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# pressure strain

## Pressure strain

Linear Pressure-Strain Model

By default in ANSYS FLUENT , the pressure-strain term, , in Equation 4.9-1 is modeled according to the proposals by Gibson and Launder [ 108], Fu et al. [ 104], and Launder [ 176, 177].

The classical approach to modeling uses the following decomposition:

where is the slow pressure-strain term, also known as the return-to-isotropy term, is called the rapid pressure-strain term, and is the wall-reflection term.

The slow pressure-strain term, , is modeled as

The rapid pressure-strain term, , is modeled as

where = 0.60, , , , and are defined as in Equation 4.9-1, , , and .

The wall-reflection term, , is responsible for the redistribution of normal stresses near the wall. It tends to damp the normal stress perpendicular to the wall, while enhancing the stresses parallel to the wall. This term is modeled as

where , , is the component of the unit normal to the wall, is the normal distance to the wall, and , where and is the von Kármán constant (= 0.4187).

is included by default in the Reynolds stress model.

Low-Re Modifications to the Linear Pressure-Strain Model

When the RSM is applied to near-wall flows using the enhanced wall treatment described in Section 4.12.4, the pressure-strain model needs to be modified. The modification used in ANSYS FLUENT specifies the values of , , , and as functions of the Reynolds stress invariants and the turbulent Reynolds number, according to the suggestion of Launder and Shima [ 179]:

 (4.9-8) (4.9-9) (4.9-10) (4.9-11)

with the turbulent Reynolds number defined as . The flatness parameter and tensor invariants, and , are defined as

 (4.9-12) (4.9-13) (4.9-14)

is the Reynolds-stress anisotropy tensor, defined as

The modifications detailed above are employed only when the enhanced wall treatment is selected in the Viscous Model dialog box.

An optional pressure-strain model proposed by Speziale, Sarkar, and Gatski [ 334] is provided in ANSYS FLUENT . This model has been demonstrated to give superior performance in a range of basic shear flows, including plane strain, rotating plane shear, and axisymmetric expansion/contraction. This improved accuracy should be beneficial for a wider class of complex engineering flows, particularly those with streamline curvature. The quadratic pressure-strain model can be selected as an option in the Viscous Model dialog box.

This model is written as follows:

where is the Reynolds-stress anisotropy tensor defined as

The mean strain rate, , is defined as

The mean rate-of-rotation tensor, , is defined by

The constants are

The quadratic pressure-strain model does not require a correction to account for the wall-reflection effect in order to obtain a satisfactory solution in the logarithmic region of a turbulent boundary layer. It should be noted, however, that the quadratic pressure-strain model is not available when the enhanced wall treatment is selected in the Viscous Model dialog box.

Low-Re Stress-Omega Model

The low-Re stress-omega model is a stress-transport model that is based on the omega equations and LRR model [ 379]. This model is ideal for modeling flows over curved surfaces and swirling flows. The low-Re stress-omega model can be selected in the Viscous Model dialog box and requires no treatments of wall reflections. The closure coefficients are identical to the – model (Section 4.5.1), however, there are additional closure coefficients, and , noted below.

The low-Re stress-omega model resembles the – model due to its excellent predictions for a wide range of turbulent flows. Furthermore, low Reynolds number modifications and surface boundary conditions for rough surfaces are similar to the – model.

Equation 4.9-4 can be re-written for the low-Re stress-omega model such that wall reflections are excluded:

Pressure strain Linear Pressure-Strain Model By default in ANSYS FLUENT , the pressure-strain term, , in Equation 4.9-1 is modeled according to the proposals by Gibson and Launder [ 108],

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## Title: Pressure strain correlation modeling for turbulent flows

Abstract: Almost all investigations of turbulent flows in academia and in the industry utilize some degree of turbulence modeling. Of the available approaches to turbulence modeling Reynolds Stress Models have the highest potential to replicate complex flow phenomena. Due to its complexity and its importance in flow evolution modeling of the pressure strain correlation mechanism is generally regarded as the key challenge for Reynolds Stress Models. In the present work, the modeling of the pressure strain correlation for complex turbulent flows is reviewed. Starting from the governing equations we outline the theory behind models for both the slow and rapid pressure strain correlation. Established models for both these are introduced and their successes and shortcomings are illustrated using simulations and comparisons to experimental and numerical studies. Recent advances and developments in this context are presented. Finally, challenges and hurdles for pressure strain correlation modeling are outlined and explained in detail to guide future investigations.

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