Academic literature on the topic 'Green's Lag Entrainment Method'

Aerodynamic solver using the transonic small-disturbance (TSD) equation has frequently been used to perform practical aeroelastic analysis for many aircraft models. In the present study, the more accurate aeroelastic analysis solver using the TSD equation was developed by considering the viscous effects of the boundary-layer. The viscous effects were considered using Green's lag-entrainment equations and an inverse boundary-layer method. Through aerodynamic analyses for several aircraft wings, the viscous-inviscid interaction approach could improve the accuracy of the aerodynamic computation using the TSD equation. Finally, the aeroelastic characteristics were investigated using comparisons of the time responses between the inviscid and viscous flows.

In the present work, we formulate a new method to represent a given Flame Describing Function by analytical expressions. The underlying idea is motivated by the observation that different types of perturbations in a burner travel with different speeds and that the arrival of a perturbation at the flame is spread out over time. We develop an analytical model for the Flame Describing Function, which consists of a superposition of several Gaussians, each characterised by three amplitude-dependent quantities: central time-lag, peak value and standard deviation. These quantities are treated as fitting parameters, and they are deduced from the original Flame Describing Function by using error minimisation and nonlinear optimisation techniques. The amplitude-dependence of the fitting parameters is also represented analytically (by linear or quadratic functions). We test our method by using it to make stability predictions for a burner with well-documented stability behaviour (Noiray's matrix burner). This is done in the time-domain with a tailored Green's function approach.

In recent years, several studies have reported beneficial effects of transcranial alternating current stimulation (tACS) in experiments regarding sound and speech perception. A new development in this field is envelope-tACS: The goal of this method is to improve cortical entrainment to the speech signal by stimulating with a waveform based on the speech envelope. One challenge of this stimulation method is timing; the electrical stimulation needs to be phase-aligned with the naturally occurring cortical entrainment to the auditory stimuli. Due to individual differences in anatomy and processing speed, the optimal time-lag between presentation of sound and applying envelope-tACS varies between participants. To better investigate the effects of envelope-tACS, we performed a speech comprehension task with a larger amount of time-lags than previous experiments, as well as an equal amount of sham conditions. No significant difference between optimal stimulation time-lag condition and best sham condition was found. Further investigation of the data revealed a significant difference between the positive and negative half-cycles of the stimulation conditions but not for sham. However, we also found a significant learning effect over the course of the experiment which was of comparable size to the effects of envelope-tACS found in previous auditory tACS studies. In this article, we discuss possible explanations for why our findings did not match up with those of previous studies and the issues that come with researching and developing envelope-tACS.

Plant growth responses to cues such as light, temperature, and humidity enable the entrainment of the circadian rhythms with diurnal cycles. For example, the temperature variations between day and night affect plant growth and accompany the time lag to light cycle. Despite its importance, there has been no systematic investigation into time lags, and the mechanisms behind the entrainment of the circadian rhythms with multiple cycles remain unknown. Here, we investigated systemically the effects of the time lag on the circadian rhythm and growth in Arabidopsis thaliana. To investigate the entrainment status of the circadian clock, the rhythm of the clock gene CIRCADIAN CLOCK ASSOCIATION 1 (CCA1) was measured with a luciferase reporter assay. As a result, the rhythm was significantly modulated by the time lag with +10°C heating for 4 h every day but not −10°C cooling. A model based on coupled cellular oscillators successfully described these rhythm modulations. In addition, seedling growth depended on the time lag of the heating cycle but not that of the cooling cycle. Based on the relationship between the CCA1 rhythms and growth, we established an estimation method for the effects of the time lag. Our results found that plant growth relates to the CCA1 rhythm and provides a method by which to estimate the appropriate combination of light–dark and temperature cycles.

The circadian clock plays an important role in agriculture, especially in highly controlled environments, such as plant factories. However, multiple environmental factors have an extremely high degree of freedom, and it is difficult to experimentally search for the optimal design conditions. A recent study demonstrated that the effect of time lags between light and temperature cycles on plant growth could be predicted by the entrainment properties of the circadian clock in Arabidopsis thaliana. Based on this prediction, it was possible to control plant growth by adjusting the time lag. However, for application in plant factories, it is necessary to verify the effectiveness of this method using commercial vegetables, such as leaf lettuce. In this study, we investigated the entrainment properties of the circadian clock and the effect of the time lag between light and temperature cycles on circadian rhythms and plant growth in Lactuca sativa L. seedlings. For evaluation of circadian rhythms, we used transgenic L. sativa L. with a luciferase reporter in the experiment and a phase oscillator model in the simulation. We found that the entrainment properties for the light and temperature stimuli and the effects of time lags on circadian rhythm and growth were similar to those of A. thaliana. Moreover, we demonstrated that changes in growth under different time lags could be predicted by simulation based on the entrainment properties of the circadian clock. These results showed the importance of designing a cultivation environment that considers the circadian clock and demonstrated a series of methods to achieve this.

