Unsteady Strain Research Articles

Sensitivity of soot formation to strain rate in steady counterflow flames determines its response under unsteady conditions

This work reports an original experimental investigation on the sooting characteristics of counterflow diffusion flames (CDFs) subject to sinusoidal oscillations of strain rates. The study was motivated by the necessity to consider transient responses of soot formation when using the laminar flamelet model to simulate soot formation in turbulent flames. Acoustic forcing was applied through loudspeakers installed at the inlet end of both the oxidizer and fuel nozzles of the counterflow burner to generate strain rate oscillations at the desired frequency and amplitudes. Particle image velocity and planar laser induced incandescence were used respectively to measure flow field and the soot volume fraction in a time-resolved manner. Counterflow flames of C2H4 and C3H8 fuels were tested with oxidizer streams of various oxygen mole fractions (XO). The experimental data revealed notable differences in unsteady soot responses between CDFs of C2H4 and C3H8 at the same XO. However, after matching the soot loadings of the two CDFs to have the same sensitivity to strain rate at steady states, their responses to unsteady strain oscillation became almost identical. We experimentally demonstrated that the unsteady response of soot formation to oscillating strain rates, as characterized by phase lag and amplitude attenuations, are strongly correlated with the sensitivity of the soot loading to strain rate under steady conditions. The results may have important implications for the development of transient flamelet models that incorporate unsteady effects on soot formation.

Extinction of non-equidiffusive premixed flames with oscillating strain rates

Extinction of premixed flames under non-uniform, unsteady strain is a phenomenon commonly observed in turbulent combustors. To assess the role of inequity in thermal and mass diffusion, represented by a global Lewis number (Le) - defined as the ratio of the mixture’s thermal diffusivity to the mass diffusivity of the deficient species, on such extinctions, we present a study of counterflow twin-flames with various Le under oscillating strain rates. Experimental results confirm that for low mean strain rates, the amplitude of strain rate oscillation required for extinction is so large that the flow temporarily alters its direction, leading to distortion of the counterflow flow-field, destabilization, and eventual extinction of the flame irrespective of Lewis number. However, for relatively large mean strain rates, extinction results from flame-response to the peak instantaneous strain rate. For Le>1 mixtures, the maximum strain rate that the flames can sustain is greater than the steady state extinction values, while Le≤1 flames extinguish at a maximum strain rate, approximately equal to the steady state strain condition. This distinctively disparate behaviors of extinctions depending on the Lewis number are analyzed and delineated using numerical simulations of unsteady flames.

Experimental Investigation of a 10 MW Prototype Axial Turbine Runner: Vortex Rope Formation and Mitigation

AbstractThe transient load fluctuations on the runner blades of prototype hydraulic turbines during load variations are one of the main causes of fatigue and eventual structural failure. A clear understanding of the dynamic loads on the runner blades is required to detect the source of the fluctuations. In this paper, an experimental investigation of vortex rope formation and mitigation in a prototype Kaplan turbine, namely, Porjus U9, is carried out. Synchronized unsteady pressure and strain measurements were performed on a runner blade during steady-state and load variation under off-cam condition. The normalized pressure fluctuation during load variations remained approximately within ±0.2Pref for all the pressure transducers installed on the blade pressure side and is even slightly lower during the transient cycle. Higher pressure fluctuations were found on the blade suction side, approximately four times higher than that of on the pressure side. The synchronous and asynchronous components of the vortex rope were clearly observed at the low discharge operating point and transient cycles. The spectral analysis of the pressure signals showed that the synchronous component appears before the asynchronous component during the load reduction, and it lasts longer during the load increase. These frequencies slightly change during the load variation. In addition, the results proved that the strain fluctuation component on the runner blade arises from the synchronous component of the vortex rope at low discharge while the asynchronous component influence is negligible.

