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It is generally believed that thrombus formation does not occur in the left ventricle (LV) because of the high speed of blood flow. However, the LV has complex internal structures such as trabeculae carneae (TC) and papillary muscles (PM) on its inner wall, which may cause blood stagnation resulting in thrombus formation. In this study, the effects of the TC, PM, and torsional motion on the hemodynamics in the LV were investigated by computational fluid dynamics (CFD) analyses. An LV model was reconstructed from magnetic resonance imaging, and the shape was modified to mimic TC and PM. Then, the CFD analyses of blood flow were performed using several different combinations of TC, PM, and torsional motion. As the results, the presence of TC decreased the time-averaged wall shear stress and increased the relative residence time (RRT) of a blood stagnation index at the apex of the LV model. The TC-induced blood stagnation was also confirmed by a transportation analysis of the passive scalar. These hemodynamic changes were attributed to the fact that TC blocked the large vortex structures generated during the diastole, thus preventing them from reaching the apex. Moreover, the PM only affected the hemodynamics in its immediate vicinity, and torsional motion caused irregular changes to the RRT level and distribution at the apex. Therefore, the complex internal structures and torsional motion of the LV could cause blood stagnation.

Internal structures of the inner wall of the left ventricle (LV), such as trabeculae carneae (TC) and papillary muscles, may reduce the blood flow velocity, resulting in thrombus formation in the LV of a healthy heart or a heart with atrial fibrillation. The purpose of the present study was to numerically clarify the effects of simplified TC models around the LV wall and atrial fibrillation on the blood flow field as a fundamental study. The LV model was constructed from magnetic resonance images, and the model considering atrial fibrillation was constructed based on the volume change data of a healthy subject from which volume increase with atrial contraction was removed. Numerical analysis was performed considering eight simplified TC models around the LV wall. The numerical results revealed that the oscillatory shear index and relative residence time (RRT) at the apex in the LV model with internal structures were larger than those in the LV model without internal structures, which indicates that the blood flow tends to stagnate. On the other hand, as a result of the LV model considering the atrial fibrillation, the time-averaged wall shear stress decreases and the RRT increases at valley points of the internal structures.

Although the blood flow velocity in a left ventricle (LV) has been considered to be sufficiently fast to prevent thrombus formation, internal wall structures, such as trabeculae carneae (TC) and papillary muscle, recently received attention as possible causes of reduced near-wall blood flow. As a fundamental consideration of this problem, this study established a method for constructing an unsteady LV model from magnetic resonance (MR) images and investigated the effect of a few simplified TC structures on the blood flow in the model. The LV model at arbitrary time steps was constructed by deforming a computational mesh generated from MR images at a reference time step. The validity of the proposed construction scheme was confirmed by comparison with the configuration of an LV model extracted from MR images. Numerical analysis was performed for the unsteady blood flow in LV models with and without two simplified TC structures. The flow field in the model with the internal structure differed from that in the model without the internal structure near the wall, and flow separation caused by the internal structure decreased wall shear stress on the rear of the internal structure. The computational results provide fundamental information for the complex interaction between the internal structures and the blood flow in an LV.

In order to examine mechanical interactions between erythrocytes and a blood vessel surface, the frictional characteristics between erythrocytes and plates in plasma have been measured by an inclined centrifuge microscope. The frictional characteristics have been properly reproduced by a numerical simulation of a rigid erythrocyte model assuming a flat bottom surface. However, validity of the assumption has not been confirmed. The purpose of this fundamental study, therefore, was to clarify the behavior of a two-dimensional circular capsule subjected to inclined centrifugal force near a plate in a fluid. An unsteady simulation was performed for various values of the angles of the inclined centrifugal force and membrane elasticity. In equilibrium states, a lubrication domain with high pressure and a large shear stress is formed between the capsule and the base plate, and the bottom surface of the capsule becomes flat with a positive attack angle. The gap distance and translational and rotational velocities increase with decreasing membrane elasticity or increasing centrifugal force angle. The attack angle increases with increasing membrane elasticity or centrifugal force angle. The results in this study qualitatively justified the assumption of the former numerical study that erythrocytes in an inclined centrifuge microscope have a flat bottom surface and its result that they have a positive attack angle in equilibrium state.

