Steady-state Performance Maps Research Articles

Measurement and Prediction of Centrifugal Compressor Axial Forces During Surge—Part II: Dynamic Surge Model

The force acting on centrifugal compressors is an important parameter to be considered throughout the operating life of these turbomachines. When the compressor is operating in surge conditions, these forces can become highly dangerous for the mechanical and aerodynamic structures. This instability is usually avoided in industrial applications, but the antisurge system may not react in time when emergency shutdowns or power failures take place. During these rapid transients, surge can develop, generating unsteady forces which can harm the close clearance components of the compressor. Therefore, the capability to predict the characteristics and the dynamics of these surge forces would allow the estimation of the off-design fatigue cycles produced on these components by surge. Currently, no validated method exists to predict the frequency and amplitude of the surge forces and determine the potential damage of these components. In this paper, a lumped parameter model, developed by using the bond graph approach to predict the dynamic surge fluid-dynamic oscillations, is presented. The model requires the geometry and the steady-state performance maps of the compressor as inputs, together with the piping system configuration characteristics. The simulator is provided with a supplementary tool to estimate the axial force frequency and amplitude, taking into consideration all the contributions to the axial fluid-dynamic thrust, the stiffness-damping of the thrust bearing, and the mass of the rotor. The model was tuned and validated using the test case axial force data from the Southwest Research Institute (SWRI) facility. The model has shown good agreement with the experimental results which implies that it can offer significant information about the severity of a surge event and the quantification of the machine performance losses together with possible damage to the close clearance components. This study is a first important step that can lead to schedule optimization for maintenance and repair activities.

A generalized framework for perturbation-based derivative estimation in multivariable extremum-seeking

In the context of model-free optimization of dynamic nonlinear multiple-input-single-output (MISO) systems using extremum-seeking (ES), accurate and fast derivative estimation of the systems steady-state performance map is essential. This paper presents a generalized derivative estimator (DE) framework for unknown MISO static maps. To this extent, the map input is perturbed with sinusoidal dither signals with different frequencies. Using the proposed framework, the derivatives can be estimated up to an arbitrary order, for maps with an arbitrary number of inputs. Conditions on the dither frequencies are provided, which optimize the DE time-scale, such that derivative estimation is as fast as possible. Simulation examples are provided to demonstrate the effectiveness of the proposed framework.

An assessment of the ultra-lean combustion direct-injection LPG (liquefied petroleum gas) engine for passenger-car applications under the FTP-75 mode

Fuel economy and emissions characteristics of the lean-burn combustion strategy were assessed in a direct-injection liquefied petroleum gas engine under urban driving conditions. This study investigated: (1) engine experiments under steady-state conditions that frequently occur during city driving and (2) zero-dimensional drive cycle simulation under the FTP-75 mode. From the engine experiments, two sets of operation maps were constructed for the lean and conventional combustion modes. The lean combustion set consisted of the lean operation between 20 and 80Nm and the stoichiometric operation for the rest of the operating envelope. The selected lean operation range was found to be the largest possible to operate under the lean condition. The entire conventional combustion set was taken at the stoichiometric condition for comparison with the lean combustion set. Then, the steady-state performance maps of the fuel consumption, emissions, and exhaust temperature of the two combustion sets were used in a vehicle model of the cycle simulation. The drive cycle simulation results showed that the fuel economy of the lean combustion set was 10.65km/l, which is lower than that of the conventional combustion set by 6.3%. Carbon dioxide emission was 146.25g/km, down by 8g/km from the conventional combustion set. The time-resolved emissions of the particle mass and particle number of the lean combustion set were 0.005g/km and 3.2×1011#/km, respectively. The particle emissions of the lean combustion set were higher than those of the conventional combustion set, but considered as acceptable levels based on the upcoming emission standards.

Steady and unsteady experimental analysis of a turbocharger for automotive applications

The paper describes the steady and unsteady performance characteristics of a small size turbocharger typically employed in automotive downsized engine applications. The analysis is carried out by experimental means using an innovative hot gas generator system specifically designed for turbocharger testing which is capable of delivering a wide range of flow rates with adequate thermodynamic characteristics. More in detail, the gas generator consists of a medium size direct injection compression ignition Internal Combustion Engine (ICE) feeding the turbine of the test article. To independently set the hot gas mass flow rate and the turbine inlet temperature, the operating parameters of the aforementioned ICE are specified through an electronic control unit in a fully automated manner.Compared to previously presented data [1] (Energy Procedia, vol. 45, pp 1116-1125, 2014), those reported herein have been collected with the help of newly installed equipment and controlling software allowing for the estimation of the thermal power transferred from the turbocharger to the environment. In particular, thanks to a first law analysis, the collected measurements have shown that the algebraic sum of the thermal power transferred to the lubricating oil as well as to the environment is roughly speaking 20–30% of the compressor total enthalpy change per unit time. Moreover, it has been shown that evaluating the compressor efficiency through classical expression based on the adiabatic assumption leads to a 5–10% relative error.The improved experimental set up also allows for higher precision transient analysis both on the cold and hot side branch of the test article. While the steady-state performance maps of the turbocharger are readily obtained with the semi-automated testing procedure, the detailed analysis of the unsteady phenomena related for instance to the occurrence of mild and deep compressor surge events, are reproduced and thoroughly analysed using the rig in more advanced operating modes.

Development of a One-Dimensional Modular Dynamic Model for the Simulation of Surge in Compression Systems

The paper deals with the development of a nonlinear one-dimensional modular dynamic model for the simulation of transient behavior of compression systems. The model is based on balance equations of mass, momentum, and energy, which are derived through a general approach and are written by using the finite difference method. The model also takes rotating mass dynamics into account through a lumped parameter approach. Moreover, it reproduces the behavior of the system in the presence of the surge phenomenon through steady-state performance maps, which represent the compressor operation in the inverse flow region by means of a third degree polynomial curve. The model is implemented through the Matlab Simulink tool, where the system of ordinary differential equations is solved by using a fourth- and fifth-order Runge–Kutta method. A sensitivity analysis is carried out to evaluate the influence on compressor outlet pressure oscillations of the model parameters, of the supplied torque, of ambient conditions and of the shape of the compressor characteristic curves. The results show that the model proves effective in capturing the physical essence of surge phenomenon without being computationally too heavy.