Effect of hydrodynamics on modelling, monitoring and control of crystallization

Crystallization is a purification method used to obtain crystalline product of a certain crystal size. It is one of the oldest industrial unit processes and commonly used in modern industry due to its good purification capability from rather impure solutions with reasonably low energy consumption. However, the process is extremely challenging to model and control because it involves inhomogeneous mixing and many simultaneous phenomena such as nucleation, crystal growth and agglomeration. All these phenomena are dependent on supersaturation, i.e. the difference between actual liquid phase concentration and solubility. Homogeneous mass and heat transfer in the crystallizer would greatly simplify modelling and control of crystallization processes, such conditions are, however, not the reality, especially in industrial scale processes. Consequently, the hydrodynamics of crystallizers, i.e. the combination of mixing, feed and product removal flows, and recycling of the suspension, needs to be thoroughly investigated. Understanding of hydrodynamics is important in crystallization, especially inlargerscale equipment where uniform flow conditions are difficult to attain. It is also important to understand different size scales of mixing; micro-, meso- and macromixing. Fast processes, like nucleation and chemical reactions, are typically highly dependent on micro- and mesomixing but macromixing, which equalizes the concentrations of all the species within the entire crystallizer, cannot be disregarded. This study investigates the influence of hydrodynamics on crystallization processes. Modelling of crystallizers with the mixed suspension mixed product removal (MSMPR) theory (ideal mixing), computational fluid dynamics (CFD), and a compartmental multiblock model is compared. The importance of proper verification of CFD and multiblock models is demonstrated. In addition, the influence of different hydrodynamic conditions on reactive crystallization process control is studied. Finally, the effect of extreme local supersaturation is studied using power ultrasound to initiate nucleation. The present work shows that mixing and chemical feeding conditions clearly affect induction time and cluster formation, nucleation, growth kinetics, and agglomeration. Consequently, the properties of crystalline end products, e.g. crystal size and crystal habit, can be influenced by management of mixing and feeding conditions. Impurities may have varying impacts on crystallization processes. As an example, manganese ions were shown to replace magnesium ions in the crystal lattice of magnesium sulphate heptahydrate, increasing the crystal growth rate significantly, whereas sodium ions showed no interaction at all. Modelling of continuous crystallization based on MSMPR theory showed that the model is feasible in a small laboratoryscale crystallizer, whereas in larger pilot- and industrial-scale crystallizers hydrodynamic effects should be taken into account. For that reason, CFD and multiblock modelling are shown to be effective tools for modelling crystallization with inhomogeneous mixing. The present work shows also that selection of the measurement point, or points in the case of multiprobe systems, is crucial when process analytical technology (PAT) is used to control larger scale crystallization. The thesis concludes by describing how control of local supersaturation by highly localized ultrasound was successfully applied to induce nucleation and to control polymorphism in reactive crystallization of L-glutamic acid.

Marketing culture of Finnish research libraries : an analysis of marketing attitude, knowledge and behaviour

