudbury, Ontario P3C 1S8, Canada. Tel.: þ1 705 688 0250x5332, þ1 705 561 9899; fax: þ1 705 688 0244. E-mail addresses: [email protected] (W.J. Kempson), [email protected]. za (R.C.W. Webber-Youngman), [email protected] (J.P. Meyer).
Energy is becoming an increasingly expensive commodity throughout the world. At the same time, mines are getting deeper and becoming more mechanized. This is resulting in higher quantities of electrical energy being used in mines. As a result of ongoing innovation, there are some effective energy saving and dissipation
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systems in use. However, there has been substantially less work done in the design of mining infrastructure systems and in particular the shaft systems, to alter the way in which these items are made up and to thus reduce the overall consumption of electrical energy in mines. All mine or shaft designs tend to move along the same route, solving questions with proven and sometimes well proven techniques. This lack of change does provide a degree of comfort to prospective investors, however, this comes at a price. The cost for changing the basic design of an installed shaft system to a more efficient one is almost never worth the capital outlay. This is because, in order to make the change, either the shaft will have to stop producing (thus incurring significant opportunity cost) or the change will take years to complete as it will be done during the weekly and annual shaft maintenance cycles, assuming that any proposed design change can be accommodated without interrupting the production cycle. Thus, inefficient design has a significant effect on the long term profitably of any shaft system. In today's world, however, tools are available for the detailed evaluation of a system, and to thus prove the efficacy of design changes before they are installed. These tools, when used in conjunction with a rational analysis technique requiring both the analysis to be completed and the validation of theoretical models against measured data, can give rise to significant savings. This paper proposes a change in the manner in which shafts are designed, which can result in significant ongoing savings in mines. In this case, it is an example of changing the manner in which shaft systems are analyzed, including the use of sophisticated analysis tools. This has resulted in changes to the structural and layout components in a shaft system, making it more efficient. This paper concentrates is deep vertical shafts. The surface fans for mines associated with these shafts consume between 15% and 20% of the total monthly electrical consumption on a mine. More than half of this energy is required just to move the ventilation air through a typical downcast shaft. This means that between 7% and 10% of the mine's total monthly electrical budget goes to waste as this fan pressure is dissipated as the ventilation air traverses the shaft. 2. Previous work done on understanding shaft ventilation systems In order to understand the development of shaft systems, we will first conduct a brief review of work which has been completed in this area. 2.1. Measurement A number of shafts have been tested in the past, specifically to measure the resistance of the shaft to the flow of ventilation air through them. Most of these tests were completed circa 1960 some of these papers are referenced here [1e6,8]. The detailed evaluation of these tests is not discussed in this paper. However a summary of the general conclusions is presented below. 2.1.1. Specific conclusions derived from the review of measured shafts As a result of the evaluation of the measurements of shaft systems, the papers for which are referenced in the previous section, the following criteria for shaft design were highlighted: i Buntons and guides should be streamlined. ii Shaft walls should be lined (i.e. smooth). iii Buntons should be spaced as far apart as possible.
Up to this point (i.e. the 1962), no definitive data was available on the actual manner in which the above systems should be designed in order to minimize the pressure losses associated shaft systems. Although some theories were postulated [9], additional data was required in order to extend our understanding as to the behavior of these systems. As a result of the difficulty in measuring the actual resistances of installed shafts and, once measured, of the high capital cost and time requirements to adapt their configuration for additional tests. Scale models were used for additional testing. 2.2. The use of scale models The use of scale models depends primarily on the use of dimensional analysis in order to understand the importance of certain parameters in the system being considered. A definition was supplied by Pankhurst [7]: “The dimensions of physical quantities can be manipulated algebraically and the results can be interpreted to provide a great deal of information about the physical processes involved in the situation considered.” Unless the geometry of the system has no effect on the physical situation to be evaluated, the first requirement of a scale model is that it should be geometrically similar to the actual system being evaluated, i.e. the distance between any two points in the modeled system must bear a constant ratio to the distance between the corresponding two points in the original system. This constant ratio is called the ‘geometrical factor’. Similarly, we define the kinematic similarity (i.e. when velocities are involved) by the condition that the velocity at any point in the one system bears a constant ratio to the velocity at the corresponding point in the other system. This is called the ‘velocity scale factor’. Various other factors, such as elastic similarity, thermal similarity, etc., are all defined in a similar fashion but are not pertinent to this discussion. Although this technique is powerful and allows a meaningful comparison of scale models with full-scale systems, it must be emphasized that this is only valid as long as the system does not require extrapolation beyond the ranges of the dimensionless parameters defined in the tests. A number of the measurements carried out and used in the evaluation of shaft resistances were done on scale models [8]. The two models generally referred to are the 1.981 m (78 inch) model and the 0.305 m (12 inch) scale models which were operated by the Council for Scientific and Industrial Research (CSIR). These models were constructed in the horizontal plane and were both configured to allow the flow in them to achieve a fully developed profile before the typical shaft obstructions interrupted this flow. As a result of practical limitations, the maximum airflow achieved in these models was half of that generally found in a typical shaft configuration. This had a direct effect on the Reynolds number used in the tests and raises some concern as to the extrapolation of the results. In order to try and define the extent to which the data from this scale model could be used, various shaft configurations were tested by Chasteau [8] and the results compared. These tests showed little correlation. In the 0.305 m (12 inch) model, the test showed little agreement even to standard pipe values. The tested values were lower than expected and the results showed that the test flow was potentially not fully developed. The results also showed that it is perhaps generally better to use direct drag measurements to determine the effect of the resistance of buntons than to use the pressure drop. This has the advantage of removing the pipe wall roughness considerations from the overall measurements.
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2.3. Design considerations and current theoretical basis for shaft evaluation Any discussion on the design of shaft systems and their evaluation with respect to the resistance they offer would not be complete without discussing the work contributed by Bromilov [9]. In order to evaluate a complete shaft system, Bromilov separated the resistances for the various items found in a shaft system and evaluated each of these items in turn. The sum of the resistances offered by each of these items is converted in to a figure which is equivalent to a standard pipe friction factor, each of these friction factors is then added arithmetically. This overall friction factor is then used in the standard Colebrook-White equation for the calculation of pressure losses in a pipe, to determine the overall pressure losses in a shaft. The various items in the shaft which are evaluated are listed below: i ii iii iv
Buntons Guides, pipes and cable Shaft walls Cages and/or skips
The base assumption of this work is that the resistance offered by each of these items is independent of the resistance offered by the others. In the context of the work produced by Bromilov, each of these will be discussed separately because the analysis techniques for each differ. 1 Buntons e The term “bunton” is a cross member in the shaft located perpendicular to the direction of airflow. As such it differs from the other items in the shaft in that the pressure losses associated with this are based on the “drag” of the bunton as it impedes the air flowing around it. The pressure losses associated with the buntons in a shaft are calculated in two steps. i The pressure losses associated with the shape of the bunton are calculated by using a drag coefficient based on the shape of the bunton which is presented to the air flow. These coefficients were calculated from the measured data of different buntons shapes in various shafts. This is evaluated in conjunction with the total cross sectional area that the bunton set presents to the airflow to obtain a frictional pressure loss for a single bunton set. The pressure losses associated with one bunton set are then multiplied to include all the bunton sets in the shaft (generally these are spaced every 5 me6 m). The coefficients of drag are taken from data available from previous measurement of pressure losses associated with difference buntons shapes [9]. ii In addition to the “drag” which buntons offer to the ventilation flow, the breakaway of boundary layers from the sides or trailing edges of the buntons causes a series of vortices which extend downstream from the bunton. These vortices add to the pressure losses which occur as ventilation air flows past the buntons. In the evaluation of the pressure losses associated with the drag of a bunton, it was assumed that these vortices dissipated before the airflow reached the following bunton set. This is not true unless the buntons are streamlined or are far apart. In order to allow for this interference which the vortices cause, an Interference Factor is used. This factor was derived by Bromilov [9]. After measuring the losses associated with 24 shaft or model shafts and calculating a linear equation which would allow for the estimation of the Interference Factor. 2 Guides, pipes and cables e The resistance offered by these is estimated by subtracting the area of these fittings from the area
3
of the shaft. This reduced shaft cross section is then used to calculate the increase in the ventilation air velocity in the shaft, based on the assumption of a constant volumetric flow rate of air through the shaft. In addition to this, the increased rubbing surface apparent in the shaft cross section as a result of the introduction of these fittings is also used. This increased air velocity, as well as the increased rubbing area is then used to calculate the pressure loss in the shaft using the ColebrookWhite equation. 3 Shaft walls e The resistance of the shaft wall is calculated using factors available for standard pipe theory for skin friction as defined by the ChezyeDarcy friction factor for pipe or duct walls. 4 Cages and skips e The calculation of the pressure losses associated with cages and skips is based on work by Stevenson [10]. This involved the construction of model cages and measuring the pressure drops across them at varying air flows in a circular wind tunnel. Curves were produced from this work which allows the prediction of the pressure losses associated with cages and skips based on their dimensions. These curves are used to calculate a “shock loss” factor which is then used to calculate the pressure loss associated with the cage or skip. It should be noted though, that any effect a cage or skip will have on the pressure losses in a shaft will be temporary as the primary flow paths in a shaft are generally design to be in the mid portion of the shaft, whereas these conveyances pass through this portion as they move up and down, but are staged, and loaded above and below this portion of the shaft.
