Total Head Loss Research Articles

Equations and characteristics of the local water head loss for fluid flow at fracture intersections

For fluid flow in fracture networks, the local water head loss will occur due to the fluid convergence or deflection at fracture intersections, which obviously affect the flow characteristics of fracture networks. In this study, equations of local water head losses for fluid flow at the fracture intersections were derived based on the work-energy principle. Then, the nonuniform flow characteristics at fracture intersections were analyzed by numerical simulations and the influences of flow characteristics including flow velocities, flow rate distributions and flow patterns in fracture intersections on local water head losses were studied. Finally, the influence of local head losses at intersections on total head losses in fracture networks was analyzed quantitatively. Through this study, a unified relationship between the local water head loss influence index Th and Reynolds number (Re) was found, by defining the influence index Th as the ratio of the normalized equivalent fracture length for the local head loss to the fracture aperture. For fluid flow in fracture networks with larger fracture apertures, smaller fracture spacing, or higher flow velocity, the influence of local head loss at the fracture intersection will be more significant. This study is beneficial for explicitly describing the local head losses at fracture intersections and quantitatively analyzing the influence of local head losses on the total head losses in fracture networks.

Studying the Impact of Diffuser Return Guide Vanes on the Energy Performance of a Multistage Centrifugal Pump

The head, efficiency, and cavitation characteristics of centrifugal pumps are highly dependent on the velocity field in front of the impeller inlet. In multistage pumps, the velocity field in front of the second and each subsequent stage is determined by the shape (design) of the diffuser return guide vanes. This current work presents the results obtained by performing a numerical study using ANSYS CFX 14.0 to determine the impact of the shape (design) of diffuser return guide vanes on the head and coefficient of efficiency of one stage of a multistage centrifugal pump. Three RGVs with different Outlet angles are studied: α6 —original RGV with α6=90 deg, RGV1 with α6=110 deg and RGV2 with α6=128 deg. The results obtained after performing CFD modeling indicate that with one of the studied RGVs, the pump stage head increases by nearly 20%, while the hydraulic coefficient of efficiency remains almost constant. Applying entropy production theory is used to determine the impact of the various components of entropy production on the total head loss in the studied pump stage. The impact of the Outlet angle of the RGV on the velocity field of the flow in front of the next impeller (stage) as well as the RGV head is also analyzed. The numerical results of the original RGV are compared with the experimental data obtained from large-scale studies of pumps performed at the Laboratory of Hydraulic Machines of the University “Angel Kanchev” of Ruse, Bulgaria. When using the modified RGVs, the head curve of the original pump can be obtained by operating at a lower speed or with a smaller impeller diameter. This may lead to an overall increase in the energy efficiency of the machine, which could be explored as a future task.

Development of Head-Loss Evaluation Application Using JAVA for Drip Irrigation System

Drip irrigation is considered as one of the most efficient irrigation methods used in agricultural field. This method of irrigation is suitable not only in saving water as well as application of fertilizer can also be done very precisely at the crop root zone through fertigation. The drip irrigation set up is a micro irrigation process and it consist of pump, pipe network (Main line, sub main line and laterals), filter unit, drippers, valves, end-cap etc. One model application was developed to introduce with drip irrigation system which will help in efficient water application and used in field to increase the yield of crop the model is developed using java programming language to estimate the major head loss, minor head loss and the total head loss of sub-main and laterals of drip irrigation and it contain two types of calculators. One kind of the calculator is to calculate the head loss when laterals emerged in one side from subs main line and another is to calculate the head loss when laterals are emerged in both sides from the sub-main line in drip irrigation system. Due to head loss when water flow through pipes, there is reduction of total energy occurs and thus uniformity of drip irrigation system is affected. It further affects the flow rate and thus precision of drip system is also reduced due to head loss.

Reduced order model for flow distribution in tapered headers of U-type heat exchangers

Reduced order model for flow distribution in tapered headers of U-type heat exchangers

A control system for low-head diversion run-of-river small hydro plants with pressure conduits considering the tailwater level variation

This paper presents a control system for low-head diversion run-of-river small hydro plants with pressure conduits. Since these hydropower plants usually have low or null water storage capacity, the water discharged through the turbines should be adapted to the possible extent to the natural river inflow. For this purpose, a control scheme aimed at maintaining a constant water level in the head pond is normally used in these cases. As an alternative, the option of maintaining a constant water level in the surge tank is studied in this paper. Furthermore, since in low-head hydro plants the tailwater level variation may represent a relatively important contribution to total head losses, it has been explicitly considered in the proposed control system. A small-perturbation stability analysis has been carried out in order to analyze the influence of the plant design and controller parameters in the plant dynamic response. Finally, in order to illustrate the applicability of the proposed control system, several simulations have been carried out using data gathered from a real hydro plant.