Experimental Investigation of a 10 MW Prototype Kaplan Turbine during Start-Up Operation

An increase in the start/stop cycles of hydraulic turbines due to the penetration of intermittent renewable energy sources is important. Hydraulic instabilities that occur in hydraulic turbines during start/stops may cause structural issues in the turbine components. High-stress fluctuations on the runner blades are expected during start-ups due to the unsteady pressure loading on the runner blades. This paper presents experiments performed on a 10 MW prototype Kaplan turbine at the Porjus Hydropower Center during a start-up cycle. Synchronized unsteady pressure and strain measurements on a runner blade and axial, bending (in two directions) and torsion strain measurements on the shaft were performed. In addition, the general parameters of the turbine (e.g., rotational speed, guide vane opening and runner blade angle) were acquired. Low-frequency fluctuations (0–15 Hz) were observed in the pressure data on the runner blade after opening the guide vanes from the completely closed position. A higher strain value was observed on the strain gauges installed on the runner blade near the hub (200–500 μ m / m ) compared to the ones near the shroud at the leading and trailing edge. The strain fluctuation level on the shaft decreased after loading the generator by further opening the guide vanes. Higher fluctuations were observed in the torsion strain compared to axial and bending strain. In addition, the torsion strain peak-to-peak value reached 12 times its corresponding value at 61% guide vane opening.

A Numerical Simulation to the Influence of Unsteady Strain Flow on Twin Premixed Flames

The aim of this paper was to examine the response of twin premixed flames formed in a counterflow configuration to the presence of an unsteady straining flow. We began by describing the problem mathematically using the thermodiffusive model with constant density and then adopted a finite elements approach to solve the problem numerically. The study has shown that the role of flow on flame propagation is determined by three main parameters, namely, flow amplitude A, strain rate ε, and fuel Lewis number LeF. For LeF ≥ 1, the flow is seen to promote flame extinction, while LeF < 1 the flow clearly enhances the flame reactivity. Qualitatively, it has been shown that for LeF = 1, there exists a critical value of A (that varies with ε) below which the reactivity decreases monotonically with A. For small LeF < 1, on the other hand, the reactivity was seen to increase with A. For LeF > 1, however, a nonmonotonic dependence, especially for small ε, is predicted.

Strain response analysis of adhesively bonded extended composite wind turbine blade suffering unsteady aerodynamic loads

Abstract Extending blades of wind turbine in service is the most effective method for increasing energy production. Adhesively bonding technology increases less mass and has simpler operation process, which is more suitable for extending blades in service. But unsteady aerodynamic loads on the blades due to stochastic turbulent inflow may lead to fatigue damage and even failure. This paper presented a study on strain response and fatigue life of adhesively bonded extended composite wind turbine blade suffering unsteady aerodynamic loads. Firstly, a loading method that applies periodic distributed aerodynamic loads on the blade was proposed to accurately simulate the unsteady distributed loads on the real extended blades in service. Secondly, strain response behaviors to unsteady aerodynamic loads and strain distribution behaviors in the adhesively bonded area were revealed. Finally, fatigue damage was predicted with unsteady aerodynamic load spectrums, rainflow cycle-counting algorithm, Goodman diagram and Miner's linear superposition principle. Based on the findings obtained from this study, the feasibility of adhesively bonding technology for extending blade was affirmed and a few potential future directions of study were addressed to reduce the risk of adhesively bonded structures.

Unsteady Aerodynamic Force Sensing from Strain Data

A simple approach for computing unsteady aerodynamic forces from simulated measured strain data is proposed in this study. First, the deflection and slope of the structure are computed from the unsteady strain. Velocities and accelerations of the structure are computed using the autoregressive moving average model, online parameter estimator, low-pass filter, and a least-squares curve fitting method, together with analytical derivatives with respect to time. Finally, aerodynamic forces over the wing are computed using modal aerodynamic influence coefficient matrices, a rational function approximation, and a time-marching algorithm. A cantilevered rectangular wing is used to validate the simple approach. Unsteady aerodynamic forces as well as wing deflections, velocities, accelerations, and strains are computed using the CFL3D computational fluid dynamics code and the MSC/NASTRAN finite element analysis code; and these CFL3D/NASTRAN-based results are assumed as measured quantities. Computed deflections, velocities, accelerations, and unsteady aerodynamic forces are compared with the CFL3D/NASTRAN-based results. Computed aerodynamic forces based on lifting-surface theory at subsonic speeds are in good agreement with the target aerodynamic forces generated using CFL3D code with the Euler equation. This research demonstrates the feasibility of obtaining induced drag and lift forces through the use of distributed sensor technology with measured strain data.

