Aircraft Engine Committee Best 1993 Paper Award: Control-Oriented High-Frequency Turbomachinery Modeling: General One-Dimensional Model Development

1995 ◽  
Vol 117 (3) ◽  
pp. 320-335 ◽  
Author(s):  
O. O. Badmus ◽  
K. M. Eveker ◽  
C. N. Nett
Keyword(s):  
High Frequency ◽  
Linear Models ◽  
Nonlinear Models ◽  
Model Development ◽  
Rotating Stall ◽  
Combustion Heat ◽  
Compression System ◽  
One Dimensional ◽  
System Models ◽  
Turbojet Engine

In this paper, an approach for control-oriented high-frequency turbomachinery modeling previously developed by the authors is applied to develop one-dimensional unsteady compressible viscous flow models for a generic turbojet engine and a generic compression system. We begin by developing models for various components commonly found in turbomachinery systems. These components include: ducting without combustion, blading, ducting with combustion, heat soak, blading with heat soak, inlet, nozzle, abrupt area change with incurred total pressure losses, flow splitting, bleed, mixing, and the spool. Once the component models have been developed, they are combined to form system models for a generic turbojet engine and a generic compression system. These models are developed so that they can be easily modified and used with appropriate maps to form a model for a specific rig. It is shown that these system models are explicit (i.e., can be solved with any standard ODE solver without iteration) due to the approach used in their development. Furthermore, since the nonlinear models are explicit, explicit analytical linear models can be derived from the nonlinear models. The procedure for developing these analytical linear models is discussed. An interesting feature of the models developed here is the use of effective lengths within the models, as functions of axial Mach number and nondimensional rotational speed, for rotating components. These effective lengths account for the helical path of the flow as it moves through a rotating component. Use of these effective lengths in the unsteady conservation equations introduces a nonlinear dynamic lag consistent with experimentally observed compressor lag and replaces less accurate linear first-order empirical lags proposed to account for this phenomenon. Models of the type developed here are expected to prove useful in the design and simulation of (integrated) surge control and rotating stall avoidance schemes.

scholarly journals Control-Oriented High-Frequency Turbomachinery Modeling: General 1D Model Development

1993 ◽  
Author(s):  
O. O. Badmus ◽  
K. M. Eveker ◽  
C. N. Nett
Keyword(s):  
High Frequency ◽  
Linear Models ◽  
Nonlinear Models ◽  
Model Development ◽  
Rotating Stall ◽  
Combustion Heat ◽  
Compression System ◽  
Flow Models ◽  
System Models ◽  
Turbojet Engine

In this paper, an approach for control-oriented high–frequency turbomachinery modeling previously developed by the authors is applied to develop 1D unsteady compressible viscous flow models for a generic turbojet engine and a generic compression system. We begin by developing models for various components which are commonly found in turbomachinery systems. These components include: ducting without combustion, blading, ducting with combustion, heat soak, blading with heat soak, inlet, nozzle, abrupt area change with incurred total pressure losses, flow splitting, bleed, mixing, and the spool. Once the component models have been developed, they are combined to form system models for a generic turbojet engine and a generic compression system. These models are developed so that they can be easily modified and used with appropriate maps to form a model for a specific rig. It is shown that these system models are explicit (i.e. can be solved with any standard ODE solver without iteration) due to the approach used in their development. Furthermore, since the nonlinear models are explicit, explicit analytical linear models can be derived from the nonlinear models. The procedure for developing these analytical linear models is discussed. An interesting feature of the models developed here is the use of effective lengths within the models, as functions of axial Mach number and nondimensional rotational speed, for rotating components. These effective lengths account for the helical path of the flow as it moves through a rotating component. Use of these effective lengths in the unsteady conservation equations introduces a nonlinear dynamic lag consistent with experimentally observed compressor lag and replaces less accurate linear first order empirical lags proposed to account for this phenomenon. Models of the type developed here are expected to prove useful in the design and simulation of (integrated) surge control and rotating stall avoidance schemes.

