Drag Force Formulation Research Articles

General integral model for a jet in wavy current environment

An integral model for the simulation and prediction of the mixing and diffusion of submerged wastewater discharge in the form of a jet flow in a coastal dynamic environment is still lacking in the literature. In this study, a general integral model was developed to simulate and predict the movement and dilution process of jets in still water, currents, waves, and wavy current environments. Specifically, starting from the fundamental Navier–Stokes equations combined with the conservation equations of mass and scalar quantities, the equations of movement and the governing equations of mass, momentum, buoyancy, and scalar quantities were derived. Furthermore, the model employs an entrainment closure approach that distinguishes the contribution of transverse and azimuthal shear mechanisms and contains a quadratic-law turbulent drag force mechanism. A comparison with the basic experimental data for jets in still water, currents, waves, and wavy current environments supports the choice and magnitude of the entrainment coefficients contained in the entrainment formulation as well as the unified calculation formula of the drag force coefficient contained in the drag force formulation. The range of applicability of the model is carefully evaluated, and several model limitations, beyond which the integral model becomes invalid, are proposed. The general integral model provides a reliable technical approach to studying the movement and dilution process of jets in a wavy current environment and may be used to study the effects of waves and tidal currents on jets for a much wider range of source and ambient conditions than have been studied experimentally thus far.

Revisiting wind wave growth with fully coupled direct numerical simulations

We investigate wind wave growth by direct numerical simulations solving for the two-phase Navier–Stokes equations. We consider the ratio of the wave speed$c$to the wind friction velocity$u_*$from$c/u_*= 2$to 8, i.e. in the slow to intermediate wave regime; and initial wave steepness$ak$from 0.1 to 0.3; the two being varied independently. The turbulent wind and the travelling, nearly monochromatic waves are fully coupled without any subgrid-scale models. The wall friction Reynolds number is 720. The novel fully coupled approach captures the simultaneous evolution of the wave amplitude and shape, together with the underwater boundary layer (drift current), up to wave breaking. The wave energy growth computed from the time-dependent surface elevation is in quantitative agreement with that computed from the surface pressure distribution, which confirms the leading role of the pressure forcing for finite amplitude gravity waves. The phase shift and the amplitude of the principal mode of surface pressure distribution are systematically reported, to provide direct evidence for possible wind wave growth theories. Intermittent and localised airflow separation is observed for steep waves with small wave age, but its effect on setting the phase-averaged pressure distribution is not drastically different from that of non-separated sheltering. We find that the wave form drag force is not a strong function of wave age but closely related to wave steepness. In addition, the history of wind wave coupling can affect the wave form drag, due to the wave crest shape and other complex coupling effects. The normalised wave growth rate we obtain agrees with previous studies. We make an effort to clarify various commonly adopted underlying assumptions, and to reconcile the scattering of the data between different previous theoretical, numerical and experimental results, as we revisit this longstanding problem with new numerical evidence.

Experimental Investigation on Heat Transfer Enhancement with Passive Inserts in Flat Tubes in due Consideration of an Efficiency Assessment

This paper presents results of an experimental investigation on pressure drop and heat transfer for a wide range of Reynolds and Prandtl numbers ranging from 8 < Pr < 60 and 40 < Re < 3500, for flat tubes without and with passive inserts. For three different kinds of passive insert designs, the impact on heat and momentum transfer due to coaction of the total set of passive inserts with different shape and amount was investigated. Experimental results were analyzed regarding two main aspects: Heat transfer mechanisms and pressure drop induced by friction and form drag forces due to the presence of different shapes. After heat and momentum transfer mechanisms for each passive insert design were analyzed, heat transfer and pressure drop enhancement were compared to each other, leading to an efficiency discussion. Different concepts for efficiency evaluation, which are cited in literature, were applied to the presented experimental data. Pros and cons of the different concepts are discussed. Finally, we propose an equation for evaluation of total performance, which fully respects the energetic and exergetic aspects of heat transfer and pressure drop enhancement.

