arXiv subjects

Zhenhua Xia

Publications and source records attributed to Zhenhua Xia.

10 recordsLinked to original sources

arXiv2026

Mapping-based exact-integral formulation of skin-friction transformations for zero-pressure-gradient compressible turbulent boundary layers

A long-standing route to efficient surface-drag prediction in zero-pressure-gradient compressible turbulent boundary layers is to map the skin-friction coefficient $C_f$ and momentum-thickness Reynolds number $Re_θ$ onto their `incompressible' counterparts. Reassessment against an extensive DNS database shows that existing formulations do not consistently recover the reference incompressible skin-friction behaviour, even when transformed data exhibit improved collapse. We define the mapped `incompressible' state as a constant-property counterpart of the physical compressible boundary layer and derive the transformation factors from prescribed mean-velocity and wall-normal-coordinate mappings. This definition-first approach links skin-friction scaling to the full-layer accuracy of the underlying velocity transformation and exposes inherited outer-layer errors. Van Driest's theory is recast in a finite-Re exact-integral form, with the classical vD I and II transformations recovered as leading-order asymptotic reductions. Their limitations at finite Reynolds numbers are quantified, and the historical success of vD II is traced to a fortuitous cancellation of truncation errors. The exact-integral formulation then yields modified transformations assessed through a priori scaling and standalone a posteriori prediction of $C_f$ from prescribed macroscopic and wall-thermal inputs. The VIPL-based modified transformation gives the best overall performance. Across $0.30 \leq M_\infty \leq 13.64$ and $-0.55 \leq \varTheta \leq 2.85$, its prediction errors remain below $11\%$, with a mean error of $3.07\%$. Overall, the analysis places skin-friction transformations on a mapping-based exact-integral footing, relating them directly to prescribed mean-flow mappings while avoiding the leading-order asymptotic truncations that limit classical van Driest theory at finite Reynolds numbers.

physics.flu-dyn↗

arXiv2023

Three-dimensional sedimentation patterns of two interacting disks in a viscous fluid

The sedimentation of two spherical solid objects in a viscous fluid has been extensively investigated and well understood. However, a pair of flat disks (in three dimensions) settling in the fluid shows more complex hydrodynamic behaviors. The present work aims to improve understanding of this phenomenon by performing Direct Numerical Simulations (DNS) and physical experiments. The present results show that the sedimentation processes are significantly influenced by disk shape, characterized by a dimensionless moment of inertia I*, and Reynolds number of the leading disk Re. For the flatter disks with smaller I*, steady falling with enduring contact transits to periodic swinging with intermittent contacts as Re increases. The disks with larger I* tend to fall in a Drafting-Kissing-Tumbling (DKT) mode at low Re and to remain separated at high Re. Based on I* and Re, a phase diagram is created to classify the two-disk falling into ten distinctive patterns. The planar motion or three-dimensional motion of the disks is determined primarily by Re. Turbulent disturbance flows at a high Re contribute to the chaotic three-dimensional rotation of the disks. The chance for the two disks to contact is increased when I* and Re are reduced.

physics.flu-dyn↗

arXiv2022

Enhancing large-scale motions and turbulent transport in rotating plane Poiseuille flow

Based on the properties of large-scale plume currents, an injection/suction control strategy is introduced to enhance the strength of plume currents and the turbulent transport of passive scalar in rotating plane Poiseuille flow. The control keeps the classical non-penetrative condition on the stable side, and prescribes spanwise varying wall-normal velocity on the unstable side. Direct numerical simulations show that at medium rotation numbers, very weak injection/suction (the root-mean-square velocity on the controlled side is below $1\%$ of the bulk mean velocity) with properly distributed slots could significantly enhance the large-scale plume currents which have the same spatial distribution as the injection slots. In addition, if the distance between plume currents are increased, the turbulent transport efficiency can be promoted. Therefore, taking the strength and transport efficiency into account, the distance between injection slots should be slightly larger than the intrinsic distance between plume currents to achieve maximum enhancement of turbulent transport. For comparison, the control with non-penetrative condition on the unstable side and injection/suction on the stable side is also examined with simulations. It is found that the injection/suction on the stable side has much weaker influence compared with that on the unstable side. This is because that plumes are generated on the unstable side, and that controlling the origin of plumes is more effective.

physics.flu-dyn↗

arXiv2021

Analysis on numerical stability and convergence of RANS turbulence models from the perspective of coupling modes

Reynolds-averaged Navier-Stokes simulations are still the main method to study complex flows in engineering. However, traditional turbulence models cannot accurately predict flow fields with separations. In such situation, machine learning methods provide an effective way to build new data-driven turbulence closure models. Nevertheless, a bottleneck that the data-driven turbulence models encounter is how to ensure the stability and convergence of the RANS equations in posterior iterations. This paper studies the effects of different coupling modes on the convergence and stability between the RANS equations and turbulence models. Numerical results demonstrate that the frozen coupling mode, commonly used in machine learning turbulence models, may lead to divergence and instability in posterior iterations; while the mutual coupling mode can maintain good convergence and stability in the process of iterations. This research can provide a new perspective to the coupling mode for machine learning turbulence models with RANS equations in posterior iterations.

physics.flu-dyn↗

arXiv2021

Exact mathematical formulas for wall-heat flux in compressible turbulent channel flows