ПРОГРАММНОЕ ОБЕСПЕЧЕНИЕ ПРОЦЕССА РАССТАНОВКИ ДОЖДЕВАТЕЛЕЙ НА ВОДОПРОВОДЯЩЕМ ПОЯСЕ ДОЖДЕВАЛЬНОЙ МАШИНЫ

Purpose: to develop software for the process of arranging sprinklers on the water-conducting belt of a sprinkler to improve the irrigation quality. Materials and methods. As a theoretical basis for creating software, the traditional methods of algorithmization and programming based on the processes of algorithm design for solving the problem of calculating the optimal spacing and flow-pressure characteristics of deflector nozzles on the water-conducting belt of sprinklers, respectively, formalized in the form of a scheme, and writing the source code in the object-oriented programming language Python were used. Results. To replenish the domestic scientific and technical base for digitalization of engineering and reclamation work with information tools, software for the process of arranging sprinklers on water-conducting belt of a sprinkler for uniform distribution of artificial rain along the irrigated area has been developed. The algorithm graphical model is represented by three blocks. The “Source data input” block provides a choice of the type of sprinkler, the operating flow rate of irrigation water, as well as the material of the water conducting belt. In the “Intermediate and target values calculation” block, the irrigation water loss, head loss, distance between the end and first nozzles, as well as the total number of sprinklers are calculated. In the “Cyclic computation and output of results” block, head losses along the length and local pressure losses are determined for each section, the sum of which makes up the total head losses. Using the designed software, computations were performed using the example of a cantilever sprinkler with 4 sections of steel pipeline, a total flow rate of 6 l/s and a pressure at the end of the console of 10 m. It was determined that to ensure the uniform distribution of artificial irrigation along the irrigated area, it is necessary to install 9 sprinklers with variable spacing along the length console, and to provide a head at the beginning of the sprinkler machine of 23.8 m, taking into account the total head loss of 13.8 m. Conclusions: the software allows simulating the optimal arrangement of deflector nozzles of the same size on a water-conducting belt at the design stage of double-cantilever and multi-tower lateral sprinklers.

Analysis of Decision Making on Wastewater Use Technology in the Universitas Pertamina Area

Wastewater available through the sewerage system can be reused as a daily need. With a sewer system, the Universitas Pertamina Area can utilize water according to Government Regulation of the Republic of Indonesia Number 82 of 2001 Class 4. Reuse of wastewater within this scope can improve sustainable development goals. This study aims to analyze the decision-making of sewerage water treatment so that it can be reused according to the class 4 quality standard. The first alternative consists of a collection tank, bar screen, pre-sedimentation, rapid sand filter (RSF), and disinfection. The second alternative consists of a collection tank, bar screen, horizontal roughing filter (HRF), RSF, and disinfection. The two alternatives provided have met the required quality standards. However, the area of land required in alternative one is too large compared to the second alternative. This causes the second alternative to be more appropriate to be applied in the Universitas Pertamina Area. Analysis of decision-making on the use of RSF media is carried out using the Analytical Hierarchy Process (AHP). The alternative media for RSF are sand, granular active carbon (GAC), and zeolite. The criteria for BOD removal, total coliform removal, cost, headloss, and replacement period of the most appropriate zeolite media for use in the RSF unit process.

Numerical modelling of stepped helical cooling channels

The automotive industry is in the midst of a radical change of propulsion technology to meet the increasingly stringent limits on emissions and fuel consumption. Electric and hybrid power-trains are progressively replacing their internal combustion counterparts, as they are more efficient, especially in transient operation. In electric and hybrid vehicles effective cooling system operation is of utmost importance as it influences directly the efficiency and power density levels achievable by the power train. Thus, accurate analyses are needed to maximize the thermal performance of these systems. In this work an electric motor cooling jacket, that features a stepped helical geometry, is studied by means of CFD, with a particular focus on the head losses. The periodicity of the cooling channels geometry along the helical development is exploited to reduce the computational domain to a basic periodic module. The flow field is determined by applying a 3D Finite Volume approach, and numerical solutions are obtained by means of a validated incompressible solver. Novel boundary conditions are purposely developed to allow for the coupling of the inlet and outlet patches, which are roto-translated with respect to each other. The sensitivity of integral results on friction losses, with respect to the number of periodic modules included in the model, is investigated. The developed numerical model is employed to obtain a suitable correlation for the equivalent Darcy friction factor as a function of the Reynolds number only. Finally, a first estimation of the total head losses is obtained by using the Darcy Weisbach formula along with the aforementioned friction factor correlation.