Control-Oriented High-Frequency Turbomachinery Modeling: Single-Stage Compression System One-Dimensional Model

1995 ◽  
Vol 117 (1) ◽  
pp. 47-61 ◽  
Author(s):  
O. O. Badmus ◽  
S. Chowdhury ◽  
K. M. Eveker ◽  
C. N. Nett
Keyword(s):  
Experimental Data ◽  
High Frequency ◽  
Closed Loop ◽  
Rotating Stall ◽  
Single Stage ◽  
Model Parameters ◽  
Compression System ◽  
One Dimensional ◽  
First Order ◽  
Direct Model

In this paper, a one-dimensional unsteady compressible viscous flow model of a generic compression system previously developed by the authors is applied to a multistage axial compressor experimental rig configured for single-stage operation. The required model parameters and maps are identified from experimental data. The resulting model is an explicit system of nine first-order ODEs. The model inputs are compressor speed, nozzle area, compressor discharge bleed area, plenum bleed area, inlet total pressure and entropy, and nozzle and bleed exit static pressures. The model and experimental data are compared with respect to both open-loop uncontrolled and closed-loop controlled behaviors. These comparisons focus on (i) forced transients and (ii) global nonlinear dynamics and bifurcations. In all cases the agreement between the model and experimental data is excellent. Of particular interest is the ability of the model, which does not include any hysteretic maps, to predict experimentally observed hysteresis with respect to the onset and cessation of surge. This predictive capability of the model manifests itself as the coexistence of a stable equilibrium (rotating stall) and a stable periodic solution (surge) in the model at a single fixed set of system input values. Also of interest is the fact that the controllers used for closed-loop comparisons were designed directly from the model with no a posteriori tuning of controller parameters. Thus, the excellent closed-loop comparisons between the model and experimental data provide strong evidence in support of the validity of the model for use in direct model based controller design. The excellent agreement between the model and experimental data summarized above is attributed in large part to the use of effective lengths within the model, as functions of axial Mach number and nondimensional compressor rotational speed, as prescribed by the modeling technique. The use of these effective lengths proved to be far superior to the use of physical lengths. The use of these effective lengths also provided substantial improvement over the use of physical lengths coupled with fixed first-order empirical lags, as proposed by other authors for the modeling of observed compressor dynamic lag. The overall success of this model is believed to represent a positive first step toward a complete experimental validation of the approach to control-oriented high-frequency turbomachinery modeling being developed by the authors.

scholarly journals Control-Oriented High-Frequency Turbomachinery Modeling: Single-Stage Compression System 1D Model

1993 ◽  
Author(s):  
O. O. Badmus ◽  
S. Chowdhury ◽  
K. M. Eveker ◽  
C. N. Nett
Keyword(s):  
Experimental Data ◽  
High Frequency ◽  
Closed Loop ◽  
Open Loop ◽  
Rotating Stall ◽  
Single Stage ◽  
Model Parameters ◽  
Compression System ◽  
First Order ◽  
Direct Model

In this paper, a 1D unsteady compressible viscous flow model of a generic compression system previously developed by the authors is applied to a multi-stage axial compressor experimental rig configured for single–stage operation. The required model parameters and maps are identified from experimental data. The resulting model is an explicit system of 9 first order ODE’s. The model inputs are compressor speed, nozzle area, compressor discharge bleed area, plenum bleed area, inlet total pressure and entropy, and nozzle and bleed exit static pressures. The model and experimental data are compared with respect to both open–loop uncontrolled and closed–loop controlled behaviors. These comparisons focus on i) forced transients and ii) global nonlinear dynamics and bifurcations. In all cases the comparison between the model and experimental data is excellent. Of particular interest is the ability of the model, which does not include any hysteretic maps, to predict experimentally observed hysteresis with respect to the onset and cessation of surge. This predictive capability of the model manifests itself as the coexistence of a stable equilibrium (rotating stall) and a stable periodic solution (surge) in the model at a single fixed set of system input values. Also of interest is the fact that the controllers used for closed–loop comparisons were designed directly from the model with no a posteriori tuning of controller parameters. Thus, the excellent closed–loop comparisons between the model and experimental data provide strong evidence in support of the validity of the model for use in direct model based controller design. The excellent agreement between the model and experimental data summarized above is attributed in large part to the use of effective lengths within the model, as functions of axial Mach number and nondimensional compressor rotational speed, as prescribed by the modeling technique. The use of these effective lengths proved to be far superior to the use of physical lengths. The use of these effective lengths also provided substantial improvement over the use of physical lengths coupled with fixed first order empirical lags, as proposed by other authors for the modeling of observed compressor dynamic lag. The overall success of this model is believed to represent a positive first step toward a complete experimental validation of the approach to control–oriented high–frequency turbomachinery modeling being developed by the authors.