Mechanisms of development, growth, and rupture of a cerebral aneurysm have been studied by computational fluid dynamics (CFD), calculating hemodynamic parameters, such as wall shear stress, oscillatory shear index (OSI), and relative residence time (RRT). It is well known that the upstream velocity profile and upstream vessel shape influence the computational results. However, few studies have dealt with cases involving a bifurcation upstream of a cerebral aneurysm. Furthermore, the fluid-dynamic effects of multiple structural elements of upstream vessel shape, such as a bifurcation and a bend, on the results of CFD remain unknown. The purpose of this study was to elucidate the fluid-dynamic effects of multiple structural elements of upstream vessel shape such as bifurcation and bend on blood flow and hemodynamic parameters inside an aneurysm. Computations were performed for blood flow in a cerebral aneurysm with upstream sequential elements of a bifurcation, a bend, and a straight section, using four models with different upstream boundaries, i.e., before the bifurcation, after the bifurcation before the bend, after the bend, and after the straight section just before the cerebral aneurysm. The results were compared to elucidate the effect of each upstream structural element on the blood flow and hemodynamic parameters in the cerebral aneurysm. Differences in OSI and RRT resulting from changes in the velocity distribution were observed locally in the aneurysm between the models. It was also found that the effect of the bifurcation on the velocity distribution was greater than that of the bend.

Suspension flows are ubiquitous in industry and nature. Therefore, it is important to understand the rheological properties of a suspension. The key to understanding the mechanism of suspension rheology is considering changes in its microstructure. It is difficult to evaluate the influence of change in the microstructure on the rheological properties affected by the macroscopic flow field for non-colloidal particles. In this study, we propose a new method to evaluate the changes in both the microstructure and rheological properties of a suspension using particle tracking velocimetry (PTV) and a power-law fluid model. Dilute suspension (0.38%) flows with fluorescent particles in a microchannel with a circular cross section were measured under low Reynolds number conditions (Re ≈ 10−4). Furthermore, the distribution of suspended particles in the radial direction was obtained from the measured images. Based on the power-law index and dependence of relative viscosity on the shear rate, we observed that the non-Newtonian properties of the suspension showed shear-thinning. This method will be useful in revealing the relationship between microstructural changes in a suspension and its rheology.

Turbulent plane jets are prototypical free shear flows on which fundamental research can expand the overall understanding of turbulent flows. In this study, flow characteristics of the turbulent plane jets are studied by means of direct numerical simulation (DNS) based on the finite difference method. The effects of the initial conditions at the jet exit (i.e. Reynolds number and velocity profile) on the spatial development of velocity and scalar fields are mainly investigated. Meanwhile the instantaneous coherent structures, based on the Q-criterion and the local minimum of pressure, are presented. The results suggest that the plane jet flow with the higher Re (=Ubd/ν : Ub is the bulk mean velocity at the jet exit, d is the slot width, and ν is the kinematic viscosity) and the parabola velocity profile at the jet exit will correspond to the shorter potential core, furthermore, the lower Re and the parabola velocity profile will strengthen the decay of the mean field in the process of flow transition to full turbulence. The flow self-similarity will be achieved at shorter streamwise distance from the jet exit for the higher Re and the parabola velocity profile at the jet exit. Moreover, the dependency of coherent structures on the initial Reynolds number is remarkable, especially in the flow development region, but the change of initial velocity profile at the jet exit hardly acts on the scale of coherent structures. It is also observed that the scalar field is more sensitive to changes of initial conditions than the velocity field.

Elucidation of the mechanical interaction between an erythrocyte and an endothelial cell is an important issue that may lead to clarification of mechanisms of cardiovascular diseases and development of new treatments. In order to clarify the interaction, frictional characteristics of erythrocytes moving on various plates have been measured using an inclined centrifuge microscope. The objective of this study was to clarify the mechanical interaction between an erythrocyte moving in medium subject to inclined centrifugal force and endothelial cells on a plate. Three-dimensional (3D) analysis was performed with contact force models between an erythrocyte and glycocalyx on the surface of endothelial cells and two-dimensional (2D) analysis was conducted using a lubrication theory for compressible porous media and a simple erythrocyte model. In the 3D analysis, two contact force models were adopted in which shear stresses acting on the bottom surface of an erythrocyte varied proportional or inversely proportional to the distance to the base plate. As a result, the experimental frictional characteristics for an endothelia-cultured plate were properly reproduced by the inverse proportion model. In the 2D analysis using the lubrication theory, the result without the porous media qualitatively agreed with those of the experiment for the plain and material-coated plates and that of the 3D analysis without contact force models, whereas the result with the porous media was qualitatively different from those of the experiment and the 3D analysis.