In this paper, several exact expressions for the mean heat flux at the wall ($q_w$) for the compressible turbulent channel flows are derived by using the internal energy equation or the total energy equation. Two different routes, including the FIK method and the RD method, can be applied. The direct numerical simulations data of compressible channel flows at different Reynolds and Mach numbers verify the correctness of the derived formulas. Discussions related to the different energy equations, and different routes are carried out, and we may arrive at the conclusion that most of the formulas derived in the present work are just mathematically ones which generally are lack of clear physical interpretation. They can be used to estimate $q_w$, but might not be suitable for explore the underlying physics.

physics.flu-dyn↗

arXiv2020

Perturbation analysis of baroclinic torque in low-Mach-number flows

In this paper, we propse a series expansion of the baroclinic torque in low-Mach-number flows, so that the accuracy and universality of any buoyancy term could be examined analytically, and new types of buoyancy terms could be constructed and validated. We first demonstrate that the purpose of introducing a buoyancy term is to approximate the baroclinic torque, and straightforwardly the accuracy of any buoyancy term could be measured by the deviation of its curl from the baroclinic torque. Then a regular perturbation method is introduced for the elliptic equation of the hydrodynamic pressure in low-Mach-number flows, resulting in a sequence of Poisson equations, whose solutions lead to the series representation of the baroclinic torque and the new types of buoyancy terms. With the error definition of buoyancy terms and the series representation of the baroclinic torque, the classical gravitational and centrifugal buoyancy term, as well as some other previously proposed buoyancy terms are revisited. Finally, numerical simulations confirm that, with a decreasing density variation or an increasing order of our newly proposed buoyancy term, the simplified equations with one of the new types of buoyancy terms can converge to the original low-Mach-number equations.

physics.flu-dyn↗

arXiv2020

Late-time description of immiscible Rayleigh-Taylor instability: A lattice Boltzmann study

The late-time growth of single-mode immiscible Rayleigh-Taylor instability is investigated over a comprehensive range of the Reynolds numbers ($1\leq Re \leq 10000$) and Atwood numbers $(0.05 \leq A \leq 0.7)$ using an improved lattice Boltzmann multiphase method. We first reported that the instability with a moderately high Atwood number of 0.7 undergoes a sequence of distinguishing stages at high Reynolds numbers, named as the linear growth, saturated velocity growth, reacceleration and chaotic development stages. The spike and bubble at the secondary stage evolve with the constant velocities and their values agree well with the potential flow theory. Owing to the increasing strengths of the vortices, the spike and bubble are accelerated with velocities exceeding than the asymptotic values and the evolution of the instability enters into the reacceleration stage. Lastly, the curves for the spike and bubble velocities have some fluctuations at the chaotic stage and also a complex interfacial structure with large topological change is observed, while it still preserves the symmetry property. To determine the nature of the late-time growth, we also calculated the spike and bubble growth rates by using five popular statistical methods and two comparative techniques are recommended, resulting in the spike and bubble growth rates of about 0.13 and 0.022, respectively. When the Reynolds number is gradually reduced, some later stages cannot be reached successively and the structure of the evolutional interface becomes relatively smooth. Moreover, we observe that the spike growth rate shows an overall increase with the Atwood number, while it has little influence on the bubble growth rate being approximately 0.0215.

physics.flu-dyn↗

arXiv2020

On skin friction in wall-bounded turbulence

In this paper, we derive mathematical formulas for the skin friction coefficient in wall-bounded turbulence based on the Reynolds averaged streamwise momentum equation and the total stress. Specially, with the theoretical or empirical relation of the total stress, the skin friction coefficient is expressed in terms of the mean velocity and the Reynolds shear stress in an arbitrary wall-normal region $[h_0, h_1]$. The formulas are validated using the direct numerical simulation data of turbulent channel and boundary layer flows, and the results show that our formulas estimate the skin friction coefficient very accurately with an error less than $2\%$. We believe that the present integral formula can be used to determine the skin friction in turbulent channel and boundary layer flows at high Reynolds numbers where the near wall statistics are very difficult to measure accurately.

physics.flu-dyn↗

arXiv2020

Bifurcation and multiple states in plane Couette flow with spanwise rotation

We present a derivation that begins with the Navier--Stokes equation and ends with a prediction of multiple statistically stable states identical to those observed in a spanwise rotating plane Couette flow. This derivation is able to explain the presence of multiple states in fully developed turbulence and the selection of one state over the other by differently sized computational domains and different initial conditions. According to the present derivation, two and only two statistically stable states are possible in an infinitely large plane Couette flow with spanwise rotation, and that multiple states are not possible at very slow or very rapid rotation speeds. We also show the existence of limit cycles near statistically stable states.

physics.flu-dyn↗

arXiv2020

Obtaining the mean fields with known Reynolds stresses at steady state

With the rising of modern data science, data--driven turbulence modeling with the aid of machine learning algorithms is becoming a new promising field. Many approaches are able to achieve better Reynolds stress prediction, with much lower modeling error ($ε_M$), than traditional RANS models but they still suffer from numerical error and stability issues when the mean velocity fields are estimated using RANS equations with the predicted Reynolds stresses, illustrating that the error of solving the RANS equations ($ε_P$) is also very important. In the present work, the error $ε_P$ is studied separately by using the Reynolds stresses obtained from direct numerical simulation and we derive the sources of $ε_P$. For the implementations with known Reynolds stresses solely, we suggest to run an adjoint RANS simulation to make first guess on $ν_t^*$ and $S_{ij}^0$. With around 10 iterations, the error could be reduced by about one-order of magnitude in flow over periodic hills. The present work not only provides one robust approach to minimize $ε_P$, which may be very useful for the data-driven turbulence models, but also shows the importance of the nonlinear part of the Reynolds stresses in flow problems with flow separations.

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