\r\n\tIt is hoped that the upcoming book project will explore existing technical developments and the potential for projected alternative architectural paths and operation, based on the current market indicators.
",isbn:"978-1-78985-720-7",printIsbn:"978-1-78985-719-1",doi:null,price:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"bbaf96f832d3a8b509e18bf1bdaacc87",bookSignature:"Dr. Mohammad Abdul Matin",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/7401.jpg",keywords:"Network Architecture and Protocols, Telecommunication Signaling and Control, Traffic Engineering,Network Security, Network Operation and Management, Transmission Media and Systems, Network Design,Switching and Routing, Measurements and Modeling, Broadband Access, Telecommunication Software, Telecom Economics and Business",numberOfDownloads:222,numberOfWosCitations:0,numberOfCrossrefCitations:0,numberOfDimensionsCitations:0,numberOfTotalCitations:0,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"February 20th 2018",dateEndSecondStepPublish:"March 13th 2018",dateEndThirdStepPublish:"May 12th 2018",dateEndFourthStepPublish:"July 31st 2018",dateEndFifthStepPublish:"September 29th 2018",remainingDaysToSecondStep:"a year",secondStepPassed:!0,currentStepOfPublishingProcess:5,editedByType:null,editors:[{id:"12623",title:"Dr.",name:"Mohammad Abdul",middleName:null,surname:"Matin",slug:"mohammad-abdul-matin",fullName:"Mohammad Abdul Matin",profilePictureURL:"https://mts.intechopen.com/storage/users/12623/images/1967_n.jpg",biography:"Dr. Mohammad A Matin currently works at the department of Electrical and Computer Engineering, North South University (NSU), Bangladesh as an Associate Professor. He obtained his BSc. degree in Electrical and Electronic Engineering from BUET (Bangladesh), MSc degree in digital communication from Loughborough University, UK and PhD degree in wireless communication from Newcastle University, UK. He has published over 80 refereed journals and conference papers and is the author of thirteen (13) academic books and eleven (11) book chapters. He has presented invited talks in Bangladesh, and Malaysia and has served as a member of the program committee for more than 50 international conferences. Dr. Matin is currently serving as a member of editorial board of several international journals such as IEEE Communications Magazine, IET Wireless Sensor Systems (IET-WSS). He has received a number of Prizes and Scholarships including the Best student prize (Loughborough University), Commonwealth Scholarship and Overseas Research Scholarship (ORS). 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However, Verbiest [1, 2] was the first to associate changes in the diameter of the vertebral canal with the clinical features and neurogenic claudication. The reduced canal diameter was only correlated to the disc degenerative process by Kirkaldy-Willis, when the authors demonstrated that disc degeneration was directly related to the changes that lead to the physiopathology of reduced vertebral canal diameter [3].
\nBased on a study of dissection of 50 cadavers, Kirkaldy and Willis described how changes in the zygapophyseal joints and disc degeneration may lead to root impingement and, consequently, all the set of symptoms, which will be discussed in depth later [4].
\nAccording to Farfan [5], the degenerative process starts with minor trauma, which, repeated over several years, leads to spondylosis. A few years later, Farfan et al. [6] described how each segment of the lumbar spine is composed of a complex triad: two zygapophyseal joints and the disc. Because those three joints work in tandem, any disease that affects the disc will eventually compromise the joint and vice versa. The chief lesion mechanisms are torsional forces and compression overload [7].
\nFarfan also describes how the degenerative process starts between the fourth and fifth lumbar vertebrae and that after that level is compromised, based on the three-joint theory, the degeneration progresses to the proximal and distal adjacent levels. Thus, it becomes a diffuse disease that affects multiple levels of the lumbar spine. The anatomic changes are described next.
\nThe zygapophyseal joints are diarthrodial, having an articular surface, a synovial membrane, and a capsule made of collagen; they are filled with synovial fluid [8]. Their degenerative process follows a sequence described by Lewin in 1964 [9]: it starts with a synovial reaction, followed by fibrillation of the joint surface, gross degeneration of the cartilage, osteophyte formation, joint process fracture, and finally loss of the joint’s natural shape, leading to instability.
\nThe third component of this complex joint is the intervertebral disc, the largest nonvascular tissue in the human body [10], which comprises three structures: the nucleus pulposus, the annulus fibrosus, and the terminal plates [3]. Each one of these structures has its own anatomy and unique constitution, and considerable importance [10]. The annulus fibrosus is made of type I collagen, distributed in circular layers, and resistant to traction forces. The nucleus pulposus is made basically of proteoglycans, water, and type II collagen, as well as countless elastin fibers [11]. Nutrition of the disc cells occurs through diffusion, in which vessels in the subchondral space, adjacent to the terminal plate’s hyaline cartilage, carry oxygen, glucose, and small molecules, thus maintaining the disc’s homeostasis [12]. Such homeostasis allows the nucleus pulposus to withstand compressive forces without collapsing and forces to be homogeneously transferred to the annulus fibrosus in all spine movements [13].
