Number Flow Research Articles

Rutting Evaluation of Asphalt Mixtures Using Static, Dynamic, and Repeated Creep Load Tests

Flow tests (flow number and flow time) are explicatory indices for the evaluation of the rutting potential of asphalt mixtures. This study investigates the rutting susceptibility of various asphalt mixtures subjected to static and dynamic creep tests. Four wearing course gradations were selected; and asphalt mixture’s specimens were fabricated using Superpave gyratory compactor. The flow tests were performed at a single effective temperature of 54.4 $${^{\circ }}\hbox {C}$$ and a stress level of 300 kPa using asphalt mixture performance tester. Dynamic modulus ( $${\vert }{E}^{*}{\vert }$$ ) test was conducted at different temperatures and frequency levels. The test results indicate that specimens of mixtures experienced tertiary flow state in the flow number (FN) test, but no specimen achieved tertiary flow state in the flow time (FT) test. Data smoothening technique was employed for removing the resonance from the raw test data. The performance of mixtures was compared using: (a) FN values; (b) number of cycles at which the 50,000 microstrains occurred; and (c) intercept obtained from regression analysis of total permanent strain. The observed accumulated axial strains at time of termination were used for comparison purpose of mixtures as tertiary phase was not achieved in FT tests. Three statistical models were developed of the different functional formulation—i.e. Cobb–Douglas, power and first-order multiple linear regression—using $${\vert }{E}^{*}{\vert }$$ , FN, and mix volumetric data. The laboratory results were used to rank the mixtures based on their resistance to rutting. The findings of the study are envisaged to facilitate the implementation of performance-based mechanistic-empirical pavement design approach.

Critérios para os resultados do ensaio uniaxial de carga repetida de misturas asfálticas em laboratório a partir do desempenho em campo

A busca por critérios que auxiliem na seleção de misturas asfálticas em laboratório que resistam à deformação permanente em campo motivou o desenvolvimento desta pesquisa. A partir dessa motivação, o objetivo foi avaliar a relação entre os dados experimentais disponíveis no Brasil de deformação permanente em laboratório (uniaxial de carga repetida) com aqueles encontrados em campo [Afundamento em Trilha de Roda (ATR)], com vistas ao refinamento de critérios para os resultados do ensaio laboratorial em função do tráfego. A partir da organização do banco de dados de 12 trechos experimentais monitorados, utilizou-se o método estatístico dos clusters para indicar 4 categorias de Flow Number (FN). Considerou-se que FNs inferiores a 100 resistem apenas a um tráfego leve; FNs acima de 100 são indicados para um tráfego médio; superior a 300 para um tráfego pesado; e acima de 1000 para um tráfego extremamente pesado. Destaca-se ainda a relevância da continuidade do monitoramento de pistas experimentais no Brasil. Desta forma, as informações possibilitarão a verificação contínua e o refinamento dos critérios propostos nesta pesquisa.

Characterization of three-stage rutting development of asphalt mixtures

The three stage rutting behavior of several asphalt mixtures was investigated. Confinement, moisture, stress and temperature significantly affected rutting. Absence of a physically induced confinement stress by the metallic sides the wheel tracking testing mold had the highest influence on rutting, followed by temperature, moisture and lastly stress. A higher primary rutting rate indicated a lower flow number (FN) and a faster failure rate. A linear model could relate the transition point between the primary stage and the mixtures’ flow numbers. It was independent of the testing conditions, methods and types of mixtures. A new three stage model was proposed and could simulate the rutting development of mixtures better than the Francken model. The FN of mixtures under different conditions of testing could also be related to parameter ‘c’ of the new model using a similar power law equation. The primary rutting rate, the primary transition point and parameter ‘c’ of the new model could be used in mixture characterization.

Permanent deformation prediction of asphalt concrete mixtures – A synthesis to explore a rational approach