The goal of this study is elucidation of propulsion mechanism of small creatures by ciliated swimming legs. For this purpose, a ciliated pereiopod of an opossum shrimp was introduced and it was modeled with a straight cylindrical stem with 10 much narrower cylindrical poles perpendicularly projecting on the stem. Flow drag acting on the pereiopod in a steady flow, which corresponds to the thrust force by paddling of the pereiopod, was computed with a variety of clearance between each adjacent pair of cilia d and the flow velocity U. It was found that the drag increased with the increase in d to be saturated with a certain value in the range of d ≥ 0.04 mm where influence of boundary layers of adjacent cilia is negligible, and the drag agreed well with that estimated from drag of a two-dimensional cylinder. This result suggests that the opossum shrimp is propelled with the drag-based swimming and the ciliated pereiopods supply greater thrust force than tabular pereiopods with the same projection area. It was also found that the drag decreased in the range of d > 0.07 mm in which some cilia come into the boundary layer of body of the shrimp. It was optically observed that distance between adjacent cilia is around 0.07 mm on the stem and cilia near the root of the pereiopod are shorter than those near the tip. The present results suggest that the ciliated pereiopod is well designed to efficiently generate the thrust force within a limited length and mass by preventing influence of the boundary layers.

Preeclampsia (PE) is a pregnancy-induced hypertension with proteinuria that typically develops after 20 weeks of gestation. A reduction in uterine blood flow causes placental ischemia and placental release of anti-angiogenic factors such as sFlt-1 followed by PE. Although the reduced uterine perfusion pressure (RUPP) model is widely used in rats, investigating the role of genes on PE using genetically engineered animals has been problematic because it has been difficult to make a useful RUPP model in mice. To establish a RUPP model of PE in mice, we bilaterally ligated ovarian vessels distal to ovarian branches, uterine vessels, or both in ICR-strain mice at 14.5 days post coitum (dpc). Consequently, these mice had elevated BP, increased urinary albumin excretion, severe endotheliosis, and mesangial expansion. They also had an increased incidence of miscarriage and premature delivery. Embryonic weight at 18.5 dpc was significantly lower than that in sham mice. The closer to the ligation site the embryos were, the higher the resorption rate and the lower the embryonic weight. The phenotype was more severe in the order of ligation at the ovarian vessels < uterine vessels < both. Unlike the RUPP models described in the literature, this model did not constrict the abdominal aorta, which allowed BP to be measured with a tail cuff. This novel RUPP model in mice should be useful for investigating the pathogenesis of PE in genetically engineered mice and for evaluating new therapies for PE.

Pulse diagnosis in traditional Chinese medicine is said to be able to detect not only illness but also decline of health in the patients from tactile sense of the pulse in the radial artery at the wrists. This diagnosis, however, is not supported by concrete scientific evidence. The authors have proposed a non-linear spring model of subcutaneous tissue on the radial artery and one-dimensional arterial blood flow model in an arm for the purpose of scientific verification of the pulse diagnosis. They performed, in the former study, a numerical experiment with this mathematical model in which the radial artery was indented in a stepwise manner by a pressure sensor, which extract the fundamental mechanism of the pulse diagnosis, to validate the subcutaneous tissue model and to find the appropriate coefficient to fit the experimental result. They investigated, in this research, contribution of parameters of supply pressure of the blood and tube law of the artery on the change in the pressure pulse waves with the indentation steps with respect to mean value Poav and amplitude ΔPo of the pressure. It was shown that mean supply pressure affects both Poav and ΔPo, while amplitude of the supply pressure affects ΔPo. It was also shown that profile of ΔPo vs. distance of the indentation changes drastically as the artery becomes hard. Lastly, it was examined to reproduce the experimentally obtained pressure pulse waves during the indentation in their former work with the mathematical model by adjusting the parameters. The result showed better agreement than the former result, but it implied that ulnar artery had to be taken into consideration for quantitative fitting of the pulse waves to the range where the radial artery was nearly flattened by the indentation.

