Experimental Set up for the Study of Transient Flow in Marine Porous Media

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1 Experimental Set up for the Study of Transient Flow in Marine Porous Media Experimental Studies: Rivers Imam Wahyudi, Abder Khalifa, Pierre Thomas Parallel Session (parallel21), , 10:15-12:45 Experimental Studies on Waves Abstract Water flow in porous media has many applications in terrestrial, fluvial and marine structures. In the marine field, this flow is induced by waves and tides which can provoke high and transient pressure. Internal flow induced by waves in porous structures influences their mechanical behaviour. Various authors work on numerical modelling of stability of these structures (rubble mound breakwaters,...). The internal flow modelling needs transient flow laws which can be obtained by laboratory experiments that are very limited. The present paper reports an experimental set-up and results analysis conducted to determine transient flow laws in several marine porous media. Permeameter and test station have been especially developed for this study. A forced water flow going through the soil sample within the test cell, is provoked by a pump supplied from a tank. The order signal (amplitude and period of wave) is treated by PID that maintains a regulated circuit. We use an automatic regulated gate to simulate internal waves (period between 5 seconds and 15 seconds). The pressure drop is measured by pressure differential gauges. The flow-rate is measured by electromagnetic flow-meter. The setting is connected to a computer data logger. We have carried out several tests on natural granular materials (sands and gravels) and artificial materials (glass spheres and artificial blocks) under variable flow velocities and accelerations. Their results are described, analysed and compared with other experiments. The experimental coefficients of Forchheimer's law are obtained for gross materials. However, we can conclude that classic forms of Darcy and Forchheimer s laws describing in steady

2 flows are not valid for fine materials when submitted to accelerated flow. We propose a new formula for these transient flows. 1. Introduction In the marine field, water flow in porous media is induced by waves and tides which can provoke high and transient pressure. Numerical modelling of marine structures requires knowledge of the laws governing the internal flows of the structures. Generally the law of flow is defined as a relationship between hydraulic gradient (i) and velocity (v). The laws of flow are obtained experimentally by using a permeameter. The objective of the study conducted with a transient pressure permeameter is to verify the validity and to characterize the parameters of both Darcy' s and Forchheimer's laws for porous media subject to transient flows simulating waves (Wahyudi, Ph. D research in progress). This paper presents experimental set up of a permeameter generating transient flow and first experimental results. The original permeameter of which are centred on its dual operating mode, combining the methods of a constant head permeameter for steady flow and of a sine head permeameter (used to simulate the hydraulic of soils and structure that is due to wave). Examples of tests carried out on both natural materials (sand) and manufactured materials (glass sphere) are presented. 2. Experimental Set Up 2.1. Previous Experimentation Steady flow permeameters, which are better suited for studying large hydraulic gradients, have been largely described in literature [Dudgeon (1984), Mc Corquodale & al. (1985), Burchart & al.(1991), Khalifa & al. (1997)]. Very few authors, on the other hand, have described permeameters generating transient (unsteady) flows. The most important permeameters of the bibliography are presented in Table 1.

3 Table 1 Transient flow permeameters of the bibliography

4 The difference between those permeameters is principally their pressurisation system. The first two systems generate unidirectional flows using compressed air pressure [Mc Corquodale(1978) and Burchart(1991)], whereas the other two use pistons to generate oscillating flows [Smith (1991) and Van Gent (1993)]. These permeameters are mostly used to study coarse materials with diameters in the order of a few centimeters Description of The Experimental Set Up Among all the pressurisation systems presented in Table 1, none appeared satisfactory in our case. Our laboratory fittings being limited to a 7 bars pressure, we automatically discarded the compressed air system. The piston system was also discarded being too expensive and requiring sophisticated manufacturing to provide the best possible tightness and to reduce mechanical friction. We finally chose a pump-pressurisation system, which has never been used so far to simulate this type of flow. By developing and enhancing the already available experimental device previously used to study steady flow (Khalifa & al., 1997), we succeeded in designing a test stand which can characterize flow parameters in both steady and transient flow from the same materials. A schematic diagram of the experimental device is shown in Figure 1. Figure 1: Diagram of the experimental device

