Pulsatile Blood Flow Simulations in Computed Tomography(CT) Scan-Based and Idealized Geometries of Human Aorta

Blood flow in human aorta is an unsteady and complex phenomenon. The complex patterns are related to the geometrical features like curvature, bends, and branching and pulsatile nature of flow from left ventricle of heart. The aim of this work was to understand the effect of aorta geometry on the flow dynamics. To achieve this, 3D realistic and idealized models of descending aorta were reconstructed from Computed Tomography (CT) images of a female patient. The geometries were reconstructed using medical image processing code. The blood flow in aorta was assumed to be laminar and incompressible and the blood was assumed to be Newtonian fluid. A time dependent pulsatile and parabolic boundary condition was deployed at inlet. Steady and unsteady blood flow simulations were performed in real and idealized geometries of descending aorta using a Finite Volume Method (FVM) code. Analysis of Wall Shear Stress (WSS) distribution, pressure distribution, and axial velocity profiles were carried out in both geometries at steady and unsteady state conditions. The results obtained in thesis work reveal that the idealization of geometry underestimates the values of WSS especially near the region with sudden change of diameter. However, the resultant pressure and velocity in idealized geometry are close to those in real geometry

Simulating Fluid Flow in a Compressed Valve

The objective of the work is to study fluid flow behavior through a pinch valve and to estimate the flow coefficient (KV ) at different opening positions of the valve. The flow inside a compressed valve is more complex than in a straight pipe, and it is one of main topics of interest for engineers in process industry. In the present work, we have numerically simulated compressed valve flow at different opening positions. In order to simulate the flow through pinch valve, several models of the elastomeric valve tube (pinch valve tube) at different opening positions were constructed in 2D-axisymmetric and 3D geometries. The numerical simulations were performed with the CFD packages; ANSYS FLUENT and ANSYS CFX by using parallel computing. The distributions of static pressure, velocity and turbulent kinetic energy have been studied at different opening positions of the valve in both 2D-axisymmetric and 3D experiments. The flow coefficient (KV ) values have been measured at different valve openings and are compared between 2D-axisymmetric and 3D simulation results.

Numerical Investigation of Flow Past a Circular Cylinder and in a Staggered Tube Bundle Using Various Turbulence Models

Transitional flow past a three-dimensional circular cylinder is a widely studied phenomenon since this problem is of interest with respect to many technical applications. In the present work, the numerical simulation of flow past a circular cylinder, performed by using a commercial CFD code (ANSYS Fluent 12.1) with large eddy simulation (LES) and RANS (κ - ε and Shear-Stress Transport (SST) κ - ω! model) approaches. The turbulent flow for ReD = 1000 & 3900 is simulated to investigate the force coefficient, Strouhal number, flow separation angle, pressure distribution on cylinder and the complex three dimensional vortex shedding of the cylinder wake region. The numerical results extracted from these simulations have good agreement with the experimental data (Zdravkovich, 1997). Moreover, grid refinement and time-step influence have been examined. Numerical calculations of turbulent cross-flow in a staggered tube bundle continues to attract interest due to its importance in the engineering application as well as the fact that this complex flow represents a challenging problem for CFD. In the present work a time dependent simulation using κ – ε, κ - ω! and SST models are performed in two dimensional for a subcritical flow through a staggered tube bundle. The predicted turbulence statistics (mean and r.m.s velocities) have good agreement with the experimental data (S. Balabani, 1996). Turbulent quantities such as turbulent kinetic energy and dissipation rate are predicted using RANS models and compared with each other. The sensitivity of grid and time-step size have been analyzed. Model constants sensitivity study have been carried out by adopting κ – ε model. It has been observed that model constants are very sensitive to turbulence statistics and turbulent quantities.

