Transcript HYDRAULICS of steady and pulsatile flow in

EXPERIMENTAL METHODS 2010 PROJECT CAPILLARY VISCOMETER
CAPILLARY VISCOMETER
Motivation
•Advanced instrument based upon our own patent
•How to measure rheological and electric properties of blood?
•Using MATLAB and LABVIEW for instrumentation
Task prepared within the project FRVS 90/2010
EXPERIMENTAL METHODS 2010 PROJECT CAPILLARY VISCOMETER
Aim of project: Measurement of rheological properties (viscosity of liquids) using a
capillary viscometer, that is still under development. Computer control and MATLAB
software devolopment.
1–glass cylinder, 2-metallic piston, 3-pressure transducer Kulite, 4tested liquid, 5-plastic holder of needle, 6-needle, 7-calibrated
resistor (electric current needle-tank), 8-calibrated resistor (current
flowing in tank), 9-AC source (3-30V), 10-SS source for pressure
transducer (10V), 11-A/D converter, 12-procesor, 13-metallic head,
14-push bar, 15-scale of volume
EXPERIMENTAL METHODS 2010 PROJECT CAPILLARY VISCOMETER
EXPERIMENTAL METHODS 2010 PROJECT CAPILLARY VISCOMETER
Rheology of liquids / fundamentals
Constitutive equation of fluids is relationship between kinematic stimulus (flow,
characterized by rate of deformation tensor) and dynamic response (stress
tensor). The simplest linear relationship holds for the so called Newtonial fluids
(for example water, air, oils, but not more complicated liquids like yoghurt,
ketchup, polymer melts)
   
 is shear stress (one component of stress tensor) and is shear rate (one
component of tensor of rate of deformation). Coefficient of proportionality  is
dynamic viscosity (units Pa.s) – this value should be evaluated from
experiment. The equation (1) holds in this simplified one-dimensional form only
for the so called simple shear flows, e.g. flows of a layer of fluid between two
parallel plates one of them being fixed and the second one moving with a
constant velocity uw, (a similar velocity profile develops also in a narrow gap
between a steady outer cylinder and an inner rotating cylinder – this
arrangement is typically used in rotational rheometers)
 
u x
y
y

uw
uw
H
H
x
EXPERIMENTAL METHODS 2010 PROJECT CAPILLARY VISCOMETER
Simple shear flow in pipe
Simple shear flow exists also in laminar flow in a straight circular pipe, where
 w 
u x (r )
r

4 Q
R
3
volumetric flowrate [m3/s
]
w 
pipe of inner radius R
R p
axial gradient of pressure
2 x
(2,3)
Therefore by measuring flowrate and pressure drop at a steady laminar flow in a tube (capillary) it
is possible to evaluate viscosity as a ratio
   w /  w
Actual flowrate should be linear function of pressure gradient as follows from Eqs.(1-3)
R
R  w R p
Q 
 w 

4
4 
8  x
3
3
4
and this equation is known as the Hagen Poiseuille law (mention the fact that the flowrate increases very
rapidly with radius of pipe - 4th power).
In this experiment the liquid is expelled by a piston from a syringe through a thin needle manually
(therefore it is not possible to arrange a constant flowrate during the whole experimental run).
Nevertheless it is not necessary to measure the whole course of flowrate as a function of time. It will be
sufficient to record and to integrate the time course of pressure p(t). It follows from the fact that the
t end
volume is the time integral of flowrate
4 t end
4 t end

