Direct Numerical Simulation Data Research Articles

On locally embedded two-scale solution for wall-bounded turbulent flows

Recent findings on wall-bounded turbulence have prompted a new impetus for modelling development to capture and resolve the Reynolds-number-dependent influence of outer flow on near-wall turbulence in terms of the ‘foot-printing’ of the large-scale coherent structures and the scale-interaction associated ‘modulation’. We develop a two-scale method to couple a locally embedded near-wall fine-mesh direct numerical simulation (DNS) block with a global coarser mesh domain. The influence of the large-scale structures on the local fine-mesh block is captured by a scale-dependent coarse–fine domain interface treatment. The coarse-mesh resolved disturbances are directly exchanged across the interface, while only the fine-mesh resolved fluctuations around the coarse-mesh resolved variables are subject to periodic conditions in the streamwise and spanwise directions. The global near-wall coarse-mesh region outside the local fine-mesh block is governed by the augmented flow governing equations with forcing source terms generated by upscaling the space–time-averaged fine-mesh solution. The validity and effectiveness of the method are examined for canonical incompressible channel flows at several Reynolds numbers. The mean statistics and energy spectra are in good agreement with the corresponding full DNS data. The results clearly illustrate the ‘foot-printing’ and ‘modulation’ in the local fine-mesh block. Noteworthy also is that neither spectral-gap nor scale-separation is assumed, and a smooth overlap between the global-domain and the local-domain energy spectra is observed. It is shown that the mesh-count scaling with Reynolds number is potentially reduced from $O(R{e^2})$ for the conventional fully wall-resolved large-eddy simulation (LES) to $O(Re)$ for the present locally embedded two-scale LES.

Study on bubble-induced turbulence in pipes and containers with Reynolds-stress models

Bubbly flow still represents a challenge for large-scale numerical simulation. Among many others, the understanding and modelling of bubble-induced turbulence (BIT) are far from being satisfactory even though continuous efforts have been made. In particular, the buoyancy of the bubbles generally introduces turbulence anisotropy in the flow, which cannot be captured by the standard eddy viscosity models with specific source terms representing BIT. Recently, on the basis of bubble-resolving direct numerical simulation data, a new Reynolds-stress model considering BIT was developed by Ma et al. (J Fluid Mech, 883: A9 (2020)) within the Euler—Euler framework. The objective of the present work is to assess this model and compare its performance with other standard Reynolds-stress models using a systematic test strategy. We select the experimental data in the BIT-dominated range and find that the new model leads to major improvements in the prediction of full Reynolds-stress components.

A maximum entropy formalism model for the breakup of a droplet

A model for the prediction of the size and velocity distribution of daughter droplets created by the breakup of an unstable parent droplet is proposed. The basis of the model is the maximum entropy formalism, which states that the most probable joint probability density function (JPDF) for the daughter droplet population is the one that maximizes the Bayesian entropy conditional on the enforcement of a set of constraints, which are the conservation laws for the problem. The result is a closed-form expression for the JPDF. Validation against experimental and Direct Numerical Simulations data over the bag, multimode, and sheet-thinning breakup regimes is included. Predictions from the model show that the daughter droplet velocity distribution widens as the droplet size decreases. This result is due to a heightened sensitivity to drag force with lower droplet inertia and coincides with spray behavior. The velocity distribution is found to be near Gaussian. The model does not treat size and velocity as independently distributed, as generally assumed in the literature. In fact, marginal conditional densities derived from JPDF show that the distribution of size and velocity are interrelated.

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.

О КИНЕТИЧЕСКОЙ ЭНЕРГИИ ТУРБУЛЕНТНЫХ ПУЛЬСАЦИЙ ПРИ ТЕЧЕНИИ ЖИДКОСТЕЙ ПО ТРУБАМ КРУГОВОГО ПОПЕРЕЧНОГО СЕЧЕНИЯ

In the paper, formulas were obtained for calculating a number of quantities characterizing the distribution of the kinetic energy of turbulent fluctuations over the pipe section depending on the Reynolds criterion. Those quantities include the maximum value of the kinetic energy, the average value, the value on the axis. The formulas were constructed using direct numerical simulation data obtained by various authors

Super-resolution reconstruction of turbulent flow fields at various Reynolds numbers based on generative adversarial networks

This study presents a deep learning-based framework to recover high-resolution turbulent velocity fields from extremely low-resolution data at various Reynolds numbers by utilizing the concept of generative adversarial networks. A multiscale enhanced super-resolution generative adversarial network is applied as a model to reconstruct the high-resolution velocity fields, and direct numerical simulation data of turbulent channel flow with large longitudinal ribs at various Reynolds numbers are used to evaluate the performance of the model. The model is found to have the capacity to accurately reconstruct the high-resolution velocity fields from data at two different down-sampling factors in terms of the instantaneous velocity fields, two-point correlations, and turbulence statistics. The results further reveal that the model is able to reconstruct high-resolution velocity fields at Reynolds numbers that fall within the range of the training Reynolds numbers.

