Turbulent thermal boundary layer on a permeable flat plate

Vigdorovich, I. I.

doi:10.1134/s1063776107060155

Cited by 4 publications

(6 citation statements)

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“…(4. 16)]. For this reason, logarithmic law (3.5) remains valid, which is completely confirmed by, e.g., experimental data that were obtained in [19] for the pre separation flow regime.…”

Section: Vanishing Of Skin Frictionsupporting

confidence: 65%

“…(7.1) into Eq. (3.2) and the passage to the limit for the first term of the expansion 16. Measurement results for the ratio of the Reynolds tensor components in the boundary layer in adverse pressure gradient from (a) [9] and (b) [19].…”

Section: Wall Regionmentioning

confidence: 99%

“…(1.1) and the kinematic viscosity of a fluid ν. The idea of the existence of such relations when the problem depends on a finite number of gov erning parameters was formulated for the first time in [13] and was then used in a number of works, e.g., [14][15][16]. The boundary layer equations together with the closure conditions constitute a boundary value problem for the mean velocity field, which is solved, after a special change of variables [17], by the method of matched asymptotic expansions at large values of the logarithm of the Reynolds number based on the boundary layer thickness.…”

Section: Introductionmentioning

confidence: 99%

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Self-similar turbulent boundary layer with imposed pressure gradient. Four flow regimes

Vigdorovich

2014

J. Exp. Theor. Phys.

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Self similar flows of an incompressible fluid in a turbulent boundary layer, when the free stream velocity is a power function (with the exponent m) of the longitudinal coordinate, have been studied. It has been shown that there are four different self similar flow regimes corresponding to four individual similarity parameters one of which is the known Clauser parameter and the three other parameters have been estab lished for the first time. At adverse pressure gradient, when the exponent m lies in a certain range depending on Reynolds number, the problem has two solutions with different values of the boundary layer thickness and skin friction; consequently, hysteresis in a pre separation flow is possible. Separation occurs not at the mini mal value of m that corresponds to the strongest adverse pressure gradient, but at m = -0.216 -0.4 + O( ), where Re p is the Reynolds number based on longitudinal pressure gradient. The theoretical results are in good agreement with experimental data.

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“…(4. 16)]. For this reason, logarithmic law (3.5) remains valid, which is completely confirmed by, e.g., experimental data that were obtained in [19] for the pre separation flow regime.…”

Section: Vanishing Of Skin Frictionsupporting

confidence: 65%

Section: Wall Regionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Self-similar turbulent boundary layer with imposed pressure gradient. Four flow regimes

Vigdorovich

2014

J. Exp. Theor. Phys.

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“…Shu and Pop [5] studied a steady forced convection thermal boundary layer over a flat plate with a predefined surface heat flux both analytically and numerically. Vigdorovich [6] investigated a turbulent thermal boundary layer on a permeable flat plate with transpiration. Kandula et al [7] performed three-dimensional simulations on a thermal boundary layer over a flat plate with surface temperature discontinuity.…”

Section: Introductionmentioning

confidence: 99%

Quantitative Visualization of the Thermal Boundary Layer of Forced Convection on a Heated or Cooled Flat Plate with a 30° Leading Edge Using a Mach-Zehnder Interferometer

Li¹,

Komiya²

2022

JFCMV

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This study focuses on the experimental measurements of the heat transfer coefficient over a flat plate with a 30˚ leading edge. Under forced convection by a hot/cold air and flow over a cooled/heated flat plate, the thermal boundary layer and its thickness are quantitatively visualized and measured using a Mach-Zehnder interferometer. In addition, the variation in the local heat transfer coefficient is evaluated experimentally with respect to the air flow velocity and temperature. Differences within the heat transfer performance between the plates are confirmed and discussed. As a result, the average heat transfer performance is about the same for the heated plate and the cooled plate under all air velocity conditions. This contrasts with the theoretical prediction in the case of low air velocity, the reason considered was that the buoyancy at the 30˚ leading edge blocked air from flowing across the surface of the plate.