Analysis of the response of a liquid surface to the pulse action of an inclined gas jet at low Reynolds number

A mathematical description of the motion of a cavity on the liquid surface under an oblique action of a gas jet is obtained using the well-known expressions for the movement of a gas bubble in a liquid. The boundary of the viscous drag force domination over the form drag force is determined. The impingement of the gas jet on the liquid surface is considered as a dynamic object of the automatic control theory. It is found that the dynamic properties of the two-phase system "gas jet-liquid" are described by the integrator equations. Using a specially designed setup, the transient response of the "gas jet-liquid" system were experimentally obtained for the aerodynamic action at angles of 20 and 50o to the surfaces of liquids with the viscosities of 0.71 and 26.1 Pa·s (Reynolds number Re<2). The research results are necessary for the analysis of the non-contact aerodynamic method of liquid viscosity measurements. Keywords: gas jet, impingement, liquid surface, measurement, non-contact, pulse, viscosity.

Исследование реакции поверхности жидкости на импульсное воздействие наклонной газовой струи при малых числах Рэйнольдса

A mathematical description of the motion of a cavity on the liquid surface under an oblique action of a gas jet is obtained using the well-known expressions for the movement of a gas bubble in a liquid. The boundary of the viscous drag force domination over the form drag force is determined. The impingement of the gas jet on the liquid surface is considered as a dynamic object of the automatic control theory. It is found that the dynamic properties of the two-phase system "gas jet - liquid" are described by the integrator equations. Using a specially designed setup, the transient response of the "gas jet - liquid" system were experimentally obtained for the aerodynamic action at angles of 20º and 50º to the surfaces of liquids with the viscosities of 0.71 and 26.1 Pa•s (Reynolds number Re < 2). The research results are necessary for the analysis of the non-contact aerodynamic method of liquid viscosity measurements.

Boundary layer dynamics and bottom friction in combined wave–current flows over large roughness elements

In the coastal ocean, interactions of waves and currents with large roughness elements, similar in size to wave orbital excursions, generate drag and dissipate energy. These boundary layer dynamics differ significantly from well-studied small-scale roughness. To address this problem, we derived spatially and phase-averaged momentum equations for combined wave–current flows over rough bottoms, including the canopy layer containing obstacles. These equations were decomposed into steady and oscillatory parts to investigate the effects of waves on currents, and currents on waves. We applied this framework to analyse large-eddy simulations of combined oscillatory and steady flows over hemisphere arrays (diameter$D$), in which current ($U_c$), wave velocity ($U_w$) and period ($T$) were varied. In the steady momentum budget, waves increase drag on the current, and this is balanced by the total stress at the canopy top. Dispersive stresses from oscillatory flow around obstacles are increasingly important as$U_w/U_c$increases. In the oscillatory momentum budget, acceleration in the canopy is balanced by pressure gradient, added-mass and form drag forces; stress gradients are small compared to other terms. Form drag is increasingly important as the Keulegan–Carpenter number$KC=U_wT/D$and$U_c/U_w$increase. Decomposing the drag term illustrates that a quadratic relationship predicts the observed dependences of steady and oscillatory drag on$U_c/U_w$and$KC$. For large roughness elements, bottom friction is well represented by a friction factor ($f_w$) defined using combined wave and current velocities in the canopy layer, which is proportional to drag coefficient and frontal area per unit plan area, and increases with$KC$and$U_c/U_w$.

Form drag coefficient quantification on rising bubbles using particle image velocimetry

Two-phase flow transport heavily depends on the generalized interfacial drag force term in the two-fluid model. The impact of accurate design and prediction associated with thermal energy systems is highly sensitive to multi-phase heat transfer characteristics. Because of this, the interfacial drag force has been studied with rigor for some time. The steady state drag force component in particular has been well characterized for rising single bubbles but has not been previously experimentally separated into its skin and form drag components. Historically, experimental studies were unable to measure the pressure distribution around a bubble to determine the form drag force along the bubble interface. This paper presents the outcomes of an experimental study wherein a new experimental method was developed which, for the first time, separates the form and skin drag coefficients on rising bubbles. Eleven air bubbles sizes representing spheroidal, ellipsoidal, and transition to spherical cap regimes (102<Re<104) were studied in a water test loop with velocity fields measured via particle image velocimetry; pressure fields were then synthesized from these velocity fields through the Queen2 algorithm. The skin and form drag coefficients were separated for single bubbles which showed a nominal trend of increasing form drag contribution with increasing Reynolds number. This work presents a new method and new outcomes for rising bubbles over several bubble regimes and includes a comprehensive uncertainty characterization of the resulting data.

