Supersonic Flow Calculations Using a Reynolds-Stress and a Thermal Eddy Diffusivity Turbulence Model

1994 ◽  
Vol 116 (3) ◽  
pp. 469-476 ◽  
Author(s):  
T. P. Sommer ◽  
R. M. C. So ◽  
H. S. Zhang
Keyword(s):  
Turbulence Model ◽  
Eddy Diffusivity ◽  
Supersonic Flows ◽  
Equation Model ◽  
Second Order ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Real Gas Effects ◽  
Prandtl Numbers ◽  
Near Wall

A second-order model for the velocity field and a two-equation model for the temperature field are used to calculate supersonic boundary layers assuming negligible real gas effects. The modeled equations are formulated on the basis of an incompressible assumption and then extended to supersonic flows by invoking Morkovin’s hypothesis, which proposes that compressibility effects are completely accounted for by mean density variations alone. In order to calculate the near-wall flow accurately, correcting functions are proposed to render the modeled equations asymptotically consistent with the behavior of the exact equations near the wall and, at the same time, display the proper dependence on the molecular Prandtl number. Thus formulated, the near-wall second-order turbulence model for heat transfer is applicable to supersonic flows with different Prandtl numbers. The model is validated against supersonic flows with free-stream Mach numbers as high as 10 and wall temperature ratios as low as 0.3. Among the flow cases considered, the momentum thickness Reynolds number varies from ~4000 to ~21,000. Good correlation with measurements of mean velocity and temperature is obtained. Discernible improvements in the law-of-the-wall are observed, especially in the range where the log-law applies.

Velocity and Temperature Profiles in Turbulent Boundary Layer Flows Experiencing Streamwise Pressure Gradients

1997 ◽  
Vol 119 (3) ◽  
pp. 433-439 ◽  
Author(s):  
R. J. Volino ◽  
T. W. Simon
Keyword(s):  
Experimental Data ◽  
Pressure Gradient ◽  
Velocity Profiles ◽  
Temperature Profiles ◽  
Pressure Gradients ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Prandtl Numbers ◽  
Energy Equations ◽  
Near Wall

The standard turbulent law of the wall, devised for zero pressure gradient flows, has been previously shown to be inadequate for accelerating and decelerating turbulent boundary layers. In this paper, formulations for mean velocity profiles from the literature are applied and formulations for the temperature profiles are developed using a mixing length model. These formulations capture the effects of pressure gradients by including the convective and pressure gradient terms in the momentum and energy equations. The profiles which include these terms deviate considerably from the standard law of the wall; the temperature profiles more so than the velocity profiles. The new profiles agree well with experimental data. By looking at the various terms separately, it is shown why the velocity law of the wall is more robust to streamwise pressure gradients than is the thermal law of the wall. The modification to the velocity profile is useful for evaluation of more accurate skin friction coefficients from experimental data by the near-wall fitting technique. The temperature profile modification improves the accuracy with which one may extract turbulent Prandtl numbers from near-wall mean temperature data when they cannot be determined directly.

Near-Wall Modeling of Turbulent Convective Heat Transport in Film Cooling of Turbine Blades With the Aid of Direct Numerical Simulation Data

2002 ◽  
Vol 124 (3) ◽  
pp. 485-498 ◽  
Author(s):  
Djamel Lakehal
Keyword(s):  
Prandtl Number ◽  
Film Cooling ◽  
Eddy Viscosity ◽  
Turbulent Transport ◽  
Transport Coefficients ◽  
Turbine Blades ◽  
Eddy Diffusivity ◽  
Equation Model ◽  
Turbulent Prandtl Number ◽  
Near Wall

The paper presents novel developments in the DNS-based, turbulence modeling strategy of Lakehal et al. developed for calculating jets in crossflow. The particular features of the model include: 1) dynamic coupling of the high-Re k−ε with a one-equation model resolving the near-wall viscosity-affected layer; 2) inclusion of the anisotropy of turbulent transport coefficients for all transport equations; 3) near-wall variation of the turbulent Prandtl number as a function of the local Reynolds number. Most of the important aspects of the proposed model are based on known DNS statistics of channel and boundary layer flows. The model is validated against experiments for the case of film cooling of a flat plate, where coolant air is injected from a row of streamwise inclined jets. Excellent results were obtained for this configuration as compared to earlier numerical investigations reported in the open literature. The model is then extended to calculate film cooling of a symmetrical turbine blade by a row of laterally injected jets for various blowing rates. Comparison of the calculated and measured wall-temperature distributions show that only with this anisotropy eddy-viscosity/diffusivity model can the spanwise spreading of the temperature field be well predicted and the strength of the secondary vortices reduced. Furthermore, results of additional calculations show that combining the anisotropy eddy viscosity model with the DNS-based relation for turbulent Prandtl number promotes the eddy diffusivity of heat vis-a`-vis that of momentum further, leading to an enhanced spanwise spreading of the jet. The performance of this new approach improves with increasing blowing rate.