The aim of the present dissertation is to investigate the marketing culture of research libraries in Finland and to understand the awareness of the knowledge base of library management concerning modern marketing theories and practices. The study was based onthe notion that a leader in an organisation can have large impact on its culture. Therefore, it was considered important to learn about the market orientation that initiates at the top management and flows throughout the whole organisationthus resulting in a particular kind of library culture. The study attempts to examine the marketing culture of libraries by analysing the marketing attitudes, knowledge (underlying beliefs, values and assumptions), behaviour (market orientation), operational policies and activities, and their service performance (customer satisfaction). The research was based on the assumption that if the top management of libraries has market oriented behaviour, then their marketing attitudes, knowledge, operational policies and activities and service performance should also be in accordance. The dissertation attempts to connect all these theoretical threads of marketing culture. It investigates thirty three academic and special libraries in the south of Finland. The library director and three to ten customers from each library participated as respondents in this study. An integrated methodological approach of qualitative as well as quantitative methods was used to gain knowledge on the pertinent issues lying behind the marketing culture of research libraries. The analysis of the whole dissertation reveals that the concept of marketing has very varied status in the Finnish research libraries. Based on the entire findings, three kinds of marketing cultures were emerged: the strong- the high fliers; the medium- the brisk runners; and the weak- the slow walkers. The high fliers appeared to be modern marketing believers as their marketing approach was customer oriented and found to be closer to the emerging notions of contemporary relational marketing. The brisk runners were found to be traditional marketing advocates as their marketing approach is more `library centred¿than customer defined and thus is in line of `product orientation¿ i.e. traditional marketing. `Let the interested customers come to the library¿ was appeared to be the hallmark of the slow walkers. Application of conscious market orientation is not reflected in the library activities of the slow walkers. Instead their values, ideology and approach to serving the library customers is more in tuneof `usual service oriented Finnish way¿. The implication of the research is that it pays to be market oriented which results in higher customer satisfaction oflibraries. Moreover, it is emphasised that the traditional user based service philosophy of Finnish research libraries should not be abandoned but it needs to be further developed by building a relational based marketing system which will help the libraries to become more efficient and effective from the customers¿ viewpoint. The contribution of the dissertation lies in the framework showing the linkages between the critical components of the marketing culture of a library: antecedents, market orientation, facilitators and consequences. The dissertationdelineates the significant underlying dimensions of market-oriented behaviour of libraries which are namely customer philosophy, inter-functional coordination,strategic orientation, responsiveness, pricing orientation and competition orientation. The dissertation also showed the extent to which marketing attitudes, behaviour, knowledge were related and impact of market orientation on the serviceperformance of libraries. A strong positive association was found to exist between market orientation and marketing attitudes and knowledge. Moreover, it also shows that a higher market orientation is positively connected with the service performance of libraries, the ultimate result being higher customer satisfaction. The analysis shows that a genuine marketing culture represents a synthesis of certain marketing attitudes, knowledge and of selective practices. This finding is particularly significant in the sense that it manifests that marketing culture consists of a certain sets of beliefs and knowledge (which form a specific attitude towards marketing) and implementation of a certain set of activities that actually materialize the attitude of marketing into practice (market orientation) leading to superior service performance of libraries.

Packaging concept development for an assortment of medical device products

Diplomityön tavoitteena oli kehittää Wipak Oy:n valmistamille sterilointipakkauksille tulevaisuuden pakkauskonsepti. Sterilointipakkaukset luokitellaan lääkelaitedirektiivin mukaan lisätarvikkeiksi luokan 1 lääkelaitteille, ja tämä näkökulma oli vahvasti mukana konseptin kehityksessä. Lähtökohtana pakkauskonseptin suunnittelulle oli tuotteiden arvoketjussa, eli pakata tuotteet siten että pakkausten avulla voidaan tuottaa lisäarvoa arvoketjun toimijoille. Tavoitteena oli parantaa pakkausten viestintää, toimivuutta/tehokkuutta toimitusketjussa sekä vahvistaa brändin imagoa myynti- ja kuljetuspakkauksen avulla. Lääkinnälliset laitteet ja tarvikkeet ovat lainsäädännön ja normien avulla tarkasti säädeltyjä. Näiden normien vaatimukset asettavat perusteet myynti- ja kuljetuspakkausten kehittämiselle. Tämän lisäksi suunnittelussa on huomioitu asiakkaiden toiveet ja kehitystarpeet. Kirjallisuusosuudessa on keskitytty lääkinnällisten laitteiden pakkausyksiköiden toimintoihin sekä niiden kehitysnäkymiin. Pääpaino on ollut pakkausmerkintöjen ja jäljitettävyyden kehittämisellä, koska tietojen automaattisen tunnistuksen hyödyntäminen lääkintälaitteiden pakkausten arvoketjussa on kasvava trendi. Manuaalisesti tehtävät tuotevirtojen kirjaukset ketjun eri toimijoiden osalta lisäävät riskejä jäljitettävyyden kannalta ja aiheuttavat lisätyötä ja – kustannuksia ketjun kaikille osapuolille. Ehdotus uudesta pakkauskonseptista on kehitetty näiden tietojen pohjalta. Ehdotuksessa on huomioitu lainsäädännöstä ja ketjun toimijoilta tulevat tarpeet, sekä alan tulevaisuuden kehitysnäkymät. Ehdotetun pakkauskonseptin avulla saadaan lisättyä myynti- ja kuljetuspakkausten tehokkuutta, parannettua jäljitettävyyttä ja helpotettu arvoketjun alavirran toimijoiden työtä lisäämällä erillinen sisäpakkaus myyntiyksikön sisälle. Työssä on lisäksi selvitetty pakkauskonseptin kustannusvaikutukset tuotteiden hintaan. Lopussa on ehdotettu jatkotoimenpiteet suunnitelman implementoimisesta käytäntöön.

