Non Adiabatic Centrifugal Compressor Gas Dynamic Performance Definition

Most centrifugal compressors operate in conditions with negligible heat transfer (adiabatic compression). Their plant tests conditions are similar or close to adiabatic conditions. Test regulations establish measures to diminish influence of a heat transfer “compressor body – atmospheric air” to an exit temperature. Therefore a temperature rise in a compressor is used to calculate a work input coefficient and efficiency. Unlike it high pressure centrifugal compressors of gas turbines and superchargers operate in conditions with very active heat transfer with ambience, lubricant and hot turbine parts. Non adiabatic compression process evidently influence on temperatures inside a flow path, gas density, velocity triangles. But this aspect of a problem is out of the discussed problem. This problem is how to define gas dynamic performance of a compressor. The author has at his disposal hot test data of a small turbocharger compressor with the impeller diameter 48mm. Data were provided by the colleague Prof. J. Seume (Institute of Turbo machines, Hanover University, Germany): mass flow rate, total pressures and four total temperatures: directly at compressor borders and on a distance of them. The difference of values demonstrates strong heat transfer in inlet and exit pipes. The detailed study in the Institute of Turbo machines, Hanover University has shown that compression process is sufficiently non adiabatic. Unrealistic influence of rotation speed on efficiency points on it indirectly. The author applied the Universal modeling method of Prof. Y. Galerkin to reduce test data firstly. The 5-th generation computer programs were developed recently and successfully applied to model gas dynamic performances of subsonic compressors. The German colleagues made a supposition that measured temperature difference is very close to an adiabatic process at design RPM 202000. This performance was modeled with the standard complex of empirical coefficients. The roughness of cast surfaces was taken into account. Test data of TU SPb show that work input coefficient is linear function of a flow coefficient at an impeller exit independent of Mach number in subsonic area. The linear supposition was applied for transonic and supersonic flows as well. This procedure was applied with 6-th generation of computer programs. The 6-th generation program takes into account shocks and calculates losses in 3-D impellers in quasi-3-D mode. In result the modeling of performances in range of RPM 104000-202000 is more satisfactory. The set of empirical coefficients for calculation of head losses and work input coefficient can be applied for test data reducing of other small turbocharger compressor performances

Supersonic Axial Compressor Stage Simplified Analysis

Application of supersonic axial compressor stages is an effective way to decrease mass and volume of gas turbines. It is reported that stages with pressure ratio up to 2,8 and blade velocity 450 m/s can operate quite satisfactory. There is demand for stages with pressure ratio that exceeds 3.0. The possible efficiency of stages is vital for successful application. As a velocity coefficient at an impeller inlet of stages can be about 1.5 and more, shock wave losses can limit overall stage efficiency. The simplified model of a stage was used for calculations. Supersonic flow in elementary blade cascade with sharp leading edges of blades produces oblique shock wave with sub – or supersonic flow after it. This depends on an inlet velocity coefficient and an angle between shock wave front and flow direction. The normal shock wave follows if a flow is still supersonic after an oblique shock. The known equations are used to calculate head losses in shock waves. Losses in a subsonic part of a stage are estimated by an arbitrary appointed loss coefficient. The calculations were made for a gas with = 1,4 in a range of velocity coefficient =1,1 – 1,8. Shock wave angle was varied in a range = 900 – ?0, where ?0 is an angle of a sonic wave. There were calculated static pressure ratios, static polytrophic efficiency, loss coefficient, velocity coefficients after shock waves. There are two zones of an operation: – subsonic flow after an oblique shock wave with angles bigger than 720-620 (the bigger value corresponds to a smaller velocity coefficient); – supersonic flow after an oblique shock wave with angles smaller than 720-620 and a normal shock wave after. An efficiency of a calculated stage model with subsonic flow after an oblique shock wave is not less 0,88 when velocity coefficient is no more than 1,6. The corresponding pressure ratio is about 4,7. The problem is how far is the simplified model from a real 3-D stage with all her complications. The system of an oblique and following normal shock waves transforms kinetic energy in a pressure rise formally most effective. An optimal angle of an oblique shock wave lies in a range = 550 - 450 (the bigger value corresponds to a smaller velocity coefficient); The efficiency is about 88% for the velocity coefficient 1,8 and = 450. There is a fantastic pressure ratio 11 ion this case. In can be concluded that for stages with pressure ratio about 3,0 shock wave losses do not limit efficiency. The problem returns to trivial problems of preventing excessive separation after shock waves and to effective 3-D design