scholarly journals Turbulence model performance for ventilation components pressure losses

2021 ◽  
Author(s):  
Karsten Tawackolian ◽  
Martin Kriegel
Keyword(s):  
Reynolds Number ◽  
Turbulence Model ◽  
Pressure Loss ◽  
Low Reynolds Number ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Test Case ◽  
Pressure Losses ◽  
Loss Coefficients ◽  
Near Wall

AbstractThis study looks to find a suitable turbulence model for calculating pressure losses of ventilation components. In building ventilation, the most relevant Reynolds number range is between 3×104 and 6×105, depending on the duct dimensions and airflow rates. Pressure loss coefficients can increase considerably for some components at Reynolds numbers below 2×105. An initial survey of popular turbulence models was conducted for a selected test case of a bend with such a strong Reynolds number dependence. Most of the turbulence models failed in reproducing this dependence and predicted curve progressions that were too flat and only applicable for higher Reynolds numbers. Viscous effects near walls played an important role in the present simulations. In turbulence modelling, near-wall damping functions are used to account for this influence. A model that implements near-wall modelling is the lag elliptic blending k-ε model. This model gave reasonable predictions for pressure loss coefficients at lower Reynolds numbers. Another example is the low Reynolds number k-ε turbulence model of Wilcox (LRN). The modification uses damping functions and was initially developed for simulating profiles such as aircraft wings. It has not been widely used for internal flows such as air duct flows. Based on selected reference cases, the three closure coefficients of the LRN model were adapted in this work to simulate ventilation components. Improved predictions were obtained with new coefficients (LRNM model). This underlined that low Reynolds number effects are relevant in ventilation ductworks and give first insights for suitable turbulence models for this application. Both the lag elliptic blending model and the modified LRNM model predicted the pressure losses relatively well for the test case where the other tested models failed.

On the criteria for reverse transition in a two-dimensional boundary layer flow

1969 ◽  
Vol 35 (2) ◽  
pp. 225-241 ◽  
Author(s):  
M. A. Badri Narayanan ◽  
V. Ramjee
Keyword(s):  
Longitudinal Velocity ◽  
Outer Region ◽  
Transition Process ◽  
Velocity Profiles ◽  
Wall Region ◽  
Two Dimensional ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Reverse Transition ◽  
Turbulence Decay

Experiments on reverse transition were conducted in two-dimensional accelerated incompressible turbulent boundary layers. Mean velocity profiles, longitudinal velocity fluctuations $\tilde{u}^{\prime}(=(\overline{u^{\prime 2}})^{\frac{1}{2}})$ and the wall-shearing stress (TW) were measured. The mean velocity profiles show that the wall region adjusts itself to laminar conditions earlier than the outer region. During the reverse transition process, increases in the shape parameter (H) are accompanied by a decrease in the skin friction coefficient (Cf). Profiles of turbulent intensity (u’2) exhibit near similarity in the turbulence decay region. The breakdown of the law of the wall is characterized by the parameter \[ \Delta_p (=\nu[dP/dx]/\rho U^{*3}) = - 0.02, \] where U* is the friction velocity. Downstream of this region the decay of $\tilde{u}^{\prime}$ fluctuations occurred when the momentum thickness Reynolds number (R) decreased roughly below 400.

Turbulent boundary-layer interaction with a shock wave at a compression corner

1984 ◽  
Vol 143 ◽  
pp. 23-46 ◽  
Author(s):  
S. Agrawal ◽  
A. F. Messiter
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Turbulent Boundary Layer ◽  
Momentum Equation ◽  
Wall Layer ◽  
Oblique Shock Wave ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Compression Corner ◽  
Boundary Layer Interaction

The local interaction of an oblique shock wave with an unseparated turbulent boundary layer at a shallow two-dimensional compression corner is described by asymptotic expansions for small values of the non-dimensional friction velocity and the flow turning angle. It is assumed that the velocity-defect law and the law of the wall, adapted for compressible flow, provide an asymptotic representation of the mean velocity profile in the undisturbed boundary layer. Analytical solutions for the local mean-velocity and pressure distributions are derived in supersonic, hypersonic and transonic small-disturbance limits, with additional intermediate limits required at distances from the corner that are small in comparison with the boundary-layer thickness. The solutions describe small perturbations in an inviscid rotational flow, and show good agreement with available experimental data in most cases where effects of separation can be neglected. Calculation of the wall shear stress requires solution of the boundary-layer momentum equation in a sublayer which plays the role of a new thinner boundary layer but which is still much thicker than the wall layer. An analytical solution is derived with a mixing-length approximation, and is in qualitative agreement with one set of measured values.

