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Commercial aircraft and aviation in general face in flight the appearance of turbulent fields, which requires changes in airplane trajectory in order to avoid as much as possible the danger to aircraft and passengers.

June, 2022
Dată început proiect
June, 2024
Dată sfârșit proiect

Technical details

UEFISCDI Program: National Research-Development and Innovation Plan 2015 – 2020 (PNCDI III)

Program 2: Increasing the competitiveness of the Romanian economy through research, development and innovation

Subprogram 2.1: Competitiveness through research, development and innovation

Project title: Innovative method of measuring the turbulence in wind tunnel based on Kolmogorov concept of energy dissipation magnitude with application in flight forecast

Project Code: PN-III-P2-2.1-PED-2021-4147

Acronym: KEDIMA

When ICAO Amendment 75 to Annex 3 became applicable on 18 November 2010, routine voice reporting of weather, a natural consequence of the subjectivity of those reports, was no longer required. To address these deficiencies, an in situ turbulence reporting algorithm based on ICAO standard EDR index (eddy dissipation rate) began to be implemented. During these years, the calculation method of this indicator has not yet stabilized firmly, new and new modifications of the algorithm are introduced in order for this direct calculation on the plane to improve. It is important for the conception of the project KEDIMA to emphasize that, for the airplane in turbulence field, for now the calculation of EDR it is not done on the basis of the well-known definition of turbulence energy given by Kolmogorov, but it is estimated based on the vertical component of the air speed, or based on the vertical component of the resulting acceleration of the aircraft.  The approach is effective, but remains an approximate one, maybe also because it wants to be independent from the airplane.  Thus, on the one hand, EDR is dependent on the aircraft that determines and transmits these indicators, to be useful not only as a diagnosis of what happens to the source aircraft, but also as a forecast, for the transmission of information, to other aircraft which would enter the respective turbulence field. On the other hand, EDR transmitted in situ is a surrogate of the concept of turbulence, since it is not calculated starting from the basic concept (of Kolmogorov). Thus, the purpose of the project is to demonstrate that the basic EDR index of atmospheric turbulence intensity can be measured and calculated in wind tunnel according to the basic Kolmogorov concept.

Results – Phase I

Phase 1 “Development of the theoretical basis and logistics for the demonstration of the method” includes the following activities:

Act. 1.1 – Evaluation of the methods of analysis and identification of turbulence intensity for aviation diagnosis and forecasting. State of the art;

Act. 1.2 – Theoretical study of the parameters to be measured in WT for the evaluation of turbulence characteristics (EDR, Richardson number).

Act 1.3 – Development of a general test program in WT for measuring and calculating EDR and Ri.

Act. 1.4 – Purchase of equipment.

Act. 1.5 – Dissemination of results. Publication of works, participation in national or international conferences.

Turbulence is a cascade process, through which kinetic energy is transferred from large eddies to small eddies, where it dissipates in heat, and the rate of transfer from large to small is the same as the rate of heat dissipation in the smallest eddies. Navier-Stokes motion of a fluid

it is subject to viscous and inertial constraints, the latter being given by the term (u ·)u, responsible for the generation of turbulence, i.e., continuous and disordered variations of physical quantities (velocity, position, energy). The heat transfer and the frictional tension inside the flow cannot be measured directly, but only indirectly, by means of the measurement of speed and temperature fluctuations, and by means of their correlations.

Table 1: Correspondence between the levels of intensity (severity) of the turbulence phenomenon and the values of the parameter EDR [m2/3/s], for transport aircraft, medium class* moving in typical flight conditions (altitude, speed, weight ).

conf. [18]≤ 0.15> 0.15 & ≤ 0.22> 0.22 & ≤ 0.34> 0.34> 0.22
conf. ICAO 2001 [19]≤ 0.10> 0.10 & ≤ 0.30> 0.30 & ≤ 0.50> 0.50> 0.30
conf. ICAO 2007 [17]≤ 0.10> 0.10 & ≤ 0.40> 0.40 & ≤ 0.70> 0.70> 0.40
conf. ICAO2020 [20] 0.10> 0.10 & 0.20> 0.20 & 0.45> 0.45> 0.20
conf. [21]≤ 0.10> 0.10 & ≤ 0.30> 0.30 & ≤ 0.50> 0.50> 0.30
conf. [22]≤ 0.14> 0.14 & ≤ 0.34> 0.34 & ≤ 0.54> 0.54> 0.34
conf. [23]≤ 0.03> 0.03 & ≤ 0.07> 0.07 & ≤ 0.16> 0.16> 0.07
conf. [24]≤ 0.14> 0.14 & ≤ 0.23> 0.23 & ≤ 0.46> 0.46> 0.23
conf. [25]≤ 0.14> 0.14 & ≤ 0.20> 0.20 & ≤ 0.41> 0.41> 0.20

