Simultaneous measurement of velocity profile and liquid film thickness in horizontal gas–liquid slug flow by using ultrasonic Doppler method

Horizontal gas-liquid two-phase flows widely exist in chemical engineering,oil/gas production and other important industrial processes.Slug flow pattern is the main form of horizontal gas-liquid flows and characterized by intermittent motion of film region and slug region.This work aims to develop the ultrasonic Doppler method to realize the simultaneous measurement of the velocity profile and liquid film thickness of slug flow.A single-frequency single-channel transducer is adopted in the design of the field-programmable gate array based ultrasonic Doppler system.A multiple echo repetition technology is used to improve the temporal-spatial resolution for the velocity profile.An experiment of horizontal gas-liquid two-phase flow is implemented in an acrylic pipe with an inner diameter of 20 mm.Considering the aerated characteristics of the liquid slug,slug flow is divided into low-aerated slug flow,high-aerated slug flow and pseudo slug flow.The temporal-spatial velocity distributions of the three kinds of slug flows are reconstructed by using the ultrasonic velocity profile measurement.The evolution characteristics of the average velocity profile in slug flows are investigated.A novel method is proposed to derive the liquid film thickness based on the instantaneous velocity profile.The liquid film thickness can be effectively measured by detecting the position and the size of the bubbles nearly below the elongated gas bubble.Compared with the time of flight method,the film thickness measured by the Doppler system shows a higher accuracy as a bubble layer occurs in the film region.The effect of the gas distribution on the film thickness is uncovered in three kinds of slug flows.

Nitrogen monoxide vector of ultrasonic atomizing inhalation improves vertebro-basilar artery insufficiency Hemodynamic changes are detected by transcranial Doppler test

BACKGROUND： Latest researches at home and abroad indicate that glycerol trinitrate plays its function because it can metabolize into nitrogen monoxide （NO） in vivo. OBJECTIVE： To study the therapeutic effects of NO vector of ultrasonic atomizing inhalation on vertebro-basilar artery insufficiency （VBI） through transcranial Doppler （TCD） detection and serum NO content and indirect effect of TCD on cerebral blood flow changes. DESIGN： Randomized grouping and controlled clinical study. SETTING： Department of Neurology, the Fourth People＇s Hospital of Jinan. PARTICIPANTS： A total of 130 patients who were diagnosed as VBI were selected from Department of Neurology, the Fourth People＇s Hospital of Jinan from December 2001 to December 2005. The involved inpatients were checked by CT and MRI, and met the VBI diagnostic standard enacted by the Fourth National Academic Meeting of Cerebrovascular Disease in 1995. All patients and their relatives provided the confumed consent. They were randomly divided into low-dose treatment group （n =60）, high-lose treatment group （n =30） and control group （n =40）. METHODS： Patients in the low-dose and high-dose treatment groups were given ultrasonic atomizing inhalation of 3 mg and 5 mg glycerol trinitrate, respectively, for 20 minutes, once a day. In addition, ligustrazine and energy mixture were used once a day for three days in a course. Cases in the control group were only given ligustrazine and energy mixture. All selected cases accepted TCD, blood NO content was checked at the time of beginning, after the first time and after a period of treatment. According to the TCD test, VBI patients were divided into two groups （high-low flow velocity）. The vertebral artery （VA） and basal artery （BA） of left or right sides were detected by 2 Hz detector via occipital window. MAIN OUTCOME MEASURES： ①Blood flow velocity of systolic phase, blood flow velocity of diastole phase and vascular resistance in left and right VA and BA detected by using TCD before treatment, after treatment for one course; ②content of serum NO indirectly measured by using nitric acid disoxidation technique. RESULTS： All 130 VBI patients were involved in the final analysis. ①Changes of hemodynamic indexes： Systolic phase of VA and diastole phase of BA were higher in low-dose treatment group than that in the control group after first treatment, and there was significant difference （P 〈 0.05）; meanwhile, systolic phase and diastole phase of VA and systolic phase of BA were also higher in treatment group than that in the control group after one course （P 〈 0.05）. However, both systolic phase and diastole phase of VA and BA were lower in high-dose treatment group than that in the control group after first treatment and one course, and there was significant difference （P 〈 0.05）. ②Content of serum NO： After first treatment, there was no significant difference between low-dose treatment group and high-dose treatment group （P 〉 0.05）; but both groups were higher than control group, and there was significant difference （P 〈 0.05, 0.01）. CONCLUSION： NO vector of ultrasonic atomizing inhalation can improve VBI so as to improve cerebral blood-supply state.