CFD Modelling of Direct Contact Condensation in Suppression Pools by Applying Condensation Models of Separated Flow

The condensation rate has to be high in the safety pressure suppression pool systems of Boiling Water Reactors (BWR) in order to fulfill their safety function. The phenomena due to such a high direct contact condensation (DCC) rate turn out to be very challenging to be analysed either with experiments or numerical simulations. In this thesis, the suppression pool experiments carried out in the POOLEX facility of Lappeenranta University of Technology were simulated. Two different condensation modes were modelled by using the 2-phase CFD codes NEPTUNE CFD and TransAT. The DCC models applied were the typical ones to be used for separated flows in channels, and their applicability to the rapidly condensing flow in the condensation pool context had not been tested earlier. A low Reynolds number case was the first to be simulated. The POOLEX experiment STB-31 was operated near the conditions between the ’quasi-steady oscillatory interface condensation’ mode and the ’condensation within the blowdown pipe’ mode. The condensation models of Lakehal et al. and Coste & Lavi´eville predicted the condensation rate quite accurately, while the other tested ones overestimated it. It was possible to get the direct phase change solution to settle near to the measured values, but a very high resolution of calculation grid was needed. Secondly, a high Reynolds number case corresponding to the ’chugging’ mode was simulated. The POOLEX experiment STB-28 was chosen, because various standard and highspeed video samples of bubbles were recorded during it. In order to extract numerical information from the video material, a pattern recognition procedure was programmed. The bubble size distributions and the frequencies of chugging were calculated with this procedure. With the statistical data of the bubble sizes and temporal data of the bubble/jet appearance, it was possible to compare the condensation rates between the experiment and the CFD simulations. In the chugging simulations, a spherically curvilinear calculation grid at the blowdown pipe exit improved the convergence and decreased the required cell count. The compressible flow solver with complete steam-tables was beneficial for the numerical success of the simulations. The Hughes-Duffey model and, to some extent, the Coste & Lavi´eville model produced realistic chugging behavior. The initial level of the steam/water interface was an important factor to determine the initiation of the chugging. If the interface was initialized with a water level high enough inside the blowdown pipe, the vigorous penetration of a water plug into the pool created a turbulent wake which invoked the chugging that was self-sustaining. A 3D simulation with a suitable DCC model produced qualitatively very realistic shapes of the chugging bubbles and jets. The comparative FFT analysis of the bubble size data and the pool bottom pressure data gave useful information to distinguish the eigenmodes of chugging, bubbling, and pool structure oscillations.

Energetic efficiency of a deep bed swine production system

The aim of this work was to evaluate the energy flows of a commercial production system of swine deep bed in its finishing phase, located in Juiz de Fora, in the State of Minas Gerais, Brazil. Thus, an energy efficiency study was carried out by monitoring a lot of animals, during a 94-day period. The energy rate of each compound involved in the production process was quantified and the matrixes of energy consumption were determined in the form of animal feeding, electrical energy, piglets, material used as deep bed, human labor, equipment, swine buildings, production of alive swine for slaughter, organic fertilizer production (swine deep bed or swine deep litter). From the direct input energy, 80.57% correspond to animal feeding, 11.90% to pigs for slaughter and 6.76% to piglets, while from the energy output 53.45% correspond to the terminating swine and 46.55% to organic fertilizer (swine deep bed). By the results obtained, we can conclude that such production system has corresponded to an industrial and highly specialized agro ecosystem, importing a great part of the energy consumed in the production process, with 41% of energy efficiency.

Distribution of water in sandy soil applied by drip

The search for the use of water with high levels of efficiency has motivated the use of drip irrigation in several agricultural systems. However, for the efficiency be ensured, it is necessary that the water distribution in the soil profile must to be known in more details. As it is a highly variable process, function of the local characteristics, is essential the study of each case. The objective of this research was evaluating the water distribution in the soil profile, from drippers installed in surface and 0.15 m below the soil surface. The experiment was realized in the Technical Center of Irrigation (TCI) of the State University of Maringá - PR. The water monitoring in the soil profile was done with TDR probes installed in a box containing sandy soil, at the depths from 0.05 to 0.80 m; and 0.05 to 0.35 m of lateral spacing, at intervals of 0.05 m, totalizing 30 probes. The treatments were differentiated in relation of the installation depth of the emitters (0.0 and 0.15 m) and flow (1, 2, 4, 6, and 8 L h-1). The irrigation time was 8 hours continuous with reading of the TDR probes each 30 minutes. The results allowed concluding that the wet area with the emitter positioned on the soil surface was directly proportional to the flow increase. For the underground dripper, this area was substantially smaller and the water losses by percolation were higher, mainly to the flows higher than 4 L h-1, which provided to unacceptable water losses that should be avoided.