Measurement-integrated (MI) simulation is a numerical flow analysis method with a feedback mechanism from measurement of a real flow. It correctly reproduces a real flow under inherent ambiguity in a mathematical model or a computational condition. In this paper we theoretically investigated the destabilization phenomenon of MI simulation, in which analysis error suddenly increases at some critical feedback gain. This phenomenon has been considered as instability of a closed-loop feedback system, but present study treated it as that of a numerical scheme. First, the mechanism of the destabilization phenomenon was investigated based on the sufficient condition of the convergence of iterative calculation of existing MI simulation. It was found that the feedback signal in the source term destabilized the iterative calculation. Then, a new MI simulation scheme was derived by evaluating the feedback signal in the linear term to remove the cause of the destabilization. The validity of the present theoretical analysis was verified for examples treated in former studies of MI simulations: blood flow in an aneurismal aorta with ultrasonic measurement, blood flow in a cerebral aneurism with magnetic resonance measurement, Karman vortex street behind a square cylinder with PIV measurement, and fully developed turbulent flow in a square duct with ideal measurement. Occurrences of destabilization phenomenon in all the examples were well explained by the condition of this study, especially for cases of relatively small time steps and large feedback gains. Furthermore, the new MI simulation scheme realized the analysis without the destabilization phenomenon. The present theoretical result confirming that the destabilization phenomenon is not the instability of the feedback system but that of a numerical scheme is generally applicable to MI simulations using the velocity error for the feedback signal.

This paper deals with measurement-integrated (MI) simulation, which is based on the observer in dynamical system theory to obtain the exact and detailed information of real flows. In this study, we propose the MI simulation coupled with Particle Image Velocimetry (PIV) for a flow with the Karman vortex street behind a square cylinder at Reynolds number of 1200 based on the cylinder width. The validity of the PIV-MI simulation is first examined in two-dimensional numerical experiment. The effect of feedback data rate is investigated by changing the feedback frequency and the feedback area. Then effectiveness of the PIV-MI simulation is validated in experiment. As a result, the PIV-MI simulation with full feedback shows good agreement with the standard solution for both the mean velocity and the velocity fluctuation. From the viewpoint of the reduced feedback data rate, spatially limited feedback shows better results than temporarily limited feedback. It is also confirmed that the information around the cylinder is important to reproduce the wake behind the cylinder. In the result of the experimental validation, the PIV-MI simulation reproduces the experimentally obtained flow field, showing the same effect of the feedback in accordance with the numerical experiment.

In vitro blood vessel biomodeling with realistic mechanical properties and geometrical structures is helpful for training in surgical procedures, especial those used in endovascular treatment. Poly (vinyl alcohol) hydrogel (PVA-H), which is made of Poly (vinyl alcohol) (PVA) and water, may be useful as a material for blood vessel biomodeling due to its low surface friction resistance and good transparency. In order to simulate the mechanical properties of blood vessels, measurements of mechanical properties of PVA-H were carried out with a dynamic mechanical analyzer, and the storage modulus (G’) and loss modulus (G”) of PVA-H were obtained. PVA-Hs were prepared by the low-temperature crystallization method. They were made of PVA with various concentrations (C) and degrees of polymerization (DP), and made by blending two kinds of PVA having different DP or saponification values (SV). The G’ and G” of PVA-H increased, as the C or DP of PVA increased, or as the proportion of PVA with higher DP or SV increased. These results indicate that it is possible to obtain PVA-H with desirable dynamic viscoelasticity. Furthermore, it is suggested that PVA-H is stable in the temperature range of 0°C to 40°C, indicating that biomodeling made of PVA-H should be available at 37°C, the physiological temperature. The dynamic viscoelasticity of PVA-H obtained was similar to that of the dog blood vessel measured in previous reports. In conclusion, PVA-H is suggested to be useful as a material of blood vessel biomodeling.

Cardiovascular diseases are closely related to blood flow. Ultrasonic-Measurement-Integrated (UMI) simulation, in which results of ultrasonic measurement are fed back to the flow simulation, was proposed in a previous study in order to reproduce the real blood flow accurately and efficiently. The usability of the UMI simulation was confirmed by numerical experiment, but the effectiveness of this simulation was strongly affected by the accuracy of the ultrasonic measurement. In this paper, we examined the accuracy of a commercial ultrasonic measurement device by an experiment with a PVA-H straight tube phantom. By analyzing the measured color Doppler images for a developed laminar flow inside the phantom, we obtained the relationship between the color Doppler value and the Doppler velocity (C-V relationship). It was revealed that the original C-V relationship provided in the device as a color bar was not suitable for quantitative evaluation of Doppler velocity to be used in UMI simulation. Compared with the original C-V relationship, the present C-V relationship results are in far better agreement with the analytic solution. Investigation of the normalized error confirmed that the result obtained with the present C-V relationship was reliable in cases of relatively high Reynolds number in the flow domain except near the wall. The two signal conditioning factors of the device had little influence on the Doppler velocity. Finally, we investigated the effect of temporal and spatial averaging of ultrasonic measurement data to clarify the relation between the number of averagings and the level of agreement with the analytic solution.