Traffic flow development at North European company level with respect of China and Russia

The aim of the thesis is to analyze traffic flows and its development from North European companies` point of view to China and Russia using data from logistics questionnaire. Selected North European companies are large Finnish and Swedish companies. The questionnaire was sent via email to the target group. The study is based on the answers got from respondent companies from years 2006, 2009 and 2010. In the thesis Finnish Talouselämä newspaper and Swedish Affärsdata are used as a database to find the target companies for the survey. Respondents were most often logistics managers in companies. In the beginning of the thesis concepts of transportation logistics is presented, including container types, trade terms, axel loads in roads and in railways. Also there is information about warehousing types and terminals. After that, general information of Chinese and Russian transportation logistics is presented. Chinese and Russian issues are discussed in two sections. In both of them it is analyzed economic development, freight transport and trade balance. Some practical examples of factory inaugurations in China and Russia are presented that Finnish and Swedish companies have completed. In freight transport section different transportation modes, logistics outsourcing and problems of transportation logistics is discussed. The results of the thesis show that transportation flows between Europe and China is changing. Freight traffic from China to European countries will strengthen even more from the current base. When it comes to Russia and Europe, traffic flows seem to be changing from eastbound traffic to westbound traffic. It means that in the future it is expected more freight traffic from Russia to Europe. Some probable reasons for that are recent factory establishments in Russia and company interviews support also this observation. Effects of the economic recession are mainly seen in the lower transportation amounts in 2009.

Methods and Models for Accelerating Dynamic Simulation of Fluid Power Circuits

The objective of this dissertation is to improve the dynamic simulation of fluid power circuits. A fluid power circuit is a typical way to implement power transmission in mobile working machines, e.g. cranes, excavators etc. Dynamic simulation is an essential tool in developing controllability and energy-efficient solutions for mobile machines. Efficient dynamic simulation is the basic requirement for the real-time simulation. In the real-time simulation of fluid power circuits there exist numerical problems due to the software and methods used for modelling and integration. A simulation model of a fluid power circuit is typically created using differential and algebraic equations. Efficient numerical methods are required since differential equations must be solved in real time. Unfortunately, simulation software packages offer only a limited selection of numerical solvers. Numerical problems cause noise to the results, which in many cases leads the simulation run to fail. Mathematically the fluid power circuit models are stiff systems of ordinary differential equations. Numerical solution of the stiff systems can be improved by two alternative approaches. The first is to develop numerical solvers suitable for solving stiff systems. The second is to decrease the model stiffness itself by introducing models and algorithms that either decrease the highest eigenvalues or neglect them by introducing steady-state solutions of the stiff parts of the models. The thesis proposes novel methods using the latter approach. The study aims to develop practical methods usable in dynamic simulation of fluid power circuits using explicit fixed-step integration algorithms. In this thesis, twomechanisms whichmake the systemstiff are studied. These are the pressure drop approaching zero in the turbulent orifice model and the volume approaching zero in the equation of pressure build-up. These are the critical areas to which alternative methods for modelling and numerical simulation are proposed. Generally, in hydraulic power transmission systems the orifice flow is clearly in the turbulent area. The flow becomes laminar as the pressure drop over the orifice approaches zero only in rare situations. These are e.g. when a valve is closed, or an actuator is driven against an end stopper, or external force makes actuator to switch its direction during operation. This means that in terms of accuracy, the description of laminar flow is not necessary. But, unfortunately, when a purely turbulent description of the orifice is used, numerical problems occur when the pressure drop comes close to zero since the first derivative of flow with respect to the pressure drop approaches infinity when the pressure drop approaches zero. Furthermore, the second derivative becomes discontinuous, which causes numerical noise and an infinitely small integration step when a variable step integrator is used. A numerically efficient model for the orifice flow is proposed using a cubic spline function to describe the flow in the laminar and transition areas. Parameters for the cubic spline function are selected such that its first derivative is equal to the first derivative of the pure turbulent orifice flow model in the boundary condition. In the dynamic simulation of fluid power circuits, a tradeoff exists between accuracy and calculation speed. This investigation is made for the two-regime flow orifice model. Especially inside of many types of valves, as well as between them, there exist very small volumes. The integration of pressures in small fluid volumes causes numerical problems in fluid power circuit simulation. Particularly in realtime simulation, these numerical problems are a great weakness. The system stiffness approaches infinity as the fluid volume approaches zero. If fixed step explicit algorithms for solving ordinary differential equations (ODE) are used, the system stability would easily be lost when integrating pressures in small volumes. To solve the problem caused by small fluid volumes, a pseudo-dynamic solver is proposed. Instead of integration of the pressure in a small volume, the pressure is solved as a steady-state pressure created in a separate cascade loop by numerical integration. The hydraulic capacitance V/Be of the parts of the circuit whose pressures are solved by the pseudo-dynamic method should be orders of magnitude smaller than that of those partswhose pressures are integrated. The key advantage of this novel method is that the numerical problems caused by the small volumes are completely avoided. Also, the method is freely applicable regardless of the integration routine applied. The superiority of both above-mentioned methods is that they are suited for use together with the semi-empirical modelling method which necessarily does not require any geometrical data of the valves and actuators to be modelled. In this modelling method, most of the needed component information can be taken from the manufacturer’s nominal graphs. This thesis introduces the methods and shows several numerical examples to demonstrate how the proposed methods improve the dynamic simulation of various hydraulic circuits.