Design of Influent Distribution System in Domestic Wastewater Treatment Units

The efficient treatment of domestic wastewater is associated with good operational practices in wastewater treatment plants (WWTP) and the proper design of each treatment unit, which ensures the correct hydraulic performance of each WWTP. For this reason, the objective of this article was to study the design of the multiple influent distribution systems of a high-rate primary sedimentary, a UASB (Upflow Anaerobic Sludge Blanket) reactor, and an up-flow anaerobic filter (FAFA) in the WWTPs of the municipalities of San Carlos and San Roque, and in the township of Santiago, respectively, located in Antioquia-Colombia. For this purpose, the methodology proposed by Hudson in 1981 was used to evaluate the performance of the current design and, subsequently, a pre-dimensioning was carried out to distribute the flow uniformly, to have velocities within the ranges recommended by the literature, and to obtain the total head loss generated by the distribution manifold in each treatment unit evaluated. It was found that the existing design is not efficient and that the new pre-dimensioning ensures homogeneous flow distribution and provides velocities that contribute positively to the treatment process. The study concludes that the smaller the number of orifices and the larger the pipe diameter, the more uniform the flow distribution, and that the total head loss depends on both the velocity head and the head loss coefficient. The diameter of the orifice was the predominant parameter to control the inlet velocity of the treatment units.

Predictive modelling of a rapid stratified bed filter for turbidity removal from surface water

The objective of the present work was to evaluate the hydrodynamic behaviour of a stratified bed filtration column consisting of 4 cm of sand and 2 cm of limestone to remove turbidity and measuring the head loss through the filter in several runs. In this study, two types of sand were used as filtering bed material, one fine and one medium. Crushed limestone was also available. These materials were characterized to determine the average particle diameter, porosity, and permeability coefficient. These were respectively 1.7∙10 –4 m, 336.96 and 0.68 m∙day –1 for fine sand, 3.3∙10 –4 m, 654.24 and 2.59 m∙day –1 for the medium sand and 1.26∙10–3 m, 388.8 and 8.64 m∙day–1 for crushed limestone. Using these materials, hydrodynamic analyses were carried out using clean water under rapid filtration conditions. In these analyses, different filtration rates were determined to be used in each experiment. Once the filtration rates were determined, the filtration analysis was performed with synthetic turbid water prepared at 8 NTU using tap water and bentonite. From the results obtained, a predictive model was developed based on total head losses for the evaluated filter, maintaining the rapid filtration condition. As a result, a turbidity removal efficiency of 97.7% was obtained with a total head loss of 17.8 cm at a filtration rate of 153 m·day –1. The developed model predicted head loss as a function of operating time, filtration rate, and filter depth to maximise turbidity removal. The model showed excellent prediction accuracy with R2 of 0.9999, which indicates that the model predictions are not biased. It was concluded that, due to the porosity of these materials, a stratified bed of sedimentary rocks has a great potential to be used in surface water filtration processes, which implies that it could be used at the rural community level as a form of water treatment, since the

A general solution for leakage through geomembrane defects overlain by saturated tailings and underlain by highly permeable subgrade

Experimental data is presented for leakage through slits, square, and rectangular geomembrane defects overlain by silty sand tailings and underlain by a well-graded gravel. The rectangular GMB defects have a range of widths, B , lengths, L , and aspect ratios ( L / B ), and ratios of defect length to thickness of tailings above the geomembrane ( L / T ). A blade cut slit (or simulated stress crack) widens to an extent dependant on the subgrade and stress level. For L= 100 mm, increasing B (0.15 < B / L ≤ 1) from 1.6 (slit) to 100 mm (square), decreases the leakage from about twice to essentially the same as that for a circular hole of equal area. The ratio ( h 1 / H ) of head loss within the hole, h 1 , relative to the total head loss, H , is independent of loading conditions and constant for any particular hole shape ( B / L ), area ( B ∙ L ), and relative depth ( L / T ). A semi-empirical general solution is developed for a rectangle within the range of 0 ≤ B / L ≤ 1 with the solution converging to that for a strip for B / L → 0 and to a circle for B / L → 1. The solution gives calculated leakage in encouraging agreement with the experimental data. • Investigates the factors affecting leakage through a rectangular hole in a geomembrane overlain by tailings. • Studies how hole geometry affects leakage. • Provides a semi-empirical general solution for predicting leakage through quasi circular, rectangular, and strip (L » B) holes. • Investigates the physical and hydraulic response of a blade cut slit with flat and uneven ground conditions.