\nAnother anatomic area that may go unnoticed is the lateral region, including the intervertebral foramen. Lee et al. [14] subdivided this region into three zones: the afferent zone, located in the subarticular region, medially to the pedicles; the intermediate or middle zone, located below the pars interarticularis; and finally, the efferent zone, comprising the intervertebral foramen. The latter is very important in surgical cases, because a lack of identification may lead to incorrect decompression and persistence of symptoms after surgery [15]. The foramen is a relatively large orifice, which often contains the dorsal root ganglion, coated with a layer of fat for the protection of neural structures. It is delimited anteriorly by the posterior vertebral wall, proximally by the inferior edge of the superior pedicle, inferiorly by the superior edge of the inferior pedicle, and posteriorly by the zygapophyseal joints and the yellow ligament.
\nThe degenerative process can also be observed in this region, where diffuse disc bulging can also be seen, associated with loss of height—all leading to a reduced diameter of the vertebral canal. The zygapophyseal joints are also directly associated with foramen stenosis, because their hypertrophy may or may not be associated with the presence of osteophytes, thus causing radicular compression. In this case, sciatica may be observed, mimicking the symptoms of disc herniation [16].
\nThe progression of the degenerative disease still remains truly unknown [17]. However, many concepts have already been postulated. The first one concerns the definition of instability; it is defined as “excessive mobility, neural compression, or deformity.” The presence of instability may be associated with a variety of clinical and anatomic manifestations [18].
\nKirkaldy and Willis described the degenerative process in terms of evolution and divided it into three phases. However, the duration of each stage is unknown. The first phase was described as a dysfunction in which the disc exhibits chiefly biochemical changes. The second phase was called instability in which degenerative processes in the disc lead to an increase in the segment’s motion; this is when disc herniation can occur. Finally, there is the stabilization phase in which disc height reduction, facet hypertrophy, and changes in the yellow ligament occur [18]. This phase of disc degeneration is the most important for the development of the present study, because the aforementioned changes lead to a reduction of the vertebral canal diameter and to narrow lumbar spinal canal syndrome—the disease that is the object of this study.
\nAs was described by Kirkaldy and Willis, the cascading degeneration does not have a definite phase, but in the stabilization phase, lumbar canal stenosis can be observed. It may or may not cause symptoms, but if symptoms do occur, this is commonly observed in patients above 50 years of age. Currently, the most commonly performed type of spine surgery in patients over 65 years old in the United States is decompression of cauda equina roots [19].
\nBecause the population is aging and life expectancy is increasing, we were motivated to conduct this project.
\nNarrow lumbar spinal canal syndrome comprises a number of symptoms and varied clinical features [20], which is further discussed below.
\nVertebral canal stenosis, as defined by Verbiest [2], corresponds to narrowing of the vertebral canal, the lateral recess, and the intervertebral foramen, causing compression of neural elements. Vertebral canal stenosis can be divided into two main groups: congenital and acquired [21]. These main groups were further subdivided: congenital stenosis into idiopathic and achondroplasic, and acquired stenosis into degenerative, combined, spondylotic, iatrogenic, post-traumatic, and metabolic [21].
\nNarrow lumbar spinal canal syndrome may be confused with many other diseases. Such diseases must always be considered, and a detailed clinical examination may make all the difference. Among the conditions that should be investigated are disc herniation, vascular claudication, tumors, peripheral neuropathy, arthrosis of the hip or knee, and compressive insufficiency fractures [16].
\nHall et al. [22] described symptomatic canal stenosis in detail. They described that patients complain of progressive lumbar pain, associated with an incipient pain and numbness in the distal extremities. Neurogenic claudication, the commonest symptom, is characterized by pain and weakness starting in the buttocks and thighs that becomes gradually worse in the orthostatic position and during walking, but improves after sitting down or leaning forward. Less often, one can find unilateral radiculopathy [23]. Symptoms become more acute with the disease’s natural progression [24].
\nThe progression of the disease is uncertain: according to Johnson, 70% of patients remain stable for a 4-year period, 15% improve, and 15% tend to become worse. The progression to cauda equina syndrome is extremely rare, but must always be investigated, particularly because of the possibility of other causes, but also because it is an absolute indication for urgent surgery [25].
\nElderly patients may present a clinical condition very similar to neurogenic claudication, an entity called vascular claudication, associated with atherosclerosis. The pain following a walk is very similar to that in neurogenic claudication. Physical examination then becomes essential, because in a detailed examination, one can observe impotence in men, dystrophic skin, loss of hair, nail dystrophy, cyanosis, and reduced peripheral pulse. Such symptoms may be essential for the latter diagnosis [22].
\nThe best diagnostic test to distinguish both syndromes was described by Van Gelderen [26]. He had patients riding a stationary bicycle. Patients with lumbar canal stenosis tolerate the exercise, because the forward-leaning position causes symptoms to improve, whereas patients with vascular claudication do not tolerate the exercise, because the hypoxia caused by the underlying disease causes pain and peripheral cyanosis. Another very relevant sign in narrow canal syndrome is improvement when walking uphill and worsening when walking downhill, always associated with the flexion or extension of the trunk [27, 28]. It is postulated that the improvement associated with flexion and extension is directly related to stretching or folding of the yellow ligament. Trunk flexion causes tension in this ligament, thus increasing its diameter, whereas trunk extension causes it to fold into the spinal canal, thus further narrowing the canal that is already narrowed by the degenerative process [29, 30].