New Version of the Universal Modeling for Centrifugal Compressor Gas Dynamic Design

Decades ago at pre – computer era design process consisted of empirically based set of rules application to choose main flow path dimensions. Serious model tests were obligatory before compressor manufacturing to check delivery pressure and efficiency. Better flow physical models and computer progress made possible to develop quickly operating programs to predict gas dynamic performance curves of an arbitrary flow path. TU SPb set of computer programs was named “The Universal modeling method” and its application still in mid 1990th had lead to elimination of model tests in a design process of industrial centrifugal compressors. The Universal modeling state of the art including 4th generation loss and work input models were presented in conferences in Germany, Japan, Great Britain and Poland. Set of algebraic equations describe surface friction losses, flow separation and following mixing losses. Flow deceleration along surfaces and velocity gradient along a normal to surfaces are taken into account. By 4-th generation programs several dozens of compressor with delivery pressure up to 12,5 MPa, number of stages up to 8, power up to 25 mWt were designed for some Russian and foreign manufacturers. Amount of compressor installed exceeds 400 with total power close to 5 000 000 kWt. In all cases the design parameters were achieved without preceding model tests. The 4-th generation model was perfect enough to predict design point efficiency with accuracy about 2,5% if a single set of coefficients was applied. To raise accuracy of calculations to 1% or less different sets of empirical coefficients were necessary for stages with different flow rate and work coefficients. The proposed text is focused on scientific background and realization of model improvements. The main of them are more precise impeller size presentation, impeller velocity diagram schematization very close to non viscid diagram, surface roughness introduction in the loss model, shroud leakage influence on flow at an impeller inlet, etc. As a result 5-th generation model predicts efficiency curves of stages with different flow rate and work coefficients with mean deviation less than 0,5% at design point and 1,5% along all performance curves – with a single set of empirical coefficients. Then the compressors’ test performance curves were carefully correlated with the calculated ones by proper selection of empirical coefficients in models of pressure loss ant work coefficient. The stages of 16 tested compressors can be considered as 99 model stages with the range of gas dynamic and constructive parameters: flow rate coefficients 0,025 – 0,064, Euler work coefficients 0,40 – 0,85, relative hub diameter 0,258 – 0,483, outer relative diameter of a diffuser 1,316 -1,720. Stages polytrophic efficiency is 0,765 – 0,885 and surge limit ratio is 0,30 – 0,93 depends on a stage specific speed. There are samples of useful application of the stages. The new loss model is applied to 6-th and 7-th generation computer programs. Newly is described 3D impeller flow path shape. Q3D approach to impellers adds information for more profound optimization. New solution were checked and approved by CFD calculations

The optimal gas dynamic design system of industrial centrifugal compressors based on Universal modeling method

We present the modern stage of development of Universal Modeling Method, a complex of mathematical models and software for optimal design of centrifugal compressors - a new version of simplified mathematical model of efficiency and new software for variation calculations of multistage compressors. Based on this numerical calculation complex we have created a method for preliminary design of flow paths of stages - 2D and 3D impellers, vane and vaneless diffusers and return channels. The new, 9th version of its mathematical model features a quasi-3D calculation method of 2D and 3D impellers design, a new principle of pressure characteristic calculation, a new model of vaneless diffusers and much more. “Digital twin of a centrifugal compressor stage” and “3D compressor” software create digital descriptions of the flow part and its solid model (“digital twin”)

The Current State of the Engineering Method for the Optimal Gas-Dynamic Design and Calculation of Centrifugal Compressor