Taylor dispersion in non-Darcy porous media with bulk chemical reaction: a model for drug transport in impeded blood vessels

The present article discusses the solute transport process in steady laminar blood flow through a non-Darcy porous medium, as a model for drug movement in blood vessels containing deposits. The Darcy–Brinkman–Forchheimer drag force formulation is adopted to mimic a sparsely packed porous domain, and the vessel is approximated as an impermeable cylindrical conduit. The conservation equations are implemented in an axisymmetric system (R, Z) with suitable boundary conditions, assuming constant tortuosity and porosity of the medium. Newtonian flow is assumed, which is physically realistic for large vessels at high shear rates. The velocity field is expanded asymptotically, and the concentration field decomposed. Advection and dispersion coefficient expressions are rigorously derived. Extensive visualization of the influence of effective Péclet number, Forchheimer number, reaction parameter on velocity, asymptotic dispersion coefficient, mean concentration, and transverse concentration at different axial locations and times is provided. Increasing reaction parameter and Forchheimer number both decrease the dispersion coefficient, although the latter exhibits a linear decay. The maximum mean concentration is enhanced with greater Forchheimer numbers, although the centre of the solute cloud is displaced in the backward direction. Peak mean concentration is suppressed with the reaction parameter, although the centroid of the solute cloud remains unchanged. Peak mean concentration deteriorates over time since the dispersion process is largely controlled by diffusion at the large time, and therefore the breakthrough curve is more dispersed. A similar trend is computed with increasing Péclet number (large Péclet numbers imply diffusion-controlled transport). The computations provide some insight into a drug (pharmacological agents) reacting linearly with blood.

Determination of drag coefficients in automatic ball balancers at low Reynolds numbers

The precise calculation of drag forces in the technical application of automatic balancing of rotating machinery provides important information about efficiency and stability. With increasing geometric complexity of the design, this poses a challenge that can be solved with computer-aided fluid dynamic approaches. In rolling element bearings, the influence of drag induced by the lubricant is predominantly considered in the context of efficiency loss estimations, whereas the movement of the rolling elements is mainly constrained by the contact with the bearing rings and, if present, the cage. Automatic ball balancers, which are installed in rotating machinery to reduce unbalance excitation, are in design very similar to fully lubricated ball bearings missing the cage, the inner ring and the majority of the balls. Inherent to the functional principle, the balancing efficiency and stability are significantly influenced by the choice of lubricant and resulting drag forces. Therefore, the estimation of the drag coefficient based on the geometry and lubrication of automatic ball balancers plays an important role in the engineering process. With a focus on the Stokes flow regime, the drag coefficient for a single sphere in an annular flow domain is determined numerically with finite volume discretization and the SIMPLE steady state solution scheme. Based on a parameter study utilizing the presented solution approach, a simple empirical relation between the design of the automatic ball balancer and resulting drag coefficients is derived. As a result, a drag force formulation based on the balancer geometry and the lubrication fluid properties is presented, which helps to supplement a large number of published kinetic models regarding the analysis of automatic ball balancer stability and transient behavior, giving a better understanding of the influences of design decisions regarding geometry and lubricant.

Effect of interfacial drag force model on code prediction for upward adiabatic two-phase bubbly flow in vertical channels

Accurate modeling of the interfacial drag force is one of the keys to predicting thermo-fluid parameters using one-dimensional nuclear thermal-hydraulic system analysis code architected through the two-fluid model. The interfacial drag force appears in the interfacial momentum transfer term and governs the velocity slip or the relative velocity between gas and liquid phases. The most straightforward method to model the interfacial drag force is to model the force through the drag law (drag law approach). A drag coefficient and interfacial area concentration should be given to close the interfacial drag force model. Among them, the modeling of the interfacial area concentration has been one of the weakest links in the interfacial drag force modeling due to the lack of reliable data covering a wide test condition including prototypic nuclear reactor conditions and lack of physically sound interfacial area model. To avoid a considerable uncertainty in the prediction of the interfacial area concentration, Andersen and Chu (1982) proposed the interfacial drag force model using the drift-flux parameters (Andersen approach). The Andersen approach is practical for the simulation of a slow transient flow and a steady flow. Major system analysis codes such as USNRC TRACE have adopted the Andersen approach in the interfacial drag force modeling. Some attempts to improve the code performance have been considered using the drag law approach with the interfacial area transport equation. The dynamic modeling of the interfacial area concentration has the potential to improve the prediction accuracy of the interfacial area concentration in a transient flow and developing flow. Due to the importance of the improved interfacial drag force modeling, the implementation and evaluation of the interfacial area transport equation in USNRC TRACE code has been performed by Talley et al. (2011, 2013). The study claimed that the introduction of the interfacial area transport equation into the TRACE code improved the code performance in an adiabatic bubbly flow analysis significantly. The present study assessed the code calculation made by Talley et al. (2011) and identified several issues in the code calculation results. The present study analytically demonstrated that the drag law approach became identical with the Andersen approach for the distorted particle regime (or a major bubble shape regime in bubbly flow) due to the balancing-out of the interfacial area concentration (or bubble size) in the numerator and denominator of the interfacial drag force formulation. The code calculation using TRAC code endorsed the analytical assessment of the insignificant or no merit of the interfacial area transport equation in the code performance of the adiabatic bubbly flow analysis. The present study also pointed out the inconsistency of the code calculation made by Talley et al. (2011).