Modelling of combustion and sorbent reactions in three-dimensional flow environment of a circulating fluidized bed furnace

This thesis presents a three-dimensional, semi-empirical, steady state model for simulating the combustion, gasification, and formation of emissions in circulating fluidized bed (CFB) processes. In a large-scale CFB furnace, the local feeding of fuel, air, and other input materials, as well as the limited mixing rate of different reactants produce inhomogeneous process conditions. To simulate the real conditions, the furnace should be modelled three-dimensionally or the three-dimensional effects should be taken into account. The only available methods for simulating the large CFB furnaces three-dimensionally are semi-empirical models, which apply a relatively coarse calculation mesh and a combination of fundamental conservation equations, theoretical models and empirical correlations. The number of such models is extremely small. The main objective of this work was to achieve a model which can be applied to calculating industrial scale CFB boilers and which can simulate all the essential sub-phenomena: fluid dynamics, reactions, the attrition of particles, and heat transfer. The core of the work was to develop the model frame and the required sub-models for determining the combustion and sorbent reactions. The objective was reached, and the developed model was successfully used for studying various industrial scale CFB boilers combusting different types of fuel. The model for sorbent reactions, which includes the main reactions for calcitic limestones, was applied for studying the new possible phenomena occurring in the oxygen-fired combustion. The presented combustion and sorbent models and principles can be utilized in other model approaches as well, including other empirical and semi-empirical model approaches, and CFD based simulations. The main achievement is the overall model frame which can be utilized for the further development and testing of new sub-models and theories, and for concentrating the knowledge gathered from the experimental work carried out at bench scale, pilot scale and industrial scale apparatus, and from the computational work performed by other modelling methods.

Application of Computational Fluid Dynamics in Modeling Blood Flow in Human Thoracic Aorta