Exploring a reliable laboratory test parameter to predict the rutting (permanent deformation) susceptibility of asphalt concrete (AC) mixtures remains a challenge to asphalt industry. Flow Number (FN) test as part of the HMA mix- and structural- design processes is used to characterize the AC mixtures rutting resistance and optimize field performance. Cognizant of the noise-characteristic of FN test data and need to apply post-processing techniques, this study explores a new parameter – FN Index as a ratio of traditional FN (cycles) and corresponding accumulated permanent strains. The FN and dynamic modulus (DM) tests are conducted on the Superpave gyratory compacted specimens. Twelve (six wearing course and six base course) mixtures were selected including Superpave, Asphalt Institute, British Standard dense bituminous macadam, and Pakistan’s National Highway Authority gradations. Under the hypothesis of axial compression applied on the cylindrical specimen, first-order multiple linear regression models are developed for FN and FN Index as a function of the binder, volumetric parameters, gradation, and DM to estimate permanent deformation. The results indicate that FN models are strongly correlated with DM values at 38°C and 54.4°C temperature, gradation, volumetric, and Superpave rutting parameter. The predictive capability of developed models is validated using data of 16 different AC mixtures acquired from published literature. The findings of this study provide guidance to asphalt mix designers for providing cost-effective designs within specified levels of rutting resistance.

Mechanisms of asphalt mixture rutting in the dry Hamburg Wheel Tracking test and the potential to be alternative test in measuring rutting resistance

Rutting is one of the most important failures occurring in hot mix asphalt (HMA) especially in the summer season and slow moving traffic areas. Rutting is a pavement surface failure compromising the safety and ride comfort of traveling and thus needs to be accurately evaluated in a laboratory. Although the flow number (FN) test is commonly used for evaluating the rutting resistance of HMA in a laboratory, there are some shortcomings in using FN test such as the costly and complicated equipment. Another potential test that is likely to be more advantageous than the FN test for evaluating the rutting resistance is the Hamburg Wheel Tracking (HWT) test, however, it is typically conducted in wet condition, and inadequate results in dry condition have been reported. The objective in this study is to optimize the HWT test subject to dry condition to be one potential method in measuring rutting resistance in a laboratory. Two rutting mechanisms (densification and shear failure) of HMA samples conducted in the HWT device were determined by Image Processing and Analysis version 2 (IPAS2). Results indicate that HMA samples under the dry HWT test can exhibit both rutting mechanisms in which typically occur in the field. Also, the dry HWT test shows a very good R2 for a relation of creep slope with the confined and unconfined FN test. As a result, the dry HWT can be an effective tool of quantifying rutting potential with better simulating to field behavior, lower cost of equipment, and less complicated geometry that can also accommodate field cores.

Solar pavement: A new emerging technology

The present work is conducted to evaluate the feasibility of using solar pavements as a sustainable energy producer to supply electrical energy. For this purpose, we prepared two prototypes entitled as “solar panel” (solar cell embedded in rubber and Plexiglas) and “solar pavement” (solar cell embedded between two porous rubber layers) which both are capable of harvesting and converting the solar energy into photovoltaic cells. In this work, components of the new solar pavements were introduced. These two designed pavements were evaluated in terms of supply energy, surface safety movement, and structural performance. The British Pendulum Tester (BPT) and Universal Test Machine (UTM) were used for measuring surface frictional properties and determining the dynamic property of solar pavement, respectively. Moreover, the drainage test was investigated for both prototypes. To survey the feasibility of solar pavement to achieve the electrical energy through solar cells, I-V (current-voltage) measurements were carried out to record the current and voltages of the solar cells embedded in the pavement under different conditions and determine their power conversion efficiency (PCE). The BPT values for solar panel and solar pavement under the wet condition were measured as 42 and 47.8, respectively. Also, the drainage test showed that the average volumetric flow rates of solar panel and solar pavement are 0.018 and 0.042L/s, respectively. Moreover, the value of drainage test was 0.0224L/s in asphalt pavement. The solar pavement in comparison to solar panel showed a higher PCE value of 5.336%. Besides, based on the UTM results, the flow number (FN) is 1002 with 49mm deformation for solar panel and 1260 with 65mm deformation for solar pavement. The UTM results also showed that solar pavement improves rutting performance in comparison with a solar panel. Thus, adding a new layer of the solar cell and rubber solar pavement could enhance strength parameters and electricity generation for transportation application.