A theoretical model for bubble coalescence by coupling film drainage with approach processes

An improved theoretical model for simulating bubble coalescence caused by turbulence was developed. Unlike the previous models, this improved model simulated the film drainage and approach processes between two bubbles simultaneously in the condition of fully mobile interfaces, considering the influence of the variation of approach velocity, film thickness, film area/radius and interaction forces etc. with time on the bubble coalescence. The lubrication form drag force caused by flattening of colliding surface was introduced to model the approach process. The initial film thickness and radius required for film drainage process were estimated by the expressions validated by experimental data. The critical coalescence velocities for determining coalescence predicted by the improved model were consistent with available experimental data. Moreover, the proposed improved model was used to predict the size distribution in a bubble column, and a good agreement between simulated and experimental results was obtained.

Aerodynamic Design of a Solar Road Vehicle

Solar road vehicles have very specific design requirements. This makes their aerodynamic characteristics quite different from classic sedan vehicles. In the present study, the computational model of a typical solar road vehicle was developed to investigate its aerodynamic forces and flow characteristics. Computations were performed assuming the steady viscous flow and using the Reynolds-averaged Navier Stokes equations along with the k-ω turbulence model. The obtained results indicate some important findings that are commonly not present for classic sedan vehicles. In particular, a contribution of the viscous drag force to the overall drag force is considerably larger (41 %) than it is the case for the standard passenger road vehicles, where the form drag force dominates over the viscous drag force. Surface pressure distribution patterns indicate a favorable aerodynamic design of this vehicle. In particular, larger pressure coefficients on the top of the vehicle body as compared to the bottom surface contribute to increasing a downforce and thus the vehicle traction. The airfoil-shaped crosssection of the designed cockpit canopy has favorable properties with respect to reduction of the aerodynamic drag force.

The importance of riparian plant orientation in river flow: implications for flow structures and drag

In a series of high resolution numerical modelling experiments, we incorporated submerged riparian plants into a computational fluid dynamics (CFD) model used to predict flow structures and drag in river flow. Individual plant point clouds were captured using terrestrial laser scanning (TLS) and geometric characteristics quantified. In the first experiment, flow is modelled around three different plant specimens of the same species (Prunus laurocerasus). In the second experiment, the orientation of another specimen is incrementally rotated to modify the flow-facing structure when foliated and defoliated. Each plant introduces a unique disturbance pattern to the normalized downstream velocity field, resulting in spatially heterogeneous and irregularly shaped velocity profiles. The results question the extent to which generalized velocity profiles can be quantified for morphologically complex plants. Incremental changes in plant orientation introduce gradual changes to the downstream velocity field and cause a substantial range in the quantified drag response. Form drag forces are up to an order of magnitude greater for foliated plants compared to defoliated plants, although the mean drag coefficient for defoliated plants is higher (1.52 defoliated; 1.03 foliated). Variation in the drag coefficients is greatest when the plant is defoliated (up to ∼210% variation when defoliated, ∼80% when foliated).

