Circumferential Non-uniformities Research Articles

Accounting for Circumferential Flow Nonuniformity in a Multistage Axial Compressor

AbstractThe flow field in a compressor is circumferentially nonuniform due to geometric imperfections, inlet flow nonuniformities, and blade row interactions. Therefore, the flow field, as represented by measurements from discrete stationary instrumentation, can be skewed and contributes to uncertainties in both calculated one-dimensional performance parameters and aerodynamic forcing functions needed for aeromechanics analyses. Considering this challenge, this article documents a continued effort to account for compressor circumferential flow nonuniformities based on discrete, undersampled measurements. First, the total pressure field downstream of the first two stators in a three-stage axial compressor was measured across half of the annulus. The circumferential nonuniformities in the stator exit flow, including vane wake variability, were characterized. In addition, the influence of wake variation on stage performance calculations and aerodynamic forcing functions were investigated. In the present study for the compressor with an approximate pressure ratio of 1.3 at the design point, the circumferential nonuniformity in total pressure yields an approximate 2.4-point variation in isentropic efficiency and 54% variation in spectral magnitudes of the fundamental forcing frequency for the embedded stage. Furthermore, the stator exit circumferential flow nonuniformity is accounted for by reconstructing the full-annulus flow using a novel multiwavelet approximation method. Strong agreement was achieved between experiment and the reconstructed total pressure field from a small segment of measurements representing 20% coverage of the annulus. The analysis shows the wake–wake interactions from the upstream vane rows dominate the circumferentially nonuniform distributions in the total pressure field downstream of stators. The features associated with wake–wake interactions accounting for passage-to-passage variations are resolved in the reconstructed total pressure profile, yielding representative mean flow properties and aerodynamic forcing functions.

Mitigation of Boundary Layer Ingestion Circumferential Distortion Using Nonaxisymmetric Fan Exit Guide Vanes

Abstract This paper presents an assessment of the effect of nonaxisymmetric fan exit guide vanes (FEGVs) to mitigate, or even reduce to zero, the impact of circumferential flow distortion—such as created by boundary layer ingestion (BLI)—on fan rotor efficiency and vibratory structural forcing. The fan response to circumferential nonuniformities is characterized, for two-dimensional flow, in terms of the variations in incidence angle and unsteady rotor forces. FEGV designs with nonaxisymmetric exit flow angle perturbations can eliminate either of these. More importantly, nonaxisymmetric stator row designs can reduce both nonuniformities relative to the influence of an axisymmetric stator row. This suggests that design for distortion need not involve a tradeoff between performance and aeromechanics; a nonaxisymmetric aerodynamic design approach can improve both simultaneously. Analysis of the impact of stage design parameters has been carried out to determine FEGV exit flow angle variations that shield the rotor from the adverse effects of circumferential distortions representative of BLI. The results indicate that inlet distortion effects can be mitigated with realizable nonaxisymmetric FEGVs. The magnitude of the geometry variations required decreases with decreased axial rotor–stator spacing and increased flow coefficient.

Numerical Simulation of the Exit Temperature Pattern of an Aircraft Engine Using a Temperature-Dependent Turbulent Schmidt Number

Abstract This paper presents a numerical simulation for predicting the combustor exit temperature pattern of an aircraft engine, developed using the commercial fluid simulation software Ansys Fluent, which assumes a shape probability density function for the instantaneous chemistry in the conserved scalar combustion model and the standard k-ε model for turbulence. We found the compliance of the radial and circumferential non-uniformities of the exit temperature with the experimental data to be insufficient. To achieve much more accurate result, the mixing intensity was enhanced with respect to the initial calculation due to using the reduced value of the turbulent Schmidt number Sc. Numerical simulation was performed for values of the turbulent Schmidt number from Sc = 0.85 (default) up to Sc = 0.2, with results confirming the reduction of radial and circumferential non-uniformities of exit temperature. However, correlation between radial and circumferential non-uniformities is not admissible for these cases. Therefore, we propose to use a temperature-dependent formulation of the turbulent Schmidt number Sc, accounting for the increase in Sc number with increasing gas temperature. A user defined function (UDF) was used to implement the Sc number temperature dependence in Ansys Fluent. The numerical results for the proposed Schmidt number Sc temperature dependence were found to be in acceptable agreement with the experimental data both for radial and circumferential non-uniformities of the exit temperature pattern.