The aim of this study was to simulate blood flow in thoracic human aorta and understand the role of flow dynamics in the initialization and localization of atherosclerotic plaque in human thoracic aorta. The blood flow dynamics in idealized and realistic models of human thoracic aorta were numerically simulated in three idealized and two realistic thoracic aorta models. The idealized models of thoracic aorta were reconstructed with measurements available from literature, and the realistic models of thoracic aorta were constructed by image processing Computed Tomographic (CT) images. The CT images were made available by South Karelia Central Hospital in Lappeenranta. The reconstruction of thoracic aorta consisted of operations, such as contrast adjustment, image segmentations, and 3D surface rendering. Additional design operations were performed to make the aorta model compatible for the numerical method based computer code. The image processing and design operations were performed with specialized medical image processing software. Pulsatile pressure and velocity boundary conditions were deployed as inlet boundary conditions. The blood flow was assumed homogeneous and incompressible. The blood was assumed to be a Newtonian fluid. The simulations with idealized models of thoracic aorta were carried out with Finite Element Method based computer code, while the simulations with realistic models of thoracic aorta were carried out with Finite Volume Method based computer code. Simulations were carried out for four cardiac cycles. The distribution of flow, pressure and Wall Shear Stress (WSS) observed during the fourth cardiac cycle were extensively analyzed. The aim of carrying out the simulations with idealized model was to get an estimate of flow dynamics in a realistic aorta model. The motive behind the choice of three aorta models with distinct features was to understand the dependence of flow dynamics on aorta anatomy. Highly disturbed and nonuniform distribution of velocity and WSS was observed in aortic arch, near brachiocephalic, left common artery, and left subclavian artery. On the other hand, the WSS profiles at the roots of branches show significant differences with geometry variation of aorta and branches. The comparison of instantaneous WSS profiles revealed that the model with straight branching arteries had relatively lower WSS compared to that in the aorta model with curved branches. In addition to this, significant differences were observed in the spatial and temporal profiles of WSS, flow, and pressure. The study with idealized model was extended to study blood flow in thoracic aorta under the effects of hypertension and hypotension. One of the idealized aorta models was modified along with the boundary conditions to mimic the thoracic aorta under the effects of hypertension and hypotension. The results of simulations with realistic models extracted from CT scans demonstrated more realistic flow dynamics than that in the idealized models. During systole, the velocity in ascending aorta was skewed towards the outer wall of aortic arch. The flow develops secondary flow patterns as it moves downstream towards aortic arch. Unlike idealized models, the distribution of flow was nonplanar and heavily guided by the artery anatomy. Flow cavitation was observed in the aorta model which was imaged giving longer branches. This could not be properly observed in the model with imaging containing a shorter length for aortic branches. The flow circulation was also observed in the inner wall of the aortic arch. However, during the diastole, the flow profiles were almost flat and regular due the acceleration of flow at the inlet. The flow profiles were weakly turbulent during the flow reversal. The complex flow patterns caused a non-uniform distribution of WSS. High WSS was distributed at the junction of branches and aortic arch. Low WSS was distributed at the proximal part of the junction, while intermedium WSS was distributed in the distal part of the junction. The pulsatile nature of the inflow caused oscillating WSS at the branch entry region and inner curvature of aortic arch. Based on the WSS distribution in the realistic model, one of the aorta models was altered to induce artificial atherosclerotic plaque at the branch entry region and inner curvature of aortic arch. Atherosclerotic plaque causing 50% blockage of lumen was introduced in brachiocephalic artery, common carotid artery, left subclavian artery, and aortic arch. The aim of this part of the study was first to study the effect of stenosis on flow and WSS distribution, understand the effect of shape of atherosclerotic plaque on flow and WSS distribution, and finally to investigate the effect of lumen blockage severity on flow and WSS distributions. The results revealed that the distribution of WSS is significantly affected by plaque with mere 50% stenosis. The asymmetric shape of stenosis causes higher WSS in branching arteries than in the cases with symmetric plaque. The flow dynamics within thoracic aorta models has been extensively studied and reported here. The effects of pressure and arterial anatomy on the flow dynamic were investigated. The distribution of complex flow and WSS is correlated with the localization of atherosclerosis. With the available results we can conclude that the thoracic aorta, with complex anatomy is the most vulnerable artery for the localization and development of atherosclerosis. The flow dynamics and arterial anatomy play a role in the localization of atherosclerosis. The patient specific image based models can be used to diagnose the locations in the aorta vulnerable to the development of arterial diseases such as atherosclerosis.

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.

Analyzing hydraulic head of fluid flow in underground porous medium

Hydraulic head is distributed through a medium with porous aspect. The analysis of hydraulic head from one point to another is used by the Richard's equation. This equation is equivalent to the groundwater ow equation that predicts the volumetric water contents. COMSOL 3.5 is used for computation applying Richard's equation. A rectangle of 100 meters of length and 10 meters of large (depth) with 0,1 m/s fl ux of inlet as source of our fl uid is simulated. The domain have Richards' equation model in two dimension (2D). Hydraulic head increases proportional with moisture content.