2.3.1. General discussion Bromilov's [9] work was further built on by McPherson [11]. In this work McPherson simplified and metricated the calculation of shaft resistances. In addition, he proposed the use of the Colebrook-White equation for the derivation of the shaft ChezyeDarcy friction factor. This equation is based on the Moody chart for the ChezyeDarcy friction factor and is consistent with the work Bromilov presented. The theory used in McPherson's paper was consistent with that proposed by Bromilov and provides a slightly simplified methodology for the calculation of pressure losses in shaft systems. 2.4. Specific conclusions derived from the review The theory described in this section allows for the theoretical design of a shaft system with respect to the resistance that the shaft will offer to air flowing through it, but some critical questions regarding this analysis remain unanswered. These concerns are discussed in the following paragraphs. 1 The actual effect of the shaft fittings needs to be quantified as their effect on the overall pressure losses in a shaft need to be understood. This is important because as the tonnage which a given shaft produces increases, so does the quantity of support the underground operation's need, and so more services are required to go underground (for example, water, compressed air, concrete etc), this requires more and larger pipes and fittings. 2 The effect that the shaft steelwork has on the ventilation air has been quantified based on the drag resistance it offers to the airflow. This is based on measurements taken a number of years ago and has not been verified. 3 The effect that the conveyances have on the resistance of the shaft needs to be more explicitly quantified. 4 The free air velocities in equipped shafts may be as high as 12 m/ s and air velocities of up to 22 m/s may be tolerated in
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unequipped shafts. These velocities are higher than those recommended by McPherson and are indicative of the requirement to make capital assets such as the shaft work as hard as possible to service the mine's general requirements. 3. Latest analysis of shaft systems The pressure losses associated with a number of shafts at Impala Platinum were measured in order to validate the theory described above as well as to calibrate a Computational Fluid Dynamics (CFD) model which would be used to analyze the shaft systems in more detail to try and gain an understanding of the efficacy of theory as well as the actual pressure losses associated with shaft systems. The shafts which were measured are: i ii iii iv v
Impala Impala Impala Impala Impala
14 shaft 11 shaft 1 shaft 11C shaft 12N shaft
3.1. Test methodology The following measurements were made of each of the shaft system and plotted against time: 1. 2. 3. 4.
Dry-bulb temperature ( C) Relative Humidity (%) Barometric pressure (kPa) Position and speed of all the conveyances in the shaft (m/s)
The locations of the above equipment varied depending on the shaft. This equipment was placed in a portion of the shaft where the flow was deemed to be fully developed (i.e. 10 diameters from shaft entry and exit points), as well as just above stations where this was practical. The above equipment was placed in the shaft for at least 1 week. This was done during the weekly shaft inspections, which also allowed an opportunity to inspect the shaft as well as to take air velocity measurements. Although a weeks' worth of data is well in excess of the actual analysis requirement, it did allow for a long term evaluation to ensure that the measurements showed results which were typical of the shafts. It was not possible to measure the velocity of the ventilation air in the shaft on a continuous basis. Thus in order to ensure that this data was collated, velocity measurements were taken during the shaft inspection used for the installation of the testing equipment, and during its removal. In order to confirm the ventilation flow rate during the testing period, the records of the shafts primary ventilation fans (which are plotted power consumption against time for the shafts), were examined perused to ensure that they were operating consistently for the test periods in question. Once this testing had been completed, the results were compared with those from a detailed theoretical analysis using the currently available techniques [11]. The detailed analysis and the measurements were then compared with the results obtained from CFD simulations. 3.2. Computational fluid dynamic (CFD) evaluation The package used for the CFD analysis is the STAR-CCMþ from CD ADAPCO, supplied by Aerotherm in South Africa. This package allows the 3D modelling of the shaft section under consideration by solving the continuity and momentum equations inside discrete
cells. The various shaft geometries were modelled in the software using the 3D-CAD module supplied. This module allows the complete model to be developed in readiness for the mesh generation. 3.2.1. Mesh generation The various shaft sections used in this analysis were modelled in the package using the 3D-CAD modelling features and the model was created on a 1-to-1 basis with no scaling required. This model was then meshed using a combination of the built-in polyhedral mesher for volumes and the surface remesher. The nature of the problem being examined also required that the effects of the solid interfaces and the air be modelled as accurately as possible. In this regard the Prism Layer option available as part of the meshing model was selected. This model applies additional elements at the solid interface to facilitate the accurate modelling of the turbulence around these points. The length of the primary model section was chosen to be 20 m. However, to ensure that the flow regime within the shaft was fully developed before the pressure losses over the section were measured, the initial length of shaft to be simulated such that this flow regime could develop was 10x the diameter of the shaft, in this instance 80 m. This required that the model be iterated four times (i.e. the output of the simulation becomes the input of the next simulation). To ensure accurate results, a mesh refinement analysis was performed until a mesh size was found with small changes in the pressure losses, there is very little difference between the pressure drops measured for the mesh sizes of 0.15, 0.20 and 0.25 m. As a result of this analysis, it was decided to use a base size of 0.25 m. This base size is sufficiently small to allow the shaft configurations to be accurately sized, but was also sufficiently large to allow the simulations to be run efficiently. The next requirement was to determine the effect that using the prism layers would have. This setting causes the software to generate additional layers at each boundary surface, thus improving the accuracy of calculation for the surface interactions. There was, however, a negligible difference between the results from the simulations run with and without these prism layers. It was decided nonetheless to include a prism layer with a setting of 5 (i.e. five additional layers adjacent to the boundary surface) for the simulations. 3.2.2. Fluid model Selection Once the geometry had been modelled and meshed, the appropriate fluid models were selected. In this instance, the thermodynamic and body forces were assumed to be small and the fluid used for the analysis was an ideal gas. The system was modelled in three dimensions and the K-Omega turbulence model was also used. These were resolved using the SIMPLE algorithm to solve the continuity and momentum equations in every cell. The convergence requirement was set to 1 104 for the continuity and the momentum criteria. This was achieved in most cases, although in some cases a convergence of 1 101 was accepted. In all instances the simulation was run until the data showed repeatability. 3.2.3. Boundary conditions The following boundary conditions were used: i Inlet: The inlet was defined as a constant-velocity inlet for the first section simulated. Subsequent to this, the velocity profile used for the input was taken from the output of the previous simulation. ii Outlet: The outlet was defined as being a constant pressure. This was consistent throughout all the simulations.
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x T10 e Shaft barrel and buntons and pipe including flanges xi T11 e Shaft barrel and buntons and pipe including flanges and skip 1 xii T12 e Shaft barrel and buntons and pipe including flanges and skip 2 xiii T13 e Shaft barrel and buntons and pipe including flanges and man cage 1 xiv T14 e Shaft barrel and buntons and pipe including flanges and man cage 2 xv T15 e Shaft barrel and buntons and pipe including flanges and service cage
7.4m Dia Shaft Airflow Buntons Skip
Skip Conveyances 2 Deck Service Cage
2 Deck Man Cage
5
4. Results of the analysis The first portion of this section comments of the efficacy of the CFD results vs the measured results. Once this has been discussed, the next section compares the CFD results for specific section of the shaft system against the results obtained from calculation using the current theory.