Reconstructing Compressor Nonuniform Circumferential Flow Field From Spatially Undersampled Data—Part 2: Practical Application for Experiments

Abstract In the previous part of the paper, a novel method to reconstruct the compressor nonuniform circumferential flow field using spatially undersampled data points is developed. In this part of the paper, the method is applied to two compressor research articles to further demonstrate the potential of the novel method in resolving the important flow features associated with these circumferential nonuniformities. In the first experiment, the static pressure field at the leading edge of a vaned diffuser in a high-speed centrifugal compressor is reconstructed using pressure readings from nine static pressure taps placed on the hub of the diffuser. The magnitude and phase information for the first three dominant wavelets are characterized. Additionally, the method shows significant advantages over the traditional averaging methods for calculating repeatable mean values of the static pressure. While using the multi-wavelet approximation method, the errors in the mean static pressure with one dropout measurement are 70% less than the pitchwise-averaging method. In the second experiment, the full annulus total pressure field downstream of Stator 2 in a three-stage axial compressor is reconstructed from a small segment of data representing 20% coverage of the annulus. Results show very good agreement between the reconstructed total pressure profile and the experiment at a variety of spanwise locations from near hub to near shroud. The features associated with blade row interactions accounting for passage-to-passage variations are resolved in the reconstructed total pressure profile.

Flow Distortion Into the Core Engine for an Installed Variable Pitch Fan in Reverse Thrust Mode

Abstract The flow distortion at core engine entry for a variable pitch fan (VPF) in reverse thrust mode is described from a realistic flow field obtained using an integrated airframe-engine model. The model includes the VPF, core entry splitter, complete bypass nozzle flow path wrapped in a nacelle, and installed to an airframe in landing configuration through a pylon. A moving ground plane to mimic the rolling runway is included. 3D Reynolds-averaged Navier–Stokes (RANS) solutions are generated at two combinations of VPF stagger angle and rotational speed settings for the entire aircraft landing run from 140 to 20 knots. The internal reverse thrust flow field is characterized by bypass nozzle lip separation, pylon wake, and recirculation of flow turned back from the VPF. A portion of the reverse stream flow turns 180 deg with separation at the splitter leading edge to feed the core engine. The core engine feed flow exhibits circumferential and radial nonuniformities that depend on the reverse flow development at different landing speeds. The temporal dependence of the distorted flow features is also explored by an unsteady Reynolds-averaged Navier–Stokes (URANS) analysis. Total pressure and swirl angle distortion descriptors, as defined by the Society of Automotive Engineers (SAE) S-16 committee, and, total pressure loss into the core engine are described for the core feed flow at different operating conditions and landing speeds. It is observed that the radial intensity of total pressure distortion is critical to core engine operation, while the circumferential intensity is within acceptable limits. Therefore, the baseline sharp splitter edge is replaced by two larger rounded splitter edges of radii, ∼0.1x and ∼0.2x times the core duct height. This was found to reduce the radial intensity of total pressure distortion to acceptable levels. The description of the installed core feed flow distortion, as described in this study, is necessary to ascertain stable core engine operation, which powers the VPF in reverse thrust mode.

