arXiv subjects

David Weyburne

Publications and source records attributed to David Weyburne.

10 recordsLinked to original sources

arXiv2022

The Prandtl Plus Scaling Failure and its Remedy

The Prandtl Plus scaling parameters are reexamined theoretically. The flow governing equations approach is used to examine similarity issues of the inner region of wall-bounded turbulent flows as well as laminar flow cases. It is found that the Prandtl Plus parameters are in fact similarity scaling parameters for laminar sink flow but NOT the more general laminar Falkner-Skan boundary layer flows. For turbulent boundary layer flows along a wall, it is found that only turbulent sink flows show similarity with the Prandtl Plus scaling parameters. This is diametrically opposed to the accepted notion that the Prandtl Plus parameters work for every wall-bounded turbulent flow. To correct the problem with the Prandtl Plus parameters, we introduce a new set of scaling parameters that work for the Falkner-Skan boundary layer flows and satisfy the relevant part of the flow governing equations approach to similarity.

physics.flu-dyn↗

arXiv2020

The Description and Scaling Behavior for the Inner Region of the Boundary Layer for 2-D Wall-bounded Flows

A second derivative-based moment method is proposed for describing the thickness and shape of the region where viscous forces are dominant in turbulent boundary layer flows. Rather than the fixed location sublayer model presently employed, the new method defines thickness and shape parameters that are experimentally accessible without differentiation. It is shown theoretically that one of the new length parameters used as a scaling parameter is also a similarity parameter for the velocity profile. In fact, we show that this new length scale parameter removes one of the theoretical inconsistencies present in the traditional Prandtl Plus scaling's. Furthermore, the new length parameter and the Prandtl Plus scaling parameters perform identically when operating on experimental datasets if the Rotta similarity constraint (u_tau/u_e = constant) holds. This means that many of the past successes ascribed to the Prandtl Plus scaling also apply to the new parameter set but without one of the theoretical inconsistencies. Examples are offered to show how the new description method is useful in exploring the actual physics of the boundary layer.

physics.flu-dyn↗

arXiv2018

New thickness and shape parameters for describing the thermal boundary layer

New thickness and shape parameters for describing the thermal boundary layer formed by 2-D fluid flow along a heated (cooled) wall are presented. The parameters are based on probability distribution function methodology in which the thermal profile thickness and shape are described by central moments of the thermal profile. The moment based parameters are simple integrals of the temperature profile. The usefulness of the new method is demonstrated by applying the description to laminar and turbulent boundary layer datasets.

physics.flu-dyn↗

arXiv2018

Similarity of the Temperature Profile formed by Fluid Flow along a Wall

A new approach to the study of similarity of temperature profiles is presented. It is applicable for any 2-D fluid flow along an isothermal heated (cooled) wall. The approach is based on a simple concept; the area under a set of scaled temperature profile curves that show similar behavior must be equal. This leads to a new integral-based definition of temperature profile similarity. By taking simple area integrals of the scaled temperature profile and its first derivative, we also obtain a number of new results pertaining to similarity of the temperature profiles. For example, it is shown that if similarity exists, then: 1) the similarity temperature and length scaling parameters are interdependent, 2) the thermal displacement thickness must be a similar length scaling parameter, and 3) the temperature scaling parameter must be proportional to the free stream minus wall temperature values.

physics.flu-dyn↗

arXiv2017

Does the Outer Region of the Turbulent Boundary Layer Display Similar Behavior?

Recent theoretical results together with established theory have identified the displacement thickness and the velocity at the boundary layer edge as similarity scaling parameter candidates for the wall-bounded turbulent boundary layer. In the work described herein, we examine these scaling parameters along with the Prandtl Plus scaling's and the Zagarola and Smits scaling's to search for similarity in the outer region of experimental turbulent boundary layer velocity profile datasets. A new integral area method combined with the traditional chi-by-eye method is used to search for similar velocity profiles. The results indicate that strict whole profile similarity is not evident in any of the datasets we searched. However, ten datasets are found that display "similar-like" behavior using the ratio of the inner to outer thickness ratio as a search criterion. In alignment with theory, the preferred similarity scaling parameters for the similar-like behavior case are the displacement thickness and the velocity at the boundary layer edge. It was found that there are a few datasets for which the Prandtl Plus scaling and the Zagarola and Smits scaling also work.

physics.flu-dyn↗

arXiv2017

A Cautionary Note on the Zagarola and Smits Similarity Parameter for the Turbulent Boundary Layer