Modeling of distribution parameter, void fraction covariance and relative velocity covariance for upward steam-water boiling flow in vertical rod bundle

ABSTRACT In order to improve the prediction accuracy of one-dimensional interfacial force formulated by ‘Andersen’ approach, the distribution parameter in a drift–flux correlation, void fraction covariance, and relative velocity covariance has been modeled for dispersed boiling two-phase flow in a vertical rod bundle. The distribution parameter has been derived by a bubble-layer thickness model. The correlations of void fraction covariance and relative velocity covariance have been developed based on prototypic 8 × 8 rod bundle data. The correlation of void fraction covariance agrees with the bundle data with the mean absolute error, standard deviation, mean relative deviation, and mean absolute relative deviation being 0.00120, 0.0415, −0.173%, and 1.80%, respectively. The correlation of relative velocity covariance agrees with the bundle data with the mean absolute error, standard deviation, mean relative deviation, and mean absolute relative deviation being −0.00241, 0.0452, −0.0316%, and 2.52%, respectively. In view of the great importance of void fraction covariance and relative velocity covariance on the one-dimensional interfacial drag force formulation, it is highly recommended to include the void fraction covariance and relative velocity covariance in the one-dimensional formulation of interfacial drag force used in nuclear thermal-hydraulic system analysis codes.

Modeling of void fraction covariance and relative velocity covariance for upward boiling flow in vertical pipe

Drift-flux parameters have been often used to formulate one-dimensional interfacial drag force in dispersed two-phase flow, which is one of key parameters to predict void fraction using one-dimensional thermal-hydraulic codes. This approach is called “Andersen approach”, which has been widely used in one-dimensional nuclear thermal-hydraulic system analysis codes such as TRACE, RELAP5 and TRAC-BF1. However, the current formulation of one-dimensional interfacial drag force ignores important void fraction covariance and relative velocity covariance when local interfacial drag force is converted to one-dimensional interfacial drag force. The impact of neglecting void fraction covariance and relative velocity covariance on one-dimensional interfacial drag force and relative velocity has been discussed in detail. In view of the importance of the drift-flux parameters, void fraction covariance and relative velocity covariance on one-dimensional formulation of the interfacial drag force, three constitutive equations have been developed for upward boiling two-phase flow in a vertical pipe. The validity of the modeled void fraction covariance and relative velocity covariance for subcooled and bulk boiling flow in a vertical pipe has been verified by boiling R12 data taken in a vertical pipe with the diameter of 19.2mm under the pressure simulating prototypic nuclear reactor thermal-hydraulic conditions. The correlation of void fraction covariance agrees with the boiling flow data in the vertical pipe with the mean absolute error, standard deviation, mean relative deviation and mean absolute relative deviation being 0.828, 3.43, 10.3% and 33.5%, respectively. The correlation of relative velocity covariance agrees with the boiling flow data in the vertical pipe with the mean absolute error, standard deviation, mean relative deviation and mean absolute relative deviation being −0.00394, 0.0663, −0.184% and 5.11%, respectively. Due to the great importance of the void fraction covariance and relative velocity covariance on one-dimensional interfacial drag force formulation, it is highly recommended to include the void fraction covariance and relative velocity covariance in the one-dimensional formulation of the interfacial drag force used in nuclear thermal-hydraulic system analysis codes.

Advection-diffusion sediment models in a two-phase flow perspective

ABSTRACTSediment profiles in open channels are usually predicted by advection-diffusion models. Most basic forms consider the terminal settling velocity of a single particle in still clear water. Alternative forms account for hindered settling at higher concentrations. It is not known, however, how these modifications relate to mass and momentum conservation of each phase. For dilute flow, it is known that the original form can be derived from a two-phase analysis, assuming a dilute suspension, neglect of inertial effects in the momentum balance and using a linear drag force formulation. Here we study how and if it is possible to understand the hindered-settling modifications for the non-dilute case, and formulate a relation between advection-diffusion models and parameters involved in the turbulent drag force. This note verifies that the transient two-phase flow solutions converge to steady state, and compares the results to experimental data.

Numerical investigation and comparison of coarse grain CFD – DEM and TFM in the case of a 1 MWth fluidized bed carbonator simulation