2 Deck Man Cage
Pipes 4.1. Evaluation of CFD results Fig. 1. Cross section of no. 14 shaft.
iii Wall conditions: The walls were defined as a rough wall with an asperity of 10 mm. This resulted in a Yþ along the wall of approximately 90, which is acceptable. It is worth noting that using the mass flow of the fluid as the input would have been ideal. However this was not possible, suffice to say the variation of the mass flow over the test section never exceeded 2.5% of the total mass flow. This is sufficiently small to not be a concern. 3.2.4. Shaft cross section To ensure a thorough understanding of the interaction between the various items contained in a shaft, it was decided to build the CFD model systematically and to include the various pieces of equipment progressively. This would allow the effect of the individual items to be evaluated. (see Fig. 1) The following series of tests were completed. i T01 e Shaft barrel pressure losses ii T02 e Shaft barrel and one bunton across the shaft iii T03 e Shaft barrel and two vertically spaced buntons across the shaft iv T04 e Shaft barrel and full buntons set at 6 m v T05 e Shaft barrel and pipes at pipe diameter vi T06 e Shaft barrel and pipes at flange diameter vii T07 e Shaft barrel and pipe including flanges viii T08 e Shaft barrel and buntons and pipes at pipe diameter ix T09 e Shaft barrel and buntons and pipes at flange diameter
In order to compare the results of the measured data against that which was calculated using McPherson's methodology [11], and subsequently against the results from CFD model, there are two factors which must be quantified. These are, the accuracy of the calculation itself as well as the accuracy of the instrumentation and measurement methodology. The accuracy of the calculation made in accordance with the ChezyeDarcy formula is (þ15% to 15%) [13]. The accuracy of the testing methodology and the instrumentation was calculated to have an accuracy of (þ12% to 29%) [12]. In this evaluation, the first phase was to ensure that all the instruments had up to date calibration certificates and that the results that they showed were consistent between each other, this was found to be accurate. The second phase of this evaluation was to examine what effect the quoted accuracy of the instrument would have on the calculated data (for example, to calculate pressure loss, two measurements are required, and each instrument can vary up and down from the median). In addition, this data is then used to calculate the final value. For example, in order to calculate the pressure loss in a shaft accurately, the temperature at both points are required as well as the relative humidity, barometric pressure and elevation difference. This combination of factors can have the effect of increasing the calculated pressure losses by 12% or decreasing them by 29%. As can be seen from the Table 1 above, there is good correlation between the theoretical calculation and the CFD analysis for two of results. There is consistently poor correlation between
Table 1 Comparison of Measure Data vs Calculated Data vs CFD Data. Shaft no.
PLoss
No. No. No. No. No.
1.81 1.26 70% 1.22 0.95 77% 0.47 0.55 118% 0.69 0.59 85% Bratticed shaft, the measured results were not reconcilable
14 11 1 11C 12N
(measured)
(Pa/m)
PLoss
(calculated)
(Pa/m)
PLoss
(calc)/PLoss (meas)
PLoss 1.22 0.87 0.42 0.38
(CFD)
(Pa/m)
PLoss 97% 92% 76% 63%
(CFD)/PLoss (calc)
PLoss
(CFD)/PLoss (meas)
68% 71% 89% 53%
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Table 2 Summary of results (cross sections).
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the measured results and both the theoretical and CFD results, as well as between two of the measured and calculated results although the results are within the accuracy limits defined above. The differences noted between the data on the shafts above do, however, highlight the potential differences that arise when evaluating complex systems from a theoretical perspective. It is not possible to include the effects of various items such as imperfections between the lining rings, the inclusion of slinging points in the shaft, large cable pocket installations, intermediate pump
7
stations and other shaft openings. The differences noted above are attributed to these as well as the other inaccuracies noted above. In this instance the data indicates that a design allowance of the order of 30% would be appropriate.
4.2. Comparison of CFD results and current theory It should be noted that, as the shafts modeled were each of different depths, the pressure losses obtained across the shaft
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system are reported per metre length of shaft. The results for selected tests are presented in Table 2 on the following pages.
5. Discussion of basic set of CFD models As the shaft was built up and the buntons and pipes were added, there was little correlation between the theoretical pressure losses and those predicted by the CFD analysis (see results of Test No.1 through 6 above), where there are still large differences between the CFD derived pressure losses and those which are calculated. This continued (see Test No. 9), until the point at which the full shaft cross section was being evaluated. The resistance predicted by the CFD analysis equaled that of the theoretical analysis (See Test No. 10). The conclusion that was reached was that the inter-related nature of the equipment in the shaft increased the total resistance of the shaft by some 30%, as the summation of the individual CFD derived pressure losses would have been approximately 30% lower than the total depicted in Test No. 10. (See Fig. 2). This finding has two specific outcomes: i The current theory is not accurate. While the calculated results for the shaft pressure losses were similar to those of the CFD analysis, the composition of these calculations are different. Primarily, the assumption that each of the fittings in the shaft can be evaluated separately, and the result added was found wanting. ii The inter-related effect of the fittings in the shaft is stronger than was initially anticipated. In order that a shaft be designed in a manner which will limit the shaft resistance, effect which each of the shaft fittings have on each other should be considered. Should the current theory be used without this consideration being taken in to account, changes could be made to reduce the shaft resistance that are either incorrect or could not have as significant an effect as was originally thought.
6. Extended investigation of options for shaft steelwork profiles and shaft pipework One of the areas that was considered worthy of further investigation was the manner in which the resistance of piping in the shaft was calculated. The piping was therefore modeled, initially at its pipe diameter, then at the flange diameter, as is required by the theory, and finally at the pipe diameter with flanges, which has not been done before. There was not a significant increase between resistances calculated by the CFD simulations using the piping at each of the diameters (less than 1%). However, when the piping was introduced with flanges there was a significant increase in the resistance (the piping in a bare shaft showed an increase of 20%. This is a significant increase and more than sufficient to warrant avoiding the use of flanges or introducing any discontinuities in the piping as far as practically possible. Discussions with mine personnel and shaft-sinking professionals resulted in the installation and maintenance costs not being included in this analysis. This is because these costs are considered to be the same no matter what bunton shape is used. The installation and maintenance cost for the piping is not considered a cost differential here and is therefore not included in the analysis. This includes the flanges and/or other pipe connectors that could be used.
6.1. Summary of options To ensure that the recommendations made in this work are valid, a number of additional options were evaluated using the CFD technique described above. These options were evaluated and the pressure losses over the shaft length were calculated. The dimensions used for the shaft are as follows: Shaft diameter: 9 m Shaft depth: 2 000 m Average Shaft Ventilation velocity: 10 m/s
Fig. 2. Summary of resistances in shaft by items.
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6.2.2. Piping Arrangements This result shows that the judicious placement of the piping in the shaft can have a significant effect on the resistance in the shaft. This saving can be between 7% and 12% of the total resistance experienced in the shaft. The results also show that, once the most efficient position has been chosen for the piping, the use of flanges to join the pipes can increase the cost of supplying air to the mine by approximately 12%.
9m Dia Shaft Buntons
Skip
Skip
Men and Material Cage
Conveyances
C/Weight
9
6.3. Summary and conclusions The following specific points can be made from the collation of all the economic data.
Pipes (Distributed)
i The shape of the buntons is important in meeting the requirement to reduce the pressure drop in the shaft as much as is possible. ii The placement of the piping in the shaft and the use of flanged piping can have a significant deleterious effect on the pressure drops in the shaft.
Fig. 3. Typical shaft cross section.
The basic fan power required to deliver the flow rate and the calculated pressure, as well as the overall costs for the power to deliver this were calculated. This cost for the power requirement was used to evaluate the current and potential costs of the options under consideration. The cross-section of the shaft is shown in Fig. 3. The results of this analysis are presented in Tables 3 and 4 below:
6.2. Summary of results and potential savings due to reduced energy requirement 6.2.1. Bunton shapes As can be seen from Table 3, a significant saving can be made through the judicious choice of the bunton shape. This varies from 52% to 81% of the fan power costs as a direct result of the resistance the shaft offers to the flow of air through it as a result of the bunton shape. A small decrease in these costs was also noted for the streamlined buntons of 5%. These savings are consistently better than that predicted by the McPherson.