A gas kick early detection method outside riser based on Doppler ultrasonic wave during deepwater drilling

The feasibility of gas kick early detection outside the riser was analyzed based on gas-liquid multiphase flow theory.Then an experimental platform for gas kick early detection based on Doppler ultrasonic wave was established and the propagation experiments in two-phase flow of gas-water(sucrose solutions)were conducted.The time and frequency domains of the Doppler ultrasonic wave signals during the experiments were analyzed.The results show that:(1)No matter the pump was on or off,the detected average Doppler ultrasonic signal voltage increased first and then decreased with the increase of the gas void fraction,and had a quadratic function relation with gas void fraction,so the average voltage change of the monitored signals can be used to deduce the approximate gas void fraction.The Doppler ultrasonic wave signal voltage was significantly reduced in magnitude and variation in the solution with higher viscosity,and the viscosity has stronger impact on the magnitude of signal than density.(2)When the pump was stopped,the Doppler shift increased with the increase of gas void fraction,and the two showed a nearly linear relation,so the detected amount of Doppler shift can reflect the variation of gas void fraction quantitatively.When the pump was on,the sound energy produced by frequency converter had a more significant impact on amplitude spectrum than gas void fraction,so it is impossible to determine whether gas kick occurs by frequency domain signal analysis.(3)This method is a non-contact measurement,with no contact with the drilling fluid and no disruption to the drilling operation.It can quantitatively characterize the gas void fraction according to the change of Doppler ultrasonic signal,enabling earlier detection of gas kick.

Application of Color Doppler Ultrasonic Examination in Deep Vein Valvular Incompetence in Lower Limbs

By use of color Doppler Flow Imaging (CDFI), the morphologic and hemodynamic parameters such as the diameters of femoral and popliteal veins,blood flow velocity and the reflux 0f valve area were examined in lower extremity deep valvular incompetence (DVI) and normal control gr0ups. The purpose was to evaluate the value of CDFI in the diagnosis of DVI. The results demonstrated that the parameters between the two groups had a very significant difference (P<0. 001), indicating that the CDFI is non-invasive, cost-effective and safe and it might serve as a practical tool in the diagnosis of lower extremity deep va1vular incompetence.

APPROACH OF IMPROVING PRECISION IN ULTRASONIC DOPPLER BLOODSTREAM SPEED MEASUREMENT BY CHAOS-BASED FREQUENCY DETECTING

It is critical for cerebral vascular disease diagnosis through Doppler to detect the maximum and the minimum of the carotid blood flow speed accurately. A kind of Duffing system under an external periodic power with dump is introduced in the letter, numerical analysis is carried out by four-order Runge-Kutta method. An oscillator array is designed according to the frequency of the ultrasonic wave. When the external signals are inputted, computational algorithm is used to scan the array in turn and analyze the result, and the frequency can be determined. Based on the methods above, detecting the carotid blood flow speed accurately is realized. The Signal-to-Noise Ratio (SNR) of-20.23dB is obtained by the result of experiments. In conclusion, the SNR has been improved and the precision of the measured bloodstream speed has been increased, which can be 0.069% to 0.13%.

Pig model of chronic myocardial ischemia and its investigation by ultrasonic integrated backscatter and Doppler tissue imaging

Objective: To construct an animal model of chronic ischemic myocardium, and evaluate it by ultrasonic integrated backscatter (IBS) and Doppler tissue imaging (DTI). Methods: An Ameroid constrictor was placed around the porcine left circumflex coronary artery (LCX). The calibrated average image intensity (%AII), cyclic variation of IBS (CVIB), transmural gradient index (TGI) of CVIB in lateral-posterior wall (LPW), and DTI spectrum of LPW in left ventricular papillary muscle level short axis view (LVPM-SAM) and apical four chamber view (AP-4CV) at normal state, 2, 4, 6 and 8 weeks postoperatively were measured. Results: Normal %AII, CVIB and TGI were 2.29±0.32, 9.69±2.22dB and 0.22±0.08, respectively. The %AII increased gradually postoperatively. The CVIB decreased also gradually, and the decrease was higher in subepicardium than in subendocardium. Most of TGI decrease occurred from 2 to 4 weeks postoperatively and became zero at 8 weeks (P<0.01); Normal V S (peak systolic velocity) of AP-4CV was higher than that of LVPM-SAM (P<0.01). V E (peak early diastolic velocity) of AP-4CV was lower than that of LVPM-SAM (P<0.05). V S and V E were all decreased after operation (P<0.01). The decrease of V S in AP-4CV was greater than that in LVPM-SAM. Conclusion: The pathological changes of the myocardium in human ischemic heart disease (IHD) are similar to that of Ameriod model. IBS and DTI can detect echo changes and ventricular wall motion in chronic ischemic myocardium, and provide more information for clinical investigation and treatment of IHD.