Experimental and numerical investigation on head losses of a complex throttled surge tank for refined hydropower plant simulation

For a large hydropower plant (HPP) with long-distance tunnels, a surge tank needs to be installed to ensure the safety of the HPP during hydraulic transients (i.e., load changes in hydro-turbines). The head losses of the surge tank and its throttle are necessary conditions and evidence of the hydraulic design and one-dimensional (1D) simulation of the HPP. This study is conducted to investigate the head losses of a complex throttled surge tank for a refined 1D HPP simulation. Based on model experiments and computational fluid dynamics (CFD) simulations, the statistical laws of the total head loss coefficient are determined, and the dynamic refined formulas for the resistance and discharge coefficients are proposed. Finally, the proposed discharge coefficients are applied to refined 1D HPP simulations and compared with the traditional discharge coefficient. It is preliminarily revealed that the discharge coefficient undergoes a step change under load rejection and a continuous hump-shaped change under increasing loads. The water level results calculated using the proposed discharge coefficient differ by 1.69 m, i.e., 3.65% of the total height of the surge tank, compared with using the traditional discharge coefficient. This study can facilitate the understanding of hydraulic design and HPP optimization.

Determination of the Equivalent Length for Evaluating Local Head Losses in Drip Irrigation Laterals

HighlightsA hydraulic model was used to determine the value of the equivalent length for evaluating local emitter head losses in drip laterals.Dimensional analysis was used to develop an equation for predicting the equivalent length.The effects of the design variables on the equivalent length were investigated.The accuracy of the equation was validated by a previous experiment and an alternative hydraulic model.Abstract. The equivalent length is widely used in current hydraulic models to estimate local emitter head losses for the analysis and design of drip irrigation laterals. The accurate evaluation of the equivalent length is therefore required in the lateral design procedure. In this study, a finite element model was used to develop an equation to predict the equivalent length. Eight design variables were selected, and 32 lateral cases were generated using the orthogonal design. The total local head loss in the 32 laterals were firstly calculated using the local head loss coefficient multiplied by the kinetic head. The solutions were considered as exact values and being equivalent to friction head losses, and the equivalent length was computed using the Darcy-Weisbach equation. Dimensional analysis and regression procedures were then used to obtain the prediction equation related to the selected variables. The results show that the converted equivalent lengths accurately estimated the local head losses in the 32 laterals. The local head loss coefficient was the most important factor for the equivalent length, followed by the lateral diameter. The effects of the lateral inlet pressure head, flow exponent, nominal flow rate of emitter, number of emitter, emitter spacing and lateral slope were not significant. Two models were developed to predict the equivalent length, and to calculated the total local head losses. The results demonstrated satisfactory agreement with the measured value available in a previous experimental study, with RMSE = 0.202 and 0.162 m for the full and simplified model, respectively. The percent error between the measured and calculated total head losses using simplified model was from -16.5% to 14.8%, and the Camargo and Sentelhas coefficient c was higher than 0.98. The equations were therefore capable for evaluating the local head loss in the hydraulic design of drip irrigation laterals. Keywords: Dimensional analysis, Finite element method, Hydraulic design, Pressure head, Uniformity.

A numerical investigation on head losses and flow qualities for a large cavitation tunnel without impeller

In this study, a numerical investigation of the flow quality and total head loss of a large cavitation tunnel is conducted. Excluding the impeller, the entire tunnel is modeled, and calculations are conducted for the test section's maximum speed of 15 m/s. The numerical study showed that an edge chamfer eliminates the pressure drop in the test section, resulting in a constant cavitation number downstream, and that a diverging top diffuser, as opposed to a flat top, induces upward flow at the exit of the test section. Also, the effectiveness of the flow straightener and honeycomb in reducing turbulence has been validated. In the test section, the turbulence intensity is 0.10% and the uniformity is 0.20%. The 2nd corner has the highest head loss due to the shaft. Due to the relatively high speed, significant head losses are observed in the test section, diffuser, and first corner.

