Prediction of dynamic derivatives for air-breathing hypersonic vehicle using a harmonic balance method

The harmonic balance method is an efficient frequency-domain approach for computing periodically unsteady flows. Applying harmonic balance method to the rapid calculation of forced periodic motions, an efficient prediction method for dynamic derivatives is established based on the Etkin unsteady aerodynamic model. The method is firstly validated by a standard model of the hypersonic missile hyper ballistic shape, and the harmonic balance method results show great consistency with both time-domain results and experimental data, consolidating the efficiency of our numerical algorithm. The method is subsequently applied for an air-breathing hypersonic vehicle to investigate the capability of the harmonic balance method in modeling unsteady flows around complex geometric configurations. Comparisons with the results of the time-domain method demonstrate that the harmonic balance method is capable of resolving such complicated flowfield with both accuracy and efficiency. To be specific, for the air-breathing hypersonic vehicle, the maximum difference of the dynamic derivatives calculated by the harmonic balance method and the time-domain method is only 6.56%, and the harmonic balance method shows at least an order of magnitude efficiency over the general time-domain method in the current study.

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The Development and Application of a Time-Domain Harmonic Balance Flow Solver

Volume 1: Symposia, Parts A and B ◽

10.1115/fedsm2012-72200 ◽

2012 ◽

Author(s):

Pengcheng Du ◽

Fangfei Ning

Keyword(s):

Time Domain ◽

Harmonic Balance ◽

Unsteady Flows ◽

Harmonic Balance Method ◽

Balance Method ◽

Computational Time ◽

Test Cases ◽

Flow Solver ◽

The Time Domain ◽

Time Periodic

Time periodic unsteady flows are often encountered in turbomachinery. Simulating such flows using conventional time marching approach is very time-consuming and hence expensive. To handle this problem, several Fourier-based reduced order models have been developed recently. Among these, the time-domain harmonic balance method solves the governing equations purely in the time domain and there is also no need for the turbulence model to be linearized, making it easy to be implemented in an existing RANS code. Thus, the time-domain harmonic balance method was chosen and incorporated into an in-house Navier-Stokes flow solver. Several test cases were performed for the validations of the developed code. They cover standard unsteady test cases such as the low speed vortex shedding cylinder flow and the Sajben transonic diffuser under periodically oscillating back pressure. Further, two different practical turbomachinery unsteady flows were considered. One is a transonic fan under circumferential inlet distortion and the other is the rotor-stator interactions in a single stage compressor. The results illustrate the capability of the harmonic balance method in capturing the dominant nonlinear effects. The number of harmonics should be retained in the harmonic balance method is depend on the strength of the nonlinear unsteady effects and differs from case to case. With appropriate number of harmonics retained, it can resolve the unsteady flow field satisfactory, meanwhile, reducing the computational time significantly. In a word, the harmonic balance method promise to be an effective way to simulate time periodic unsteady flows.

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Multi-Harmonic Analysis of Dry Friction Damped Systems Using an Incremental Harmonic Balance Method

Journal of Applied Mechanics ◽

10.1115/1.3169175 ◽

1985 ◽

Vol 52 (4) ◽

pp. 958-964 ◽

Cited By ~ 128

Author(s):

C. Pierre ◽

A. A. Ferri ◽

E. H. Dowell

Keyword(s):

Time Domain ◽

Dry Friction ◽

Harmonic Balance ◽

Harmonic Balance Method ◽

Frequency Domain Analysis ◽

Balance Method ◽

Incremental Harmonic Balance Method ◽

Incremental Harmonic Balance ◽

The Time Domain ◽

Damped Systems

A multi-harmonic, frequency domain analysis of dry friction damped systems is presented which uses an incremental harmonic balance method. When compared with time domain solution methods, it is found that the incremental harmonic balance method can yield very accurate results with some advantages over the time domain methods. Both one and two degree-of-freedom systems are studied.