ПОВЫШЕНИЕ ТОЧНОСТИ РАСЧЕТА ПОЛЯ ТЕМПЕРАТУР ГАЗА НА ВЫХОДЕ ИЗ КАМЕРЫ СГОРАНИЯ ГТД МЕТОДОМ ТРЕХМЕРНОГО КОМПЬЮТЕРНОГО МОДЕЛИРОВАНИЯ

The problem of numerical simulation of the gas flow with the combustion of atomized liquid fuel was solved (the equilibrium combustion model pdf was used along with the partially mixed mixture model) in the annular combustion chamber of a gas turbine engine. Numerical modeling was performed in Ansys Fluent calculation complex. The purpose of the calculations was to simulate the radial and circumferential unevenness of the gas temperature pattern at the outlet of the combustion chamber. As a result of the calculations, it was found that the accuracy of modeling the radial and circumferential unevenness of the gas temperature pattern at the outlet of the combustion chamber is unsatisfactory when using the k–e turbulence model with the initial settings for the Ansys Fluent calculation complex. Moreover, the maximum value of the radial non-uniformity of the gas temperature pattern at the outlet of the combustion chamber exceeded the value obtained in the experiment by 12.61 %, and the maximum value of the circumferential non-uniformity by 12.69 %. To improve the accuracy of modeling the temperature pattern non-uniformity at the outlet of the combustion chamber, a numerical experiment was conducted to study the effect of the degree of turbulent diffusion of gas components on the value of temperature pattern non-uniformity. To reduce the non-uniformity of the temperature pattern at the outlet of the combustion chamber, the degree of turbulent diffusion of gas components was increased with respect to the initial version of the calculation, performed using the k–e model of turbulence with the initial settings for the Ansys Fluent calculation complex, by reducing the turbulent Schmidt number Sc in the turbulence model. For the initial settings of the k–e turbulence model in the Ansys Fluent calculation complex, the turbulent Schmidt number Sc = 0.85. A numerical experiment was performed for the values of Sc = 0.6, Sc = 0.4, and Sc = 0.2. The results of a numerical experiment confirmed the influence of the turbulent Schmidt number Sc on the result of calculating the gas temperature pattern at the outlet of the combustion chamber; as the value of Sc decreases, the level of the circumferential and radial non-uniformities of the gas temperature pattern decreases. However, the degree of reduction of radial and circumferential irregularities with a decrease in Sc is different. Therefore, to ensure high accuracy in calculating both the circumferential and radial non-uniformities of the gas temperature pattern, it was proposed to use a variable value of the turbulent Schmidt number Sc depending on the gas temperature instead of a constant value. The functional dependence of the turbulent Schmidt number Sc on the gas temperature was implemented in the Ansys Fluent calculation complex using the user function (UDF). The results of modeling the gas temperature pattern using the proposed UDF function for the turbulent Schmidt number Sc are in satisfactory agreement with the experimental data for both radial and circumferential non-uniformities of the gas temperature pattern at the outlet of the combustion chamber.

PREPARATION AND SIMULATION OF THE ON-LINE SiO2/S COATING FOR COKING INHIBITION IN THE INDUSTRIAL CRACKING FURNACE

Abstract Coke formation inside radiant coils is one of the main problems during thermal cracking of hydrocarbons. The on-line preparation of the coating for coking inhibition is a promising technology because it provides more flexibility to the operators on site. The SiO2/S coating was prepared on the inner surface of coils in an 8-year-served GK-VI industrial cracking furnace. The effects of the coating preparation process on the operation of TLE were studied. The coking rates of the tube with and without coating preparation were evaluated by the trend change of tube metal temperature. Simulations of the coating deposition process were further carried out using the computational fluid dynamics approach. The results showed that a significant temperature increase at the outlets of TLEs during coating preparation were due to the accumulation of SiO2 and S in a loose form under the TLE operating conditions when the concentration of coating precursors was 7500 ppm (wt. %). In the three tests, coating precursors were mainly completely consumed in tubes and TLEs. For the coated tube, the run time was extended by 4-7 days because the catalytic coking was decreased. No significant changes in the distribution of products and molar yields of main products were observed. In the simulations, it was found that increasing the inlet flow rate led to a more uniform thickness and improved the mass content of sulfur in the coating. In the tube bend section, circumferential nonuniformities for the deposition were due to circumferential differences in the temperatures and mass fractions. The mass fraction of S in the coating was within the range of 0.02%-0.1%. The control step for the SiO2/S coating deposition was kinetic. Based on the simulation results, the optimized coating preparation parameters were determined, i.e., the inlet flow rate of 15t/h, the outlet temperature of 1093K and the inlet mass concentration of 3000 ppm (wt. %).