Modeling of Liquid-Solid Flow in Industrial Scale

In the present work, liquid-solid flow in industrial scale is modeled using the commercial software of Computational Fluid Dynamics (CFD) ANSYS Fluent 14.5. In literature, there are few studies on liquid-solid flow in industrial scale, but any information about the particular case with modified geometry cannot be found. The aim of this thesis is to describe the strengths and weaknesses of the multiphase models, when a large-scale application is studied within liquid-solid flow, including the boundary-layer characteristics. The results indicate that the selection of the most appropriate multiphase model depends on the flow regime. Thus, careful estimations of the flow regime are recommended to be done before modeling. The computational tool is developed for this purpose during this thesis. The homogeneous multiphase model is valid only for homogeneous suspension, the discrete phase model (DPM) is recommended for homogeneous and heterogeneous suspension where pipe Froude number is greater than 1.0, while the mixture and Eulerian models are able to predict also flow regimes, where pipe Froude number is smaller than 1.0 and particles tend to settle. With increasing material density ratio and decreasing pipe Froude number, the Eulerian model gives the most accurate results, because it does not include simplifications in Navier-Stokes equations like the other models. In addition, the results indicate that the potential location of erosion in the pipe depends on material density ratio. Possible sedimentation of particles can cause erosion and increase pressure drop as well. In the pipe bend, especially secondary flows, perpendicular to the main flow, affect the location of erosion.

CTQ process flow development and the impact for cost of quality

Tämä työ tehtiin Kone Industrial Oy:lle Major Projects yksikköön, laatuosastolle. Kone Major Projects yksikkö keskittyy erikoisiin ja suuriin hissi- ja liukuporras projekteihin. Työn tavoitteena oli luoda harmonisoitu prosessi hissikomponenttien laaduntarkkailua varten sekä tarkastella ja vertailla kustannussäästöjä, jota tällä uudella prosessilla voidaan saavuttaa. Tavoitteena oli saavuttaa 80-prosentin kustannussäästöt laatukustannuksissa uuden laatuprosessin avulla. Työn taustana ja tutkimusongelmana ovat lisääntyneet erikoisprojektit ja niiden myötä lisääntynyt laaduntarkkailun tarve. Ongelmana laaduntarkkailussa voitiin pitää harmonisoidun ja selkeän prosessin puuttumista C-prosessikomponenttien valmistuksessa. Lisäksi kehitysprosessin aikana luotiin vanhojen työkalujen pohjalta keskeinen laaduntarkkailutyökalu, CTQ-työkalu. Työssä käsitellään ensin Konetta yhtiönä ja selvitetään Koneen keskeisimmät prosessit työn taustaksi. Teoria osuudessa käsitellään prosessin kehitykseen liittyviä teorioita sekä yleisiä laatukäsitteitä ja esitetään teorioita laadun asemasta nykypäivänä. Lopuksi käsitellään COQ eli laatukustannusten teoriaa ja esitellään teoria PAF-analyysille, jota käytetään työssä laatukustannusten vertailuun case esimerkin avulla. Työssä kuvataan CTQ prosessin luominen alusta loppuun ja case esimerkin avulla testataan uutta CTQ prosessia pilottihankkeessa. Tässä case esimerkissä projektin bracket eli johdekiinnitysklipsi tuotetaan uuden laatuprosessin avulla sekä tehdään kustannusvertailu saman projektin toisen bracketin kanssa, joka on tuotettu ennen uuden laatuprosessin implementoimista. Työn lopputuloksena CTQ prosessi saatiin luotua ja sitä pystyttiin testaamaan käytännössä case esimerkin avulla. Tulosten perusteella voidaan sanoa, että CTQ prosessin käyttö vähentää laatukustannuksia huomattavasti ja helpottaa laadunhallintaa C-prosessikomponenttien tuotannossa.