A universal velocity profile for turbulent wall flows including adverse pressure gradient boundary layers

A recently developed mixing length model of the turbulent shear stress in pipe flow is used to solve the streamwise momentum equation for fully developed channel flow. The solution for the velocity profile takes the form of an integral that is uniformly valid from the wall to the channel centreline at all Reynolds numbers from zero to infinity. The universal velocity profile accurately approximates channel flow direct numerical simulation (DNS) data taken from several sources. The universal velocity profile also provides a remarkably accurate fit to simulated and experimental flat plate turbulent boundary layer data including zero and adverse pressure gradient data. The mixing length model has five free parameters that are selected through an optimization process to provide an accurate fit to data in the range $R_\tau = 550$ to $R_\tau = 17\,207$ . Because the velocity profile is directly related to the Reynolds shear stress, certain statistical properties of the flow can be studied such as turbulent kinetic energy production. The examples presented here include numerically simulated channel flow data from $R_\tau = 550$ to $R_\tau =8016$ , zero pressure gradient (ZPG) boundary layer simulations from $R_\tau =1343$ to $R_\tau = 2571$ , zero pressure gradient turbulent boundary layer experimental data between $R_\tau = 2109$ and $R_\tau = 17\,207$ , and adverse pressure gradient boundary layer data in the range $R_\tau = 912$ to $R_\tau = 3587$ . An important finding is that the model parameters that characterize the near-wall flow do not depend on the pressure gradient. It is suggested that the new velocity profile provides a useful replacement for the classical wall-wake formulation.

The logarithmic variance of streamwise velocity and conundrum in wall turbulence

The logarithmic dependence of streamwise turbulence intensity has been observed repeatedly in recent experimental and direct numerical simulation data. However, its spectral counterpart, a well-developed $k^{-1}$ spectrum ( $k$ is the spatial wavenumber in a wall-parallel direction), has not been convincingly observed from the same data. In the present study, we revisit the spectrum-based attached eddy model of Perry and co-workers, who proposed the emergence of a $k^{-1}$ spectrum in the inviscid limit, for small but finite $z/\delta$ and for finite Reynolds numbers ( $z$ is the wall-normal coordinate, and $\delta$ is the outer length scale). In the upper logarithmic layer (or inertial sublayer), a reexamination reveals that the intensity of the spectrum must vary with the wall-normal location at order of $z/\delta$ , consistent with the early observation argued with ‘incomplete similarity’. The streamwise turbulence intensity is subsequently calculated, demonstrating that the existence of a well-developed $k^{-1}$ spectrum is not a necessary condition for the approximate logarithmic wall-normal dependence of turbulence intensity – a more general condition is the existence of a premultiplied power-spectral intensity of $O(1)$ for $O(1/\delta ) < k < O(1/z)$ . Furthermore, it is shown that the Townsend–Perry constant must be weakly dependent on the Reynolds number. Finally, the analysis is semi-empirically extended to the lower logarithmic layer (or mesolayer), and a near-wall correction for the turbulence intensity is subsequently proposed. All the predictions of the proposed model and the related analyses/assumptions are validated with high-fidelity experimental data (Samie et al., J. Fluid Mech., vol. 851, 2018, pp. 391–415).