5 The flow is forced into the cell by a pump which is supplied by a water tank. The liquid passes through the material in the cell and flows back to the water tank. A flow control pneumatic servo-valve is used to regulate the rate according to the signal order desired. The measurement bench, which consists of temperature sensors, differential pressure gauges and flow-meters, is linked to a microcomputer and a data acquisition and control system maintaining the full automation of the tests Test procedure In the first time, porous media is characterised: Particle size analysis by sieving. Determination of the material specific mass with a pycnometer in a 20 C environment Determination of the porosity of the materials in place Study of material shape by analysis of the images After that, we put the cell, connect all hydraulic circuit and check saturation and homogeneities, then we start preliminary testing. This test is carried out in a steady flow with first decreasing then increasing flow-rate. This test consists in measuring pressure drops for set flow-rate. About fifty measurements are needed to establish the relationship between pressure drop and flow-rate. From preliminary testing, we can evaluate experimentally the domain of flow-rate which can cover in transient flow. After adjusting the flow region for the material used, we continue our experiments in transient flow. For example, for the thin material the experiment in transient regime is limited to Darcy's domain but for coarse material, our investigation cover post-darcy's domain of flow-rate. 3. Experimental Results 3.1. Experimental Results in steady flow testing A preliminary test is carried out in a steady flow. Two different materials have been selected to

6 illustrate the results of the tests conducted on the permeameter: a manufactured material (uniform, 1.5-mm diameter of glass spheres) and a natural material (Hostun sand). The glass spheres test allows a comparison between our results and those found in literature. Figure 2 illustrates the relationship between hydraulic gradients and velocities in a Hostun sand and in glass spheres with a 1.5 mm diameter. Figure 2: Relationship between the hydraulic gradient (i) and velocity (v) in steady flow (Hostun Sand and Glass Spheres) There is no presence of hysteresis between the increasing and decreasing flowrate curves. The test has developed at the maximum hydraulic gradient of 350. The parabola-shaped curve reveals that the range of validity of the Darcy's linear law has been greatly exceeded. Figure 2 also gives the equation of the parabola representing Forchheimer's law. The law coefficients a and b for Hostun sands are respectively 2029 s/m and s 2 /m 2, and for glass spheres are respectively 61 s/m and 1397 s 2 /m 2. On this scale, the linear section of the curve is not visible. A more accurate analysis situates the limit of validity of Darcy's law, for Hostun sand at the hydraulic gradient (i) of 20 with a 5% drift error. The limit, which is more commonly expressed as the Reynolds dimensionless number (Re), is situated at 5.6 for Hostun sands. For glass spheres with 1.5 mm diameter Forchheimer's law is directly applied Experimental Results in Transient Flow Testing a. Brute experimental results and phase shift of pressure - debit

The principal test is carried out for different accelerations. Both period (T) and amplitude of debit ( Q) are variable. In this article, we present an example to explain some steps of calculation.

The tests have been carried out with hydraulic gradients lower than the limit of validity of Darcy's law, which has been set from the steady flow tests.

7 The principal test is carried out for different accelerations. Both period (T) and amplitude of debit ( Q) are variable. In this article, we present an example to explain some steps of calculation. Some results of the tests conducted on the same materials simulating marine wave with a period between 5 and 15 seconds are presented here as examples. The tests have been carried out with hydraulic gradients lower than the limit of validity of Darcy's law, which has been set from the steady flow tests. Figure 3 presents the curves of both pressure and flow-rate as a function of time. We note that the profile of flow-rate is sinusoidal and there is a period phase shift between this profile and the response of the evolution of pressure drops. This periode phase shift is due to the fact that the measurement apparatus are placed in different position, and the measurements are not taken in the same time. During post-processing, we manage to get pressures maximum and minimum coincide with the flow-rates (see figure 3). Figure 3: relationship between pressure drops and flow-rate versus time. (Hostun sand and Glass spheres) b. Presentation of the acceleration portion First, we compare between the transient and steady hydraulic gradient. After evaluation of two parameters "a" and "b" from steady preliminary test, we multiply these values by the experimental velocity signal obtained in transient flow. And then, we obtain the calculated hydraulic gradient of steady flow which will be compared with the transient flow one. The