R

p

R
V   Q dt 
  x dt  8  L   pdt
8

t
t
t
start
start
start
L is length of needle, R is radius of needle and tstart, tend times of begin and end of the piston displacement.
EXPERIMENTAL METHODS 2010 PROJECT CAPILLARY VISCOMETER
Measurement procedure
 Check electrical connection of pressure transducer, connect 9V battery to its feeding (be
careful about polarity), switch on NI-USB-62781 and start the program “Strikacka”.
 Record temperature of the tested liquid by a portable thermometer. Fill the syringe by
tested liquid, select and attach a needle. Expel air bubbles from the syringe’s content.
Record volume of the sucked in liquid (using a grade on the syringe), usually 20 ml.
Record geometry of needle (radius R and length L).
 Fill the dialog forms in the “Strikacka” screen. Sampling rate (1 kHz recommended),
scale factor for U1 channel (pressure transducer - this value has no effect upon recorded
data, this scale is important only for graphics). Specify file name of results. Fill the item
(“Header row”) with information about the needle (geometry), initial volume and the
type of tested liquid.
 Switch on “Write” button and start to expel the liquid from syringe by pushing a piston.
Observe recorded pressure on screen. As soon as all liquid is expelled switch the write
button “Off”.
 All data are stored in the specified text file. The file can be imported to MATLAB or
Excel program. The first row is header following rows contain time, voltage (output of
pressure transducer). That is all what you need to evaluate viscosity using the theory
described above.
EXPERIMENTAL METHODS 2010 PROJECT CAPILLARY VISCOMETER
LABVIEW
Experiment is controlled by National Instruments software and is implemented as VI program
STRIKACKA
Under preparation
Scales of voltages (only for graph, data will be
stored always in Volts, without any scaling).
File name, where time and 3
corresponding voltages will be
recorded, after switching button
WRITE.
EXPERIMENTAL METHODS 2010 PROJECT CAPILLARY VISCOMETER
MATLAB programming
Simplest processing suitable only for Newtonian liquids (electrical resistance is not recorded)
t=a(1:end,1);
p=a(1:end,2);
ndata=length(t);
nconst=ndata/20+2;
pm=mean(p(1:nconst))
ps=std(p(1:nconst));
plim=pm+5*ps;
i=1;
while p(i)<plim & i<ndata/2
i=i+1;
end
nstart=i
pme=mean(p(ndata-nconst:ndata))
pse=std(p(ndata-nconst:ndata));
plim=pme+5*pse;
i=ndata;
while p(i)<plim & i>nstart+5
i=i-1;
end
nend=i
% pbar subtracted atmospheric pressure and recalculated by calibration
% constant of Kulite
pbar=(p-(pme+pm)/2)/14.303e-8;
% integral of pressure
dtdata=(t(ndata)-t(1))/(ndata-1);
pint=sum(pbar(nstart:nend))*dtdata;
% mju=pi.d^4/(128L.V/pint)
% Gamma = 4V/(pi.d^3.deltat).
mju=3.141*dn^4/(128*ln*vstart/pint)
gamma=4*vstart/(3.141*dn^3*(t(nend)-t(nstart)))
EXPERIMENTAL METHODS 2010 PROJECT CAPILLARY VISCOMETER
MATLAB programming
Advanced processing of non-Newtonian liquids (electrical resistance is used for flowrate measurement)
% dn-diameter of needle, Ln-length of needle
% dp-diameter of piston
% rf-fixed resistance
% vstart-initial volume
% vend-final volume
% kp= calibration constant of pressure transducer (=1/14.303e-3)
t=a(1:end,1);
p=a(1:end,2);
u1=a(1:end,3);
u2=a(1:end,4);
ndata=length(t)
nconst=ndata/20+2;
pm=mean(p(1:nconst))
ps=std(p(1:nconst));
plim=pm+5*ps;
i=1;
while p(i)<plim & i<ndata/2
i=i+1;
end
nstart=i
pme=mean(p(ndata-nconst:ndata))
pse=std(p(ndata-nconst:ndata));
plim=pme+5*pse;
i=ndata;
while p(i)<plim & i>nstart+5