7. Conclusion The initial work undertaken for the evaluation of the resistance that shaft systems offer to the ventilation air flowing through them was started circa 1960. This work consisted of both a theoretical evaluation as well an experimental. This work was built on by McPherson [11]. As shaft have got deeper, the cost for moving large amounts of ventilation through them has increased. This has been matched by the exponential increase in the cost for electrical energy. The development of methodologies which have been used for the evaluation of the shaft systems have followed good engineering practice. The calculation methodologies were developed using well developed equation for the derivation of drag and pipe friction. These methodologies were then compared to measurements from actual shafts as well as scaled models. A factor was introduced to allow this data to be used (The interference factor). This has resulted in analysis techniques which seem to accurately predict the pressure losses in shaft systems. However no detailed work had been done to validate the assumptions required for this
Table 3 Energy savings apparent due to bunton shapes. Item
Description
Shaft PLoss m(Pa)
Ratio differences
Rand (savings over 20 years LOM) (R 1000)
Canadian dollars (savings over 20 years LOM) ($C 1000)
1.01
Airflow buntons
822
1.00 (Baseline)
e
e
1.02
Streamlined buntons
774
0.94
5738
7615
1.03
Square buntons
1608
1.92
94 046
124 762
1.04
I-beam buntons
1324
1.61
60 413
80 143
Schematic of bunton cross section
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W.J. Kempson et al. / Applied Thermal Engineering xxx (2015) 1e11
Table 4 Energy savings apparent due to piping arrangements. Item
Description
Shaft PLoss (Pa)
Ratio differences
Rand (savings over 20 years LOM) (R 1000)
Canadian dollars (savings over 20 years LOM) ($C 1000)
2.01
Piping along shaft edge (no flanges) Piping away from shaft edge (no flanges) Piping distributed around shaft (no flanges) Distributed piping with flange
857
1.13
12 114
16 071
819
1.08
7 651
10 150
755
1.00 (Baseline)
e
e
867
1.14
13 310
17 657
2.02 2.03 2.04
Piping along shaft edge
Piping away from shaft
work or the undertaken a detailed analysis to understand the actual mechanism for pressure losses in the system. In this regard it was decided that there would be potential benefit to completing a detailed CFD analysis of a shaft system. In addition, as there was no reliable up to date to calibrate this CFD model, measurements were taken of a number of shafts to help with this validation. In addition calculation of the anticipated shaft pressure losses were completed using the procedure laid down by McMPherson. This work was completed and while the measurements showed differences to those of both the theoretical calculations as well as the CFD analysis, there was sufficient correlation to allow the model to be used for a more detailed evaluation. This evaluation primarily consisted of building a shaft system using the CFD analysis, piece by piece. This allowed the measurement of the anticipate pressure loss over individual members of the shaft system. For example the actual pressure losses measured as the result of the inclusion of the buntons was isolated and evaluated, similarly with the pipes, pipe flanges, fittings etc. The most significant conclusion derived from this analysis is that the two primary assumptions used for the theoretical calculations of shaft systems are incorrect. These assumption are described in detailed in Section 2.3: The assumption made by both Bromilov [9] and McPherson [11] that the resistance offered by the individual items in the shaft could be evaluated separately and summed arithmetically is incorrect. The CFD analysis showed that the individual evaluation would result in a total resistance of approximately 30% less the actual pressure loss in the shaft system. The evaluation of the effect that the pipes and guides have on the resistance of the shaft is not accurate. The current manner does not accurately account for the use of pipe flanges or the changes in resistance which occur as a result of the placement of the piping.
Piping distributed
As a result of the above, it is recommended that future shafts be design using the CFD methodology recommended here. The current trend for the design of shaft systems is moving further away from the operation envelopes that current shafts were designed in (i.e. shaft are getting deeper, with faster moving skips, high ventilation velocities, different styles of buntons and increasing quantities of pipes for underground services). This will make the current theory which was used to predict shaft resistance less accurate and could give rise to the design of inefficient systems if the current theory is used. As is shown in the data, the use of the CFD analysis can result in significant savings (potentially as much as 70%) in the cost of the electrical energy required to push ventilation air through the shaft. Acknowledgements This work was possible as a result of the efforts of the following people: 1 James Janse van Rensburg, Group Ventilation Manager at Impala Platinum, who facilitated use being able to various shafts at Impala Platinum. 2 Prof R.C.W. Webber-Youngmann, for his patience and guidance in the completion of this work. 3 Prof J.P. Meyer for his patience and guidance in the completion of this work. 4 Lister Sinclair, Head of Mining at Hatch Africa, for his guidance in the completion of this work. References [1] V.A.L. Chasteau, Investigation into the resistance to airflow of the pioneer shafts at Buffelsfontein gold mining Co, Ltd (Part II), J. Mine Vent. Soc. S. Afr. (1959) 138e146 (June). [2] M. Bareza, M.J. Martinson, Ventilation resistance of some vertical downcast shafts in the rand mine group, J. S. Afr. Inst. Min. Metallurgy (1961) 56e61 (October).
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W.J. Kempson et al. / Applied Thermal Engineering xxx (2015) 1e11 [3] V.A.L. Chasteau, Investigation into the resistance to air flow of no. 1 shaft, vaal reefs exploration and mining company (paper ii), J. Mine Vent. Soc. S. Afr. (1961) 138e146 (January). [4] D.F.H. Graves, Airflow resistance in downcast shafts equipped with streamlined buntons, J. S. Afr. Inst. Min. Metallurgy (1962) 99e106 (June). [5] J.F. Kemp, Analysis of the air flow in downcast shafts with reference to the trailing-hose method of resistance measurement, J. Mine Vent. Soc. S. Afr. (1962) 321e335 (January). [6] JdeV. Lambrechts, T.E. Deacon, Improvements in ventilation capacity by smooth lining of upcast shafts, J. S. Afr. Inst. Min. Metallurgy (1962) 61e66 (February). [7] R.C. Pankhurst, Introductory survey. Dimensional Analysis and Scale Factors, Chapman and Hall, London, 1964, pp. 13e19, 53e55. [8] V.A.L. Chasteau, Equipment and techniques used for scale model investigations of mine shaft resistance to air flow in the CSIR laboratories, J. Mine Vent. Soc. S. Afr. (1962) 362e369 (May).
11
[9] J.G. Bromilov, The estimation and the reduction of the aerodynamic resistance of mine shafts, Trans. Inst. Min. Eng. (1960) 449e474 (May). [10] Stevenson A, Mine ventilation investigation. Shaft pressure losses due to cages, Unpublished thesis, Royal College of Science and Technology, Glasgow. Also as: The estimation and the reduction of the aerodynamic resistance of mine shafts. Transactions of the Institution of Mining Engineers, Glasgow, 1956. [11] M.J. McPherson, The resistance to airflow of mine shafts, Proc. 3rd Mine Vent. Symp. (1987) 465e477 (October). [12] W.J. Kempson, R.C.W. Webber-Youngman, J.P. Meyer, Optimizing Shaft Pressure Losses through Computational Fluid Dynamic Modeling, University of Pretoria, 2012 (January). [13] F.M. White, Fluid Mechanics, 2nd edition, McGraw-Hill, New York, 1986, pp. 308e314.