\nThe physical examination of a patient with lumbar canal stenosis starts with the careful observation, followed by a very thorough physical examination. One must always consider the differential diagnosis from the other above-mentioned conditions; however, when compared to disc herniation, there are some subtle differences, such as age above 50 years, insidious onset, improvement with trunk flexion and worsening with its extension, and localized motor weakness. Signs of dura mater tension and muscular contraction are rarely found. Typically, a trunk flexion position is observed, due to the increased canal diameter in that position. The presence of a reduced arc of movement is associated with the joint’s degenerative process and not directly with the lumbar canal stenosis. Analogous to Phalen’s test, Kemp’s test is described in the literature, in which the patient is kept in trunk extension for 30 s and claudication symptoms appear [31].
\nRadiological diagnosis includes several examinations: common radiography, computed tomography (CT), and magnetic resonance imaging (MRI). In selected cases, myelography or myelotomography may be necessary [32].
\nThe study of neural function and conduction speed can be performed either by electroneuromyography or by sensitive-motor evoked potentials [32].
\nRadiographs must be obtained in four incidences: frontal, orthostatic lateral, flexion, and extension. Then one must look for degenerative changes, such as reduced disc space, sclerosis of vertebral plateaus, sclerosis and hypertrophy of articular facets, closeness of spinous processes, and the diameter of the intervertebral foramina. In dynamic radiography, one can notice the presence of anteroposterior translation [33].
\nComputed tomography is a very important advance in the diagnosis of vertebral stenosis, because it shows important bone details, including the central canal, the lateral recess, the foramen, the joint facets, and their degree of degeneration [34]. CT is, however, criticized for its high rate of radiologic findings without correlation to the patient’s symptoms [33].
\nMRI provides images of soft tissue with excellent quality, including ligaments, neural tissue, and the intervertebral discs. It is more sensitive for diagnosing lumbar stenosis than tomography. MRI findings include signal weakening at T2, with dehydration and rupture of the annulus in multiple discs; changes in terminal plates; void signal; enlarged yellow ligaments; and reduced vertebral canal [35].
\nFor many years, myelography was the gold-standard exam for diagnosing lumbar stenosis, but although today’s water-soluble contrast is less toxic, patients still have nausea, vomiting, headache, and dizziness. Myelography is an invasive exam, although it shows the dimensions of the dural sac and the neural roots in detail. Myelography findings include the partial or total interruption of contrast flow, and the dynamic examination may reveal a dynamic compression of neural structures [36]. It should be noted that electromyography is not routinely used in lumbar stenosis, because 80% of symptomatic patients have changes in one or both legs, making it necessary only for differential diagnosis, particularly to distinguish it from diseases that affect peripheral nerves [37].
\nThe canal’s diameter may be calculated by several different techniques. We used Hamanishi’s technique, widely used [38], on which the calculation to determine the presence of stenosis is based. That is, Hamanishi considers a diameter of less than 100 mm2 to define stenosis in patients with clinical symptoms and characteristic images [39].
\nThe treatment of lumbar canal stenosis may be divided into two main types: clinical or conservative and surgical [40], each of them comprising several different modalities.
\nWhen a thorough clinical examination has been performed and there is confirmation from imaging exams, electrodiagnosis is not needed, as results are often inconclusive and, when positive, do not have an influence on either the clinical or the surgical treatment [41].
\nGenerally, clinical treatment is preferred by over 50% of patients [42], and they mostly evolve satisfactorily. However, a small fraction suffers a more severe progression, with more unfavorable natural history and serious, limiting symptoms [43].
\nMany lumbar canal stenosis patients have symptoms of unilateral radiculopathy. In such cases, the most likely cause is herniation, which may affect a root in an already stenotic canal. When this happens, treatment should be more focused on the disc herniation. Despite the large number of articles in the literature, there is no consensus about when to operate such patients and, if surgery is performed, what the best technique would be [44].
\nDrug treatment does not offer many possibilities. The indiscriminate and frequent use of anti-inflammatory medications for chronic lumbar pain does not have a proven satisfactory response [45] and may be associated with gastrointestinal and renal complications. Its use should be very restricted and avoided in elderly patients with narrow lumbar spinal canal syndrome [45].
\nSimple painkillers, muscle relaxants, and opioids may be of value. They are indicated for treating and controlling the pain but have no effect on the treatment of neurogenic claudication [45]. Gabapentin has been shown to be a safe medication; it may be taken orally and has a positive effect on patients with neurogenic claudication and the sensory alterations, which are very common in these patients [46].
\nCorticosteroids are also used indiscriminately. The idea is that there is an inflammatory process associated with the mechanical compression that could benefit from the medication, but this theory was not proven by Natour’s study [47].
\nPhysiotherapy, or more broadly rehabilitation, is a second non-surgical approach. Manual therapy, stretching, and muscular strengthening play an important role, in addition to the exercises. Patients who suffer from canal stenosis have, in addition to pain, a significant muscle loss, which severely limits their activities and progressively worsens their clinical condition, which leads to further impairments [48, 49].
\nThe recommended activities include manual therapy, strengthening, and walking training, as well as exercises that improves proprioception. In addition, weight loss is important, because obese patients have been described to have a worse prognosis [47]. Cycling is a very much recommended activity, not only because patients tolerate it well, but it also allows them to improve their conditioning and does not impact other joints that may also be degenerated, such as the hip and the knee [50].
\nZarife et al. [51], in a study comparing two types of conservative treatments—physiotherapy and peridural corticosteroids—concluded that, in a 6-month follow-up, both methods were effective in improving the patients’ condition and ability to walk, which suggested that clinical treatment is important and effective in these delicate and active patients.