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On the Extension of a Harmonic Balance Method for the Simulation of Compressor Casing Treatments

Volume 2C: Turbomachinery ◽

10.1115/gt2016-56990 ◽

2016 ◽

Author(s):

Christian Voigt ◽

Graham Ashcroft

Keyword(s):

Time Domain ◽

Harmonic Balance ◽

Harmonic Balance Method ◽

Balance Method ◽

Nonlinear Frequency ◽

Transonic Compressor ◽

Frequency Domain Methods ◽

Blade Tip ◽

The Time Domain ◽

Casing Treatments

In recent years both linear and nonlinear frequency domain methods have become increasingly popular in the simulation and investigation of time-periodic flows in turbomachinery. In this work the extension of an alternating frequency/time domain Harmonic Balance method to support arbitrary inter-domain block interfaces, with possibly different frames of reference, is described in detail. The approach outlined is based on the time-domain, area-based interpolation algorithm originally developed for the investigation of casing treatments. In this paper, it is shown that by solving the domain coupling problem in the time-domain it is possible to accurately and efficiently capture the flow physics of such complex, nonlinear problems as blade tip interaction with casing treatments in transonic compressors. To demonstrate and verify the basic algorithm the advection of a simple entropy disturbance in a subsonic duct flow is first computed. Secondly, unsteady flow due to rotor-stator interaction in a transonic compressor stage is simulated and the data compared with reference numerical methods. Finally, to validate the method a single stage transonic axial compressor with casing treatments is simulated and the results are compared with previously published time-domain simulations as well as experimental data based on particle image velocimetry measurements in the blade tip region.

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The time-domain method of weighted residuals (MWR): Moving from grid-based methods to node-based meshless techniques

2009 International Conference on Electromagnetics in Advanced Applications ◽

10.1109/iceaa.2009.5297512 ◽

2009 ◽

Cited By ~ 1

Author(s):

Zhizhang Chen ◽

Yi-qiang Yu ◽

Michel M. Ney

Keyword(s):

Time Domain ◽

Time Domain Method ◽

Weighted Residuals ◽

Method Of Weighted Residuals ◽

Domain Method ◽

The Time Domain ◽

Grid Based

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Effects of blood volume changes on characteristic impedance of the pulmonary artery

AJP Heart and Circulatory Physiology ◽

10.1152/ajpheart.1982.242.2.h197 ◽

1982 ◽

Vol 242 (2) ◽

pp. H197-H202 ◽

Cited By ~ 3

Author(s):

J. P. Dujardin ◽

D. N. Stone ◽

C. D. Forcino ◽

L. T. Paul ◽

H. P. Pieper

Keyword(s):

Pulmonary Artery ◽

Blood Volume ◽

Time Domain ◽

Volume Expansion ◽

Characteristic Impedance ◽

Main Pulmonary Artery ◽

Time Domain Method ◽

Frequency Domain Method ◽

Domain Method ◽

The Time Domain

Experiments were performed on eight anesthetized dogs to study the response of the characteristic impedance (Zc) of the main pulmonary artery to changes in circulating blood volume. Pressure and flow were measured in the proximal main pulmonary artery under control conditions, after hemorrhage (-15% of the estimated blood volume), again under control conditions, and finally after volume expansion (+30% of the estimated blood volume). Two different methods were used to determine Zc from these recordings. With the frequency-domain method values for Zc were obtained by averaging the input impedance moduli between 2 and 15 Hz. With the time-domain method Zc was derived as the slope of the early ejection pressure-flow relationship. The values for Zc obtained with the two methods were not statistically different. In the time-domain method the average increase in Zc with hemorrhage was 30.7 +/- 7.4 (SE) %, and the average decrease with volume expansion was -21.1 +/- 5.0 (SE) %. Because the time-domain method allowed the values of Zc during control conditions and after hemorrhage to be obtained in the same pressure range, it was concluded that the observed changes were caused by a change in the activity of the smooth muscle in the pulmonary arterial wall. Similarly, it was concluded that the decrease in Zc after volume expansion was active in nature.

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Servo System Identification Using Relay Feedback: A Time-Domain Approach

Journal of Manufacturing Science and Engineering ◽

10.1115/1.4007715 ◽

2012 ◽

Vol 134 (6) ◽

Cited By ~ 10

Author(s):

Jia Liu ◽

Jianhua Wu ◽

Zhenhua Xiong ◽

Xiangyang Zhu

Keyword(s):

System Identification ◽

Dynamic Characteristics ◽

Time Domain ◽

Oscillation Amplitude ◽

Servo System ◽

Time Domain Method ◽

Relay Feedback ◽

Servo Systems ◽

Domain Method ◽

The Time Domain

In servo systems, the dynamic characteristics may not only differ between axes but may also vary with moving directions for a single axis. The direction dependent characteristics would result in additional tracking or positioning error and degrade the performance of the system. In this paper, relay feedback tests are successfully applied to identify the dynamic characteristics in servo systems. A time-domain method is used to analyze the relay feedback other than the conventional describing function (DF) method. The time-domain method utilizes the same oscillation parameters (oscillation amplitude and half period) as the DF method for system identification. However, the time-domain method takes several advantages: First, the direction dependent characteristics of the system can be properly revealed; second, no approximation is made in this method, so that the exact expressions of the amplitudes and the periods of the limit cycles under relay feedback can be derived. A feedforward compensator is then designed using the estimated values of the system parameters. Simulation results show that the identification results through the time-domain method are more accurate than the DF method and are more robust under different relay parameters. Real time experiments show that the feedforward compensator designed by the proposed method compensates disturbances related to the direction and hence improves the tracking and positioning performance of the servo system.