In the practice of centrifugal compressor designing, different engineering techniques are widely used because flow motion differential equations cannot be integrated, and Computational fluid dynamics cannot resolve the problem as a whole. Engineering personal computers’ programs are based on experimental data and the gas dynamics theory. The universal modeling method’s (UMM) mathematical model is a set of equations that determine the pressure loss in the elements of the centrifugal compressor flow path. By the earlier versions of the UMM, dozens of process compressors were designed. Several sets of empirical coefficients for stages of different specific speeds were applied. The paper presents the current state of the universal modeling method that was recently improved. The models of the centrifugal compressor characteristic calculation are described. A new model of the loading factor characteristic, an improved version of the compressor efficiency, and being based on a CFD-calculation vaneless diffuser model are samples of the improvements. Careful identification and verification demonstrate effective characteristic simulation with a single set of empirical coefficients. Centrifugal compressor new design examples of a turbo expander unit and a turbocharger are presented. The calculated characteristics are compared with the test results. For both objects, the experiments confirmed the calculated gas-dynamic characteristics with sufficient accuracy for engineering methods

Design, Plant Test and CFD Calculation of a Turbocharger for a Low-Speed Engine

Various approaches and techniques are used to design centrifugal compressors. These are engineering one-dimensional and quasi-three-dimensional programs, as well as CFD Computational Fluid Dynamics (CFD) programs. The final judgment about the effectiveness of the design is given by testing the compressor or its model. A centrifugal compressor for an internal combustion engine turbocharger was designed jointly by the Research Laboratory “Gas Dynamics of Turbomachines” of Peter the Great St. Petersburg Polytechnic University (SPbPU) and RPA (Research and Production Association) “Turbotekhnika”. To check its dimensionless characteristics, the compressor was tested with two geometrically similar impellers with a diameter of 175 (TKR 175E) and 140 mm (TKR 140E). The mathematical model of the Universal Modeling Method calculates the efficiency in the design mode for all tests of both compressors with an error of 0.89%, and the efficiency for the entire characteristic with an error of 1.55%. The characteristics of the TKR 140E compressor were calculated using the ANSYS commercial CFD software. For TKR-140E, a significant discrepancy in the value of the efficiency was obtained, but a good agreement in the area of operation, which was not achieved in previous calculations. According to the calculation, the work coefficient is overestimated by 9%, which corresponds to the results of previous calculations by the authors

Synthesis of Aromatic Polyimides Based on 3,4′-Oxydianiline by One-Pot Polycondensation in Molten Benzoic Acid and Their Application as Membrane Materials for Pervaporation

A series of aromatic polyimides based on the asymmetrical diamine 3,4ʹ-oxydianiline and various tetracarboxylic acid dianhydrides, both “rigid” and “flexible” structure, have been synthesized using the original method of one-pot high-temperature catalytic polycondensation in molten benzoic acid. The synthesized polyimides were investigated using fourier-transform infrared (FTIR) and 1H NMR spectroscopy, gel permeation chromatography (GPC), differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), thermomechanical analysis (TMA) and wide-angle X-ray scattering (WAXS). It was found that the synthesized polyimides, depending on the used dianhydride, are characterized by different solubility in organic solvent and molten benzoic acid, molecular weight, glass transition temperature (Tg) from 198 to 270 °C, an amorphous or semi crystalline structure with the degree of crystallinity from 41 to 52%. The influence of the method of synthesis on the formation of the crystalline phase of polyimides was studied, and the obtained results were compared with the literature data. The effect of dianhydride chemical structure on the performance of polyimide in pervaporation more specifically, dehydratation of azeotropic isopropanol solution was investigated and compared with the commercially available polyetherimide Ultem 1000™. Membrane structure was studied using scanning electron microscopy. It was found that polyimide PI-DA is the most effective for separation of 88 wt.% isopropanol/12 wt.% water mixture compared to the polyimide PI-6FDA and commercial polyetherimide Ultem 1000™ demonstrating normalized permeation flux of 2.77 kg µm m−2 h−1 and separation factor of 264 (water content in permeate 97 wt.%)