An equivalent dissipation rate model for capturing history effects in non-premixed flames

The effects of strain rate history on turbulent flames have been studied in the past decades with 1D counter flow diffusion flame (CFDF) configurations subjected to oscillating strain rates. In this work, these unsteady effects are studied for complex hydrocarbon fuel surrogates at engine relevant conditions with unsteady strain rates experienced by flamelets in a typical spray flame. Tabulated combustion models are based on a steady scalar dissipation rate (SDR) assumption and hence cannot capture these unsteady strain effects; even though they can capture the unsteady chemistry. In this work, 1D CFDF with varying strain rates are simulated using two different modeling approaches: steady SDR assumption and unsteady flamelet model. Comparative studies show that the history effects due to unsteady SDR are directly proportional to the temporal gradient of the SDR. A new equivalent SDR model based on the history of a flamelet is proposed. An averaging procedure is constructed such that the most recent histories are given higher weights. This equivalent SDR is then used with the steady SDR assumption in 1D flamelets. Results show a good agreement between tabulated flamelet solution and the unsteady flamelet results. This equivalent SDR concept is further implemented and compared against 3D spray flames (Engine Combustion Network Spray A). Tabulated models based on steady SDR assumption under-predict autoignition and flame lift-off when compared with an unsteady Representative Interactive Flamelet (RIF) model. However, equivalent SDR model coupled with the tabulated model predicted autoignition and flame lift-off very close to those reported by the RIF model. This model is further validated for a range of injection pressures for Spray A flames. The new modeling framework now enables tabulated models with significantly lower computational cost to account for unsteady history effects.

Numerical investigation of soot-flame-vortex interaction

Because the numerical simulation of soot production in turbulent flames is quite challenging, it is useful to consider simpler aerodynamic configurations retaining unsteady strain rate and curvature effects. The present article reports detailed numerical simulations of a planar vortex interacting with a sooting laminar diffusion flame formed by a parallel flow of acetylene and air. Calculations are carried out to reproduce the experimental data reported by Cetegen and Basu (2006). Compared to previous numerical works on this configuration based on simple two-equations soot models, a detailed numerical mechanism, accounting for 97 gaseous species and 59 solid BINs, is considered here to represent the chemistry in the gas phase and the production and oxidation of soot particles. Three different vortex strengths are considered and vortices are formed by pulsing the air or the fuel streams, allowing comparisons between the calculated soot-vortex-flame interactions with LII images. Calculations adequately retrieve experimental data when the vortex is initiated at the fuel side. Differences are observed when the vortex is formed on the air side. The simulations, however, are useful for examining strain rate and curvature effects on soot volume fractions of small spherical particles and large aggregates, and to study physical processes underlying the soot production. It is shown that the variability of the soot volume fraction is highly correlated to the response of soot precursors to flame curvature. Soot variability in the mixture fraction space depends on the behavior of large aggregates that, being characterized by high Schmidt numbers, are more sensitive to the convective motion imposed by the vortex compared to the gaseous phase. The observed behavior has to be reproduced by the models developed for numerical simulations in order to obtain an accurate prediction of soot production in turbulent flames.

Unsteady dynamics of PAH and soot particles in laminar counterflow diffusion flames

Due to their low chemical time scales, the production of soot particles in turbulent diffusion flames is highly impacted by large range of local strain rate fluctuations.In order to understand the response of soot production to strain rate fluctuations, unsteady laminar counterflow diffusion flames with an imposed oscillating strain rate are investigated both analytically and numerically. First an analytical linearized model is developed to predict the unsteady response of a flame quantity of interest from information on laminar steady flames. Three critical parameters governing flame response are identified: the Stokes number which compares the characteristic time associated to the mean imposed strain rate to the oscillation frequency, the Damköhler number associated to the quantity of interest, and a third one characterizing the response of this quantity to an imposed steady strain rate. This model is then applied to soot predictions. Parallely, the response of soot production in propane-air counterflow diffusion flames to unsteady strain harmonic oscillations is studied numerically using a detailed sectional soot model. A wide range of frequencies and amplitudes are considered. A specific trend is highlighted for soot precursors and particles production according to their respective chemical time scales: the bigger the PAH or soot particle, the higher its chemical time scale, resulting in a more damped and phase-lagged response. The particle size distribution evolves accordingly during the considered oscillations, so that the quasi-steady state behavior is not verified for high frequencies. The numerical results are compared to those obtained by the analytical approach and a very good agreement is obtained at low amplitudes. Non-linear response of soot precursors and soot particles production to strain oscillations are finally discussed in case of high oscillation amplitudes and the limits of the proposed analytical model are identified.