Гидравлический расчет трубопровода с учетом длин влияния местных сопротивлений и их интерференции

The design and calculation of pipelines taking into account the mutual influence of local resistances is an urgent task in the hydraulics of pressure flows. The analysis and results of the hydraulic calculation of the Valtec metal-polymer pipeline are given, taking into account the lengths of the influence of local resistances of their mutual influence (interference). Tabular data on the lengths of influence of local resistances, coefficients of mutual influence used in the developed program of the Delhi (Object Pascal) environment are given. A graph of the dependence of specific pressure losses per 1 meter of pipeline length on the flow rate for the Valtec pipeline with an equivalent roughness of Δe/ d = 0.007 mm, obtained experimentally and data for a similar pipeline according to the reference data tables with an equivalent roughness of Δe / d = 0.01 mm, is presented. The results of the calculations and the interface of the Delphi 7 environment application program with the data in a tabular form for the hydraulic calculation of the total pressure losses in pipelines are shown, taking into account reference and experimental values of coefficients of local resistances. The data of the results of the hydraulic calculation of the total head losses, taking into account the specifi c linear pressure loss per 1 meter of the pipeline length without local resistances, are given to determine the head losses by length. The developed program can be used in the design, layout and hydraulic calculation of metal-polymer pipelines with specifi ed parameters.

Physical modelling of energy losses at surcharged three-way junction manholes in drainage system.

Motivated by the observation that vortex flow structure was evident in the energy loss at the surcharged junction manhole due to changes of hydraulic and geometrical parameters, a physical model was used to calculate energy loss coefficients and investigate the relationship between flow structure and energy loss at the surcharged three-way junction manhole. The effects of the flow discharge ratio, the connected angle between two inflow pipes, the manhole geometry, and the downstream water depth on the energy loss were analyzed based on the quantified energy loss coefficients and the identified flow structure. Moreover, two empirical formulae for head loss coefficients were validated by the experimental data. Results indicate that the effect of flow discharge ratio and connected angle are significant, while the effect of downstream water depth is not obvious. With the increase of the lateral inflow discharge, the flow velocity distribution and vortex structure are both enhanced. It is also found that a circular manhole can reduce local energy loss when compared to a square manhole. In addition, the tested empirical formulae can reproduce the trend of total head loss coefficient.

Comparison and Validation of Models for the Design of Optimal Economic Pipe Diameters: A Case Study in the Anseba Region, Eritrea

An optimal design for a pressurized flow pipe network is characterized by being economical and contributing the least amount of losses during water transmission through the system. The diameter of a pipe in a network system that delivers the desired effect with the minimum amount of waste and expenses is referred to as an optimal pipe size. The Life-Cycle Cost Analysis (LCCA) model is widely recognized as the recommended standard technique to estimate the optimal pipe size for any pipe flow network system. Numerous empirical formulas have been proposed to simplify the computations required in this economic analysis model. This study seeks to compare the various empirical models that have been proposed by different authors based on a variety of physical variables involved in fluid flow dynamics. Eleven different empirical equations were chosen in order to select the optimal diameter for the network at the Hamelmalo Agricultural College farm located in the Anseba region of Eritrea for the distribution of water to the different sub-plots. The estimated diameters were compared to the standard diameter calculated using the standard LCCA method. This comparison was based on the estimated total head losses and economic analysis of the pipe diameters chosen for such network. Moreover, a statistical analysis was conducted to obtain the best-fit recommended modeled diameter for the network. The Bresse’s model performance was the most adequate when compared with the LCCA model.

Hydrodynamic evaluation of a filter bed of porous material from stratified sedimentary rocks for the removal of turbidity in surface waters

• Treatment and potabilization of raw water, extracted from surface and subway sources, are necessary to provide safe quality water for consumption. • Hydrodynamic analyses stablished the filtration rate on 120 m/day under rapid filtration. • The filtration process for turbidity remotion purposes has very well exceeded the standards of drinking water. In this study, the behavior of a filter bed of stratified sedimentary rocks was evaluated through the analysis of turbidity removal efficiency and head losses. Two types of sands were used as materials, fine and medium, as well as crushed limestone. The materials were characterized to determine the average particle diameter, porosity, and permeability coefficient, obtaining respectively 0.17 mm, 0.39, and 1 × 10 −3 cm/s for fine sand, 0.33 mm, 0.41, and 3 × 10 −3 cm/s for medium sand, and 1.26 mm, 0.45, and 1 × 10 −2 cm/s for crushed limestone. Hydrodynamic analyses of the clean filter under conditions of rapid filtration were carried out, by which the different rates of filtration to be used in each experiment were determined, establishing a direct correlation between the rate of filtration and the thickness of the bed; in this way, it was possible to determine the maximum bed thickness that could be used to maintain a rate of rapid filtration higher than 120 m/day. A hydrodynamic study with synthetic turbid water prepared at 8 NTU using tap water and bentonite was also carried out. Total head losses and turbidity removal were studied for each material at a rate of 153 m/day with removal efficiencies of 93.7% for medium sand with a loss of 23 cm and 67.8% for limestone with a loss of 4.5 cm and a rate of 389 m/day. It is recommended to use the medium sand and limestone type material for use in surface water filtration processes.