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Optimising shaft pressure losses through computational fluid dynamic modelling W.J. Kempson a, b, c, *, R.C.W. Webber-Youngman b, J.P. Meyer c a
Hatch, 40 Elm Street, Unit ND 255, Sudbury, Ontario P3C 1S8, Canada University of Pretoria, Department of Mining Engineering, Private Bag X20 Hatfield, Pretoria 0028, South Africa c University of Pretoria, Department of Mechanical and Aeronautical Engineering, Private Bag X20 Hatfield, Pretoria 0028, South Africa b
h i g h l i g h t s We measure the pressure losses on five shaft systems. We calculate the pressure losses for the above shafts using current theory. All of the shafts which were measured are evaluated using CFD analysis. The results of the measured shaft, the theoretical evaluation and the CFD analysis are compared. An economic evaluation of the different shaft layouts is completed.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 May 2014 Received in revised form 11 April 2015 Accepted 24 April 2015 Available online xxx
In recent years, substantial progress has been made with respect to the definition and control of the primary energy requirements in underground mines. Little has, however been done to develop a more detailed understanding of how to limit the various pressure losses which are intrinsic to shaft systems. This is in spite of the fact that more than half of the pressures generated by the ventilation fans in deep level mines are dissipated as pressure losses within the shaft system. This paper presents research which has been completed to optimize the pressure losses which occur in shaft systems as a result of the ventilation air flowing through them. In this regard, the response of various shafts to the ventilation air flowing through them was measured. These results were evaluated against the current theory for the calculation of shaft pressure losses. Finally the results of the measurements and calculations were used to calibrate a Computational Fluid Dynamics model of the shaft systems. This model was then iterated to allow meaningful conclusions as to the specific make up of the shaft equipment which contributes the most to pressure losses in shaft. The results of the above analysis demonstrated that the current theory used for the evaluation of these pressure losses is deficient. The paper discusses these conclusions and the specific ramifications of the analysis. Finally, the understandings gained with regards to the above research are applied to the design and layout of equipment in mine shafts. In this regard, the shape and orientation of the shaft steelwork is evaluated and its specific interaction with the piping and fitting is evaluated. Coming out of this evaluation are specific recommendations for the design of future shaft systems. These recommendations are based on the above models and offer specific savings on the lifetime operating costs of shaft systems. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Mine shaft Deep level mines Pressure losses Shaft ventilation Shaft CFD evaluation Shaft design recommendation Bunton design
1. Introduction
* Corresponding author. 40 Elm Street, Unit ND 255, Sudbury, Ontario P3C 1S8, Canada. Tel.: þ1 705 688 0250x5332, þ1 705 561 9899; fax: þ1 705 688 0244. E-mail addresses: [email protected] (W.J. Kempson), [email protected]. za (R.C.W. Webber-Youngman), [email protected] (J.P. Meyer).
Energy is becoming an increasingly expensive commodity throughout the world. At the same time, mines are getting deeper and becoming more mechanized. This is resulting in higher quantities of electrical energy being used in mines. As a result of ongoing innovation, there are some effective energy saving and dissipation
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systems in use. However, there has been substantially less work done in the design of mining infrastructure systems and in particular the shaft systems, to alter the way in which these items are made up and to thus reduce the overall consumption of electrical energy in mines. All mine or shaft designs tend to move along the same route, solving questions with proven and sometimes well proven techniques. This lack of change does provide a degree of comfort to prospective investors, however, this comes at a price. The cost for changing the basic design of an installed shaft system to a more efficient one is almost never worth the capital outlay. This is because, in order to make the change, either the shaft will have to stop producing (thus incurring significant opportunity cost) or the change will take years to complete as it will be done during the weekly and annual shaft maintenance cycles, assuming that any proposed design change can be accommodated without interrupting the production cycle. Thus, inefficient design has a significant effect on the long term profitably of any shaft system. In today's world, however, tools are available for the detailed evaluation of a system, and to thus prove the efficacy of design changes before they are installed. These tools, when used in conjunction with a rational analysis technique requiring both the analysis to be completed and the validation of theoretical models against measured data, can give rise to significant savings. This paper proposes a change in the manner in which shafts are designed, which can result in significant ongoing savings in mines. In this case, it is an example of changing the manner in which shaft systems are analyzed, including the use of sophisticated analysis tools. This has resulted in changes to the structural and layout components in a shaft system, making it more efficient. This paper concentrates is deep vertical shafts. The surface fans for mines associated with these shafts consume between 15% and 20% of the total monthly electrical consumption on a mine. More than half of this energy is required just to move the ventilation air through a typical downcast shaft. This means that between 7% and 10% of the mine's total monthly electrical budget goes to waste as this fan pressure is dissipated as the ventilation air traverses the shaft. 2. Previous work done on understanding shaft ventilation systems In order to understand the development of shaft systems, we will first conduct a brief review of work which has been completed in this area. 2.1. Measurement A number of shafts have been tested in the past, specifically to measure the resistance of the shaft to the flow of ventilation air through them. Most of these tests were completed circa 1960 some of these papers are referenced here [1e6,8]. The detailed evaluation of these tests is not discussed in this paper. However a summary of the general conclusions is presented below. 2.1.1. Specific conclusions derived from the review of measured shafts As a result of the evaluation of the measurements of shaft systems, the papers for which are referenced in the previous section, the following criteria for shaft design were highlighted: i Buntons and guides should be streamlined. ii Shaft walls should be lined (i.e. smooth). iii Buntons should be spaced as far apart as possible.
Up to this point (i.e. the 1962), no definitive data was available on the actual manner in which the above systems should be designed in order to minimize the pressure losses associated shaft systems. Although some theories were postulated [9], additional data was required in order to extend our understanding as to the behavior of these systems. As a result of the difficulty in measuring the actual resistances of installed shafts and, once measured, of the high capital cost and time requirements to adapt their configuration for additional tests. Scale models were used for additional testing. 2.2. The use of scale models The use of scale models depends primarily on the use of dimensional analysis in order to understand the importance of certain parameters in the system being considered. A definition was supplied by Pankhurst [7]: “The dimensions of physical quantities can be manipulated algebraically and the results can be interpreted to provide a great deal of information about the physical processes involved in the situation considered.” Unless the geometry of the system has no effect on the physical situation to be evaluated, the first requirement of a scale model is that it should be geometrically similar to the actual system being evaluated, i.e. the distance between any two points in the modeled system must bear a constant ratio to the distance between the corresponding two points in the original system. This constant ratio is called the ‘geometrical factor’. Similarly, we define the kinematic similarity (i.e. when velocities are involved) by the condition that the velocity at any point in the one system bears a constant ratio to the velocity at the corresponding point in the other system. This is called the ‘velocity scale factor’. Various other factors, such as elastic similarity, thermal similarity, etc., are all defined in a similar fashion but are not pertinent to this discussion. Although this technique is powerful and allows a meaningful comparison of scale models with full-scale systems, it must be emphasized that this is only valid as long as the system does not require extrapolation beyond the ranges of the dimensionless parameters defined in the tests. A number of the measurements carried out and used in the evaluation of shaft resistances were done on scale models [8]. The two models generally referred to are the 1.981 m (78 inch) model and the 0.305 m (12 inch) scale models which were operated by the Council for Scientific and Industrial Research (CSIR). These models were constructed in the horizontal plane and were both configured to allow the flow in them to achieve a fully developed profile before the typical shaft obstructions interrupted this flow. As a result of practical limitations, the maximum airflow achieved in these models was half of that generally found in a typical shaft configuration. This had a direct effect on the Reynolds number used in the tests and raises some concern as to the extrapolation of the results. In order to try and define the extent to which the data from this scale model could be used, various shaft configurations were tested by Chasteau [8] and the results compared. These tests showed little correlation. In the 0.305 m (12 inch) model, the test showed little agreement even to standard pipe values. The tested values were lower than expected and the results showed that the test flow was potentially not fully developed. The results also showed that it is perhaps generally better to use direct drag measurements to determine the effect of the resistance of buntons than to use the pressure drop. This has the advantage of removing the pipe wall roughness considerations from the overall measurements.