Experimental and computational investigation of novel vertical tail buffet suppression method for high sweep delta wing

Our research aim is to investigate the buffet alleviation effect of static or vibrating bulges attached on the forebody surface of the model. Experiments and numerical simulations on a model consisting of a sharp-edged, 70°-leading edge sweep delta wing and twin swept back vertical tails were conducted. Models with different bulges were tested and computed at 10 and 20 m/s of free stream velocity at angles of attack ranging from 20°-50°. Dynamic strain gauge and multichannel data acquisition and analysis system were employed for the measurement of unsteady root strain on the vertical tails. Experimental and computational results show that both static and vibrating bulges behave effectively as a novel tool to alleviate tail buffet, and the alleviation effect depends largely on the vibrating frequency. Besides, one-sided bulge can only alleviate the buffeting response for the tail of the same side, and it has no obvious alleviation effect for the opposite tail. Results of the spectral analysis reveal that there are generally three peaks of spectral density for aircrafts of this configuration, and bulges used in this paper could alleviate tail buffeting, but the total lift and drag of the whole model show no obvious deviation compared to the base model and the dominant frequency of the vibration of the tails has not shifted.

The turbulence vorticity as a window to the physics of friction-drag reduction by oscillatory wall motion

DNS data for channel flow, subjected to spanwise (in-plane) wall oscillations at a friction Reynolds number of 1025, are used to examine the turbulence interactions that cause the observed substantial reduction in drag provoked by the forcing. Following a review of pertinent interactions between the forcing-induced unsteady Stokes strain and the Reynolds stresses, identified in previous work by the present authors, attention is focused on the equations governing the components of the enstrophy, with particular emphasis placed on the wall-normal and the spanwise components. The specific objective is to study the mechanisms by which the Stokes strain modifies the enstrophy field, and thus the turbulent stresses. As such, the present analysis sheds fresh light on the drag-reduction processes, illuminating the interactions from a different perspective than that analysed in previous work. The investigation focuses on the periodic rise and fall in the drag and phase-averaged properties during the actuation cycle at sub-optimal actuation conditions, in which case the drag oscillates by around ±2% around the time-averaged 20% drag-reduction margin. The results bring out the important role played by specific strain-related production terms in the enstrophy-component equations, and also identifies vortex tilting/stretching in regions of high skewness as being responsible for the observed strong increase in the spanwise enstrophy components during the drag-reduction phase. Simultaneously, the wall-normal enstrophy component, closely associated with near-wall streak intensity, diminishes, mainly as a result of a reduction in a production term that involves the correlation between wall-normal vorticity fluctuations and the spanwise derivative of wall-normal-velocity fluctuations, which pre-multiplies the streamwise shear strain.

Spanwise oscillatory wall motion in channel flow: drag-reduction mechanisms inferred from DNS-predicted phase-wise property variations at

AbstractA direct-numerical-simulation-based study is presented, which focuses on the response of near-wall turbulence and skin friction to the imposition of an oscillatory spanwise wall motion in channel flow. One point of contrast to earlier studies is the relatively high Reynolds number of the flow, namely $Re_\tau =1000$ in the unforced baseline flow. Another is the focus on transients in the drag that are in the form of moderate oscillatory variations in the skin friction and near-wall turbulence around the low-drag state at a sub-optimal actuation period. These conditions allow phase-averaged statistics to be extracted, during the periodic drag decrease and rise, that shed light on the interaction between turbulence and the unsteady Stokes strain. Results are presented for, among others, the phase-averaged second moments of stochastic fluctuations and their budgets, enstrophy components and joint probability density functions. The study identifies velocity skewness – the wall-normal derivative of the angle of the velocity vector – as playing a significant role in the streak-damping process during the drag-reduction phase. Furthermore, the phase-wise asymmetry in the skewness is identified as the source of a distinctive hysteresis in all properties, wherein the drag decrease progresses over a longer proportion of the actuation cycle than the drag increase. This feature, coupled with the fact that the streak-generation time scale limits the ability of the streaks to re-establish themselves during the low-skewness phase when the actuation period is sufficiently short, is proposed to drive the drag-reduction process. The observations in the study thus augment a previously identified mechanism proposed by two of the present authors, in which the drag-reduction process was linked to the rate of change in the Stokes strain in the upper region of the viscous sublayer where the streaks are strongest. Furthermore, an examination of the stochastic-stress budgets and the enstrophy lead to conclusions contrasting with those recently proposed by other authors, according to which the drag-reduction process is linked to increases in enstrophy and turbulence-energy dissipation. It is shown, both for the transient drag-reduction phase and the periodic drag fluctuations around the low-drag state, that the drag decrease/increase phases are correlated with decreases/increases in both enstrophy and dissipation.