\nPeridural corticosteroids are another type of non-surgical treatment for narrow lumbar spinal canal syndrome, as opposed to oral corticosteroids, which were shown to be ineffective for this condition [47]. Peridural corticosteroids have some advantages, which are discussed below. There are several possibilities for their administration, with or without radioscopy, as well as several techniques: interlaminar, caudal, and transforaminal. Despite their limited benefits, their use may have lasting efficacy in many patients [52].
\nCosgrove et al. [53] published an article in 2011 in which the efficacy of peridural corticosteroids was evaluated and showed that women obtained greater benefits than men and that clinical results were not related to MR findings, which was also found in Natour’s study [47]. Although Cosgrove et al. [53] observed better results among women, as per the general literature, women are normally affected compared to men.
\nSimilarly to the above-mentioned article, Charles et al. [54] showed that peridural corticosteroids produce a satisfactory response in lumbar stenosis. The results of the study showed that patients with associated radiculopathy have a better response than do patients with claudication and that 25% of patients respond more favorably up to 2 years after the procedure.
\nHowever, we also found some articles in which the use of peridural corticosteroids did not deliver the expected satisfaction, in addition to causing complications such as meningitis, arachnoiditis, aseptic meningitis, and increased serum corticosteroids [55]. Fukusaki et al. [56] compared the use of analgesics in isolation and in combination with peridural corticosteroids and reported no complications; however, the results after 3 months were unsatisfactory, with all symptoms returning.
\nSurgical treatment is considered the last resort for patients with treating lumbar canal stenosis. Because surgery is performed in patients over 65 years of age, there is significant morbidity and mortality, which increase with associated diseases and patient age, making it mandatory to assess the risks and benefit of the surgery [57].
\nAiraksinen’s study [58] showed that patients over 50 years old who underwent decompression and arthrodesis evolved with a significantly reduced ability to return to work. That reduction was even greater in older patients.
\nThere are articles that report surgical results, with conflicting results. Hurri et al. [59], in a 12-year follow-up study, did not find any differences between surgical and non-surgical results, showing that regardless of surgery, the outcome is the same. Another study comparing operated and non-operated patients was the Maine Lumbar Spine Study [60, 61], in which operated patients were followed up for a period from 4 to 10 years. Results showed that operated patients had better postoperative results than non-operated patients, with an average of 72% satisfaction among the former and 52% among the latter at 4 years of follow-up. The same comparison made at 10 years showed inferior results, but operated patients still had a perception of improvement.
\nTurner et al. [62] performed a meta-analysis and found that 64% of patients showed good results after surgical treatment, for a period varying from 3 to 6 years.
\nSurgical treatment is indicated when clinical treatment fails or neurological symptoms worsen [63]. Today, there are several different surgical techniques. The classical technique is laminectomy, performed by an incision along the midline followed by decompression, removing up to 50% of facets. In addition, there are minimally invasive techniques, such as opening and decompressing only one side of the lamina, which is called recalibration [64]. Interspinous spacers have been recently included in the surgical arsenal for canal stenosis, but studies are still under way, and there are no studies yet evaluating for an adequate follow-up period. For this reason, the actual benefit of this kind of surgery is not yet well established. However, it is known that it does offer some advantages, such as short hospitalization periods and limited bleeding. Its indication takes into account that by tensioning the yellow ligament, the canal diameter is increased [65].
\nThe median approach with broad exposure of the spine has the advantage of satisfactorily exposing the spinal canal, which allows the intervertebral foramina to be viewed, broad decompression to happen up to the efferent zone with direct view, and roots to be evaluated. However, care must be taken to preserve half of the facets; otherwise, postoperative instability will occur as an iatrogenic complication that may compromise the results for the patient. The main problem with this broad approach is blood loss, which may be large or even catastrophic in some cases, because muscular lesion leads to large arterial and venous bleeding [63].
\nThe indication for instrumentation and fusion varies in the literature, with some authors indicating fusion in the presence of degenerative spondylolisthesis or if there is a translation greater than 5 mm in dynamic X-rays. Instrumentation may also be indicated in cases of degenerative scoliosis in which the neural foramen is compressed on the concave side of the curvature and resection of more than 50% of the articular facet is needed in order to decompress the root stuck inside [66, 67].
\nThe minimally invasive approach in spinal canal stenosis associated with foraminal stenosis may be indicated for patients with lumbar and radicular pain associated with stenosis in imaging exams, but its main contraindication is the presence of instability in X-rays, associated with a scoliosis of more than 10° in X-rays, in the orthostatic position. The main complication is recurring symptoms, in approximately 20% of cases, with reoperation being necessary, with broad exposure of the spine [68].
\nInterspinous spacers are a new generation of implants. Their mechanism of action is by blocking extension, as well as tensioning the stenosis level, which theoretically increases the spinal canal diameter. Studies have shown that such an increase may reach 20% of the initial diameter [69], but these studies are questioned due to the possibility of commercial interests. They are indicated for lumbar canal stenosis patients with two levels of stenosis, but they are not used in the L5-S1 level and are contraindicated for patients with degenerative spondylolisthesis or radiological signs of instability [70].