Comparative analysis of single-crater parameters in ultrasonic-assisted and unassisted micro-EDM of Ti6Al4V using discharge plasma imaging

Ultrasonic-assisted micro-electro-discharge machining(EDM)has the potential to enhance processing responses such as material removal rate(MRR)and surface finish.To understand the reasons for this enhancement,the physical mechanisms responsible for the individual discharges and the craters that they form need to be explored.This work examines features of craters formed by single discharges at various parameter values in both conventional and ultrasonic-assistedEDM of Ti6Al4V.High-speed imaging of the plasma channel is performed,and data on the individual discharges are captured in real-time.A 2D axisymmetric model using finite element software is established to model crater formation.On the basis of simulation and experimental results,a comparative study is then carried out to examine the effects of ultrasonic vibrational assistance on crater geometry.For every set ofEDM parameters,the crater diameter and depth from a single discharge are found to be higher in ultrasonic-assistedEDM than in conventionalEDM.The improved crater geometry and the reduced bulge formation at the crater edges are attributed to the increased melt pool velocity and temperature predicted by the model.

Determining rock crack stress thresholds using ultrasonic through-transmission measurements

The crack initiation stress threshold is widely used in excavation industries as rock spalling strength when designing deep underground structures to avoid unwanted brittle failures.While various strain-based methods have been developed for the estimation of this critical design parameter,such methods are destructive and often requires subjective interpretations of the stress–strain curves,particularly in rocks with pre-existing microcracks or high porosity.This study explore the applicability of non-destructive ultrasonic through-transmission methods for determining rock damage levels by assessing the changes in transmitted signal characteristics during loading.The change in velocity,amplitude,dominant frequency,and root-mean-square voltage are investigated with four different rock types including marble,sandstone,granite,and basalt under various stress levels.Results suggest the rate of signal variations can be reliably used to estimate crack closure and crack initiation stress levels across the tested rocks before failure.Comparison of the results between the conventional techniques and the new proposed methods based on ultrasonic monitoring are further discussed.

Remote sensing of air pollution incorporating integrated-path differential-absorption and coherent-Doppler lidar

An innovative complex lidar system deployed on an airborne rotorcraft platform for remote sensing of atmospheric pollution is proposed and demonstrated.The system incorporates integrated-path differential absorption lidar(DIAL) and coherent-doppler lidar(CDL) techniques using a dual tunable TEA CO_(2)laser in the 9—11 μm band and a 1.55 μm fiber laser.By combining the principles of differential absorption detection and pulsed coherent detection,the system enables agile and remote sensing of atmospheric pollution.Extensive static tests validate the system’s real-time detection capabilities,including the measurement of concentration-path-length product(CL),front distance,and path wind speed of air pollution plumes over long distances exceeding 4 km.Flight experiments is conducted with the helicopter.Scanning of the pollutant concentration and the wind field is carried out in an approximately 1 km slant range over scanning angle ranges from 45°to 65°,with a radial resolution of 30 m and10 s.The test results demonstrate the system’s ability to spatially map atmospheric pollution plumes and predict their motion and dispersion patterns,thereby ensuring the protection of public safety.