Empirical Correlation of Permanent Deformation Tests for Evaluating the Rutting Response of Conventional Asphaltic Concrete Mixtures

Rutting or permanent deformation is one of the severe distresses manifested in flexible pavements caused by the various mechanisms such as densification, lateral plastic flow, and/or loss of materials under wheel path due to repeated heavy traffic loads. Various laboratory tests have been devised to determine the rutting propensity and to optimize the field performance of hot mix asphalt (HMA) mixtures as a part of the HMA mix and structural design processes. Although various approaches exist to predict the permanent deformation of HMA, this study develops a relationship of flow number (FN), dynamic modulus (DM), and uniaxial repeated-load permanent deformation (RLPD) to enable the trade-off analysis among them. Also, a novel parameter, FN index, is explored and used to determine the rutting potential of HMA mixtures. Twelve globally practiced HMA mixtures are investigated with three different performance grade binders and single limestone aggregate source. Superpave gyratory compacted specimens are subjected to performance testing (FN, DM, and RLPD) and results indicate a strong correlation of FN index with DM and exhibit better correspondence than the traditional FN (cycles) parameter.

Characterization of the rutting potential of modified asphalt binders and its correlation with the mixture’s rut resistance

This study was intended to evaluate the susceptibility of asphalt binders and mixtures to rutting. The binders have the same high PG grade (PG 76-xx) and a dense-graded gradation curve was used to produce the mixtures. Three types of polymers – Elvaloy®, SBS and SBR – and polyphosphoric acid (PPA) were selected. The tests included softening point, oscillatory shear (parameter G∗/sinδ), multiple stress creep and recovery (Jnr) and flow number (FN). The rankings of binder and mixture parameters (Jnr, G∗/sinδ, softening point and FN) are the same only for Jnr and FN, and the applicability of G∗/sinδ to modified materials is questionable.

Application of bipolar coagulation hemostasis in laparoscopic ovarian endometriosis cyst stripping

Objective To investigate the effect of bipolar coagulation hemostasis on ovarian function in patients with laparoscopic ovarian endometriosis cyst stripping. Methods From January 2015 to February 2016, 88 cases of ovarian endometriosis cyst were selected by using the random number table method.They were randomly divided into observation group and control group, 44 cases in each group.The observation group was treated with bipolar coagulation hemostasis, and the control group was treated with endoscopic suturing.The luteinizing hormone(LH), follicle stimulating hormone(FSH), estradiol(E2), sinus follicle number(FO) and ovarian stroma systolic blood flow velocity peak preoperation, postoperation and postoperative 6 months were detected. Results The E2 levels in the observation group postoperation and postoperative 6 months were (190.03±30.88)pmol/L and (179.82±29.94)pmol/L, which were significantly lower than those in the control group[(230.04±32.22)pmol/L and (232.49±28.41)pmol/L, t=5.947, 9.465, all P 0.05). Conclusion The application of different hemostatic methods in laparoscopic ovarian endometriosis cyst stripping have effect on ovarian reserve function, but bipolar coagulation and hemostasis can significantly decrease ovarian reserve function, and it should be used as little as possible during the operation. Key words: Cysts; Endometriosis; Laparoscopy

Small morphing wing aerial vehicle dynamic modelling basing on simulation and flight test

Morphing wings can be more stable and more robust to gust in the flow of low Reynolds number compared with normal fixed wings. In contrast to big airplanes, small ones with morphing wings can rely on passive wing deformation to reduce disturbance rather than active control by multi-control surfaces. Engineering modelling for the prototype in the paper ignores aeroelastic effect because of the small deformation amount in terms of static aeroelasticity and high modal frequency in terms of dynamic aeroelasticity. Aerodynamic coefficients are determined through flight test and software calculation. An accurate trim condition is solved using a 6DOF flight model. The preciseness of the trim result is proved by comparing experiment results. The longitudinal and lateral state-space equations benchmarked against trim point is built. Dynamic response of the non-control perturbation motion are analysed.

Experimental Investigation of Brazilian 14-X B Hypersonic Scramjet Aerospace Vehicle

The Brazilian hypersonic scramjet aerospace vehicle 14-X B is a technological demonstrator of a hypersonic airbreathing propulsion system based on the supersonic combustion (scramjet) to be tested in flight into the Earth’s atmosphere at an altitude of 30 km and Mach number 7. The 14-X B has been designed at the Prof. Henry T. Nagamatsu Laboratory of Aerothermodynamics and Hypersonics, Institute for Advanced Studies (IEAv), Brazil. The IEAv T3 Hypersonic Shock Tunnel is a ground-test facility able to produce high Mach number and high enthalpy flows in the test section close to those encountered during the flight of the 14-X B into the Earth’s atmosphere at hypersonic flight speeds. A 1 m long stainless steel 14-X B model was experimentally investigated at T3 Hypersonic Shock Tunnel, for freestream Mach numbers ranging from 7 to 8. Static pressure measurements along the lower surface of the 14-X B, as well as high-speed Schlieren photographs taken from the 5.5° leading edge and the 14.5° deflection compression ramp, provided experimental data. Experimental data was compared to the analytical theoretical solutions and the computational fluid dynamics (CFD) simulations, showing good qualitative agreement and in consequence demonstrating the importance of these methods in the project of the 14-X B hypersonic scramjet aerospace vehicle.