Enhanced burning rates in hydrogen-enriched turbulent premixed flames by diffusion of molecular and atomic hydrogen

Direct numerical simulations (DNS) of fuel-lean turbulent premixed hydrogen-enriched flames are analyzed to improve understanding of local effects of molecular diffusion of fast-diffusing, low-Lewis-number hydrogen species (H2 and H) on the overall burning rates of reactant mixtures. Although it is often assumed that the importance of molecular diffusion decreases with increasing turbulence intensity, our analysis reveals that, on the contrary, diffusion of molecular and atomic hydrogen can remain the rate-controlling processes even at high Karlovitz numbers (Ka≫1). Three-dimensional DNS with detailed chemical kinetics and species transport of turbulent premixed hydrogen-air and hydrogen/ammonia-air flames in the regimes of thin and distributed reaction zones are performed and analyzed at different reactant temperatures and pressure levels. The DNS data reveal a significant impact of H2 and H diffusion in all flames analyzed. In particular, the magnitude of H2 diffusion, occurring from low progress variable near the flame elements of the turbulent reaction front that exhibit convex (positive) curvature towards the fresh mixture, is greatly enhanced at high pressure through increased spatial gradients, resulting in localized equivalence-ratio enrichment and super-adiabatic conditions that accelerate and strengthen the flame front. Moreover, for higher reactant temperatures, back diffusion of atomic hydrogen, transported from the reaction zone into unburnt regions from negatively curved reaction layers surrounding them, facilitates the occurrence of localized spontaneous ignition events at the trailing edges of reaction fronts. For certain conditions these events, induced by differential diffusion, can become the dominant process controlling the overall rate of reactants consumption.

Data-driven model development for large-eddy simulation of turbulence using gene-expression programing

We apply the gene-expression programing (GEP) method to develop subgrid-scale models for large-eddy simulations (LESs) of turbulence. The GEP model is trained based on Galilean invariants and tensor basis functions, and the training data are from direct numerical simulation (DNS) of incompressible isotropic turbulence. The model trained with GEP has been explicitly tested, showing that the GEP model can not only provide high correlation coefficients in a priori tests but also show great agreement with filtered DNS data when applied to LES. Compared to commonly used models like the dynamic Smagorinsky model and the dynamic mixed model, the GEP model provides significantly improved results on turbulence statistics and flow structures. Based on an analysis of the explicitly given model equation, the enhanced predictions are related to the fact that the GEP model is less dissipative and that it introduces high-order terms closely related to vorticity distribution. Furthermore, the GEP model with the explicit equation is straightforward to be applied in LESs, and its additional computational cost is substantially smaller than that of models trained with artificial neural networks with similar levels of predictive accuracies in a posteriori tests.

High-fidelity reconstruction of turbulent flow from spatially limited data using enhanced super-resolution generative adversarial network

In this study, a deep learning-based approach is applied with the aim of reconstructing high-resolution turbulent flow fields using minimal flow field data. A multi-scale enhanced super-resolution generative adversarial network with a physics-based loss function is introduced as a model to reconstruct the high-resolution flow fields. The model capability to reconstruct high-resolution laminar flows is examined using direct numerical simulation data of laminar flow around a square cylinder. The results reveal that the model can accurately reproduce the high-resolution flow fields even when limited spatial information is provided. The DNS data of turbulent channel flow at two friction Reynolds numbers Reτ=180 and 550 are used to assess the ability of the model to reconstruct the high-resolution wall-bounded turbulent flow fields. The instantaneous and statistical results obtained from the model agree well with the ground truth data, indicating that the model can successfully learn to map the coarse flow fields to the high-resolution ones. Furthermore, the possibility of performing transfer learning for the case of turbulent channel flow is thoroughly examined. The results indicate that the amount of the training data and the time required for training can be effectively reduced without affecting the performance of the model. The computational cost of the proposed model is also found to be effectively low. These results demonstrate that using high-fidelity training data with physics-guided generative adversarial network-based models can be practically efficient in reconstructing high-resolution turbulent flow fields from extremely coarse data.

Scale-space energy density for inhomogeneous turbulence based on filtered velocities

The energy spectrum is commonly used to describe the scale dependence of turbulent fluctuations in homogeneous isotropic turbulence. In contrast, one-point statistical quantities, such as the turbulent kinetic energy, are mainly employed for inhomogeneous turbulence models. Attempts have been made to describe the scale dependence of inhomogeneous turbulence using the second-order structure function and two-point velocity correlation. However, unlike the energy spectrum, expressions for the energy density in the scale space fail to satisfy the requirement of being non-negative. In this study, a new expression for the scale-space energy density based on filtered velocities is proposed to clarify the reasons behind the negative values of the energy density and to obtain a better understanding of inhomogeneous turbulence. The new expression consists of homogeneous and inhomogeneous parts; the former is always non-negative, while the latter can be negative because of the turbulence inhomogeneity. Direct numerical simulation data of homogeneous isotropic turbulence and a turbulent channel flow are used to evaluate the two parts of the energy density and turbulent energy. It was found that the inhomogeneous part of the turbulent energy shows non-zero values near the wall and at the centre of a channel flow. In particular, the inhomogeneous part of the energy density changes its sign depending on the scale. A concave profile of the filtered-velocity variance at the wall accounts for the negative value of the energy density in the region very close to the wall.