Experimental and Numerical Investigation of Annular Casing Impingement Arrays for Faster Casing Response

The transient heat transfer facility (THTF) was developed to test full-scale high pressure compressor and turbine casing air systems using gas turbine engine representative secondary air system conditions. Transient casing response together with blade and disk responses governs achievable tip clearances in both compressors and turbines. This paper investigates the use of air impingement as a means to speed up the casing response. The thermal growth of the casing was characterized by surface temperature rise over a given period to assess achievable dynamic response. The experimental setup resembles a typical aircraft engine with features that can lead to circumferential temperature nonuniformities, as evident from the experimental results. The experimental data were compared against numerical predictions from a conjugate heat transfer (CHT) model. The studies show the significance of analyzing the full annulus, at engine representative conditions and the benefit of an impingement array to potentially speed up casing response for future engines.

Aerodynamic performance analysis and optimization of a turbine duct with low degree of partial admission

A partial admission turbine duct with outlet-to-inlet area ratio greater than unity can increase the admission degree of the downstream turbine stage and, thus improve the performance of a multistage turbine with a low partial admission degree. However, the upstream flow structures of ducts, such as secondary flow, especially the circumferential nonuniformities originating from the effect of the partial admission, make the flow in ducts complex. The complexity of the flow has a negative impact on the performance of ducts. In the present investigation, numerical study of the flow behavior within ducts is done to evaluate the effect of the partial admission on the performance of the ducts. The study is carried out with regard to two cases, i.e. which are with the same duct geometry but are at different working conditions to highlight the impact of partial admission on the performance of ducts. Case 1 is used as baseline. It is designed based on circumferential mass-averaged flow conditions at ducts inlet. It causes the circumferential nonuniformities originating from the partial admission to have no impact on the performance of case 1. Case 2, which considers partial admission, is compared with case 1 to know the impact of the partial admission on the performance of ducts, and to give guidelines to design a duct for the partial admission turbines. Since the duct inlet conditions is a result of the interaction between partial admission turbine and duct, a straightforward way to consider the effect of the partial admission is to simulate the flows in ducts and upstream turbines contemporaneously. Comparative results indicate that the mixing of main flow in the admitted channel and the windage fluid from the unadmitted channel occurs at the duct inlet close to the duct circumferential wall. The adverse pressure gradient of case 2 in that region becomes larger than that of case 1. As a result, the flow separates at that region deteriorating the performance of ducts. Based on the simulation results of the previous cases, case 2’s circumferential wall surface, which is along the gas swirling direction is shrunk to accelerate the flow and, thereby, overcome the adverse pressure gradient imposed by the effect of the partial admission. The results show that the separation is restrained and the decrease in total pressure loss is 52.9%.

Accounting for Unsteady Interaction in Transonic Stages

This paper discusses the importance of the unsteady interaction in transonic turbomachinery stages. Although the flow in a turbomachine is inherently unsteady, most current calculations for routine design work exploit the steady state assumption. In fact, unsteady flow effects are often taken into account for mechanical integrity checks, such as blade flutter or forced response, or heat transfer issues associated with circumferential nonuniformities, whereas steady state calculations are usually selected for the aerodynamic design. In this work, some cases are discussed in which significant departures are found between steady and time-averaged results, and the basic fluid mechanisms responsible for them are examined. Finally, a current perspective of unsteady computational fluid dynamics (CFD) calculations for the aerodynamic design is given.