Energetic sustainability of three arabica coffee growing systems used by family farming units in Espírito Santo state

Three growing systems of Arabica coffee were evaluated under the energy perspective, in the state of Espírito Santo in Brazil. The systems are conventional cultivation (CC), cultivation with good agricultural practices (CGP) and organic farming (OF). It was made a comparison of the energy flows within these three systems to show sustainable levels of each one based on production average data of several family-farming units. Therefore, we analyzed crop yield, total energy efficiency reverse (TEER), energy efficiency of ripe coffee (EERC) and non-renewable energy efficiency (NREE). OF system had values for TEER, EERC and NREE of 3.3 4.7 and 7.9 respectively. Yet CC showed values of 1.8, 1.9 and 1.6 for TEER, EERC and NREE respectively. Furthermore, CGP presented values for TEER, EERC and NREE of 0.7, 1.3 and 1.4 respectively. The highest yield was observed in CGP, reaching an amount of 1794 kg ha-1(17,455 MJ); however, this system expends more energy than it converts. Thus, over those points, OF is the most sustainable system.

Low-flow estimates in regions of extrapolation of the regionalization equations: a new concept

ABSTRACT Knowledge of natural water availability, which is characterized by low flows, is essential for planning and management of water resources. One of the most widely used hydrological techniques to determine streamflow is regionalization, but the extrapolation of regionalization equations beyond the limits of sample data is not recommended. This paper proposes a new method for reducing overestimation errors associated with the extrapolation of regionalization equations for low flows. The method is based on the use of a threshold value for the maximum specific low flow discharge estimated at the gauging sites that are used in the regionalization. When a specific low flow, which has been estimated using the regionalization equation, exceeds the threshold value, the low flow can be obtained by multiplying the drainage area by the threshold value. This restriction imposes a physical limit to the low flow, which reduces the error of overestimating flows in regions of extrapolation. A case study was done in the Urucuia river basin, in Brazil, and the results showed the regionalization equation to perform positively in reducing the risk of extrapolation.

E-PORT. Improving efficiency of Finnish port community by intelligent systems Final report of the Mobile Port project

The management of port-related supply chains is challenging due to the complex and heterogeneous operations of the ports with several actors and processes. That is why the importance of information sharing is emphasised in the ports. However, the information exchange between different port-related actors is often cumbersome and it still involves a lot of manual work and paper. Major ports and port-related actors usually have advanced information systems in daily use but these systems are seldom interoperable with each other, which prevents economies of scale to be reached. Smaller ports and companies might not be equipped with electronic data transmission at all. This is the final report of the Mobile port (MOPO) project, which has sought ways to improve the management and control of port-related sea and inland traffic with the aid of ICT technologies. The project has studied port community systems (PCS) used worldwide, evaluated the suitability of a PCS for the Finnish port operating environment and created a pilot solution of a Finnish PCS in the port of HaminaKotka. Further, the dry port concept and its influences on the transportation system have been explored. The Mobile Port project comprised of several literature reviews, interviews of over 50 port-related logistics and/or ICT professionals, two different kinds of simulation models as well as designing and implementing of the pilot solution of the Finnish PCS. The results of these multiple studies are summarised in this report. Furthermore, recommendations for future actions and the topics for further studies are addressed in the report. The study revealed that the information sharing in a typical Finnish port-related supply chain contains several bottlenecks that cause delays in shipments and waste resources. The study showed that many of these bottlenecks could be solved by building a port community system for the Finnish port community. Almost 30 different kinds of potential services or service entities of a Finnish PCS were found out during the study. The basic requirements, structure, interfaces and operation model of the Finnish PCS were also defined in the study. On the basis of the results of the study, a pilot solution of the Finnish PCS was implemented in the port of HaminaKotka. The pilot solution includes a Portconnect portal for the Finnish port community system (available at https://www.portconnect.fi) and two pilot applications, which are a service for handling the information flows concerning the movements of railway wagons and a service for handling the information flows between Finnish ports and Finland-Russian border. The study also showed that port community systems can be used to improve the environmental aspects of logistics in two different ways: 1) PCSs can bring direct environmental benefits and 2) PCSs can be used as an environmental tool in a port community. On the basis of the study, the development of the Finnish port community system should be continued by surveying other potential applications for the Finnish PCS. It is also important to study if there is need and resources to extend the Finnish PCS to operate in several ports or even on a national level. In the long run, it could be reasonable to clarify whether there would be possibilities to connect the Finnish PCS as a part of Baltic Sea wide, European-wide or even worldwide maritime and port-related network in order to get the best benefit from the system