Flame-flow interactions and flow reversal

The interaction of a premixed methane/air flame with flow unsteadiness is studied computationally using a stagnation-point flow configuration. The problem is of fundamental interest and also relevant for turbulent combustion in the laminar flamelet regime. In the present study, of particular interest is the flame residing in a weakly strained flow field such that the flame is stabilized away from the viscous boundary layer adjacent to the stagnation plane and is free to move in response to flow perturbations. An unsteady sinusoidal strain rate field is imposed on the flame, and an extensive parametric study is conducted by varying the frequency and amplitude of strain rate fluctuation. It is found that for high frequencies and large amplitudes, flow direction reverses upstream of the flame, thereby establishing a new stagnation plane in the preheat zone ahead of the flame. This observation indicates that the flame strongly affects the upstream flow field and could also possibly explain the reported occurence of flow reversal in experimental studies of turbulent jet flames. Effects of other key parameters such as the Lewis number, mean flame speed, and gas expansion ratio on flame-flow interaction and flow reversal are studied by investigating highly lean (Le<1) and rich (Le>1) hydrogen/air flames. The physical mechanism responsible for flow reversal phenomenon is explained.

On the formation and early evolution of soot in turbulent nonpremixed flames

A Direct Numerical Simulation (DNS) of soot formation in an n-heptane/air turbulent nonpremixed flame has been performed to investigate unsteady strain effects on soot growth and transport. For the first time in a DNS of turbulent combustion, Polycyclic Aromatic Hydrocarbons (PAH) are included via a validated, reduced chemical mechanism. A novel statistical representation of soot aggregates based on the Hybrid Method of Moments is used [M.E. Mueller, G. Blanquart, H. Pitsch, Combust. Flame 156 (2009) 1143–1155], which allows for an accurate state-of-the-art description of soot number density, volume fraction, and morphology of the aggregates. In agreement with previous experimental studies in laminar flames, Damköhler number effects are found to be significant for PAH. Soot nucleation and growth from PAH are locally inhibited by high scalar dissipation rate, thus providing a possible explanation for the experimentally observed reduction of soot yields at increasing levels of mixing in turbulent sooting flames. Furthermore, our data indicate that soot growth models that rely on smaller hydrocarbon species such as acetylene as a proxy for large PAH molecules ignore or misrepresent the effects of turbulent mixing and hydrodynamic strain on soot formation due to differences in the species Damköhler number. Upon formation on the rich side of the flame, soot is displaced relative to curved mixture fraction iso-surfaces due to differential diffusion effects between soot and the gas-phase. Soot traveling towards the flame is oxidized, and aggregates displaced away from the flame grow primarily by condensation of PAH on the particle surface. In contrast to previous DNS studies based on simplified soot and chemistry models, surface reactions are found to contribute barely to the growth of soot, for nucleation and condensation processes occurring in the fuel stream are responsible for the most of soot mass generation. Furthermore, the morphology of the soot aggregates is found to depend on the location of soot in mixture fraction space. Aggregates having the largest primary particles populate the region closest to the location of peak soot growth. On the contrary, the aggregates with the largest number of primary particles are located much further into the fuel stream.

Effects of equivalence ratio variation on lean, stratified methane–air laminar counterflow flames

The effects of equivalence ratio variations on flame structure and propagation have been studied computationally. Equivalence ratio stratification is a key technology for advanced low emission combustors. Laminar counterflow simulations of lean methane–air combustion have been presented which show the effect of strain variations on flames stabilized in an equivalence ratio gradient, and the response of flames propagating into a mixture with a time-varying equivalence ratio. ‘Back supported’ lean flames, whose products are closer to stoichiometry than their reactants, display increased propagation velocities and reduced thickness compared with flames where the reactants are richer than the products. The radical concentrations in the vicinity of the flame are modified by the effect of an equivalence ratio gradient on the temperature profile and thermal dissociation. Analysis of steady flames stabilized in an equivalence ratio gradient demonstrates that the radical flux through the flame, and the modified radical concentrations in the reaction zone, contribute to the modified propagation speed and thickness of stratified flames. The modified concentrations of radical species in stratified flames mean that, in general, the reaction rate is not accurately parametrized by progress variable and equivalence ratio alone. A definition of stratified flame propagation based upon the displacement speed of a mixture fraction dependent progress variable was seen to be suitable for stratified combustion. The response times of the reaction, diffusion, and cross-dissipation components which contribute to this displacement speed have been used to explain flame response to stratification and unsteady fluid dynamic strain.