Analyses of steady and unsteady flows in a turbocharger’s radial turbine

This study presents the aerodynamic behaviours of a twin-entry radial inflow turbine under steady and transient conditions. The influence of the volute tongue is depicted by a low momentum wake propagating toward the rotor entry, but its effect does not extend beyond a circumferential position of 60°, and more total pressure loss is revealed with respect to the hub side. The transient simulations carried out at different operating conditions and Fast Fourier Transform analysis of static pressure fluctuations induced by the components’ interactions have revealed a space-time periodic behaviour which has been described by a double Fourier decomposition. The flow simulations considering the two sides subject to both non-pulsatile and pulsatile flows conditions have revealed the existing rotor and tongue potential effects and interaction effects the rotor and volute, in addition to the circumferential and spanwise flow non-uniformities at the volute exit, which are more accentuated with a pulsatile flow at inlet. The results of Fast Fourier Transform analysis of temporal pressure fluctuations at the inter-space depict an unsteady behaviour related to the pulsatile frequencies which are characterised by high amplitudes. On the other hand, the spatial pressure fluctuations for the non-pulsatile and pulsatile flows conditions seem to have the same dominant modes since Fast Fourier Transform analysis was carried out at a fixed instant.

Identification of Spinning Mode in the Unsteady Flow Field of a Low Pressure Turbine

This paper presents an experimental investigation of the vane-blade unsteady interaction in an unshrouded low pressure (LP) turbine research rig with uneven blade/vane count (72 blades and 96 vanes). The rig was designed in cooperation with MTU Aero Engines and considerable efforts were put on the adjustment of all relevant model parameters. In particular blade count ratio, airfoil aspect ratio, reduced mass flow, reduced speed, and Mach and Reynolds numbers were chosen to reproduce the full scale LP turbine at take off condition. Measurements by means of a fast-response pressure probe were performed adopting a phase-locked acquisition technique in order to provide the time resolved flow field downstream of the turbine rotor. The probe has been fully traversed both in circumferential and radial traverses. The rotor exit is characterized by strong perturbations due to the tip leakage vortex and the rotor blade wake. Circumferential nonuniformities due to the upstream vane wake and to the downstream exit guide vane potential effects are also identified. Furthermore, in the present configuration with an uneven blade/vane count the nonuniformities due to the stator and rotor row are misaligned along the whole turbine circumference and create a spinning mode that rotates in direction opposite to the rotor at a high frequency. The aeroacoustic theory is employed to explain such further unsteady pattern. The variations of the exit flow angle within a cycle of such pattern are not negligible and almost comparable to the ones within the blade passing period.

Toward a High Order Throughflow––Investigation of the Nonlinear Harmonic Method Coupled With an Immersed Boundary Method for the Modeling of the Circumferential Stresses

Capturing a level of modeling of the flow inside a multistage turbomachine, such as unsteadiness for example, can be done at different levels of detail, either by capturing all deterministic features of the flow with a pure unsteady method or by settling for an approximated solution at a lower computational cost. The harmonic methods stand in this second category. Among them, the “nonlinear harmonic method” (NLHM) from He and Ning [1998, “Efficient Approach for Analysis of Unsteady Viscous Flows in Turbomachines,” AIAA J., 36, pp. 2005–2012] revealed the most efficient. This method consists of solving the fully nonlinear 3D steady problem and a linearized perturbation system in the frequency domain. As it has been shown by the authors that the circumferential variations exhibit a harmonic behavior, it is proposed here to adapt the NLHM to the throughflow model, where the main nonlinear system would be the common throughflow equations and the auxiliary system would give access to the circumferential stresses. As the numerical local explicit impermeability conditions are unsupported by Fourier series, the adaptation of this technique to the throughflow model relies on a reformulation of the blade effect by a smooth force field as in the “immersed boundary method” from Peskin [2002, “The Immersed Boundary Method,” Acta Numerica, 11, pp. 1–39]. A simple example of an inviscid flow around a cylinder will illustrate the preceding developments, bringing back the mean effect of the circumferential nonuniformities into the meridional flow.