Driver of Demand in Cargo and Passenger Traffic Between Penta Ports

Maritime transport moves around 6 billion tonnes of freight every year. The freight consists of liquid bulks (45%), dry bulks (23%) and general cargo (32%). Freight traffic and transports chains vary according to region, commodity and the origin and the destination of freight. In the European Union the ports sector handles over 90% of the trade with third countries. The share of intra-EU trade is approximately 30% of the total transportation and the number of passengers is over 200 million every year. The Baltic Sea has more than 50,000 vessels a year pass the Skaw at the northernmost tip of Denmark on their way into or out of the Baltic. Roughly 60% to 70% of these vessels are cargo vessels and 17% to 25% tankers. Ports and maritime transport play a crucial role in global commerce today. Today’s business environment is changing rapidly, and the constant changes create challenges for the transport industry and maritime traffic. Ports have to adapt to continuous changes in economic structures, logistics demands, and people’s travel and leisure patterns. In order to ensure the competitiveness of sea connections, the ports need to fully enhance multilateral cross-border understanding and cooperation. In this report the focus is on liner traffic between five ports in the Central Baltic Region: Stockholm, Tallinn, Helsinki Turku and Naantali. The report defines the drivers of the demand for cargo and passenger traffic and highlights the most important factors. The economic situation and foreign trade of each county are elaborated on with detailed information about the flows of traffic between the five ports. Based on expert interviews, the main characteristics of each port, including strengths and weaknesses, are presented. The report is based on primary and secondary data. Primary data was received through interviews and mail surveys. Secondary data was attained through a literature research, statistics, data given by the PENTA ports and webpages. The report is divided into two main parts: the drivers creating the demand for transport and the results of current cargo and passenger flows between PENTA ports.

Benefits and challenges of supply chain finance business process automation : A case study in ING Bank

Supply chain finance, a financial product provided by the bank, has gained increasing attention and popularity over the last few years. Supply chain finance helps the corporate clients to optimize their financial flows along the supply chain. One characteristic of supply chain finance is that it aims to provide automated solutions. Therefore, the business process automation of supply chain finance is a very interesting and important topic for study. In this study, the business process automation of supply chain finance within the case organization, ING, is analysed. The purpose is to: (1) Identify the benefits to understand the importance to automate supply chain finance business process; (2) Find out the existing automation degree in the supply chain finance business process within the case bank to see what’s the situation now and how to improve in the future; (3) Discover the challenges in the further automation of supply chain finance business process. Firstly, the study finds out that supply chain finance business process automation can bring many benefits to the bank. Automation can improve productivity by using less time and human labour in the business process, and by providing scalable solutions. Automation can also improve quality of the service by reducing the human errors. Last but not least, automation can improve internal governance by providing enhanced visibility of the business process. Because of these potential benefits, many banks are actively seeking solutions to automate their supply chain finance business process. Then, the current automation situation with the case bank is analysed with the help of business process modelling. The supply chain finance business process within the case bank can be further divided into several sub processes: daily transaction, buyer sales and setup, supplier onboarding, contract management, customer services and supports, and contract termination. The study finds out that the daily transaction process is already a highly automated, which is carried out through the web-based trading platform. However, for other business the automation degree is relatively low. Among these business processes, supplier onboarding is most needed for further automation. Then, some solutions are also suggested to automate the supplier onboarding business process. In the end, the study also foresees some challenges during the further automation of supply chain finance business process in the case bank. Some suggestions are also given to deal with these challenges.