Many studies have been carried out on the relationship between the occurrence and progression of circulatory diseases and hemodynamics. However, it is difficult to obtain accurate and detailed information on blood flow in the living body with existing experimental and numerical methods. The authors have previously proposed the Ultrasonic-Measurement-Integrated (UMI) simulation and shown that the blood flow in an aortic aneurysm can be accurately reproduced when feedback signals derived from the difference between measured and computed Doppler velocities are fed back to the numerical simulation. In the present study, we performed a fundamental numerical experiment in which UMI simulation was applied to a developed laminar pipe flow using an axisymmetric model in order to understand the effect of the feedback law on the accuracy of UMI simulation systematically. The effect of two types of ultrasonic probes, the linear scanning type and the sector scanning type, and the effect of 70° and 110° irradiating angles of the ultrasonic beam in the linear probe were investigated. It was confirmed that the result of UMI simulation asymptotically approached the standard solution of developed laminar flow downstream of the feedback domain in all cases using the linear probe and the sector probe with axisymmetric feedback. Under the present conditions, a linear probe with a radiation angle of 70° was most effective, whereas there was not so much improvement in the accuracy in the case using the sector probe. The effect of the singularity of the axisymmetric coordinate on the pipe axis was observed in the axial velocity profile near the entrance of the feedback domain, but disappeared some distance downstream in that domain.

We are pleased to present the issue “Biomedical Flow Dynamics.” Biomedical engineering has been globally recognized as an engineering field for biomedical applications. From now, the combination of biomedical engineering with flow dynamics will unravel a new research field for engineering and science in biomedical applications. This transdisciplinary research that combines flow dynamics and biomedical engineering will enable the progress of research pertaining to cells and bodies under the emerging biological, computational simulations, and experimental engineering techniques. Therefore, this special issue tries to cover various research topics. We think that the papers are of great significance to all fields. Moreover, we believe that the researches will directly influence the quality of life. We sincerely appreciate the wonderful opportunity given to us by the JBSE's editorial board members. Furthermore, we would like to express our sincere gratitude to all the authors and reviewers for their excellent contributions and making this special issue fruitful. Finally, we are thankful to the JBSE editorial office for their technical assistance.

Cellular and animal experiments and computational fluid dynamics (CFD) have revealed that mechanisms of the initiation, growth and rupture of a cerebral aneurysm are related to hemodynamics. By direct observation of a cerebral aneurysm during craniotomy, thinning or thickening sites can be found on the aneurysmal wall. The thinning site of a cerebral aneurysm is considered to be at high risk of rupture. In addition, the thickening site of a cerebral aneurysm is not necessarily in a stable state since arteriosclerosis may have occurred. Hence, information on wall conditions, i.e., thinning and thickening, of a cerebral aneurysm is beneficial for clinical diagnosis and treatment. In this study, a hemodynamic parameter to effectively estimate the thinness or thickness of cerebral aneurysmal walls was investigated. CFD of hemodynamics in cerebral aneurysms developed at the anterior communicating artery (ACoA), a common site of cerebral aneurysms, was performed, and characteristic distributions of hemodynamic parameters were investigated by comparing the computational results with clinical images. As a result, a high value of the time-averaged wall shear stress (TAWSS) was found to be present at thinning sites, while a low TAWSS and a high relative residence time (RRT) of an indicator of blood retention were observed at thickening sites. Thinning and thickening sites each have their own characteristics distribution of hemodynamic parameters.

In this paper, direct numerical simulation (DNS) is carried out to investigate the flat plate boundary layer with heat transfer affected by a wake of a square bar. The bar is installed parallel to the plate and normal to the flow direction at the beginning of the boundary layer. The gap between the bar and the plate is varied in two cases. The fractional step method based on the Runge-Kutta and central difference schemes is used in the simulation. The instantaneous structures along with the statistical characteristics of the flow and thermal fields are presented and discussed. The results show that, in the large-gap case (C/d＝3.0), Karman vortices are shed from the bar and they perturb the boundary layer by advecting the fluid wallward and outward in turn. In the small-gap case (C/d＝0.25), however, the positive vortices shed from the lower side of the bar are small and the large negative vortices shed from the upper side of the bar dominate over the boundary layer, resulting in the strong backward sweep motions of fluid near the plate. Such motions contribute to the reduction in skin friction in comparison with the large-gap case. On the other hand, the thermal boundary layer in the small-gap case is strongly suppressed by the large negative vortices. This results in the larger temperature gradient and more active heat transfer in comparison with the large-gap case. These indicate that careful design is required to enhance heat transfer through a flat plate by utilizing a wake of a square bar.