An Experimental/Computational Study of Airflow in the Combustor–Diffuser System of a Gas Turbine for Power Generation

This paper presents an experimental/computational study of cold flow in the combustor–diffuser system of industrial gas turbines employing can-annular combustors and impingement-cooled transition pieces. The primary objectives were to determine flow interactions between the prediffuser and dump chamber, to evaluate circumferential flow nonuniformities around transition pieces and combustors, and to identify the pressure loss mechanisms. Flow experiments were conducted in an approximately one-third geometric scale, 360-deg annular test model simulating practical details of the prototype including the support struts, transition pieces, impingement sleeves, and can-annular combustors. Wall static pressures and velocity profiles were measured at selected locations in the test model. A three-dimensional computational fluid dynamic analysis employing a multidomain procedure was performed to supplement the flow measurements. The complex geometric features of the test model were included in the analysis. The measured data correlated well with the computations. The results revealed strong interactions between the prediffuser and dump chamber flows. The prediffuser exit flow was distorted, indicating that the uniform exit conditions typically assumed in the diffuser design were violated. The pressure varied circumferentially around the combustor casing and impingement sleeve. The circumferential flow nonuniformities increased toward the inlet of the turbine expander. A venturi effect causing flow to accelerate and decelerate in the dump chamber was also identified. This venturi effect could adversely affect impingement cooling of the transition piece in the prototype. The dump chamber contained several recirculation regions contributing to the losses. Approximately 1.2 dynamic head at the prediffuser inlet was lost in the combustor–diffuser, much of it in the dump chamber where the fluid passed though narrow pathways. A realistic test model and three-dimensional analysis used in this study provided new insight into the flow characteristics of practical combustor–diffuser systems.

Computation of unsteady flow through steam turbine blade rows at partial admission

Partial admission in the steam turbine is associated with strong unsteady flow effects on aerodynamic performance. This paper presents a first-of-its-kind computational study of the problem. The unsteady flow field in multiple blade passages and multiple blade rows is governed by the quasi three-dimensional unsteady Navier-Stokes equations, closed by a mixing-length turbulence model. The partial admission is introduced by blocking one segmental arc (or several segmental arcs) of the inlet guide vane of the first stage. The flow equations are solved by using a time-dependent finite volume method. The calculated unsteady force on rotor blades for a turbine stage at partial admission compares well with the corresponding experimental data. The present results show that a cyclic pumping and sucking phenomenon occurs in the rotor blade row of the first stage, resulting in large unsteady loading and marked mixing loss. For a single stage at a given admission rate, a blocking arrangement with two flow segments is shown to be much more detrimental than one arc of admission, because of the extra mixing loss. The results for a two-stage case, however, suggest that the decaying rate of circumferential non-uniformities could be far more important for performance. For this reason, an enhanced mixing loss in the first stage might be beneficial to the overall efficiency of a multistage turbine.

Numerical Investigation of Enhanced Dilution Zone Mixing in a Reverse Flow Gas Turbine Combustor

An advanced method for dilution zone mixing in a reverse flow gas turbine combustor was numerically investigated. For long mixing lengths associated with reverse flow combustors (X/H > 2.0), pattern factor was found to be mainly driven by nozzle-to-nozzle fuel flow and/or circumferential airflow variations; conventional radially injected dilution jets could not effectively mix out circumferential nonuniformities. To enhance circumferential mixing, dilution jets were angled to produce a high circumferential (swirl) velocity component. The jets on the outer liner were angled in one direction while the jets on the inner liner were angled in the opposite direction, thus enhancing turbulent shear at the expense of jet penetration. Three-dimensional CFD calculations were performed on a three-nozzle (90 deg) sector, with different fuel flow from each nozzle (90, 100, and 110 percent of design fuel flow). The computations showed that the optimum configuration of angled jets reduced the pattern factor by 60 percent compared to an existing conventional dilution hole configuration. The radial average temperature profile was adequately controlled by the inner-to-outer liner dilution flow split.