\nPostoperative care of lumbar canal stenosis patients may vary slightly, but basically, patients are instructed to walk on the first day after surgery. Longer rest is indicated for patients with incidental durotomy, in which case the recommendation is at least 2 days rest. Deambulation with the aid and training by a physiotherapist is very important [71]. Rehabilitation exercises must include stretching the posterior muscles of the thighs and legs, training trunk flexibility, and strengthening the abdominal and paravertebral muscles. Improving cardiopulmonary capacity is also a target of rehabilitation, always respecting the patients’ limits [72].
\nThe need for orthesis is very much relative. Their use is generally not indicated. In osteoporotic patients, when there is the risk of an acute failure of implants, their use may be indicated for a period of up to 6 weeks, but overall, the literature is highly controversial about this subject [73].
\nThe complications observed in surgery for lumbar canal stenosis may be divided into complications in the operated area and systemic complications. The most commonly observed systemic complications are urinary retention, worsening of heart failure in previously affected patients, delirium, and thoracic pain. Such symptoms are usually temporary, but they increase hospitalization time [74].
\nSurgical complications vary according to the series. Jolles et al. [75] report sensorial and motor defict, dura mater lesions with cerebrospinal fluid fistula, surgical site hematoma, and superficial and deep infection.
\nEpidemiologically, surgery for lumbar canal stenosis has the same incidence of complications as knee arthroplasties, but greater than hip arthroplasties [76]. Mortality is currently at an average of 10%, but it increases with patient age. Clinical complications vary from 3 to 31% [77]. However, the most common complication observed in lumbar canal stenosis surgery is incidental durotomy, with an average incidence of 16%, increasing in case of reoperation [78]. Cerebrospinal fluid fistula, with leakage of cerebrospinal fluid, is the chief cause of reoperation in the first 2 days after surgery [79].
\nIn conclusion, lumbar canal stenosis is a complex syndrome, which comprises degenerative processes in the lumbar spine. This degeneration may lead to a painful and limiting clinical condition, which must always be investigated through an exhaustive study of imaging examinations. Even though treatment is varied, with a large number of possibilities found in the literature, studies usually compare different techniques, either surgical or conservative, to find the most effective one. Apparently, the surgical approach with decompression, either associated with arthrodesis or not, has provided not only the best clinical results but also a greater incidence of complications and mortality, which must always be weighed together with the patient before surgery.
\nIndustrial machines and devices with rotating operating parts are difficult to model due to their complex geometry, the transition of elements of the discrete model between the rotating and non-rotating parts, the importance of the quality of elements of the discrete model, and the fact that in most cases, it is necessary to take into account the time step (elements rotate in relation to the casing). It is also troublesome that very often the calculations are stabilised only after a few rotations of the operating element. However, the use of computational fluid dynamics methods to model this group of machines and equipment is justified, as it enables:
Determining the internal and external characteristics of machines and devices in virtual space
Imaging and observing the flow phenomena in the machine itself (especially when for various reasons it is impossible to measure physical quantities of the flowing medium)
Designing equipment for which there are no design guidelines (e.g. differentials, mixers)
Improving the efficiency of machinery and equipment
In this chapter, selected examples of numerical calculations will be described, showing the possibility of using CFD methods to solve machine and equipment problems with a rotating operating element, often found in industrial practice.
\nThe innovative vane pump described in study [1] was subjected to the analysis of flow phenomena. In this solution, the pump is integrated into the BLDC permanent magnet electric motor. Due to its design, which differs from the standard solutions, it was necessary to check whether cavitation could occur in the suction channel of the pump. The main objective of the CFD simulation was to determine the areas where cavitation is likely to occur [2] and its intensity depending on the rotational velocity. The subject of the study is a positive displacement pump with integrated electric drive, consisting of an impeller embedded in a casing. Unlike conventional gear and vane pumps [3, 4, 5, 6, 7, 8, 9, 10], the pump impeller and motor stator are immovable components, while the pump casing rotates with the rotor of the electric motor. Figure 1 shows the 3D model of the analysed pump.
\n(a) 3D model of the vane pump with integrated mechatronic electric drive and (b) 3D model of the operating fluid volume filling the pump.
An important problem is to examine the flow in the suction channel of the pump, as it is exposed to the adverse effects of cavitation, which can develop as a result of a too high value of negative pressure occurring in the suction area.
\nOn the basis of the three-dimensional model of the pump, a geometric model of the volume of operating fluid filling its interior was prepared (Figure 1b). As expected, the result is a very complex structure in terms of geometry. Due to the particular interest in the phenomena occurring in the suction channel of the pump, the calculations used a fragment of the geometric model of the operating fluid volume filling the interior of the pump, which is the volume of oil filling the pump from the inlet to the suction kidneys supplying the fluid to the inter-vane spaces (Figure 2a). The separated volume is contained in the immovable elements of the structure, which further simplifies the formulation of the flow problem and the choice of calculation parameters.
\n(a) Suction channel geometry and (b) discrete model.
Based on the three-dimensional pump model, the simplified geometric model of the operating fluid volume filling the suction channel was discretized using a tetrahedral grid. The result is a geometric model divided into 144,390 tetrahedral elements with 29,711 nodes, as shown in Figure 2b.
\nThe next step in formulating the flow problem is to select the type and define the boundary conditions for relevant fragments of the geometry. In the analysed case, the conditions concerning the fluid inflow and outflow were set as shown in Figure 2a.