* aircraft are considered to be part of the heavy class if their mass at take-off is greater than or equal to 136000 kg, they are part of the medium class if at take-off their mass is greater than 7000 kg, but less than 136000 kg and are part of from the light class if at take-off their mass is less than or equal to 7000 kg [26].

**MOG = “moderate or greater”, turbulence of moderate or greater intensity.

Results dissemination

1. New strategy for the safety and comfort of the passengers and aircraft crew during atmospheric turbulence – D. Enciu, I. Ursu, G. Tecuceanu, 7th European Conference on Structural Control (EACS 2022), 10-13 July 2022, Warsaw, Poland


An airplane trip can be psychological terrifying for any traveler. If, during the flight, the airplane meets a turbulent air front, then the scenario is perfect for a Hollywood movie, and the panic among passengers increases proportionally with the severity of the turbulence. In this paper, a new approach of the turbulence mitigation methodology is proposed based on a solid background using an active control vibration. The experimental model is represented by a realistic, elastic airplane wing model controlled by an electric linear servoactuator. The mathematical model is completed by numerical simulations and experiments in the subsonic wind tunnel upgraded with a turbulence generator. The qualification of an emergent technology of this type will have double impact: for the passengers – safety and mental comfort increasing given by the significant reduction of the dynamic effects produced by the turbulent field; for the airplane – weight optimization based on the loads control generated by the atmospheric turbulence.

2. On the evaluation of turbulence parameters in the Wind Tunnel – D. Enciu, I. Ursu, G. Tecuceanu,  International Conference of Aerospace Sciences „AEROSPATIAL 2022”, 13-14 October 2022, INCAS, Bucharest, Romania


Commercial aircraft and aviation, in general, face in flight the appearance of turbulent fields, which requires immediate changes in airplane trajectory in order to avoid as much as possible the danger to aircraft and passengers. Up until 2010, the International Civil Aviation Organization (ICAO) [1] considered AIREPs (an automated report of weather conditions encountered during flight) and PIREPs (pilot report about weather conditions encountered during flight) a turbulence intensity indicators. In order to avoid the subjectivity of those reports, which were dependent on the type of aircraft, air speed, pilot experience, the reaction of the crew and the movement of unsecured objects around the cabin, an in situ turbulence reporting algorithm based on ICAO standard EDR index (eddy dissipation rate) has been considered [2]. The EDR index is defined as the cubic root of the turbulence energy per unit time and mass [3]. In turbulent motion there is a cascading process, through which kinetic energy is transferred from the larger eddies to the lowest eddies, where it dissipates in heat, and the energy transfer rate from the larger eddies to a smaller ones is the same as the rate of energy dissipation in heat in the smallest eddies. This is how the process of dissipation and decay of fractal-generated turbulence takes place. The theoretical background is based on the Kolmogorov approach [4], [5]. The determination of the order of magnitude of the energy dissipation during the turbulent motion has as reference the procedure described in [6]. The intensity of turbulence will be identified in the INCAS subsonic wind tunnel (WT). The turbulence is produced by a passive turbulence generator [7]. A Big Data volume is in this way obtained and becomes the basis of statistical calculations for turbulence diagnosis and forecasting.

3. Towards improving passangers safety and comfort based on turbulence test in aerodynamic tunnelD. Enciu, I. Ursu, The 8th Conference of the Sustainable Solutions for Energy and Environment (EENVIRO 2022), 16-20 October, UTCB, Bucharest, Romania


First, the article outlines the elements of an ongoing research project, aiming to demonstrate that the basic ICAO standard EDR (Eddy Dissipation Rate) index of atmospheric turbulence intensity, defined as the cubic root of the turbulence energy per unit time and mass, can be measured and calculated in Wind Tunnel (WT) according to the basic Kolmogorov concept. This involves showing that EDR index calculated in WT, taking a sufficient number of velocity measuring points, can be an objective measure of turbulence intensity, independent of the body immersed in the fluid. Secondly, it is shown that these measurements are accompanied by intermediate active vibration control tests. For this purpose, a Turbulence Generator was built and installed in the WT and an intelligent wing model with implemented LQG active control was introduced in the WT. These two procedures, complementary in substance, aim to demonstrate the consistency of the flight approach based on the objectivity of this ICAO standard EDR index and the vibration reduction methodology in a turbulent atmospheric environment.