IMPROVING THE METHOD OF DETERMINING THE VALUE OF WATER LEVELS IN VERTICAL WELLS OF GROUP WATER COLLECTION

Purpose. Reconstruction of water supply systems to meet the increased water needs of consumers is a complex, time-consuming and expensive task. Reconstruction options include expanding existing water intakes or building new ones anywhere in the existing water supply network. The variety of options is accompanied by changes in water consumption in the sections of the networks and, importantly, in the flow distribution. The introduction of additional sources into the existing water supply systems requires a detailed study of the factors affecting the technical characteristics of the systems and responsible for the economic component of the project. Methodology. The influence of the determining factors on the total head losses in the water distribution network during the reconstruction of the water supply system is analyzed. An algorithm for finding the optimal network points for connecting an additional power source is proposed, which includes determining the optimal flow distribution and the corresponding technical changes for each selected option; total capacity of pumping stations and heads; analysis of the complete set of the water supply system of the accepted options; an economic analysis of the construction investment and operating costs that will accompany the operation of the water supply system design options. Findings. The choice of the optimal connection points for additional power sources depends on the amount of water flow in the network sections and the flow distribution. It is shown that the nodes of the end sections of the network most correspond to the conditions for searching for optimal points and can be fed from different directions, depending on the amount of additional flow. With an additional water flow rate no more than two nodal flow rates, the total head losses in the network sections are minimal. When an additional flow rate of more than two nodal flows enters the final node, an increase in head losses is observed, which can have critical values depending on its increase. The introduction of additional water flows into the network, which exceed two nodal ones, requires the use of intermediate network nodes located at sections with a higher throughput as connection points. Originality. The analysis of the factors influencing the choice of points of connection of additional power sources of the water supply network during its expansion is carried out. The analysis of the points was carried out with limited ranges of the values of water consumption of additional feeding − less and equal to the nodal ones, two and three times larger than the nodal ones. The ways of finding the optimal option for choosing a network node as a point of connection of additional power are shown. Practical value. The use of the analysis results will make it possible to most effectively search for the optimal variant of reconstruction of water supply systems, take into account the influence of determining factors on the characteristics of networks with changes in water consumption and flow distribution. The use of the analysis results will make it possible to most effectively search for the optimal variant of reconstruction of water supply systems, take into account the influence of determining factors on the characteristics of networks with changes in water consumption and flow distribution.

Numerical simulation and optimization of centrifugal compressor return channels: methods and results

The authors actively use their engineering Universal Modelling Method for gas-dynamic design of centrifugal compressors for industrial partners. Currently, there are two approaches to improving the Method: improving the preliminary design and increasing the accuracy of gas-dynamic characteristics calculation. Computational Fluid Dynamics (CFD) methods give good results for the flow path stator part. Recently, massive CFD calculations of the vaneless diffusers (VLD) characteristics were generalized by a system of algebraic equations, which replaced the previous more complex mathematical model in the Method. Then, based on CFD optimization of a large series of return channels (RCh), corrections were made to the preliminary design of this element of the flow path.This paper presents the results of the joint CFD optimization of a vaneless diffuser and a return channel. Stator elements have many geometric parameters. For a stage with the flow rate coefficient of 0.0597 and the loading factor of 0.60, only the VLD relative radial length D 4/D 2, the number and the inlet angle of the return channel vanes were optimized. Engineering calculations and design experience predicted an optimal value of D 4/D2 within the interval 1.9 - 2.0. CFD optimization demonstrated almost linear reduction of the total head loss towards the end of the investigated range D 4/D2 = 2.3. After careful optimization of the U-bend, the optimization of D 4/D2 was repeated. The influence of on the loss coefficient has decreased, but the value of D 4/D 2 = 2.3 is still far from optimum. It significantly exceeds technically acceptable radial size. The result obtained influenced the design plan of future calculation experiments with a large series of stator elements of the stages in a practically significant range of design parameters.