\nIn order to obtain the most accurate results of the simulation, the “pressure inlet” condition at the inlet and the “mass flow rate” at the outlet were assumed. The mass flow rate was determined using the formula:
where q is the specific mass flow rate; z is the number of vanes; b is the width of a vane; w is the thickness of a vane; R1 is the small race radius; and R2 is the large race radius.
\nOn this basis, the numerical values entered into the simulation for each impeller velocity were obtained. Within the framework of the study, the analysis of the operating medium flow through the suction channel of the vane pump was performed for various rotational velocity values—changed within the range of 500–3000 rpm.
\nFigure 3 shows the pressure distributions in the suction channel of the tested pump for the generic geometry. For each of the cases considered, the lowest pressure occurs in one of the channels supplying fluid to the suction kidneys directly at the inlet to the channel. It was found that the negative pressures for the whole range of rotational velocities are higher than the pressure of oil evaporation, which prevents the occurrence of cavitation phenomena.
\nGeneric geometry—suction channel pressure distribution for different rotational velocities: (a) 500 rpm, (b) 1000 rpm, (c) 1500 rpm, (d) 2000 rpm, (e) 2500 rpm and (f) 3000 rpm.
The results of the calculations, apart from pressure distributions, were presented in the form of velocity distributions in the considered area, which are presented in Figure 4. From the obtained velocity distributions, it appears that the rotational velocity of the pump significantly influences the velocity of fluid flow in one of the supply channels for both the generic and the modified geometry. It is worth noting that the area where the highest velocities were identified corresponds to the area of the lowest pressures observed in the suction channel. The velocity of the fluid decreases with the lowering of the rotational velocity, but in the case of simplified geometry, it is slightly lower.
\nGeneric geometry—suction channel velocity distribution for different velocities: (a) 500 rpm, (b) 1000 rpm, (c) 1500 rpm, (d) 2000 rpm, (e) 2500 rpm and (f) 3000 rpm.
Figure 5 shows the fluid flow in the form of streamlines, for which the inflow plane to the domain is assigned as the beginning. The results obtained confirm the previous assumptions that the fluid flows evenly and without major turbulences through both inlet channels. Uneven velocity distribution and different pressure values due to asymmetrical layout of channels did not affect the fluid flow. The results obtained on the basis of numerical calculations are the basis for evaluation of the structure of channels supplying fluid to the inter-vane volumes.
\nGeneric geometry—streamlines in the investigated suction channel area for different velocities: (a) 500 rpm, (b) 1000 rpm, (c) 1500 rpm, (d) 2000 rpm, (e) 2500 rpm and (f) 3000 rpm.
Another object under consideration with rotating operating elements was a radial fan. The aim of the numerical simulation was to improve its efficiency. The flow of real gas through a fan with a finite amount of blades is carried out by the cost of loss of energy, called hydraulic losses. Those losses are a consequence of the friction of air molecules occurring on the blade walls and fan housing, vortexes developed in the gas stream, etc. The influence of hydraulic losses on the working characteristic of the radial fan is described by a hydraulic efficiency coefficient, which is defined as the ratio of the useful power to the power delivered by the impeller. This coefficient also defines the real delivery height to the theoretical delivery height—obtained for the finite amount of impeller blades. The impeller geometry considered in possible options, i.e. with eight (factory option) and nine (suggested option) vanes, are shown in Figures 6 and 7.
\nImpeller shape: eight vanes.
Impeller shape: nine vanes.
For the calculations, the model of impeller according to the enclosed documentation was used as the output model. Calculations have been made for both impeller variants. For both of the cases, the discrete model was based on tetrahedral elements (as exemplary shown in Figure 8). Elements near walls were compacted. The flow was modelled as turbulent, using the RANS method and the two-equation turbulence model k-ε.
\nDiscrete model with division into tetrahedral elements on the impeller and vanes.
In the first stage of the study, the analysis of the impeller with eight (Figure 6) and nine (Figure 7) vanes was carried out. For the eight vanes, the results of the simulation were also compared with the available results in the technical documentation and found to be similar (Figure 9). Furthermore, the overall performance of the two types of impellers found with aid of CFD calculation maintains in similar level.
\nComparison of the calculation results and the results of the technical documentation for the impeller with the eight and nine vanes.
In order to verify the correctness of the calculation of the main dimensions of the impeller, a theoretical design process was carried out. On the basis of known designs, the influence of impeller parameters on its performance, compression and efficiency was simulated. It was necessary to maintain the existing parameters of the impeller, improving only its efficiency. The modifications were limited by the external dimensions of the impeller in order to be able to work with the existing collecting volute.
\nAfter a number of variant combinations, the outlet angle of the vane was changed to 23° and the vane profile modified to improve efficiency. The results show that by changing the outlet angle, the average efficiency for the eight-vane impeller was increased by 2.3% and for the nine-vane impeller by 2.9% in relation to the basic eight-vane impeller.
\nFigure 10 shows a comparison of the flow images for the impellers with eight and nine vanes with a 23° outlet angle.
\nTotal velocity [m/s] distribution for calculated impeller operating points with eight and nine vanes.
The best results were obtained for the nine-vane impeller and the changed outlet angle. An average efficiency increase of 2.9% was achieved in relation to the impeller from the technical documentation. The flow images are correct. There are no particularly dangerous phenomena, such as interruption of flow or turbulence.