different curves are plotted in perfect sine and put on original axis. Figure 4 presents the relationship between hydraulic gradient and velocity versus time.

That difference of hydraulic gradient (i tr -i p ) is due to the acceleration term.

8 different curves are plotted in perfect sine and put on original axis. Figure 4 presents the relationship between hydraulic gradient and velocity versus time. From this figure, we may see the difference between hydraulic gradient of steady flow (i p ) and transient flow (i tr ). That difference of hydraulic gradient (i tr -i p ) is due to the acceleration term. Figure 4: Relationship between the hydraulic gradient and velocity versus time (Hostun sand and glass spheres 1.5 mm) The more traditional representation of hydraulic gradient versus velocity is given in Figure 5 for the various total accelerations. The total acceleration (û/t) is defined by the ratio of amplitude of velocity and the period.

9 Figure 5: Relationship between hydraulic gradient versus velocity for various total accelerations. (Hostun sand and glass spheres 1.5 mm) The evolution of the hydraulic gradient as a function of velocity is remarkably linear for all tests. The slope of the curves corresponds to the permeability according to Darcy and varies from one test to another according to the acceleration. These results demonstrate that the classic Darcy's law and Forchheimer law describing steady flow can not be applied generally to transient flow. We can notice that under little accelerations, these curves approach the

10 steady flow curve, contrary to the case of great acceleration where curves move away from steady flow curve. c. Analysis The acceleration for every point is defined by the velocity derivation. We consider that the acceleration (dv/dt) is always phase shift with the hydraulic gradient (i tr - i p ), so we propose to add the value /2 to the velocity derivation. It's namely new acceleration. Then we may write a relationship between (i tr - i p ) and the new expression of acceleration. From this relationship, we obtained a linear function. 1 for each total acceleration (û/t). Then we have obtained a relationship between "c" and (û/t) as a power function. So the expression of the acceleration term becomes: 2 Where "p" and "q" are experimental coefficients depending on materials. Figure 5 shows the good agreement obtained between the experimental results and those predicted by the correlation proposed. We will compare the value predicted by this expression and the

11 experimental one. Figure 5. Comparison between measured and calculated values (Hostun sand and glass spheres 1.5 mm) Also, we have checked directly the results of each experiment and finally the new expression for the transient Darcy flow type is obtained:

12 3 with "a" as the coefficient of steady flow (Darcy). The law coefficients a, p and q depend on the nature of the material. For Hostun sands, a = 2029 s/m, p=265 and q= And for the transient Post-Darcy flow type :.. 4 with "a and b" as coefficients of the steady flow (Forchheimer law). The law coefficients a, b, p and q depend on the nature of the material. For 1.5 mm diameter of Glass sphere, we have a = 61 s/m, b = 1397 s 2 /m 2, p =.1.54 and q = Van Gent (1995) and Smith (1991) have studied coarse materials: gravel, rock and glass spheres. To calculate the transient flow law, Van Gent has modified the coefficient "b" and saved the coefficient "a". Smith has modified both coefficients "a" and "b". In our formula the both coefficients "a" and "b" are not changed using a new expression of the acceleration. 4. Summary and Conclusions In this paper, we have described the elements used to design a dual operating mode permeameter. The first operating method, which is similar to a steady flow permeameter. The addition of a control servovalve enables the operation of the permeameter in a different mode usually used in transient flow permeameters.