Assessment of turbulence models using DNS data of compressible plane free shear layer flow

The present paper uses the detailed flow data produced by direct numerical simulation (DNS) of a three-dimensional, spatially developing plane free shear layer to assess several commonly used turbulence models in compressible flows. The free shear layer is generated by two parallel streams separated by a splitter plate, with a naturally developing inflow condition. The DNS is conducted using a high-order discontinuous spectral element method (DSEM) for various convective Mach numbers. The DNS results are employed to provide insights into turbulence modelling. The analyses show that with the knowledge of the Reynolds velocity fluctuations and averages, the considered strong Reynolds analogy models can accurately predict temperature fluctuations and Favre velocity averages, while the extended strong Reynolds analogy models can correctly estimate the Favre velocity fluctuations and the Favre shear stress. The pressure–dilatation correlation and dilatational dissipation models overestimate the corresponding DNS results, especially with high compressibility. The pressure–strain correlation models perform excellently for most pressure–strain correlation components, while the compressibility modification model gives poor predictions. The results of an a priori test for subgrid-scale (SGS) models are also reported. The scale similarity and gradient models, which are non-eddy viscosity models, can accurately reproduce SGS stresses in terms of structure and magnitude. The dynamic Smagorinsky model, an eddy viscosity model but based on the scale similarity concept, shows acceptable correlation coefficients between the DNS and modelled SGS stresses. Finally, the Smagorinsky model, a purely dissipative model, yields low correlation coefficients and unacceptable accumulated errors.

Comparison of the Reactive Scalar Gradient Evolution between Homogeneous MILD Combustion and Premixed Turbulent Flames

Moderate or intense low-oxygen dilution (MILD) combustion is a novel combustion technique that can simultaneously improve thermal efficiency and reduce emissions. This paper focuses on the differences in statistical behaviours of the surface density function (SDF = magnitude of the reaction progress variable gradient) between conventional premixed flames and exhaust gas recirculation (EGR) type homogeneous-mixture combustion under MILD conditions using direct numerical simulations (DNS) data. The mean values of the SDF in the MILD combustion cases were found to be significantly smaller than those in the corresponding premixed flame cases. Moreover, the mean behaviour of the SDF in response to the variations of turbulence intensity were compared between MILD and premixed flame cases, and the differences are explained in terms of the strain rates induced by fluid motion and the ones arising from flame displacement speed. It was found that the effects of dilatation rate were much weaker in the MILD combustion cases than in the premixed flame cases, and the reactive scalar gradient in MILD combustion cases preferentially aligns with the most compressive principal strain-rate eigendirection. By contrast, the reactive scalar gradient preferentially aligned with the most extensive principal strain-rate eigendirection within the flame in the premixed flame cases considered here, but the extent of this alignment weakened with increasing turbulence intensity. This gave rise to a predominantly positive mean value of normal strain rate in the premixed flames, whereas the mean normal strain rate remained negative, and its magnitude increased with increasing turbulence intensity in the MILD combustion cases. The mean value of the reaction component of displacement speed assumed non-negligible values in the MILD combustion cases for a broader range of reaction progress variable, compared with the conventional premixed flames. Moreover, the mean displacement speed increased from the unburned gas side to the burned gas side in the conventional premixed flames, whereas the mean displacement speed in MILD combustion cases decreased from the unburned gas side to the middle of the flame before increasing mildly towards the burned gas side. These differences in the mean displacement speed gave rise to significant differences in the mean behaviour of the normal strain rate induced by the flame propagation and effective strain rate, which explains the differences in the SDF evolution and its response to the variation of turbulence intensity between the conventional premixed flames and MILD combustion cases. The tangential fluid-dynamic strain rate assumed positive mean values, but it was overcome by negative mean values of curvature stretch rate to yield negative mean values of stretch rate for both the premixed flames and MILD combustion cases. This behaviour is explained in terms of the curvature dependence of displacement speed. These findings suggest that the curvature dependence of displacement speed and the scalar gradient alignment with local principal strain rate eigendirections need to be addressed for modelling EGR-type homogeneous-mixture MILD combustion.