Heat transport by parallel-roll convection in a rectangular container

1987 ◽  
Vol 185 ◽  
pp. 205-234 ◽  
Author(s):  
R. W. Walden ◽  
Paul Kolodner ◽  
A. Passner ◽  
C. M. Surko
Keyword(s):  
Rayleigh Number ◽  
Heat Transport ◽  
Critical Rayleigh Number ◽  
Equation Model ◽  
Onset Of Convection ◽  
Infinite Layer ◽  
Lateral Extent ◽  
Prandtl Numbers ◽  
Rayleigh Numbers ◽  
Good Agreement

Heat-transport measurements are reported for thermal convection in a rectangular box of aspect’ ratio 10 x 5. Results are presented for Rayleigh numbers up to 35Rc, Prandtl numbers between 2 and 20, and wavenumbers between 0.6 and 1.0kc, where Rc and kc are the critical Rayleigh number and wavenumber for the onset of convection in a layer of infinite lateral extent. The measurements are in good agreement with a phenomenological model which combines the calculations of Nusselt number, as a function of Rayleigh number and roll wavenumber for two-dimensional convection in an infinite layer, with a nonlinear amplitude-equation model developed to account for sidewell attenuation. The appearance of bimodal convection increases the heat transport above that expected for simple parallel-roll convection.

Density fluctuation correlations in free turbulent binary mixing

1994 ◽  
Vol 279 ◽  
pp. 239-278 ◽  
Author(s):  
P. Chassaing ◽  
G. Harran ◽  
L. Joly
Keyword(s):  
Density Fluctuation ◽  
Fluid Motion ◽  
Variable Density ◽  
Second Order ◽  
Decay Rates ◽  
Entrainment Rate ◽  
Mean Velocity ◽  
Independent Variables ◽  
Binary Mixing ◽  
Reynolds Averaging

This paper is devoted to the analysis of the turbulent mass flux and, more generally, of the density fluctuation correlation (d.f.c.) effects in variable-density fluid motion. The situation is restricted to the free turbulent binary mixing of an inhomogeneous round jet discharging into a quiescent atmosphere. Based on conventional (Reynolds) averaging, a ternary regrouping of the correlations occurring in the statistical averaging of the open equations is first introduced. Then an exact algebraic relationship between the d.f.c. terms and the second-order moments is demonstrated. Some consequences of this result on the global behaviour of variable-density jets are analytically discussed. The effects of the d.f.c. terms are shown to give a qualitative explanation of the influence of the ratio of the densities of the inlet jet and ambient fluid on the centerline decay rates of mean velocity and mass fraction, the entrainment rate and the restructuring of the jet. Finally, the sensitivity of second-order modelling to the d.f.c. terms is illustrated and it is suggested that such terms should be considered as independent variables in the closing procedure.

Measurements in adverse-pressure-gradient turbulent boundary layers with a step change in surface roughness

1975 ◽  
Vol 70 (3) ◽  
pp. 573-593 ◽  
Author(s):  
W. H. Schofield
Keyword(s):  
Surface Roughness ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Leading Edge ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Step Change ◽  
Internal Layer ◽  
Mean Velocity ◽  
Law Of The Wall

The response of turbulent boundary layers to sudden changes in surface roughness under adverse-pressure-gradient conditions has been studied experimentally. The roughness used was in the ‘d’ type array of Perry, Schofield & Joubert (1969). Two cases of a rough-to-smooth change in surface roughness were considered in the same arbitrary adverse pressure gradient. The two cases differed in the distance of the surface discontinuity from the leading edge and gave two sets of flow conditions for the establishment and growth of the internal layer which develops downstream from a change in surface roughness. These conditions were in turn different from those in the zero-pressure-gradient experiments of Antonia & Luxton. The results suggest that the growth of the new internal layer depends solely on the new conditions at the wall and scales with the local roughness length of that wall. Mean velocity profiles in the region after the step change in roughness were accurately described by Coles’ law of the wall-law of the wake combination, which contrasts with the zero-pressure-gradient results of Antonia & Luxton. The skin-friction coefficient after the step change in roughness did not overshoot the equilibrium distribution but made a slow adjustment downstream of the step. Comparisons of mean profiles indicate that similar defect profile shapes are produced in layers with arbitrary adverse pressure gradients at positions where the values of Clauser's equilibrium parameter β (= δ*τ−10dp/dx) are similar, provided that the pressure-gradient history and local values of the pressure gradient are also similar.

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