Correlating creep properties of bituminous binders with anti-rutting performance of corresponding mixtures

In the experimental study described in this paper, rutting properties of different bituminous binders and those of corresponding mixtures characterized by common composition and volumetrics were investigated and compared. Single shear creep-recovery (SSCR) tests were carried out on binders for the determination of their creep compliance rate (CCR), whereas bituminous mixtures were evaluated by referring to their Flow Number (FN), derived from repeated compressive loading tests. Analysis of experimental data revealed the existence of a strong correlation between rutting parameter of binders and permanent deformation response of mixtures. This confirmed the potential of the proposed testing procedure of being adopted for the evaluation of rutting properties of bituminous binders and for their consequent performance-related ranking.

Simulation of dissolution in porous media in three dimensions with lattice Boltzmann, finite-volume, and surface-rescaling methods.

We present a pore-scale dissolution model for the simulation of reactive transport in complex porous media such as those encountered in carbon-storage injection processes. We couple a lattice Boltzmann model for flow calculation with a finite-volume method for solving chemical transport equations, and allow the computational grid to change as mineral surfaces are dissolved according to first-order reaction kinetics. We appraise this scheme for use with high Péclet number flows in three-dimensional geometries and show how the popular first-order convection scheme is affected by severe numerical diffusion when grid Péclet numbers exceed unity, and confirm that this can be overcome relatively easily by using a second-order method in conjunction with a flux-limiter function. We then propose a surface rescaling method which uses parabolic elements to counteract errors in surface area exposed by the Cartesian grid and avoid the use of more complex embedded surface methods when surface reaction kinetics are incorporated. Finally, we compute dissolution in an image of a real porous limestone rock sample injected with HCl for different Péclet numbers and obtain dissolution patterns in concordance with theory and experimental observation. A low injection flow rate was shown to lead to erosion of the pore space concentrated at the face of the rock, whereas a high flow rate leads to wormhole formation.

Achieving the Inside–Outside Coupling During Network Simulation of Isothermal Drying of a Porous Medium in a Turbulent Flow

The problem of isothermal (slow) drying of a porous medium in the form of a square bluff body resting on a flat surface while being exposed to turbulent air flow is investigated in this paper. The porous medium is represented by a pore-network model consisting of a network of volume-less nodes connected to each other via narrow throats. As the air flows past the water-saturated network, the water evaporates in the network and the evaporated water vapors diffuse through the air inside the network to advect away in the outside domain. In the history of such simulations coupling the ‘outside–inside’ processes during drying, this paper investigates, for the first time, the effect of turbulent flow on drying of a porous medium after coupling the outside-the-network flow and transport with the inside-the-network drying and liquid redistribution. Also, a commercial software package is used for the first time to obtain the outside flow. The water redistribution inside the network is predicted by the invasion-percolation algorithm after assuming the dominance of capillary forces over viscous and gravity forces. The outside velocity field is first obtained using the $$k\hbox {-}\varepsilon $$ model in ANSYS Fluent package. Then, the velocity field is used in a finite-volume-based code in order to solve for mass transfer outside the network using the regular convective-diffusive species transport equation. The drying mechanism and vapor transport inside the pore network is coupled with the outside mass-transfer simulation by considering a flux-balancing condition at the top surface of the network. After achieving grid independence and demonstrating the suitability of the no-slip boundary condition for the network top, the effects of the outside-flow Reynolds number and different turbulent flow models on several global drying parameters such as evaporation or drying rate, cumulative drying time, and top-surface saturation were studied. The resistance to vapor transport within the network was observed to dominate the enhanced vapor transport outside the network through the use of turbulent flow. Though the effect of variations in the network throat-size distribution upon saturation distribution within the network was found to be significant, its effect on the drying rate evolution was minimal. The concentration boundary layer thickness, which is employed to set the mass-transfer boundary condition in pore-network simulations and has been hitherto taken as constant in the literature, was found to change not only with position on the network top, but was also found to decline with time due to the drying of the network top.