Observation of Doppler shift f_(D) modulated by the internal kink mode using conventional reflectometry in the EAST tokamak

In this paper we present a new experimental observation using a conventional reflectometry technique,poloidal correlation reflectometry(PCR),in the Experimental Advanced Superconducting Tokamak(EAST).The turbulence spectrum detected by the PCR system exhibits an asymmetry and induced Doppler shift f_(D)during the internal kink mode(IKM)rotation phase.This Doppler shift f_(D)is the target measurement of Doppler reflectometry,but captured by conventional reflectometry.Results show that the Doppler shift f_(D)is modulated by the periodic changes in the effective angle between the probing wave and cutoff layer normal,but not by plasma turbulence.The fishbone mode and saturated long-lived mode are typical IKMs,and this modulation phenomenon is observed in both cases.Moreover,the value of the Doppler shift f_(D)is positively correlated with the amplitude of the IKM,even when the latter is small.However,the positive and negative frequency components of the Doppler shift f_(D)can be asymmetric,which is related to the plasma configuration.A simulated analysis is performed by ray tracing to verify these observations.These results establish a clear link between f_(D)and IKM rotation,and are helpful for studying the characteristics of IKM and related physical phenomena.

Microstructure and forming mechanism of metals subjected to ultrasonic vibration plastic forming: A mini review

Compared with traditional plastic forming,ultrasonic vibration plastic forming has the advantages of reducing the forming force and improving the surface quality of the workpiece.This technology has a very broad application prospect in industrial manufactur-ing.Researchers have conducted extensive research on the ultrasonic vibration plastic forming of metals and laid a deep foundation for the development of this field.In this review,metals were classified according to their crystal structures.The effects of ultrasonic vibration on the microstructure of face-centered cubic,body-centered cubic,and hexagonal close-packed metals during plastic forming and the mech-anism underlying ultrasonic vibration forming were reviewed.The main challenges and future research direction of the ultrasonic vibra-tion plastic forming of metals were also discussed.

Improving fatigue properties of normal direction ultrasonic vibration assisted face grinding Inconel 718 by regulating machined surface integrity

Fatigue properties are crucial for critical aero-engine components in extreme serviceenvironments,which are significantly affected by surface integrity(SI)indexes(especially surface topography,residual stressσ_(res),and microhardness)after machining processes.Normal-direction ultrasonic vibration-assisted face grinding(ND-UVAFG)has advantages in improving the machinability of Inconel 718,but there is a competitive relationship between higher compressiveσ_(res)and higher surface roughness R_(a)in affecting fatigue strength.The lack of a quantitative relationship between multiple SI indexes and fatigue strength makes theindeterminacy of a regulatory strategy for improving fatigue properties.In this work,a model of fatigue strength(σ_f)_(sur)considering multiple SI indexes was developed.Then,high-cycle fatigue tests were carried out on Inconel 718 samples with different SI characteristics,and the influence of ND-UVAFG process parameters on SI was analyzed.Based on SI indexes data,the(σ_f)_(sur)distribution in the grinding surface layer for ND-UVAFG Inconel 718 samples was determined using the developed model,and then the fatigue crack initiation(FCI)sites were furtherpredicted.The predicted FCI sites corresponded well with the experimental results,therebyverifying this model.A strategy for improving the fatigue life was proposed in this work,which was to transfer the fatigue source from the machined surface to the bulk material by controlling the SI indexes.Finally,a critical condition of SI indexes that FCI sites appeared on the surface or in bulk material was given by fitting the predicted results.According to the critical condition,an SI field where FCI sites appeared in the bulk material could be obtained.In this field,thefatigue life of Inconel 718 samples could be improved by approximately 140%.

Damage Evolution of Ballastless Track Concrete Exposed to Flexural Fatigue Loads:The Application of Ultrasonic Pulse Velocity,Impact-echo and Surface Electrical Resistance Method

In order to clarify the fatigue damage evolution of concrete exposed to flexural fatigue loads,ultrasonic pulse velocity(UPV),impact-echo technology and surface electrical resistance(SR) method were used.Damage variable based on the change of velocity of ultrasonic pulse(Du) and impact elastic wave(Di)were defined according to the classical damage theory.The influences of stress level,loading frequency and concrete strength on damage variable were measured.The experimental results show that Du and Di both present a three-stages trend for concrete exposed to fatigue loads.Since impact elastic wave is more sensitive to the microstructure damage in stage Ⅲ,the critical damage variable,i e,the damage variable before the final fracture of concrete of Di is slightly higher than that of Du.Meanwhile,the evolution of SR of concrete exposed to fatigue loads were analyzed and the relationship between SR and Du,SR and Di of concrete exposed to fatigue loads were established.It is found that the SR of concrete was decreased with the increasing fatigue cycles,indicating that surface electrical resistance method can also be applied to describe the damage of ballastless track concrete exposed to fatigue loads.