If highly precise elucidation of the blood flow characteristics in a carotid bifurcation was possible, it would be widely applicable to diagnosis of circulatory diseases such as arteriosclerosis and cerebrovascular disease. This study was conducted to establish a new flow-dividing ratio estimation method applicable to an unsteady flow on a two-dimensional ultrasonic-measurement-integrated simulation of a carotid artery bifurcation for which it has been previously difficult to obtain a stable solution. In this new method, the flow-dividing ratio was directly adjusted by specifying the flow rate in a branch so that the difference of the Doppler velocities in the external carotid artery was decreased. The effectiveness of the proposed method was confirmed by a numerical experiment using the actual shape of a carotid artery bifurcation, and the superiority of the two-dimensional ultrasonic-measurement-integrated simulation over the ordinary simulation in terms of the reproducibility of the blood flow structure was clarified by analysis using clinical ultrasound data.

In the present study, the flow characteristics of a spatially evolving plane jet are investigated, focusing on the dynamics of coherent structure (CS), flow transition, and evolution. Instantaneous and statistical properties obtained by direct numerical simulation (DNS) are discussed noting the influence of the Reynolds number, by analyzing the velocity and scalar fields. It is discovered that the plane jet is clearly dependent on the Reynolds number, especially in the near field. The evolution and scale of CS have a strong dependence on the Reynolds number, which shows significant effects on the transport of the momentum and scalar. The increase of the Reynolds number develops a more contorted interface between the ambient fluid and plane jet, with a smaller scale. A moderate Reynolds number is a good condition for the study of the transition from a laminar jet to a turbulent jet in detail. The results show that, because of a low Reynolds number, the growth of two initial shear layers at the jet boundary is accelerated and the velocity fluctuation is advanced from two-dimensional to three-dimensional. Furthermore, the Reynolds number dependency of the plane jet is more significant on the condition of low Reynolds number.

The effects of external and internal disturbances on the development of boundary layer with heat transfer are investigated by means of direct numerical simulation (DNS) based on the finite difference scheme. The fractional step method is used to solve the governing equations. The external disturbance is generated by a regular turbulence-generating grid, while the internal disturbance is generated by a tripping object mounted on the wall. In order to clarify the momentum and heat transfer mechanism in a boundary layer under these effects, the instantaneous and statistical characteristics of velocity and temperature fields are presented and discussed along with their interactions. The results show that the boundary layer in the case with grid turbulence becomes turbulent even though the Reynolds number based on the momentum thickness is low. On the other hand, in the case with the tripping object, only low-amplitude fluctuations are generated in the vicinity of the tripping object and the boundary layer does not fully developed. The grid increases the skin friction and enhances heat transfer more significantly than the tripping object. It is also found that strong strain in the viscous sublayer, which is induced by the vortical motion in the buffer layer, contributes to the enhancement of heat transfer.

The gradient diffusion hypothesis for turbulent mass fluxes of reactive scalar is investigated by using direct numerical simulations (DNS) of a planar jet with a second-order chemical reaction A+B→R. Reactants A and B are separately supplied in the jet and ambient fluids, respectively. DNS is performed at three different Damköhler numbers, i.e, Da=0.1, 1, and 10. Eddy diffusivity and turbulent Schmidt number of reactive species are calculated from the DNS results. The results show that the longitudinal (x-direction) eddy diffusivity of reactant A near the jet centerline is always positive, whereas the longitudinal eddy diffusivities of reactant B and product R can be negative near the jet centerline. Near the jet centerline, the lateral (y-direction) eddy diffusivity of reactant A, DtA,y, becomes small, but the lateral eddy diffusivity of reactant B, DtB,y, becomes large because of the chemical reaction. In the outer region of the jet flow, the chemical reaction has the opposite effect on DtA,y and DtB,y, and the chemical reaction makes DtA,y large, but DtB,y small. It is concluded that the gradient diffusion hypothesis is largely affected by the chemical reaction, and this effect of chemical reaction should be taken into account when the gradient diffusion model is used to estimate turbulent mass fluxes of reactive scalar.