scholarly journals Estimating Tree Diameter and Volume with a Taper Model and Large-Scale Photo Measurements

2001 ◽  
Vol 18 (4) ◽  
pp. 110-118 ◽  
Author(s):  
R.J. Hall ◽  
Y. Wang ◽  
D.J. Morgan
Keyword(s):  
Large Scale ◽  
Linear Models ◽  
Nonlinear Models ◽  
Model Development ◽  
Tree Height ◽  
Field Measurements ◽  
Tree Diameter ◽  
Volume Estimates ◽  
Total Tree ◽  
Taper Model

Abstract Large-scale photo (LSP) mensurational procedures were developed, in part, to reduce field costs by replacing much of the ground sampling with less expensive photo measurements. The conventional LSP approach uses photo measurements of tree height and crown area, which serve as independent variables in models, to predict tree diameter or volume. This study compared 18 linear and nonlinear model forms for estimating tree diameters and assessed the use of a provincial taper model to estimate total tree volume from LSP data. On average, linear models produce R2, root mean square error, and mean bias values that were at least equivalent to, if not statistically better than, nonlinear models for the range of data evaluated. For lodgepole pine, white spruce and a composite of two deciduous species (trembling aspen and balsam poplar), total volume estimates were not statistically different from those estimated from field measurements. A comparative analysis of LSP and field sampling costs suggests the use of taper models in LSP mensuration could save considerable cost and effort in data collection and model development. This finding may result in an increased use of LSP in operational forest inventory work. North J. Appl. For. 18(4):110–118.

High-frequency, "quantum" and electromechanical effects in quasi-one-dimensional charge density wave conductors

2013 ◽  
Vol 183 (1) ◽  
pp. 33-54 ◽  
Author(s):  
Vadim Ya. Pokrovskii ◽  
Sergey G. Zybtsev ◽  
Maksim V. Nikitin ◽  
Irina G. Gorlova ◽  
Venera F. Nasretdinova ◽  
...  
Keyword(s):  
Charge Density ◽  
High Frequency ◽  
Charge Density Wave ◽  
Density Wave ◽  
One Dimensional ◽  
Electromechanical Effects

Simulation-based site amplification model for shallow bedrock sites in Korea

2021 ◽  
pp. 875529302098198
Author(s):  
Muhammad Aaqib ◽  
Duhee Park ◽  
Muhammad Bilal Adeel ◽  
Youssef M A Hashash ◽  
Okan Ilhan
Keyword(s):  
Linear Models ◽  
Site Response ◽  
Site Amplification ◽  
One Dimensional ◽  
Nonlinear Component ◽  
Nonlinear Site Response ◽  
Simulation Based ◽  
Linear And Nonlinear ◽  
Input Motion ◽  
Nonlinear Components