The Present State and Future Prospects of a Manpower Pool as Part of Project Business

This research focused on operation of a manpower pool within a service business unit in Company X and aimed to identify how the operation should be improved in order to get most out of it concerning the future prospects of the service business unit. This was done by analyzing the current state of the manpower pool related operations in means of project business, project management and business models. The objective was to deepen the understanding and to highlight possible areas of improvement. The research was conducted as a qualitative single-case study utilizing also an action research method; the research approach was a combination of conceptual, action-oriented and constructive approaches. The primary data was collected with executing a comprehensive literature review and semi-structured theme interviews. The main results described how the manpower pool operates as part of the service business unit in project business by participating in different types of delivery projects; process flows for the project types were mapped. Project management was analyzed especially from the resource management point of view, and an Excel-based skills analysis model was constructed for this purpose. Utilization of operational business models was also studied to define strategic direction for development activities. The results were benchmarked against two competitors in order to specify lessons to be learnt from their use of operational business models.

Strategic external deployment of intellectual assets

Globalization, pervasiveness of technology and ICT, and the buildup of information societies and policies have lead to a growing abundance of knowledge and highly educated labour supply that is distributed widely. These changes have shifted the foundation of competitiveness to valuable knowledge resources which are now distributed widely across the globe, across actors in the value chain and across educated individuals in multiple organizations. Against this backdrop, the paradigm of open innovation (OI) has emerged as a new response to managing the increased amount of boundary-spanning knowledge flows in and out of the innovation process. The outbound mode of open innovation, that is to say the external exploitation of knowledge assets outside of the firm’s own products and services, has been the less-researched aspect of the concept and so far typically seen as concerning the outlicensing of unused technological assets to generate additional revenue. Given that open innovation is essentially a framework for the holistic structuring and management of crossboundary knowledge flows to improve a firm’s innovative performance, a close integration to corporate strategy seems imperative in order to fully benefit from it. Integrating open innovation to strategy leads to elevating its role from a fringe activity to a central innovation management issue that needs to be systematically managed. Building a structure that allows effective management necessitates linking open innovation activities to each phase of the innovation process. Previously, the connection between outbound OI and the earlier stages of innovation has not been studied. The thesis finds that connecting outbound OI to the entire innovation process of the firm, including the fuzzy front end of innovation, is critical for attaining strategic objectives and to the successful implementation and management of the activity. The practical purpose for the research is to enable companies to fully utilize their potential for outbound open innovation and to be able to implement and manage it from a strategic standpoint.

On the development of an unstructured grid solver for inert and reactive high speed flow simulations

An unstructured grid Euler solver for reactive compressible flow applications is presented. The method is implemented in a cell centered, finite volume context for unstructured triangular grids. Three different schemes for spatial discretization are implemented and analyzed. Time march is implemented in a time-split fashion with independent integrators for the flow and chemistry equations. The capability implemented is tested for inert flows in a hypersonic inlet and for inert and reactive supersonic flows over a 2-D wedge. The results of the different schemes are compared with each other and with independent calculations using a structured grid code. The strengths and the possible weaknesses of the proposed methods are discussed.

An experimental/numerical study of the turbulent boundary layer development along a surface with a sudden change in roughness

A theory for the description of turbulent boundary layer flows over surfaces with a sudden change in roughness is considered. The theory resorts to the concept of displacement in origin to specify a wall function boundary condition for a kappa-epsilon model. An approximate algebraic expression for the displacement in origin is obtained from the experimental data by using the chart method of Perry and Joubert(J.F.M., vol. 17, pp. 193-122, 1963). This expression is subsequently included in the near wall logarithmic velocity profile, which is then adopted as a boundary condition for a kappa-epsilon modelling of the external flow. The results are compared with the lower atmospheric observations made by Bradley(Q. J. Roy. Meteo. Soc., vol. 94, pp. 361-379, 1968) as well as with velocity profiles extracted from a set of wind tunnel experiments carried out by Avelino et al.( 7th ENCIT, 1998). The measurements are found to be in good agreement with the theoretical computations. The skin-friction coefficient was calculated according to the chart method of Perry and Joubert(J.F.M., vol. 17, pp. 193-122, 1963) and to a balance of the integral momentum equation. In particular, the growth of the internal boundary layer thickness obtained from the numerical simulation is compared with predictions of the experimental data calculated by two methods, the "knee" point method and the "merge" point method.