A Novel On-Site-Real-Time Method for Identifying Characteristic Parameters Using Ultrasonic Echo Groups and Neural Network

On-site and real-time non-destructive measurement of elastic constants for materials of a component in a in-service structure is a challenge due to structural complexities,such as ambiguous boundary,variable thickness,nonuniform material properties.This work develops for the first time a method that uses ultrasound echo groups and artificial neural network(ANN)for reliable on-site real-time identification of material parameters.The use of echo groups allows the use of lower frequencies,and hence more accommodative to structural complexity.To train the ANNs,a numerical model is established that is capable of computing the waveform of ultrasonic echo groups for any given set of material properties of a given structure.The waveform of an ultrasonic echo groups at an interest location on the surface the structure with material parameters varying in a predefined range are then computed using the numerical model.This results in a set of dataset for training the ANN model.Once the ANN is trained,the material parameters can be identified simultaneously using the actual measured echo waveform as input to the ANN.Intensive tests have been conducted both numerically and experimentally to evaluate the effectiveness and accuracy of the currently proposed method.The results show that the maximum identification error of numerical example is less than 2%,and the maximum identification error of experimental test is less than 7%.Compared with currently prevailing methods and equipment,the proposefy the density and thickness,in addition to the elastic constants.Moreover,the reliability and accuracy of inverse prediction is significantly improved.Thus,it has broad applications and enables real-time field measurements,which has not been fulfilled by any other available methods or equipment.

Understanding the spatial interaction of ultrasounds based on three-dimensional dual-frequency ultrasonic field numerical simulation

A transient 3D model was established to investigate the effect of spatial interaction of ultrasounds on the dual-frequency ultrasonic field in magnesium alloy melt.The effects of insertion depth and tip shape of the ultrasonic rods,input pressures and their ratio on the acoustic field distribution were discussed in detail.Additionally,the spacing,angle,and insertion depth of two ultrasonic rods significantly affect the interaction between distinct ultrasounds.As a result,various acoustic pressure distributions and cavitation regions are obtained.The spherical rods mitigate the longitudinal and transversal attenuation of acoustic pressure and expand the cavitation volume by 53.7%and 31.7%,respectively,compared to the plate and conical rods.Increasing the input pressure will enlarge the cavitation region but has no effect on the acoustic pressure distribution pattern.The acoustic pressure ratio significantly affects the pressure distribution and the cavitation region,and the best cavitation effect is obtained at the ratio of 2:1(P15:P20).

Decoupling of temporal/spatial broadening effects in Doppler wind LiDAR by 2D spectral analysis

Pulse echo accumulation is commonly employed in coherent Doppler wind LiDAR(light detection and ranging)under the assumption of steady wind.Here,the measured spectral data are analyzed in the time dimension and frequency dimension to cope with the temporal wind shear and achieve the optimal accumulation time.A hardware-efficient algorithm combining the interpolation and cross-correlation is used to enhance the wind retrieval accuracy by reducing the frequency sampling interval and then reduce the spectral width calculation error.Moreover,the temporal broadening effect and spatial broadening effect are decoupled according to the strategy we developed.

Effective separation of coal gasification fine slag: Role of classification and ultrasonication in enhancing flotation

Effective separation of residual carbon and ash is the basis for the resource utilization of coal gasification fine slag(CGFS).The conventional flotation process of CGFS has the bottlenecks of low carbon recovery and high collector dosage.In order to address these issues,CGFS sample taken from Shaanxi,China was used as the study object in this paper.A new process of size classification-fine grain ultrasonic pretreatment flotation(SC-FGUF)was proposed and its separation effect was compared with that of wholegrain flotation(WGF)as well as size classification-fine grain flotation(SC-FGF).The mechanism of its enhanced separation effect was revealed through flotation kinetic fitting,flotation flow foam layer stability,particle size composition,surface morphology,pore structure,and surface chemical property analysis.The results showed that compared with WGF,pre-classification could reduce the collector dosage by 84.09%and the combination of pre-classification and ultrasonic pretreatment could increase the combustible recovery by 17.29%and up to 93.46%.The SC-FGUF process allows the ineffective adsorption of coarse residual carbon to collector during flotation stage to be reduced by pre-classification,and the tightly embedded state of fine CGFS particles is disrupted and surface oxidizing functional group occupancy was reduced by ultrasonic pretreatment,thus carbon and ash is easier to be separated in the flotation process.In addition,some of the residual carbon particles were broken down to smaller sizes in the ultrasonic pretreatment,which led to an increase in the stability of flotation flow foam layer and a decrease in the probability of detachment of residual carbon particles from the bubbles.Therefore,SCFGUF could increase the residual carbon recovery and reduce the flotation collector dosage,which is an innovative method for carbon-ash separation of CGFS with good application prospect.