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2.3. Design considerations and current theoretical basis for shaft evaluation Any discussion on the design of shaft systems and their evaluation with respect to the resistance they offer would not be complete without discussing the work contributed by Bromilov [9]. In order to evaluate a complete shaft system, Bromilov separated the resistances for the various items found in a shaft system and evaluated each of these items in turn. The sum of the resistances offered by each of these items is converted in to a figure which is equivalent to a standard pipe friction factor, each of these friction factors is then added arithmetically. This overall friction factor is then used in the standard Colebrook-White equation for the calculation of pressure losses in a pipe, to determine the overall pressure losses in a shaft. The various items in the shaft which are evaluated are listed below: i ii iii iv
Buntons Guides, pipes and cable Shaft walls Cages and/or skips
The base assumption of this work is that the resistance offered by each of these items is independent of the resistance offered by the others. In the context of the work produced by Bromilov, each of these will be discussed separately because the analysis techniques for each differ. 1 Buntons e The term “bunton” is a cross member in the shaft located perpendicular to the direction of airflow. As such it differs from the other items in the shaft in that the pressure losses associated with this are based on the “drag” of the bunton as it impedes the air flowing around it. The pressure losses associated with the buntons in a shaft are calculated in two steps. i The pressure losses associated with the shape of the bunton are calculated by using a drag coefficient based on the shape of the bunton which is presented to the air flow. These coefficients were calculated from the measured data of different buntons shapes in various shafts. This is evaluated in conjunction with the total cross sectional area that the bunton set presents to the airflow to obtain a frictional pressure loss for a single bunton set. The pressure losses associated with one bunton set are then multiplied to include all the bunton sets in the shaft (generally these are spaced every 5 me6 m). The coefficients of drag are taken from data available from previous measurement of pressure losses associated with difference buntons shapes [9]. ii In addition to the “drag” which buntons offer to the ventilation flow, the breakaway of boundary layers from the sides or trailing edges of the buntons causes a series of vortices which extend downstream from the bunton. These vortices add to the pressure losses which occur as ventilation air flows past the buntons. In the evaluation of the pressure losses associated with the drag of a bunton, it was assumed that these vortices dissipated before the airflow reached the following bunton set. This is not true unless the buntons are streamlined or are far apart. In order to allow for this interference which the vortices cause, an Interference Factor is used. This factor was derived by Bromilov [9]. After measuring the losses associated with 24 shaft or model shafts and calculating a linear equation which would allow for the estimation of the Interference Factor. 2 Guides, pipes and cables e The resistance offered by these is estimated by subtracting the area of these fittings from the area
3
of the shaft. This reduced shaft cross section is then used to calculate the increase in the ventilation air velocity in the shaft, based on the assumption of a constant volumetric flow rate of air through the shaft. In addition to this, the increased rubbing surface apparent in the shaft cross section as a result of the introduction of these fittings is also used. This increased air velocity, as well as the increased rubbing area is then used to calculate the pressure loss in the shaft using the ColebrookWhite equation. 3 Shaft walls e The resistance of the shaft wall is calculated using factors available for standard pipe theory for skin friction as defined by the ChezyeDarcy friction factor for pipe or duct walls. 4 Cages and skips e The calculation of the pressure losses associated with cages and skips is based on work by Stevenson [10]. This involved the construction of model cages and measuring the pressure drops across them at varying air flows in a circular wind tunnel. Curves were produced from this work which allows the prediction of the pressure losses associated with cages and skips based on their dimensions. These curves are used to calculate a “shock loss” factor which is then used to calculate the pressure loss associated with the cage or skip. It should be noted though, that any effect a cage or skip will have on the pressure losses in a shaft will be temporary as the primary flow paths in a shaft are generally design to be in the mid portion of the shaft, whereas these conveyances pass through this portion as they move up and down, but are staged, and loaded above and below this portion of the shaft.
2.3.1. General discussion Bromilov's [9] work was further built on by McPherson [11]. In this work McPherson simplified and metricated the calculation of shaft resistances. In addition, he proposed the use of the Colebrook-White equation for the derivation of the shaft ChezyeDarcy friction factor. This equation is based on the Moody chart for the ChezyeDarcy friction factor and is consistent with the work Bromilov presented. The theory used in McPherson's paper was consistent with that proposed by Bromilov and provides a slightly simplified methodology for the calculation of pressure losses in shaft systems. 2.4. Specific conclusions derived from the review The theory described in this section allows for the theoretical design of a shaft system with respect to the resistance that the shaft will offer to air flowing through it, but some critical questions regarding this analysis remain unanswered. These concerns are discussed in the following paragraphs. 1 The actual effect of the shaft fittings needs to be quantified as their effect on the overall pressure losses in a shaft need to be understood. This is important because as the tonnage which a given shaft produces increases, so does the quantity of support the underground operation's need, and so more services are required to go underground (for example, water, compressed air, concrete etc), this requires more and larger pipes and fittings. 2 The effect that the shaft steelwork has on the ventilation air has been quantified based on the drag resistance it offers to the airflow. This is based on measurements taken a number of years ago and has not been verified. 3 The effect that the conveyances have on the resistance of the shaft needs to be more explicitly quantified. 4 The free air velocities in equipped shafts may be as high as 12 m/ s and air velocities of up to 22 m/s may be tolerated in
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unequipped shafts. These velocities are higher than those recommended by McPherson and are indicative of the requirement to make capital assets such as the shaft work as hard as possible to service the mine's general requirements. 3. Latest analysis of shaft systems The pressure losses associated with a number of shafts at Impala Platinum were measured in order to validate the theory described above as well as to calibrate a Computational Fluid Dynamics (CFD) model which would be used to analyze the shaft systems in more detail to try and gain an understanding of the efficacy of theory as well as the actual pressure losses associated with shaft systems. The shafts which were measured are: i ii iii iv v
Impala Impala Impala Impala Impala
14 shaft 11 shaft 1 shaft 11C shaft 12N shaft
3.1. Test methodology The following measurements were made of each of the shaft system and plotted against time: 1. 2. 3. 4.
Dry-bulb temperature ( C) Relative Humidity (%) Barometric pressure (kPa) Position and speed of all the conveyances in the shaft (m/s)
The locations of the above equipment varied depending on the shaft. This equipment was placed in a portion of the shaft where the flow was deemed to be fully developed (i.e. 10 diameters from shaft entry and exit points), as well as just above stations where this was practical. The above equipment was placed in the shaft for at least 1 week. This was done during the weekly shaft inspections, which also allowed an opportunity to inspect the shaft as well as to take air velocity measurements. Although a weeks' worth of data is well in excess of the actual analysis requirement, it did allow for a long term evaluation to ensure that the measurements showed results which were typical of the shafts. It was not possible to measure the velocity of the ventilation air in the shaft on a continuous basis. Thus in order to ensure that this data was collated, velocity measurements were taken during the shaft inspection used for the installation of the testing equipment, and during its removal. In order to confirm the ventilation flow rate during the testing period, the records of the shafts primary ventilation fans (which are plotted power consumption against time for the shafts), were examined perused to ensure that they were operating consistently for the test periods in question. Once this testing had been completed, the results were compared with those from a detailed theoretical analysis using the currently available techniques [11]. The detailed analysis and the measurements were then compared with the results obtained from CFD simulations. 3.2. Computational fluid dynamic (CFD) evaluation The package used for the CFD analysis is the STAR-CCMþ from CD ADAPCO, supplied by Aerotherm in South Africa. This package allows the 3D modelling of the shaft section under consideration by solving the continuity and momentum equations inside discrete
cells. The various shaft geometries were modelled in the software using the 3D-CAD module supplied. This module allows the complete model to be developed in readiness for the mesh generation. 3.2.1. Mesh generation The various shaft sections used in this analysis were modelled in the package using the 3D-CAD modelling features and the model was created on a 1-to-1 basis with no scaling required. This model was then meshed using a combination of the built-in polyhedral mesher for volumes and the surface remesher. The nature of the problem being examined also required that the effects of the solid interfaces and the air be modelled as accurately as possible. In this regard the Prism Layer option available as part of the meshing model was selected. This model applies additional elements at the solid interface to facilitate the accurate modelling of the turbulence around these points. The length of the primary model section was chosen to be 20 m. However, to ensure that the flow regime within the shaft was fully developed before the pressure losses over the section were measured, the initial length of shaft to be simulated such that this flow regime could develop was 10x the diameter of the shaft, in this instance 80 m. This required that the model be iterated four times (i.e. the output of the simulation becomes the input of the next simulation). To ensure accurate results, a mesh refinement analysis was performed until a mesh size was found with small changes in the pressure losses, there is very little difference between the pressure drops measured for the mesh sizes of 0.15, 0.20 and 0.25 m. As a result of this analysis, it was decided to use a base size of 0.25 m. This base size is sufficiently small to allow the shaft configurations to be accurately sized, but was also sufficiently large to allow the simulations to be run efficiently. The next requirement was to determine the effect that using the prism layers would have. This setting causes the software to generate additional layers at each boundary surface, thus improving the accuracy of calculation for the surface interactions. There was, however, a negligible difference between the results from the simulations run with and without these prism layers. It was decided nonetheless to include a prism layer with a setting of 5 (i.e. five additional layers adjacent to the boundary surface) for the simulations. 3.2.2. Fluid model Selection Once the geometry had been modelled and meshed, the appropriate fluid models were selected. In this instance, the thermodynamic and body forces were assumed to be small and the fluid used for the analysis was an ideal gas. The system was modelled in three dimensions and the K-Omega turbulence model was also used. These were resolved using the SIMPLE algorithm to solve the continuity and momentum equations in every cell. The convergence requirement was set to 1 104 for the continuity and the momentum criteria. This was achieved in most cases, although in some cases a convergence of 1 101 was accepted. In all instances the simulation was run until the data showed repeatability. 3.2.3. Boundary conditions The following boundary conditions were used: i Inlet: The inlet was defined as a constant-velocity inlet for the first section simulated. Subsequent to this, the velocity profile used for the input was taken from the output of the previous simulation. ii Outlet: The outlet was defined as being a constant pressure. This was consistent throughout all the simulations.