Circumferential tube skin temperature profiles in thermal cracking coils

AbstractUniform temperature distributions in cracking furnaces favor the run length of the production cycle of the furnace and the tube metal life. The coupled simulation of the furnace and the reactor tubes by means of the zone method is extended to permit the calculation of circumferential nonuniformities under reaction conditions. Circumferential tube skin temperatures were found to vary over 50°C and more, due to “shadow effects.” As a result, nonuniform coking rates and coke layers are obtained. The model and computational scheme presented here can be used as a guide for plant operators and as a tool for designing.

A simple and unified model for spanwise mixing in multistage axial flow compressors

A basic equation system for meridional throughflow fields in multistage axial flow compressors has been deduced, containing many unknown correlation terms, which describe different kinds of spanwise mixing mechanism in a unified form. The equation system shows that spanwise mixing of meridional flows in compressors is attributed to three kinds of mechanism: molecular motion, turbulent diffusion, and circumferential non-uniformities, the last of which includes secondary flow effects and others. Therefore the equation system unifies the two models for spanwise mixing analyses by Adkins & Smith (1981) and Gallimore & Cumpsty (1986). With three kinds of apparent mixing coefficients defined and introduced into the basic equation system, a novel, much simpler equation system, without additional unknown correlation terms included, has been obtained. This novel equation system makes throughflow computations including mixing far easier for multistage compressors. It has been rigorously shown that these apparent mixing coefficients contain full information of all the three kinds of mixing mechanism, so that the simpler equation system can also be taken as a unified model for meridional flows with all the kinds of the mixing effects. Calculations of the flow through multistage machines have been made by incorporating the new model into a streamline curvature throughflow calculation method and the improved agreement with experimental data has been obtained. It is believed that the simpler equation system can be applied to the flows not only in subsonic but in transonic and supersonic compressors if an appropriate model is proposed for the apparent mixing coefficients.

The Importance of Circumferential Non-uniformities in a Passage-Averaged Quasi-Three-Dimensional Turbomachinery Design System

The purpose of this paper is to show, for both rotating and non-rotating blade rows, the importance of including circumferential non-uniform flow effects in a quasi-three-dimensional blade design system. The paper follows from previous publications on the system in which the mathematical analysis and computerized system are detailed. Results are presented for a different stack of the nozzle guide vane presented previously and for a turbine rotor. In the former case it is again found that the blade force represents a major contribution to the radial pressure gradient, while for the rotor the radial pressure gradient is dominated by centrifugal effects. In both examples the effects of circumferential non-uniformities are detailed and discussed.

Velocity measurements in a pump volute with a non-rotating impeller

A Plexiglas laboratory pump with rectangular cross sections was tested and volute velocities were measured with a laser velocimeter. First, the pump with a four bladed rotating impeller was run at three flowrates. Second, the rotating impeller was replaced with a 32-bladed non-rotating impeller with forward facing blades that imparted a swirl to the flow under forced circulation that simulated the rotating impeller case. Velocity measurements in the discharge region and flow visualization in the entire volute indicate that the proper general flow characteristics were achieved with the flow swirler but the unsteady ‘jet-wake’ regions were eliminated. Thus similitude was attained between the rotating and non-rotating impellers allowing study of volute flow characteristics without rotating impeller effects. Two non-rotating impellers were used to provide data for comparison to future steady state theoretical analyses. One produced a flow field that represented 121% of the nominal capacity and the other represented 160% of the nominal capacity. Detailed velocity traverses were made in the volute region for both swirlers. Circumferential non-uniformities (up to 275% from the mean) were found and were largest for the 160% simulated capacity. These are not due to rotating impeller effects and are attributed to the mismatch between the exit angle of the swirler and the volute. Radial non-uniformities in velocity were also seen (up to 22%) and the largest variations were observed for 121% simulated capacity. Finally, axial variations up to 30% were observed and these also were largest for 121% simulated capacity.