13 A preliminary test is worked in steady flow. We present the results obtained with tests carried out on Hostun sands with a mean diameter of 0.3 mm and glass spheres 1.5 mm of diameter. These results demonstrate that in steady flow and with large hydraulic gradients, water flows through materials are governed by the parabolic Forchheimer's law. In transient state, the attempt to set signal orders for 5-15 seconds period sine waves by permeameter proves successful in simulating such conditions. We have presented the results of Hostun sand and 1.5 mm diameter of glass spheres. The first analysis shows that the law of steady flow are not valid when soils are subjected to transient flows. A new formula for transient flow is proposed, where both steady flow coefficients, "a" and "b", are not changed using a new expression of the acceleration. We will continue working with the other materials, modelling the coefficients "a", "b", "p" and "q", and modelling flow in structure using the transient flow law. Acknowledgments Funds were provided by grants from the French Department of Research and Technology and the European Regional Development Fund. The assistance and cooperation of Dr Garnier (LCPC), Pr. Comiti and Dr. Montillet (LGP) are sincerely appreciated. Special thanks to Mr. Coue for his involvement in the production of the experimental devices. References 1. Burchart, H.F., Christensen, C, "On Stationary and Non-stationary Porous Flow in Coarse Granular Materials". MAST G6-S Project I, Wave action on and in coastal structures, Aalborg university, Denmark. 2. Dudgeon, C.R., "Non-Darcy Flow of Groundwater". PhD Thesis, University of New South Wales. 3. Hall, K., Smith, G.M., Turcke, D. J. (1994). "Development of a Non-Linear Porous Media Flow Relationship for Oscillatory Unsteady Flow". Journ. of coast. Reseach, vol. 10, n 1, pp:

14 4. Hannoura, A.A., 1978, " Numerical and experimental modelling of unsteady flow in rockfill embankment ". Ph.D. thesis, University Windsor, Ontario. 5. Khalifa, Wahyudi, Thomas, Bouchelaghem, "Experimental Set-Up For The Study of Flow in Soils", ISSN , J. Oceanogr., 1997, vol. 22, Mc Corquodale, J.A., Hannoura, A.A., (1985a & 1985b) "Rubblemounds: Hydraulic Conductivity Equation" and "Rubblemounds: Numerical Modelling of Wave Motion" ASCE Journal of the Waterway, Port, Coastal and Ocean Division, 111 (5). pp and pp Smith, G. M., (1991), "Comparison of Stationary and oscillatory Flow Through Porous Media", Msc. Thesis, Queen's University. 8. Van-Gent, M.A.R. (1993). "Stationary and Oscillatory Flow Coarse Porous Media". Communications on Hydraulic and Geotechnical Engineering, TU Delft. p Wahyudi, In progress, "Etude Théorique et Expérimentale des Ecoulements Darciens et Non-Darciens dans les Sols et Ouvrages Littoraux", Nantes University. Imam Wahyudi: Lecture of Civil Engineering Dept Sultan Agung Islamic University Thesis Student Institut Universitaire de Technologie St. Nazaire, Laboratoire Génie Civil de Nantes Saint- Nazaire F Saint-Nazaire France wahyudi@iutsn.univ-nantes.fr Abder Khalifa: Doctor Institut Universitaire de Technologie St. Nazaire, Laboratoire Génie Civil de Nantes Saint- Nazaire F Saint-Nazaire France Pierre Thomas: Professor Institut Universitaire de Technologie St. Nazaire, Laboratoire Génie Civil de Nantes Saint- Nazaire F Saint-Nazaire France

Darcy's Law. Laboratory 2 HWR 531/431

Darcy's Law. Laboratory 2 HWR 531/431 Darcy's Law Laboratory HWR 531/431-1 Introduction In 1856, Henry Darcy, a French hydraulic engineer, published a report in which he described a series of experiments he had performed in an attempt to quantify