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x T10 e Shaft barrel and buntons and pipe including flanges xi T11 e Shaft barrel and buntons and pipe including flanges and skip 1 xii T12 e Shaft barrel and buntons and pipe including flanges and skip 2 xiii T13 e Shaft barrel and buntons and pipe including flanges and man cage 1 xiv T14 e Shaft barrel and buntons and pipe including flanges and man cage 2 xv T15 e Shaft barrel and buntons and pipe including flanges and service cage
7.4m Dia Shaft Airflow Buntons Skip
Skip Conveyances 2 Deck Service Cage
2 Deck Man Cage
5
4. Results of the analysis The first portion of this section comments of the efficacy of the CFD results vs the measured results. Once this has been discussed, the next section compares the CFD results for specific section of the shaft system against the results obtained from calculation using the current theory.
2 Deck Man Cage
Pipes 4.1. Evaluation of CFD results Fig. 1. Cross section of no. 14 shaft.
iii Wall conditions: The walls were defined as a rough wall with an asperity of 10 mm. This resulted in a Yþ along the wall of approximately 90, which is acceptable. It is worth noting that using the mass flow of the fluid as the input would have been ideal. However this was not possible, suffice to say the variation of the mass flow over the test section never exceeded 2.5% of the total mass flow. This is sufficiently small to not be a concern. 3.2.4. Shaft cross section To ensure a thorough understanding of the interaction between the various items contained in a shaft, it was decided to build the CFD model systematically and to include the various pieces of equipment progressively. This would allow the effect of the individual items to be evaluated. (see Fig. 1) The following series of tests were completed. i T01 e Shaft barrel pressure losses ii T02 e Shaft barrel and one bunton across the shaft iii T03 e Shaft barrel and two vertically spaced buntons across the shaft iv T04 e Shaft barrel and full buntons set at 6 m v T05 e Shaft barrel and pipes at pipe diameter vi T06 e Shaft barrel and pipes at flange diameter vii T07 e Shaft barrel and pipe including flanges viii T08 e Shaft barrel and buntons and pipes at pipe diameter ix T09 e Shaft barrel and buntons and pipes at flange diameter
In order to compare the results of the measured data against that which was calculated using McPherson's methodology [11], and subsequently against the results from CFD model, there are two factors which must be quantified. These are, the accuracy of the calculation itself as well as the accuracy of the instrumentation and measurement methodology. The accuracy of the calculation made in accordance with the ChezyeDarcy formula is (þ15% to 15%) [13]. The accuracy of the testing methodology and the instrumentation was calculated to have an accuracy of (þ12% to 29%) [12]. In this evaluation, the first phase was to ensure that all the instruments had up to date calibration certificates and that the results that they showed were consistent between each other, this was found to be accurate. The second phase of this evaluation was to examine what effect the quoted accuracy of the instrument would have on the calculated data (for example, to calculate pressure loss, two measurements are required, and each instrument can vary up and down from the median). In addition, this data is then used to calculate the final value. For example, in order to calculate the pressure loss in a shaft accurately, the temperature at both points are required as well as the relative humidity, barometric pressure and elevation difference. This combination of factors can have the effect of increasing the calculated pressure losses by 12% or decreasing them by 29%. As can be seen from the Table 1 above, there is good correlation between the theoretical calculation and the CFD analysis for two of results. There is consistently poor correlation between
Table 1 Comparison of Measure Data vs Calculated Data vs CFD Data. Shaft no.
PLoss
No. No. No. No. No.
1.81 1.26 70% 1.22 0.95 77% 0.47 0.55 118% 0.69 0.59 85% Bratticed shaft, the measured results were not reconcilable
14 11 1 11C 12N
(measured)
(Pa/m)
PLoss
(calculated)
(Pa/m)
PLoss
(calc)/PLoss (meas)
PLoss 1.22 0.87 0.42 0.38
(CFD)
(Pa/m)
PLoss 97% 92% 76% 63%
(CFD)/PLoss (calc)
PLoss
(CFD)/PLoss (meas)
68% 71% 89% 53%
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W.J. Kempson et al. / Applied Thermal Engineering xxx (2015) 1e11
Table 2 Summary of results (cross sections).
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the measured results and both the theoretical and CFD results, as well as between two of the measured and calculated results although the results are within the accuracy limits defined above. The differences noted between the data on the shafts above do, however, highlight the potential differences that arise when evaluating complex systems from a theoretical perspective. It is not possible to include the effects of various items such as imperfections between the lining rings, the inclusion of slinging points in the shaft, large cable pocket installations, intermediate pump
7
stations and other shaft openings. The differences noted above are attributed to these as well as the other inaccuracies noted above. In this instance the data indicates that a design allowance of the order of 30% would be appropriate.
4.2. Comparison of CFD results and current theory It should be noted that, as the shafts modeled were each of different depths, the pressure losses obtained across the shaft
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W.J. Kempson et al. / Applied Thermal Engineering xxx (2015) 1e11
system are reported per metre length of shaft. The results for selected tests are presented in Table 2 on the following pages.
5. Discussion of basic set of CFD models As the shaft was built up and the buntons and pipes were added, there was little correlation between the theoretical pressure losses and those predicted by the CFD analysis (see results of Test No.1 through 6 above), where there are still large differences between the CFD derived pressure losses and those which are calculated. This continued (see Test No. 9), until the point at which the full shaft cross section was being evaluated. The resistance predicted by the CFD analysis equaled that of the theoretical analysis (See Test No. 10). The conclusion that was reached was that the inter-related nature of the equipment in the shaft increased the total resistance of the shaft by some 30%, as the summation of the individual CFD derived pressure losses would have been approximately 30% lower than the total depicted in Test No. 10. (See Fig. 2). This finding has two specific outcomes: i The current theory is not accurate. While the calculated results for the shaft pressure losses were similar to those of the CFD analysis, the composition of these calculations are different. Primarily, the assumption that each of the fittings in the shaft can be evaluated separately, and the result added was found wanting. ii The inter-related effect of the fittings in the shaft is stronger than was initially anticipated. In order that a shaft be designed in a manner which will limit the shaft resistance, effect which each of the shaft fittings have on each other should be considered. Should the current theory be used without this consideration being taken in to account, changes could be made to reduce the shaft resistance that are either incorrect or could not have as significant an effect as was originally thought.
6. Extended investigation of options for shaft steelwork profiles and shaft pipework One of the areas that was considered worthy of further investigation was the manner in which the resistance of piping in the shaft was calculated. The piping was therefore modeled, initially at its pipe diameter, then at the flange diameter, as is required by the theory, and finally at the pipe diameter with flanges, which has not been done before. There was not a significant increase between resistances calculated by the CFD simulations using the piping at each of the diameters (less than 1%). However, when the piping was introduced with flanges there was a significant increase in the resistance (the piping in a bare shaft showed an increase of 20%. This is a significant increase and more than sufficient to warrant avoiding the use of flanges or introducing any discontinuities in the piping as far as practically possible. Discussions with mine personnel and shaft-sinking professionals resulted in the installation and maintenance costs not being included in this analysis. This is because these costs are considered to be the same no matter what bunton shape is used. The installation and maintenance cost for the piping is not considered a cost differential here and is therefore not included in the analysis. This includes the flanges and/or other pipe connectors that could be used.
6.1. Summary of options To ensure that the recommendations made in this work are valid, a number of additional options were evaluated using the CFD technique described above. These options were evaluated and the pressure losses over the shaft length were calculated. The dimensions used for the shaft are as follows: Shaft diameter: 9 m Shaft depth: 2 000 m Average Shaft Ventilation velocity: 10 m/s
Fig. 2. Summary of resistances in shaft by items.
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6.2.2. Piping Arrangements This result shows that the judicious placement of the piping in the shaft can have a significant effect on the resistance in the shaft. This saving can be between 7% and 12% of the total resistance experienced in the shaft. The results also show that, once the most efficient position has been chosen for the piping, the use of flanges to join the pipes can increase the cost of supplying air to the mine by approximately 12%.
