MECH 529 – Laboratory 10
“Hydraulic Ram Pump Modeling”
Thomas H. Bradley, PhD.
(970) 491-3539, Thomas.Bradley@Colostate.edu
Introduction:
A hydraulic ram pump is a type of water pump that is particularly interesting for
developing world applications. It uses only the passive dynamics of hydraulic systems (no
electricity or conventional power) to pump water uphill. A schematic of the hydraulic ram
pump is shown in Figure 1. The way that the pump works is that the input tank provides a
little bit of pressure to the supply pipe. The supply pipe is a long pipe made of steel or
other non-compliant piping material. When the water rushes through the supply pipe and
through the supply valve, it creates a drag force on the supply valve, closing it. The sudden
closing of the supply valve creates a pressure spike in the right side of the supply pipe
because of the hydraulic inertia of the fluid in the supply pipe. This pressure spike opens
the delivery valve and allows the water to flow into the delivery tank. The delivery tank
has a bladder of air which creates a hydraulic capacitance. This hydraulic capacitance
stores the pressure of the pressure spike to pump water uphill to the output tank. As the
water flows up the delivery valve, the pressure under the supply valve decreases until the
supply valve opens again and the delivery valve closes. The cycle repeats at approximately
1 Hz to pump water up hill.
You can find a YouTube video of a ram pump in action at this link.
Learning Objectives:
1) Test a number of the computer modeling techniques that we have learned in the
ME529 laboratory with the construction of an model of a complicated dynamic
(mechanical, hydraulic, pneumatic) system
1
Output Tank
Waste Delivery Tank
Input Water Supply Water
(Low Press.)
Supply Valve
Input Tank
Delivery Valve
Supply Pipe
Figure 1. Schematic of the hydraulic ram pump 1
Task 1 – Hydraulic Ram Pump Component Modeling
To model the hydraulic ram pump we will use all of the techniques that we learned
in class. Go!
Figure 2. System dynamics schematic of the hydraulic ram pump (copy from board)
1 Wilson, D., All About Hydraulic Ram Pumps, Atlas Publications. NC : 1992.
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Now we can break this schematic model into corresponding equations and Simulink
blocks:
1. gh P R1q1
1 q1 P1
dq1 Eqn 1
2. P1 P2 I P1
dt P2
qdot1
Eqn 2
dP2 1
3. qc qc P2_dot
dt Csup Eqn 3
4. q1 qc q2 q3 q1
q2 qc
5. q3 q4 q5
q3
Eqn 4
2 q5
q
q4
1 q3
6. m1 P2 A AC d 2 sign(q 2 ) mg
x A
Eqn 5
2 0 q2
xddot 1
q2 P2 k 1
P2
7. Eqn 6
L x1
tau1
1 1
q2
8.
P2
Eqn 7
L1 x1 tau 1 valve width
2
1 q
m2 P2 P3 A
Eqn 8
9. x AC d 3 sign(q3 ) mg
A
q3
P2 xddot 2
2 0 P3
q3 P2 P3 k 2
eqn 9
10. tau2
P2 q3
P3
x2
2
Eqn 10
11.
L2 x2 tau 2 valve width
P3 gz q5 r2
eqn 11
12.
P3 q5
dP3 1
13.
Eqn 12
q4
dt Cdeliv q4 P3_dot
Task 2 – Construction of the System Model Eqn 13
To construct the system model use the same techniques that we have been using all
semester. Start with the equations that are differential equations. These variables whose
derivatives are part of the equations of motion will be the states of our system {q1, P2, x1, x2,
P3}. Place integrators into Simulink whose inputs are the derivatives of the state variables
and whose outputs are the state variables. I have also placed blank subsystems for the
other variables so we can keep track of them. The Simulink workspace is shown in Figure
3.
The only part of the construction of the model that is a little tricky is the valves. We
have to make them so that they have hard stops at the end of their travel. Mathematically
this requires a double integrator that has limits on position. The contact with the valve
travel limit resets the velocity integrator output to zero unless the acceleration forces the
valve to leave contact. I have the valve dynamic models done for you at this link.
Now the only thing left to do is string everything together.
When you simulate the system, use MATLAB™’s ODE23S solver for stiff systems.
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Task 3 – Homework
xddot x Your task is to plot the relationship between the efficiency of the
ram pump and the height that it is pumping water to. The pumping
X1 efficiency is defined as the ratio between the integral of the flow that
goes to the output reservoir and the integral of the flow that goes into the
xddot x
pump (
q dt ). The pumping height is the difference between the output
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X2 q dt
1
In 1 Out1
tank height (z) and the input tank height (h). The pumping efficiency
should sort of settle out after a few seconds of pumping.
P1 You will have to again call your Simulink™ simulation from
1 MATLAB™ using the commands:
s simoptions = simset('SrcWorkspace', 'current');
sim('RamPump',[0 100],simoptions);
in Pdot 2
out P 2
I calculate the efficiency of the ram pump in Simulink™ and use a
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To Workspace block (with Array selected and Sampling Time = 1) to get
s the data to the workspace.
in Pdot 3
out P 3
1) Explain the cyclic function of the ram pump in detail with graphs
showing the system dynamics. Find discrepancies between what the
1 model is doing and what you think the dynamics should be (ringing,
s
chattering, etc.)
in qdot 1 2) Vary the height difference in the model and plot the pumping
out q 1
efficiency as a function of height.
In1 Out 1 % ME 324 HYDRAULIC RAM PUMP MODEL
q2 g = 9.81; %acceleration due to gravity, m/s/s
L1 = .02;% length of the throw of the supply valve, m
L2 = .02;% length of the throw of the delivery valve, m
In1 Out 1 k1 = 1e-3;% constant associated with the oriface in supply valve, sort of like a 1/Resistance,
m3/Pa/s
k2 = 1e-3;% constant associated with the oriface in delivery valve, sort of like a 1/Resistance,
q3 m3/Pa/s
rho = 1000; % density of water, kg/m3
A0 = 0.00114; % valve area for water to flow through, m2
Cd = 1.0;% valve drag coefficient, -
In1 Out 1 A = 2*A0;% Valve Area exposed to pressure from water, m2
m1 = 2.5;% mass of the movable part of the supply valve, kg
m2 = .25;% mass of the movable part of the delivery valve, kg
qc z = 14.38 ;% height of the output tank water level, m
h = 3.54 ;% height of the input tank, m
V_supply_cap = 0.1; %m3 volume of the supply capacitance
In1 Out 1 C_supply_cap = 1* V_supply_cap / 2.2e9; % 2.2e9Pa is the bulk modulus of water
V_delivery_cap = .25; %m3 volume of the delivery capacitance
C_delivery_cap = V_delivery_cap / 287.06 / 293; % is the bulk modulus of air
q4 R1 = 1e2;% resistance in the input pipe, Pa-s/m3
R2 = 1e4; % resistance in the output pipe, Pa-s/m3
L = 15.04; % length of the supply pipe, m
In1 Out 1 I = rho*L/(pi*(.02/2)^2);%inertia in the pipe = rho*L/A
q5 Writeup due 5/7/ at the beginning of Laboratory.
Fully document your homework solutions using this handout as a template. All
problem statements must be copied to the solutions. All diagrams and plots must be
labeled with units and symbols, and must be captioned.
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