A new simulation-based site amplification model for shallow sites with thickness less than 30 m in Korea is developed. The site amplification model consists of linear and nonlinear components that are developed from one-dimensional linear and nonlinear site response analyses. A suite of measured shear wave velocity profiles is used to develop corresponding randomized profiles. A VS30 scaled linear amplification model and a model dependent on both VS30 and site period are developed. The proposed linear models compare well with the amplification equations developed for the western United States (WUS) at short periods but show a distinct curved bump between 0.1 and 0.5 s that corresponds to the range of site natural periods of shallow sites. The response at periods longer than 0.5 s is demonstrated to be lower than those of the WUS models. The functional form widely used in both WUS and central and eastern North America (CENA), for the nonlinear component of the site amplification model, is employed in this study. The slope of the proposed nonlinear component with respect to the input motion intensity is demonstrated to be higher than those of both the WUS and CENA models, particularly for soft sites with VS30 < 300 m/s and at periods shorter than 0.2 s. The nonlinear component deviates from the models for generic sites even at low ground motion intensities. The comparisons highlight the uniqueness of the amplification characteristics of shallow sites that a generic site amplification model is unable to capture.

Roles of vanes in diffuser on stability of centrifugal compressor

2019 ◽  
Vol 233 (14) ◽  
pp. 5380-5392
Author(s):  
Wangzhi Zou ◽  
Xiao He ◽  
Wenchao Zhang ◽  
Zitian Niu ◽  
Xinqian Zheng
Keyword(s):  
High Pressure ◽  
Centrifugal Compressor ◽  
Dynamic Pressure ◽  
Pressure Ratio ◽  
Pressure Rise ◽  
Rotating Stall ◽  
Centrifugal Compressors ◽  
Compression System ◽  
The Stability ◽  
Rotating Instability

The stability considerations of centrifugal compressors become increasingly severe with the high pressure ratios, especially in aero-engines. Diffuser is the major subcomponent of centrifugal compressor, and its performance greatly influences the stability of compressor. This paper experimentally investigates the roles of vanes in diffuser on component instability and compression system instability. High pressure ratio centrifugal compressors with and without vanes in diffuser are tested and analyzed. Rig tests are carried out to obtain the compressor performance map. Dynamic pressure measurements and relevant Fourier analysis are performed to identify complex instability phenomena in the time domain and frequency domain, including rotating instability, stall, and surge. For component instability, vanes in diffuser are capable of suppressing the emergence of rotating stall in the diffuser at full speeds, but barely affect the characteristics of rotating instability in the impeller at low and middle speeds. For compression system instability, it is shown that the use of vanes in diffuser can effectively postpone the occurrence of compression system surge at full speeds. According to the experimental results and the one-dimensional flow theory, vanes in diffuser turn the diffuser pressure rise slope more negative and thus improve the stability of compressor stage, which means lower surge mass flow rate.

Performance Modeling of Desiccant Wheels: 1 — Model Development

2008 ◽  
Author(s):  
Chaoqin Zhai ◽  
David H. Archer ◽  
John C. Fischer
Keyword(s):  
Model Development ◽  
Axial Direction ◽  
Performance Model ◽  
Design Parameters ◽  
Residual Water ◽  
One Dimensional ◽  
Operating Variables ◽  
Steady State Operation ◽  
Rotary Speed ◽  
The Impact

This paper presents the development of an equation based model to simulate the combined heat and mass transfer in the desiccant wheels. The performance model is one dimensional in the axial direction. It applies a lumped formulation in the thickness direction of the desiccant and the substrate. The boundary conditions of this problem represent the inlet outside/process and building exhaust/regeneration air conditions as well as the adiabatic condition of the two ends of the desiccant composite. The solutions of this model are iterated until the wheel reaches periodic steady state operation. The modeling results are obtained as the changes of the outside/process and building exhaust/regeneration air conditions along the wheel depth and the wheel rotation. This performance model relates the wheel’s design parameters, such as the wheel dimension, the channel size and the desiccant properties, and the wheel’s operating variables, such as the rotary speed and the regeneration air flowrate, to its operating performance. The impact of some practical issues, such as wheel purge, residual water in the desiccant and the wheel supporting structure, on the wheel performance has also been investigated.

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