This work focuses on a comparison between the Euler-Euler Two Fluid Model (TFM) approach and the coupled coarse grain discrete element CFD-DEM numerical model for the simulation of a 1MWth CFB carbonator reactor located at TU Darmstadt (TUD). The effect of the drag force formulation and its associated application in the numerical model for both approaches in terms of their numerical accuracy, compared to experimental data is investigated, by implementing either the conventional Gidaspow model or the advanced EMMS one. Moreover, for the coarse grain CFD – DEM model, the range of values for important numerical parameters as the particle per parcel and cell to parcel size ratios are investigated to shed light on the necessary resolution such a model should have in order to reproduce valid and not parameter dependent numerical results. An adequate cell length to parcel diameter ratio is found to be around 2.6 while as concerns the parcel to particle diameter ratio a value around 58.5 proved to be sufficient, at least for the range of parameters investigated in this paper (size of riser, flow rates and particles average diameter). The EMMS model improved the accuracy of results derived by the coarse grain CFD – DEM model, while further research on the appropriate drag models for the coarse grain CFD – DEM is a sine qua non for its successful implementation in similar studies. For instance it is of interest to answer whether the individual particles slip velocity instead of the particles cell averaged slip, should be used for the calculation of the momentum interexchange coefficient (β) as well as the treatment of different particle diameters in the EMMS equation scheme.

Analysis of vertical co-current air-water flow with the Neptune_CFD

A two-fluid modelling approach with interface sharpening is applied for numerical simulations of flooding waves in air-water co-current flow in vertical pipe. The simulation capability of Neptune_CFD code is analysed. The results are compared with experimental data and with the simulations performed with the computational code ANSYS CFX. Isothermal flow of air and water in the churn flow regime is modelled. Turbulence is modelled for each phase separately using URANS approach. A typical geometry of a test section in the vicinity of the liquid injector is used as the computational domain. In general, both computational codes predicted similar wave frequency values for the pipe with internal diameter of 32mm and show good agreement with the experimental data. Detailed analysis of local flow phenomena in the case of 2D Neptune_CFD simulation however reveals a significant accumulation of liquid in the centre of the pipe that may be attributed to the axisymmetric assumption, drag force formulation, and possible numerical errors. It was demonstrated that the liquid accumulation in the centre of the pipe can be avoided by the simulations in the full 3D domain due to asymmetric nature of the churn flow.

Dynamic Modeling of Critical Velocities for the Pushing/Engulfment Transition in the Si-SiC System Under Gravity Conditions

An extended non-steady-state model for the interaction between a solid particle and an advancing solid/liquid interface based on the dynamic model of Catalina et al. (Metall Mater Trans A 31:2559–2568, 2000) is used to calculate the critical velocities for the pushing/engulfment transition in Si-SiC system under microgravity and under normal gravity conditions. The aim of this study was to explain the abnormal behavior of the critical velocity in experiments. The simulations were carried out for two cases of the drag force formulation. The effects of the non-spherical form of the particles as well as the cluster formation were also taken into account. It is found that in the presence of the gravity force, the particles will be engulfed when the particle size exceeds a certain limit which does not depend on the choice of the drag force formulation.

Form drag effect on the onset of non-linear convection and Hopf bifurcation in binary fluid saturating a tall porous cavity

This paper reports a numerical study of natural convection in at all porous enclosure filled with a binary fluid. The Darcy–Dupuis model, which includes effects of the form drag force, is adopted to describe the flow in the porous medium. The two vertical walls of the cavity are subject to constant gradients of temperature while the two horizontal ones are kept adiabatic and impermeable. Concentration gradients are assumed to be induced either by the imposition of constant gradients of solute on the vertical walls of the system (a=0; double diffusive convection) or by the Soret effect (a=1). Governing parameters of the problem under study are the thermal Rayleigh number RT, form drag parameter G, buoyancy ratio φ, Lewis number. Le, normalized porosity ε, and aspect ratio of the cavity A. The case of equal and opposing thermal and solutal buoyancy forces, φ=-1, is considered. For this situation, an equilibrium solution corresponding to the rest state is possible and the resulting onset of motion can be either supercritical or subcritical. A semi-analytical solution, valid for an infinite layer (A≫1) assuming parallel flow, is derived. Based on the linear stability theory, the onset of motion from the rest state is predicted for both double diffusive and Soret convection. The onset of Hopf bifurcation, characterizing the transition from a convective steady state to oscillatory state, is also studied. The influence of the governing parameters on the onset of motion and the resulting fluid flow, temperature and concentration fields is discussed in detail. The existence of supercritical, subcritical and oscillatory convective modes is demonstrated. A good agreement is found between the predictions of the parallel flow approximation and the numerical results obtained by solving the full governing equations. The existence of multiple solutions and traveling waves for a given set of the governing parameter is demonstrated and leads to the existence of a bistability phenomenon. Overall, the form drag behaves as a stabilizing effect and is seen to affect considerably the onset of subcritical convection and Hopf bifurcation.