Results – Phase II

Phase 2 „Testing, evaluation and preliminary demonstration of the methodology” includes the following activities:

Act. 2.1 – Installation, calibration, and testing of existing and purchased hardware equipment

Act. 2.2 – Software development for data acquisition and analysis

Act. 2.3 – A first Big Data acquisition campaign for several air velocities in the WT, in the absence and presence of the wing model

Act. 2.4 – Data collection and analysis, EDR and Ri calculation

Act. 2.5 – Comparison between EDR and Ri data collected in WT and those from aviation standards corresponding to some types of aircraft

Act. 2.6 – Dissemination of results. Publication of works, participation in national or international conferences.

The measurement campaign carried out in the first Phase of the project aimed at establishing the necessary performances of the passive turbulence generator and establishing the functional parameters of the thermoanemometry installation, as well as the initial adjustments of the wind tunnel to find the flow region with the dissipative turbulent regime, according to the theory of flow behind a grid, and the optimal way to explore the region of interest. For this, a grid with square meshes was made, perpendicular to the flow direction in the experimental chamber of the subsonic tunnel.

For the simultaneous measurement of two components of the flow velocity in the subsonic wind tunnel, the DANTEC StreamLine Pro precision thermoanemometry system was used, with two independent channels and a 55R51 hot-wire x-probe. This has two filaments oriented at 90 degrees to each other and 45 degrees to the flow.

A traverse system was used to explore the flow, which performs a depth scan downstream the turbulence generator mounted in the experimental chamber. The passive turbulence generator produced a quasi-homogeneous turbulence in the experimental chamber and allowed the verification of the working hypotheses. The measurements demonstrated the occurrence of controlled turbulence, sufficiently intense, at working speeds of 15, 20 and 30 m/s.

For data processing, a MATLAB function was written and used. It receives as input data two components of the velocity, axial and lateral, and calculates the values for the kinematic viscosity of air at different temperatures based on an interpolated curve from standard values, as well as the turbulence kinetic energy, ε, the Reynolds number relative to the grid mesh size, and the flow turbulence index.

In conclusion, the test campaigns in the wind tunnel have materialized in a prodigious amount of data (big data), which, through processing during the next Phase, will allow the definition and testing of Kolmogorov’s theory of turbulence and will mark a significant step towards understanding the EDR metric as a parameter independent of fluid-structure influence.

Results dissemination

1. WoS Article

A. Toader, I. Ursu, D. Enciu, G. Tecuceanu, Towards nonconservative conditions for equilibrium stability. Applications to switching systems with control delay, Communications in Nonlinear Science and Numerical Simulation, 121 (2023) 107188

2. WoS Proceedings

D. Enciu, I. Ursu, Towards improving passengers safety and comfort based on turbulence tests in aerodynamic tunnel, IOP Conference Series: Earth and Environmental Science, 1185 012007

3. BDI Proceedings

I. Ursu, A. Toader,  G. Tecuceanu, D.Enciu, Input-to-state stability of a time-invariant system with control delay and additive disturbances, Proceedings in Applied Mathematics and Mechanics 2023;e202300152.

4. Input-to-state stability of a time-invariant system with control delay and additive disturbances – I. Ursu, A. Toader, G. Tecuceanu, D. Enciu, 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2023), 30 May – 2 June 2023, Dresden, Germany


We consider a class of linear time invariant systems with control delay and additive disturbances. A state predictive feedback method is first applied to compensate the actuator delay. In this way, a closed loop system free of delay is achieved. It allows to ensure input-to-state-stability of the closed loop system. Applications are given for the lateral-directional stability of an airplane with two controls, on the aileron and on the rudder, in correlation with compliance with some regulatory flight conditions.