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“…Closure condition (1) is derived without invoking any special hypotheses on the nature of the turbulent motion only from the reasoning of dimensional invariance [1]. Representations analogous to (1) are also valid for the other Reynolds stress components.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Scaling laws for turbulent boundary layer flows in favorable and adverse pressure gradient

Vigdorovich

2009

Proc Appl Math and Mech

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An analytical theory is proposed to describe incompressible plane and axisymmetric turbulent boundary layer flows in favorable and adverse pressure gradients for near-equilibrium conditions. Scaling laws for the mean velocity, the Reynolds stress components, and the skin friction have been established. A universal friction law makes it possible to represent the skin friction distributions corresponding to different Reynolds numbers and pressure gradients in terms of a function of one variable. The theory is based on general physical assumptions and does not involve any special hypotheses on the nature of the turbulent motion. Formulation of the problemWe consider a two-dimensional incompressible turbulent boundary layer flow on a plane profile or an axisymmetric body. In the latter case, we consider a thick body when the boundary layer thickness is much less than the distance from the axis of symmetry. We show that in the general case, the shear stress can be represented in the formHere, y is the distance from the wall, u is the rotational component of the longitudinal mean velocity in the boundary layer, i. e., the difference between the full mean velocity and its irrotational part, ∆ is the boundary layer thickness, U e is the velocity at the outer edge of the boundary layer, r is the radius specifying the body shape in the axisymmetric case (j = 1), and T is a usual function of the four variables and a functional of a curve L in the phase plane (z 1 , z 2 ) defined parametrically on the basis of the function γ(ξ) as z 1 = dγ/dξ, z 2 = d 2 γ/dξ 2 . Closure condition (1) is derived without invoking any special hypotheses on the nature of the turbulent motion only from the reasoning of dimensional invariance [1]. Representations analogous to (1) are also valid for the other Reynolds stress components.The Reynolds-averaged Navier-Stokes equations along with the closure conditions give us a well-posed boundary-value problem for the mean velocity field. We rewrite the equations for a dimensionless stream function Ψ(ξ, η) and seek the solution as ξ → ∞ [2,3]. Thus, the small parameter in the problem is the reciprocal of the logarithm of the Reynolds number based on a characteristic boundary layer thickness. In this limit process, the derivatives with respect to ξ can be neglected and in the outer region of the boundary layer, the problem is reduced to an ordinary differential equation for the function f (η) related to the velocity defectHere, L 0 is the point in the phase plane with coordinates (0, 0). In this limit process, the functional T specifying in equation (2) the turbulent shear stress degenerates to a usual function of two variables. Equation (2) depends on a single parameter γ, which varies within finite limits: −1 < γ ≤ 1. The solution has a singularity as γ → −1. In this case, the outer region of the boundary layer takes a two-layer structure. An intermediate region where the velocity obeys the square root law appears above the logarithmic sublayer which is typical of the flows at strong adverse pressu...

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Turbulent thermal boundary layer on a permeable flat plate

Cited by 4 publications

References 5 publications

Self-similar turbulent boundary layer with imposed pressure gradient. Four flow regimes

Self-similar turbulent boundary layer with imposed pressure gradient. Four flow regimes

Quantitative Visualization of the Thermal Boundary Layer of Forced Convection on a Heated or Cooled Flat Plate with a 30° Leading Edge Using a Mach-Zehnder Interferometer

Scaling laws for turbulent boundary layer flows in favorable and adverse pressure gradient

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Turbulent thermal boundary layer on a permeable flat plate

Cited by 4 publications

References 5 publications

Self-similar turbulent boundary layer with imposed pressure gradient. Four flow regimes

Self-similar turbulent boundary layer with imposed pressure gradient. Four flow regimes

Quantitative Visualization of the Thermal Boundary Layer of Forced Convection on a Heated or Cooled Flat Plate with a 30&#176; Leading Edge Using a Mach-Zehnder Interferometer

Scaling laws for turbulent boundary layer flows in favorable and adverse pressure gradient

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Product

Resources

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Quantitative Visualization of the Thermal Boundary Layer of Forced Convection on a Heated or Cooled Flat Plate with a 30° Leading Edge Using a Mach-Zehnder Interferometer