\nAnother object of the study was a single-stage centrifugal pump with a spiral volute cooperating with two similar types of impellers, commonly used in such a device. Those impellers are denoted as W13 and W17. The W17 impeller differs from the W13 impeller only by the shape of a vane. Both impellers had eight vanes each. The analysis of the impellers with the two-dimensional peculiarity method for non-viscous medium suggested higher cavitation resistance of the W13 impeller.
\nIn the first stage, calculations were made of the undetermined flow through the pump without cavitation in order to determine the most favourable boundary conditions to be applied when analysing the flow through the pump and determining the calculation characteristics of the pump and the impeller.
\nThe calculations reflect the full three-dimensional geometry of the pump (Figure 11) consisting of a straight section of the pipeline before the inlet to the impeller, a centrifugal impeller, a spiral collecting volute, a diffuser, and a short section of pipeline after the pump.
\nThe calculation area under consideration and its characteristic cross sections (W13 impeller pump).
Separate discreet models have been built in the inlet and outlet impeller areas. On the cylindrical surface between the impeller and the volute, these models were not connected by common nodes and remained unfit. Thus, during the calculation it was possible to use the “sliding mesh” technique, which is used to model the rotation of the impeller in relation to the stationary casing. The discrete model is built with approximately 1.3 million tetrahedral elements in total. The elements were also compacted near the vane surface and in the area between the impeller and the collecting channel (Figure 12).
\nDiscrete model by type of tetrahedral element of the impeller surface, on the hub and rear disc side.
The mathematical model of the flow is described by the Reynolds-averaged Navier-Stokes equations (RANS). For the description of the turbulence, a two-equation k-ε model was used. The following control surfaces were used, where static pressure was monitored during the calculation:
The inlet section at the beginning of the suction channel (A-A)
The cylindrical surface at the outlet from the impeller inter-vane channel (B-B)
The cross section at the end of the diffuser (C-C)
The outlet section at the end of the cylindrical section of the pipeline (D-D)
Calculations were made according to the scheme:
\nIn the inlet section (A-A), a homogeneous velocity field was set with the value resulting from the flow rate and the channel section area c = Q/A and the direction corresponding to the connector axis (“velocity inlet” boundary condition). In cross section (D-D), a high static pressure of 1000 kPa was set so that the pressure in the impeller would not drop below the saturation vapour pressure (“pressure outlet” boundary condition). A two-phase flow “mixture” model was selected for the calculations. During the calculations, equations describing the formation of the gaseous phase (cavitation) were excluded. This approach is suggested by ANSYS Fluent.
\nOn the internal walls of the flow channel, the condition of zero velocity of the fluid in relation to the wall was set. The increase of static pressure (increase of hydrostatic height) between inlet and outlet cross sections of the pump was the expected value and allowed to reproduce flow characteristics. During the calculations, the average static pressure was monitored on the four control surfaces mentioned above. The calculations were interrupted after repeated oscillations of the static pressure on these surfaces were obtained, which took place after 6–8 rotations of the impeller. An example of a pressure pulsation diagram is shown in Figure 13. A fixed time step of Δt = 5,75E–5 s, corresponding to an impeller rotation by 1°, was used for the calculations.
\nExample pressure pulsation diagram as pressure difference between vane outlet (interface_2) and inlet (inlet), depending on iteration (time).
The calculated flow characteristics of the entire pump and the W13 impeller are presented in Figure 14. The course of the relevant experimental characteristics is also presented.
\nPump and impeller flow characteristics W13 determined by calculation of the transient flow (spiral collecting channel model): comparison with experimental data.
The pump characteristics indicate a pressure increase between the cross sections A-A and C-C, characteristics of the impeller—between sections A-A and B-B. The pressure drop in the suction channel is insignificant compared to the pressure drop in the impeller.
\nCavitation in the pump is associated with a pressure drop in the suction area of the first degree [11]. This causes the fluid-vapour biphasic flow to occur and the continuity of the flow through the pump to be interrupted. In centrifugal pumps, cavitation shall be characterised by a clearly visible disturbance in the following characteristics: flow H = f(Q), power consumption P = f(Q) and efficiency η = f(Q). If the suction height increases at a given velocity and flow rate (or the intake height decreases), then the boundary value of the suction height at which the pump enters the cavitation state is obtained. In this way, taking into account a certain safety margin, it is possible to obtain a curve of the required excess of the energy of a fluid at the pump inlet section over the energy of evaporation of this fluid in the form of NPSH = f(Q) (net positive suction head). The NPSH parameter expresses the “suction power” of the pump:
where ps is the absolute pressure at the inlet cross section of the pump and cs is the fluid velocity at the pump inlet cross section (average). Typically, this surplus is related to a state where the first-stage total head drops by 3% (NPSH3).
\nDetermination of the cavitation state in the impeller for a given flow rate requires many calculations of the pressure distribution in the inter-vane space at the decreasing inlet pressure. The simulation assumes that a simplified geometric model of a collective channel can be used to determine the flow characteristics of the impeller itself. Instead of a spiral, an axial-symmetrical guide was used as a drainage element for the medium.
\nDue to the symmetry of geometry, the flow through the impeller is determined. The elimination of pressure pulsations has significantly accelerated the iterative calculation process. The flow field in the impeller still remained a periodic-symmetric field, but it was the same in all the vane channels. This allowed the calculation area to be limited to one inter-vane channel of the impeller. As a result, the calculation time corresponding to one characteristic point has been reduced.