9m Dia Shaft Buntons
Skip
Skip
Men and Material Cage
Conveyances
C/Weight
9
6.3. Summary and conclusions The following specific points can be made from the collation of all the economic data.
Pipes (Distributed)
i The shape of the buntons is important in meeting the requirement to reduce the pressure drop in the shaft as much as is possible. ii The placement of the piping in the shaft and the use of flanged piping can have a significant deleterious effect on the pressure drops in the shaft.
Fig. 3. Typical shaft cross section.
The basic fan power required to deliver the flow rate and the calculated pressure, as well as the overall costs for the power to deliver this were calculated. This cost for the power requirement was used to evaluate the current and potential costs of the options under consideration. The cross-section of the shaft is shown in Fig. 3. The results of this analysis are presented in Tables 3 and 4 below:
6.2. Summary of results and potential savings due to reduced energy requirement 6.2.1. Bunton shapes As can be seen from Table 3, a significant saving can be made through the judicious choice of the bunton shape. This varies from 52% to 81% of the fan power costs as a direct result of the resistance the shaft offers to the flow of air through it as a result of the bunton shape. A small decrease in these costs was also noted for the streamlined buntons of 5%. These savings are consistently better than that predicted by the McPherson.
7. Conclusion The initial work undertaken for the evaluation of the resistance that shaft systems offer to the ventilation air flowing through them was started circa 1960. This work consisted of both a theoretical evaluation as well an experimental. This work was built on by McPherson [11]. As shaft have got deeper, the cost for moving large amounts of ventilation through them has increased. This has been matched by the exponential increase in the cost for electrical energy. The development of methodologies which have been used for the evaluation of the shaft systems have followed good engineering practice. The calculation methodologies were developed using well developed equation for the derivation of drag and pipe friction. These methodologies were then compared to measurements from actual shafts as well as scaled models. A factor was introduced to allow this data to be used (The interference factor). This has resulted in analysis techniques which seem to accurately predict the pressure losses in shaft systems. However no detailed work had been done to validate the assumptions required for this
Table 3 Energy savings apparent due to bunton shapes. Item
Description
Shaft PLoss m(Pa)
Ratio differences
Rand (savings over 20 years LOM) (R 1000)
Canadian dollars (savings over 20 years LOM) ($C 1000)
1.01
Airflow buntons
822
1.00 (Baseline)
e
e
1.02
Streamlined buntons
774
0.94
5738
7615
1.03
Square buntons
1608
1.92
94 046
124 762
1.04
I-beam buntons
1324
1.61
60 413
80 143
Schematic of bunton cross section
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W.J. Kempson et al. / Applied Thermal Engineering xxx (2015) 1e11
Table 4 Energy savings apparent due to piping arrangements. Item
Description
Shaft PLoss (Pa)
Ratio differences
Rand (savings over 20 years LOM) (R 1000)
Canadian dollars (savings over 20 years LOM) ($C 1000)
2.01
Piping along shaft edge (no flanges) Piping away from shaft edge (no flanges) Piping distributed around shaft (no flanges) Distributed piping with flange
857
1.13
12 114
16 071
819
1.08
7 651
10 150
755
1.00 (Baseline)
e
e
867
1.14
13 310
17 657
2.02 2.03 2.04
Piping along shaft edge
Piping away from shaft
work or the undertaken a detailed analysis to understand the actual mechanism for pressure losses in the system. In this regard it was decided that there would be potential benefit to completing a detailed CFD analysis of a shaft system. In addition, as there was no reliable up to date to calibrate this CFD model, measurements were taken of a number of shafts to help with this validation. In addition calculation of the anticipated shaft pressure losses were completed using the procedure laid down by McMPherson. This work was completed and while the measurements showed differences to those of both the theoretical calculations as well as the CFD analysis, there was sufficient correlation to allow the model to be used for a more detailed evaluation. This evaluation primarily consisted of building a shaft system using the CFD analysis, piece by piece. This allowed the measurement of the anticipate pressure loss over individual members of the shaft system. For example the actual pressure losses measured as the result of the inclusion of the buntons was isolated and evaluated, similarly with the pipes, pipe flanges, fittings etc. The most significant conclusion derived from this analysis is that the two primary assumptions used for the theoretical calculations of shaft systems are incorrect. These assumption are described in detailed in Section 2.3: The assumption made by both Bromilov [9] and McPherson [11] that the resistance offered by the individual items in the shaft could be evaluated separately and summed arithmetically is incorrect. The CFD analysis showed that the individual evaluation would result in a total resistance of approximately 30% less the actual pressure loss in the shaft system. The evaluation of the effect that the pipes and guides have on the resistance of the shaft is not accurate. The current manner does not accurately account for the use of pipe flanges or the changes in resistance which occur as a result of the placement of the piping.
Piping distributed
As a result of the above, it is recommended that future shafts be design using the CFD methodology recommended here. The current trend for the design of shaft systems is moving further away from the operation envelopes that current shafts were designed in (i.e. shaft are getting deeper, with faster moving skips, high ventilation velocities, different styles of buntons and increasing quantities of pipes for underground services). This will make the current theory which was used to predict shaft resistance less accurate and could give rise to the design of inefficient systems if the current theory is used. As is shown in the data, the use of the CFD analysis can result in significant savings (potentially as much as 70%) in the cost of the electrical energy required to push ventilation air through the shaft. Acknowledgements This work was possible as a result of the efforts of the following people: 1 James Janse van Rensburg, Group Ventilation Manager at Impala Platinum, who facilitated use being able to various shafts at Impala Platinum. 2 Prof R.C.W. Webber-Youngmann, for his patience and guidance in the completion of this work. 3 Prof J.P. Meyer for his patience and guidance in the completion of this work. 4 Lister Sinclair, Head of Mining at Hatch Africa, for his guidance in the completion of this work. References [1] V.A.L. Chasteau, Investigation into the resistance to airflow of the pioneer shafts at Buffelsfontein gold mining Co, Ltd (Part II), J. Mine Vent. Soc. S. Afr. (1959) 138e146 (June). [2] M. Bareza, M.J. Martinson, Ventilation resistance of some vertical downcast shafts in the rand mine group, J. S. Afr. Inst. Min. Metallurgy (1961) 56e61 (October).
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W.J. Kempson et al. / Applied Thermal Engineering xxx (2015) 1e11 [3] V.A.L. Chasteau, Investigation into the resistance to air flow of no. 1 shaft, vaal reefs exploration and mining company (paper ii), J. Mine Vent. Soc. S. Afr. (1961) 138e146 (January). [4] D.F.H. Graves, Airflow resistance in downcast shafts equipped with streamlined buntons, J. S. Afr. Inst. Min. Metallurgy (1962) 99e106 (June). [5] J.F. Kemp, Analysis of the air flow in downcast shafts with reference to the trailing-hose method of resistance measurement, J. Mine Vent. Soc. S. Afr. (1962) 321e335 (January). [6] JdeV. Lambrechts, T.E. Deacon, Improvements in ventilation capacity by smooth lining of upcast shafts, J. S. Afr. Inst. Min. Metallurgy (1962) 61e66 (February). [7] R.C. Pankhurst, Introductory survey. Dimensional Analysis and Scale Factors, Chapman and Hall, London, 1964, pp. 13e19, 53e55. [8] V.A.L. Chasteau, Equipment and techniques used for scale model investigations of mine shaft resistance to air flow in the CSIR laboratories, J. Mine Vent. Soc. S. Afr. (1962) 362e369 (May).
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[9] J.G. Bromilov, The estimation and the reduction of the aerodynamic resistance of mine shafts, Trans. Inst. Min. Eng. (1960) 449e474 (May). [10] Stevenson A, Mine ventilation investigation. Shaft pressure losses due to cages, Unpublished thesis, Royal College of Science and Technology, Glasgow. Also as: The estimation and the reduction of the aerodynamic resistance of mine shafts. Transactions of the Institution of Mining Engineers, Glasgow, 1956. [11] M.J. McPherson, The resistance to airflow of mine shafts, Proc. 3rd Mine Vent. Symp. (1987) 465e477 (October). [12] W.J. Kempson, R.C.W. Webber-Youngman, J.P. Meyer, Optimizing Shaft Pressure Losses through Computational Fluid Dynamic Modeling, University of Pretoria, 2012 (January). [13] F.M. White, Fluid Mechanics, 2nd edition, McGraw-Hill, New York, 1986, pp. 308e314.
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