Abstract:This study presents a new rheometry technique which requires a free surface velocity field as an input. By minimising the difference between observed and simulated data, we show here that it is possible to estimate the three parameters of an assumed Ellis rheological law. The dam-break problem is considered here with molasses as the working fluid. The free surface velocity is evaluated by seeding the free surface with buoyant particles and using particle tracking velocimetry. The parameter identification is su… Show more
“…A fourth-order polynomial (red dashed line in figure 5a) is fitted to the scattered data with the condition that its derivative vanishes at the origin, which ensures that φ(0) = 0. This polynomial is differentiated to obtain a prediction for the constitutive law (red dashed line in figure 5b), which shows reasonable agreement with the constitutive law used in the simulations of Al-Behadili et al (2019). The simulations included relatively small amounts of inertia and surface tension, which are not accounted for in our inversion method, although the latter could be included in the pressure gradient.…”
Section: Flux-based Methodsmentioning
confidence: 66%
“…Figure 5.Inferring the constitutive law from the free-surface velocity data of Al-Behadili et al. (2019). ( a ) predicted using our inversion method applied to their data (circles and squares) with a polynomial best fit (red dashed line) and the correct shape (black continuous line).…”
Section: Inversion Methods For Transient Flowsmentioning
confidence: 99%
“…The constitutive law is simply recovered from φ(τ ) = dΦ/dτ . By way of an example, we apply this inverse approach to the data of Al-Behadili et al (2019). Their figures 5 and 6 show the flow thickness and free-surface velocity at three times for a dam break of an Ellis fluid calculated from a full Navier-Stokes simulation.…”
Section: Flux-based Methodsmentioning
confidence: 99%
“…Previous methods for inferring the rheology of a fluid from its free surface typically involve comparing observations with simulated predictions (Piau & Debiane 2005; Sayag & Worster 2013; Sellier 2016; Al-Behadili et al. 2019). Simulated predictions are obtained from a forward model, which calculates the free-surface shape for given fluid properties.…”
We develop direct inversion methods for inferring the rheology of a fluid from observations of its shallow flow. First, the evolution equation for the free-surface flow of an inertia-less current with general constitutive law is derived. The relationship between the volume flux of fluid and the basal stress,
$\tau _b$
, is encapsulated by a single function
$F(\tau _b)$
, which depends only on the constitutive law. The inversion method consists of (i) determining the flux and basal stress from the free-surface evolution, (ii) comparing the flux with the basal stress to constrain
$F$
and (iii) inferring the constitutive law from
$F$
. Examples are presented for both steady and transient free-surface flows demonstrating that a wide range of constitutive laws can be directly obtained. For flows in which the free-surface velocity is known, we derive a different method, which circumvents the need to calculate the flux.
“…A fourth-order polynomial (red dashed line in figure 5a) is fitted to the scattered data with the condition that its derivative vanishes at the origin, which ensures that φ(0) = 0. This polynomial is differentiated to obtain a prediction for the constitutive law (red dashed line in figure 5b), which shows reasonable agreement with the constitutive law used in the simulations of Al-Behadili et al (2019). The simulations included relatively small amounts of inertia and surface tension, which are not accounted for in our inversion method, although the latter could be included in the pressure gradient.…”
Section: Flux-based Methodsmentioning
confidence: 66%
“…Figure 5.Inferring the constitutive law from the free-surface velocity data of Al-Behadili et al. (2019). ( a ) predicted using our inversion method applied to their data (circles and squares) with a polynomial best fit (red dashed line) and the correct shape (black continuous line).…”
Section: Inversion Methods For Transient Flowsmentioning
confidence: 99%
“…The constitutive law is simply recovered from φ(τ ) = dΦ/dτ . By way of an example, we apply this inverse approach to the data of Al-Behadili et al (2019). Their figures 5 and 6 show the flow thickness and free-surface velocity at three times for a dam break of an Ellis fluid calculated from a full Navier-Stokes simulation.…”
Section: Flux-based Methodsmentioning
confidence: 99%
“…Previous methods for inferring the rheology of a fluid from its free surface typically involve comparing observations with simulated predictions (Piau & Debiane 2005; Sayag & Worster 2013; Sellier 2016; Al-Behadili et al. 2019). Simulated predictions are obtained from a forward model, which calculates the free-surface shape for given fluid properties.…”
We develop direct inversion methods for inferring the rheology of a fluid from observations of its shallow flow. First, the evolution equation for the free-surface flow of an inertia-less current with general constitutive law is derived. The relationship between the volume flux of fluid and the basal stress,
$\tau _b$
, is encapsulated by a single function
$F(\tau _b)$
, which depends only on the constitutive law. The inversion method consists of (i) determining the flux and basal stress from the free-surface evolution, (ii) comparing the flux with the basal stress to constrain
$F$
and (iii) inferring the constitutive law from
$F$
. Examples are presented for both steady and transient free-surface flows demonstrating that a wide range of constitutive laws can be directly obtained. For flows in which the free-surface velocity is known, we derive a different method, which circumvents the need to calculate the flux.
“…A twin experiment is employed where the "observed" flow dynamics information from the field is imitated with a forward model, numerically simulating the lava with known viscosity parameters as normal. The rheology of the flow is then recovered by comparing the free surface velocities between the forward and inverse models, using an objective function [1]. Lava has been described as largely Newtonian [7,5], with viscosity varying exponentially with temperature [6].…”
Lava flows are challenging to simulate in the field in real time because the rheology might not be known a priori, and standard rheometry instruments are unsuitable for measuring lava on volcanoes. However, we aim to determine the lava rheology using only information about the flow dynamics.In this numerical study, we model the spreading of a lava column down a hill using lubrication theory. The lava rheology is treated as Newtonian and temperature-dependent with viscosity µ = µ 0 e −αT where µ 0 and α are unknown parameters and T is the temperature. A twin experiment method is used where the forward experiment produces the surface height over time (output) with known µ 0 and α (input), and then the inverse experiment involves finding the viscosity parameters from the free surface velocity using the Bound Optimization BY Quadratic Approximation (BOBYQA) method. The input parameters µ 0 and α were both recovered within 11 % of their true values.
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