An exact solution for a model of pressure-dependent plasticity in an un-steady plane strain process

Abstract An incompressible material obeying a pressure-dependent yield condition is confined between two planar plates which are inclined at an angle 2 α . The plates intersect in a hinged line and the angle α slowly decreases from an initial value. An initial/boundary value problem for the flow of the material is formulated and solved for the stress and the velocity fields, the solution being in closed form. The material is assumed to obey a special case of the double slip and rotation model, which generalises the classical plastic potential model and is also a variant of the double shearing model. The solution for the velocity field may exhibit sliding or sticking at the plates. Solutions which exhibit sticking may have a rigidly rotating zone in the region adjacent to the plates. It is shown that sliding occurs when the value of α is less than a certain critical value α c ; that sticking occurs without a rigid zone if α exceeds or equals α c but is less than a second critical value α 0 ; and that sticking with a rigid zone adjacent to the plates occurs if α exceeds α 0 . The values of α c and α 0 coincide for a certain range of model parameters. Solutions which exhibit sliding are singular. Qualitative features of the solution found are compared with those of the solution for the classical plastic potential model.

Identification of pulse shapes during transverse impact on composite beams and plates

A test facility for transverse shock loading of beams and plates at small impact velocities (up to 40 km/sec) is described. The impact contact force and unsteady strains are determined for a transverse impact on fiber-layered beams and plates from fiberglass and carbon fiber-reinforced plastic. Pulse shapes are determined for various impact velocities in the range of 5–40 m/sec. The shock loading and unsteady strain of composite beams and plates are calculated by the finite element method. The finite elements take into account transverse shears according to the Timoshenko theory and the viscoelastic material behavior according to the Voigt model.

Analytical study on effects of strain distribution in welding start/end on welding distortion

A welding distortion prediction method based on the inherent strain concept is presented. In the proposed method, welding distortion of large-welded structures could be estimated by elastic analysis using the result of thermal-elastic–plastic analysis and the result of smaller welded joints or components. Thermal-elastic–plastic analysis is performed to calculate residual plastic strain distribution, which is the input data for the elastic analysis of welding distortion. The obtained residual plastic strain distribution is mapped to non-deformed finite element models to calculate welding distortion by elastic analysis. The mapping procedure is done in different ways for welding start/end parts and the rest of the weld length in order to take into consideration the unsteady strain distribution at the start/end of welds. For start/end parts, strain distribution used is identical with thermal-elastic–plastic analysis. For the part except start/end parts, strain distribution obtained by thermal-elastic–plastic analysis is extracted from the centre of weld length and is extruded along the welding direction. The proposed method was applied to the welding distortion prediction of joints with weld length of 900 and 1200 mm based on the thermal-elastic–plastic analysis result of a joint with weld length 600 mm. The estimated results were in good agreement with the thermal-elastic–plastic analysis results of models of corresponding weld length to show the validity of the proposed method.

溶接変形に及ぼす始終端部の影響に関する解析的検討

A welding distortion prediction method based on inherent strain concept was presented. In the proposed method, welding distortion of large welded structures could be estimated by elastic analysis using the result of thermal-elastic-plastic analysis result of smaller welded joints or components. Thermal-elastic-plastic analysis is performed to calculate residual plastic strain distribution, which is the input data for the elastic analysis of welding distortion. The obtained residual plastic strain distribution is mapped to non-deformed finite element models to calculate welding distortion by elastic analysis. The mapping procedure is done in different ways for welding start/end parts and the rest of weld length in order to take into consideration of unsteady strain distribution at start/end of welds. For start/end parts, strain distribution used is identical with thermal-elastic-plastic analysis. For the part except start/end parts, strain distribution obtained by thermal-elastic-plastic analysis is extracted from the center of weld length and is extruded along welding direction. The proposed method was applied to the welding distortion prediction of joints with weld length 900 mm and 1200 mm based on thermal-elastic-plastic analysis result of a joint with weld length 600 mm. The estimated results were in good agreement with the thermal-elastic-plastic analysis results of models of corresponding weld length to show the validity of the proposed method.