Effect of aggregate gradation on permanent deformation behavior of a warm mix asphalt

Abstract In this study, the rut susceptibility of warm mix asphalt (WMA) was evaluated by laboratory material characterization tests that included repeated creep testing using universal testing machine (UTM-5P) on WMA and conventional hot mix asphalt (HMA) mixtures. With regard to the fact that aggregate makes up a high proportion of volume and mass of mixtures, this parameter is considered as an important constituent of asphalt concrete. So, one aggregate source, three gradations and three different percentages of Sasobit® content were used to manufacture mixtures. Four creep parameters, namely, flow number (FN), creep stiffness (CS), creep strain slope (CSS) and secondary initial point (SIP), were used to analyze the test results. The primary objective of this research effort was to conduct a comparison between permanent deformation of HMA and WMA mixtures and also to evaluate the effect of aggregate gradation and different Sasobit® contents on introduced creep parameters. Analysis of data shows that the creep behavior of both asphalt mixtures (HMA and WMA) was influenced by aggregate gradation and also by Sasobit® content. Comparison of test results between HMA and WMA exhibits that, in general, WMA mixtures exhibit improved rut resistance compared to conventional mixtures. Also, it is concluded that creep strength of WMA mixes are more susceptible to change in aggregate gradation compared to HMA mixes, while increasing in Sasobit® content produce more stable mixtures. In addition, it is determined that finer aggregate gradations were more influenced by change in the Sasobit® content.

Evaluation of rutting potential for asphalt concrete mixes containing copper slag

Copper slag (CS) is a by-product of the copper extraction process, which can be used as coarse and/or fine aggregate in hot mix asphalt (HMA) pavements. This study used CS as a replacement of the fine aggregate with a percentage of up to 40% by total aggregate weight. The objective of this study was to evaluate the effect of CS on the rutting potential of the asphalt concrete mix using two methods. One method is based on the Dynamic modulus |E*| testing result. Actual pavement temperature data from a test section were used with the developed |E*| master curves. EverStressFE finite element program was used to perform a linear elastic load-deformation analysis for a pavement section and to determine the vertical resilient strain in a 40-mm HMA surface layer. The M-E PDG permanent deformation model was used with and Excel Visual Basic for Applications code to predict the accumulated rutting for different CS mixes for 10 million ESALs. The other method used the data from the flow number (FN) test. Based on the |E*| approach, the results indicated that adding 5% CS in the mix increased the predicted rutting from 0.59 to 0.98 mm at 10 million ESALs (increase by 68%). When 40% CS was used, rutting increased by more than 700% compared with the control mix. After analysing the FN results with the Francken model, the results indicated a decrease in FN as CS content is increased, indicating higher rutting potential. The decrease in FN ranged from 9% for 5% CS to 95% for 40% CS. The mixes containing up to 10% CS satisfied the minimum FN criteria for rutting. A calibration process for the M-E PDG distress prediction models that allows the use of waste and by-product materials such as CS should be considered in the future.

Pseudo-turbulent heat flux and average gas–phase conduction during gas–solid heat transfer: flow past random fixed particle assemblies

Fluctuations in the gas-phase velocity can contribute significantly to the total gas-phase kinetic energy even in laminar gas–solid flows as shown by Mehrabadi et al. (J. Fluid Mech., vol. 770, 2015, pp. 210–246), and these pseudo-turbulent fluctuations can also enhance heat transfer in gas–solid flow. In this work, the pseudo-turbulent heat flux arising from temperature–velocity covariance, and average fluid-phase conduction during convective heat transfer in a gas–solid flow are quantified and modelled over a wide range of mean slip Reynolds number and solid volume fraction using particle-resolved direct numerical simulations (PR-DNS) of steady flow through a random assembly of fixed isothermal monodisperse spherical particles. A thermal self-similarity condition on the local excess temperature developed by Tenneti et al. (Intl J. Heat Mass Transfer, vol. 58, 2013, pp. 471–479) is used to guarantee thermally fully developed flow. The average gas–solid heat transfer rate for this flow has been reported elsewhere by Sun et al. (Intl J. Heat Mass Transfer, vol. 86, 2015, pp. 898–913). Although the mean velocity field is homogeneous, the mean temperature field in this thermally fully developed flow is inhomogeneous in the streamwise coordinate. An exponential decay model for the average bulk fluid temperature is proposed. The pseudo-turbulent heat flux that is usually neglected in two-fluid models of the average fluid temperature equation is computed using PR-DNS data. It is found that the transport term in the average fluid temperature equation corresponding to the pseudo-turbulent heat flux is significant when compared to the average gas–solid heat transfer over a significant range of solid volume fraction and mean slip Reynolds number that was simulated. For this flow set-up a gradient-diffusion model for the pseudo-turbulent heat flux is found to perform well. The Péclet number dependence of the effective thermal diffusivity implied by this model is explained using a scaling analysis. Axial conduction in the fluid phase, which is often neglected in existing one-dimensional models, is also quantified. As expected, it is found to be important only for low Péclet number flows. Using the exponential decay model for the average bulk fluid temperature, a model for average axial conduction is developed that verifies standard assumptions in the literature. These models can be used in two-fluid simulations of heat transfer in fixed beds. A budget analysis of the mean fluid temperature equation provides insight into the variation of the relative magnitude of the various terms over the parameter space.