\nA discrete model consisting of about 300,000 hexahedral cells was used. Since the discrete model remains stationary during the calculation, a moving reference frame was used which rotates at the impeller velocity.
\nFor the calculations, the “velocity inlet” and “pressure outlet” boundary conditions were used on the outer surface of the annular collecting channel and the two-phase flow “mixture” model. During the calculation, the average static pressure value at the cross sections A-A (inlet) and B-B (outlet from the impeller inter-vane channel) was monitored.
\nCavitation test in the impeller was performed for several selected values of the flow rate. Calculations were carried out in which equations describing cavitation and two-phase flow were included. The static pressure at the outlet was gradually reduced from 800 to 580 kPa.
\nIt was found that the lowest pressure in the impeller was initially higher than the saturated vapour pressure pmin > pv; then it was already limited by the pv value. For each set outlet pressure, the static inlet pressure was recorded. In the W13 impeller, cavitation occurs on the impeller vanes, close to the incidence edge on the concave side of the vane. In the W17 impeller, cavitation appears on the convex side of the vane (for Q = 70 m3/h). Selected images of the development of cavitation are presented in Figures 15 and 16.
\nCavitation development image on the impeller W13 disc surface at Q = 70 m3/h and decreasing static pressure at the inlet (percentage of gas phase is given).
Cavitation development image on the impeller W17 disc surface at Q = 70 m3/h and decreasing static inlet pressure (percentage of gas phase is given).
When the outlet pressure is further reduced, it reaches a constant boundary value, depending on the flow rate—fully developed cavitation. Further lowering of the outlet pressure leads to a loss of convergence and interruption of the calculation.
\nCavitation image – model with spiral collection channel and immovable impeller (Moving Reference Frame) – Figure 17. Cavitation image – model with spiral collecting channel and rotating impeller (Moving Mesh) – Figure 18.
\nCavitation area for parameters: (a) inlet = 189 kPa and outlet = 800 kPa, (b) inlet = 95 kPa and outlet = 700 kPa, (c) inlet = 58 kPa and outlet = 650 kPa, (d) inlet = 27 kPa and outlet = 622 kPa and (e) inlet = 27 kPa and outlet = 600 kPa. The percentage of gas phase is given.
Cavitation area for parameters: (a) inlet = 28.3 kPa and outlet = 675 kPa, (b) inlet = 27.8 kPa and outlet = 650 kPa and (c) inlet = 27.8 kPa and outlet = 622 kPa. The percentage of gas phase is given.
The cavitation fields for the axial-symmetric model are correctly symmetrical. However, the behaviour of the tested impellers is different:
Impeller W13: cavitation is formed on the concave side of the vane.
Impeller W17: cavitation is formed on the convex side of the vane.
The calculations converge quickly. However, the cavitation fields in the moving reference frame model are non-physical, and the cavitation area expands very quickly. Cavitation starts in the direction of the smallest radius of the collecting spiral. The moving mesh model produces the best results (mainly physical). However, the problem is the slow convergence of calculations and their long duration.
\nThe different cavitation properties of the two impellers can be explained by the significantly different inlet angle of the β1 vane—30°40′ (W13) and 21° (W17)—as with the same other geometric data, resulted in a very different position of the ideal inflow point. This is confirmed by the experimental characteristics of the pumps H = f(Q) and η = f(Q) from operation.
\nThe analyses indicated the possibility of obtaining information on cavitation resistance of the designed structure through the rational use of CFD programs. The alternative solution of designing a prototype pump and carrying out a series of experiments may be challenging.
\nThe CFD analysis made it possible to identify areas where cavitation is more likely to occur and to assess its intensity in relation to the rotational velocity. The results showed that one of the inlet channels has both negative pressure and increased fluid flow velocity. Calculations made for different pump rotational velocities and different suction channel geometries have shown that the intensity of these phenomena increases with the rotational velocity. However, these phenomena are not strong enough to contribute to the development of the phenomenon of cavitation. A series of simulations for different suction channel geometries have confirmed that no modification of the suction channel geometry is required. Considering the designs presented here the cavitation occurred either on the convex or concave side of the vane. The main difference between the vanes was the angle of its inclination. Hence there is a specific angle between 30 and 21° at which the transition occurs. The volumetric flow rate was unchanged in both of the impeller designs, although the inlet pressures were found to be different. For blades inclined at 30°, the inlet pressures were almost twice lower than in the case of 21°. Hence lower inclination of blades is more immune to cavitation development.
\nThe CFD calculations were made to check the selection of the main dimensions of the radial fan. After performing many variant calculations, it was found that by changing the number of blades and the outlet angle of the blades, it is possible to increase the efficiency of the fan. It appeared that the efficiency is greater for impellers with greater amount of vanes. Furthermore the efficiency increased when the vanes were inclined to 23°, and as stated above, at such angle the cavitation occurs at higher inlet pressures and represent higher immunity to cavitation. Therefore the increase of efficiency may be partially a consequence of lack of cavitation.
\nIt was found that the characteristics of the centrifugal pump from CFD calculations are consistent with the characteristics obtained experimentally. Based on the CFD analysis, cavitation resistance of the designed centrifugal pump was determined.
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