Scheduling dynamic dataflow graphs with model checking

With the shift towards many-core computer architectures, dataflow programming has been proposed as one potential solution for producing software that scales to a varying number of processor cores. Programming for parallel architectures is considered difficult as the current popular programming languages are inherently sequential and introducing parallelism is typically up to the programmer. Dataflow, however, is inherently parallel, describing an application as a directed graph, where nodes represent calculations and edges represent a data dependency in form of a queue. These queues are the only allowed communication between the nodes, making the dependencies between the nodes explicit and thereby also the parallelism. Once a node have the su cient inputs available, the node can, independently of any other node, perform calculations, consume inputs, and produce outputs. Data ow models have existed for several decades and have become popular for describing signal processing applications as the graph representation is a very natural representation within this eld. Digital lters are typically described with boxes and arrows also in textbooks. Data ow is also becoming more interesting in other domains, and in principle, any application working on an information stream ts the dataflow paradigm. Such applications are, among others, network protocols, cryptography, and multimedia applications. As an example, the MPEG group standardized a dataflow language called RVC-CAL to be use within reconfigurable video coding. Describing a video coder as a data ow network instead of with conventional programming languages, makes the coder more readable as it describes how the video dataflows through the different coding tools. While dataflow provides an intuitive representation for many applications, it also introduces some new problems that need to be solved in order for data ow to be more widely used. The explicit parallelism of a dataflow program is descriptive and enables an improved utilization of available processing units, however, the independent nodes also implies that some kind of scheduling is required. The need for efficient scheduling becomes even more evident when the number of nodes is larger than the number of processing units and several nodes are running concurrently on one processor core. There exist several data ow models of computation, with different trade-offs between expressiveness and analyzability. These vary from rather restricted but statically schedulable, with minimal scheduling overhead, to dynamic where each ring requires a ring rule to evaluated. The model used in this work, namely RVC-CAL, is a very expressive language, and in the general case it requires dynamic scheduling, however, the strong encapsulation of dataflow nodes enables analysis and the scheduling overhead can be reduced by using quasi-static, or piecewise static, scheduling techniques. The scheduling problem is concerned with nding the few scheduling decisions that must be run-time, while most decisions are pre-calculated. The result is then an, as small as possible, set of static schedules that are dynamically scheduled. To identify these dynamic decisions and to find the concrete schedules, this thesis shows how quasi-static scheduling can be represented as a model checking problem. This involves identifying the relevant information to generate a minimal but complete model to be used for model checking. The model must describe everything that may affect scheduling of the application while omitting everything else in order to avoid state space explosion. This kind of simplification is necessary to make the state space analysis feasible. For the model checker to nd the actual schedules, a set of scheduling strategies are de ned which are able to produce quasi-static schedulers for a wide range of applications. The results of this work show that actor composition with quasi-static scheduling can be used to transform data ow programs to t many different computer architecture with different type and number of cores. This in turn, enables dataflow to provide a more platform independent representation as one application can be fitted to a specific processor architecture without changing the actual program representation. Instead, the program representation is in the context of design space exploration optimized by the development tools to fit the target platform. This work focuses on representing the dataflow scheduling problem as a model checking problem and is implemented as part of a compiler infrastructure. The thesis also presents experimental results as evidence of the usefulness of the approach.

Energy saving potential in reservoir pumping

Pumping systems account for up to 22 % of the energy consumed by electrical motors in European industry. Many studies have shown that there is also a lot of potential for energy savings in these systems with the improvement of devices, flow control or surrounding sys-tem. The best method for more energy efficient pumping has to be found for each system separately. This thesis studies how energy saving potential in reservoir pumping system is affected by surrounding variables, such as the static head variation and friction factor. The objective is to create generally applicable graphs to quickly compare methods for reducing pumping system’s energy costs. The gained results are several graphs showcasing how the chosen variables affect energy saving potential of the pumping system in one specific case. To judge if these graphs are generally applicable, more testing with different pumps and environments are required.