This thesis focuses on the prediction of favourable pressure gradient turbulent boundary layer flows. Particularly, the focus is on mild favourable pressure gradient turbulent boundary layers and relaminarising turbulent boundary layers (where the favourable pressure gradient is relatively large.) The calculations were performed on ANSYS FLUENT software, and the turbulence models used are the Spalart-Allamaras model and k-ω ​SST model. Furthermore, an integral method called Green's Lag Entrainment method is also used, which was originally designed for the prediction of turbulent flows. A MATLAB code was developed to simulate the test cases using Green's Lag Entrainment method (1977). A limited set of mild favourable pressure gradient experiments on a low-speed wind tunnel and the measurements were made using Particle Image Velocimetry. It should be noted that in the PIV experiment, the flow acceleration was mild (owing to mild FPG), and hence it stayed turbulent and did not relaminarise. In the present study, three re-laminarisation experiments/DNS computations were considered as test cases. 1)An initial zero-pressure turbulent boundary layer of Re_θ=1120=, ​subjected to a strong favourable pressure gradient over a region in the wind tunnel relaminarised at x = 73cm from the leading edge of the flat plate. This was originally studied by Patwardhan using experiments, and he also re-created in direct numerical simulations, and the agreement between them was good. We will refer to this case as the Low Re case of Patwardhan (2014). 2) Similarly, the initial zero pressure gradient turbulent boundary layer of Re_θ=1900, ​subjected to strong favourable pressure gradient different in magnitude (whilst keeping the same non-dimensional free-stream velocity distribution) over a much larger region than the Low Re case of Patwardhan re-laminarises at x = 87cm from the leading edge of the flat plate. Again, this also was originally studied by Patwardhan using experiments and direct numerical simulations, and the agreement between them was good. We will refer to this case as the High Re case of Patwardhan. 3)An experiment published in literature by Bourassa & Thomas (2009) where the initial Reynolds is much higher, perhaps the highest in the whole literature concerning re-laminarising flows of Re_θ=4590.​ Studies using RANS turbulence models and Green's Lag Entrainment method were performed on all the above cases. The overall conclusion is that while the prediction upstream of the onset of relaminarisation is fairly good. But it is interesting to see that the integral method agrees more closely with the experiments and DNS computations than the RANS turbulence models for all three cases upstream of relaminarisation. After relaminarisation, for all three cases, both the RANS turbulence models and the integral method fared poorly. Since the model didn't fare well downstream of the relaminarisation, another set of FLUENT calculations was devised where the flow was calculated without any turbulence model, i.e., a laminar model is solved. The results from these laminar calculations showed a good agreement in the relaminarisation zone for Patwarhdan's Low and High Re cases. This is consistent with the Ranjan & Narasimha (2018) improved version of the quasi-laminar theory, which was developed to explain the later stages of flow relaminarisation. References: [1]   Green J. E., Weeks D. J., Brooman J. W. F., “Prediction of Turbulent Boundary Layers and Wakes in Compressible Flow by Lag Entrainment Method, A. R. C., R & M. No. 3791, 1977. [2] Patwardhan S. S., “Effect of favourable pressure gradients on turbulence in boundary layers”, A Ph.D. Thesis, Indian Institute of Science, Bangalore, 2014. [3] Bourassa, C. & Thomas, F. O., An experimental investigation of a highly accelerated turbulent boundary layer. J. Fluid Mech. 634, 359–404. 2009. [4]   Rajesh Rajan & Roddam Narasimha, "An assessment of the two-layer quasi-laminar theory of relaminarization through recent high-Re accelerated TBL experiments, arXiv preprint arXiv:1611.09746, 2018.