Characteristics of reattached boundary layer in shock wave and turbulent boundary layer interaction

The reattached boundary layer in the interaction of an oblique shock wave with a flat-plate turbulent boundary layer at Mach number 2.25 is studied by means of Direct Numerical Simulation (DNS). The numerical results are carefully compared with available experimental and DNS data in terms of turbulence statistics, wall pressure and skin friction. The coherent vortex structures are significantly enhanced due to the shock interaction, and the reattached boundary layer is characterized by large-scale structures in the outer region. The space-time correlation of fluctuating wall shear stress and streamwise velocity fluctuation reveals that the structural inclination angle exhibits a gradual decrease during the recovery process. The scale interactions are analyzed by using a two-point amplitude modulation correlation. A possible mechanism is proposed to account for the strong amplitude modulation in the downstream region. Moreover, the mean skin-friction is decomposed to understand the physically informed contributions. Unlike the upstream Turbulent Boundary Layer (TBL), the contribution associated with the Turbulence Kinetic Energy (TKE) production is greatly amplified, while the spatial growth contribution induced by the pressure gradient largely inhibits skin-friction generation. Based on bidimensional empirical mode decomposition, the turbulence kinetic energy production contribution is further split into different terms with specific spanwise length scales.

Flame Surface Density based mean reaction rate closure for Reynolds averaged Navier Stokes methodology in turbulent premixed Bunsen flames with non-unity Lewis number

The Flame Surface Density (FSD) based mean reaction rate closure proposed by Prof. K.N.C. Bray and co-workers in the context of Reynolds Averaged Navier-Stokes simulations has been a-priori analysed using a Direct Numerical Simulation (DNS) database of turbulent premixed Bunsen flames with different characteristic Lewis numbers representing the strict flamelet regime (i.e. high Damköhler number and low Karlovitz number combustion). The statistical behaviours of stretch factor, orientation factor and wrinkling length scale have been assessed for non-unity Lewis number conditions to identify their Lewis number dependencies. The assumption of presumed bimodal distribution has been found to be rendered invalid close to the nozzle exit where the unresolved wrinkling remains relatively small even when the flow parameters at the nozzle exit represent high Damköhler number and low Karlovitz number conditions. Although the PDF of reaction progress variable shows some resemblance to a bimodal distribution away from the nozzle exit, the Bray-Moss-Libby expressions which can be derived for infinitely large values of Damköhler number have been found to show considerable deviations from the Reynolds averaged reaction progress variable and reaction progress variable variance extracted from DNS data even though these cases represent the wrinkled/corrugated flamelets regime combustion based on nozzle exit conditions. This suggests that it might be necessary to solve a modelled scalar variance transport equation even in the strict flamelet regime instead of using the algebraic relation for the scalar variance. It has been found that the characteristic Lewis number has a major influence on the orientation factor, wrinkling length scale, and the stretch factor. Furthermore, these parameters are found to be (sometimes strong) functions of the axial distance from the nozzle exit. Known parameterisations for the wrinkling length scale and the stretch factor have been shown to be unable to capture the correct variation across the flame brush based on a-priori analysis of DNS data. The variability of the orientation factor and the inadequacy of existing relations to approximate other quantities such as the stretch factor, wrinkling factor and the Reynolds averaged reaction progress variable have the potential to severely limit the performance of algebraic FSD based mean reaction rate closures in turbulent premixed flames within the flamelet regime.

Interpretable data-driven methods for subgrid-scale closure in LES for transcritical LOX/GCH4 combustion

Although data-driven methods have shown high accuracy as closure models for simulating turbulent flames, these models are often criticized for lack of physical interpretability, wherein they provide answers but no insight into their underlying rationale. In this work, we show that two interpretable machine learning algorithms, namely the random forest regressor and the sparse symbolic regression, can offer opportunities for discovering analytic expressions for subgrid-scale (SGS) terms of a turbulent transcritical flame. These transcritical conditions are found in various combustion systems that operate under high pressures that surpass the thermodynamic critical limit of fuel-oxidizer mixtures, and require the consideration of complex fluid behaviors that can cast doubts on the validity of existing subgrid-scale (SGS) models in large-eddy simulations. To this end, direct numerical simulations (DNS) of transcritical liquid-oxygen/gaseous-methane (LOX/GCH4) inert and reacting flows are performed. Using this data, a priori analysis is performed on the Favre-filtered DNS data to compare the accuracy of random forest SGS-models with conventional physics-based SGS-models. SGS stresses calculated with the gradient model are shown to have good agreement with the exact terms extracted from filtered DNS. Results demonstrate that random forests can perform as effectively as algebraic models when modeling subgrid stresses, when trained on a sufficiently representative database and with a suitable choice of the feature set. The employment of the random forest feature importance score is shown to enable the discovery of a analytic model for subgrid-scale stresses through sparse symbolic regression. The generalizability of random forest and sparse symbolic regression is demonstrated by modeling the subgrid-scale temperature, a term that arises from filtering the non-linear real-fluid equation-of-state, with good accuracy.