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Research on the Identification Methods of Friction in Kinematical Joints of Mechanical Systems

World Tribology Congress III, Volume 1 ◽

10.1115/wtc2005-63258 ◽

2005 ◽

Author(s):

Ziying Wu ◽

Hongzhao Liu ◽

Lilan Liu ◽

Pengfei Li ◽

Daning Yuan

Keyword(s):

Frequency Domain ◽

Time Domain ◽

Time Domain Method ◽

Estimation Accuracy ◽

Frequency Domain Method ◽

Linkage Mechanism ◽

Identification Methods ◽

Low Snr ◽

Domain Method ◽

The Time Domain

This paper describes two approaches for the simultaneous identification of the coulomb and viscous parameters in kinematical joints. One is a time-domain method (TDM) and the other is a frequency-domain method (FDM). Simulation shows that both of the two methods have good performances in identifying friction at high SNR (90dB). But at low SNR (20dB), the estimation accuracy of the frequency-domain method is higher than that of the time-domain method. A field experiment employing a linkage mechanism driven by motor is also carried out. The experimental results obtained by the two approaches are almost identical under different experiment conditions. It has been concluded that the presented identification methods of friction in kinematical joints are correct and applicable.

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Periodic response analysis of a misaligned rotor system by harmonic balance method with alternating frequency/time domain technique

Science China Technological Sciences ◽

10.1007/s11431-016-6101-7 ◽

2016 ◽

Vol 59 (11) ◽

pp. 1717-1729 ◽

Cited By ~ 10

Author(s):

HongLiang Li ◽

YuShu Chen ◽

Lei Hou ◽

ZhiYong Zhang

Keyword(s):

Time Domain ◽

Harmonic Balance ◽

Harmonic Balance Method ◽

Rotor System ◽

Balance Method ◽

Response Analysis ◽

Periodic Response

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Separating Cloud and Drizzle Signals in Radar Doppler Spectra Using a Parametric Time Domain Method

Journal of Atmospheric and Oceanic Technology ◽

10.1175/jtech-d-20-0061.1 ◽

2020 ◽

Vol 37 (9) ◽

pp. 1669-1680

Author(s):

Shashank S. Joshil ◽

Cuong M. Nguyen ◽

V. Chandrasekar ◽

J. Christine Chiu ◽

Yann Blanchard

Keyword(s):

Remote Sensing ◽

Time Domain ◽

Marine Boundary Layer ◽

Time Domain Method ◽

Radar Signal ◽

Liquid Water Path ◽

Microphysical Properties ◽

Observation Volume ◽

Domain Method ◽

The Time Domain

AbstractThe ability to separate cloud and drizzle returns in active remote sensing observations is important for understanding the microphysics of clouds and precipitation. Yet, robust separations remain challenging in radar remote sensing. Prior methods for cloud and drizzle separation for radar observations use the properties of the Doppler spectra such as skewness. However, these methods have challenges when the drizzle becomes dominant in the observation volume. This paper presents a parametric time domain method (PTDM) that separates cloud and drizzle using the Doppler spectra measurements without assuming any prior properties of cloud and drizzle. The advantage of PTDM is that it can estimate the signal properties in the time domain and can obtain the cloud and drizzle estimates simultaneously. Based on our radar signal simulations, the uncertainty in estimated power and velocity from PTDM are within 2 dB and 0.02 m s−1, respectively. We have also evaluated the PTDM algorithm using observations from the Atmospheric Radiation Measurement (ARM) Program W-band cloud radar in the Clouds, Aerosols, and Precipitation in the Marine Boundary Layer (CAP-MBL) campaign at the Azores in 2009–10. Two cases corresponding to light and moderate drizzling conditions are considered for the study. The statistics of the estimates obtained show that the PTDM method performs well in separating the cloud and drizzle returns. Finally, the estimated cloud and drizzle reflectivity from PTDM were used to retrieve their corresponding microphysical properties, showing that the retrieved liquid water path agrees to 25 g m−2 with the benchmark microwave method.

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