Function investigation of stone mastic asphalt (SMA) mixture partly containing basic oxygen furnace (BOF) slag.

In this paper, the effect of the size gradations of basic oxygen furnace (BOF) slag on the functional performances of stone mastic asphalt (SMA) mixture including skid and deformation resistances was investigated. The industrially produced BOF slag coarse aggregates (BSCA) with size gradations of 4.75-9.5 mm and 9.5-16 mm were used. SMA mixtures were designed according to Marshall procedure. British pendulum number (BPN), indicating the skid resistance of asphalt mixture, was measured by a British pendulum skid resistance device. Flow number (FN) and Marshall quotient (MQ), reflecting the deformation resistance of asphalt mixture, were determined, respectively, based on the results of dynamic creep test and Marshall test (stability and flow value). Showed that BSCA with a size gradation of 9.5-16 mm performed better in improving the skid and deformation resistance of SMA mixture than BSCA with a size gradation of 4.75-9.5 mm. Furthermore, BSCA with combined size gradations, namely, 4.75-16 mm, worked the best. These conclusions would benefit the future extensive utilization of BSCA in asphalt pavement.

A Recent Performance Analysis of the Crop Sector and its Determinants in North-Eastern Karnataka

The performance of the crop sector among Karnataka's four divisions viz; Gulbarga, Belgaum, Mysore and Bangalore has been analyzed for a period of 30 years i.e. 1980/81–2009/2010. Compound annual growth rates of area, production and yield were estimated by fitting semi-log trend equation. To explore the factors determining the growth of the crop sector, a Multiple Regression Model has been fitted. The crop sector has been observed to have diversified out of staple food grains viz., coarse cereals, pulses and oilseeds towards high value crops; fruits and vegetables. Fruits and vegetables registered significantly high growth in area, production and yield during the study period. The growth in area under cereals has drastically declined while cereals production is stagnate. The performance of pulses has shown no improvements across the study periods. The performance of oilseeds was only impressive during the pre economic reform period; but rapidly slumped in the subsequent periods. The factors identified to favour the growth of crop sector in the state include fertiliser consumption, area under the crop, net irrigated area, flow of credit and number of regulated markets. The study has suggested some policy implications also.

Blood flow indices in single and multiple bearing does

The aim of present study was to examine the changes in blood flow indices throughout pregnancy in singleton and multiple pregnant does. Doppler scanning was done to assess resistance index (RI), pulsatility index (PI), time-averaged maximum velocity (TAMV) and blood flow volume (Vol). The placentomes were investigated for blood indices on day 45 as an echogenic structure on the surface of the endometrium. Transrectal ultrasonography was performed every 30 days during the overage of the pregnancy. Diameters of largest six placentomes from each doe were measured using an ultrasonography device, and the mean values of placentome diameters were calculated. Values of RI and PI exhibited a steady decrease toward term and declined more rapidly and earlier in multiple than in single pregnancies. Values of RI and PI were negatively correlated with placetome size; however, values of TAMV and Vol were positively correlated with placentome size. In singleton and multiple pregnancies, the placentome size showed an increase toward term, but there is no difference in placentome size between single and multiple bearing does. In conclusion, the values of TAMV and Vol for multiple pregnancies were significantly higher than for singleton at any gestational month to satisfy the high foetal demand of nutrients and dissolved oxygen for foetal progression. Knowing the relationship between the foetal number and blood flow parameters could be used in the clinical management of such pregnancies and the early detection or prediction adverse pregnancy outcome.