KEY 192A Learning Lab #2 Mass and Energy BalancesOctober 23, 2017
The Artificial Heart
Primary Topic: Conservation of Mass and Conservation of Energy
Supporting Topics: Algebra, calculus (MATH 117,118,124, 125, 126, 160); Work, Energy, Kinematics (PHYS 141); Engineering Thermodynamics (MECH 337)
Technical Objectives:
- Explainthe difference between a thermodynamic system and its surroundings.
- Explain the difference between an open system and a closed system.
- Explain each term in the conservation of mass for an open system.
- Explain each term in the conservation of energy for an open system.
- Calculate the power required for an artificial heart based on engineering assumptions.
1. Thermodynamic Systems
1.1 System, System Boundary and Surroundings
System –
Surroundings–
System Boundary –
Example 1. The human being as a system.
Known: You are being asked to design a life support system for a manned Mars mission.
Find: Draw a system boundary around a human occupant and identify all mass and energy that flows in an out of the human system and must therefore be dealt with in the surroundings.
2. Mass and Energy Balances for Open Systems (i.e. Control Volume Analysis)
An open system is a system that exchanges mass (as well as heat and work) with the surroundings. Open systems are analyzed using control volume analysis. Consider once again the AbioCorTM implantable replacement heart:
Actual SystemControl Volume Analysis
2.1 Conservation of Mass
In the artificial heart above, blood flows in and out, and blood can, in principle accumulate within the heart. The conservation of mass for a control volume keeps track of the amount of mass that flows in and out of a control volume. In words, the conservation of mass says:
Mathematically, the conservation of mass can be written as follows:
(1.1)
where is a mass flow rate in [kg/s] or [lbm/s].
2.2 Conservation of Mass at Steady State
By definition, once a system is at steady state, the entire system is no longer changing with time. For a control volume at steady state, the conservation of mass reduces to:
(1.2)
Equation 1.2 has to be true. Consider, for example, the artificial heart above. What would happen to the artificial heart if ?
3. The Conservation of Energy for a Control Volume
Consider again the artificial heart:
In addition to heat,, and electrical power,, which cross the system boundary, the mass that flows through the control surface carries along its own energy! This energy is in the form of internal energy, potential energy, kinetic energy and flow work.
Taking into account, , flow energy and flow work, we can now formulate the conservation of energy for an open system:
(1.3)
where E is the total energy contained in the system, is the rate at which is heat is transferred into the system, is the power produced by the system, g is the acceleration due to gravity, zi is the height above sea level of each fluid inlet or exit, vi is the velocity of each fluid inlet or exit, hi is the enthalpy of each fluid inlet or exit (enthalpy is a thermodynamic property that includes internal energy, pressure and specific volume).
3.1 Conservation of Mass at Steady State
Equation (1.3) is the most general form of the conservation of energy for a control volume. For systems at steady state the equation becomes:
(1.4)
For systems at steady state, with only one inlet and one outlet:
(1.5)
3.2 Conservation of Energy for a Liquid Pump. For a liquid pump, equation (1.5) reduces to the following simple equation:
(1.6)
where P1 is the inlet pressure, P2 the exit pressure, is the density and the mass flow rate.
Design of the Week Assignment
This week’s design of the week is the AbioCorTM Implantable Replacement Heart, which was manufactured by Abiomed in the early 2000’s. The AbioCor was the first ever fully implantable replacement heart and was implanted into Robert L. Tools in 2001 and he lived for 151 days. Abiomed no longer produces the AbioCor. Today, the Total Artificial Heart by SynCardia Systems, LLC is a commercially available, temporary transplantable heart, which is designed to provide complete function of “a failed human heart in patients suffering from end-stage biventricular (both sides) heart failure”. Designed to keep patients alive while they wait for a human donor, it has been successfully implanted in over 1000 patients.
- (5 minutes) Read the documents on the course web site.
- (10 minutes). On the back of the page:
- List 5 technical challengesthat the developers of the AbioCor and Syncardia had to overcome prior to clinical testing.
- List 5 non-technical challenges that Abiomed and SynCardia may have faced during the development and clinical testing of their artificial heart products.
- Discuss the business implications of one of the non-technical issues.
- Solve the Following Engineering Problem
Known: The human heart delivers blood at a volumetric flow rate of approximately 5 liters/min. The pressure rise through the heart is approximately 120 mm Hg. Assume that the heart operates adiabatically.
Find: The minimum power required to pump blood through the human body in Watts.
Schematic Diagram and Given Data:
Engineering Model:
Analysis