5. On the stability of a time-invariant linear system with time-delay and disturbances with application to aerospace engineering – D. Enciu, I. Ursu, A. Toader, 30th Annual Conference on Applied and Industrial Mathematics (CAIM 2023), 14 – 18 September 2023, Iasi, Romania


The beauty of the mathematical equations is highlighted by presenting a practical, real application in controlling the flight stability of an airplane in a turbulent atmospheric field. This paper presents a linear mathematical model with actuator delay in the control chain and external disturbances. The time-delay is compensated by applying a state predictive feedback method and the perturbation is treated according to the basic Kolmogorov concept.

6. A Model for Turbulent Flow Energy Dissipation – practical aspects of turbulent flow investigations – C. Stoica, I. Ursu, D. Enciu, A. –M. Panait, the 40th “Caius Iacob” Conference on Fluid Mechanics and its Technical Applications, 19 – 20 October 2023, Bucharest, Romania


Abstract. This paper describes the authors recent practical explorations of turbulent flow physics, aiming to model the energy dissipation in accordance with the Kolmogorov theory. A simple experiment consisting in a static turbulence generating grid installed in the Subsonic Wind Tunnel at INCAS and a hot wire two filament probe coupled with a thermal probe mounted on a computer-controlled positioning system was used to scan the resulting turbulent flow. The chosen station points behind the grid, at two different heights (distances from the tunnel floor) and three airspeeds were set up so that the flow is explored in all its interesting regions- the chaotic turbulent, the dissipative quasi-ergodic and the outside flow, not masked by the turbulence generating grid. The final purpose of the work was to find the region where the ergodic assumption applies and for that region to compute the EDR – Eddy Dissipation Rate – as a measure of the behavior of uniformly turbulent flow. Turbulent flow modelling is important in order to mitigate the problems it poses to general aviation when occurring in free flight. Turbulence, especially of the so-called “clear air “type, is almost impossible to detect and generates extraneous structural loading on airframes, reducing their working life and MTBF – Mean Time Between Failures. Understanding, predicting and accurately measuring the phenomenon and its effects is therefore of the greatest importance to general aviation. The work is drafted in support of the activities in the KEDIMA project and describes part of the practical exploration phase, namely the data gathering procedure. Data collected in this measurement campaign will be used to test the fit to a Kolmogorov turbulent flow model and to calculate a most important parameter, the Eddie Dissipation Rate.

7. The stability of a linear time-invariant system with control delay. Application to the stability of the aircraft control chain in conditions of atmospheric turbulence – A. Toader, D. Enciu, I. Ursu, 20th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2023), 12-16 November 2023, Rome, Italy


A class of time-invariant linear systems with control delay and additive disturbances is considered. Through a predictive state feedback method, the control delay is compensated, reaching a closed-loop system without delay. Based on a theorem of F. Mazenc, S.-I. Niculescu, M. Krstic, stability is ensured in the presence of disturbances. The application is made on the control chain of an airplane, in the presence of Dryden-type atmospheric turbulence.

8. An innovative method to evaluate the Eddy Dissipation Rate (EDR) in a subsonic wind tunnel – preliminary results of KEDIMA project – A. A. Radu, A. –M. Panait, I. Ursu, invited lecture, Ovidius University of Constanța, 07 November 2023


Turbulence means random, unpredictable – chaotic fluid flow. This fluid motion is characterized by nonlinearity, vorticity, diffusivity, and energy dissipation. When it shows up in the atmosphere, turbulence becomes an aviation hazard. Over the course of time, it has been the most dangerous and difficult to tackle hazard, being the leading weather-related cause of aircraft accidents and incidents. The Eddy Dissipation Rate (EDR) is an aircraft-independent measure of turbulence intensity and it is defined as the cube root of the dissipation rate of turbulence kinetic energy. The larger the EDR is, the stronger the turbulence is. EDR is a parameter used to determine the amount of energy lost by the viscous forces in the turbulent flow and it represents the transmission rate of the disturbance energy from the larger-scale vortex to the smaller-scale vortex. It has become the atmospheric turbulence metric required by the International Civil Aviation Organization (ICAO) for routine turbulence reporting. One of the major objectives of KEDIMA project is to determine the EDR values in a subsonic wind tunnel. The experimental set-up encompassed a propeller, a grid, a hot-wire probe and temperature sensors. The analysis performed here relied on hot-wire data taken downstream of the grid in a flow with nominal mean velocities of 15, 20, and 30 m/s. These are preliminary results for KEDIMA project.

Additional information can be obtained at I.N.C.A.S. Bucharest
Research & development

Dr. math. Daniela Enciu
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