Reynolds Analogy Based on the Theory of Stochastic Equations and Equivalence of Measures

Dmitrenko, A. V.

doi:10.1007/s10891-021-02296-8

Cited by 9 publications

(4 citation statements)

References 40 publications

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“…d(ρ)col st dτ So, the formula for critical Reynolds number was written as and in according with data [52][53][54][55][56][57], the theoretical value for critical Reynolds number is U m is the average velocity on the jet axis, h the width of the initial section of the jet. The definition of the value of the critical point is found from the equation…”

Section: Critical Reynolds Number and Critical Pointmentioning

confidence: 99%

“…, here L is the scale of disturbance. So using these formulas, the equation for the critical point in the plane jet was determined [58]: and in according with data [52][53][54][55][56][57][58], the theoretical value for critical point Then, taking into account the definition of the velocity u 1 of laminar motion in a plane jet [61,64].…”

Section: Critical Reynolds Number and Critical Pointmentioning

confidence: 99%

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An estimation of the velocity profile for the laminar-turbulent transition in the plane jet on the basis of the theory of stochastic equations and equivalence of measures

Dmitrenko

Selivanov

2022

Adv. Aerodyn.

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The theory of stochastic equations and the theory of equivalence of measures previously applied to flows in the boundary layer and in the pipe are considered to calculate the velocity profile of the flat jet. This theory previously made it possible to determine the critical Reynolds number and the critical point for the flow of the plane jet. Here based on these results the analytical dependence for the index of the velocity profile is derived. Velocity profiles are calculated for a laminar-turbulent transition in the jet. This formula reliably reflects an increase of the energy transferred from a deterministic state to a random one with an increase of the index of the velocity profile. Results show satisfactory agreement with the known experimental data for the velocity profile of the flat jet. Using obtained results it is possible to determine the location of technical devices for laminarization of the flow in the jet. This is important both for reducing friction in the flow around aerodynamic vehicles and for maintaining the jet profile if it is necessary to ensure the stability of the flow characteristics. Also the obtained relations can be useful for researching of the processes in combustion chambers, in the case of welding and in other technical devices.

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Section: Critical Reynolds Number and Critical Pointmentioning

confidence: 99%

Section: Critical Reynolds Number and Critical Pointmentioning

confidence: 99%

An estimation of the velocity profile for the laminar-turbulent transition in the plane jet on the basis of the theory of stochastic equations and equivalence of measures

Dmitrenko

Selivanov

2022

Adv. Aerodyn.

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“…The profiles of averaged velocity and temperature were also determined in [91][92][93].The friction coefficients and heat transfer coefficients were obtained in [84,85]. Also, the second-order correlations were presented in [91,[93][94][95][96][97][98]. The correlation dimension of the attractor in the boundary layer was calculated in [99,100].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Equations of Hydrodynamic Theory of Plasma

Dmitrenko

2024

Fluids

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Stochastic equations of the hydrodynamic theory of plasma are presented in relation to strong external fields. It is shown that the use of these stochastic equations makes it possible to obtain new theoretical solutions for plasma as a result of its heating in a strong external electric field. Theoretical solutions for the conductivity of turbulent plasma when heated in an external electric field of 100 V/cm are considered. Calculated values for the electron drift velocity, electron mobility, electron collision frequency, and the Coulomb logarithm in the region of strong electric fields are obtained. Here we consider experiments on turbulent heating of hydrogen plasma in the range of electric field strength of 100 < E < 1000. The calculated dependences of plasma conductivity are in satisfactory agreement with experimental data for heating plasma in a strong electric field. It is shown that the plasma turbulence in the region of strong electric fields E ~1000 V/cm is close to 100%. For the first time, it is confirmed that the derived dependences for collision frequency, drift velocity, and other values include the degree of turbulence of plasma, which makes it possible to correctly describe experimental data for heating plasma even with strong electric fields. In addition, it was determined that the scatter of experimental data may be associated with the variability of the function in the expression for the heat flux density. For the first time, it is shown theoretically that the experimentally determined fact of the possibility of the existence of an approximate constancy of plasma conductivity in the region E = 100–1000 V/cm can occur with an error of ~30%. The results show significant advantages of the stochastic hydrodynamic plasma theory over other methods that are not yet able to satisfactorily as well as qualitatively and quantitatively predict long-known experimental data while taking into account the degree of turbulence.

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“…The Reynolds analogy between friction and heat transfer in a pipe and on a plate in turbulent flow was studied using the solution of stochastic equations [7].…”

Section: Introductionmentioning

confidence: 99%

Euler’s Equation of Continuity: Additional Terms of High Order of Smallness—An Overview

Ovsyannikov

2021

Fluids

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Professor N.E. Zhukovsky was a famous Russian mechanic and engineer. In 1876 he defended his master’s thesis at Moscow University. At a careful reading of N.E. Zhukovsky’s master’s thesis in 1997, V.A. Bubnov—a professor at the Moscow City Pedagogical University—discovered terms of the second order of smallness in the continuity equation for an incompressible fluid. Zhukovsky calculated them, but did not use the amount of substance in the balance. Ten years later, the author found high-order terms in Euler’s derivation of the 1752 continuity equation for an incompressible fluid. The physical meaning of the additional terms became clear after the derivation in 2006 of the continuity equation with terms of high order of smallness for a compressible gas. The higher order terms of the smallness of the continuity equation penetrate into the inhomogeneous part of the wave equation and lead to the generation of self-oscillations, vibrations, sound, and the initial stage of turbulent pulsations. The stochastic approach ensured success in modeling turbulent flows. The use of high-order terms of smallness of the Euler continuity equation makes it possible to transfer the description of some part of the motions from the stochastic part of the equation to the deterministic part. The article contains a review of works with the derivation of the inhomogeneous wave equation. These works use additional terms of a high order of smallness in the continuity equation.

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Reynolds Analogy Based on the Theory of Stochastic Equations and Equivalence of Measures

Cited by 9 publications

References 40 publications

An estimation of the velocity profile for the laminar-turbulent transition in the plane jet on the basis of the theory of stochastic equations and equivalence of measures

An estimation of the velocity profile for the laminar-turbulent transition in the plane jet on the basis of the theory of stochastic equations and equivalence of measures

Stochastic Equations of Hydrodynamic Theory of Plasma

Euler’s Equation of Continuity: Additional Terms of High Order of Smallness—An Overview

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