Influence of molecular transport on burning rate and conditioned species concentrations in highly turbulent premixed flames

Apparent inconsistency between (i) experimental and direct numerical simulation (DNS) data that show the significant influence of differential diffusion on the turbulent burning rate and (ii) recent complex-chemistry DNS data that indicate mitigation of the influence of differential diffusion on conditioned profiles of various local flame characteristics at high Karlovitz numbers, is explored by analysing new DNS data obtained from lean hydrogen–air turbulent flames. Both aforementioned effects are observed by analysing the same DNS data provided that the conditioned profiles are sampled from the entire computational domain. On the contrary, the conditioned profiles sampled at the leading edge of the mean flame brush do not indicate the mitigation, but are significantly affected by differential diffusion phenomena, e.g. because reaction zones are highly curved at the leading edge. This observation is consistent with a significant increase in the computed turbulent burning velocity with decreasing Lewis number, with all the results considered jointly being consonant with the leading point concept of premixed turbulent combustion. The concept is further supported by comparing DNS data obtained by allowing for preferential diffusion solely for a single species, either atomic or molecular hydrogen.

Error propagation and conditioning analysis of DNS data of turbulent viscoelastic channel flows

In the context of drag reduction phenomenon, direct numerical simulation (DNS) of turbulent viscoelastic flows is a very useful tool able to provide information that is not possible with experiments and that can be used for modeling purposes. A rare and challenging task is to provide measures for statistical errors that are present in DNS data. In the present communication, we employ a method to quantify the statistical convergence of the DNS turbulent viscoelastic channel flows from the unbalance on the mean momentum equation. In addition, we conduct a conditioning analysis of the resultant numerical linear system of this problem. We compare results from different research groups. We found that DNS databases of viscoelastic flows can induce high error propagation in the mean velocity. As a consequence, larger sampling times are needed to achieve a statistically converged Reynolds stress tensor. The conditioning analysis has shown that elasticity enhances conditioning. • We discuss the DNS importance for turbulence modeling. • Uncertainty and statistical error are analyzed in the DNS context. • Equations for mean viscoelastic turbulence (VT) are ill-conditioned. • Error propagation in the mean velocity field related to VT is high. • Statistical quantities, like Reynolds stress, in VT need to be more converged.

Pressure reconstruction of a planar turbulent flow field within a multiply connected domain with arbitrary boundary shapes

This paper reports for the first time the implementation procedures and validation results for pressure reconstruction of a planar turbulent flow field within a multiply connected domain that has arbitrary inner and outer boundary shapes. The pressure reconstruction algorithm used in this study is the rotating parallel-ray omni-directional integration algorithm that offers high-level of accuracy in the reconstructed pressure. While preserving the nature and advantage of the parallel ray omni-directional pressure reconstruction at places with flow data, the new implementation of the algorithm is capable of processing an arbitrary number of inner void areas with arbitrary boundary shapes. Validation of the multiply connected domain pressure reconstruction code is conducted using the Johns Hopkins DNS (Direct Numerical Simulation) isotropic turbulence databases [J. Graham et al., J. Turbul. 17(2), 181 (2016)], with 1000 statistically independent pressure gradient field realizations embedded with random noise used to gauge the code performance. For further validation, the code is also applied for pressure reconstruction from the DNS data [E. Johnsen and T. Colonius, J. Fluid Mech., 629, 231 (2009)] about a shock-induced non-spherical bubble collapse in water. It is demonstrated that the parallel-ray omni-directional integration algorithm outperforms the Poisson equation approach in terms of the accuracy for the pressure reconstruction from error embedded pressure gradients in both simply connected and multiply connected domains.