Non-Kramers doublet ground state in a quaternary cubic compound PrRu_(2)In_(2)Zn_(18) investigated by ultrasonic measurements

We performed ultrasonic measurements on a quaternary cubic compound PrRu_(2)In_(2)Zn_(18) to explore the ground state properties derived from non-Kramers Γ_(3) doublet of Pr^(3+).PrRu_(2)In_(2)Zn_(18) is a quaternary derivative of the ternary compound PrRu_(2)Zn_(20) that exhibits a structural phase transition at T_S=138 K.In PrRu_(2)In_(2)Zn_(18),the Zn atoms at the 16c site in PrRu_(2)Zn_(20) are selectively replaced by In atoms.A monotonic increase was observed in the temperature dependence of elastic constants C_L=(C_(11)+2C_(12)+4C_(44))/3 and C_(T)=(C_(11)-C_(12)+C_(44))/3 in the temperature range around T_(S) to which an elastic softening was observed in(C_(11)-C_(12))/2 for PrRu_(2)Zn_(20).The disappearance of the softening indicates that the structural transition in PrRu_(2)Zn_(20) is suppressed by the substitution of Zn ions by In ones with a larger ionic radius.Alternatively,the C_(T) of PrRu_(2)In_(2)Zn_(18) exhibits a precursor Curie-type elastic softening toward low temperatures being responsible for the non-Kramers Γ_(3) ground state.We discuss the ground state and the evolution of the elastic properties of the different single-crystal samples of PrRu_(2)In_(2)Zn_(18) grown under different conditions.

Hybrid pedestrian positioning system using wearable inertial sensors and ultrasonic ranging

Pedestrian positioning system(PPS)using wearable inertial sensors has wide applications towards various emerging fields such as smart healthcare,emergency rescue,soldier positioning,etc.The performance of traditional PPS is limited by the cumulative error of inertial sensors,complex motion modes of pedestrians,and the low robustness of the multi-sensor collaboration structure.This paper presents a hybrid pedestrian positioning system using the combination of wearable inertial sensors and ultrasonic ranging(H-PPS).A robust two nodes integration structure is developed to adaptively combine the motion data acquired from the single waist-mounted and foot-mounted node,and enhanced by a novel ellipsoid constraint model.In addition,a deep-learning-based walking speed estimator is proposed by considering all the motion features provided by different nodes,which effectively reduces the cumulative error originating from inertial sensors.Finally,a comprehensive data and model dual-driven model is presented to effectively combine the motion data provided by different sensor nodes and walking speed estimator,and multi-level constraints are extracted to further improve the performance of the overall system.Experimental results indicate that the proposed H-PPS significantly improves the performance of the single PPS and outperforms existing algorithms in accuracy index under complex indoor scenarios.

Detection of internal crack growth in polyethylene pipe using guided wave ultrasonic testing

Despite the success of guided wave ultrasonic inspection for internal defect detection in steel pipes,its application on polyethylene(PE)pipe remains relatively unexplored.The growth of internal cracks in PE pipe severely affects its pressure-holding capacity,hence the early detection of internal cracks is crucial for effective pipeline maintenance strategies.This study extends the scope of guided wave-based ultrasonic testing to detect the growth of internal cracks in a natural gas distribution PE pipe.Laboratory experiments and a finite element model were planned to study the wave-crack interaction at different stages of axially oriented internal crack growth with a piezoceramic transducer-based setup arranged in a pitch-catch configuration.Mode dispersion analysis supplemented with preliminary experiments was performed to isolate the optimal inspection frequency,leading to the selection of the T(0,1)mode at 50-kHz for the investigation.A transmission index based on the energy of the T(0,1)mode was developed to trace the extent of simulated crack growth.The findings revealed an inverse linear correlation between the transmission index and the crack depth for crack growth beyond 20%crack depth.