i=i-1;
end
nend=i
% pbar subtracted atmospheric pressure and recalculated by calivration
% constant of Kulite
pbar=(p-(pme+pm)/2)*kp;
%BINING
dtdata=(t(ndata)-t(1))/(ndata-1);
nb=round(0.03/dtdata)
dt=dtdata*nb;
nbin=floor(ndata/nb)
i=1;
for ibin=1:nbin
tmean=0;
pmean=0;
u1max=0;
u2max=0;
for j=1:nb
tmean=tmean+t(i);
pmean=pmean+pbar(i);
u1max=max(u1max,u1(i));
u2max=max(u2max,u2(i));
i=i+1;
end
tb(ibin)=tmean/nb;
pb(ibin)=pmean/nb;
u1b(ibin)=u1max;
u2b(ibin)=u2max;
end
%
nbstart=floor(nstart/nb);
nbend=floor(nend/nb);
u1start=mean(u1b(1:nbstart-1));
u2start=mean(u2b(1:nbstart-1));
u1end=mean(u1b(nbend+1:nbin));
u2end=mean(u2b(nbend+1:nbin));
% even now it is possible to cut off initial and ending part
tr=tb(nbstart:nbend);
pr=pb(nbstart:nbend);
u1r=u1b(nbstart:nbend);
u2r=u2b(nbstart:nbend);
m=length(tr)
%filtration of pressure and voltage
prf=max(0,sgolayfilt(pr,2,19));
u1rf=sgolayfilt(u1r,2,19);
u2rf=sgolayfilt(u2r,2,19);
% recalculate voltages to volumes
k=vstart*u1start/u2start;
vr=k*u2rf./u1rf;
% flowrate
for i=2:m-1
dvdt(i)=max(0,-(vr(i+1)-vr(i-1))/(2*dt));
end
dvdt(1)=-(vr(2)-vr(1))/dt;
dvdt(m)=-(vr(m)-vr(m-1))/dt;
dvdtf=max(0,sgolayfilt(dvdt,2,19));
%
gamv=32*dvdtf/(3.141*dn^3);
%recalculated to pascals
tauw=dn*prf/(4*ln)*1e5;
% mean viscosity
mjuv=tauw./gamv;
mju=mean(mjuv)
plot(gamv,tauw,'ro')
EXPERIMENTAL METHODS 2010 PROJECT CAPILLARY VISCOMETER
LABORATORY REPORT
1. Front page: Title, authors, date
2. Content, list of symbols
3. Introduction, aims of project, references
4. Description of experimental setup
5. Theory and software design (MATLAB program)
6. Geometry of needles (D,L), processed volumes, used liquids
7. Experiments: Recorded time courses of pressure (graph)
8. Results: Viscosities (table) or graph (viscosity-temperature/shear rate)
9. Conclusion (identify interesting results and problems encountered)
EXPERIMENTAL METHODS 2010 PROJECT CAPILLARY VISCOMETER
LABORATORY REPORT
Exp.
No.
Liquid
Tem Viscosity
perat from table
ure
[Pa.s]
[C]
1
Water
26
0.00095
0.8
2
Milk
30
Not known
0.8
3
Viscosity
Needle D
from
(nominal)
experiment [mm]
Needle D
Length pf
(calibration needle L
) [mm]
[mm]
0.624
Length
Volume
measured [ml]
[mm]
tstart/tend
Flowrate
[ml/s]
Shear
rate [1/s]
Shear
stress
[Pa]
File name
EXPERIMENTAL METHODS 2011 PROJECT CAPILLARY VISCOMETER
LABVIEW improved
Experiment is controlled by National Instruments software and is implemented as VI program
PUTEMP
supply voltage
to Kulite
Voltages: pressure,
fixed resistor, syringe
Under preparation
T-thermocouple
Volume of liquid is
evaluated from voltages
EXPERIMENTAL METHODS 2011 PROJECT CAPILLARY VISCOMETER
LABVIEW improved
Experiment is controlled by National Instruments software and is implemented as VI program
PUTEMP
root mean square of
voltage at trimmer (fixed
resistor)
ratio of voltages
Usyringe/Utrimmer is
proportional to volume
root mean square of
voltage at syringe
(variable liquid column)
EXPERIMENTAL METHODS 2011 PROJECT CAPILLARY VISCOMETER
LABVIEW improved
Experiment is controlled by National Instruments software and is implemented as VI program
PUTEMP
recorded
volume (relative)
2
1.8
0.028
0.026
1.6
0.024
1.4
0.022
1.2
0.02
1
0.018
0.8
0.016
0.6
0.014
0.4
0.012
0.2
0
0.01
0
2
4
6
8
10
recorded pressure
(voltage)
12
14
16
18
EXPERIMENTAL METHODS 2011 PROJECT CAPILLARY VISCOMETER
LABVIEW improved
Calibration (repeated experiment with water)
2.5
recorded volume
(relative) by
Labview
2
1.5
1
Volume in ml (from
scale on syringe)
0.5
0
0
5
10
15
20
25