Simulation of transitional flows through a turbine blade cascade with heat transfer for various flow conditions

Straka, Petr; Příhoda, Jaromír; Kožíšek, Martin; Fürst, Jiří

doi:10.1051/epjconf/201714302118

Cited by 8 publications

(4 citation statements)

References 13 publications

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“…This enables one to focus just on the flow through one spatial period, which contains only one profile-see domain Ω and profile P on Figure 1. This approach is used, for example, in the previous papers [9][10][11] (numerical analysis and numerical calculations) and other works [1][2][3][4][5][6][7][8]12 (qualitative analysis). We use the same geometrical description of the flow field as in the papers [6][7][8] : We assume that the fluid basically flows into the cascade through the straight line 𝛾 in (the x 2 -axis, the inflow) and leaves the cascade through the straight line 𝛾 out , whose equation is x 1 = d (the outflow).…”

Section: The Reduced Problem To One Spatial Periodmentioning

confidence: 99%

Existence of steady flows of a viscous incompressible fluid through a profile cascade and their L^r‐regularity

Neustupa

2021

Math Methods in App Sciences

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The paper deals with the steady Navier-Stokes problem, describing a flow of a viscous incompressible fluid through a spatially periodic profile cascade. Using the reduction to one spatial period Ω, the problem is formulated by means of boundary conditions of three types: the conditions of periodicity on curves Γ 0 and Γ 1 , the Dirichlet boundary conditions on Γ in and Γ P , and an artificial boundary condition on Γ out (see Figure 1). For "small data," we consider the so-called "do nothing" boundary condition on Γ out and prove the existence and uniqueness of a weak and strong solution in the L r -framework. For "large data," we consider an appropriately modified "do nothing" condition on Γ out and prove the existence of a weak and strong solution.

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Section: The Reduced Problem To One Spatial Periodmentioning

confidence: 99%

Existence of steady flows of a viscous incompressible fluid through a profile cascade and their L^r‐regularity

Neustupa

2021

Math Methods in App Sciences

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“…This approach is used e.g. in papers [10]- [12] and [34]- [36], where the qualitative analysis of corresponding mathematical models is studied, and in papers [8], [22], [39], devoted to the numerical analysis of the models or corresponding numerical calculations.…”

Section: Introductionmentioning

confidence: 99%

The maximum regularity property of the steady Stokes problem associated with a flow through a profile cascade

Neustupa¹

2020

Preprint

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We deal with a steady Stokes-type problem, associated with a flow of a Newtonian incompressible fluid through a spatially periodic profile cascade. The used mathematical model is based on the reduction to one spatial period, represented by a bounded 2D domain Ω. The corresponding Stokes-type problem is formulated by means of the Stokes equation, equation of continuity and three types of boundary conditions: the conditions of periodicity on the curves Γ 0 and Γ 1 , the Dirichlet boundary conditions on Γ in and Γ p and an artificial "do nothing"-type boundary condition on Γ out . (See Fig. 1.) We explain on the level of weak solutions the sense in which the last condition is satisfied. We show that, although domain Ω is not smooth and different types of boundary conditions meet in the corners of Ω, the considered problem has a strong solution with the so called maximum regularity property.

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“…This approach is used e.g. in [8], [20], [36], where the authors present the numerical analysis of the models or corresponding numerical simulations, and in the papers, [10]- [12] and [29]- [31], devoted to theoretical analysis of the mathematical models.…”

Section: Introductionmentioning

confidence: 99%

The maximum regularity property of the steady Stokes problem associated with a flow through a profile cascade in $L^r$-framework

Neustupa¹

2020

Preprint

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The paper deals with the Stokes problem, associated with a flow of a viscous incompressible fluid through a spatially periodic profile cascade. We use results from [32] (the maximum regularity property in the L 2 -framework) and [33] (the weak solvability in W 1,r ), and extend the findings on the maximum regularity property to the general L r -framework (for 1 < r < ∞). Using the reduction to one spatial period Ω, the problem is formulated by means of boundary conditions of three types: the conditions of periodicity on curves Γ 0 and Γ 1 , the Dirichlet boundary conditions on Γ in and Γ P and an artificial "do nothing"-type boundary condition on Γ out (see Fig. 1). We show that, although domain Ω is not smooth and different types of boundary conditions "meet" in the vertices of ∂Ω, the considered problem has a strong solution with the maximum regularity property for "smooth" data. We explain the sense in which the "do nothing" boundary condition is satisfied for both weak and strong solutions.

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Simulation of transitional flows through a turbine blade cascade with heat transfer for various flow conditions

Cited by 8 publications

References 13 publications

Existence of steady flows of a viscous incompressible fluid through a profile cascade and their L^r‐regularity

Existence of steady flows of a viscous incompressible fluid through a profile cascade and their L^r‐regularity

The maximum regularity property of the steady Stokes problem associated with a flow through a profile cascade

The maximum regularity property of the steady Stokes problem associated with a flow through a profile cascade in $L^r$-framework

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Simulation of transitional flows through a turbine blade cascade with heat transfer for various flow conditions

Cited by 8 publications

References 13 publications

Existence of steady flows of a viscous incompressible fluid through a profile cascade and their Lr‐regularity

Existence of steady flows of a viscous incompressible fluid through a profile cascade and their Lr‐regularity

The maximum regularity property of the steady Stokes problem associated with a flow through a profile cascade

The maximum regularity property of the steady Stokes problem associated with a flow through a profile cascade in $L^r$-framework

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Product

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Existence of steady flows of a viscous incompressible fluid through a profile cascade and their L^r‐regularity

Existence of steady flows of a viscous incompressible fluid through a profile cascade and their L^r‐regularity