Zagarola and Smits developed an empirical velocity parameter for scaling the outer region of the turbulent boundary layer velocity profile that has been widely applied to experimental datasets. Plots of the scaled defect profiles indicate that most datasets display similar-like behavior using the Zagarola and Smits scaling parameter. In the work herein, it is shown that the common practice of finding similarity behavior using the defect profile is often incomplete in the sense that not all of the criteria for similarity have been checked for compliance. When full compliance is checked, it is found that most of the datasets which display defect similarity do not satisfy all the criteria required for similarity. The nature of this contradiction and noncompliance is described in detail. It is shown that the original datasets used by Zagarola and Smits display this flawed similarity behavior. Hence, a careful reassessment of any claims in the literature is required for those groups that attempted to use the defect profile and the Zagarola and Smits type of velocity scaling parameter to assert similarity of the velocity profile.

physics.flu-dyn↗

arXiv2017

Inner/Outer Ratio Similarity Scaling for 2-D Wall-bounded Turbulent Flows

The turbulent boundary layer scaling parameters for the velocity profile are usually associated with either the inner viscous region or the outer boundary layer region. It has been a long-held view that complete similarity of the velocity profile can only occur if the inner and outer region scaling parameters change proportionally as one moves from station to station along the wall. However, it appears that complete similarity is not possible for the wall-bounded turbulent boundary layer. Hence, the outer/inner ratio would seem to be of little use. However, recent revelations revive the need for identifying likely experimental datasets that display outer region similarity. It is our contention that likely datasets can be identified by finding datasets in which the inner-outer thickness ratio is almost constant. This inner-outer thickness ratio is usually associated with the Rotta scaling ratio. Unfortunately, the Rotta ratio proportional change condition has never been shown to be a similarity requirement. In contrast, we show that a recently developed thickness ratio based on the integral moment method must change proportionately from station to station if similarity is present.

physics.flu-dyn↗

arXiv2016

A Cautionary Note on the Thermal Boundary Layer Similarity Scaling for the Turbulent Boundary Layer

Wang and Castillo have developed empirical parameters for scaling the temperature profile of the turbulent boundary layer flowing over a heated wall in the paper X. Wang and L. Castillo, J. Turbul., 4, 1(2003). They presented experimental data plots that showed similarity type behavior when scaled with their new scaling parameters. However, what was actually plotted, and what actually showed similarity type behavior, was not the temperature profile but the defect profile formed by subtracting the temperature in the boundary layer from the temperature in the bulk flow. We show that if the same data and same scaling is replotted as just the scaled temperature profile, similarity is no longer prevalent. This failure to show both defect profile similarity and temperature profile similarity is indicative of false similarity. The nature of this false similarity problem is discussed in detail.

physics.flu-dyn↗

arXiv2015

Are Defect Profile Similarity Criteria Different Than Velocity Profile Similarity Criteria for the Turbulent Boundary Layer?

The use of the defect profile instead of the experimentally observed velocity profile for the search for similarity parameters has become firmly imbedded in the turbulent boundary layer literature. However, a search of the literature reveals that there are no theoretical reasons for this defect profile preference over the more traditional velocity profile. In the report herein, we use the flow governing equation approach to develop similarity criteria for the two profiles. Results show that the derived similarity criteria are identical. Together with previous work that found that defect profile similarity must be accompanied by velocity profile similarity, then ones expectations must be that either profile can be used to search for similarity in experimental datasets. The choice should therefore be dictated by which one works best for experimental investigations, which in this case is the velocity profile.

physics.flu-dyn↗

arXiv2015

The Prevalence of Similarity of the Turbulent Wall-bounded Velocity Profile

Castillo and George (Castillo, L. and George, W., AIAA J. 39, 41(2001)) developed a flow governing equation approach for describing the turbulent outer boundary layer region. The approach was used to develop similarity criteria for the mean velocity and Reynolds shear stress profiles. Using the criteria as a guide, Castillo, George, and coworkers examined an extensive set of experimental datasets and claim that most of these turbulent velocity boundary layers appear to be similar boundary layers when scaled with the Zagarola and Smits (Zagarola, M. and Smits, A., J. Fluid Mech. 373, 33(1998)) velocity parameter. In the work herein it is shown that their success at showing scaled profile similarity in many of those datasets is flawed due to a similarity problem that occurs when one combines the defect profile and the Zagarola and Smits type of velocity scaling parameter. The same problem has been identified in other papers in the literature and may in fact be widespread. We conclude that similarity of the turbulent velocity profile is not as prevalent as was claimed by Castillo, George, and coworkers. The result has implications as to the accepted paradigm of the scaling of the turbulent boundary layer.

physics.flu-dyn↗