Transitional boundary layer parameters in zero and variable pressure gradient flows, typical of turbomachinery applications, are predicted using an integral method of the linear combination type. The code used is that of Dey and Narasimha and the turbulent layer is calculated by a lag-entrainment method. The predictions of test data represent an improvement upon earlier methods; although reasonable agreement is obtained for these low Reynolds number test cases further refinement of predictive correlations to account for free-stream turbulence effects on laminar boundary layers and transition inception is indicated. The transitional parameters are found to be particularly sensitive to the initial conditions selected for the turbulent layer. Techniques are identified for overcoming this sensitivity and for adequately representing the transition region. Free-stream turbulence effects are quite strong, particularly on the velocity profile of the laminar layer. Modifications to laminar methods are advocated to account for the strong effects on the velocity profile and the early formation of turbulent spots.

The axial exhaust downstream of a gas turbine in a combined cycle plant includes an annular diffuser with struts and a closed hub carrying the turbine rotor bearing. Flow separation occurs at the blunt end of the hub and can also occur on the casing wall and on the struts. A zonal method for the computation of the flow in such diffusers is described. A throughflow code is used for the axisymmetric core flow, a lag-entrainment-integral-method for the blockage of the boundary layers and the wake of the hub. For cases with separated flow a semi-inverse procedure for the coupling is needed. Additional empirical information is required such as a term related to the closing of the hub separation, correlations for the skin friction and the form factor and an estimate of the losses based on a dissipation coefficient. Experimental data from annular diffuser test cases from the literature and from a typical turbine diffuser are used to validate the method. The location of the separation in the diffuser is calculated correctly and the prediction of the pressure recovery is promising, suggesting that this is a useful tool for the preliminary design of highly loaded annular configurations.

The control of profile drag on a circular cylinder was studied experimentally at Reynolds numbers, ranging from 160 to 400, using an acoustic active control system. The investigation has been carried by, quantitatively, hot-wire to measure the mean and fluctuating velocities and, qualitatively, by using smoke-wire flow visualization technique to examine the formation of the flow field down-stream of the cylinder. The present active control method is able to influence the rate of entrainment from main flow into the wake flow. When the Reynolds number is relatively small, it is the size of the cylinder and the induced sound field velocity as well as Reynolds number which are the significant parameters in determining the controlling reverse and optimum phase lag angels. The reported control strategy is able to alter the profile drag of a two-dimensional circular cylinder. At optimum lag angle and low Reynolds number the profile drag was reduced by 9%.

The control of vortex shedding and wake from a circular cylinder was studied experimentally at Reynolds numbers, ranging from 160 to 400, using an acoustic active control system. The investigation has been carried by, quantitatively, hot-wire to measure the mean and fluctuating velocities and, qualitatively, by using smoke-wire flow visualization technique to examine the formation of the flow field downstream of the cylinder. The present active control method is able to influence the rate of entrainment from main flow into the wake flow. When the Reynolds number is relatively small, it is the size of the cylinder and the induced sound field velocity rather than Reynolds number which are the significant parameters in determining the controlling reverse and optimum phase lag angels.

The study of liquid dynamics in LNG tanks is getting more and more important with the actual trend of LNG tankers sailing with partially filled tanks. The effect of sloshing liquid in the tanks on pressure levels at the tank walls and on the overall ship motion indicates the relevance of an accurate simulation of the fluid behaviour. This paper presents the simulation of sloshing LNG by a compressible two-phase model and the validation of the numerical model on model-scale sloshing experiments. The details of the numerical model, an improved Volume Of Fluid (iVOF) method, are presented in the paper. The program has been developed initially to study the sloshing of liquid fuel in spacecraft. The micro-gravity environment requires a very accurate and robust description of the free surface. Later, the numerical model has been used for calculations for different offshore applications, including green water loading. The model has been extended to take two-phase flow effects into account. These effects are particularly important for sloshing in tanks. The complex mixture of the liquid and gas phase around the free surface imposes a challenge to numerical simulation. The two-phase flow effects (air entrapment and entrainment) are strongly affected by both the filling ratio of the tank and the irregular motion of the tank in typical offshore conditions. The velocity field and pressure distribution around the interface of air and LNG, being continuous across the free surface, requires special attention. By using a newly-developed gravity-consistent discretisation, spurious velocities at the free surface are prevented. The equation of state applied in the compressible cells in the flow domain induces the need to keep track on the pressure distribution in both phases, as the gas density is directly coupled to the gas pressure. The numerical model is validated on a 1:10 model-scale sloshing model experiment. The paper shows the results of this validation for different filling ratios and for different types of motion of the sloshing tank.